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-The Project Gutenberg EBook of The Theory and Practice of Model Aeroplaning, by 
-V. E. Johnson
-
-This eBook is for the use of anyone anywhere at no cost and with
-almost no restrictions whatsoever.  You may copy it, give it away or
-re-use it under the terms of the Project Gutenberg License included
-with this eBook or online at www.gutenberg.org/license
-
-
-Title: The Theory and Practice of Model Aeroplaning
-
-Author: V. E. Johnson
-
-Release Date: October 21, 2012 [EBook #41135]
-
-Language: English
-
-Character set encoding: ISO-8859-1
-
-*** START OF THIS PROJECT GUTENBERG EBOOK THE THEORY AND PRACTICE ***
-
-
-
-
-Produced by Chris Curnow, Mark Young and the Online
-Distributed Proofreading Team at http://www.pgdp.net (This
-file was produced from images generously made available
-by The Internet Archive)
-
-
-
-
-
-
-
-
+*** START OF THE PROJECT GUTENBERG EBOOK 41135 ***
 
 [Illustration: THE MOST IMPORTANT "TOOL" IN THE BUILDING OF MODEL
 AEROPLANES.
@@ -86,14 +51,14 @@ model aeroplanes what has already been done for model yachts and
 locomotives. To achieve the best results, theory and practice must go
 hand in hand.
 
-From a series of carefully conducted experiments empirical formulæ can
+From a series of carefully conducted experiments empirical formulæ can
 be obtained which, combined later with mathematical induction and
 deduction, may lead, not only to a more accurate and generalized law
 than that contained in the empirical formula, but to valuable
 deductions of a totally new type, embodying some general law hitherto
 quite unknown by experimentalists, which in its turn may serve as a
 foundation or stepping stone for suggesting other experiments and
-empirical formulæ which may be of especial importance, to be treated
+empirical formulæ which may be of especial importance, to be treated
 in _their_ turn like their predecessor. By "especial importance," I
 mean not only to "model," but "Aeroplaning" generally.
 
@@ -143,31 +108,31 @@ CONTENTS
     INTRODUCTION.
                                                                    PAGE
 
-    §§ 1-5. The two classes of models--First requisite of a model
-    aeroplane. § 6. An art in itself. § 7. The leading principle      1
+    §§ 1-5. The two classes of models--First requisite of a model
+    aeroplane. § 6. An art in itself. § 7. The leading principle      1
 
 
     CHAPTER I.
 
     THE QUESTION OF WEIGHT.
 
-    §§ 1-2. Its primary importance both in rubber and
-    power-driven models--Professor Langley's experiences. § 3.
-    Theoretical aspect of the question. § 4. Means whereby more
+    §§ 1-2. Its primary importance both in rubber and
+    power-driven models--Professor Langley's experiences. § 3.
+    Theoretical aspect of the question. § 4. Means whereby more
     weight can be carried--How to obtain maximum strength with
-    minimum weight. § 5. Heavy models versus light ones               4
+    minimum weight. § 5. Heavy models versus light ones               4
 
 
     CHAPTER II.
 
     THE QUESTION OF RESISTANCE.
 
-    § 1. The chief function of a model in the medium in which it
-    travels. § 2. Resistance considered as load percentage. § 3.
-    How made up. § 4. The shape of minimum resistance. § 5. The
-    case of rubber-driven models. § 6. The aerofoil
-    surface--Shape and material as affecting this question. § 7.
-    Skin friction--Its coefficient. § 8. Experimental proofs of
+    § 1. The chief function of a model in the medium in which it
+    travels. § 2. Resistance considered as load percentage. § 3.
+    How made up. § 4. The shape of minimum resistance. § 5. The
+    case of rubber-driven models. § 6. The aerofoil
+    surface--Shape and material as affecting this question. § 7.
+    Skin friction--Its coefficient. § 8. Experimental proofs of
     its existence and importance                                      7
 
 
@@ -175,15 +140,15 @@ CONTENTS
 
     THE QUESTION OF BALANCE.
 
-    § 1. automatic stability essential in a flying model. § 2.
-    theoretical researches on this question. §§ 3-6. a brief
+    § 1. automatic stability essential in a flying model. § 2.
+    theoretical researches on this question. §§ 3-6. a brief
     summary of the chief conclusions arrived at--remarks on and
     deductions from the same--conditions for automatic stability.
-    § 7. theory and practice--stringfellow--pénaud--tatin--the
+    § 7. theory and practice--stringfellow--pénaud--tatin--the
     question of fins--clarke's models--some further
-    considerations. § 8. longitudinal stability. § 9. transverse
-    stability. § 10. the dihedral angle. § 11. different forms of
-    the latter. § 12. the "upturned" tip. § 13. the most
+    considerations. § 8. longitudinal stability. § 9. transverse
+    stability. § 10. the dihedral angle. § 11. different forms of
+    the latter. § 12. the "upturned" tip. § 13. the most
     efficient section                                                13
 
 
@@ -193,52 +158,52 @@ CONTENTS
 
     SECTION I.--RUBBER MOTORS.
 
-    § 1. Some experiments with rubber cord. § 2. Its extension
-    under various weights. § 3. The laws of elongation
-    (stretching)--Permanent set. § 4. Effects of elongation on
-    its volume. § 5. "Stretched-twisted" rubber cord--Torque
+    § 1. Some experiments with rubber cord. § 2. Its extension
+    under various weights. § 3. The laws of elongation
+    (stretching)--Permanent set. § 4. Effects of elongation on
+    its volume. § 5. "Stretched-twisted" rubber cord--Torque
     experiments with rubber strands of varying length and number.
-    § 6. Results plotted as graphs--Deductions--Various
+    § 6. Results plotted as graphs--Deductions--Various
     relations--How to obtain the most efficient
     results--Relations between the torque and the number of
     strands, and between the length of the strands and their
-    number. § 7. Analogy between rubber and "spring"
-    motors--Where it fails to hold. § 8. Some further practical
-    deductions. § 9. The number of revolutions that can be given
-    to rubber motors. § 10. The maximum number of turns. § 11.
-    "Lubricants" for rubber. § 12. Action of copper upon rubber.
-    § 12A. Action of water, etc. § 12B. How to preserve rubber.
-    § 13. To test rubber. § 14. The shape of the section. § 15.
-    Size of section. § 16. Geared rubber motors. § 17. The only
-    system worth consideration--Its practical difficulties. § 18.
+    number. § 7. Analogy between rubber and "spring"
+    motors--Where it fails to hold. § 8. Some further practical
+    deductions. § 9. The number of revolutions that can be given
+    to rubber motors. § 10. The maximum number of turns. § 11.
+    "Lubricants" for rubber. § 12. Action of copper upon rubber.
+    § 12A. Action of water, etc. § 12B. How to preserve rubber.
+    § 13. To test rubber. § 14. The shape of the section. § 15.
+    Size of section. § 16. Geared rubber motors. § 17. The only
+    system worth consideration--Its practical difficulties. § 18.
     Its advantages                                                   24
 
     SECTION II.--OTHER FORMS OF MOTORS.
 
-    § 18A. _Spring motors_; their inferiority to rubber. § 18B.
-    The most efficient form of spring motor. § 18C. _Compressed
-    air motors_--A fascinating form of motor, "on paper." § 18D.
+    § 18A. _Spring motors_; their inferiority to rubber. § 18B.
+    The most efficient form of spring motor. § 18C. _Compressed
+    air motors_--A fascinating form of motor, "on paper." § 18D.
     The pneumatic drill--Application to a model aeroplane--Length
-    of possible flight. § 18E. The pressure in motor-car tyres.
-    § 19. Hargraves' compressed air models--The best results
-    compared with rubber motors. § 20. The effect of heating the
+    of possible flight. § 18E. The pressure in motor-car tyres.
+    § 19. Hargraves' compressed air models--The best results
+    compared with rubber motors. § 20. The effect of heating the
     air in its passage from the reservoir to the motor--The great
     gain in efficiency thereby attained--Liquid air--Practical
-    drawbacks to the compressed-air motor. § 21. Reducing
-    valves--Lowest working pressure. § 22. The inferiority of
-    this motor compared with the steam engine. § 22A. Tatin's
-    air-compressed motor. § 23. _Steam engine_--Steam engine
+    drawbacks to the compressed-air motor. § 21. Reducing
+    valves--Lowest working pressure. § 22. The inferiority of
+    this motor compared with the steam engine. § 22A. Tatin's
+    air-compressed motor. § 23. _Steam engine_--Steam engine
     model--Professor Langley's models--His experiment with
-    various forms of motive power--Conclusions arrived at. § 24.
+    various forms of motive power--Conclusions arrived at. § 24.
     His steam engine models--Difficulties and failures--and final
     success--The "boiler" the great difficulty--His model
-    described. § 25. The use of spirit or some very volatile
-    hydrocarbon in the place of water. § 26. Steam turbines.
-    § 27. Relation between "difficulty in construction" and the
-    "size of the model." § 28. Experiments in France. § 29.
-    _Petrol motors._--But few successful models. § 30. Limit to
-    size. § 31. Stanger's successful model described and
-    illustrated. § 32. One-cylinder petrol motors. § 33.
+    described. § 25. The use of spirit or some very volatile
+    hydrocarbon in the place of water. § 26. Steam turbines.
+    § 27. Relation between "difficulty in construction" and the
+    "size of the model." § 28. Experiments in France. § 29.
+    _Petrol motors._--But few successful models. § 30. Limit to
+    size. § 31. Stanger's successful model described and
+    illustrated. § 32. One-cylinder petrol motors. § 33.
     _Electric motors_                                                39
 
 
@@ -246,20 +211,20 @@ CONTENTS
 
     PROPELLERS OR SCREWS.
 
-    § 1. The position of the propeller. § 2. The number of
-    blades. § 3. Fan _versus_ propeller. § 4. The function of a
-    propeller. § 5. The pitch. § 6. Slip. § 7. Thrust. § 8. Pitch
-    coefficient (or ratio). § 9. Diameter. § 10. Theoretical
-    pitch. § 11. Uniform pitch. § 12. How to ascertain the pitch
-    of a propeller. § 13. Hollow-faced blades. § 14. Blade area.
-    § 15. Rate of rotation. § 16. Shrouding. § 17. General
-    design. § 18. The shape of the blades. § 19. Their general
-    contour--Propeller design--How to design a propeller. § 20.
+    § 1. The position of the propeller. § 2. The number of
+    blades. § 3. Fan _versus_ propeller. § 4. The function of a
+    propeller. § 5. The pitch. § 6. Slip. § 7. Thrust. § 8. Pitch
+    coefficient (or ratio). § 9. Diameter. § 10. Theoretical
+    pitch. § 11. Uniform pitch. § 12. How to ascertain the pitch
+    of a propeller. § 13. Hollow-faced blades. § 14. Blade area.
+    § 15. Rate of rotation. § 16. Shrouding. § 17. General
+    design. § 18. The shape of the blades. § 19. Their general
+    contour--Propeller design--How to design a propeller. § 20.
     Experiments with propellers--Havilland's design for
     experiments--The author experiments on dynamic thrust and
-    model propellers generally. § 21. Fabric-covered screws.
-    § 22. Experiments with twin propellers. § 23. The Fleming
-    Williams propeller. § 24. Built-up _v._ twisted wooden
+    model propellers generally. § 21. Fabric-covered screws.
+    § 22. Experiments with twin propellers. § 23. The Fleming
+    Williams propeller. § 24. Built-up _v._ twisted wooden
     propellers                                                       52
 
 
@@ -268,14 +233,14 @@ CONTENTS
     THE QUESTION OF SUSTENTATION.
     THE CENTRE OF PRESSURE.
 
-    § 1. The centre of pressure--Automatic stability. § 2.
-    Oscillations. § 3. Arched surfaces and movements of the
-    centre of pressure--Reversal. § 4. The centre of gravity and
-    the centre of pressure. § 5. Camber. § 6. Dipping front
+    § 1. The centre of pressure--Automatic stability. § 2.
+    Oscillations. § 3. Arched surfaces and movements of the
+    centre of pressure--Reversal. § 4. The centre of gravity and
+    the centre of pressure. § 5. Camber. § 6. Dipping front
     edge--Camber--The angle of incidence and camber--Attitude of
-    the Wright machine. § 7. The most efficient form of camber.
-    § 8. The instability of a deeply cambered surface. § 9.
-    Aspect ratio. § 10. Constant or varying camber. § 11. Centre
+    the Wright machine. § 7. The most efficient form of camber.
+    § 8. The instability of a deeply cambered surface. § 9.
+    Aspect ratio. § 10. Constant or varying camber. § 11. Centre
     of pressure on arched surfaces                                   78
 
 
@@ -284,10 +249,10 @@ CONTENTS
     MATERIALS FOR AEROPLANE
     CONSTRUCTION.
 
-    § 1. The choice strictly limited. § 2. Bamboo. § 3.
-    Ash--spruce-- whitewood--poplar. § 4. Steel. § 5. Umbrella
-    section steel. § 6. Steel wire. § 7. Silk. § 8. Aluminium and
-    magnalium. § 9. Alloys. § 10. Sheet ebonite--Vulcanized
+    § 1. The choice strictly limited. § 2. Bamboo. § 3.
+    Ash--spruce-- whitewood--poplar. § 4. Steel. § 5. Umbrella
+    section steel. § 6. Steel wire. § 7. Silk. § 8. Aluminium and
+    magnalium. § 9. Alloys. § 10. Sheet ebonite--Vulcanized
     fibre--Sheet celluloid--Mica                                     86
 
 
@@ -296,16 +261,16 @@ CONTENTS
     HINTS ON THE BUILDING OF MODEL
     AEROPLANES.
 
-    § 1. The chief difficulty to overcome. § 2. General
-    design--The principle of continuity. § 3. Simple monoplane.
-    § 4. Importance of soldering. § 5. Things to avoid. § 6.
-    Aerofoil of metal--wood--or fabric. § 7. Shape of aerofoil.
-    § 8. How to camber an aerocurve without ribs. § 9. Flexible
-    joints. § 10. Single surfaces. § 11. The rod or tube carrying
-    the rubber motor. § 12. Position of the rubber. § 13. The
-    position of the centre of pressure. § 14. Elevators and
-    tails. § 15. Skids _versus_ wheels--Materials for skids.
-    § 16. Shock absorbers, how to attach--Relation between the
+    § 1. The chief difficulty to overcome. § 2. General
+    design--The principle of continuity. § 3. Simple monoplane.
+    § 4. Importance of soldering. § 5. Things to avoid. § 6.
+    Aerofoil of metal--wood--or fabric. § 7. Shape of aerofoil.
+    § 8. How to camber an aerocurve without ribs. § 9. Flexible
+    joints. § 10. Single surfaces. § 11. The rod or tube carrying
+    the rubber motor. § 12. Position of the rubber. § 13. The
+    position of the centre of pressure. § 14. Elevators and
+    tails. § 15. Skids _versus_ wheels--Materials for skids.
+    § 16. Shock absorbers, how to attach--Relation between the
     "gap" and the "chord"                                            93
 
 
@@ -313,12 +278,12 @@ CONTENTS
 
     THE STEERING OF THE MODEL.
 
-    § 1. A problem of great difficulty--Effects of propeller
-    torque. § 2. How obviated. § 3. The two-propeller
-    solution--The reason why it is only a partial success. § 4.
-    The _speed_ solution. § 5. Vertical fins. § 6. Balancing tips
-    or ailerons. § 7. Weighting. § 8. By means of transversely
-    canting the elevator. § 9. The necessity for some form of
+    § 1. A problem of great difficulty--Effects of propeller
+    torque. § 2. How obviated. § 3. The two-propeller
+    solution--The reason why it is only a partial success. § 4.
+    The _speed_ solution. § 5. Vertical fins. § 6. Balancing tips
+    or ailerons. § 7. Weighting. § 8. By means of transversely
+    canting the elevator. § 9. The necessity for some form of
     "keel"                                                          105
 
 
@@ -326,27 +291,27 @@ CONTENTS
 
     THE LAUNCHING OF THE MODEL.
 
-    § 1. The direction in which to launch them. § 2. The
+    § 1. The direction in which to launch them. § 2. The
     velocity--wooden aerofoils and fabric-covered
-    aerofoils--Poynter's launching apparatus. § 3. The launching
-    of very light models. § 4. Large size and power-driven
-    models. § 5. Models designed to rise from the
-    ground--Paulhan's prize model. § 6. The setting of the
-    elevator. § 7. The most suitable propeller for this form of
-    model. § 8. Professor Kress' method of launching. § 9. How to
-    launch a twin screw model. § 10. A prior revolution of the
-    propellers. § 11. The best angle at which to launch a model     109
+    aerofoils--Poynter's launching apparatus. § 3. The launching
+    of very light models. § 4. Large size and power-driven
+    models. § 5. Models designed to rise from the
+    ground--Paulhan's prize model. § 6. The setting of the
+    elevator. § 7. The most suitable propeller for this form of
+    model. § 8. Professor Kress' method of launching. § 9. How to
+    launch a twin screw model. § 10. A prior revolution of the
+    propellers. § 11. The best angle at which to launch a model     109
 
 
     CHAPTER XI.
 
     HELICOPTER MODELS.
 
-    § 1. Models quite easy to make. § 2. Sir George Cayley's
-    helicopter model. § 3. Phillips' successful power-driven
-    model. § 4. Toy helicopters. § 5. Incorrect and correct way
-    of arranging the propellers. § 6. Fabric covered screws. § 7.
-    A design to obviate weight. § 8. The question of a fin or
+    § 1. Models quite easy to make. § 2. Sir George Cayley's
+    helicopter model. § 3. Phillips' successful power-driven
+    model. § 4. Toy helicopters. § 5. Incorrect and correct way
+    of arranging the propellers. § 6. Fabric covered screws. § 7.
+    A design to obviate weight. § 8. The question of a fin or
     keel.                                                           113
 
 
@@ -359,39 +324,39 @@ CONTENTS
 
     MODEL FLYING COMPETITIONS.
 
-    § 1. A few general details concerning such. § 2. Aero Models
-    Association's classification, etc. § 3. Various points to be
+    § 1. A few general details concerning such. § 2. Aero Models
+    Association's classification, etc. § 3. Various points to be
     kept in mind when competing                                     119
 
 
     CHAPTER XIV.
 
-    USEFUL NOTES, TABLES, FORMULÆ, ETC.
-
-    § 1. Comparative velocities. § 2. Conversions. § 3. Areas of
-    various shaped surfaces. § 4. French and English measures.
-    § 5. Useful data. § 6. Table of equivalent inclinations. § 7.
-    Table of skin friction. § 8. Table I. (metals). § 9. Table
-    II. (wind pressures). § 10. Wind pressure on various shaped
-    bodies. § 11. Table III. (lift and drift) on a cambered
-    surface. § 12. Table IV. (lift and drift)--On a plane
-    aerofoil--Deductions. § 13. Table V. (timber). § 14. Formula
-    connecting weight lifted and velocity. § 15. Formula
+    USEFUL NOTES, TABLES, FORMULÆ, ETC.
+
+    § 1. Comparative velocities. § 2. Conversions. § 3. Areas of
+    various shaped surfaces. § 4. French and English measures.
+    § 5. Useful data. § 6. Table of equivalent inclinations. § 7.
+    Table of skin friction. § 8. Table I. (metals). § 9. Table
+    II. (wind pressures). § 10. Wind pressure on various shaped
+    bodies. § 11. Table III. (lift and drift) on a cambered
+    surface. § 12. Table IV. (lift and drift)--On a plane
+    aerofoil--Deductions. § 13. Table V. (timber). § 14. Formula
+    connecting weight lifted and velocity. § 15. Formula
     connecting models of similar design but different weights.
-    § 16. Formula connecting power and speed. § 17. Propeller
-    thrust. § 18. To determine experimentally the static thrust
-    of a propeller. § 19. Horse-power and the number of
-    revolutions. § 20. To compare one model with another. § 21.
-    Work done by a clockwork spring motor. § 22. To ascertain the
-    horse-power of a rubber motor. § 23. Foot-pounds of energy in
+    § 16. Formula connecting power and speed. § 17. Propeller
+    thrust. § 18. To determine experimentally the static thrust
+    of a propeller. § 19. Horse-power and the number of
+    revolutions. § 20. To compare one model with another. § 21.
+    Work done by a clockwork spring motor. § 22. To ascertain the
+    horse-power of a rubber motor. § 23. Foot-pounds of energy in
     a given weight of rubber--Experimental determination of.
-    § 24. Theoretical length of flight. § 25. To test different
-    motors. § 26. Efficiency of a model. § 27. Efficiency of
-    design. § 28. Naphtha engines. § 29. Horse-power and weight
-    of model petrol motors. § 30. Formula for rating the same.
-    § 30A. Relation between static thrust of propeller and total
-    weight of model. § 31. How to find the height of an
-    inaccessible object (kite, balloon, etc.). § 32. Formula for
+    § 24. Theoretical length of flight. § 25. To test different
+    motors. § 26. Efficiency of a model. § 27. Efficiency of
+    design. § 28. Naphtha engines. § 29. Horse-power and weight
+    of model petrol motors. § 30. Formula for rating the same.
+    § 30A. Relation between static thrust of propeller and total
+    weight of model. § 31. How to find the height of an
+    inaccessible object (kite, balloon, etc.). § 32. Formula for
     I.H.P. of model steam engines                                   125
 
     APPENDIX A. Some models which have won medals at open
@@ -525,7 +490,7 @@ MODEL AEROPLANING
 INTRODUCTION.
 
 
-§ 1. Model Aeroplanes are primarily divided into two classes: first,
+§ 1. Model Aeroplanes are primarily divided into two classes: first,
 models intended before all else to be ones that shall _fly_; secondly,
 _models_, using the word in its proper sense of full-sized machines.
 Herein model aeroplanes differ from model yachts and model
@@ -535,7 +500,7 @@ but when you try to build a scale model of an "Antoinette" monoplane,
 _including engine_, it cannot be made to fly unless the scale be a
 very large one. If, for instance, you endeavoured to make a 1/10 scale
 model, your model petrol motor would be compelled to have eight
-cylinders, each 0·52 bore, and your magneto of such size as easily to
+cylinders, each 0·52 bore, and your magneto of such size as easily to
 pass through a ring half an inch in diameter. Such a model could not
 possibly work.[1]
 
@@ -543,25 +508,25 @@ possibly work.[1]
     1910, some really very fine working drawings of a prize-winning
     Antoinette monoplane model.
 
-§ 2. Again, although the motor constitutes the _chief_, it is by no
+§ 2. Again, although the motor constitutes the _chief_, it is by no
 means the sole difficulty in _scale_ model aeroplane building. To
 reproduce to scale at _scale weight_, or indeed anything approaching it,
 _all_ the _necessary_--in the case of a full-sized machine--framework is
 not possible in a less than 1/5 scale.
 
-§ 3. Special difficulties occur in the case of any prototype taken.
-For instance, in the case of model Blériots it is extremely difficult
+§ 3. Special difficulties occur in the case of any prototype taken.
+For instance, in the case of model Blériots it is extremely difficult
 to get the centre of gravity sufficiently forward.
 
-§ 4. Scale models of actual flying machines _that will fly_ mean
+§ 4. Scale models of actual flying machines _that will fly_ mean
 models _at least_ 10 or 12 feet across, and every other dimension in
 like proportion; and it must always be carefully borne in mind that
 the smaller the scale the greater the difficulties, but not in the
 same proportion--it would not be _twice_ as difficult to build a
-¼-in. scale model as a ½-in., but _four_, _five_ or _six_ times as
+¼-in. scale model as a ½-in., but _four_, _five_ or _six_ times as
 difficult.
 
-§ 5. Now, the _first_ requirement of a model aeroplane, or flying
+§ 5. Now, the _first_ requirement of a model aeroplane, or flying
 machine, is that it shall FLY.
 
 As will be seen later on--unless the machine be of large size, 10 feet
@@ -570,7 +535,7 @@ twisted rubber strands, and this to be efficient requires to be long,
 and is of practically uniform weight throughout; this alone alters the
 entire _distribution of weight_ on the machine and makes:
 
-§ 6. "=Model Aeroplaning an Art in itself=," and as such we propose to
+§ 6. "=Model Aeroplaning an Art in itself=," and as such we propose to
 consider it in the following pages.
 
 We have said that the first requisite of a model aeroplane is that it
@@ -581,7 +546,7 @@ flights and scientific study what is required is a machine in which
 minute detail is of secondary importance, but which does along its
 main lines "_approximate_ to the real thing."
 
-§ 7. Simplicity should be the first thing aimed at--simplicity means
+§ 7. Simplicity should be the first thing aimed at--simplicity means
 efficiency, it means it in full-sized machines, still more does it
 mean it in models--and this very question of simplicity brings us to
 that most important question of all, namely, the question of _weight_.
@@ -590,7 +555,7 @@ FOOTNOTE:
 
 [1] The smallest working steam engine that the writer has ever heard
 of has a net weight of 4 grains. One hundred such engines would be
-required to weigh one ounce. The bore being 0·03 in., and stroke 1/32
+required to weigh one ounce. The bore being 0·03 in., and stroke 1/32
 of an inch, r.p.m. 6000 per min., h.p. developed 1/489000 ("Model
 Engineer," July 7, 1910). When working it hums like a bee.
 
@@ -602,7 +567,7 @@ CHAPTER I.
 THE QUESTION OF WEIGHT.
 
 
-§ 1. The following is an extract from a letter that appeared in the
+§ 1. The following is an extract from a letter that appeared in the
 correspondence columns of "The Aero."[2]
 
 "To give you some idea how slight a thing will make a model behave
@@ -616,7 +581,7 @@ bends under the strain of the rubber, put light silk on the planes,
 and use an aluminium[4] propeller. The result will surpass all
 expectations."
 
-§ 2. The above refers, of course, to a rubber-motor driven model. Let
+§ 2. The above refers, of course, to a rubber-motor driven model. Let
 us turn to a steam-driven prototype. I take the best known example of
 all, Professor Langley's famous model. Here is what the professor has
 to say on the question[5]:--
@@ -636,7 +601,7 @@ How to obtain the maximum strength with the minimum of weight is one
 of the, if not the most, difficult problems which the student has to
 solve.
 
-§ 3. The theoretical reason why _weight_ is such an all-important item
+§ 3. The theoretical reason why _weight_ is such an all-important item
 in model aeroplaning, much more so than in the case of full-size
 machines, is that, generally speaking, such models do not fly fast
 enough to possess a high weight carrying capacity. If you increase the
@@ -644,20 +609,20 @@ area of the supporting surface you increase also the resistance, and
 thereby diminish the speed, and are no better off than before. The
 only way to increase the weight carrying capacity of a model is to
 increase its speed. This point will be recurred to later on. One of
-Mr. T.W.K. Clarke's well-known models, surface area 1¼ sq. ft.,
-weight 1¼ lb., is stated to have made a flight of 300 yards
+Mr. T.W.K. Clarke's well-known models, surface area 1¼ sq. ft.,
+weight 1¼ lb., is stated to have made a flight of 300 yards
 carrying 6 oz. of lead. This works out approximately at 21 oz. per sq.
 ft.
 
 The velocity (speed) is not stated, but some earlier models by the
-same designer, weight 1½ lb., supporting area 1½ sq. ft., i.e.,
+same designer, weight 1½ lb., supporting area 1½ sq. ft., i.e.,
 at rate of 16 oz. per sq. ft., travelled at a rate of 37 ft. per
 second, or 25 miles an hour.
 
 The velocity of the former, therefore, would certainly not be less
 than 30 miles an hour.
 
-§ 4. Generally speaking, however, models do not travel at anything
+§ 4. Generally speaking, however, models do not travel at anything
 like this velocity, or carry anything like this weight per sq. ft.
 
 An average assumption of 13 to 15 miles an hour does nor err on the
@@ -678,7 +643,7 @@ manner.
 (in writing) the weight and result of every trial and every experiment
 in the alteration and change of material used. WEIGH EVERYTHING.
 
-§ 5. The reader must not be misled by what has been said, and think
+§ 5. The reader must not be misled by what has been said, and think
 that a model must not weigh anything if it is to fly well. A heavy
 model will fly much better against the wind than a light one, provided
 that the former _will_ fly. To do this it must fly _fast_. To do this
@@ -705,7 +670,7 @@ CHAPTER II.
 THE QUESTION OF RESISTANCE.
 
 
-§ 1. It is, or should be, the function of an aeroplane--model or
+§ 1. It is, or should be, the function of an aeroplane--model or
 otherwise--to pass through the medium in which it travels in such a
 manner as to leave that medium in as motionless a state as possible,
 since all motion of the surrounding air represents so much power
@@ -714,17 +679,17 @@ wasted.
 Every part of the machine should be so constructed as to move through
 the air with the minimum of disturbance and resistance.
 
-§ 2. The resistance, considered as a percentage of the load itself,
+§ 2. The resistance, considered as a percentage of the load itself,
 that has to be overcome in moving a load from one place to another,
-is, according to Mr. F.W. Lanchester, 12½ per cent. in the case of
-a flying machine, and 0·1 per cent. in the case of a cargo boat, and
+is, according to Mr. F.W. Lanchester, 12½ per cent. in the case of
+a flying machine, and 0·1 per cent. in the case of a cargo boat, and
 of a solid tyre motor car 3 per cent., a locomotive 1 per cent. Four
 times at least the resistance in the case of aerial locomotion has to
 be overcome to that obtained from ordinary locomotion on land. The
 above refer, of course, to full-sized machines; for a model the
 resistance is probably nearer 14 or 15 per cent.
 
-§ 3. This resistance is made up of--
+§ 3. This resistance is made up of--
 
     1. Aerodynamic resistance.
     2. Head resistance.
@@ -743,7 +708,7 @@ possible. To reduce the second, contours of ichthyoid, or fish-like,
 form should be used, so that the resultant stream-line flow of the
 medium shall keep in touch with the surface of the body.
 
-§ 4. As long ago as 1894 a series of experiments were made by the
+§ 4. As long ago as 1894 a series of experiments were made by the
 writer[6] to solve the following problem: given a certain length and
 breadth, to find the shape which will offer the least resistance. The
 experiments were made with a whirling table 40 ft. in diameter, which
@@ -789,7 +754,7 @@ propellers; no rudder is shown, and the long steel vertical mast
 extending both upwards and downwards through the centre would render
 it suitable only for landing on water.
 
-§ 5. In the case of a rubber-driven model, there is no containing body
+§ 5. In the case of a rubber-driven model, there is no containing body
 part, so to speak, a long thin stick, or tubular construction if
 preferred, being all that is necessary.
 
@@ -802,7 +767,7 @@ considerable rigidity, especially longitudinally. If the model be a
 biplane, then all the upright struts between the two aerofoils should
 be given a shape, a vertical section of which is shown in Fig. 3.
 
-§ 6. In considering this question of resistance, the substance of
+§ 6. In considering this question of resistance, the substance of
 which the aerofoil surface is made plays a very important part, as
 well as whether that surface be plane or curved. For some reason not
 altogether easy to determine, fabric-covered planes offer
@@ -825,16 +790,16 @@ later when considering the aerofoil proper.
 [Illustration: FIG. 3.--HORIZONTAL SECTION OF VERTICAL STRUT
 (ENLARGED.)]
 
-§ 7. Allusion has been made in this chapter to skin friction, but no
+§ 7. Allusion has been made in this chapter to skin friction, but no
 value given for its coefficient.[8] Lanchester's value for planes from
-½ to 1½ sq. ft. in area, moving about 20 to 30 ft. per second, is
+½ to 1½ sq. ft. in area, moving about 20 to 30 ft. per second, is
 
-    0·009 to 0·015.
+    0·009 to 0·015.
 
-Professor Zahm (Washington) gives 0·0026 lb. per sq. ft. at 25 ft. per
-second, and at 37 ft. per second, 0·005, and the formula
+Professor Zahm (Washington) gives 0·0026 lb. per sq. ft. at 25 ft. per
+second, and at 37 ft. per second, 0·005, and the formula
 
-    _f_ = 0·00000778_l_^{·93}_v_^{1·85}
+    _f_ = 0·00000778_l_^{·93}_v_^{1·85}
 
 _f_ being the average friction in lb. per sq. in., _l_ the length in
 feet, and _v_ the velocity in ft. per second. He also experimented
@@ -842,10 +807,10 @@ with various kinds of surfaces, some rough, some smooth, etc.
 
 His conclusion is:--"All even surfaces have approximately the same
 coefficient of skin friction. Uneven surfaces have a greater
-coefficient." All formulæ on skin friction must at present be accepted
+coefficient." All formulæ on skin friction must at present be accepted
 with reserve.
 
-§ 8. The following three experiments, however, clearly prove its
+§ 8. The following three experiments, however, clearly prove its
 _existence_, and _that it has considerable effect_:--
 
 1. A light, hollow celluloid ball, supported on a stream of air
@@ -881,13 +846,13 @@ CHAPTER III.
 THE QUESTION OF BALANCE.
 
 
-§ 1. It is perfectly obvious for successful flight that any model
+§ 1. It is perfectly obvious for successful flight that any model
 flying machine (in the absence of a pilot) must possess a high degree
 of automatic stability. The model must be so constructed as to be
 naturally stable, _in the medium through which it is proposed to drive
 it_. The last remark is of the greatest importance, as we shall see.
 
-§ 2. In connexion with this same question of automatic stability, the
+§ 2. In connexion with this same question of automatic stability, the
 question must be considered from the theoretical as well as from the
 practical side, and the labours and researches of such men as
 Professors Brian and Chatley, F.W. Lanchester, Captain Ferber,
@@ -951,7 +916,7 @@ of gravity.
 (P) An aeroplane is a conservative system, and stability is greatest
 when the kinetic energy is a maximum. [Illustration, the pendulum.]
 
-§ 3. Referring to A. Models with a plane or flat surface are not
+§ 3. Referring to A. Models with a plane or flat surface are not
 unstable, and will fly well without a tail; such a machine is called a
 simple monoplane.
 
@@ -961,7 +926,7 @@ Showing balance weight A (movable), and also his winding-up gear--a
 very handy device.]
 
 
-§ 4. Referring to D. Many model builders make this mistake, i.e., the
+§ 4. Referring to D. Many model builders make this mistake, i.e., the
 mistake of getting as low a centre of gravity as possible under the
 quite erroneous idea that they are thereby increasing the stability of
 the machine. Theoretically the _centre of gravity should be the centre
@@ -980,7 +945,7 @@ This action is the probable cause of many failures.
 
 [Illustration: FIG. 5.--THE STRINGFELLOW MODEL MONOPLANE OF 1848.]
 
-§ 5. Referring to E. If the propulsive action does not pass through
+§ 5. Referring to E. If the propulsive action does not pass through
 the centre of gravity the system again becomes "acentric." Even
 supposing condition D fulfilled, and we arrive at the following most
 important result, viz., that for stability:--
@@ -991,31 +956,31 @@ THIS SAME POINT.
 
 [Illustration: FIG. 6.--THE STRINGFELLOW MODEL TRIPLANE OF 1868.]
 
-§ 6. Referring to F and N--the problem of longitudinal stability.
+§ 6. Referring to F and N--the problem of longitudinal stability.
 There is one absolutely essential feature not mentioned in F or N, and
 that is for automatic longitudinal stability _the two surfaces, the
 aerofoil proper and the balancer_ (elevator or tail, or both), _must
 be separated by some considerable distance, a distance not less than
 four times the width of the main aerofoil_.[9] More is better.
 
-[Illustration: FIG. 7. _PÉNAUD 1871_]
+[Illustration: FIG. 7. _PÉNAUD 1871_]
 
-§ 7. With one exception (Pénaud) early experimenters with model
+§ 7. With one exception (Pénaud) early experimenters with model
 aeroplanes had not grasped this all-important fact, and their models
 would not fly, only make a series of jumps, because they failed to
 balance longitudinally. In Stringfellow's and Tatin's models the main
 aerofoil and balancer (tail) are practically contiguous.
 
-Pénaud in his rubber-motored models appears to have fully realised
+Pénaud in his rubber-motored models appears to have fully realised
 this (_vide_ Fig. 7), and also the necessity for using long strands of
 rubber. Some of his models flew 150 ft., and showed considerable
 stability.
 
 [Illustration: FIG. 8.--TATIN'S AEROPLANE (1879).
 
-Surface 0·7 sq. metres, total weight 1·75 kilogrammes, velocity of
+Surface 0·7 sq. metres, total weight 1·75 kilogrammes, velocity of
 sustentation 8 metres a second. Motor, compressed air (for description
-see § 23, ch. iv). Revolved round and round a track tethered to a post
+see § 23, ch. iv). Revolved round and round a track tethered to a post
 at the centre. In one of its jumps it cleared the head of a
 spectator.]
 
@@ -1060,7 +1025,7 @@ angle). With a larger and more efficient propeller than the one here
 shown some excellent flights were obtained. Constructed of bamboo and
 nainsook. Stayed with steel wire.]
 
-§ 8. Referring to I. This, again, is of primary importance in
+§ 8. Referring to I. This, again, is of primary importance in
 longitudinal stability. The Farman machine has three such
 planes--elevator, main aerofoil, tail the Wright originally had _not_,
 but is now being fitted with a tail, and experiments on the
@@ -1072,7 +1037,7 @@ type. The writer has made many experiments with vertical fins, and has
 found the machine very stable, even when the fin or vertical keel is
 placed some distance above the centre of gravity.
 
-§ 9. The question of transverse (side to side) stability at once
+§ 9. The question of transverse (side to side) stability at once
 brings us to the question of the dihedral angle, practically similar
 in its action to a flat plane with vertical fins.
 
@@ -1081,7 +1046,7 @@ in its action to a flat plane with vertical fins.
 Eight feathers, two corks, a thin rod, a piece of whalebone, and a
 piece of thread.]
 
-§ 10. The setting up of the front surface at an angle to the rear, or
+§ 10. The setting up of the front surface at an angle to the rear, or
 the setting of these at corresponding compensatory angles already
 dealt with, is nothing more nor less than the principle of the
 dihedral angle for longitudinal stability.
@@ -1095,7 +1060,7 @@ stability. For, on the machine heeling over, the side which is
 required to rise gains resistance by its new position, and that which
 is required to sink loses it.
 
-§ 11. The dihedral angle principle may take many forms.
+§ 11. The dihedral angle principle may take many forms.
 
 As in Fig. 12 _a_ is a monoplane, the rest biplanes. The angles and
 curves are somewhat exaggerated. It is quite a mistake to make the
@@ -1113,14 +1078,14 @@ It is evident that the righting moment of a unit of surface of an
 aeroplane is greater at the outer edge than elsewhere, owing to the
 greater lever arm.
 
-§ 12. The "upturned tip" dihedral certainly appears to have the
+§ 12. The "upturned tip" dihedral certainly appears to have the
 advantage.
 
 _The outer edges of the aerofoil then should be turned upward for the
 purpose of transverse stability, while the inner surface should remain
 flat or concave for greater support._
 
-§ 13. The exact most favourable outline of transverse section for
+§ 13. The exact most favourable outline of transverse section for
 stability, steadiness and buoyancy has not yet been found; but the
 writer has found the section given in Fig. 13, a very efficient one.
 
@@ -1142,7 +1107,7 @@ THE MOTIVE POWER.
 
 SECTION I.--RUBBER MOTORS.
 
-§ 1. Some forty years have elapsed since Pénaud first used elastic
+§ 1. Some forty years have elapsed since Pénaud first used elastic
 (rubber) for model aeroplanes, and during that time no better
 substitute (in spite of innumerable experiments) has been found. Nor
 for the smaller and lighter class of models is there any likelihood of
@@ -1156,7 +1121,7 @@ distorted (twisted or stretched, or both) without either fracture or a
 LARGE _permanent_ alteration of shape is very small. Not so rubber--it
 far surpasses in this respect even steel springs.
 
-§ 2. Let us take a piece of elastic (rubber) cord, and stretch it with
+§ 2. Let us take a piece of elastic (rubber) cord, and stretch it with
 known weights and observe carefully what happens. We shall find that,
 first of all: _the extension is proportional to the weight
 suspended_--but soon we have an _increasing_ increase of extension. In
@@ -1165,8 +1130,8 @@ rubber cord remained 1/8 of an inch longer, and at the end of an hour
 recovered itself to the extent of 1/16, remaining finally permanently
 1/16 of an inch longer. Length of elastic cord used in this experiment
 8-1/8 inches, 3/16 of an inch thick. Suspended weights, 1 oz. up to 64
-oz. Extension from ¼ inch up to 24-5/8 inches. Graph drawn in Fig.
-14, No. B abscissæ extension in eighths of an inch, ordinates weights
+oz. Extension from ¼ inch up to 24-5/8 inches. Graph drawn in Fig.
+14, No. B abscissæ extension in eighths of an inch, ordinates weights
 in ounces. So long as the graph is a straight line it shows the
 extension is proportional to the suspended weight; afterwards in
 excess.
@@ -1189,16 +1154,16 @@ It is true it is stretched--twisted--far beyond what is called the
 nearly so quickly as is commonly supposed, but in spite of this and
 other drawbacks its advantages far more than counterbalance these.
 
-§ 3. Experimenting with cords of varying thickness we find that: _the
+§ 3. Experimenting with cords of varying thickness we find that: _the
 extension is inversely proportional to the thickness_. If we leave a
 weight hanging on a piece of rubber cord (stretched, of course, beyond
 its "elastic limit") we find that: _the cord continues to elongate as
 long as the weight is left on_. For example: a 1 lb. weight hung on a
 piece of rubber cord, 8-1/8 inches long and 1/8 of an inch thick,
-stretched it--at first--6¼ inches; after two minutes this had
+stretched it--at first--6¼ inches; after two minutes this had
 increased to 6-5/8 (3/8 of an inch more). One hour later 1/8 of an
 inch more, and sixteen hours later 1/8 of an inch more, i.e. a sixteen
-hours' hang produced an additional extension of ¾ of an inch. On a
+hours' hang produced an additional extension of ¾ of an inch. On a
 thinner cord (half the thickness) same weight produced _an additional
 extension_ (_after_ 14 _hours_) _of _10-3/8 _in_.
 
@@ -1213,7 +1178,7 @@ weight suspended_--true only within the limits of elasticity.
 
 [Illustration: FIG. 15.--EXTENSION AND INCREASE IN VOLUME.]
 
-§ 4. =When a Rubber Cord is stretched there is an Increase of
+§ 4. =When a Rubber Cord is stretched there is an Increase of
 Volume.=--On stretching a piece of rubber cord to _twice_ its
 original (natural) length, we should perhaps expect to find that the
 string would only be _half_ as thick, as would be the case if the
@@ -1222,13 +1187,13 @@ cord as accurately as possible with a micrometer, measuring to the
 one-thousandth of an inch, we at once perceive that this is not the
 case, being about _two-thirds_ of its former volume.
 
-§ 5. In the case of rubber cord used for a motive power on model
+§ 5. In the case of rubber cord used for a motive power on model
 aeroplanes, the rubber is _both_ twisted and stretched, but chiefly
 the latter.
 
 Thirty-six strands of rubber, weight about 56 grammes, at 150 turns
 give a torque of 4 oz. on a 5-in. arm, but an end thrust, or end pull,
-of about 3½ lb. (Ball bearings, or some such device, can be used to
+of about 3½ lb. (Ball bearings, or some such device, can be used to
 obviate this end thrust when desirable.) A series of experiments
 undertaken by the writer on the torque produced by twisted rubber
 strands, varying in number, length, etc., and afterwards carefully
@@ -1240,12 +1205,12 @@ length.
 The following are the principal results arrived at. For graphs, see
 Fig. 16.
 
-§ 6. A. Increasing the number of (rubber) strands by _one-half_
+§ 6. A. Increasing the number of (rubber) strands by _one-half_
 (length and thickness of rubber remaining constant) increases the
 torque (unwinding tendency) _twofold_, i.e., doubles the motive power.
 
 B. _Doubling_ the number of strands increases the torque _more than
-three times_--about 3-1/3 times, 3 times up to 100 turns, 3½ times
+three times_--about 3-1/3 times, 3 times up to 100 turns, 3½ times
 from 100 to 250 turns.
 
 C. _Trebling_ the number of strands increases the torque at least
@@ -1261,11 +1226,11 @@ one-half_. (In few strands one-third, in 30 and over one-half.)
 
 [Illustration: FIG. 16.--TORQUE GRAPHS OF RUBBER MOTORS.
 
-    Abscissæ = Turns. Ordinates = Torque measured in 1/16 of an oz.
+    Abscissæ = Turns. Ordinates = Torque measured in 1/16 of an oz.
     Length of arm, 5 in.
 
     A.  38 strands of new rubber, 2 ft. 6 in. long; 58 grammes weight.
-    B.  36 strands, 2 ft. 6 in. long; end thrust at 150 turns, 3½ lb.
+    B.  36 strands, 2 ft. 6 in. long; end thrust at 150 turns, 3½ lb.
     C.  32 strands, 2 ft. 6 in. long.
     D.  24    "        "        "
     E.  18    "        "        "     weight 28 grammes.
@@ -1297,7 +1262,7 @@ H. _The length of the rubber strands twice[13] in feet the number of
 the strands in inches_,[14] e.g., if the number of strands is 12 their
 length should be 2 ft., if 18, 3 ft., and so on.
 
-§ 7. Experiments with 32 to 38 strands 2 ft. 6 in. long give a torque
+§ 7. Experiments with 32 to 38 strands 2 ft. 6 in. long give a torque
 curve almost precisely similar to that obtained from experiments made
 with flat spiral steel springs, similar to those used in watches and
 clocks; and, as we know, the torque given by such springs is very
@@ -1316,7 +1281,7 @@ cube of its thickness, also proportional to the modulus of elasticity
 of the substance used, and inversely proportional to the length of the
 strip.
 
-§ 8. Referring back to A, B, C, there are one or two practical
+§ 8. Referring back to A, B, C, there are one or two practical
 deductions which should be carefully noted.
 
 Supposing we have a model with one propeller and 36 strands of
@@ -1328,7 +1293,7 @@ sight of when thinking of using two propellers.
 
 Experiments on--
 
-§9. =The Number of Revolutions= (turns) =that can be given to Rubber
+§9. =The Number of Revolutions= (turns) =that can be given to Rubber
 Motors= led to interesting results, e.g., the number of turns to
 produce a double knot in the cord from end to end were, in the case of
 rubber, one yard long:--
@@ -1345,7 +1310,7 @@ proportion. For instance, 8 strands double knot at 310, and 4 at 440
 The reason, of course, is the more the strands the greater the
 distance they have to travel round themselves.
 
-§ 10. =The Maximum Number of Turns.=--As to the maximum number of
+§ 10. =The Maximum Number of Turns.=--As to the maximum number of
 permissible turns, rubber has rupture stress of 330 lb. per sq. in.,
 _but a very high permissible stress_, as much as 80 per cent. The
 resilience (power of recovery after distortion) in tension of rubber
@@ -1360,7 +1325,7 @@ trying for a record flight, using new elastic, as many as even 500 or
 600 or even more turns have been given in the case of 32-36 strands a
 yard in length; but such a severe strain soon spoils the rubber.
 
-§ 11. =On the Use of "Lubricants."=--One of the drawbacks to rubber is
+§ 11. =On the Use of "Lubricants."=--One of the drawbacks to rubber is
 that if it be excessively strained it soon begins to break up. One of
 the chief causes of this is that the strands stick together--they
 should always be carefully separated, if necessary, after a
@@ -1418,7 +1383,7 @@ another freely and easily, and prevent the throwing of undue strain on
 some particular portion, and absolutely prevent the strands from
 sticking together.
 
-§ 12. =The Action of Copper upon Rubber.=--Copper, whether in the form
+§ 12. =The Action of Copper upon Rubber.=--Copper, whether in the form
 of the metal, the oxides, or the soluble salts, has a marked injurious
 action upon rubber.
 
@@ -1430,7 +1395,7 @@ _copper_. In no case should the strands be placed upon bare metal. I
 always cover mine with a piece of valve tubing, which can easily be
 renewed from time to time.
 
-§ 12A. =The Action of Water, etc., on Rubber.=--Rubber is quite
+§ 12A. =The Action of Water, etc., on Rubber.=--Rubber is quite
 insoluble in water; but it must not be forgotten that it will absorb
 about 25 per cent. into its pores after soaking for some time.
 
@@ -1439,14 +1404,14 @@ bi-sulphide, petroleum spirit, benzene and its homologues found in
 coal-tar naphtha, dissolve rubber readily. Alcohol is absorbed by
 rubber, but is not a solvent of it.
 
-§ 12B. =How to Preserve Rubber.=--In the first place, in order that it
+§ 12B. =How to Preserve Rubber.=--In the first place, in order that it
 shall be _possible_ to preserve and keep rubber in the best condition
 of efficiency, it is absolutely essential that the rubber shall be,
 when obtained, fresh and of the best kind. Only the best Para rubber
 should be bought; to obtain it fresh it should be got in as large
 quantities as possible direct from a manufacturer or reliable rubber
 shop. The composition of the best Para rubber is as follows:--Carbon,
-87·46 per cent.; hydrogen, 12·00 per cent.; oxygen and ash, 0·54 per
+87·46 per cent.; hydrogen, 12·00 per cent.; oxygen and ash, 0·54 per
 cent.
 
 In order to increase its elasticity the pure rubber has to be
@@ -1467,7 +1432,7 @@ compression.
 
 Deteriorated rubber is absolutely useless for model aeroplanes.
 
-§ 13. =To Test Rubber.=--Good elastic thread composed of pure Para
+§ 13. =To Test Rubber.=--Good elastic thread composed of pure Para
 rubber and sulphur should, if properly made, stretch to seven times
 its length, and then return to its original length. It should also
 possess a stretching limit at least ten times its original length.
@@ -1479,7 +1444,7 @@ with which the strands are cut. When examined under a microscope (not
 too powerful) the strands having the least ragged edge, i.e., the best
 cut, are to be preferred.
 
-§ 14. =The Section--Strip or Ribbon versus Square.=--In section the
+§ 14. =The Section--Strip or Ribbon versus Square.=--In section the
 square and not the ribbon or strip should be used. The edge of the
 strip I have always found more ragged under the microscope than the
 square. I have also found it less efficient. Theoretically no doubt a
@@ -1487,7 +1452,7 @@ round section would be best, but none such (in small sizes) is on the
 market. Models have been fitted with a tubular section, but such
 should on no account be used.
 
-§ 15. =Size of the Section.=--One-sixteenth or one-twelfth is the best
+§ 15. =Size of the Section.=--One-sixteenth or one-twelfth is the best
 size for ordinary models; personally, I prefer the thinner. If more
 than a certain number of strands are required to provide the necessary
 power, a larger size should be used. It is not easy to say _what_ this
@@ -1495,7 +1460,7 @@ number is, but fifty may probably be taken as an outside limit.
 Remember the size increases by area section; twice the _sectional_
 height and breadth means four times the rubber.
 
-§ 16. =Geared Rubber Motors.=--It is quite a mistake to suppose that
+§ 16. =Geared Rubber Motors.=--It is quite a mistake to suppose that
 any advantage can be obtained by using a four to one gearing, say; all
 that you do obtain is one-fourth of the power minus the increased
 friction, minus the added weight. This presumes, of course, you make
@@ -1509,7 +1474,7 @@ turns, but, as we have seen, you must increase the number of strands
 to get the same thrust, and you have this to counteract any advantage
 you gain as well as added weight and friction.
 
-§ 17. The writer has tried endless experiments with all kinds of
+§ 17. The writer has tried endless experiments with all kinds of
 geared rubber motors, and the only one worth a moment's consideration
 is the following, viz., one in which two gear wheels--same size,
 weight, and number of teeth--are made use of, the propeller being
@@ -1532,7 +1497,7 @@ B. The weight must be a minimum. This is best attained by using solid
 wheels, and lightening by drilling and turning.
 
 C. The friction must be a minimum. Use the lightest ball bearings
-obtainable (these weigh only 0·3 gramme), adjust the wheels so that
+obtainable (these weigh only 0·3 gramme), adjust the wheels so that
 they run with the greatest freedom, but see that the teeth overlap
 sufficiently to stand the strain and slight variations in direction
 without fear of slipping. Shallow teeth are useless.
@@ -1559,7 +1524,7 @@ gained--the writer speaks from experience. The requisite number of
 rubber strands to give the best result must be determined by
 experiment.
 
-§ 18. One advantage in using such a motor as this is that the two
+§ 18. One advantage in using such a motor as this is that the two
 equal strands untwisting in opposite directions have a decided
 steadying effect on the model, similar almost to the case in which two
 propellers are used.
@@ -1578,7 +1543,7 @@ each propeller.
 
 SECTION II.--OTHER FORMS OF MOTORS.
 
-§ 18A. =Spring Motors.=--This question has already been dealt with
+§ 18A. =Spring Motors.=--This question has already been dealt with
 more or less whilst dealing with rubber motors, and the superiority of
 the latter over the former pointed out. Rubber has a much greater
 superiority over steel or other springs, because in stretch-twisted
@@ -1593,7 +1558,7 @@ different distributions of weight on the model, and its effect on the
 balance of the machine; but effects such as this can be brought about
 without a change of motor.
 
-§ 18B. A more efficient form of spring motor, doing away with gearing
+§ 18B. A more efficient form of spring motor, doing away with gearing
 troubles, is to use a long spiral spring (as long as the rubber
 strands) made of medium-sized piano wire, similar in principle to
 those used in some roller-blinds, but longer and of thinner steel.
@@ -1603,7 +1568,7 @@ forms of spring motors, but none can compare with rubber.
 
 The long spiral form of steel spring is, however, much the best.
 
-§ 18C. =Compressed Air Motors.=--This is a very fascinating form of
+§ 18C. =Compressed Air Motors.=--This is a very fascinating form of
 motor, on paper, and appears at first sight the ideal form. It is so
 easy to write: "Its weight is negligible, and it can be provided free
 of cost; all that is necessary is to work a bicycle pump for as many
@@ -1613,10 +1578,10 @@ central rib of the machine, and the engine mechanism necessary for
 conveying this stored-up energy to the revolving propeller need weigh
 only a few ounces." Another writer recommends "a pressure of 300 lb."
 
-§ 18D. A pneumatic drill generally works at about 80 lb. pressure,
+§ 18D. A pneumatic drill generally works at about 80 lb. pressure,
 and when developing 1 horse-power, uses about 55 cubic ft. of free air
 per minute. Now if we apply this to a model aeroplane of average size,
-taking a reservoir 3 ft. long by 1½ in. internal diameter, made of
+taking a reservoir 3 ft. long by 1½ in. internal diameter, made of
 magnalium, say--steel would, of course, be much better--the weight of
 which would certainly not be less than 4 oz., we find that at 80 lb.
 pressure such a motor would use
@@ -1625,25 +1590,25 @@ pressure such a motor would use
 
 cub. ft. per minute.
 
-Now 80 lb. is about 5½ atmospheres, and the cubical contents of the
+Now 80 lb. is about 5½ atmospheres, and the cubical contents of the
 above motor some 63 cub. in. The time during which such a model would
 fly depends on the H.P. necessary for flight; but a fair allowance
 gives a flight of from 10 to 30 sec. I take 80 lb. pressure as a fair
 practical limit.
 
-§ 18E. The pressure in a motor-car tyre runs from 40 to 80 lb.,
+§ 18E. The pressure in a motor-car tyre runs from 40 to 80 lb.,
 usually about 70 lb. Now 260 strokes are required with an ordinary
 inflator to obtain so low a pressure as 70 lb., and it is no easy job,
 as those who have done it know.
 
-§ 19. Prior to 1893 Mr. Hargraves (of cellular kite fame) studied the
+§ 19. Prior to 1893 Mr. Hargraves (of cellular kite fame) studied the
 question of compressed-air motors for model flying machines. His motor
 was described as a marvel of simplicity and lightness, its cylinder
 was made like a common tin can, the cylinder covers cut from sheet tin
 and pressed to shape, the piston and junk rings of ebonite.
 
-One of his receivers was 23-3/8 in. long, and 5·5 in. diameter, of
-aluminium plate 0·2 in. thick, 3/8 in. by 1/8 in. riveting strips were
+One of his receivers was 23-3/8 in. long, and 5·5 in. diameter, of
+aluminium plate 0·2 in. thick, 3/8 in. by 1/8 in. riveting strips were
 insufficient to make tight joints; it weighed 26 oz., and at 80 lb.
 water pressure one of the ends blew out, the fracture occurring at the
 bend of the flange, and not along the line of rivets. The receiver
@@ -1652,11 +1617,11 @@ not to be had at that date in Sydney. With a receiver of this
 character, and the engine referred to above, a flight of 343 ft. was
 obtained, this flight being the best. (The models constructed by him
 were not on the aeroplane, but ornithoptere, or wing-flapping
-principle.) The time of flight was 23 _seconds_, with 54½ double
+principle.) The time of flight was 23 _seconds_, with 54½ double
 vibrations of the engines. The efficiency of this motor was estimated
 to be 29 per cent.
 
-§ 20. By using compressed air, and heating it in its passage to the
+§ 20. By using compressed air, and heating it in its passage to the
 cylinder, far greater efficiency can be obtained. Steel cylinders can
 be obtained containing air under the enormous pressure of 120
 atmospheres.[19] This is practically liquid air. A 20-ft. cylinder
@@ -1670,7 +1635,7 @@ cylinders; but this would mean a very great range in the initial
 working pressure, entailing not-to-be-thought-of weight in the form of
 multi-cylinder compound engines, variable expansion gear, etc.
 
-§ 21. This means relinquishing the advantages of the high initial
+§ 21. This means relinquishing the advantages of the high initial
 pressure, and the passing of the air through a reducing valve, whereby
 a constant pressure, say, of 90 to 150, according to circumstances,
 could be maintained. By a variation in the ratio of expansion the air
@@ -1678,7 +1643,7 @@ could be worked down to, say, 30 lb.
 
 The initial loss entailed by the use of a reducing valve may be in a
 great measure restored by heating the air before using it in the motor
-cylinders; by heating it to a temperature of only 320°F., by means of
+cylinders; by heating it to a temperature of only 320°F., by means of
 a suitable burner, the volume of air is increased by one half, the
 consumption being reduced in the same proportion; the consumption of
 air used in this way being 24 lb. per indicated horse-power per hour.
@@ -1690,7 +1655,7 @@ it reaches a limit below which it cannot usefully be employed. The air
 then remaining is dead and useless, adding only to the weight of the
 aeroplane.
 
-§ 22. From calculations made by the writer the _entire_ weight of a
+§ 22. From calculations made by the writer the _entire_ weight of a
 compressed-air model motor plant would be at least _one-third_ the
 weight of the aeroplane, and on a small scale probably one-half, and
 cannot therefore hold comparison with the _steam engine_ discussed in
@@ -1701,13 +1666,13 @@ anything useful or anything superior to results obtained with
 infinitely less expense by means of rubber can be brought to pass with
 a bicycle pump, a bit of magnalium tube, and 60 lb. pressure.
 
-§ 22A. In Tatin's air-compressed motor the reservoir weighed 700
+§ 22A. In Tatin's air-compressed motor the reservoir weighed 700
 grammes, and had a capacity of 8 litres. It was tested to withstand a
 pressure of 20 atmospheres, but was worked only up to seven. The
 little engine attached thereto weighed 300 grammes, and developed a
 motive power of 2 kilogram-metres per second (_see_ ch. iii.).
 
-§ 23. =Steam-Driven Motors.=--Several successful steam-engined model
+§ 23. =Steam-Driven Motors.=--Several successful steam-engined model
 aeroplanes have been constructed, the most famous being those of
 Professor Langley.
 
@@ -1716,7 +1681,7 @@ experimented with compressed air, carbonic-acid gas, electricity, and
 other methods of obtaining energy, he finally settled upon the steam
 engine (the petrol motor was not available at that time, 1893). After
 many months' work it was found that the weight could not be reduced
-below 40 lb., whilst the engine would only develop ½ H.P., and
+below 40 lb., whilst the engine would only develop ½ H.P., and
 finally the model was condemned. A second apparatus to be worked by
 compressed air was tried, but the power proved insufficient. Then came
 another with a carbonic-acid gas engine. Then others with various
@@ -1728,28 +1693,28 @@ be with the engines, which were made surprisingly light after
 sufficient experiment. _The great difficulty was to make a boiler of
 almost no weight which would give steam enough._
 
-§ 24. At last a satisfactory boiler and engine were produced.
+§ 24. At last a satisfactory boiler and engine were produced.
 
-The engine was of 1 to 1½ H.P., total weight (including moving
+The engine was of 1 to 1½ H.P., total weight (including moving
 parts) 26 oz. The cylinders, two in number, had each a diameter of
-1¼ in., and piston stroke 2 in.
+1¼ in., and piston stroke 2 in.
 
 The boiler, with its firegrate, weighed a little over 5 lb. It
 consisted of a continuous helix of copper tubing, 3/8 in. external
 diameter, the diameter of the coil being 3 in. altogether. Through the
-centre of this was driven the blast from an "Ælopile," a modification
+centre of this was driven the blast from an "Ælopile," a modification
 of the naphtha blow-torch used by plumbers, the flame of which is
-about 2000° F.[20] The pressure of steam issuing into the engines
+about 2000° F.[20] The pressure of steam issuing into the engines
 varied from 100 to 150 lb. per sq. in.; 4 lb. weight of water and
 about 10 oz. of naphtha could be carried. The boiler evaporated 1 lb.
 of water per minute.
 
-The twin propellers, 39 in. in diam., pitch 1¼, revolved from 800
+The twin propellers, 39 in. in diam., pitch 1¼, revolved from 800
 to 1000 a minute. The entire aeroplane was 15 ft. in length, the
 aerofoils from tip to tip about 14 ft., and the total weight slightly
 less than 30 lb., of which _one-fourth was contained in the
 machinery_. Its flight was a little over half a mile in length, and of
-1½ minutes' duration. Another model flew for about three-quarters
+1½ minutes' duration. Another model flew for about three-quarters
 of a mile, at a rate of about 30 miles an hour.
 
 It will be noted that engine, generator, etc., work out at about 7 lb.
@@ -1763,7 +1728,7 @@ nothing,[21] the real trouble, in fact the only one, being the steam
 generator. An economization of weight means a waste of steam, of which
 models can easily spend their only weight in five minutes.
 
-§ 25. One way to economize without increased weight in the shape of a
+§ 25. One way to economize without increased weight in the shape of a
 condenser is to use spirit (methylated spirit, for instance) for both
 fuel and boiler, and cause the exhaust from the engines to be ejected
 on to the burning spirit, where it itself serves as fuel. By using
@@ -1771,7 +1736,7 @@ spirit, or some very volatile hydrocarbon, instead of water, we have a
 further advantage from the fact that such vaporize at a much lower
 temperature than water.
 
-§ 26. When experimenting with an engine of the turbine type we must
+§ 26. When experimenting with an engine of the turbine type we must
 use a propeller of small diameter and pitch, owing to the very high
 velocity at which such engines run.
 
@@ -1780,7 +1745,7 @@ leave such motors alone, as the very highest technical skill, combined
 with many preliminary disappointments and trials, are sure to be
 encountered before success is attained.
 
-§ 27. And the smaller the model the more difficult the problem--halve
+§ 27. And the smaller the model the more difficult the problem--halve
 your aeroplane, and your difficulties increase anything from fourfold
 to tenfold.
 
@@ -1789,7 +1754,7 @@ steel tubing (the former for safety), with a magnalium container for
 the spirit, and a working pressure of from 150 to 200 lb. per sq. in.
 Anything less than this would not be worth consideration.
 
-§ 28. Some ten months after Professor Langley's successful model
+§ 28. Some ten months after Professor Langley's successful model
 flights (1896), experiments were made in France at Carquenez, near
 Toulon. The total weight of the model aeroplane in this case was 70
 lb.; the engine power a little more than 1 H.P. Twin screws were
@@ -1801,7 +1766,7 @@ Langley's distance (of best flight), nearly one mile, duration 1 min.
 total breadth of this large model was rather more than 6 metres, and
 the surface a little more than 8 sq. metres.
 
-§ 29. =Petrol Motors.=--Here it would appear at first thought is the
+§ 29. =Petrol Motors.=--Here it would appear at first thought is the
 true solution of the problem of the model aeroplane motor. Such a
 motor has solved the problem of aerial locomotion, as the steam engine
 solved that of terrestrial and marine travel, both full sized and
@@ -1813,7 +1778,7 @@ model; and if in the case of full sized machines, then why not models.
 
 (_Illustrations by permission from electros supplied by the "Aero."_)]
 
-§ 30. The exact size of the smallest _working_ model steam engine that
+§ 30. The exact size of the smallest _working_ model steam engine that
 has been made I do not know,[22] but it is or could be surprisingly
 small; not so the petrol motor--not one, that is, that would _work_.
 The number of petrol motor-driven model aeroplanes that have actually
@@ -1832,9 +1797,9 @@ in 1908.
     special plugs used on this motor. (_Illustrations by permission
     from electros supplied by the "Aero."_)
 
-§ 31. The following are the chief particulars of this interesting
+§ 31. The following are the chief particulars of this interesting
 machine:--The engine is a four-cylinder one, and weighs (complete with
-double carburetter and petrol tank) 5½ lb., and develops 1¼ H.P.
+double carburetter and petrol tank) 5½ lb., and develops 1¼ H.P.
 at 1300 revolutions per minute.
 
 [Illustration: FIG. 22.--ONE-CYLINDER PETROL MOTOR.
@@ -1850,7 +1815,7 @@ cylinder of steel, cast-iron heads, aluminium crank-case, double float
 feed carburetter, ignition by single coil and distributor. The
 aeroplane being 7 ft. 6 in. long, and having a span 8 ft.
 
-§ 32. =One-cylinder Petrol Motors.=--So far as the writer is aware no
+§ 32. =One-cylinder Petrol Motors.=--So far as the writer is aware no
 success has as yet attended the use of a single-cylinder petrol motor
 on a model aeroplane. Undoubtedly the vibration is excessive; but this
 should not be an insuperable difficulty. It is true it is heavier in
@@ -1860,13 +1825,13 @@ aeroplane is one of considerable importance. A badly balanced
 propeller even will seriously interfere with and often greatly curtail
 the length of flight.
 
-§ 33. =Electric Motors.=--No attempt should on any account be made to
+§ 33. =Electric Motors.=--No attempt should on any account be made to
 use electric motors for model aeroplanes. They are altogether too
 heavy, apart even from the accumulator or source of electric energy,
 for the power derivable from them. To take an extreme case, and
 supposing we use a 2-oz. electric motor capable of driving a propeller
 giving a static thrust of 3 oz.,[23] on weighing one of the smallest
-size accumulators without case, etc., I find its weight is 4½ oz.
+size accumulators without case, etc., I find its weight is 4½ oz.
 One would, of course, be of no use; at least three would be required,
 and they would require practically short circuiting to give sufficient
 amperage (running them down, that is, in some 10 to 15 seconds). Total
@@ -1903,7 +1868,7 @@ mechanical help available.
 [21] Model Steam Turbines. "Model Engineer" Series, No. 13, price
 6_d._
 
-[22] See Introduction, note to § 1.
+[22] See Introduction, note to § 1.
 
 [23] The voltage, etc., is not stated.
 
@@ -1915,7 +1880,7 @@ CHAPTER V.
 PROPELLERS OR SCREWS.
 
 
-§ 1. The design and construction of propellers, more especially the
+§ 1. The design and construction of propellers, more especially the
 former, is without doubt one of the most difficult parts of model
 aeroplaning.
 
@@ -1979,7 +1944,7 @@ In the case of petrol or similar driven models the position of the
 propeller can be safely copied from actual well-recognised and
 successful full-sized machines.
 
-§ 2. =The Number of Blades.=--Theoretically the number of blades does
+§ 2. =The Number of Blades.=--Theoretically the number of blades does
 not enter into consideration. The mass of air dealt with by the
 propeller is represented by a cylinder of indefinite length, whose
 diameter is the same as that of the screw, and the rate at which this
@@ -2004,7 +1969,7 @@ evenly distributed over a larger area, but the weight is considerably
 increased, and in models a greater advantage is gained by keeping down
 the weight than might follow from the use of more blades.
 
-§ 3. =Fan versus Propeller.=--It must always be most carefully borne
+§ 3. =Fan versus Propeller.=--It must always be most carefully borne
 in mind that a fan (ventilating) and a propeller are not the same
 thing. Because many blades are found in practice to be efficient in
 the case of the former, it is quite wrong to assume that the same
@@ -2035,14 +2000,14 @@ A fan requires to be so designed as to create a thrust when stationary
 (static thrust), and a propeller whilst moving through the air
 (dynamic thrust).
 
-§ 4. =The Function of a Propeller= is to produce dynamic thrust; and
+§ 4. =The Function of a Propeller= is to produce dynamic thrust; and
 the great advantage of the use of a propeller as a thrusting or
 propulsive agent is that its surface is always active. It has no
 _dead_ points, and its motion is continuous and not reciprocating, and
 it requires no special machinery or moving parts in its construction
 and operation.
 
-§ 5. =The Pitch= of a propeller or screw is the linear distance a
+§ 5. =The Pitch= of a propeller or screw is the linear distance a
 screw moves, backwards or forwards, in one complete revolution. This
 distance is purely a theoretical one. When, for instance, a screw is
 said to have a pitch of 1 ft., or 12 in., it means that the model
@@ -2052,7 +2017,7 @@ a nut on a bolt with one thread per foot. In a yielding fluid such as
 water or air it does not practically advance this distance, and hence
 occurs what is known as--
 
-§ 6. =Slip=, which may be defined as the distance which ought to be
+§ 6. =Slip=, which may be defined as the distance which ought to be
 traversed, but which is lost through imperfections in the propelling
 mechanism; or it may be considered as power which should have been
 used in driving the model forward. In the case of a locomotive running
@@ -2071,7 +2036,7 @@ ground.
 
 Taking "slip" into account, then--
 
-_The speed of the model in feet per minute = pitch (in feet) ×
+_The speed of the model in feet per minute = pitch (in feet) ×
 revolutions per minute -- slip (feet per minute)._
 
 This slip wants to be made small--just how small is not yet known.
@@ -2085,14 +2050,14 @@ In the case of aerial propellers a slip of 25 per cent. is quite good,
 40 per cent. bad; and there are certain reasons for assuming that
 possibly about 15 per cent. may be the best.
 
-§ 7. It is true that slip represents energy lost; but some slip is
+§ 7. It is true that slip represents energy lost; but some slip is
 essential, because without slip there could be no "thrust," this same
 thrust being derived from the reaction of the volume of air driven
 backwards.
 
 The thrust is equal to--
 
-_Weight of mass of air acted on per second × slip velocity in feet per
+_Weight of mass of air acted on per second × slip velocity in feet per
 second._
 
 In the case of an aeroplane advancing through the air it might be
@@ -2105,26 +2070,26 @@ advancing on to "undisturbed" air, the "slip" velocity is reduced, but
 the undisturbed air is equivalent to acting upon a greater mass of
 air.
 
-§ 8. =Pitch Coefficient or Pitch Ratio.=--If we divide the pitch of a
+§ 8. =Pitch Coefficient or Pitch Ratio.=--If we divide the pitch of a
 screw by its diameter we obtain what is known as pitch coefficient or
 ratio.
 
 The mean value of eighteen pitch coefficients of well-known full-sized
-machines works out at 0·62, which, as it so happens, is exactly the
+machines works out at 0·62, which, as it so happens, is exactly the
 same as the case of the Farman machine propeller considered alone,
-this ratio varying from 0·4 to 1·2; in the case of the Wright's
+this ratio varying from 0·4 to 1·2; in the case of the Wright's
 machine it is (probably) 1. The efficiency of their propeller is
 admitted on all hands. Their propeller is, of course, a slow-speed
-propeller, 450 r.p.m. The one on the Blériot monoplane (Blériot XI.)
-pitch ratio 0·4, r.p.m. 1350.
+propeller, 450 r.p.m. The one on the Blériot monoplane (Blériot XI.)
+pitch ratio 0·4, r.p.m. 1350.
 
-In marine propulsion the pitch ratio is generally 1·3 for a slow-speed
-propeller, decreasing to 0·9 for a high-speed one. In the case of
+In marine propulsion the pitch ratio is generally 1·3 for a slow-speed
+propeller, decreasing to 0·9 for a high-speed one. In the case of
 rubber-driven model aeroplanes the pitch ratio is often carried much
 higher, even to over 3.
 
-Mr. T.W.K. Clarke recommends a pitch angle of 45°, or less, at the
-tips, and a pitch ratio of 3-1/7 (with an angle of 45°). Within limits
+Mr. T.W.K. Clarke recommends a pitch angle of 45°, or less, at the
+tips, and a pitch ratio of 3-1/7 (with an angle of 45°). Within limits
 the higher the pitch ratio the better the efficiency. The higher the
 pitch ratio the slower may be the rate of revolution. Now in a rubber
 motor we do not want the rubber to untwist (run out) too quickly; with
@@ -2133,18 +2098,18 @@ like it. It certainly revolves with an abnormally high percentage of
 slip. And for efficiency it is certainly desirable to push this ratio
 to its limit; but there is also the question of the
 
-§ 9. =Diameter.=--"The diameter (says Mr. T.W.K. Clarke) should be
+§ 9. =Diameter.=--"The diameter (says Mr. T.W.K. Clarke) should be
 equal to one-quarter the span of the machine."
 
 If we increase the diameter we shall decrease the pitch ratio. From
 experiments which the writer has made he prefers a lower pitch ratio
-and increased diameter, viz. a pitch ratio of 1·5, and a diameter of
+and increased diameter, viz. a pitch ratio of 1·5, and a diameter of
 one-third to even one-half the span, or even more.[27] Certainly not
 less than one-third. Some model makers indulge in a large pitch ratio,
 angle, diameter, and blade area as well, but such a course is not to
 be recommended.
 
-§ 10. =Theoretical Pitch.=--Theoretically the pitch (from boss to
+§ 10. =Theoretical Pitch.=--Theoretically the pitch (from boss to
 tip) should at all points be the same; the boss or centre of the blade
 at right angles to the plane of rotation, and the angle decreasing as
 one approaches the tips. This is obvious when one considers that the
@@ -2165,38 +2130,38 @@ points A, B, C ... (Fig. 24), showing the angles at which the
 corresponding parts of the blade at A, B, C ... in Fig. 23 must be set
 in order that a uniform pitch may be obtained.
 
-§ 11. If the pitch be not uniform then there will be some portions of
+§ 11. If the pitch be not uniform then there will be some portions of
 the blade which will drag through the air instead of affording useful
 thrust, and others which will be doing more than they ought, putting
 air in motion which had better be left quiet. This uniform total pitch
 for all parts of the propeller is (as already stated) a decreasing
 rate of pitch from the centre to the edge. With a total pitch of 5
-ft., and a radius of 4 ft., and an angle at the circumference of 6°,
+ft., and a radius of 4 ft., and an angle at the circumference of 6°,
 then the angle of pitch at a point midway between centre and
-circumference should be 12°, in order that the total pitch may be the
+circumference should be 12°, in order that the total pitch may be the
 same at all parts.
 
-§ 12. =To Ascertain the Pitch of a Propeller.=--Take any point on one
+§ 12. =To Ascertain the Pitch of a Propeller.=--Take any point on one
 of the blades, and carefully measure the inclination of the blade at
 that point to the plane of rotation.
 
-If the angle so formed be about 19° (19·45),[28] i.e., 1 in 3, and the
+If the angle so formed be about 19° (19·45),[28] i.e., 1 in 3, and the
 point 5 in. from the centre, then every revolution this point will
 travel a distance
 
-    2 {pi} _r_ = 2 × 22/7 × 5 = 31·34.
+    2 {pi} _r_ = 2 × 22/7 × 5 = 31·34.
 
 Now since the inclination is 1 in 3,[29] the propeller will travel
 forward theoretically one-third of this distance, or
 
-    31·43/3 = 10·48 = 10½ in. approx.
+    31·43/3 = 10·48 = 10½ in. approx.
 
 Similarly any other case may be dealt with. If the propeller have a
 uniform _constant angle_ instead of a uniform pitch, then the pitch
 may be calculated at a point about one-third the length of the blade
 from the tip.
 
-§ 13. =Hollow-Faced Blades.=[30]--It must always be carefully borne
+§ 13. =Hollow-Faced Blades.=[30]--It must always be carefully borne
 in mind that a propeller is nothing more nor less than a particular
 form of aeroplane specially designed to travel a helical path. It
 should, therefore, be hollow faced and partake of the "stream line"
@@ -2210,7 +2175,7 @@ increasing pitch from the cutting to the trailing edge (considering,
 of course, any particular section). In such a case the pitch is the
 _mean effective pitch_.
 
-§ 14. =Blade Area.=--We have already referred to the fact that the
+§ 14. =Blade Area.=--We have already referred to the fact that the
 function of a propeller is to produce dynamic thrust--to drive the
 aeroplane forward by driving the air backwards. At the same time it is
 most desirable for efficiency that the air should be set in motion as
@@ -2221,7 +2186,7 @@ be accelerated to the smallest velocity.
 In marine engineering in slow-speed propellers (where cavitation[31]
 does not come in) narrow blades are usually used. In high-speed marine
 propellers (where cavitation is liable to occur) the projected area of
-the blades is sometimes as much as 0·6 of the total disk area. In the
+the blades is sometimes as much as 0·6 of the total disk area. In the
 case of aerial propellers, where cavitation does not occur, or not
 unless the velocity be a very high one (1500 or more a minute), narrow
 blades are the best. Experiments in marine propulsion also show that
@@ -2248,14 +2213,14 @@ only wasted, but inimical to good flights, being our old bugbear
 Requisite strength and stiffness, of course, set a limit on the final
 narrowness of the blades, apart from other considerations.
 
-§ 15. The velocity with which the propeller is rotated has also an
+§ 15. The velocity with which the propeller is rotated has also an
 important bearing on this point; but a higher speed than 900 r.p.m.
 does not appear desirable, and even 700 or less is generally
 preferable.[32] In case of twin-screw propellers, with an angle at the
-tips of 40° to 45°, as low a velocity of 500 or even less would be
+tips of 40° to 45°, as low a velocity of 500 or even less would be
 still better.[33]
 
-§ 16. =Shrouding.=--No improvement whatever is obtained by the use of
+§ 16. =Shrouding.=--No improvement whatever is obtained by the use of
 any kind of shrouding or ring round the propeller tips, or by
 corrugating the surface of the propeller, or by using cylindrical or
 cone-shaped propeller chamber or any kind of air guide either before
@@ -2271,7 +2236,7 @@ A TUBE OF AIR.]
 
 A CYLINDER OF AIR.]
 
-§ 17. =General Design.=--The propeller should be so constructed as to
+§ 17. =General Design.=--The propeller should be so constructed as to
 act upon a tube and not a "cylinder" of air. Many flying toys
 (especially the French ones) are constructed with propellers of the
 cylinder type. Ease of manufacture and the contention that those
@@ -2281,7 +2246,7 @@ favour. But all the central cut away part offers resistance in the
 line of travel, instead of exerting its proportionate propulsive
 power, and their efficiency is affected by such a practice.
 
-§ 18. A good =Shape= for the blades[34] is rectangular with rounded
+§ 18. A good =Shape= for the blades[34] is rectangular with rounded
 corners; the radius of the circle for rounding off the corners may be
 taken as about one-quarter of the width of the blade. The shape is not
 _truly rectangular, for the width of this rectangular at (near) the
@@ -2293,9 +2258,9 @@ strength to keep down the weight). _The pitch uniform and large._
 
 [Illustration: FIG. 27.--O T = 1/3 O P.]
 
-§ 19. =The Blades, two in number=, and hollow faced--the maximum
+§ 19. =The Blades, two in number=, and hollow faced--the maximum
 concavity being one-third the distance from the entering to the
-trailing edge; the ratio of A T to O P (the width) being 0·048 or 1 :
+trailing edge; the ratio of A T to O P (the width) being 0·048 or 1 :
 21, these latter considerations being founded on the analogy between a
 propeller and the aerofoil surface. (If the thickness be varied from
 the entering to the trailing edge the greatest thickness should be
@@ -2312,19 +2277,19 @@ curved as in Fig. 28, then the straight edge must be made the
 _trailing_ edge. And if both be curved as in Fig. 29, then the
 _concave_ edge must be the trailing edge.
 
-§ 19. =Propeller Design.=--To design a propeller, proceed as follows.
+§ 19. =Propeller Design.=--To design a propeller, proceed as follows.
 Suppose the diameter 14 in. and the pitch three times the diameter,
 i.e. 52 in. (See Fig. 30.)
 
 Take one-quarter scale, say. Draw a centre line A B of convenient
-length, set of half the pitch 52 in. -- ¼ scale = 5¼ in. = C - D.
+length, set of half the pitch 52 in. -- ¼ scale = 5¼ in. = C - D.
 Draw lines through C and D at right angles to C D.
 
-With a radius equal to half the diameter (i.e. in this case 1¾ in.)
+With a radius equal to half the diameter (i.e. in this case 1¾ in.)
 of the propeller, describe a semicircle E B F and complete the
 parallelogram F H G E. Divide the semicircle into a number of equal
 parts; twelve is a convenient number to take, then each division
-subtends an angle of 15° at the centre D.
+subtends an angle of 15° at the centre D.
 
 Divide one of the sides E G into the same number of equal parts
 (twelve) as shown. Through these points draw lines parallel to F E or
@@ -2335,24 +2300,24 @@ parallel to F H or E G as shown. The line drawn through the successive
 intersections of these lines is the path of the tip of the blade
 through half a revolution, viz. the line H S O T E.
 
-S O T X gives the angle at the tip of the blades = 44°.
+S O T X gives the angle at the tip of the blades = 44°.
 
 Let the shape of the blade be rectangular with rounded corners, and
 let the breadth at the tip be twice that at the boss.
 
-Then the area (neglecting the rounded off corners) is 10½ sq. in.
+Then the area (neglecting the rounded off corners) is 10½ sq. in.
 
 [Illustration: FIG. 30.--PROPELLER DESIGN.
 
-One quarter scale. Diameter 14 in. Pitch 52 in. Angle at tip 44°.]
+One quarter scale. Diameter 14 in. Pitch 52 in. Angle at tip 44°.]
 
-The area being that of a rectangle 7 in. × 1 in. = 7 sq. in. plus area
-of two triangles, base ½ in., height 7 in. Now area of triangle =
-half base × height. Therefore area of both triangles = ½ in. × 7
-in. = 3½ sq. in. Now the area of the disc swept out by the
+The area being that of a rectangle 7 in. × 1 in. = 7 sq. in. plus area
+of two triangles, base ½ in., height 7 in. Now area of triangle =
+half base × height. Therefore area of both triangles = ½ in. × 7
+in. = 3½ sq. in. Now the area of the disc swept out by the
 propeller is
 
-    {pi}/4 × (diam.)²  ({pi} = 22/7)
+    {pi}/4 × (diam.)²  ({pi} = 22/7)
 
 [Illustration: FIG. 31.--PROPELLER DESIGN.
 
@@ -2361,9 +2326,9 @@ full-sized.]
 
 And if _d_ A _r_ = the "disc area ratio" we have
 
-    (_d_ A _r_) × {pi}/4 × (14)² = area of blade = 10½,
+    (_d_ A _r_) × {pi}/4 × (14)² = area of blade = 10½,
 
-whence _d_ A _r_ = 0·07 about.
+whence _d_ A _r_ = 0·07 about.
 
 [Illustration: FIG. 32.]
 
@@ -2372,7 +2337,7 @@ whence _d_ A _r_ = 0·07 about.
 In Fig. 31 set off A B equal to the pitch of the propeller (42 in.),
 one-eighth scale. Set off B C at right angles to A B and equal to
 
-    {pi} × diameter = 22/7 × 14 = 44 in. to scale 5½ in.
+    {pi} × diameter = 22/7 × 14 = 44 in. to scale 5½ in.
 
 Divide B C into a convenient number of equal parts in the figure; five
 only are taken, D, E, F, G, H; join A D, A E, A F, A G, A H and
@@ -2387,7 +2352,7 @@ the blade.
 Similarly any other design may be dealt with; in a propeller of 14 in.
 diameter the diameter of the "boss" should not be more than 10/16 in.
 
-§ 20. =Experiments with Propellers.=--The propeller design shown in
+§ 20. =Experiments with Propellers.=--The propeller design shown in
 Figs. 32 and 33, due to Mr. G. de Havilland,[35] is one very suitable
 for experimental purposes. A single tube passing through a T-shaped
 boss forms the arms. On the back of the metal blade are riveted four
@@ -2482,24 +2447,24 @@ Metal propellers of constant angle, as well as wooden ones of uniform
 (constant) pitch, were tested; the former gave good results, but not
 so good as the latter.
 
-The best angle of pitch (at the tip) was found to be from 20° to 30°.
+The best angle of pitch (at the tip) was found to be from 20° to 30°.
 
 In all cases when the slip was as low as 25 per cent., or even
 somewhat less, nearly 20 per cent., a distinct "back current" of air
 was given out by the screw. This "slip stream," as it is caused, is
 absolutely necessary for efficiency.
 
-§ 21. =Fabric-covered= screws did not give very efficient results; the
+§ 21. =Fabric-covered= screws did not give very efficient results; the
 only point in their use on model aeroplanes is their extreme
 lightness. Two such propellers of 6 in. diameter can be made to weigh
 less than 1/5 oz. the pair; but wooden propellers (built-up principle)
 have been made 5 in. diameter and 1/12 oz. in weight.
 
-§ 22. Further experiments were made with twin screws mounted on model
+§ 22. Further experiments were made with twin screws mounted on model
 aeroplanes. In one case two propellers, both turning in the _same_
 direction, were mounted (without any compensatory adjustment for
-torque) on a model, total weight 1½ lb. Diameter of each propeller
-14 in.; angle of blade at tip 25°. The result was several good
+torque) on a model, total weight 1½ lb. Diameter of each propeller
+14 in.; angle of blade at tip 25°. The result was several good
 flights--the model (_see_ Fig. 49c) was slightly unsteady across the
 wind, that was all.
 
@@ -2515,7 +2480,7 @@ alterations were made, but always with the same result. These
 experiments have since been confirmed, and there seems no doubt that
 the double-curved shaped blade _is_ superior. (See Fig. 39.)
 
-§ 23. =The Fleming-Williams Propeller.=--A chapter on propellers would
+§ 23. =The Fleming-Williams Propeller.=--A chapter on propellers would
 scarcely be complete without a reference to the propeller used on a
 machine claiming a record of over a quarter of a mile. This form of
 propeller, shown in the group in Fig. 36 (top right hand), was found
@@ -2530,7 +2495,7 @@ on one side.]
 
 [Illustration: FIG. 40.--THE FLEMING-WILLIAMS MODEL.]
 
-It possesses large blade area, large pitch angle--more than 45° at the
+It possesses large blade area, large pitch angle--more than 45° at the
 tip--and large diameter. These do not combine to propeller efficiency
 or to efficient dynamic thrust; but they do, of course, combine to
 give the propeller a very slow rotational velocity. Provided they give
@@ -2550,15 +2515,15 @@ On the score of efficiency, when it is desired to make a limited
 number of turns give the longest flight (which is the problem one
 always has to face when using a rubber motor) it is better to make use
 of an abnormal diameter, say, more than half the span, and using a tip
-pitch angle of 25°, than to make use of an abnormal tip pitch 45° and
+pitch angle of 25°, than to make use of an abnormal tip pitch 45° and
 more, and large blade area. In a large pitch angle so much energy is
 wasted, not in dynamic thrust, but in transverse upsetting torque. On
 no propeller out of dozens and dozens that I have tested have I ever
-found a tip-pitch of more than 35° give a good dynamic thrust; and for
+found a tip-pitch of more than 35° give a good dynamic thrust; and for
 length of flight velocity due to dynamic thrust must be given due
 weight, as well as the duration of running down of the rubber motor.
 
-§ 24. Of built up or carved out and twisted wooden propellers, the
+§ 24. Of built up or carved out and twisted wooden propellers, the
 former give the better result; the latter have an advantage, however,
 in sometimes weighing less.
 
@@ -2571,9 +2536,9 @@ obtained with the two propellers behind, one revolving in the
 immediate rear of the other. Flying, of course, with the wind,
 _weight_ is of paramount importance in these little models, and in
 both these cases the "single stick" can be made use of. _See also_ ch.
-iv., § 28.
+iv., § 28.
 
-[25] _See also_ ch. viii., § 5.
+[25] _See also_ ch. viii., § 5.
 
 [26] Save in case of some models with fabric-covered propellers. Some
 dirigibles are now being fitted with four-bladed wooden screws.
@@ -2582,26 +2547,26 @@ dirigibles are now being fitted with four-bladed wooden screws.
 
 [28] Vide Equivalent Inclinations--Table of.
 
-[29] One in 3 or 0·333 is the _sine_ of the angle; similarly if the
-angle were 30° the sine would be 0·5 or ½, and the theoretical
+[29] One in 3 or 0·333 is the _sine_ of the angle; similarly if the
+angle were 30° the sine would be 0·5 or ½, and the theoretical
 distance travelled one-half.
 
 [30] _Flat-Faced Blades._--If the blade be not hollow-faced--and we
 consider the screw as an inclined plane and apply the Duchemin formula
 to it--the velocity remaining the same, the angle of maximum thrust is
-35¼°. Experiments made with such screws confirm this.
+35¼°. Experiments made with such screws confirm this.
 
 [31] Cavitation is when the high speed of the screw causes it to carry
 round a certain amount of the medium with it, so that the blades
 strike no undisturbed, or "solid," air at all, with a proportionate
 decrease in thrust.
 
-[32] In the Wright machine r.p.m. = 450; in Blériot XI. r.p.m. = 1350.
+[32] In the Wright machine r.p.m. = 450; in Blériot XI. r.p.m. = 1350.
 
 [33] Such propellers, however, require a considerable amount of
 rubber.
 
-[34] But _see also_ § 22.
+[34] But _see also_ § 22.
 
 [35] "Flight," March 10, 1910. (Illustration reproduced by
 permission.)
@@ -2616,7 +2581,7 @@ CHAPTER VI.
 THE QUESTION OF SUSTENTATION THE CENTRE OF PRESSURE.
 
 
-§ 1. Passing on now to the study of an aeroplane actually in the air,
+§ 1. Passing on now to the study of an aeroplane actually in the air,
 there are two forces acting on it, the upward lift due to the air
 (i.e. to the movement of the aeroplane supposed to be continually
 advancing on to fresh, undisturbed _virgin_ air), and the force due to
@@ -2653,12 +2618,12 @@ in the wind causes exactly an opposite effect.
 
 [Illustration: FIG. 42.]
 
-§ 2. The danger lies in "oscillations" being set up in the line of
+§ 2. The danger lies in "oscillations" being set up in the line of
 flight due to changes in the position of the centre of pressure. Hence
 the device of an elevator or horizontal tail for the purpose of
 damping out such oscillations.
 
-§ 3. But the aerofoil surface is not flat, owing to the increased
+§ 3. But the aerofoil surface is not flat, owing to the increased
 "lift" given by arched surfaces, and a much more complicated set of
 phenomena then takes place, the centre of pressure moving forward
 until a certain critical angle of incidence is reached, and after
@@ -2673,14 +2638,14 @@ pressure at varying angles, and especially to determine at what angle
 
 [Illustration: FIG. 43.]
 
-§ 4. Natural automatic stability (the only one possible so far as
+§ 4. Natural automatic stability (the only one possible so far as
 models are concerned) necessitates permanent or a permanently
 recurring coincidence (to coin a phrase) of the centre of gravity and
 the centre of pressure: the former is, of course, totally unaffected
 by the vagaries of the latter, any shifting of which produces a couple
 tending to destroy equilibrium.
 
-§ 5. As to the best form of camber (for full sized machine) possibly
+§ 5. As to the best form of camber (for full sized machine) possibly
 more is known on this point than on any other in the whole of
 aeronautics.
 
@@ -2694,13 +2659,13 @@ surfaces for models.
 
 [Illustration: FIG. 45.--ANOTHER EFFICIENT FORM.
 
-Ratio of B D to A C 1 to 17. AD rather more than ¼ of A C.]
+Ratio of B D to A C 1 to 17. AD rather more than ¼ of A C.]
 
 The next question, after having decided the question of aerocurve, or
 curvature of the planes, is at what angle to set the cambered surface
 to the line of flight. This brings us to the question of the--
 
-§ 6. =Dipping Front Edge.=--The leading or front edge is not
+§ 6. =Dipping Front Edge.=--The leading or front edge is not
 tangential to the line of flight, but to a relative upward wind. It is
 what is known as the "cyclic up-current," which exists in the
 neighbourhood of the entering edge. Now, as we have stated before, it
@@ -2727,21 +2692,21 @@ angle--is one best determined by experiment on the model in question.
 
 But _if at any angle, that angle either way should be a very small
 one_. If you wish to be very scientific you can give the underside of
-the front edge a negative angle of 5° to 7° for about one-eighth of
+the front edge a negative angle of 5° to 7° for about one-eighth of
 the total length of the section, after that a positive angle,
 gradually increasing until you finally finish up at the trailing edge
-with one of 4°. Also, the form of cambered surface should be a
+with one of 4°. Also, the form of cambered surface should be a
 paraboloid--not arc or arc of circles. The writer does not recommend
 such an angle, but prefers an attitude similar to that adopted in the
 Wright machine, as in Fig. 47.
 
-§ 7. Apart from the attitude of the aerocurve: _the greatest depth of
+§ 7. Apart from the attitude of the aerocurve: _the greatest depth of
 the camber should be at one-third of the length of the section from
 the front edge, and the total depth measured from the top surface to
 the chord at this point should not be more than one-seventeenth of the
 length of section_.
 
-§ 8. It is the greatest mistake in model aeroplanes to make the camber
+§ 8. It is the greatest mistake in model aeroplanes to make the camber
 otherwise than very slight (in the case of surfaced aerofoils the
 resistance is much increased), and aerofoils with anything but a _very
 slight_ arch are liable to be very unstable, for the aerocurve has
@@ -2754,10 +2719,10 @@ chord to the line of flight, its altitude, etc., are not the only
 important matters one must consider in the case of the aerofoil, we
 must also consider--
 
-§ 9. Its =Aspect Ratio=, i.e. the ratio of the span (length) of the
+§ 9. Its =Aspect Ratio=, i.e. the ratio of the span (length) of the
 aerofoil to the chord--usually expressed by span/chord. In the Farman
-machine this ratio is 5·4; Blériot, 4·3; Short, 6 to 7·5; Roe
-triplane, 7·5; a Clark flyer, 9·6.
+machine this ratio is 5·4; Blériot, 4·3; Short, 6 to 7·5; Roe
+triplane, 7·5; a Clark flyer, 9·6.
 
 Now the higher the aspect ratio the greater should be the efficiency.
 Air escaping by the sides represents loss, and the length of the sides
@@ -2779,12 +2744,12 @@ aspect ratio than a monoplane, and a triplane (see above) a higher
 ratio still.
 
 It will be noticed the Clark model given has a considerably higher
-aspect ratio, viz. 9·6. And even this can be exceeded.
+aspect ratio, viz. 9·6. And even this can be exceeded.
 
 _An aspect ratio of_ 10:1 _or even_ 12:1 _should be used if
 possible._[37]
 
-§ 10. =Constant or Varying Camber.=--Some model makers vary the camber
+§ 10. =Constant or Varying Camber.=--Some model makers vary the camber
 of their aerofoils, making them almost flat in some parts, with
 considerable camber in others; the tendency in some cases being to
 flatten the central portions of the aerofoil, and with increasing
@@ -2799,7 +2764,7 @@ of more or less elastic materials, assumes a natural camber, more or
 less, when driven horizontally through the air. Reference has been
 made to a reversal of the--
 
-§ 11. =Centre of Pressure on Arched Surfaces.=--Wilbur Wright in his
+§ 11. =Centre of Pressure on Arched Surfaces.=--Wilbur Wright in his
 explanation of this reversal says: "This phenomenon is due to the fact
 that at small angles the wind strikes the forward part of the aerofoil
 surface on the upper side instead of the lower, and thus this part
@@ -2807,7 +2772,7 @@ altogether ceases to lift, instead of being the most effective part of
 all." The whole question hangs on the value of the critical angle at
 which this reversal takes place; some experiments made by Mr. M.B.
 Sellers in 1906 (published in "Flight," May 14, 1910) place this angle
-between 16° and 20°. This angle is much above that used in model
+between 16° and 20°. This angle is much above that used in model
 aeroplanes, as well as in actual full-sized machines. But the
 equilibrium of the model might be upset, not by a change of attitude
 on its part, but on that of the wind, or both combined. By giving (as
@@ -2831,14 +2796,14 @@ CHAPTER VII.
 MATERIALS FOR AEROPLANE CONSTRUCTION.
 
 
-§ 1. The choice of materials for model aeroplane construction is more
+§ 1. The choice of materials for model aeroplane construction is more
 or less limited, if the best results are to be obtained. The lightness
 absolutely essential to success necessitates--in addition to skilful
 building and best disposition of the materials--materials of no undue
 weight relative to their strength, of great elasticity, and especially
 of great resilience (capacity to absorb shock without injury).
 
-§ 2. =Bamboo.=--Bamboo has per pound weight a greater resilience than
+§ 2. =Bamboo.=--Bamboo has per pound weight a greater resilience than
 any other suitable substance (silk and rubber are obviously useless as
 parts of the _framework_ of an aeroplane). On full-sized machines the
 difficulty of making sufficiently strong connections and a liability
@@ -2869,11 +2834,11 @@ to thin T strips of light metal, such as aluminium. Thin thread, or
 silk, is preferable to very thin wire for lashing purpose, as the
 latter "gives" too much, and cuts into the fibres of the wood as well.
 
-§ 3. =Ash=, =Spruce=, =Whitewood= are woods that are also much used by
+§ 3. =Ash=, =Spruce=, =Whitewood= are woods that are also much used by
 model makers. Many prefer the last named owing to its uniform freedom
 from knots and ease with which it can be worked. It is stated 15 per
 cent. additional strength can be imparted by using hot size and
-allowing it to soak into the wood at an increase only of 3·7 per cent.
+allowing it to soak into the wood at an increase only of 3·7 per cent.
 of weight. It is less than half the weight of bamboo, but has a
 transverse rupture of only 7,900 lb. per sq. in. compared to 22,500 in
 the case of bamboo tubing (thickness one-eighth diameter) and a
@@ -2889,7 +2854,7 @@ seasoning, and should be so treated when in the structure that it
 cannot absorb moisture.
 
 If we take the resilience of ash as 1, then (according to Haswell)
-relative resilience of beech is 0·86, and spruce 0·64.
+relative resilience of beech is 0·86, and spruce 0·64.
 
 The strongest of woods has a weight when well seasoned of about 40 lb.
 per cub. ft. and a tenacity of about 10,000 lb. per sq. in.
@@ -2898,7 +2863,7 @@ per cub. ft. and a tenacity of about 10,000 lb. per sq. in.
 
 A very effective French Toy Monoplane.]
 
-§ 4. =Steel.=--Ash has a transverse rupture of 14,300 lb. per sq. in.,
+§ 4. =Steel.=--Ash has a transverse rupture of 14,300 lb. per sq. in.,
 steel tubing (thickness = 1/30 its diameter) 100,000 lb. per sq. in.
 Ash weighs per cub. ft. 47 lb., steel 490. Steel being more than ten
 times as heavy as ash--but a transverse rupture stress seven times as
@@ -2909,7 +2874,7 @@ transverse rupture of 22,500 lb. per sq. in., and a weight of 55 lb.
 per cub. ft.
 
 Steel then is nine times as heavy as bamboo--and has a transverse
-rupture stress 4·4 times as great. In comparing these three substances
+rupture stress 4·4 times as great. In comparing these three substances
 it must be carefully borne in mind that lightness and strength are not
 the only things that have to be provided for in model aeroplane
 building; there is the question of _resistance_--we must offer as
@@ -2927,23 +2892,23 @@ accurate thickness throughout, the price being about 18s. a lb.
 Although suitable steel tubing is not yet procurable under ordinary
 circumstances, umbrella steel is.
 
-§ 5. =Umbrella Section Steel= is a section 5/32 in. by 1/8 in. deep, 6
-ft. long weighing 2·1 oz., and a section 3/32 in. across the base by
-1/8 in. deep, 6 ft. long weighing 1·95 oz.
+§ 5. =Umbrella Section Steel= is a section 5/32 in. by 1/8 in. deep, 6
+ft. long weighing 2·1 oz., and a section 3/32 in. across the base by
+1/8 in. deep, 6 ft. long weighing 1·95 oz.
 
 It is often stated that umbrella ribs are too heavy--but this entirely
 depends on the length you make use of, in lengths of 25 in. for small
 aerofoils made from such lengths it is so; but in lengths of 48 in.
 (two such lengths joined together) the writer has used it with great
 success; often making use of it now in his larger models; the
-particular size used by him weighs 13½ grammes, to a length of 25
+particular size used by him weighs 13½ grammes, to a length of 25
 in. He has never had one of these aerofoils break or become
 kinked--thin piano wire is used to stay them and also for spars when
 employed--the front and ends of the aerofoil are of umbrella steel,
 the trailing edge of steel wire, comparatively thin, kept taut by
 steel wire stays.
 
-§ 6. =Steel Wire.=--Tensile strength about 300,000 lb. per sq. in. For
+§ 6. =Steel Wire.=--Tensile strength about 300,000 lb. per sq. in. For
 the aerofoil framework of small models and for all purposes of
 staying, or where a very strong and light tension is required, this
 substance is invaluable. Also for framework of light fabric covered
@@ -2951,11 +2916,11 @@ propellers as well as for skids and shock absorber--also for hooks to
 hold the rubber motor strands, etc. No model is complete without it in
 some form or another.
 
-§ 7. =Silk.=--This again is a _sine qua non_. Silk is the strongest of
+§ 7. =Silk.=--This again is a _sine qua non_. Silk is the strongest of
 all organic substances for certain parts of aeroplane construction. It
-has, in its best form, a specific gravity of 1·3, and is three times
+has, in its best form, a specific gravity of 1·3, and is three times
 as strong as linen, and twice as strong in the thread as hemp. Its
-finest fibres have a section of from 0·0010 to 0·0015 in diameter. It
+finest fibres have a section of from 0·0010 to 0·0015 in diameter. It
 will sustain about 35,000 lb. per sq. in. of its cross section; and
 its suspended fibre should carry about 150,000 ft. of its own
 material. This is six times the same figure for aluminium, and equals
@@ -2968,7 +2933,7 @@ weighs 62 lb. per cub. ft., steel has, we have seen, 490 lb., thus
 paying due regard to this and to its very high tensile strength it is
 superior to even steel wire stays.
 
-§ 8. =Aluminium and Magnalium.=--Two substances about which a great
+§ 8. =Aluminium and Magnalium.=--Two substances about which a great
 deal has been heard in connection with model aeroplaning; but the
 writer does not recommend their use save in the case of fittings for
 scale models, not actual flyers, unless especially light ones meant
@@ -2981,7 +2946,7 @@ also less in section, resistance to air travel is again less as in the
 case of wood. In fact, steel scores all round. Weight of magnalium :
 weight of aluminium :: 8:9.
 
-§ 9. =Alloys.=--During recent years scores, hundreds, possibly
+§ 9. =Alloys.=--During recent years scores, hundreds, possibly
 thousands of different alloys have been tried and experimented on, but
 steel still easily holds its own. It is no use a substance being
 lighter than another volume for volume, it must be _lighter and
@@ -2989,7 +2954,7 @@ stronger weight for weight_, to be superior for aeronautical purpose,
 and if the difference be but slight, question of _bulk_ may decide it
 as offering _less resistance_.
 
-§ 10. =Sheet Ebonite.=--This substance is sometimes useful for
+§ 10. =Sheet Ebonite.=--This substance is sometimes useful for
 experiments with small propellers, for it can be bent and moulded in
 hot water, and when cold sets and keeps its shape. _Vulcanized fibre_
 can be used for same purpose. _Sheet celluloid_ can be used in the
@@ -3032,7 +2997,7 @@ CHAPTER VIII.
 HINTS ON THE BUILDING OF MODEL AEROPLANES.
 
 
-§ 1. The chief difficulty in the designing and building of model
+§ 1. The chief difficulty in the designing and building of model
 aeroplanes is to successfully combat the conflicting interests
 contained therein. Weight gives stability, but requires extra
 supporting surface or a higher speed, i.e. more power, i.e. more
@@ -3051,25 +3016,25 @@ require special attention; but there are certain general rules and
 features which if not adhered to and carefully carried out, or as
 carefully avoided, will cause endless trouble and failure.
 
-§ 2. In constructing a model aeroplane, or, indeed, any piece of
+§ 2. In constructing a model aeroplane, or, indeed, any piece of
 aerial apparatus, it is very important not to interrupt the continuity
 of any rib, tube, spar, etc., by drilling holes or making too thinned
 down holding places; if such be done, additional strength by binding
 (with thread, not wire), or by slipping a small piece of slightly
 larger tube over the other, must be imparted to the apparatus.
 
-§ 3. Begin by making a simple monoplane, and afterwards as you gain
+§ 3. Begin by making a simple monoplane, and afterwards as you gain
 skill and experience proceed to construct more elaborate and
 scientific models.
 
-§ 4. Learn to solder--if you do not know how to--it is absolutely
+§ 4. Learn to solder--if you do not know how to--it is absolutely
 essential.
 
-§ 5. Do not construct models (intended for actual flight) with a
+§ 5. Do not construct models (intended for actual flight) with a
 tractor screw-main plane in front and tail (behind). Avoid them as you
 would the plague. Allusion has already been made in the Introduction
 to the difficulty of getting the centre of gravity sufficiently
-forward in the case of Blériot models; again with the main aerofoil in
+forward in the case of Blériot models; again with the main aerofoil in
 front, it is this aerofoil and not the balancing elevator, or tail,
 that _first_ encounters the upsetting gust, and the effect of such a
 gust acting first on the larger surface is often more than the
@@ -3089,26 +3054,26 @@ air, caused by the resistance, the model generally running in such
 air--the slip of the screw is reduced to a corresponding degree--may
 even vanish altogether, and what is known as negative slip occur.
 
-§ 6. Wooden or metal aerofoils are more efficient than fabric covered
+§ 6. Wooden or metal aerofoils are more efficient than fabric covered
 ones. But they are only satisfactory in the smaller sizes, owing, for
 one thing, to the smash with which they come to the ground. This being
 due to the high speed necessary to sustain their weight. For
 larger-sized models fabric covered aerofoils should be used.
 
-§ 7. As to the shape of such, only three need be considered--the (_a_)
+§ 7. As to the shape of such, only three need be considered--the (_a_)
 rectangular, (_b_) the elongated ellipse, (_c_) the chamfered rear
 edge.
 
 [Illustration: FIG. 48.--(_a_), (_b_), (_c_).]
 
-§ 8. The stretching of the fabric on the aerofoil framework requires
+§ 8. The stretching of the fabric on the aerofoil framework requires
 considerable care, especially when using silk. It is quite possible,
 even in models of 3 ft. to 4 ft. spread, to do without "ribs," and
 still obtain a fairly correct aerocurve, if the material be stretched
 on in a certain way. It consists in getting a correct longitudinal and
 transverse tension. We will illustrate it by a simple case. Take a
 piece of thickish steel pianoforte wire, say, 18 in. long, bend it
-round into a circle, allowing ½ in. to 1 in. to overlap, tin and
+round into a circle, allowing ½ in. to 1 in. to overlap, tin and
 solder, bind this with soft very thin iron wire, and again solder
 (always use as little solder as possible). Now stitch on to this a
 piece of nainsook or silk, deforming the circle as you do so until it
@@ -3128,7 +3093,7 @@ rubber cord, a very useful method of fastening, since it acts as an
 excellent shock absorber, and "gives" when required, and yet
 possesses quite sufficient practical rigidity.
 
-§ 9. Flexible joints are an advantage in a biplane; these can be made
+§ 9. Flexible joints are an advantage in a biplane; these can be made
 by fixing wire hooks and eyes to the ends of the "struts," and holding
 them in position by binding with silk or thread. Rigidity is obtained
 by use of steel wire stays or thin silk cord.
@@ -3137,11 +3102,11 @@ by use of steel wire stays or thin silk cord.
 
 Showing the position of C. of G., or point of support.]
 
-§ 10. Owing to the extra weight and difficulties of construction on so
+§ 10. Owing to the extra weight and difficulties of construction on so
 small a scale it is not desirable to use "double surface" aerofoils
 except on large size power-driven models.
 
-§ 11. It is a good plan not to have the rod or tube carrying the
+§ 11. It is a good plan not to have the rod or tube carrying the
 rubber motor connected with the outrigger carrying the elevator,
 because the torque of the rubber tends to twist the carrying
 framework, and interferes with the proper and correct action of the
@@ -3155,12 +3120,12 @@ Shown without rubber or propellers. Designed and constructed by the
 writer. As a test it was fitted with two 14 in. propellers revolving
 in the _same_ direction, and made some excellent flights under these
 conditions, rolling slightly across the wind, but otherwise keeping
-quite steady. Total weight, 1½ lb.; length, 6 ft.; span of main
+quite steady. Total weight, 1½ lb.; length, 6 ft.; span of main
 aerofoil, 5 ft. Constructed of bamboo, cane, and steel wire. Front
 skids steel wire. Back skids cane. Aerofoil covering nainsook.]
 
 
-§ 12. Some builders place the rubber motor above the rod, or bow frame
+§ 12. Some builders place the rubber motor above the rod, or bow frame
 carrying the aerofoils, etc., the idea being that the pull of the
 rubber distorts the frame in such a manner as to "lift" the elevator,
 and so cause the machine to rise rapidly in the air. This it does; but
@@ -3174,7 +3139,7 @@ Fleming-Williams type. This machine flew well when provided with an
 abnormal amount of rubber, owing to the poor dynamic thrust given by
 the propellers.]
 
-§ 13. In the Clarke models with the small front plane, the centre of
+§ 13. In the Clarke models with the small front plane, the centre of
 pressure is slightly in front of the main plane.
 
 The balancing point of most models is generally slightly in front, or
@@ -3192,7 +3157,7 @@ piece. 8. Brass brazed fittings. 9. Ball-bearing thrust. 10. Flat
 aluminium "L" piece. (_The above illustrations taken (by permission)
 from Messrs. Gamage's catalogue on Model Aviation._)]
 
-§ 14. The elevator (or tail) should be of the non-lifting type--in
+§ 14. The elevator (or tail) should be of the non-lifting type--in
 other words, the entire weight should be carried by the main aerofoil
 or aerofoils; the elevator being used simply as a balancer.[39] If the
 machine be so constructed that part of the weight be carried by the
@@ -3209,7 +3174,7 @@ thrust, and stay.
 (_The above illustrations taken (by permission) from Messrs. Gamage's
 catalogue on Model Aviation._)]
 
-§ 15. In actual flying models "skids" should be used and not "wheels";
+§ 15. In actual flying models "skids" should be used and not "wheels";
 the latter to be of any real use must be of large diameter, and the
 weight is prohibitive. Skids can be constructed of cane, imitation
 whalebone, steel watch or clock-spring, steel pianoforte wire. Steel
@@ -3217,7 +3182,7 @@ mainsprings are better than imitation whalebone, but steel pianoforte
 wire best of all. For larger sized models bamboo is also suitable, as
 also ash or strong cane.
 
-§ 16. Apart from or in conjunction with skids we have what are termed
+§ 16. Apart from or in conjunction with skids we have what are termed
 "shock absorbers" to lessen the shock on landing--the same substances
 can be used--steel wire in the form of a loop is very effectual;
 whalebone and steel springs have a knack of snapping. These shock
@@ -3226,7 +3191,7 @@ and part front landing as well as a direct front landing. For this
 purpose they should be lashed to the main frame by thin indiarubber
 cord.
 
-§ 17. In the case of a biplane model the "gap" must not be less than
+§ 17. In the case of a biplane model the "gap" must not be less than
 the "chord"--preferably greater.
 
 In a double monoplane (of the Langley type) there is considerable
@@ -3242,15 +3207,15 @@ pitch be very large; with a well designed propeller this is not by any
 means essential. If the propeller revolve clockwise, place it towards
 the right hand of the machine, and vice versa.
 
-§ 18. In designing a model to fly the longest possible distance the
+§ 18. In designing a model to fly the longest possible distance the
 monoplane type should be chosen, and when desiring to build one that
 shall remain the longest time in the air the biplane or triplane type
 should be adopted.[40] For the longest possible flight twin propellers
 revolving in opposite directions[41] are essential. To take a concrete
 case--one of the writer's models weighed complete with a single
-propeller 8½ oz. It was then altered and fitted with two propellers
+propeller 8½ oz. It was then altered and fitted with two propellers
 (same diameter and weight); this complete with double rubber weighed
-10¼ oz. The advantage double the power. Weight increased only 20
+10¼ oz. The advantage double the power. Weight increased only 20
 per cent., resistance about 10 per cent., total 30 per cent. Gain 70
 per cent. Or if the method of gearing advocated (see Geared Motors) be
 adopted then we shall have four bunches of rubber instead of two, and
@@ -3258,7 +3223,7 @@ can thereby obtain so many more turns.[42] The length of the strands
 should be such as to render possible at least a thousand turns.
 
 The propellers should be of large diameter and pitch (not less than
-35° at the tips), of curved shape, as advocated in § 22 ch. v.; the
+35° at the tips), of curved shape, as advocated in § 22 ch. v.; the
 aerofoil surface of as high an aspect ratio as possible, and but
 slight camber if any; this is a very difficult question, the question
 of camber, and the writer feels bound to admit he has obtained as long
@@ -3275,7 +3240,7 @@ straight course, combined with a rudder and universally jointed
 elevator.
 
 The manner of winding up the propellers has already been referred to
-(_see_ chap. iii., § 9). A winder is essential.
+(_see_ chap. iii., § 9). A winder is essential.
 
 Another form of aerofoil is one of wood (as in Clarke's flyers) or
 metal, such a machine relying more on the swiftness of its flight than
@@ -3299,7 +3264,7 @@ from 5 oz. to 10 oz. is likely to prove the most suitable. It is not
 too large to experiment with without difficulty, nor is it so small as
 to require the skill of a jeweller almost to build the necessary
 mechanism. The propeller speed has already been discussed (_see_ ch.
-v., § 15). The model will, of course, be flown with the wind. The
+v., § 15). The model will, of course, be flown with the wind. The
 _total_ length of the model should be at least twice the span of the
 main aerofoil.
 
@@ -3332,7 +3297,7 @@ CHAPTER IX.
 THE STEERING OF THE MODEL.
 
 
-§ 1. Of all the various sections of model aeroplaning that which is
+§ 1. Of all the various sections of model aeroplaning that which is
 the least satisfactory is the above.
 
 The torque of the propeller naturally exerts a twisting or tilting
@@ -3342,7 +3307,7 @@ depending on whether the pitch of the screw be a right or left handed
 one. There are various devices by which the torque may be
 (approximately) got rid of.
 
-§ 2. In the case of a monoplane, by not placing the rod carrying the
+§ 2. In the case of a monoplane, by not placing the rod carrying the
 rubber motor in the exact centre of the main aerofoil, but slightly to
 one side, the exact position to be determined by experiment.
 
@@ -3351,7 +3316,7 @@ centre, but placing the bracket carrying the bearing in which the
 propeller shaft runs at right angles horizontally to the rod to obtain
 the same effect.
 
-§ 3. The most obvious solution of the problem is to use _two_ equal
+§ 3. The most obvious solution of the problem is to use _two_ equal
 propellers (as in the Wright biplane) of equal and opposite pitch,
 driven by two rubber motors of equal strength.
 
@@ -3386,7 +3351,7 @@ solution at all.[45] The torque of the propeller and consequent
 tilting of the aeroplane is not the only cause at work diverting the
 machine from its course.
 
-§ 4. As it progresses through the air it is constantly meeting air
+§ 4. As it progresses through the air it is constantly meeting air
 currents of varying velocity and direction, all tending to make the
 model deviate more or less from its course; the best way, in fact, the
 only way, to successfully overcome such is by means of _speed_, by
@@ -3395,7 +3360,7 @@ miles an hour, as is usual in built up fabric-covered aerofoils, but a
 velocity of twenty to thirty miles an hour, attainable only in models
 (petrol or steam driven) or by means of wooden or metal aerofoils.
 
-§ 5. Amongst devices used for horizontal steering are vertical "FINS."
+§ 5. Amongst devices used for horizontal steering are vertical "FINS."
 These should be placed in the rear above the centre of gravity. They
 should not be large, and can be made of fabric tightly stretched over
 a wire frame, or of a piece of sheet magnalium or aluminium, turning
@@ -3405,17 +3370,17 @@ and the size of a boat, but allow for the difference of medium. The
 frame carrying the pivot and fin should be made to slide along the rod
 or backbone of the model in order to find the most efficient position.
 
-§ 6. Steering may also be attempted by means of little balancing tips,
+§ 6. Steering may also be attempted by means of little balancing tips,
 or ailerons, fixed to or near the main aerofoil, and pivoted (either
 centrally or otherwise) in such a manner that they can be rotated one
 in one direction (tilted) and the other in the other (dipped), so as
 to raise one side and depress the other.
 
-§ 7. The model can also be steered by giving it a cant to one side by
+§ 7. The model can also be steered by giving it a cant to one side by
 weighting the tip of the aerofoil on that side on which it is desired
 it should turn, but this method is both clumsy and "weighty."
 
-§ 8. Another way is by means of the elevator; and this method, since
+§ 8. Another way is by means of the elevator; and this method, since
 it entails no additional surfaces entailing extra resistance and
 weight, is perhaps the most satisfactory of all.
 
@@ -3423,14 +3388,14 @@ It is necessary that the elevator be mounted on some kind of universal
 joint, in order that it may not only be "tipped" or "dipped," but also
 canted sideways for horizontal steering.
 
-§ 9. A vertical fin in the rear, or something in the nature of a
+§ 9. A vertical fin in the rear, or something in the nature of a
 "keel," i.e. a vertical fin running down the backbone of the machine,
 greatly assists this movement.
 
-If the model be of the tractor screw and tail (Blériot) type, then the
+If the model be of the tractor screw and tail (Blériot) type, then the
 above remarks _re_ elevator apply _mutatis mutandis_ to the tail.
 
-§ 10. It is of the most vital importance that the propeller torque
+§ 10. It is of the most vital importance that the propeller torque
 should be, as far as possible, correctly balanced. This can be tested
 by balancing the model transversely on a knife edge, winding up the
 propeller, and allowing it to run down, and adjusting matters until
@@ -3467,10 +3432,10 @@ CHAPTER X.
 THE LAUNCHING OF THE MODEL.
 
 
-§ 1. Generally speaking, the model should be launched into the air
+§ 1. Generally speaking, the model should be launched into the air
 _against the wind_.
 
-§ 2. It should (theoretically) be launched into the air with a
+§ 2. It should (theoretically) be launched into the air with a
 velocity equal to that with which it flies. If it launch with a
 velocity in excess of that it becomes at once unstable and has to
 "settle down" before assuming its normal line of flight. If the
@@ -3483,7 +3448,7 @@ such as the well-known Clarke flyers, require to be practically
 Other fabric-covered models capable of sustentation at a velocity of 8
 to 10 miles an hour, may just be "released."
 
-§ 3. Light "featherweight" models designed for long flights when
+§ 3. Light "featherweight" models designed for long flights when
 travelling with the wind should be launched with it. They will not
 advance into it--if there be anything of a breeze--but, if well
 designed, just "hover," finally sinking to earth on an even keel. Many
@@ -3491,12 +3456,12 @@ ingenious pieces of apparatus have been designed to mechanically
 launch the model into the air. Fig. 50 is an illustration of a very
 simple but effective one.
 
-§ 4. For large size power-driven models, unless provided with a
+§ 4. For large size power-driven models, unless provided with a
 chassis and wheels to enable them to run along and rise from the
 ground under their own power, the launching is a problem of
 considerable difficulty.
 
-§ 5. In the case of rubber-driven models desired to run along and rise
+§ 5. In the case of rubber-driven models desired to run along and rise
 from the ground under their own power, this rising must be
 accomplished quickly and in a short space. A model requiring a 50 ft.
 run is useless, as the motor would be practically run out by that
@@ -3508,7 +3473,7 @@ words, its velocity of sustentation must be a low one.
 
 (_Reproduced by permission from the "Model Engineer."_)]
 
-§ 6. It will not do to tip up the elevator to a large angle to make it
+§ 6. It will not do to tip up the elevator to a large angle to make it
 rise quickly, because when once off the ground the angle of the
 elevator is wrong for actual flight and the model will probably turn a
 somersault and land on its back. I have often seen this happen. If the
@@ -3521,16 +3486,16 @@ device which shall maintain the elevator at a comparatively large
 angle while the model is on the ground, but allowing of this angle
 being reduced when free flight is commenced.
 
-§ 7. The propeller most suitable to "get the machine off the ground"
+§ 7. The propeller most suitable to "get the machine off the ground"
 is one giving considerable statical thrust. A small propeller of fine
 pitch quickly starts a machine, but is not, of course, so efficient
 when the model is in actual flight. A rubber motor is not at all well
 adapted for the purpose just discussed.
 
-§ 8. Professor Kress uses a polished plank (down which the models slip
+§ 8. Professor Kress uses a polished plank (down which the models slip
 on cane skids) to launch his models.
 
-§ 9. When launching a twin-screw model the model should be held by
+§ 9. When launching a twin-screw model the model should be held by
 each propeller, or to speak more correctly, the two brackets holding
 the bearings in which the propeller shafts run should be held one in
 each hand in such a way, of course, as to prevent the propellers from
@@ -3541,12 +3506,12 @@ position is attained, and boldly push the machine into the air (moving
 forward if necessary) and release both brackets and screws
 simultaneously.[46]
 
-§ 10. In launching a model some prefer to allow the propellers to
+§ 10. In launching a model some prefer to allow the propellers to
 revolve for a few moments (a second, say) _before_ actually launching,
 contending that this gives a steadier initial flight. This is
 undoubtedly the case, see note on page 111.
 
-§ 11. In any case, unless trying for a height prize, do not point the
+§ 11. In any case, unless trying for a height prize, do not point the
 nose of the machine right up into the air with the idea that you will
 thereby obtain a better flight.
 
@@ -3567,7 +3532,7 @@ hand--is to hold the machine with both hands above the head, the right
 hand grasping it ready to launch it, and the left holding the two
 propellers. Release the propellers and allow them a brief interval
 (about half a second) to start. Then launch boldly into the air. The
-writer has easily launched 1½ lb. models by this means, even in a
+writer has easily launched 1½ lb. models by this means, even in a
 high wind. Never launch a model by one hand only.
 
 
@@ -3578,19 +3543,19 @@ CHAPTER XI.
 HELICOPTER MODELS.
 
 
-§ 1. There is no difficulty whatever about making successful model
+§ 1. There is no difficulty whatever about making successful model
 helicopters, whatever there may be about full-sized machines.
 
-§ 2. The earliest flying models were helicopters. As early as 1796 Sir
+§ 2. The earliest flying models were helicopters. As early as 1796 Sir
 George Cayley constructed a perfectly successful helicopter model (see
 ch. iii.); it should be noticed the screws were superimposed and
 rotated in opposite directions.
 
-§ 3. In 1842 a Mr. Phillips constructed a successful power-driven
+§ 3. In 1842 a Mr. Phillips constructed a successful power-driven
 model helicopter. The model was made entirely of metal, and when
 complete and charged weighed 2 lb. It consisted of a boiler or steam
 generator and four fans supported between eight arms. The fans had an
-inclination to the horizon of 20°, and through the arms the steam
+inclination to the horizon of 20°, and through the arms the steam
 rushed on the principle of Hero's engines (Barker's Mill Principle
 probably). By the escape of steam from the arms the fans were caused
 to revolve with immense energy, so much so that the model rose to an
@@ -3606,7 +3571,7 @@ actually flew.
 
 The helicopter is but a particular phase of the aeroplane.
 
-§ 4. The simplest form of helicopter is that in which the torque of
+§ 4. The simplest form of helicopter is that in which the torque of
 the propeller is resisted by a vertical loose fabric plane, so
 designed as itself to form a propeller, rotating in the opposite
 direction. These little toys can be bought at any good toy shop from
@@ -3617,7 +3582,7 @@ horizontally rotating propellers for lifting purposes.
 
 [Illustration: FIG. 51.--INCORRECT WAY OF ARRANGING SCREWS.]
 
-§ 5. There is one essential point that must be carefully attended to,
+§ 5. There is one essential point that must be carefully attended to,
 and that is, _that the horizontal propulsive thrust must be in the
 same plane as the vertical lift_, or the only effect will be to cause
 our model to turn somersaults. I speak from experience.
@@ -3627,12 +3592,12 @@ direction their "lifting" powers will be materially increased, as they
 will (like an ordinary aeroplane) be advancing on to fresh undisturbed
 air.
 
-§ 6. I have not for ordinary purposes advocated very light weight wire
+§ 6. I have not for ordinary purposes advocated very light weight wire
 framework fabric-covered screws, but in a case like this where the
 thrust from the propeller has to be more than the total weight of the
 machine, these might possibly be used with advantage.
 
-§ 7. Instead of using two long vertical rods as well as one long
+§ 7. Instead of using two long vertical rods as well as one long
 horizontal one for the rubber strands, we might dispense with the two
 vertical ones altogether and use light gearing to turn the torque
 action through a right angle for the lifting screws, and use three
@@ -3642,7 +3607,7 @@ considerable saving of weight.
 
 [Illustration: FIG. 52.--CORRECT MANNER. A, B, C = Screws.]
 
-§ 8. The model would require something in the nature of a vertical fin
+§ 8. The model would require something in the nature of a vertical fin
 or keel to give the sense of direction. Four propellers, two for
 "lift" and two for "drift," would undoubtedly be a better
 arrangement.
@@ -3754,7 +3719,7 @@ CHAPTER XIII.
 MODEL FLYING COMPETITIONS.
 
 
-§ 1. From time to time flying competitions are arranged for model
+§ 1. From time to time flying competitions are arranged for model
 aeroplanes. Sometimes these competitions are entirely open, but more
 generally they are arranged by local clubs with both closed and open
 events.
@@ -3793,7 +3758,7 @@ And one for the best all-round model.
 
 The models are divided into classes:--
 
-§ 2. _Aero Models Association's Classification, etc._
+§ 2. _Aero Models Association's Classification, etc._
 
     A.   Models of 1 sq. ft. surface and under.
     B.     "       2 sq. ft.     "       "
@@ -3847,7 +3812,7 @@ point.
 
 The models are practically always launched by hand.
 
-§ 3. Those who desire to win prizes at such competitions would do well
+§ 3. Those who desire to win prizes at such competitions would do well
 to keep the following points well in mind.
 
 1. The distance is always measured in a straight line. It is
@@ -3914,7 +3879,7 @@ weight, more especially if your model be a biplane, or the number of
 flights may be restricted to the number "one."
 
 12. Since the best "gliding" angle and "flying" angle are not the
-same, being, say, 7° in the former case and 1°-3°, say, in the latter,
+same, being, say, 7° in the former case and 1°-3°, say, in the latter,
 an adjustable angle might in some cases be advantageous.
 
 13. Never turn up at a competition with a model only just finished and
@@ -3958,48 +3923,48 @@ model.
 
 CHAPTER XIV.
 
-USEFUL NOTES, TABLES, FORMULÆ, ETC.
+USEFUL NOTES, TABLES, FORMULÆ, ETC.
 
 
-§ 1. COMPARATIVE VELOCITIES.
+§ 1. COMPARATIVE VELOCITIES.
 
     Miles per hr.    Feet per sec.     Metres per sec.
-         10       =     14·7        =      4·470
-         15       =     22          =      6·705
-         20       =     29·4        =      8·940
-         25       =     36·7        =     11·176
-         30       =     44          =     13·411
-         35       =     51·3        =     15·646
+         10       =     14·7        =      4·470
+         15       =     22          =      6·705
+         20       =     29·4        =      8·940
+         25       =     36·7        =     11·176
+         30       =     44          =     13·411
+         35       =     51·3        =     15·646
 
-§ 2. A metre = 39·37079 inches.
+§ 2. A metre = 39·37079 inches.
 
     _In order to convert_:--
-               Metres into inches multiply by 39·37
-                     "     feet        "       3·28
-                     "     yards       "       1·09
-                     "     miles       "       0·0006214
-    Miles per hour into ft. per min. multiply by 88·0
-         "    min.      "       sec.      "      88·0
-         "    hr. into kilometres per hr. "       1·6093
-         "       "     metres per sec.    "       0·44702
-         Pounds into grammes multiply by 453·593
-             "       kilogrammes   "       0·4536
-
-§ 8. Total surface of a cylinder = circumference of base × height + 2
+               Metres into inches multiply by 39·37
+                     "     feet        "       3·28
+                     "     yards       "       1·09
+                     "     miles       "       0·0006214
+    Miles per hour into ft. per min. multiply by 88·0
+         "    min.      "       sec.      "      88·0
+         "    hr. into kilometres per hr. "       1·6093
+         "       "     metres per sec.    "       0·44702
+         Pounds into grammes multiply by 453·593
+             "       kilogrammes   "       0·4536
+
+§ 8. Total surface of a cylinder = circumference of base × height + 2
 area of base.
 
-Area of a circle = square of diameter × 0·7854.
+Area of a circle = square of diameter × 0·7854.
 
-Area of a circle = square of rad. × 3·14159.
+Area of a circle = square of rad. × 3·14159.
 
-Area of an ellipse = product of axes × 0·7854.
+Area of an ellipse = product of axes × 0·7854.
 
-Circumference of a circle = diameter × 3·14159.
+Circumference of a circle = diameter × 3·14159.
 
-Solidity of a cylinder = height × area of base.
+Solidity of a cylinder = height × area of base.
 
-Area of a circular ring = sum of diameters × difference of diameters ×
-0·7854.
+Area of a circular ring = sum of diameters × difference of diameters ×
+0·7854.
 
 For the area of a sector of a circle the rule is:--As 360 : number of
 degrees in the angle of the sector :: area of the sector : area of
@@ -4012,72 +3977,72 @@ triangle formed by the radii and the chord.
 The areas of corresponding figures are as the squares of corresponding
 lengths.
 
-  § 4.  1 mile     =   1·609 kilometres.
+  § 4.  1 mile     =   1·609 kilometres.
         1 kilometre   =   1093 yards.
-        1 oz.         =   28·35 grammes.
-        1 lb.         =   453·59   "
-        1 lb.         =   0·453 kilogrammes.
-        28 lb.        =   12·7       "
-        112 lb.       =   50·8       "
+        1 oz.         =   28·35 grammes.
+        1 lb.         =   453·59   "
+        1 lb.         =   0·453 kilogrammes.
+        28 lb.        =   12·7       "
+        112 lb.       =   50·8       "
         2240 lb.      =   1016       "
-        1 kilogram    =   2·2046 lb.
-        1 gram        =   0·0022 lb.
+        1 kilogram    =   2·2046 lb.
+        1 gram        =   0·0022 lb.
         1 sq. in.     =   645 sq. millimetres.
-        1 sq. ft.     =   0·0929 sq. metres.
-        1 sq. yard    =   0·836      "
-        1 sq. metre   =   10·764 sq. ft.
+        1 sq. ft.     =   0·0929 sq. metres.
+        1 sq. yard    =   0·836      "
+        1 sq. metre   =   10·764 sq. ft.
 
-§ 5. One atmosphere = 14·7 lb. per sq. in. = 2116 lb. per sq. ft. =
+§ 5. One atmosphere = 14·7 lb. per sq. in. = 2116 lb. per sq. ft. =
 760 millimetres of mercury.
 
-A column of water 2·3 ft. high corresponds to a pressure of 1 lb. per
+A column of water 2·3 ft. high corresponds to a pressure of 1 lb. per
 sq. in.
 
 1 H.P. = 33,000 ft.-lb. per min. = 746 watts.
 
-Volts × amperes = watts.
+Volts × amperes = watts.
 
-{pi} = 3·1416. _g_ = 32·182 ft. per sec. at London.
+{pi} = 3·1416. _g_ = 32·182 ft. per sec. at London.
 
-§ 6. TABLE OF EQUIVALENT INCLINATIONS.
+§ 6. TABLE OF EQUIVALENT INCLINATIONS.
 
      Rise.            Angle in Degs.
-    1 in 30               1·91
-    1 "  25               2·29
-    1 "  20               2·87
-    1 "  18               3·18
-    1 "  16               3·58
-    1 "  14               4·09
-    1 "  12               4·78
-    1 "  10               5·73
-    1 "   9               6·38
-    1 "   8               7·18
-    1 "   7               8·22
-    1 "   6               9·6
-    1 "   5              11·53
-    1 "   4              14·48
-    1 "   3              19·45
-    1 "   2              30·00
-    1 " {square root}2   45·00
-
-§ 7. TABLE OF SKIN FRICTION.
+    1 in 30               1·91
+    1 "  25               2·29
+    1 "  20               2·87
+    1 "  18               3·18
+    1 "  16               3·58
+    1 "  14               4·09
+    1 "  12               4·78
+    1 "  10               5·73
+    1 "   9               6·38
+    1 "   8               7·18
+    1 "   7               8·22
+    1 "   6               9·6
+    1 "   5              11·53
+    1 "   4              14·48
+    1 "   3              19·45
+    1 "   2              30·00
+    1 " {square root}2   45·00
+
+§ 7. TABLE OF SKIN FRICTION.
 
 Per sq. ft. for various speeds and surface lengths.
 
   -----------------+-------------+-------------+-------------+------------
   Velocity of Wind | 1 ft. Plane | 2 ft. Plane | 4 ft. Plane | 8 ft. Plane
   -----------------+-------------+-------------+-------------+------------
-         10        |   ·00112    |   ·00105    |   ·00101    |   ·000967
-         15        |   ·00237    |   ·00226    |   ·00215    |   ·00205
-         20        |   ·00402    |   ·00384    |   ·00365    |   ·00349
-         25        |   ·00606    |   ·00579    |   ·00551    |   ·00527
-         30        |   ·00850    |   ·00810    |   ·00772    |   ·00736
-         35        |   ·01130    |   ·0108     |   ·0103     |   ·0098
+         10        |   ·00112    |   ·00105    |   ·00101    |   ·000967
+         15        |   ·00237    |   ·00226    |   ·00215    |   ·00205
+         20        |   ·00402    |   ·00384    |   ·00365    |   ·00349
+         25        |   ·00606    |   ·00579    |   ·00551    |   ·00527
+         30        |   ·00850    |   ·00810    |   ·00772    |   ·00736
+         35        |   ·01130    |   ·0108     |   ·0103     |   ·0098
   -----------------+-------------+-------------+-------------+------------
 
 This table is based on Dr. Zahm's experiments and the equation
 
-    _f_ = 0·00000778_l_^{-0·07}_v_^{1·85}
+    _f_ = 0·00000778_l_^{-0·07}_v_^{1·85}
 
 Where _f_ = skin friction per sq. ft.; _l_ = length of surface; _v_ =
 velocity in feet per second.
@@ -4086,23 +4051,23 @@ In a biplane model the head resistance is probably from twelve to
 fourteen times the skin friction; in a racing monoplane from six to
 eight times.
 
-§ 8. TABLE I.--(METALS).
+§ 8. TABLE I.--(METALS).
 
   --------------+------------+-----------------+-------------
      Material   |  Specific  | Elasticity E[A] |  Tenacity
                 |  Gravity   |                 | per sq. in.
   --------------+------------+-----------------+-------------
-  Magnesium     |    1·74    |                 |   {22,000-
+  Magnesium     |    1·74    |                 |   {22,000-
                 |            |                 |   {32,000
-  Magnalium[B]  |  2·4-2·57  |      10·2       |
+  Magnalium[B]  |  2·4-2·57  |      10·2       |
   Aluminium- }  |            |                 |
-    Copper[C]}  |    2·82    |                 |    54,773
-  Aluminium     |    2·6     |      11·1       |    26,535
-  Iron          | 7·7 (about)|       29        |    54,000
-  Steel         | 7·8 (about)|       32        |   100,000
-  Brass         |  7·8-8·4   |       15        |    17,500
-  Copper        |    8·8     |       36        |    33,000
-  Mild Steel    |    7·8     |       30        |    60,000
+    Copper[C]}  |    2·82    |                 |    54,773
+  Aluminium     |    2·6     |      11·1       |    26,535
+  Iron          | 7·7 (about)|       29        |    54,000
+  Steel         | 7·8 (about)|       32        |   100,000
+  Brass         |  7·8-8·4   |       15        |    17,500
+  Copper        |    8·8     |       36        |    33,000
+  Mild Steel    |    7·8     |       30        |    60,000
                 |            |                 |
   --------------+------------+-----------------+-------------
   [A] E in millions of lb. per sq. in.
@@ -4113,43 +4078,43 @@ eight times.
       increase of density.
   --------------+------------+-----------------+-------------
 
-§ 9. TABLE II.--WIND PRESSURES.
+§ 9. TABLE II.--WIND PRESSURES.
 
-    _p_ = _kv²_.
+    _p_ = _kv²_.
 
-_k_ coefficient (mean value taken) ·003 (miles per hour) = 0·0016 ft.
+_k_ coefficient (mean value taken) ·003 (miles per hour) = 0·0016 ft.
 per second. _p_ = pressure in lb. per sq. ft. _v_ = velocity of wind.
 
     Miles per hr.   Ft. per sec.   Lb. per sq. ft.
-         10             14·7          0·300
-         12             17·6          0·432
-         14             20·5          0·588
-         16             23·5          0·768
-         18             26·4          0·972
-         20             29·35         1·200
-         25             36·7          1·875
-         30             43·9          2·700
-         35             51·3          3·675
-
-§ 10. Representing normal pressure on a plane surface by 1; pressure
-on a rod (round section) is 0·6; on a symmetrical elliptic cross
-section (axes 2:1) is 0·2 (approx.). Similar shape, but axes 6:1, and
-edges sharpened (_see_ ch. ii., § 5), is only 0·05, or 1/20, and for
-the body of minimum resistance (_see_ ch. ii., § 4) about 1/24.
-
-§ 11. TABLE III.--LIFT AND DRIFT.
+         10             14·7          0·300
+         12             17·6          0·432
+         14             20·5          0·588
+         16             23·5          0·768
+         18             26·4          0·972
+         20             29·35         1·200
+         25             36·7          1·875
+         30             43·9          2·700
+         35             51·3          3·675
+
+§ 10. Representing normal pressure on a plane surface by 1; pressure
+on a rod (round section) is 0·6; on a symmetrical elliptic cross
+section (axes 2:1) is 0·2 (approx.). Similar shape, but axes 6:1, and
+edges sharpened (_see_ ch. ii., § 5), is only 0·05, or 1/20, and for
+the body of minimum resistance (_see_ ch. ii., § 4) about 1/24.
+
+§ 11. TABLE III.--LIFT AND DRIFT.
 
 On a well shaped aerocurve or correctly designed cambered surface.
-Aspect ratio 4·5.
+Aspect ratio 4·5.
 
     Inclination.   Ratio Lift to Drift.
-           0°            19:1
-        2·87°            15:1
-        3·58°            16:1
-        4·09°            14:1
-        4·78°            12:1
-        5·73°           9·6:1
-        7·18°           7·9:1
+           0°            19:1
+        2·87°            15:1
+        3·58°            16:1
+        4·09°            14:1
+        4·78°            12:1
+        5·73°           9·6:1
+        7·18°           7·9:1
 
 Wind velocity 40 miles per hour. (The above deduced from some
 experiments of Sir Hiram Maxim.)
@@ -4158,28 +4123,28 @@ At a velocity of 30 miles an hour a good aerocurve should lift 21 oz.
 to 24 oz. per sq. ft.
 
 
-§ 12. TABLE IV.--LIFT AND DRIFT.
+§ 12. TABLE IV.--LIFT AND DRIFT.
 
 On a plane aerofoil.
 
-    N = P(2 sin {alpha}/1 + sin² {alpha})
+    N = P(2 sin {alpha}/1 + sin² {alpha})
 
     Inclination.   Ratio Lift to Drift.
-         1°              58·3:1
-         2°              29·2:1
-         3°              19·3:1
-         4°              14·3:1
-         5°              11·4:1
-         6°               9·5:1
-         7°               8·0:1
-         8°               7·0:1
-         9°               6·3:1
-        10°               5·7:1
-
-    P = 2_kd_ AV² sin {alpha}.
+         1°              58·3:1
+         2°              29·2:1
+         3°              19·3:1
+         4°              14·3:1
+         5°              11·4:1
+         6°               9·5:1
+         7°               8·0:1
+         8°               7·0:1
+         9°               6·3:1
+        10°               5·7:1
+
+    P = 2_kd_ AV² sin {alpha}.
 
 A useful formula for a single plane surface. P = pressure supporting
-the plane in pounds per square foot, _k_ a constant = 0·003 in miles
+the plane in pounds per square foot, _k_ a constant = 0·003 in miles
 per hour, _d_ = the density of the air.
 
 A = the area of the plane, V relative velocity of translation through
@@ -4187,9 +4152,9 @@ the air, and {alpha} the angle of flight.
 
 Transposing we have
 
-    AV² = P/(2_kd_ sin {alpha})
+    AV² = P/(2_kd_ sin {alpha})
 
-If P and {alpha} are constants; then AV² = a constant or area is
+If P and {alpha} are constants; then AV² = a constant or area is
 inversely as velocity squared. Increase of velocity meaning diminished
 supporting surface (_and so far as supporting surface goes_), diminished
 resistance and skin friction. It must be remembered, however, that while
@@ -4197,7 +4162,7 @@ the work of sustentation diminishes with the speed, the work of
 penetration varies as the cube of the speed.
 
 
-§ 13. TABLE V.--TIMBER.
+§ 13. TABLE V.--TIMBER.
 
   Column Headings:
 
@@ -4213,28 +4178,28 @@ penetration varies as the cube of the speed.
   ---------------+-----+-------+-------------+-------+-----+-----+----
     A            |B    | C     |  D          |E      |F    |G    | H
   ---------------+-----+-------+-------------+-------+-----+-----+----
-  Ash            | ·79 | 43-52 |14,000-17,000| 622   |4·69 |1·55 |13·0
-  Bamboo         |     |  25[A]|    6300[53] |       |3·07 |3·20 |
-  Beech          | ·69 |  43   |10,000-12,000| 850   |     |1·65 |19·8
-  Birch          | ·71 |  45   |   15,000    | 550   |     |3·28 |12·2
-  Box            |1·28 |  80   |20,000-23,000| 815   |     |     |10·2
-  Cork           | ·24 |  15   |             |       |     |     |
+  Ash            | ·79 | 43-52 |14,000-17,000| 622   |4·69 |1·55 |13·0
+  Bamboo         |     |  25[A]|    6300[53] |       |3·07 |3·20 |
+  Beech          | ·69 |  43   |10,000-12,000| 850   |     |1·65 |19·8
+  Birch          | ·71 |  45   |   15,000    | 550   |     |3·28 |12·2
+  Box            |1·28 |  80   |20,000-23,000| 815   |     |     |10·2
+  Cork           | ·24 |  15   |             |       |     |     |
   Fir (Norway    |     |       |             |       |     |     |
-    Spruce)      | ·51 |  32   | 9,000-11,000| 450   |3·01 |1·70 |14·0
+    Spruce)      | ·51 |  32   | 9,000-11,000| 450   |3·01 |1·70 |14·0
   American       |     |       |             |       |     |     |
-    Hickory      |     |  49   |   11,000    | 800   |3·47 |2·40 |16·3
+    Hickory      |     |  49   |   11,000    | 800   |3·47 |2·40 |16·3
   Honduras       |     |       |             |       |     |     |
-    Mahogany     | ·56 |  35   |   20,000    | 750   |3·40 |1·60 |21·4
-  Maple          | ·68 |  44   |   10,600    | 750   |     |     |17·0
+    Mahogany     | ·56 |  35   |   20,000    | 750   |3·40 |1·60 |21·4
+  Maple          | ·68 |  44   |   10,600    | 750   |     |     |17·0
   American White |     |       |             |       |     |     |
-    Pine         | ·42 |  25   |   11,800    | 450   |2·37 |1·39 |18·0
-  Lombardy Poplar|     |  24   |    7,000    | 550   |2·89 | 0·77|22·9
+    Pine         | ·42 |  25   |   11,800    | 450   |2·37 |1·39 |18·0
+  Lombardy Poplar|     |  24   |    7,000    | 550   |2·89 | 0·77|22·9
   American Yellow|     |       |             |       |     |     |
-    Poplar       |     |  44   |   10,000    |       |3·63 |1·40 |
-  Satinwood      | ·96 |  60   |             |1,033  |     |     |17·2
-  Spruce         | ·50 |  31   |   12,400    | 450   |     |     |14·5
+    Poplar       |     |  44   |   10,000    |       |3·63 |1·40 |
+  Satinwood      | ·96 |  60   |             |1,033  |     |     |17·2
+  Spruce         | ·50 |  31   |   12,400    | 450   |     |     |14·5
   Tubular Ash,   |     |       |             |       |     |     |
-   _t_ = 1/8 _d_ |     |  47   |             |       |3·50 |1·55 |
+   _t_ = 1/8 _d_ |     |  47   |             |       |3·50 |1·55 |
   ---------------+-----+-------+-------------+-------+-----+-----+----
 
                          _t_ = thickness: _d_ = diameter.
@@ -4242,15 +4207,15 @@ penetration varies as the cube of the speed.
   [A] Given elsewhere as 55 and 22,500 (_t_ = 1/3_d_), evidently
   regarded as solid.
 
-§ 14.--=Formula connecting the Weight Lifted in Pounds per Square Foot
+§ 14.--=Formula connecting the Weight Lifted in Pounds per Square Foot
 and the Velocity.=--The empirical formula
 
-    W = (V²C)/_g_
+    W = (V²C)/_g_
 
     Where W   = weight lifted in lb. per sq. ft.
           V   = velocity in ft. per sec.
-          C   = a constant = 0·025.
-          _g_ = 32·2, or 32 approx.
+          C   = a constant = 0·025.
+          _g_ = 32·2, or 32 approx.
 
 may be used for a thoroughly efficient model. This gives
 (approximately)
@@ -4259,12 +4224,12 @@ may be used for a thoroughly efficient model. This gives
      21 oz.     "        "      30       "
       6 oz.     "        "      15       "
       4 oz.     "        "      12       "
-    2·7 oz.     "        "      10       "
+    2·7 oz.     "        "      10       "
 
 Remember the results work out in feet per second. To convert
 (approximately) into miles per hour multiply by 2/3.
 
-§ 15. =Formula connecting Models of Similar Design, but Different
+§ 15. =Formula connecting Models of Similar Design, but Different
 Weights.=
 
     D {proportional to} {square root}W.
@@ -4283,10 +4248,10 @@ design is not, strictly speaking, similar, but not too much reliance
 must be placed on the above. The record for a 1 oz. model to date is
 over 300 yards (with the wind, of course), say 750 ft. in calm air.
 
-§ 16. =Power and Speed.=--The following formula, given by Mr. L. Blin
+§ 16. =Power and Speed.=--The following formula, given by Mr. L. Blin
 Desbleds, between these is--
 
-    W/W{0} = (3_v{0}_)/(4_v_) + ¼(_v_/_v{0}_)³.
+    W/W{0} = (3_v{0}_)/(4_v_) + ¼(_v_/_v{0}_)³.
 
     Where   _v{0}_ = speed of minimum power
               W{0} = work done at speed _v{0}_.
@@ -4302,7 +4267,7 @@ times as great as the original one. The "speed of minimum power" being
 the speed at which the aeroplane must travel for the minimum
 expenditure of power.
 
-§ 17. The thrust of the propeller has evidently to balance the
+§ 17. The thrust of the propeller has evidently to balance the
 
     Aerodynamic resistance                        = R
     The head resistance (including skin friction) = S
@@ -4320,12 +4285,12 @@ This is the thrust which the propeller should be designed to give. Now
 supposing the propeller's efficiency to be 80 per cent., then P--the
 minimum propulsion power
 
-    = (4/3)R × 100/80 × 100/75 × _v_.
+    = (4/3)R × 100/80 × 100/75 × _v_.
 
 Where 25 per cent. is the slip of the screw, _v_ the velocity of the
 aeroplane.
 
-§ 18. =To determine experimentally the Static Thrust of a
+§ 18. =To determine experimentally the Static Thrust of a
 Propeller.=--Useful for models intended to raise themselves from the
 ground under their own power, and for helicopters.
 
@@ -4356,7 +4321,7 @@ increased load when the propeller is on is therefore
 
 All this increased power is not, however, expended on the propeller.
 
-The lost power in the motor increases as C²R.
+The lost power in the motor increases as C²R.
 
 R = resistance of armature and C = current. If we deduct 10 per cent.
 for this then the propeller is actually driven by 56 watts.
@@ -4367,42 +4332,42 @@ Now 746 watts = 1 h.p.
 
 at the observed number of revolutions per minute.
 
-§ 19. N.B.--The h.p. required to drive a propeller varies as the cube
+§ 19. N.B.--The h.p. required to drive a propeller varies as the cube
 of the revolutions.
 
 _Proof._--Double the speed of the screw, then it strikes the air twice
 as hard; it also strikes twice as much air, and the motor has to go
 twice as fast to do it.
 
-§ 20. To compare one model with another the formula
+§ 20. To compare one model with another the formula
 
-    Weight × velocity (in ft. per sec.)/horse-power
+    Weight × velocity (in ft. per sec.)/horse-power
 
 is sometimes useful.
 
-§ 21. =A Horse-power= is 33,000 lb. raised one foot in one minute, or
+§ 21. =A Horse-power= is 33,000 lb. raised one foot in one minute, or
 550 lb. one foot in one second.
 
-A clockwork spring raised 1 lb. through 4½ ft. in 3 seconds. What
+A clockwork spring raised 1 lb. through 4½ ft. in 3 seconds. What
 is its h.p.?
 
-         1 lb. through 4½ ft. in 3 seconds
+         1 lb. through 4½ ft. in 3 seconds
     is   1 lb.    "    90 ft.  " 1 minute.
 
           {therefore} Work done is 90 ft.-lb.
-           = 90/33000 = 0·002727 h.p.
+           = 90/33000 = 0·002727 h.p.
 
-The weight of the spring was 6¾ oz. (this is taken from an actual
-experiment), i.e. this motor develops power at the rate of 0·002727
-h.p. for 3½ seconds only.
+The weight of the spring was 6¾ oz. (this is taken from an actual
+experiment), i.e. this motor develops power at the rate of 0·002727
+h.p. for 3½ seconds only.
 
-§ 22. =To Ascertain the H.P. of a Rubber Motor.= Supposing a propeller
+§ 22. =To Ascertain the H.P. of a Rubber Motor.= Supposing a propeller
 wound up to 250 turns to run down in 15 seconds, i.e. at a mean speed
 of 1200 revolutions per minute or 20 per second. Suppose the mean
 thrust to be 2 oz., and let the pitch of the propeller be 1 foot. Then
 the number of foot-pounds of energy developed
 
-    = (2 oz. × 1200 revols. × 1 ft. (pitch)) / 16 oz.
+    = (2 oz. × 1200 revols. × 1 ft. (pitch)) / 16 oz.
 
 = 150 ft.-lb. per minute.
 
@@ -4410,12 +4375,12 @@ But the rubber motor runs down in 15 seconds.
 
     {therefore} Energy really developed is
 
-          = (150 × 15) / 60 = 37·5 ft.-lb.
+          = (150 × 15) / 60 = 37·5 ft.-lb.
 
-The motor develops power at rate of 150/33000 = 0·004545 h.p., but for
+The motor develops power at rate of 150/33000 = 0·004545 h.p., but for
 15 seconds only.
 
-§ 23. =Foot-pounds of Energy in a Given Weight of Rubber=
+§ 23. =Foot-pounds of Energy in a Given Weight of Rubber=
 (experimental determination of).
 
          Length of rubber    36 yds.
@@ -4423,8 +4388,8 @@ The motor develops power at rate of 150/33000 = 0·004545 h.p., but for
          Number of turns     = 200.
 
     12 oz. were raised 19 ft. in 5 seconds.
-    i.e. ¾ lb. was raised 19 × 12 ft. in 1 minute.
-    i.e. 1 lb. was raised 19 × 3 × 3 ft. in 1 minute.
+    i.e. ¾ lb. was raised 19 × 12 ft. in 1 minute.
+    i.e. 1 lb. was raised 19 × 3 × 3 ft. in 1 minute.
                                = 171 ft. in 1 minute.
 
 i.e. 171 ft.-lb. of energy per minute. But actual time was 5 seconds.
@@ -4434,25 +4399,25 @@ yards, i.e. 36 strands 1 yard each at 200 turns is
 
     = 171/12 ft.-lb.
 
-    = 14¼ ft.-lb.
+    = 14¼ ft.-lb.
 
 This allows nothing for friction or turning the axle on which the cord
 was wound. Ball bearings were used; but the rubber was not new and
 twenty turns were still unwound at the end of the experiment. Now
 allowing for friction, etc. being the same as on an actual model, we
-can take ¾ of a ft.-lb. for the unwound amount and estimate the
+can take ¾ of a ft.-lb. for the unwound amount and estimate the
 total energy as 15 ft.-lb. as a minimum. The energy actually developed
-being at the rate of 0·0055 h.p., or 1/200 of a h.p. if supposed
+being at the rate of 0·0055 h.p., or 1/200 of a h.p. if supposed
 uniform.
 
-§ 24. The actual energy derivable from 1 lb. weight of rubber is
+§ 24. The actual energy derivable from 1 lb. weight of rubber is
 stated to be 300 ft.-lb. On this basis 2-7/16 oz. should be capable of
-giving 45·7 ft.-lb. of energy, i.e. three times the amount given
+giving 45·7 ft.-lb. of energy, i.e. three times the amount given
 above. Now the motor-rubber not lubricated was only given 200
 turns--lubricated 400 could have been given it, 600 probably before
 rupture--and the energy then derivable would certainly have been
-approximating to 45 ft.-lb., i.e. 36·25. Now on the basis of 300
-ft.-lb. per lb. a weight of ½ oz. (the amount of rubber carried in
+approximating to 45 ft.-lb., i.e. 36·25. Now on the basis of 300
+ft.-lb. per lb. a weight of ½ oz. (the amount of rubber carried in
 "one-ouncers") gives 9 ft.-lb. of energy. Now assuming the gliding
 angle (including weight of propellers) to be 1 in 8; a perfectly
 efficient model should be capable of flying eight times as great a
@@ -4460,7 +4425,7 @@ distance in a horizontal direction as the energy in the rubber motor
 would lift it vertically. Now 9 ft.-lb. of energy will lift 1 oz. 154
 ft. Therefore theoretically it will drive it a distance (in yards) of
 
-    (8 × 154)/3 = 410·6 yards.
+    (8 × 154)/3 = 410·6 yards.
 
 Now the greatest distance that a 1 oz. model has flown in perfectly
 calm air (which never exists) is not known. Flying with the wind 500
@@ -4475,36 +4440,36 @@ too high; all the writer desires to show is the method of working out.
 Mr. T.W.K. Clarke informs me that in his one-ouncers the gliding
 angle is about 1 in 5.
 
-§ 25. =To Test Different Motors or Different Powers of the Same Kind
+§ 25. =To Test Different Motors or Different Powers of the Same Kind
 of Motor.=--Test them on the same machine, and do not use different
 motors or different powers on different machines.
 
-§ 26. =Efficiency of a Model.=--The efficiency of a model depends on
+§ 26. =Efficiency of a Model.=--The efficiency of a model depends on
 the weight carried per h.p.
 
-§ 27. =Efficiency of Design.=--The efficiency of some particular
+§ 27. =Efficiency of Design.=--The efficiency of some particular
 design depends on the amount of supporting surface necessary at a
 given speed.
 
-§ 28. =Naphtha Engines=, that is, engines made on the principle of the
+§ 28. =Naphtha Engines=, that is, engines made on the principle of the
 steam engine, but which use a light spirit of petrol or similar agent
 in their generator instead of water with the same amount of heat, will
 develop twice as much energy as in the case of the ordinary steam
 engine.
 
-§ 29.=Petrol Motors.=
+§ 29.=Petrol Motors.=
 
     Horse-power.     No. of Cylinders.   Weight.
-        ¼                Single          4½ lb.
-        ½ to ¾             "             6½  "
-        1½               Double          9   "
+        ¼                Single          4½ lb.
+        ½ to ¾             "             6½  "
+        1½               Double          9   "
 
-§ 30. =The Horse-power of Model Petrol Motors.=--Formula for rating of
+§ 30. =The Horse-power of Model Petrol Motors.=--Formula for rating of
 the above.
 
     (R.P.M. = revolutions per minute.)
 
-    H.P. = ((Bore)² × stroke × no. of cylinders × R.P.M.)/12,000
+    H.P. = ((Bore)² × stroke × no. of cylinders × R.P.M.)/12,000
 
 If the right-hand side of the equation gives a less h.p. than that
 stated for some particular motor, then it follows that the h.p. of the
@@ -4512,19 +4477,19 @@ motor has been over-estimated.
 
 [Illustration: FIG. 56.]
 
-§ 30A. =Relation between Static Thrust of Propeller and Total Weight
-of Model.=--The thrust should be approx. = ¼ of the weight.
+§ 30A. =Relation between Static Thrust of Propeller and Total Weight
+of Model.=--The thrust should be approx. = ¼ of the weight.
 
-§ 31. =How to find the Height of an Inaccessible Object by Means of
+§ 31. =How to find the Height of an Inaccessible Object by Means of
 Three Observations taken on the Ground (supposed flat) in the same
 Straight Line.=--Let A, C, B be the angular elevations of the object
 D, as seen from these points, taken in the same straight line. Let the
 distances B C, C A and A B be _a_, _b_, _c_ respectively. And let
 required height P D = _h_; then by trigonometry we have (see Fig. 56)
 
-    _h²_ = _abc_/(_a_ cot²A - _c_ cot²C + _b_ cot²B).
+    _h²_ = _abc_/(_a_ cot²A - _c_ cot²C + _b_ cot²B).
 
-§ 32. =Formula= for calculating the I.H.P. (indicated horse-power) of
+§ 32. =Formula= for calculating the I.H.P. (indicated horse-power) of
 a single-cylinder double-acting steam-engine.
 
 Indicated h.p. means the h.p. actually exerted by the steam in the
@@ -4532,7 +4497,7 @@ cylinder without taking into account engine friction. Brake h.p. or
 effective h.p. is the actual h.p. delivered by the crank shaft of the
 engine.
 
-    I.H.P. = (2 × S × R × A × P)/33,000.
+    I.H.P. = (2 × S × R × A × P)/33,000.
 
     Where    S = stroke in feet.
              R = revolutions per minute.
@@ -4548,17 +4513,17 @@ TABLE VI.
     ---------+----------+---------+----------+---------+---------
      Cut-off | Constant | Cut-off | Constant | Cut-off | Constant
     ---------+----------+---------+----------+---------+---------
-       1/6   |   ·566   |   3/8   |   ·771   |   2/3   |  ·917
-       1/5   |   ·603   |    ·4   |   ·789   |    ·7   |  ·926
-       1/4   |   ·659   |   1/2   |   ·847   |   3/4   |  ·937
-        ·3   |   ·708   |    ·6   |   ·895   |    ·8   |  ·944
-       1/3   |   ·743   |   5/8   |   ·904   |   7/8   |  ·951
+       1/6   |   ·566   |   3/8   |   ·771   |   2/3   |  ·917
+       1/5   |   ·603   |    ·4   |   ·789   |    ·7   |  ·926
+       1/4   |   ·659   |   1/2   |   ·847   |   3/4   |  ·937
+        ·3   |   ·708   |    ·6   |   ·895   |    ·8   |  ·944
+       1/3   |   ·743   |   5/8   |   ·904   |   7/8   |  ·951
     ---------+----------+---------+----------+---------+---------
 
-Rule.--"Add 14·7 to gauge pressure of boiler, this giving 'absolute
+Rule.--"Add 14·7 to gauge pressure of boiler, this giving 'absolute
 steam pressure,' multiply this sum by the number opposite the fraction
 representing the point of cut-off in the cylinder in accompanying
-table. Subtract 17 from the product and multiply the remainder by 0·9.
+table. Subtract 17 from the product and multiply the remainder by 0·9.
 The result will be very nearly the M.E.P." (R.M. de Vignier.)
 
 
@@ -4614,11 +4579,11 @@ carried.
 FLYERS.]
 
 For illustrations, etc., of the Fleming-Williams model, _see_ ch. v.,
-§ 23.
+§ 23.
 
 (Fig. 60.) This is another well-constructed and efficient model, the
 shape and character of the aerofoil surfaces much resembling those of
-the French toy monoplane AL-MA (see § 4, ch. vii.), but they are
+the French toy monoplane AL-MA (see § 4, ch. vii.), but they are
 supported and held in position by quite a different method, a neat
 little device enabling the front plane to become partly detached on
 collision with any obstacle. The model is provided with a keel (below
@@ -4653,7 +4618,7 @@ On the morning of the competition a flight of about 320 yards
 being launched against the wind so as to gain altitude, and then
 flying away with the breeze behind the writer. Duration of flight 50
 seconds. The following are the chief particulars of the
-model:--Weight, 7½ oz. Area of supporting surface, 1-1/3 sq. ft.
+model:--Weight, 7½ oz. Area of supporting surface, 1-1/3 sq. ft.
 Total length, 4 ft. Span of main aerofoil, 25 in. Aspect ratio, 4 : 1.
 Diameter of propeller, 14 in. Two strand geared rubber motor, carrying
 altogether 28 strands of 1/16 square rubber cord 43 in. long. The
@@ -4910,7 +4875,7 @@ SOLE ENGLISH AGENTS for the Books of--
 
                1  6
 
-    =A Handbook of Formulæ, Tables, and Memoranda=, for
+    =A Handbook of Formulæ, Tables, and Memoranda=, for
     Architectural Surveyors and others engaged in Building. By J.T.
     HURST. Fifteenth edition, 512 pp. royal 32mo, roan. (_1905_)
 
@@ -4970,7 +4935,7 @@ SOLE ENGLISH AGENTS for the Books of--
     =Spons' Architects' and Builders' Pocket Price-Book=,
     Memoranda, Tables and Prices. Edited by CLYDE YOUNG. Revised by
     STANFORD M. BROOKS. Illustrated, 552 pp. 16mo, leather cloth
-    (size 6½ in. by 3¾ in. by ½ in. thick). Issued annually
+    (size 6½ in. by 3¾ in. by ½ in. thick). Issued annually
 
     _net_      3  0
 
@@ -5048,7 +5013,7 @@ SOLE ENGLISH AGENTS for the Books of--
 
     _net_      2  0
 
-    =New Formulæ for the Loads and Deflections= of Solid Beams and
+    =New Formulæ for the Loads and Deflections= of Solid Beams and
     Girders. By W. DONALDSON. Second edition, 8vo. (_1872_)
 
                4  6
@@ -5304,7 +5269,7 @@ SOLE ENGLISH AGENTS for the Books of--
 
               10  6
 
-    =A Pocket Book of Useful Formulæ and Memoranda,= for Civil and
+    =A Pocket Book of Useful Formulæ and Memoranda,= for Civil and
     Mechanical Engineers. By Sir G.L. MOLESWORTH and H.B. MOLESWORTH. With
     an Electrical Supplement by W.H. MOLESWORTH. Twenty-sixth edition, 760
     illus. 901 pp. royal 32mo, French morocco, gilt edges. (_1908_)
@@ -5816,7 +5781,7 @@ SOLE ENGLISH AGENTS for the Books of--
 
     _net_      3  6
 
-    =Röntgen Rays= and Phenomena of the Anode and Cathode. By E.P.
+    =Röntgen Rays= and Phenomena of the Anode and Cathode. By E.P.
     THOMPSON and W.A. ANTHONY. 105 illus. 204 pp. 8vo. (_New York, 1896_)
 
     _net_      4  6
@@ -6033,26 +5998,26 @@ SOLE ENGLISH AGENTS for the Books of--
     (_See also_ WATER SUPPLY.)
 
     =Pumps:= Historically, Theoretically and Practically Considered. By
-    P.R. BJÖRLING. Second edition, 156 illus. 234 pp. crown 8vo. (_1895_)
+    P.R. BJÖRLING. Second edition, 156 illus. 234 pp. crown 8vo. (_1895_)
 
                7  6
 
-    =Pump Details.= By P.R. BJÖRLING. 278 illus. 211 pp. crown 8vo.
+    =Pump Details.= By P.R. BJÖRLING. 278 illus. 211 pp. crown 8vo.
     (_1892_)
 
                7  6
 
     =Pumps and Pump Motors:= A Manual for the use of Hydraulic Engineers.
-    By P.R. BJÖRLING. Two vols. 261 plates, 369 pp. royal 4to. (_1895_).
+    By P.R. BJÖRLING. Two vols. 261 plates, 369 pp. royal 4to. (_1895_).
 
     _net_   1 10  0
 
-    =Practical Handbook on Pump Construction.= By P.R. BJÖRLING. Second
+    =Practical Handbook on Pump Construction.= By P.R. BJÖRLING. Second
     edition, 9 plates, 90 pp. crown 8vo. (_1904_)
 
                5  0
 
-    =Water or Hydraulic Motors.= By P.R. BJÖRLING. 206 illus. 287 pp.
+    =Water or Hydraulic Motors.= By P.R. BJÖRLING. 206 illus. 287 pp.
     crown 8vo. (_1903_)
 
                9  0
@@ -6098,7 +6063,7 @@ SOLE ENGLISH AGENTS for the Books of--
 
                5  0
 
-    =Practical Hydrostatics and Hydrostatic Formulæ.= By E.S. GOULD. 27
+    =Practical Hydrostatics and Hydrostatic Formulæ.= By E.S. GOULD. 27
     illus. 114 pp. 18mo, boards. (_New York, 1903_)
 
     _net_      2  0
@@ -6120,7 +6085,7 @@ SOLE ENGLISH AGENTS for the Books of--
 
                5  0
 
-    =Simple Hydraulic Formulæ.= By T.W. STONE. 9 plates, 98 pp. crown 8vo.
+    =Simple Hydraulic Formulæ.= By T.W. STONE. 9 plates, 98 pp. crown 8vo.
     (_1881_)
 
                4  0
@@ -6224,7 +6189,7 @@ SOLE ENGLISH AGENTS for the Books of--
 
                9  0
 
-    =Spons' Encyclopædia of the Industrial Arts,= Manufactures and
+    =Spons' Encyclopædia of the Industrial Arts,= Manufactures and
     Commercial Products. 1500 illus. 2100 pp. super-royal 8vo. (_1882_) In
     2 Vols. cloth
 
@@ -6273,7 +6238,7 @@ SOLE ENGLISH AGENTS for the Books of--
 
     _net_   2  2  0
 
-    =Facts, Figures, and Formulæ for Irrigation Engineers.= By R.B.
+    =Facts, Figures, and Formulæ for Irrigation Engineers.= By R.B.
     BUCKLEY. With illus. 239 pp. large 8vo. (_1908_)
 
     _net_     10  6
@@ -6882,7 +6847,7 @@ SOLE ENGLISH AGENTS for the Books of--
               12  6
 
     =Atlas of Designs concerning Blast Furnace Practice.= By M.A.
-    PAVLOFF. 127 plates, 14 in. by 10½ in. oblong, sewed.
+    PAVLOFF. 127 plates, 14 in. by 10½ in. oblong, sewed.
     (_1902_)
 
     _net_   1  1  0
@@ -6890,7 +6855,7 @@ SOLE ENGLISH AGENTS for the Books of--
     =Album of Drawings relating to the Manufacture of Open Hearth
     Steel.= By M.A. PAVLOFF.
 
-    Part I. Open Hearth Furnaces. 52 plates, 14 in. by 10½ in.
+    Part I. Open Hearth Furnaces. 52 plates, 14 in. by 10½ in.
     oblong folio in portfolio. (_1904_)
 
     _net_     12  0
@@ -7186,7 +7151,7 @@ SOLE ENGLISH AGENTS for the Books of--
     =Spons' Architects' and Builders' Pocket Price Book=,
     Memoranda, Tables and Prices. Edited by CLYDE YOUNG. Revised by
     STANFORD M. BROOKS. Illustrated, 552 pp. 16mo, leather cloth
-    (size 6½ in. by 3¾ in. by ½ in. thick). Issued annually
+    (size 6½ in. by 3¾ in. by ½ in. thick). Issued annually
 
     _net_      3  0
 
@@ -7247,7 +7212,7 @@ SOLE ENGLISH AGENTS for the Books of--
 
     _net_      3  0
 
-    =Formulæ for Railway Crossings and Switches.= By J. GLOVER. 9
+    =Formulæ for Railway Crossings and Switches.= By J. GLOVER. 9
     illus. 28 pp. royal 32mo. (_1896_)
 
                2  6
@@ -7468,8 +7433,8 @@ SOLE ENGLISH AGENTS for the Books of--
 
     TELEGRAPH CODES.
 
-    =New Business Code.= 320 pp. narrow 8vo. (Size 4¾ in. by
-    7¾ in. and ½ in. thick, and weight 10 oz.) (_New York,
+    =New Business Code.= 320 pp. narrow 8vo. (Size 4¾ in. by
+    7¾ in. and ½ in. thick, and weight 10 oz.) (_New York,
     1909_)
 
     _net_   1 10  0
@@ -7509,7 +7474,7 @@ SOLE ENGLISH AGENTS for the Books of--
 
                4  6
 
-    =Formulæ and Tables for Heating.= By J.H. KINEALY. 18 illus. 53
+    =Formulæ and Tables for Heating.= By J.H. KINEALY. 18 illus. 53
     pp. 8vo. (_New York, 1899_)
 
                3  6
@@ -8031,7 +7996,7 @@ Aeroplanes.
 
     Biplane type;--Wright, Farman, Voisin, Cody, Herring-Curtis.
 
-    Monoplanes;--Rep, Antoinette, Santos Dumont, and Blériot.
+    Monoplanes;--Rep, Antoinette, Santos Dumont, and Blériot.
 
 Each of these machines are here shown in End View, Plan and Elevation.
 
@@ -8152,12 +8117,12 @@ how to make and fly them.
 
   The OE ligature has been replaced by the separate characters.
 
-  The fractions ¼, ½ and ¾ are represented using the Latin-1 characters,
+  The fractions ¼, ½ and ¾ are represented using the Latin-1 characters,
   but other fractions use the / and - symbols, e.g. 3/8 or 2-5/8.
 
-  The exponents 2 and 3 are represented using ² and ³ respectively, but
+  The exponents 2 and 3 are represented using ² and ³ respectively, but
   other exponents are indicated by the caret character, for example,
-  v^{1·85}
+  v^{1·85}
 
   Subscripts are simply enclosed in braces, e.g. W{0}.
 
@@ -8165,12 +8130,12 @@ how to make and fly them.
   in braces: {alpha}, {pi}, {therefore}, {square root} and
   {proportional to}.
 
-  The skin friction formulæ given on pages 11 and 128 have been corrected
-  by comparison with other sources. Respectively, the formulæ were
+  The skin friction formulæ given on pages 11 and 128 have been corrected
+  by comparison with other sources. Respectively, the formulæ were
   originally printed as
-      _f_ = 0·00000778_l_^{9·3}_v_^{1·85}
+      _f_ = 0·00000778_l_^{9·3}_v_^{1·85}
   and
-      _f_ = 0·00000778_l_ - ^{00·7}_v_^{1·85}
+      _f_ = 0·00000778_l_ - ^{00·7}_v_^{1·85}
 
   In ambiguous cases, the text has been left as it appears in the
   original book.
@@ -8182,366 +8147,4 @@ how to make and fly them.
 End of the Project Gutenberg EBook of The Theory and Practice of Model
 Aeroplaning, by V. E. Johnson
 
-*** END OF THIS PROJECT GUTENBERG EBOOK THE THEORY AND PRACTICE ***
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+*** END OF THE PROJECT GUTENBERG EBOOK 41135 ***
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       The Project Gutenberg eBook of The Theory and Practice of Model Aeroplaning, by V.E. Johnson
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-The Project Gutenberg EBook of The Theory and Practice of Model Aeroplaning, by 
-V. E. Johnson
-
-This eBook is for the use of anyone anywhere at no cost and with
-almost no restrictions whatsoever.  You may copy it, give it away or
-re-use it under the terms of the Project Gutenberg License included
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-
-
-Title: The Theory and Practice of Model Aeroplaning
-
-Author: V. E. Johnson
-
-Release Date: October 21, 2012 [EBook #41135]
-
-Language: English
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-
+<div>*** START OF THE PROJECT GUTENBERG EBOOK 41135 ***</div>
 
 <div class="figcenter" style="width: 640px;">
 <img src="images/i_002.jpg" width="640" height="300" alt="" title="" />
@@ -209,14 +170,14 @@ achieve the best results, theory and practice must go hand
 in hand.</p>
 
 <p>From a series of carefully conducted experiments empirical
-formulæ can be obtained which, combined later with
+formulæ can be obtained which, combined later with
 mathematical induction and deduction, may lead, not only
 to a more accurate and generalized law than that contained
 in the empirical formula, but to valuable deductions of a
 totally new type, embodying some general law hitherto
 quite unknown by experimentalists, which in its turn may
 serve as a foundation or stepping stone for suggesting other
-experiments and empirical formulæ which may be of especial
+experiments and empirical formulæ which may be of especial
 importance, to be treated in <i>their</i> turn like their predecessor.
 By "especial importance," I mean not only to "model," but
 "Aeroplaning" generally.</p>
@@ -280,31 +241,31 @@ duly acknowledged.</p>
 <td class="toctxt">&nbsp;</td>
 <td class="tocpag"><small>PAGE</small></td>
 </tr><tr>
-<td class="toctxt">§§ 1-5. The two classes of models&mdash;First requisite of a model
-aeroplane. §&nbsp;6. An art in itself. §&nbsp;7. The leading principle</td>
+<td class="toctxt">§§ 1-5. The two classes of models&mdash;First requisite of a model
+aeroplane. §&nbsp;6. An art in itself. §&nbsp;7. The leading principle</td>
 <td class="tocpag">1</td>
 </tr><tr>
 <td colspan="2" class="tocnum"><a href="#CHAPTER_I">CHAPTER I.</a></td>
 </tr><tr>
 <td colspan="2" class="toctit">THE QUESTION OF WEIGHT.</td>
 </tr><tr>
-<td class="toctxt">§§&nbsp;1-2. Its primary importance both in rubber and power-driven
-models&mdash;Professor Langley's experiences. §&nbsp;3. Theoretical
-aspect of the question. §&nbsp;4. Means whereby more weight
+<td class="toctxt">§§&nbsp;1-2. Its primary importance both in rubber and power-driven
+models&mdash;Professor Langley's experiences. §&nbsp;3. Theoretical
+aspect of the question. §&nbsp;4. Means whereby more weight
 can be carried&mdash;How to obtain maximum strength with
-minimum weight. §&nbsp;5. Heavy models versus light ones.</td>
+minimum weight. §&nbsp;5. Heavy models versus light ones.</td>
 <td class="tocpag">4</td>
 </tr><tr>
 <td colspan="2" class="tocnum"><a href="#CHAPTER_II">CHAPTER II.</a></td>
 </tr><tr>
 <td colspan="2" class="toctit">THE QUESTION OF RESISTANCE.</td>
 </tr><tr>
-<td class="toctxt">§&nbsp;1. The chief function of a model in the medium in which it
-travels. §&nbsp;2. Resistance considered as load percentage.
-§&nbsp;3. How made up. §&nbsp;4. The shape of minimum resistance.
-§&nbsp;5. The case of rubber-driven models. §&nbsp;6. The aerofoil
+<td class="toctxt">§&nbsp;1. The chief function of a model in the medium in which it
+travels. §&nbsp;2. Resistance considered as load percentage.
+§&nbsp;3. How made up. §&nbsp;4. The shape of minimum resistance.
+§&nbsp;5. The case of rubber-driven models. §&nbsp;6. The aerofoil
 surface&mdash;Shape and material as affecting this question.
-§&nbsp;7. Skin friction&mdash;Its coefficient. §&nbsp;8. Experimental proofs
+§&nbsp;7. Skin friction&mdash;Its coefficient. §&nbsp;8. Experimental proofs
 of its existence and importance.</td>
 <td class="tocpag">7</td>
 </tr><tr>
@@ -312,16 +273,16 @@ of its existence and importance.</td>
 </tr><tr>
 <td colspan="2" class="toctit">THE QUESTION OF BALANCE.</td>
 </tr><tr>
-<td class="toctxt">§&nbsp;1. Automatic stability essential in a flying model. §&nbsp;2.
-Theoretical researches on this question. §§&nbsp;3-6. A brief
+<td class="toctxt">§&nbsp;1. Automatic stability essential in a flying model. §&nbsp;2.
+Theoretical researches on this question. §§&nbsp;3-6. A brief
 <span class="pagenum"><a name="Page_viii" id="Page_viii">[viii]</a></span>summary of the chief conclusions arrived at&mdash;Remarks on
 and deductions from the same&mdash;Conditions for automatic
-stability. §&nbsp;7. Theory and practice&mdash;Stringfellow&mdash;Pénaud&mdash;Tatin&mdash;The
+stability. §&nbsp;7. Theory and practice&mdash;Stringfellow&mdash;Pénaud&mdash;Tatin&mdash;The
 question of Fins&mdash;Clarke's models&mdash;Some
-further considerations. §&nbsp;8. Longitudinal stability.
-§&nbsp;9. Transverse stability. §&nbsp;10. The dihedral angle.
-§&nbsp;11. Different forms of the latter. §&nbsp;12. The "upturned"
-tip. §&nbsp;13. The most efficient section.</td>
+further considerations. §&nbsp;8. Longitudinal stability.
+§&nbsp;9. Transverse stability. §&nbsp;10. The dihedral angle.
+§&nbsp;11. Different forms of the latter. §&nbsp;12. The "upturned"
+tip. §&nbsp;13. The most efficient section.</td>
 <td class="tocpag">13</td>
 </tr><tr>
 <td colspan="2" class="tocnum"><a href="#CHAPTER_IV">CHAPTER IV.</a></td>
@@ -330,54 +291,54 @@ tip. §&nbsp;13. The most efficient section.</td>
 </tr><tr>
 <td colspan="2" class="tocsec"><span class="smcap"><a href="#Section_I">Section I.</a>&mdash;Rubber Motors.</span></td>
 </tr><tr>
-<td class="toctxt">§&nbsp;1. Some experiments with rubber cord. §&nbsp;2. Its extension
-under various weights. §&nbsp;3. The laws of elongation
-(stretching)&mdash;Permanent set. §&nbsp;4. Effects of elongation
-on its volume. §&nbsp;5. "Stretched-twisted" rubber cord&mdash;Torque
+<td class="toctxt">§&nbsp;1. Some experiments with rubber cord. §&nbsp;2. Its extension
+under various weights. §&nbsp;3. The laws of elongation
+(stretching)&mdash;Permanent set. §&nbsp;4. Effects of elongation
+on its volume. §&nbsp;5. "Stretched-twisted" rubber cord&mdash;Torque
 experiments with rubber strands of varying length
-and number. §&nbsp;6. Results plotted as graphs&mdash;Deductions&mdash;Various
+and number. §&nbsp;6. Results plotted as graphs&mdash;Deductions&mdash;Various
 relations&mdash;How to obtain the most efficient
 results&mdash;Relations between the torque and the number of
 strands, and between the length of the strands and their
-number. §&nbsp;7. Analogy between rubber and "spring"
-motors&mdash;Where it fails to hold. §&nbsp;8. Some further practical
-deductions. §&nbsp;9. The number of revolutions that
-can be given to rubber motors. §&nbsp;10. The maximum
-number of turns. §&nbsp;11. "Lubricants" for rubber. §&nbsp;12.
-Action of copper upon rubber. §&nbsp;12<span class="smcap">A</span>. Action of water, etc.
-§&nbsp;12<span class="smcap">B</span>. How to preserve rubber. §&nbsp;13. To test rubber.
-§&nbsp;14. The shape of the section. §&nbsp;15. Size of section.
-§&nbsp;16. Geared rubber motors. §&nbsp;17. The only system worth
-consideration&mdash;Its practical difficulties. §&nbsp;18. Its advantages. </td>
+number. §&nbsp;7. Analogy between rubber and "spring"
+motors&mdash;Where it fails to hold. §&nbsp;8. Some further practical
+deductions. §&nbsp;9. The number of revolutions that
+can be given to rubber motors. §&nbsp;10. The maximum
+number of turns. §&nbsp;11. "Lubricants" for rubber. §&nbsp;12.
+Action of copper upon rubber. §&nbsp;12<span class="smcap">A</span>. Action of water, etc.
+§&nbsp;12<span class="smcap">B</span>. How to preserve rubber. §&nbsp;13. To test rubber.
+§&nbsp;14. The shape of the section. §&nbsp;15. Size of section.
+§&nbsp;16. Geared rubber motors. §&nbsp;17. The only system worth
+consideration&mdash;Its practical difficulties. §&nbsp;18. Its advantages. </td>
 <td class="tocpag">24</td>
 </tr><tr>
 <td colspan="2" class="tocsec"><span class="smcap"><a href="#Section_II">Section II.</a>&mdash;Other Forms of Motors.</span></td>
 </tr><tr>
-<td class="toctxt">§&nbsp;18<span class="smcap">A</span>. <i>Spring motors</i>; their inferiority to rubber. §&nbsp;18<span class="smcap">B</span>. The
-most efficient form of spring motor. §&nbsp;18<span class="smcap">C</span>. <i>Compressed air
-motors</i>&mdash;A fascinating form of motor, "on paper." §&nbsp;18<span class="smcap">D</span>.
+<td class="toctxt">§&nbsp;18<span class="smcap">A</span>. <i>Spring motors</i>; their inferiority to rubber. §&nbsp;18<span class="smcap">B</span>. The
+most efficient form of spring motor. §&nbsp;18<span class="smcap">C</span>. <i>Compressed air
+motors</i>&mdash;A fascinating form of motor, "on paper." §&nbsp;18<span class="smcap">D</span>.
 The pneumatic drill&mdash;Application to a model aeroplane&mdash;Length
-<span class="pagenum"><a name="Page_ix" id="Page_ix">[ix]</a></span>of possible flight. §&nbsp;18<span class="smcap">E</span>. The pressure in motor-car
-tyres. §&nbsp;19. Hargraves' compressed air models&mdash;The best
-results compared with rubber motors. §&nbsp;20. The effect of
+<span class="pagenum"><a name="Page_ix" id="Page_ix">[ix]</a></span>of possible flight. §&nbsp;18<span class="smcap">E</span>. The pressure in motor-car
+tyres. §&nbsp;19. Hargraves' compressed air models&mdash;The best
+results compared with rubber motors. §&nbsp;20. The effect of
 heating the air in its passage from the reservoir to the
 motor&mdash;The great gain in efficiency thereby attained&mdash;Liquid
 air&mdash;Practical drawbacks to the compressed-air
-motor. §&nbsp;21. Reducing valves&mdash;Lowest working pressure.
-§&nbsp;22. The inferiority of this motor compared with the
-steam engine. §&nbsp;22<span class="smcap">A</span>. Tatin's air-compressed motor.
-§&nbsp;23. <i>Steam engine</i>&mdash;Steam engine model&mdash;Professor
+motor. §&nbsp;21. Reducing valves&mdash;Lowest working pressure.
+§&nbsp;22. The inferiority of this motor compared with the
+steam engine. §&nbsp;22<span class="smcap">A</span>. Tatin's air-compressed motor.
+§&nbsp;23. <i>Steam engine</i>&mdash;Steam engine model&mdash;Professor
 Langley's models&mdash;His experiment with various forms of
-motive power&mdash;Conclusions arrived at. §&nbsp;24. His steam
+motive power&mdash;Conclusions arrived at. §&nbsp;24. His steam
 engine models&mdash;Difficulties and failures&mdash;and final success&mdash;The
 "boiler" the great difficulty&mdash;His model described.
-§&nbsp;25. The use of spirit or some very volatile hydrocarbon
-in the place of water. §&nbsp;26. Steam turbines. §&nbsp;27.
+§&nbsp;25. The use of spirit or some very volatile hydrocarbon
+in the place of water. §&nbsp;26. Steam turbines. §&nbsp;27.
 Relation between "difficulty in construction" and the
-"size of the model." §&nbsp;28. Experiments in France. §&nbsp;29.
-<i>Petrol motors.</i>&mdash;But few successful models. §&nbsp;30. Limit
-to size. §&nbsp;31. Stanger's successful model described and
-illustrated. §&nbsp;32. One-cylinder petrol motors. §&nbsp;33. <i>Electric
+"size of the model." §&nbsp;28. Experiments in France. §&nbsp;29.
+<i>Petrol motors.</i>&mdash;But few successful models. §&nbsp;30. Limit
+to size. §&nbsp;31. Stanger's successful model described and
+illustrated. §&nbsp;32. One-cylinder petrol motors. §&nbsp;33. <i>Electric
 motors</i>.</td>
 <td class="tocpag">39</td>
 </tr><tr>
@@ -385,20 +346,20 @@ motors</i>.</td>
 </tr><tr>
 <td colspan="2" class="toctit">PROPELLERS OR SCREWS.</td>
 </tr><tr>
-<td class="toctxt">§&nbsp;1. The position of the propeller. §&nbsp;2. The number of blades.
-§&nbsp;3. Fan <i>versus</i> propeller. §&nbsp;4. The function of a propeller.
-§&nbsp;5. The pitch. §&nbsp;6. Slip. §&nbsp;7. Thrust. §&nbsp;8. Pitch coefficient
-(or ratio). §&nbsp;9. Diameter. §&nbsp;10. Theoretical pitch.
-§&nbsp;11. Uniform pitch. §&nbsp;12. How to ascertain the pitch of
-a propeller. §&nbsp;13. Hollow-faced blades. §&nbsp;14. Blade area.
-§&nbsp;15. Rate of rotation. §&nbsp;16. Shrouding. §&nbsp;17. General
-design. §&nbsp;18. The shape of the blades. §&nbsp;19. Their general
+<td class="toctxt">§&nbsp;1. The position of the propeller. §&nbsp;2. The number of blades.
+§&nbsp;3. Fan <i>versus</i> propeller. §&nbsp;4. The function of a propeller.
+§&nbsp;5. The pitch. §&nbsp;6. Slip. §&nbsp;7. Thrust. §&nbsp;8. Pitch coefficient
+(or ratio). §&nbsp;9. Diameter. §&nbsp;10. Theoretical pitch.
+§&nbsp;11. Uniform pitch. §&nbsp;12. How to ascertain the pitch of
+a propeller. §&nbsp;13. Hollow-faced blades. §&nbsp;14. Blade area.
+§&nbsp;15. Rate of rotation. §&nbsp;16. Shrouding. §&nbsp;17. General
+design. §&nbsp;18. The shape of the blades. §&nbsp;19. Their general
 contour&mdash;Propeller design&mdash;How to design a propeller.
-§&nbsp;20. Experiments with propellers&mdash;Havilland's design for
+§&nbsp;20. Experiments with propellers&mdash;Havilland's design for
 experiments&mdash;The author experiments on dynamic thrust
-and model propellers generally. §&nbsp;21. Fabric-covered
-screws. §&nbsp;22. Experiments with twin propellers. §&nbsp;23.
-The Fleming Williams propeller. §&nbsp;24. Built-up <i>v.</i> twisted
+and model propellers generally. §&nbsp;21. Fabric-covered
+screws. §&nbsp;22. Experiments with twin propellers. §&nbsp;23.
+The Fleming Williams propeller. §&nbsp;24. Built-up <i>v.</i> twisted
 wooden propellers</td>
 <td class="tocpag">52</td>
 </tr><tr>
@@ -408,25 +369,25 @@ wooden propellers</td>
 THE QUESTION OF SUSTENTATION.<br />
 THE CENTRE OF PRESSURE.</td>
 </tr><tr>
-<td class="toctxt">§&nbsp;1. The centre of pressure&mdash;Automatic stability. §&nbsp;2. Oscillations.
-§&nbsp;3. Arched surfaces and movements of the centre
-of pressure&mdash;Reversal. §&nbsp;4. The centre of gravity and the
-centre of pressure. §&nbsp;5. Camber. §&nbsp;6. Dipping front edge&mdash;Camber&mdash;The
+<td class="toctxt">§&nbsp;1. The centre of pressure&mdash;Automatic stability. §&nbsp;2. Oscillations.
+§&nbsp;3. Arched surfaces and movements of the centre
+of pressure&mdash;Reversal. §&nbsp;4. The centre of gravity and the
+centre of pressure. §&nbsp;5. Camber. §&nbsp;6. Dipping front edge&mdash;Camber&mdash;The
 angle of incidence and camber&mdash;Attitude
-of the Wright machine. §&nbsp;7. The most efficient form of
-camber. §&nbsp;8. The instability of a deeply cambered surface.
-§&nbsp;9. Aspect ratio. §&nbsp;10. Constant or varying camber.
-§&nbsp;11. Centre of pressure on arched surfaces</td>
+of the Wright machine. §&nbsp;7. The most efficient form of
+camber. §&nbsp;8. The instability of a deeply cambered surface.
+§&nbsp;9. Aspect ratio. §&nbsp;10. Constant or varying camber.
+§&nbsp;11. Centre of pressure on arched surfaces</td>
 <td class="tocpag">78</td>
 </tr><tr>
 <td colspan="2" class="tocnum"><a href="#CHAPTER_VII">CHAPTER VII.</a></td>
 </tr><tr>
 <td colspan="2" class="toctit">MATERIALS FOR AEROPLANE CONSTRUCTION.</td>
 </tr><tr>
-<td class="toctxt">§&nbsp;1. The choice strictly limited. §&nbsp;2. Bamboo. §&nbsp;3. Ash&mdash;spruce&mdash;whitewood&mdash;poplar.
-§&nbsp;4. Steel. §&nbsp;5. Umbrella
-section steel. §&nbsp;6. Steel wire. §&nbsp;7. Silk. §&nbsp;8. Aluminium
-and magnalium. §&nbsp;9. Alloys. §&nbsp;10. Sheet ebonite&mdash;Vulcanized
+<td class="toctxt">§&nbsp;1. The choice strictly limited. §&nbsp;2. Bamboo. §&nbsp;3. Ash&mdash;spruce&mdash;whitewood&mdash;poplar.
+§&nbsp;4. Steel. §&nbsp;5. Umbrella
+section steel. §&nbsp;6. Steel wire. §&nbsp;7. Silk. §&nbsp;8. Aluminium
+and magnalium. §&nbsp;9. Alloys. §&nbsp;10. Sheet ebonite&mdash;Vulcanized
 fibre&mdash;Sheet celluloid&mdash;Mica.</td>
 <td class="tocpag">86</td>
 </tr><tr>
@@ -434,16 +395,16 @@ fibre&mdash;Sheet celluloid&mdash;Mica.</td>
 </tr><tr>
 <td colspan="2" class="toctit">HINTS ON THE BUILDING OF MODEL AEROPLANES.</td>
 </tr><tr>
-<td class="toctxt">§&nbsp;1. The chief difficulty to overcome. §&nbsp;2. General design&mdash;The
-principle of continuity. §&nbsp;3. Simple monoplane. §&nbsp;4.
-Importance of soldering. §&nbsp;5. Things to avoid. §&nbsp;6. Aerofoil
-of metal&mdash;wood&mdash;or fabric. §&nbsp;7. Shape of aerofoil.
-§&nbsp;8. How to camber an aerocurve without ribs. §&nbsp;9. Flexible
-joints. §&nbsp;10. Single surfaces. §&nbsp;11. The rod or tube carrying
-the rubber motor. §&nbsp;12. Position of the rubber.
-§&nbsp;13. The position of the centre of pressure. §&nbsp;14. Elevators
-and tails. §&nbsp;15. Skids <i>versus</i> wheels&mdash;Materials for
-skids. §&nbsp;16. Shock absorbers, how to attach&mdash;Relation
+<td class="toctxt">§&nbsp;1. The chief difficulty to overcome. §&nbsp;2. General design&mdash;The
+principle of continuity. §&nbsp;3. Simple monoplane. §&nbsp;4.
+Importance of soldering. §&nbsp;5. Things to avoid. §&nbsp;6. Aerofoil
+of metal&mdash;wood&mdash;or fabric. §&nbsp;7. Shape of aerofoil.
+§&nbsp;8. How to camber an aerocurve without ribs. §&nbsp;9. Flexible
+joints. §&nbsp;10. Single surfaces. §&nbsp;11. The rod or tube carrying
+the rubber motor. §&nbsp;12. Position of the rubber.
+§&nbsp;13. The position of the centre of pressure. §&nbsp;14. Elevators
+and tails. §&nbsp;15. Skids <i>versus</i> wheels&mdash;Materials for
+skids. §&nbsp;16. Shock absorbers, how to attach&mdash;Relation
 between the "gap" and the "chord"</td>
 <td class="tocpag">93</td>
 </tr><tr>
@@ -453,39 +414,39 @@ between the "gap" and the "chord"</td>
 </tr><tr>
 <td colspan="2" class="toctit">THE STEERING OF THE MODEL.</td>
 </tr><tr>
-<td class="toctxt">§&nbsp;1. A problem of great difficulty&mdash;Effects of propeller torque.
-§&nbsp;2. How obviated. §&nbsp;3. The two-propeller solution&mdash;The
-reason why it is only a partial success. §&nbsp;4. The <i>speed</i>
-solution. §&nbsp;5. Vertical fins. §&nbsp;6. Balancing tips or ailerons.
-§&nbsp;7. Weighting. §&nbsp;8. By means of transversely canting
-the elevator. §&nbsp;9. The necessity for some form of "keel".</td>
+<td class="toctxt">§&nbsp;1. A problem of great difficulty&mdash;Effects of propeller torque.
+§&nbsp;2. How obviated. §&nbsp;3. The two-propeller solution&mdash;The
+reason why it is only a partial success. §&nbsp;4. The <i>speed</i>
+solution. §&nbsp;5. Vertical fins. §&nbsp;6. Balancing tips or ailerons.
+§&nbsp;7. Weighting. §&nbsp;8. By means of transversely canting
+the elevator. §&nbsp;9. The necessity for some form of "keel".</td>
 <td class="tocpag">105</td>
 </tr><tr>
 <td colspan="2" class="tocnum"><a href="#CHAPTER_X">CHAPTER X.</a></td>
 </tr><tr>
 <td colspan="2" class="toctit">THE LAUNCHING OF THE MODEL.</td>
 </tr><tr>
-<td class="toctxt">§&nbsp;1. The direction in which to launch them. §&nbsp;2. The velocity&mdash;wooden
+<td class="toctxt">§&nbsp;1. The direction in which to launch them. §&nbsp;2. The velocity&mdash;wooden
 aerofoils and fabric-covered aerofoils&mdash;Poynter's
-launching apparatus. §&nbsp;3. The launching of very light
-models. §&nbsp;4. Large size and power-driven models. §&nbsp;5.
+launching apparatus. §&nbsp;3. The launching of very light
+models. §&nbsp;4. Large size and power-driven models. §&nbsp;5.
 Models designed to rise from the ground&mdash;Paulhan's prize
-model. §&nbsp;6. The setting of the elevator. §&nbsp;7. The most
-suitable propeller for this form of model. §&nbsp;8. Professor
-Kress' method of launching. §&nbsp;9. How to launch a twin
-screw model. §&nbsp;10. A prior revolution of the propellers.
-§&nbsp;11. The best angle at which to launch a model</td>
+model. §&nbsp;6. The setting of the elevator. §&nbsp;7. The most
+suitable propeller for this form of model. §&nbsp;8. Professor
+Kress' method of launching. §&nbsp;9. How to launch a twin
+screw model. §&nbsp;10. A prior revolution of the propellers.
+§&nbsp;11. The best angle at which to launch a model</td>
 <td class="tocpag">109</td>
 </tr><tr>
 <td colspan="2" class="tocnum"><a href="#CHAPTER_XI">CHAPTER XI.</a></td>
 </tr><tr>
 <td colspan="2" class="toctit">HELICOPTER MODELS.</td>
 </tr><tr>
-<td class="toctxt">§&nbsp;1. Models quite easy to make. §&nbsp;2. Sir George Cayley's helicopter
-model. §&nbsp;3. Phillips' successful power-driven model.
-§&nbsp;4. Toy helicopters. §&nbsp;5. Incorrect and correct way of
-arranging the propellers. §&nbsp;6. Fabric covered screws. §&nbsp;7.
-A design to obviate weight. §&nbsp;8. The question of a fin or
+<td class="toctxt">§&nbsp;1. Models quite easy to make. §&nbsp;2. Sir George Cayley's helicopter
+model. §&nbsp;3. Phillips' successful power-driven model.
+§&nbsp;4. Toy helicopters. §&nbsp;5. Incorrect and correct way of
+arranging the propellers. §&nbsp;6. Fabric covered screws. §&nbsp;7.
+A design to obviate weight. §&nbsp;8. The question of a fin or
 keel.</td>
 <td class="tocpag">113</td>
 </tr><tr>
@@ -499,40 +460,40 @@ keel.</td>
 </tr><tr>
 <td colspan="2" class="toctit">MODEL FLYING COMPETITIONS.</td>
 </tr><tr>
-<td class="toctxt">§&nbsp;1. A few general details concerning such. §&nbsp;2. Aero Models
-Association's classification, etc. §&nbsp;3. Various points to be
+<td class="toctxt">§&nbsp;1. A few general details concerning such. §&nbsp;2. Aero Models
+Association's classification, etc. §&nbsp;3. Various points to be
 kept in mind when competing.</td>
 <td class="tocpag">119</td>
 </tr><tr>
 <td colspan="2" class="tocnum"><a href="#CHAPTER_XIV">CHAPTER XIV.</a></td>
 </tr><tr>
-<td colspan="2" class="toctit">USEFUL NOTES, TABLES, FORMULÆ, ETC.</td>
+<td colspan="2" class="toctit">USEFUL NOTES, TABLES, FORMULÆ, ETC.</td>
 </tr><tr>
-<td class="toctxt">§&nbsp;1. Comparative velocities. §&nbsp;2. Conversions. §&nbsp;3. Areas of
-various shaped surfaces. §&nbsp;4. French and English measures.
-§&nbsp;5. Useful data. §&nbsp;6. Table of equivalent inclinations.
-§&nbsp;7. Table of skin friction. §&nbsp;8. Table I. (metals). §&nbsp;9.
-Table II. (wind pressures). §&nbsp;10. Wind pressure on various
-shaped bodies. §&nbsp;11. Table III. (lift and drift) on a
-cambered surface. §&nbsp;12. Table IV. (lift and drift)&mdash;On a
-plane aerofoil&mdash;Deductions. §&nbsp;13. Table V. (timber). §&nbsp;14.
-Formula connecting weight lifted and velocity. §&nbsp;15.
+<td class="toctxt">§&nbsp;1. Comparative velocities. §&nbsp;2. Conversions. §&nbsp;3. Areas of
+various shaped surfaces. §&nbsp;4. French and English measures.
+§&nbsp;5. Useful data. §&nbsp;6. Table of equivalent inclinations.
+§&nbsp;7. Table of skin friction. §&nbsp;8. Table I. (metals). §&nbsp;9.
+Table II. (wind pressures). §&nbsp;10. Wind pressure on various
+shaped bodies. §&nbsp;11. Table III. (lift and drift) on a
+cambered surface. §&nbsp;12. Table IV. (lift and drift)&mdash;On a
+plane aerofoil&mdash;Deductions. §&nbsp;13. Table V. (timber). §&nbsp;14.
+Formula connecting weight lifted and velocity. §&nbsp;15.
 Formula connecting models of similar design but different
-weights. §&nbsp;16. Formula connecting power and speed. §&nbsp;17.
-Propeller thrust. §&nbsp;18. To determine experimentally the
-static thrust of a propeller. §&nbsp;19. Horse-power and the
-number of revolutions. §&nbsp;20. To compare one model with
-another. §&nbsp;21. Work done by a clockwork spring motor.
-§&nbsp;22. To ascertain the horse-power of a rubber motor.
-§&nbsp;23. Foot-pounds of energy in a given weight of rubber&mdash;Experimental
-determination of. §&nbsp;24. Theoretical length
-of flight. §&nbsp;25. To test different motors. §&nbsp;26. Efficiency
-of a model. §&nbsp;27. Efficiency of design. §&nbsp;28. Naphtha
-engines. §&nbsp;29. Horse-power and weight of model petrol
-motors. §&nbsp;30. Formula for rating the same. §&nbsp;30<span class="smcap">A</span>. Relation
+weights. §&nbsp;16. Formula connecting power and speed. §&nbsp;17.
+Propeller thrust. §&nbsp;18. To determine experimentally the
+static thrust of a propeller. §&nbsp;19. Horse-power and the
+number of revolutions. §&nbsp;20. To compare one model with
+another. §&nbsp;21. Work done by a clockwork spring motor.
+§&nbsp;22. To ascertain the horse-power of a rubber motor.
+§&nbsp;23. Foot-pounds of energy in a given weight of rubber&mdash;Experimental
+determination of. §&nbsp;24. Theoretical length
+of flight. §&nbsp;25. To test different motors. §&nbsp;26. Efficiency
+of a model. §&nbsp;27. Efficiency of design. §&nbsp;28. Naphtha
+engines. §&nbsp;29. Horse-power and weight of model petrol
+motors. §&nbsp;30. Formula for rating the same. §&nbsp;30<span class="smcap">A</span>. Relation
 between static thrust of propeller and total weight of
-model. §&nbsp;31. How to find the height of an inaccessible
-object (kite, balloon, etc.). §&nbsp;32. Formula for I.H.P. of
+model. §&nbsp;31. How to find the height of an inaccessible
+object (kite, balloon, etc.). §&nbsp;32. Formula for I.H.P. of
 model steam engines.</td>
 <td class="tocpag">125</td>
 </tr><tr>
@@ -684,7 +645,7 @@ which cause (by being tilted or dipped) the aeroplane to rise or fall
 <h2><a name="INTRODUCTION" id="INTRODUCTION"></a>INTRODUCTION.</h2>
 
 
-<p>§ 1. Model Aeroplanes are primarily divided into two
+<p>§ 1. Model Aeroplanes are primarily divided into two
 classes: first, models intended before all else to be ones that
 shall <i>fly</i>; secondly, <i>models</i>, using the word in its proper sense
 of full-sized machines. Herein model aeroplanes differ from
@@ -695,7 +656,7 @@ build a scale model of an "Antoinette" monoplane, <i>including
 engine</i>, it cannot be made to fly unless the scale be a
 very large one. If, for instance, you endeavoured to make
 a 1/10 scale model, your model petrol motor would be compelled
-to have eight cylinders, each 0·52 bore, and your
+to have eight cylinders, each 0·52 bore, and your
 magneto of such size as easily to pass through a ring half an
 inch in diameter. Such a model could not possibly work.<a name="FNanchor_1_1" id="FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a></p>
 
@@ -703,19 +664,19 @@ inch in diameter. Such a model could not possibly work.<a name="FNanchor_1_1" id
 1910, some really very fine working drawings of a prize-winning
 Antoinette monoplane model.</p></blockquote><p><span class="pagenum"><a name="Page_2" id="Page_2">[2]</a></span></p>
 
-<p>§ 2. Again, although the motor constitutes the <i>chief</i>, it
+<p>§ 2. Again, although the motor constitutes the <i>chief</i>, it
 is by no means the sole difficulty in <i>scale</i> model aeroplane
 building. To reproduce to scale at <i>scale weight</i>, or indeed
 anything approaching it, <i>all</i> the <i>necessary</i>&mdash;in the case of a
 full-sized machine&mdash;framework is not possible in a less than
 1/5 scale.</p>
 
-<p>§ 3. Special difficulties occur in the case of any prototype
-taken. For instance, in the case of model Blériots it is
+<p>§ 3. Special difficulties occur in the case of any prototype
+taken. For instance, in the case of model Blériots it is
 extremely difficult to get the centre of gravity sufficiently
 forward.</p>
 
-<p>§ 4. Scale models of actual flying machines <i>that will fly</i>
+<p>§ 4. Scale models of actual flying machines <i>that will fly</i>
 mean models <i>at least</i> 10 or 12 feet across, and every other
 dimension in like proportion; and it must always be carefully
 borne in mind that the smaller the scale the greater
@@ -723,7 +684,7 @@ the difficulties, but not in the same proportion&mdash;it would
 not be <i>twice</i> as difficult to build a &frac14;-in. scale model as a
 &frac12;-in., but <i>four</i>, <i>five</i> or <i>six</i> times as difficult.</p>
 
-<p>§ 5. Now, the <i>first</i> requirement of a model aeroplane, or
+<p>§ 5. Now, the <i>first</i> requirement of a model aeroplane, or
 flying machine, is that it shall <span class="smcap">FLY</span>.</p>
 
 <p>As will be seen later on&mdash;unless the machine be of large
@@ -733,7 +694,7 @@ be efficient requires to be long, and is of practically uniform
 weight throughout; this alone alters the entire <i>distribution
 of weight</i> on the machine and makes:</p>
 
-<p>§ 6. "<b>Model Aeroplaning an Art in itself</b>," and
+<p>§ 6. "<b>Model Aeroplaning an Art in itself</b>," and
 as such we propose to consider it in the following pages.</p>
 
 <p>We have said that the first requisite of a model aeroplane
@@ -745,7 +706,7 @@ what is required is a machine in which minute detail is of<span class="pagenum">
 secondary importance, but which does along its main lines
 "<i>approximate</i> to the real thing."</p>
 
-<p>§ 7. Simplicity should be the first thing aimed at&mdash;simplicity
+<p>§ 7. Simplicity should be the first thing aimed at&mdash;simplicity
 means efficiency, it means it in full-sized machines,
 still more does it mean it in models&mdash;and this very question
 of simplicity brings us to that most important question of
@@ -762,7 +723,7 @@ all, namely, the question of <i>weight</i>.</p>
 <h2>THE QUESTION OF WEIGHT.</h2>
 
 
-<p>§ 1. The following is an extract from a letter that
+<p>§ 1. The following is an extract from a letter that
 appeared in the correspondence columns of "The Aero."<a name="FNanchor_2_2" id="FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a></p>
 
 <blockquote><p>"To give you some idea how slight a thing will make a
@@ -777,7 +738,7 @@ under the strain of the rubber, put light silk on the planes,
 and use an aluminium<a name="FNanchor_4_4" id="FNanchor_4_4"></a><a href="#Footnote_4_4" class="fnanchor">[4]</a> propeller. The result will surpass
 all expectations."</p></blockquote>
 
-<p>§ 2. The above refers, of course, to a rubber-motor
+<p>§ 2. The above refers, of course, to a rubber-motor
 driven model. Let us turn to a steam-driven prototype. I
 take the best known example of all, Professor Langley's
 famous model. Here is what the professor has to say on
@@ -799,7 +760,7 @@ getting all the parts of the right strength and proportion."</p></blockquote>
 minimum of weight is one of the, if not the most, difficult
 problems which the student has to solve.</p>
 
-<p>§ 3. The theoretical reason why <i>weight</i> is such an all-important
+<p>§ 3. The theoretical reason why <i>weight</i> is such an all-important
 item in model aeroplaning, much more so than in
 the case of full-size machines, is that, generally speaking,
 such models do not fly fast enough to possess a high weight
@@ -821,7 +782,7 @@ rate of 37 ft. per second, or 25 miles an hour.</p>
 <p>The velocity of the former, therefore, would certainly not
 be less than 30 miles an hour.</p>
 
-<p>§ 4. Generally speaking, however, models do not travel
+<p>§ 4. Generally speaking, however, models do not travel
 at anything like this velocity, or carry anything like this
 weight per sq. ft.<span class="pagenum"><a name="Page_6" id="Page_6">[6]</a></span></p>
 
@@ -846,7 +807,7 @@ and noting (in writing) the weight and result of every
 trial and every experiment in the alteration and change of
 material used. <span class="smcap">Weigh everything.</span></p>
 
-<p>§ 5. The reader must not be misled by what has been said,
+<p>§ 5. The reader must not be misled by what has been said,
 and think that a model must not weigh anything if it is to
 fly well. A heavy model will fly much better against the
 wind than a light one, provided that the former <i>will</i> fly.
@@ -867,7 +828,7 @@ we will now consider.</p>
 <h2>THE QUESTION OF RESISTANCE.</h2>
 
 
-<p>§ 1. It is, or should be, the function of an aeroplane&mdash;model
+<p>§ 1. It is, or should be, the function of an aeroplane&mdash;model
 or otherwise&mdash;to pass through the medium in which
 it travels in such a manner as to leave that medium in as
 motionless a state as possible, since all motion of the surrounding
@@ -877,10 +838,10 @@ air represents so much power wasted.</p>
 to move through the air with the minimum of disturbance
 and resistance.</p>
 
-<p>§ 2. The resistance, considered as a percentage of the
+<p>§ 2. The resistance, considered as a percentage of the
 load itself, that has to be overcome in moving a load from
 one place to another, is, according to Mr. F.W. Lanchester,
-12&frac12; per cent. in the case of a flying machine, and 0·1 per
+12&frac12; per cent. in the case of a flying machine, and 0·1 per
 cent. in the case of a cargo boat, and of a solid tyre motor
 car 3 per cent., a locomotive 1 per cent. Four times at
 least the resistance in the case of aerial locomotion has to be
@@ -888,7 +849,7 @@ overcome to that obtained from ordinary locomotion on
 land. The above refer, of course, to full-sized machines; for
 a model the resistance is probably nearer 14 or 15 per cent.</p>
 
-<p>§ 3. This resistance is made up of&mdash;</p>
+<p>§ 3. This resistance is made up of&mdash;</p>
 
 <ul><li>1. Aerodynamic resistance.</li>
 <li>2. Head resistance.</li>
@@ -909,7 +870,7 @@ be used, so that the resultant stream-line flow of the
 medium shall keep in touch with the surface of the
 body.</p>
 
-<p>§ 4. As long ago as 1894 a series of experiments were
+<p>§ 4. As long ago as 1894 a series of experiments were
 made by the writer<a name="FNanchor_6_6" id="FNanchor_6_6"></a><a href="#Footnote_6_6" class="fnanchor">[6]</a> to solve the following problem: given
 a certain length and breadth, to find the shape which will
 offer the least resistance. The experiments were made with
@@ -964,7 +925,7 @@ the long steel vertical mast extending both upwards and
 downwards through the centre would render it suitable only
 for landing on water.</p>
 
-<p>§ 5. In the case of a rubber-driven model, there is no
+<p>§ 5. In the case of a rubber-driven model, there is no
 containing body part, so to speak, a long thin stick, or
 tubular construction if preferred, being all that is necessary.</p>
 
@@ -978,7 +939,7 @@ especially longitudinally. If the model be a biplane, then
 all the upright struts between the two aerofoils should be
 given a shape, a vertical section of which is shown in Fig. 3.</p>
 
-<p>§ 6. In considering this question of resistance, the
+<p>§ 6. In considering this question of resistance, the
 substance of which the aerofoil surface is made plays a very
 important part, as well as whether that surface be plane or
 curved. For some reason not altogether easy to determine,
@@ -1008,22 +969,22 @@ considering the aerofoil proper.</p>
 (enlarged.)</span></span>
 </div>
 
-<p>§ 7. Allusion has been made in this chapter to skin
+<p>§ 7. Allusion has been made in this chapter to skin
 friction, but no value given for its coefficient.<a name="FNanchor_8_8" id="FNanchor_8_8"></a><a href="#Footnote_8_8" class="fnanchor">[8]</a> Lanchester's
 value for planes from &frac12; to l&frac12; sq. ft. in area, moving about
 20 to 30 ft. per second, is</p>
 
 <p class="cen">
-0·009 to 0·015.
+0·009 to 0·015.
 </p>
 
-<p>Professor Zahm (Washington) gives 0·0026 lb. per
-sq. ft. at 25 ft. per second, and at 37 ft. per second, 0·005,
+<p>Professor Zahm (Washington) gives 0·0026 lb. per
+sq. ft. at 25 ft. per second, and at 37 ft. per second, 0·005,
 and the formula</p>
 
 <p class="cen">
 <ins class="mycorr" title="Correction: See Transcriber's Note at end of text">
-<i>f</i> = 0·00000778<i>l</i><sup>&nbsp;·93</sup><i>v</i><sup>1·85</sup></ins>
+<i>f</i> = 0·00000778<i>l</i><sup>&nbsp;·93</sup><i>v</i><sup>1·85</sup></ins>
 </p>
 
 <p class="noin"><i>f</i> being the average friction in lb. per sq. in., <i>l</i> the length in
@@ -1033,10 +994,10 @@ smooth, etc.</p>
 
 <p>His conclusion is:&mdash;"All even surfaces have approximately
 the same coefficient of skin friction. Uneven surfaces
-have a greater coefficient." All formulæ on skin friction
+have a greater coefficient." All formulæ on skin friction
 must at present be accepted with reserve.<span class="pagenum"><a name="Page_12" id="Page_12">[12]</a></span></p>
 
-<p>§ 8. The following three experiments, however, clearly
+<p>§ 8. The following three experiments, however, clearly
 prove its <i>existence</i>, and <i>that it has considerable effect</i>:&mdash;</p>
 
 <p>1. A light, hollow celluloid ball, supported on a stream
@@ -1066,14 +1027,14 @@ below, and the drop will be about 8 ft. (Prof. Tait.)</p>
 <h2>THE QUESTION OF BALANCE.</h2>
 
 
-<p>§ 1. It is perfectly obvious for successful flight that any
+<p>§ 1. It is perfectly obvious for successful flight that any
 model flying machine (in the absence of a pilot) must
 possess a high degree of automatic stability. The model
 must be so constructed as to be naturally stable, <i>in the
 medium through which it is proposed to drive it</i>. The last
 remark is of the greatest importance, as we shall see.</p>
 
-<p>§ 2. In connexion with this same question of automatic
+<p>§ 2. In connexion with this same question of automatic
 stability, the question must be considered from the theoretical
 as well as from the practical side, and the labours and
 researches of such men as Professors Brian and Chatley,
@@ -1144,7 +1105,7 @@ behind the centre of gravity.</p>
 is greatest when the kinetic energy is a maximum. (Illustration,
 the pendulum.)</p>
 
-<p>§ 3. Referring to A. Models with a plane or flat surface
+<p>§ 3. Referring to A. Models with a plane or flat surface
 are not unstable, and will fly well without a tail; such a
 machine is called a simple monoplane.</p>
 
@@ -1155,7 +1116,7 @@ Showing balance weight A (movable), and also his winding-up
 gear&mdash;a very handy device.</span>
 </div>
 
-<p>§ 4. Referring to D. Many model builders make this
+<p>§ 4. Referring to D. Many model builders make this
 mistake, i.e., the mistake of getting as low a centre of
 gravity as possible under the quite erroneous idea that
 they are thereby increasing the stability of the machine.
@@ -1180,7 +1141,7 @@ couple tending to upset the machine.</p>
 <span class="caption"><span class="smcap">Fig. 5.&mdash;The Stringfellow Model Monoplane of 1848.</span></span>
 </div>
 
-<p>§ 5. Referring to E. If the propulsive action does not
+<p>§ 5. Referring to E. If the propulsive action does not
 pass through the centre of gravity the system again becomes
 "acentric." Even supposing condition D fulfilled, and we
 arrive at the following most important result, viz., that for
@@ -1196,7 +1157,7 @@ same point.</span></p>
 <span class="caption"><span class="smcap">Fig. 6.&mdash;The Stringfellow Model Triplane of 1868.</span></span>
 </div>
 
-<p>§ 6. Referring to F and N&mdash;the problem of longitudinal
+<p>§ 6. Referring to F and N&mdash;the problem of longitudinal
 stability. There is one absolutely essential feature
 not mentioned in F or N, and that is for automatic
 longitudinal stability <i>the two surfaces, the aerofoil proper and
@@ -1206,17 +1167,17 @@ the width of the main aerofoil</i>.<a name="FNanchor_9_9" id="FNanchor_9_9"></a>
 
 <div class="figcenter">
 <img src="images/i_033b.jpg" width="320" height="188" alt="" title="" /><br />
-<span class="caption"><span class="smcap">Fig. 7. PÉNAUD 1871</span></span>
+<span class="caption"><span class="smcap">Fig. 7. PÉNAUD 1871</span></span>
 </div>
 
-<p>§ 7. With one exception (Pénaud) early experimenters
+<p>§ 7. With one exception (Pénaud) early experimenters
 with model aeroplanes had not grasped this all-important
 fact, and their models would not fly, only make a series of
 jumps, because they failed to balance longitudinally. In<span class="pagenum"><a name="Page_18" id="Page_18">[18]</a></span>
 Stringfellow's and Tatin's models the main aerofoil and
 balancer (tail) are practically contiguous.</p>
 
-<p>Pénaud in his rubber-motored models appears to have
+<p>Pénaud in his rubber-motored models appears to have
 fully realised this (<i>vide</i> Fig. 7), and also the necessity for
 using long strands of rubber. Some of his models flew
 150 ft., and showed considerable stability.</p>
@@ -1224,9 +1185,9 @@ using long strands of rubber. Some of his models flew
 <div class="figcenter">
 <img src="images/i_034.jpg" width="320" height="158" alt="" title="" /><br />
 <span class="caption"><span class="smcap">Fig. 8.&mdash;Tatin's Aeroplane (1879).</span><br />
-Surface 0·7 sq. metres, total weight 1·75 kilogrammes,
+Surface 0·7 sq. metres, total weight 1·75 kilogrammes,
 velocity of sustentation 8 metres a second. Motor,
-compressed air (for description see §&nbsp;23, ch. iv). Revolved
+compressed air (for description see §&nbsp;23, ch. iv). Revolved
 round and round a track tethered to a post at the
 centre. In one of its jumps it cleared the head of a
 spectator.</span>
@@ -1282,7 +1243,7 @@ flights were obtained. Constructed of bamboo and
 nainsook. Stayed with steel wire.</span>
 </div>
 
-<p>§ 8. Referring to I. This, again, is of primary importance
+<p>§ 8. Referring to I. This, again, is of primary importance
 in longitudinal stability. The Farman machine has three
 such planes&mdash;elevator, main aerofoil, tail the Wright originally
 had <i>not</i>, but is now being fitted with a tail, and experiments
@@ -1296,7 +1257,7 @@ experiments with vertical fins, and has found the machine
 very stable, even when the fin or vertical keel is placed some
 distance above the centre of gravity.</p>
 
-<p>§ 9. The question of transverse (side to side) stability
+<p>§ 9. The question of transverse (side to side) stability
 at once brings us to the question of the dihedral angle,
 practically similar in its action to a flat plane with vertical
 fins.</p>
@@ -1308,7 +1269,7 @@ Eight feathers, two corks, a thin rod, a piece of whalebone,
 and a piece of thread.</span>
 </div>
 
-<p>§ 10. The setting up of the front surface at an angle to
+<p>§ 10. The setting up of the front surface at an angle to
 the rear, or the setting of these at corresponding compensatory
 angles already dealt with, is nothing more nor less than
 the principle of the dihedral angle for longitudinal stability.</p>
@@ -1326,7 +1287,7 @@ heeling over, the side which is required to rise gains resistance
 by its new position, and that which is required to sink
 loses it.</p>
 
-<p>§ 11. The dihedral angle principle may take many forms.</p>
+<p>§ 11. The dihedral angle principle may take many forms.</p>
 
 <p>As in Fig. 12 <i>a</i> is a monoplane, the rest biplanes. The
 angles and curves are somewhat exaggerated. It is quite
@@ -1347,14 +1308,14 @@ efficient for sustentation and equilibrium combined.</p>
 surface of an aeroplane is greater at the outer edge than
 elsewhere, owing to the greater lever arm.</p>
 
-<p>§ 12. The "upturned tip" dihedral certainly appears to
+<p>§ 12. The "upturned tip" dihedral certainly appears to
 have the advantage.</p>
 
 <p><i>The outer edges of the aerofoil then should be turned
 upward for the purpose of transverse stability, while the inner
 surface should remain flat or concave for greater support.</i></p>
 
-<p>§ 13. The exact most favourable outline of transverse
+<p>§ 13. The exact most favourable outline of transverse
 section for stability, steadiness and buoyancy has not yet
 been found; but the writer has found the section given in
 Fig. 13, a very efficient one.</p>
@@ -1371,7 +1332,7 @@ Fig. 13, a very efficient one.</p>
 
 <p class="cen"><span class="smcap"><a name="Section_I" id="Section_I"></a>Section I.&mdash;Rubber Motors.</span></p>
 
-<p>§ 1. Some forty years have elapsed since Pénaud first used
+<p>§ 1. Some forty years have elapsed since Pénaud first used
 elastic (rubber) for model aeroplanes, and during that time
 no better substitute (in spite of innumerable experiments)
 has been found. Nor for the smaller and lighter class of
@@ -1387,7 +1348,7 @@ stretched, or both) without either fracture or a <span class="smcap">Large</span
 alteration of shape is very small. Not so rubber&mdash;it
 far surpasses in this respect even steel springs.</p>
 
-<p>§ 2. Let us take a piece of elastic (rubber) cord, and
+<p>§ 2. Let us take a piece of elastic (rubber) cord, and
 stretch it with known weights and observe carefully what
 happens. We shall find that, first of all: <i>the extension is
 proportional to the weight suspended</i>&mdash;but soon we have an
@@ -1404,7 +1365,7 @@ Suspended weights, 1 oz.
 up to 64 oz. Extension
 from &frac14; inch up to 24-5/8
 inches. Graph drawn in
-Fig. 14, No. B abscissæ
+Fig. 14, No. B abscissæ
 extension in eighths of
 an inch, ordinates
 weights in ounces. So
@@ -1445,7 +1406,7 @@ efficiency falls off, but with care not nearly so quickly as is
 commonly supposed, but in spite of this and other drawbacks
 its advantages far more than counterbalance these.</p>
 
-<p>§ 3. Experimenting with cords of varying thickness we
+<p>§ 3. Experimenting with cords of varying thickness we
 find that: <i>the extension is inversely proportional to the thickness</i>.
 If we leave a weight hanging on a piece of rubber
 cord (stretched, of course, beyond its "elastic limit") we
@@ -1475,7 +1436,7 @@ elasticity.</p>
 <span class="caption"><span class="smcap">Fig. 15.&mdash;Extension and Increase in Volume.</span></span>
 </div>
 
-<p>§ 4. <b>When a Rubber Cord is stretched there is
+<p>§ 4. <b>When a Rubber Cord is stretched there is
 an Increase of Volume.</b>&mdash;On stretching a piece of<span class="pagenum"><a name="Page_27" id="Page_27">[27]</a></span>
 rubber cord to <i>twice</i> its original (natural) length, we should
 perhaps expect to find that the string would only be <i>half</i> as
@@ -1485,7 +1446,7 @@ as accurately as possible with a micrometer, measuring to the<span class="pagenu
 one-thousandth of an inch, we at once perceive that this is
 not the case, being about <i>two-thirds</i> of its former volume.</p>
 
-<p>§ 5. In the case of rubber cord used for a motive power
+<p>§ 5. In the case of rubber cord used for a motive power
 on model aeroplanes, the rubber is <i>both</i> twisted and stretched,
 but chiefly the latter.</p>
 
@@ -1504,7 +1465,7 @@ case) from an arm 5 in. in length.</p>
 <p>The following are the principal results arrived at. For
 graphs, see Fig. 16.</p>
 
-<p>§ 6. A. Increasing the number of (rubber) strands by
+<p>§ 6. A. Increasing the number of (rubber) strands by
 <i>one-half</i> (length and thickness of rubber remaining constant)
 increases the torque (unwinding tendency) <i>twofold</i>, i.e.,
 doubles the motive power.</p>
@@ -1529,7 +1490,7 @@ constant) <i>diminishes</i> the number of turns by <i>one-third</i><span class="
 <img src="images/i_045.jpg" width="640" height="167" alt="" title="" />
 <div class="caption"><span class="smcap">Fig. 16.&mdash;Torque Graphs of Rubber Motors.</span>
 <table border="0" cellpadding="0" cellspacing="0" summary="">
-<tr><td align="left">Abscissæ = Turns.</td><td align="left">Ordinates = Torque measured in 1/16 of an oz. Length of arm, 5 in.</td></tr>
+<tr><td align="left">Abscissæ = Turns.</td><td align="left">Ordinates = Torque measured in 1/16 of an oz. Length of arm, 5 in.</td></tr>
 <tr><td align="left">A.</td><td align="left">38 strands of new rubber, 2 ft. 6 in. long; 58 grammes weight.</td></tr>
 <tr><td align="left">B.</td><td align="left">36 strands, 2 ft. 6 in. long; end thrust at 150 turns, 3&frac12; lb.</td></tr>
 <tr><td align="left">C.</td><td align="left">32 strands, 2 ft. 6 in. long.</td></tr>
@@ -1569,7 +1530,7 @@ number of the strands in inches</i>,<a name="FNanchor_14_14" id="FNanchor_14_14"
 strands is 12 their length should be 2 ft., if 18, 3 ft., and
 so on.</p>
 
-<p>§ 7. Experiments with 32 to 38 strands 2 ft. 6 in. long
+<p>§ 7. Experiments with 32 to 38 strands 2 ft. 6 in. long
 give a torque curve almost precisely similar to that obtained
 from experiments made with flat spiral steel springs, similar
 to those used in watches and clocks; and, as we know, the
@@ -1590,7 +1551,7 @@ i.e., to the breadth and the cube of its thickness, also proportional
 to the modulus of elasticity of the substance used,
 and inversely proportional to the length of the strip.</p>
 
-<p>§ 8. Referring back to A, B, C, there are one or two
+<p>§ 8. Referring back to A, B, C, there are one or two
 practical deductions which should be carefully noted.</p>
 
 <p>Supposing we have a model with one propeller and
@@ -1603,7 +1564,7 @@ thinking of using two propellers.</p>
 
 <p>Experiments on&mdash;</p>
 
-<p>§9. <b>The Number of Revolutions</b> (turns) <b>that can
+<p>§9. <b>The Number of Revolutions</b> (turns) <b>that can
 be given to Rubber Motors</b> led to interesting results,
 e.g., the number of turns to produce a double knot in the cord
 from end to end were, in the case of rubber, one yard long:&mdash;</p>
@@ -1625,7 +1586,7 @@ at 310, and 4 at 440 (and not at 620), 16 at 200, and 8 at
 more the strands the greater the distance they have to travel
 round themselves.</p>
 
-<p>§ 10. <b>The Maximum Number of Turns.</b>&mdash;As to
+<p>§ 10. <b>The Maximum Number of Turns.</b>&mdash;As to
 the maximum number of permissible turns, rubber has
 rupture stress of 330 lb. per sq. in., <i>but a very high permissible
 stress</i>, as much as 80 per cent. The resilience
@@ -1643,7 +1604,7 @@ more turns have been given in the case of 32-36 strands a
 yard in length; but such a severe strain soon spoils the
 rubber.</p>
 
-<p>§ 11. <b>On the Use of "Lubricants."</b>&mdash;One of the
+<p>§ 11. <b>On the Use of "Lubricants."</b>&mdash;One of the
 drawbacks to rubber is that if it be excessively strained it
 soon begins to break up. One of the chief causes of this is
 that the strands stick together&mdash;they should always be
@@ -1706,7 +1667,7 @@ the coils slip over one another freely and easily, and prevent
 the throwing of undue strain on some particular portion,
 and absolutely prevent the strands from sticking together.</p>
 
-<p>§ 12. <b>The Action of Copper upon Rubber.</b>&mdash;Copper,
+<p>§ 12. <b>The Action of Copper upon Rubber.</b>&mdash;Copper,
 whether in the form of the metal, the oxides, or the
 soluble salts, has a marked injurious action upon rubber.</p>
 
@@ -1719,7 +1680,7 @@ case should the strands be placed upon bare metal. I
 always cover mine with a piece of valve tubing, which can
 easily be renewed from time to time.</p>
 
-<p>§ 12<span class="smcap">A</span>. <b>The Action of Water, etc., on Rubber.</b>&mdash;Rubber
+<p>§ 12<span class="smcap">A</span>. <b>The Action of Water, etc., on Rubber.</b>&mdash;Rubber
 is quite insoluble in water; but it must not be
 forgotten that it will absorb about 25 per cent. into its pores
 after soaking for some time.</p>
@@ -1729,7 +1690,7 @@ carbon bi-sulphide, petroleum spirit, benzene and its homologues
 found in coal-tar naphtha, dissolve rubber readily.
 Alcohol is absorbed by rubber, but is not a solvent of it.</p>
 
-<p>§ 12B. <b>How to Preserve Rubber.</b>&mdash;In the first
+<p>§ 12B. <b>How to Preserve Rubber.</b>&mdash;In the first
 place, in order that it shall be <i>possible</i> to preserve and keep<span class="pagenum"><a name="Page_35" id="Page_35">[35]</a></span>
 rubber in the best condition of efficiency, it is absolutely
 essential that the rubber shall be, when obtained, fresh and
@@ -1737,8 +1698,8 @@ of the best kind. Only the best Para rubber should be
 bought; to obtain it fresh it should be got in as large
 quantities as possible direct from a manufacturer or reliable
 rubber shop. The composition of the best Para rubber is
-as follows:&mdash;Carbon, 87·46 per cent.; hydrogen, 12·00 per
-cent.; oxygen and ash, 0·54 per cent.</p>
+as follows:&mdash;Carbon, 87·46 per cent.; hydrogen, 12·00 per
+cent.; oxygen and ash, 0·54 per cent.</p>
 
 <p>In order to increase its elasticity the pure rubber has to
 be vulcanised before being made into the sheet some
@@ -1761,7 +1722,7 @@ It should be subjected to no tension or compression.</p>
 <p>Deteriorated rubber is absolutely useless for model
 aeroplanes.</p>
 
-<p>§ 13. <b>To Test Rubber.</b>&mdash;Good elastic thread composed
+<p>§ 13. <b>To Test Rubber.</b>&mdash;Good elastic thread composed
 of pure Para rubber and sulphur should, if properly
 made, stretch to seven times its length, and then return to
 its original length. It should also possess a stretching
@@ -1775,7 +1736,7 @@ cut. When examined under a microscope (not too powerful)
 the strands having the least ragged edge, i.e., the best cut,
 are to be preferred.</p>
 
-<p>§ 14. <b>The Section&mdash;Strip or Ribbon versus
+<p>§ 14. <b>The Section&mdash;Strip or Ribbon versus
 Square.</b>&mdash;In section the square and not the ribbon or strip
 should be used. The edge of the strip I have always found
 more ragged under the microscope than the square. I have
@@ -1784,7 +1745,7 @@ section would be best, but none such (in small sizes) is
 on the market. Models have been fitted with a tubular
 section, but such should on no account be used.</p>
 
-<p>§ 15. <b>Size of the Section.</b>&mdash;One-sixteenth or one-twelfth
+<p>§ 15. <b>Size of the Section.</b>&mdash;One-sixteenth or one-twelfth
 is the best size for ordinary models; personally, I
 prefer the thinner. If more than a certain number of
 strands are required to provide the necessary power, a larger
@@ -1793,7 +1754,7 @@ is, but fifty may probably be taken as an outside limit.
 Remember the size increases by area section; twice the
 <i>sectional</i> height and breadth means four times the rubber.</p>
 
-<p>§ 16. <b>Geared Rubber Motors.</b>&mdash;It is quite a mistake
+<p>§ 16. <b>Geared Rubber Motors.</b>&mdash;It is quite a mistake
 to suppose that any advantage can be obtained by using a
 four to one gearing, say; all that you do obtain is one-fourth
 of the power minus the increased friction, minus the added
@@ -1809,7 +1770,7 @@ have seen, you must increase the number of strands to get<span class="pagenum"><
 the same thrust, and you have this to counteract any
 advantage you gain as well as added weight and friction.</p>
 
-<p>§ 17. The writer has tried endless experiments with all
+<p>§ 17. The writer has tried endless experiments with all
 kinds of geared rubber motors, and the only one worth a
 moment's consideration is the following, viz., one in which
 two gear wheels&mdash;same size, weight, and number of teeth&mdash;are
@@ -1836,7 +1797,7 @@ attained by using solid wheels, and lightening by drilling and
 turning.</p>
 
 <p>C. The friction must be a minimum. Use the lightest
-ball bearings obtainable (these weigh only 0·3 gramme),
+ball bearings obtainable (these weigh only 0·3 gramme),
 adjust the wheels so that they run with the greatest freedom,
 but see that the teeth overlap sufficiently to stand the strain
 and slight variations in direction without fear of slipping.
@@ -1870,7 +1831,7 @@ advantage will be gained&mdash;the writer speaks from experience.
 The requisite number of rubber strands to give the
 best result must be determined by experiment.</p>
 
-<p>§ 18. One advantage in using such a motor as this is
+<p>§ 18. One advantage in using such a motor as this is
 that the two equal strands untwisting in opposite directions
 have a decided steadying effect on the model, similar almost
 to the case in which two propellers are used.</p>
@@ -1890,7 +1851,7 @@ strands to each propeller.</p>
 
 <p class="cen"><span class="smcap"><a name="Section_II" id="Section_II">Section II</a>.&mdash;Other Forms of Motors</span>.</p>
 
-<p>§ 18<span class="smcap">A</span>. <b>Spring Motors.</b>&mdash;This question has already
+<p>§ 18<span class="smcap">A</span>. <b>Spring Motors.</b>&mdash;This question has already
 been dealt with more or less whilst dealing with rubber
 motors, and the superiority of the latter over the former
 pointed out. Rubber has a much greater superiority over
@@ -1907,7 +1868,7 @@ of different distributions of weight on the model, and its
 effect on the balance of the machine; but effects such as
 this can be brought about without a change of motor.</p>
 
-<p>§ 18<span class="smcap">B</span>. A more efficient form of spring motor, doing away
+<p>§ 18<span class="smcap">B</span>. A more efficient form of spring motor, doing away
 with gearing troubles, is to use a long spiral spring (as long
 as the rubber strands) made of medium-sized piano wire,
 similar in principle to those used in some roller-blinds, but
@@ -1920,7 +1881,7 @@ rubber.</p>
 <p>The long spiral form of steel spring is, however, much
 the best.</p>
 
-<p>§ 18<span class="smcap">C</span>. <b>Compressed Air Motors.</b>&mdash;This is a very
+<p>§ 18<span class="smcap">C</span>. <b>Compressed Air Motors.</b>&mdash;This is a very
 fascinating form of motor, on paper, and appears at first sight
 the ideal form. It is so easy to write: "Its weight is negligible,
 and it can be provided free of cost; all that is necessary is
@@ -1932,7 +1893,7 @@ conveying this stored-up energy to the revolving propeller
 need weigh only a few ounces." Another writer recommends
 "a pressure of 300 lb."</p>
 
-<p>§ 18<span class="smcap">D</span>. A pneumatic drill generally works at about 80 lb.<span class="pagenum"><a name="Page_41" id="Page_41">[41]</a></span>
+<p>§ 18<span class="smcap">D</span>. A pneumatic drill generally works at about 80 lb.<span class="pagenum"><a name="Page_41" id="Page_41">[41]</a></span>
 pressure, and when developing 1 horse-power, uses about
 55 cubic ft. of free air per minute. Now if we apply this to
 a model aeroplane of average size, taking a reservoir 3 ft.
@@ -1951,20 +1912,20 @@ during which such a model would fly depends on the H.P.
 necessary for flight; but a fair allowance gives a flight of from
 10 to 30 sec. I take 80 lb. pressure as a fair practical limit.</p>
 
-<p>§ 18<span class="smcap">E</span>. The pressure in a motor-car tyre runs from 40 to
+<p>§ 18<span class="smcap">E</span>. The pressure in a motor-car tyre runs from 40 to
 80 lb., usually about 70 lb. Now 260 strokes are required
 with an ordinary inflator to obtain so low a pressure as
 70 lb., and it is no easy job, as those who have done it know.</p>
 
-<p>§ 19. Prior to 1893 Mr. Hargraves (of cellular kite fame)
+<p>§ 19. Prior to 1893 Mr. Hargraves (of cellular kite fame)
 studied the question of compressed-air motors for model
 flying machines. His motor was described as a marvel
 of simplicity and lightness, its cylinder was made like a
 common tin can, the cylinder covers cut from sheet tin
 and pressed to shape, the piston and junk rings of ebonite.</p>
 
-<p>One of his receivers was 23-3/8 in. long, and 5·5 in.
-diameter, of aluminium plate 0·2 in. thick, 3/8 in. by 1/8 in.
+<p>One of his receivers was 23-3/8 in. long, and 5·5 in.
+diameter, of aluminium plate 0·2 in. thick, 3/8 in. by 1/8 in.
 riveting strips were insufficient to make tight joints; it
 weighed 26 oz., and at 80 lb. water pressure one of the ends
 blew out, the fracture occurring at the bend of the flange,
@@ -1978,7 +1939,7 @@ ornithoptere, or wing-flapping principle.) The time of flight
 was 23 <i>seconds</i>, with 54&frac12; double vibrations of the engines.
 The efficiency of this motor was estimated to be 29 per cent.</p>
 
-<p>§ 20. By using compressed air, and heating it in its
+<p>§ 20. By using compressed air, and heating it in its
 passage to the cylinder, far greater efficiency can be obtained.
 Steel cylinders can be obtained containing air under the
 enormous pressure of 120 atmospheres.<a name="FNanchor_19_19" id="FNanchor_19_19"></a><a href="#Footnote_19_19" class="fnanchor">[19]</a> This is practically
@@ -1994,7 +1955,7 @@ range in the initial working pressure, entailing not-to-be-thought-of
 weight in the form of multi-cylinder compound
 engines, variable expansion gear, etc.</p>
 
-<p>§ 21. This means relinquishing the advantages of the
+<p>§ 21. This means relinquishing the advantages of the
 high initial pressure, and the passing of the air through a
 reducing valve, whereby a constant pressure, say, of 90 to
 150, according to circumstances, could be maintained. By
@@ -2004,7 +1965,7 @@ down to, say, 30 lb.</p>
 <p>The initial loss entailed by the use of a reducing valve
 may be in a great measure restored by heating the air before
 using it in the motor cylinders; by heating it to a temperature
-of only 320°F., by means of a suitable burner, the
+of only 320°F., by means of a suitable burner, the
 volume of air is increased by one half, the consumption<span class="pagenum"><a name="Page_43" id="Page_43">[43]</a></span>
 being reduced in the same proportion; the consumption of
 air used in this way being 24 lb. per indicated horse-power
@@ -2017,7 +1978,7 @@ reaches a limit below which it cannot usefully be employed.
 The air then remaining is dead and useless, adding only to
 the weight of the aeroplane.</p>
 
-<p>§ 22. From calculations made by the writer the <i>entire</i>
+<p>§ 22. From calculations made by the writer the <i>entire</i>
 weight of a compressed-air model motor plant would be at
 least <i>one-third</i> the weight of the aeroplane, and on a small
 scale probably one-half, and cannot therefore hold comparison
@@ -2030,14 +1991,14 @@ results obtained with infinitely less expense by means of
 rubber can be brought to pass with a bicycle pump, a bit of
 magnalium tube, and 60 lb. pressure.</p>
 
-<p>§ 22<span class="smcap">A</span>. In Tatin's air-compressed motor the reservoir
+<p>§ 22<span class="smcap">A</span>. In Tatin's air-compressed motor the reservoir
 weighed 700 grammes, and had a capacity of 8 litres. It was
 tested to withstand a pressure of 20 atmospheres, but was
 worked only up to seven. The little engine attached thereto
 weighed 300 grammes, and developed a motive power of
 2 kilogram-metres per second (<i>see</i> ch. iii.).</p>
 
-<p>§ 23. <b>Steam-Driven Motors.</b>&mdash;Several successful
+<p>§ 23. <b>Steam-Driven Motors.</b>&mdash;Several successful
 steam-engined model aeroplanes have been constructed, the
 most famous being those of Professor Langley.</p>
 
@@ -2061,7 +2022,7 @@ were made surprisingly light after sufficient experiment.
 <i>The great difficulty was to make a boiler of almost no weight
 which would give steam enough.</i></p>
 
-<p>§ 24. At last a satisfactory boiler and engine were
+<p>§ 24. At last a satisfactory boiler and engine were
 produced.</p>
 
 <p>The engine was of 1 to 1&frac12; H.P., total weight (including
@@ -2072,8 +2033,8 @@ each a diameter of 1&frac14; in., and piston stroke 2 in.</p>
 It consisted of a continuous helix of copper tubing, 3/8 in.
 external diameter, the diameter of the coil being 3 in.
 altogether. Through the centre of this was driven the blast
-from an "Ælopile," a modification of the naphtha blow-torch
-used by plumbers, the flame of which is about 2000° F.<a name="FNanchor_20_20" id="FNanchor_20_20"></a><a href="#Footnote_20_20" class="fnanchor">[20]</a>
+from an "Ælopile," a modification of the naphtha blow-torch
+used by plumbers, the flame of which is about 2000° F.<a name="FNanchor_20_20" id="FNanchor_20_20"></a><a href="#Footnote_20_20" class="fnanchor">[20]</a>
 The pressure of steam issuing into the engines varied from<span class="pagenum"><a name="Page_45" id="Page_45">[45]</a></span>
 100 to 150 lb. per sq. in.; 4 lb. weight of water and about
 10 oz. of naphtha could be carried. The boiler evaporated
@@ -2101,7 +2062,7 @@ fact the only one, being the steam generator. An economization
 of weight means a waste of steam, of which models
 can easily spend their only weight in five minutes.</p>
 
-<p>§ 25. One way to economize without increased weight in
+<p>§ 25. One way to economize without increased weight in
 the shape of a condenser is to use spirit (methylated spirit,
 for instance) for both fuel and boiler, and cause the exhaust
 from the engines to be ejected on to the burning spirit,
@@ -2110,7 +2071,7 @@ volatile hydrocarbon, instead of water, we have a further
 advantage from the fact that such vaporize at a much
 lower temperature than water.<span class="pagenum"><a name="Page_46" id="Page_46">[46]</a></span></p>
 
-<p>§ 26. When experimenting with an engine of the turbine
+<p>§ 26. When experimenting with an engine of the turbine
 type we must use a propeller of small diameter and pitch,
 owing to the very high velocity at which such engines run.</p>
 
@@ -2120,7 +2081,7 @@ highest technical skill, combined with many preliminary
 disappointments and trials, are sure to be encountered before
 success is attained.</p>
 
-<p>§ 27. And the smaller the model the more difficult the
+<p>§ 27. And the smaller the model the more difficult the
 problem&mdash;halve your aeroplane, and your difficulties increase
 anything from fourfold to tenfold.</p>
 
@@ -2130,7 +2091,7 @@ magnalium container for the spirit, and a working pressure
 of from 150 to 200 lb. per sq. in. Anything less than this
 would not be worth consideration.</p>
 
-<p>§ 28. Some ten months after Professor Langley's successful
+<p>§ 28. Some ten months after Professor Langley's successful
 model flights (1896), experiments were made in
 France at Carquenez, near Toulon. The total weight of
 the model aeroplane in this case was 70 lb.; the engine
@@ -2144,7 +2105,7 @@ maximum velocity was greater&mdash;30 to 40 miles per hour.
 The total breadth of this large model was rather more than
 6 metres, and the surface a little more than 8 sq. metres.</p>
 
-<p>§ 29. <b>Petrol Motors.</b>&mdash;Here it would appear at first
+<p>§ 29. <b>Petrol Motors.</b>&mdash;Here it would appear at first
 thought is the true solution of the problem of the model
 aeroplane motor. Such a motor has solved the problem of
 aerial locomotion, as the steam engine solved that of terres<span class="pagenum"><a name="Page_47" id="Page_47">[47]</a></span>trial
@@ -2162,7 +2123,7 @@ in the case of full sized machines, then why not models.</p>
 [Illustrations by permission from electros supplied by the &quot;Aero.&quot;]</span>
 </div>
 
-<p>§ 30. The exact size of the smallest <i>working</i> model steam
+<p>§ 30. The exact size of the smallest <i>working</i> model steam
 engine that has been made I do not know,<a name="FNanchor_22_22" id="FNanchor_22_22"></a><a href="#Footnote_22_22" class="fnanchor">[22]</a> but it is or could<span class="pagenum"><a name="Page_48" id="Page_48">[48]</a></span>
 be surprisingly small; not so the petrol motor&mdash;not one,
 that is, that would <i>work</i>. The number of petrol motor-driven
@@ -2190,7 +2151,7 @@ motor.</p>
 (<i>Illustrations by permission from electros supplied by the "Aero."</i>)
 </div></div>
 
-<p>§ 31. The following are the chief particulars of this
+<p>§ 31. The following are the chief particulars of this
 interesting machine:&mdash;The engine is a four-cylinder one,
 and weighs (complete with double carburetter and petrol tank)
 5&frac12; lb., and develops 1&frac14; H.P. at 1300 revolutions per minute.<span class="pagenum"><a name="Page_50" id="Page_50">[50]</a></span></p>
@@ -2212,7 +2173,7 @@ feed carburetter, ignition by single coil and distributor.
 The aeroplane being 7 ft. 6 in. long, and having a span
 8 ft.</p>
 
-<p>§ 32. <b>One-cylinder Petrol Motors.</b>&mdash;So far as the
+<p>§ 32. <b>One-cylinder Petrol Motors.</b>&mdash;So far as the
 writer is aware no success has as yet attended the use of a
 single-cylinder petrol motor on a model aeroplane. Undoubtedly
 the vibration is excessive; but this should not be
@@ -2223,7 +2184,7 @@ a model aeroplane is one of considerable importance. A
 badly balanced propeller even will seriously interfere with
 and often greatly curtail the length of flight.</p>
 
-<p>§ 33. <b>Electric Motors.</b>&mdash;No attempt should on any
+<p>§ 33. <b>Electric Motors.</b>&mdash;No attempt should on any
 account be made to use electric motors for model aeroplanes.
 They are altogether too heavy, apart even from the accumulator
 or source of electric energy, for the power derivable
@@ -2249,7 +2210,7 @@ their uses.</p>
 <p class="cen"><b>PROPELLERS OR SCREWS</b>.</p>
 
 
-<p>§ 1. The design and construction of propellers, more
+<p>§ 1. The design and construction of propellers, more
 especially the former, is without doubt one of the most
 difficult parts of model aeroplaning.</p>
 
@@ -2318,7 +2279,7 @@ of the elastic motor</i>, if good flights are desired.</p>
 of the propeller can be safely copied from actual well-recognised
 and successful full-sized machines.</p>
 
-<p>§ 2. <b>The Number of Blades.</b>&mdash;Theoretically the
+<p>§ 2. <b>The Number of Blades.</b>&mdash;Theoretically the
 number of blades does not enter into consideration. The
 mass of air dealt with by the propeller is represented by a
 cylinder of indefinite length, whose diameter is the same as
@@ -2347,7 +2308,7 @@ weight is considerably increased, and in models a greater
 advantage is gained by keeping down the weight than might
 follow from the use of more blades.</p>
 
-<p>§ 3. <b>Fan versus Propeller.</b>&mdash;It must always be most<span class="pagenum"><a name="Page_55" id="Page_55">[55]</a></span>
+<p>§ 3. <b>Fan versus Propeller.</b>&mdash;It must always be most<span class="pagenum"><a name="Page_55" id="Page_55">[55]</a></span>
 carefully borne in mind that a fan (ventilating) and a propeller
 are not the same thing. Because many blades are
 found in practice to be efficient in the case of the former, it
@@ -2381,14 +2342,14 @@ possible.</p>
 when stationary (static thrust), and a propeller whilst moving
 through the air (dynamic thrust).</p>
 
-<p>§ 4. <b>The Function of a Propeller</b> is to produce
+<p>§ 4. <b>The Function of a Propeller</b> is to produce
 dynamic thrust; and the great advantage of the use of a
 propeller as a thrusting or propulsive agent is that its surface
 is always active. It has no <i>dead</i> points, and its motion is continuous
 and not reciprocating, and it requires no special
 machinery or moving parts in its construction and operation.<span class="pagenum"><a name="Page_56" id="Page_56">[56]</a></span></p>
 
-<p>§ 5. <b>The Pitch</b> of a propeller or screw is the linear
+<p>§ 5. <b>The Pitch</b> of a propeller or screw is the linear
 distance a screw moves, backwards or forwards, in one complete
 revolution. This distance is purely a theoretical one.
 When, for instance, a screw is said to have a pitch of 1 ft.,
@@ -2399,7 +2360,7 @@ nut on a bolt with one thread per foot. In a yielding fluid
 such as water or air it does not practically advance this
 distance, and hence occurs what is known as&mdash;</p>
 
-<p>§ 6. <b>Slip</b>, which may be defined as the distance which
+<p>§ 6. <b>Slip</b>, which may be defined as the distance which
 ought to be traversed, but which is lost through imperfections
 in the propelling mechanism; or it may be considered
 as power which should have been used in driving the model
@@ -2421,7 +2382,7 @@ ground.</p>
 
 <p>Taking "slip" into account, then&mdash;</p>
 
-<p><i>The speed of the model in feet per minute = pitch (in feet) ×
+<p><i>The speed of the model in feet per minute = pitch (in feet) ×
 revolutions per minute&mdash; slip (feet per minute).</i></p>
 
 <p>This slip wants to be made small&mdash;just how small is not
@@ -2438,14 +2399,14 @@ quite good, 40 per cent. bad; and there are certain reasons
 for assuming that possibly about 15 per cent. may be the
 best.</p>
 
-<p>§ 7. It is true that slip represents energy lost; but some
+<p>§ 7. It is true that slip represents energy lost; but some
 slip is essential, because without slip there could be no
 "thrust," this same thrust being derived from the reaction
 of the volume of air driven backwards.</p>
 
 <p>The thrust is equal to&mdash;</p>
 
-<p><i>Weight of mass of air acted on per second × slip velocity
+<p><i>Weight of mass of air acted on per second × slip velocity
 in feet per second.</i></p>
 
 <p>In the case of an aeroplane advancing through the air it
@@ -2459,28 +2420,28 @@ advancing on to "undisturbed" air, the "slip"
 velocity is reduced, but the undisturbed air is equivalent to
 acting upon a greater mass of air.</p>
 
-<p>§ 8. <b>Pitch Coefficient or Pitch Ratio.</b>&mdash;If we
+<p>§ 8. <b>Pitch Coefficient or Pitch Ratio.</b>&mdash;If we
 divide the pitch of a screw by its diameter we obtain what
 is known as pitch coefficient or ratio.</p>
 
 <p>The mean value of eighteen pitch coefficients of well-known
-full-sized machines works out at 0·62, which, as it so happens,
+full-sized machines works out at 0·62, which, as it so happens,
 is exactly the same as the case of the Farman machine propeller
-considered alone, this ratio varying from 0·4 to 1·2;<span class="pagenum"><a name="Page_58" id="Page_58">[58]</a></span>
+considered alone, this ratio varying from 0·4 to 1·2;<span class="pagenum"><a name="Page_58" id="Page_58">[58]</a></span>
 in the case of the Wright's machine it is (probably) 1. The
 efficiency of their propeller is admitted on all hands. Their
 propeller is, of course, a slow-speed propeller, 450 r.p.m. The
-one on the Blériot monoplane (Blériot XI.) pitch ratio 0·4,
+one on the Blériot monoplane (Blériot XI.) pitch ratio 0·4,
 r.p.m. 1350.</p>
 
-<p>In marine propulsion the pitch ratio is generally 1·3 for
-a slow-speed propeller, decreasing to 0·9 for a high-speed
+<p>In marine propulsion the pitch ratio is generally 1·3 for
+a slow-speed propeller, decreasing to 0·9 for a high-speed
 one. In the case of rubber-driven model aeroplanes the
 pitch ratio is often carried much higher, even to over 3.</p>
 
-<p>Mr. T.W.K. Clarke recommends a pitch angle of 45°,
+<p>Mr. T.W.K. Clarke recommends a pitch angle of 45°,
 or less, at the tips, and a pitch ratio of 3-1/7 (with an angle
-of 45°). Within limits the higher the pitch ratio the better
+of 45°). Within limits the higher the pitch ratio the better
 the efficiency. The higher the pitch ratio the slower may
 be the rate of revolution. Now in a rubber motor we do
 not want the rubber to untwist (run out) too quickly; with
@@ -2490,20 +2451,20 @@ high percentage of slip. And for efficiency it is certainly
 desirable to push this ratio to its limit; but there is also the
 question of the</p>
 
-<p>§ 9. <b>Diameter.</b>&mdash;"The diameter (says Mr. T. W.K.
+<p>§ 9. <b>Diameter.</b>&mdash;"The diameter (says Mr. T. W.K.
 Clarke) should be equal to one-quarter the span of the
 machine."</p>
 
 <p>If we increase the diameter we shall decrease the pitch
 ratio. From experiments which the writer has made he
 prefers a lower pitch ratio and increased diameter, viz. a
-pitch ratio of 1·5, and a diameter of one-third to even one-half
+pitch ratio of 1·5, and a diameter of one-third to even one-half
 the span, or even more.<a name="FNanchor_27_27" id="FNanchor_27_27"></a><a href="#Footnote_27_27" class="fnanchor">[27]</a> Certainly not less than
 one-third. Some model makers indulge in a large pitch
 ratio, angle, diameter, and blade area as well, but such a
 course is not to be recommended.</p>
 
-<p>§ 10. <b>Theoretical Pitch.</b>&mdash;Theoretically the pitch<span class="pagenum"><a name="Page_59" id="Page_59">[59]</a></span>
+<p>§ 10. <b>Theoretical Pitch.</b>&mdash;Theoretically the pitch<span class="pagenum"><a name="Page_59" id="Page_59">[59]</a></span>
 (from boss to tip) should at all points be the same; the
 boss or centre of the blade at right angles to the plane of
 rotation, and the angle decreasing as one approaches the
@@ -2535,7 +2496,7 @@ parts of the blade at A, B, C ... in
 Fig. 23 must be set in order that a uniform pitch may be
 obtained.</p>
 
-<p>§ 11. If the pitch be not uniform then there will be
+<p>§ 11. If the pitch be not uniform then there will be
 some portions of the blade which will drag through the air
 instead of affording useful thrust, and others which will be<span class="pagenum"><a name="Page_60" id="Page_60">[60]</a></span>
 doing more than they ought, putting air in motion which
@@ -2543,27 +2504,27 @@ had better be left quiet. This uniform total pitch for all
 parts of the propeller is (as already stated) a decreasing rate
 of pitch from the centre to the edge. With a total pitch of
 5 ft., and a radius of 4 ft., and an angle at the circumference
-of 6°, then the angle of pitch at a point midway between
-centre and circumference should be 12°, in order that the
+of 6°, then the angle of pitch at a point midway between
+centre and circumference should be 12°, in order that the
 total pitch may be the same at all parts.</p>
 
-<p>§ 12. <b>To Ascertain the Pitch of a Propeller.</b>&mdash;Take
+<p>§ 12. <b>To Ascertain the Pitch of a Propeller.</b>&mdash;Take
 any point on one of the blades, and carefully measure the
 inclination of the blade at that point to the plane of rotation.</p>
 
-<p>If the angle so formed be about 19° (19·45),<a name="FNanchor_28_28" id="FNanchor_28_28"></a><a href="#Footnote_28_28" class="fnanchor">[28]</a> i.e., 1 in 3,
+<p>If the angle so formed be about 19° (19·45),<a name="FNanchor_28_28" id="FNanchor_28_28"></a><a href="#Footnote_28_28" class="fnanchor">[28]</a> i.e., 1 in 3,
 and the point 5 in. from the centre, then every revolution
 this point will travel a distance</p>
 
 <p class="cen">
-2 &#960; <i>r</i> = 2 × 22/7 × 5 = 31·34.<br />
+2 &#960; <i>r</i> = 2 × 22/7 × 5 = 31·34.<br />
 </p>
 
 <p>Now since the inclination is 1 in 3,<a name="FNanchor_29_29" id="FNanchor_29_29"></a><a href="#Footnote_29_29" class="fnanchor">[29]</a> the propeller will
 travel forward theoretically one-third of this distance, or</p>
 
 <p class="cen">
-31·43/3 = 10·48 = 10&frac12; in. approx.<br />
+31·43/3 = 10·48 = 10&frac12; in. approx.<br />
 </p>
 
 <p>Similarly any other case may be dealt with. If the propeller
@@ -2571,7 +2532,7 @@ have a uniform <i>constant angle</i> instead of a uniform
 pitch, then the pitch may be calculated at a point about one-third
 the length of the blade from the tip.</p>
 
-<p>§ 13. <b>Hollow-Faced Blades.</b><a name="FNanchor_30_30" id="FNanchor_30_30"></a><a href="#Footnote_30_30" class="fnanchor">[30]</a>&mdash;It must always be<span class="pagenum"><a name="Page_61" id="Page_61">[61]</a></span>
+<p>§ 13. <b>Hollow-Faced Blades.</b><a name="FNanchor_30_30" id="FNanchor_30_30"></a><a href="#Footnote_30_30" class="fnanchor">[30]</a>&mdash;It must always be<span class="pagenum"><a name="Page_61" id="Page_61">[61]</a></span>
 carefully borne in mind that a propeller is nothing more nor
 less than a particular form of aeroplane specially designed to
 travel a helical path. It should, therefore, be hollow faced
@@ -2586,7 +2547,7 @@ necessity an increasing pitch from the cutting to the trailing
 edge (considering, of course, any particular section). In
 such a case the pitch is the <i>mean effective pitch</i>.</p>
 
-<p>§ 14. <b>Blade Area.</b>&mdash;We have already referred to the
+<p>§ 14. <b>Blade Area.</b>&mdash;We have already referred to the
 fact that the function of a propeller is to produce dynamic
 thrust&mdash;to drive the aeroplane forward by driving the air
 backwards. At the same time it is most desirable for
@@ -2599,7 +2560,7 @@ air should be accelerated to the smallest velocity.</p>
 cavitation<a name="FNanchor_31_31" id="FNanchor_31_31"></a><a href="#Footnote_31_31" class="fnanchor">[31]</a> does not come in) narrow blades are usually
 used. In high-speed marine propellers (where cavitation is
 liable to occur) the projected area of the blades is sometimes
-as much as 0·6 of the total disk area. In the case of aerial
+as much as 0·6 of the total disk area. In the case of aerial
 propellers, where cavitation does not occur, or not unless the
 velocity be a very high one (1500 or more a minute),
 narrow blades are the best. Experiments in marine propulsion
@@ -2628,14 +2589,14 @@ good flights, being our old bugbear "weight in excess."</p>
 <p>Requisite strength and stiffness, of course, set a limit on
 the final narrowness of the blades, apart from other considerations.</p>
 
-<p>§ 15. The velocity with which the propeller is rotated has
+<p>§ 15. The velocity with which the propeller is rotated has
 also an important bearing on this point; but a higher speed
 than 900 r.p.m. does not appear desirable, and even 700 or
 less is generally preferable.<a name="FNanchor_32_32" id="FNanchor_32_32"></a><a href="#Footnote_32_32" class="fnanchor">[32]</a> In case of twin-screw propellers,
-with an angle at the tips of 40° to 45°, as low a velocity of
+with an angle at the tips of 40° to 45°, as low a velocity of
 500 or even less would be still better.<a name="FNanchor_33_33" id="FNanchor_33_33"></a><a href="#Footnote_33_33" class="fnanchor">[33]</a></p>
 
-<p>§ 16. <b>Shrouding.</b>&mdash;No improvement whatever is <span class="pagenum"><a name="Page_63" id="Page_63">[63]</a></span>obtained
+<p>§ 16. <b>Shrouding.</b>&mdash;No improvement whatever is <span class="pagenum"><a name="Page_63" id="Page_63">[63]</a></span>obtained
 by the use of any kind of shrouding or ring round
 the propeller tips, or by corrugating the surface of the propeller,
 or by using cylindrical or cone-shaped propeller
@@ -2656,7 +2617,7 @@ A Cylinder of Air.</td>
 </table>
 </div>
 
-<p>§ 17. <b>General Design.</b>&mdash;The propeller should be so
+<p>§ 17. <b>General Design.</b>&mdash;The propeller should be so
 constructed as to act upon a tube and not a "cylinder" of
 air. Many flying toys (especially the French ones) are
 constructed with propellers of the cylinder type. Ease of
@@ -2668,7 +2629,7 @@ in the line of travel, instead of exerting its proportionate
 propulsive power, and their efficiency is affected by such a
 practice.<span class="pagenum"><a name="Page_64" id="Page_64">[64]</a></span></p>
 
-<p>§ 18. A good <b>Shape</b> for the blades<a name="FNanchor_34_34" id="FNanchor_34_34"></a><a href="#Footnote_34_34" class="fnanchor">[34]</a> is rectangular with
+<p>§ 18. A good <b>Shape</b> for the blades<a name="FNanchor_34_34" id="FNanchor_34_34"></a><a href="#Footnote_34_34" class="fnanchor">[34]</a> is rectangular with
 rounded corners; the radius of the circle for rounding off
 the corners may be taken as about one-quarter of the width
 of the blade. The shape is not <i>truly rectangular, for the
@@ -2685,11 +2646,11 @@ pitch uniform and large.</i></p>
 <span class="caption"><span class="smcap">Fig. 27.</span>&mdash;O T = 1/3 O P.</span>
 </div>
 
-<p>§ 19. <b>The Blades, two in number</b>, and hollow
+<p>§ 19. <b>The Blades, two in number</b>, and hollow
 faced&mdash;the maximum concavity being one-third the distance
 from the entering to the trailing edge; the ratio of A T
 to O P (the width) being
-0·048 or 1 : 21, these
+0·048 or 1 : 21, these
 latter considerations being
 founded on the analogy
 between a propeller and the
@@ -2716,7 +2677,7 @@ must be made the <i>trailing</i> edge. And if both be curved
 as in Fig. 29, then the <i>concave</i> edge must be the trailing
 edge.</p>
 
-<p>§ 19. <b>Propeller Design.</b>&mdash;To design a propeller, proceed
+<p>§ 19. <b>Propeller Design.</b>&mdash;To design a propeller, proceed
 as follows. Suppose the diameter 14 in. and the pitch
 three times the diameter, i.e. 52 in. (See Fig. 30.)</p>
 
@@ -2730,7 +2691,7 @@ case 1&frac34; in.) of the propeller, describe a semicircle E B F
 and complete the parallelogram F H G E. Divide the semicircle
 into a number of equal parts; twelve is a convenient
 number to take, then each division subtends an angle of
-15° at the centre D.</p>
+15° at the centre D.</p>
 
 <p>Divide one of the sides E G into the same number of
 equal parts (twelve) as shown. Through these points draw
@@ -2742,7 +2703,7 @@ drawn through the successive intersections of these lines is
 the path of the tip of the blade through half a revolution,
 viz. the line H S O T E.</p>
 
-<p>S O T X gives the angle at the tip of the blades = 44°.</p>
+<p>S O T X gives the angle at the tip of the blades = 44°.</p>
 
 <p>Let the shape of the blade be rectangular with rounded
 corners, and let the breadth at the tip be twice that at the
@@ -2754,17 +2715,17 @@ boss.</p>
 <div class="figcenter">
 <img src="images/i_082.jpg" width="320" height="640" alt="" title="" /><br />
 <span class="caption"><span class="smcap">Fig. 30.&mdash;Propeller Design.</span><br />
-One quarter scale. Diameter 14 in. Pitch 52 in. Angle at tip 44°.</span>
+One quarter scale. Diameter 14 in. Pitch 52 in. Angle at tip 44°.</span>
 </div>
 
-<p>The area being that of a rectangle 7 in. × 1 in. = 7 sq.
+<p>The area being that of a rectangle 7 in. × 1 in. = 7 sq.
 in. plus area of two triangles, base &frac12; in., height 7 in. Now
-area of triangle = half base × height. Therefore area of
-<span class="pagenum"><a name="Page_67" id="Page_67">[67]</a></span>both triangles = &frac12; in. × 7 in. = 3&frac12; sq. in. Now the area
+area of triangle = half base × height. Therefore area of
+<span class="pagenum"><a name="Page_67" id="Page_67">[67]</a></span>both triangles = &frac12; in. × 7 in. = 3&frac12; sq. in. Now the area
 of the disc swept out by the propeller is</p>
 
 <p class="cen">
-&#960;/4 × (diam.)<sup>2</sup>  <span style="padding-left:3em;">(&#960; = 22/7)</span>
+&#960;/4 × (diam.)<sup>2</sup>  <span style="padding-left:3em;">(&#960; = 22/7)</span>
 </p>
 
 <div class="figcenter">
@@ -2778,10 +2739,10 @@ are full-sized.</span>
 <p>And if <i>d</i> A <i>r</i> = the "disc area ratio" we have</p>
 
 <p class="cen">
-(<i>d</i> A <i>r</i>) × &#960;/4 × (14)<sup>2</sup> = area of blade = 10&frac12;,<br />
+(<i>d</i> A <i>r</i>) × &#960;/4 × (14)<sup>2</sup> = area of blade = 10&frac12;,<br />
 </p>
 
-<p>whence <i>d</i> A <i>r</i> = 0·07 about.</p>
+<p>whence <i>d</i> A <i>r</i> = 0·07 about.</p>
 
 <div class="figcenter" style="width: 500px;">
 <img src="images/i_084.jpg" width="500" height="180" alt="" title="" /><br />
@@ -2800,7 +2761,7 @@ are full-sized.</span>
 A B and equal to</p>
 
 <p>
-&#960; × diameter = 22/7 × 14 = 44 in. to scale 5&frac12; in.<br />
+&#960; × diameter = 22/7 × 14 = 44 in. to scale 5&frac12; in.<br />
 </p>
 
 <p>Divide B C into a convenient number of equal parts in
@@ -2819,7 +2780,7 @@ the blade.</p>
 of 14 in. diameter the diameter of the "boss" should
 not be more than 10/16 in.</p>
 
-<p>§ 20. <b>Experiments with Propellers.</b>&mdash;The propeller
+<p>§ 20. <b>Experiments with Propellers.</b>&mdash;The propeller
 design shown in Figs. 32 and 33, due to Mr. G. de
 Havilland,<a name="FNanchor_35_35" id="FNanchor_35_35"></a><a href="#Footnote_35_35" class="fnanchor">[35]</a> is one very suitable for experimental purposes.
 A single tube passing through a T-shaped boss forms the
@@ -2941,26 +2902,26 @@ ones of uniform (constant) pitch, were tested; the former
 gave good results, but not so good as the latter.</p>
 
 <p>The best angle of pitch (at the tip) was found to be
-from 20° to 30°.</p>
+from 20° to 30°.</p>
 
 <p>In all cases when the slip was as low as 25 per cent., or
 even somewhat less, nearly 20 per cent., a distinct "back
 current" of air was given out by the screw. This "slip
 stream," as it is caused, is absolutely necessary for efficiency.</p>
 
-<p>§ 21. <b>Fabric-covered</b> screws did not give very efficient
+<p>§ 21. <b>Fabric-covered</b> screws did not give very efficient
 results; the only point in their use on model aeroplanes is
 their extreme lightness. Two such propellers of 6 in.
 diameter can be made to weigh less than 1/5 oz. the pair; but
 wooden propellers (built-up principle) have been made 5 in.
 diameter and 1/12 oz. in weight.</p>
 
-<p>§ 22. Further experiments were made with twin screws
+<p>§ 22. Further experiments were made with twin screws
 mounted on model aeroplanes. In one case two propellers,
 both turning in the <i>same</i> direction, were mounted (without
 any compensatory adjustment for torque) on a model, total
 weight 1&frac12; lb. Diameter of each propeller 14 in.; angle of
-blade at tip 25°. The result was several good flights&mdash;the
+blade at tip 25°. The result was several good flights&mdash;the
 model (<i>see</i> Fig. 49c) was slightly unsteady across the wind,
 that was all.</p>
 
@@ -2977,7 +2938,7 @@ with the same result. These experiments have since been
 confirmed, and there seems no doubt that the double-curved
 shaped blade <i>is</i> superior. (See Fig. 39.)<span class="pagenum"><a name="Page_75" id="Page_75">[75]</a></span></p>
 
-<p>§ 23. <b>The Fleming-Williams Propeller.</b>&mdash;A
+<p>§ 23. <b>The Fleming-Williams Propeller.</b>&mdash;A
 chapter on propellers would scarcely be complete without a
 reference to the propeller used on a machine claiming a
 record of over a quarter of a mile. This form of propeller,
@@ -3001,7 +2962,7 @@ to test it was flat-faced on one side.
 </div>
 
 <p>It possesses large blade area, large pitch angle&mdash;more
-than 45° at the tip&mdash;and large diameter. These do not
+than 45° at the tip&mdash;and large diameter. These do not
 combine to propeller efficiency or to efficient dynamic thrust;
 but they do, of course, combine to give the propeller a very
 slow rotational velocity. Provided they give <i>sufficient</i>
@@ -3025,18 +2986,18 @@ of rubber used is very great for a 10 oz. model, namely,
 limited number of turns give the longest flight (which is the
 problem one always has to face when using a rubber motor)
 it is better to make use of an abnormal diameter, say, more
-than half the span, and using a tip pitch angle of 25°, than
-to make use of an abnormal tip pitch 45° and more, and
+than half the span, and using a tip pitch angle of 25°, than
+to make use of an abnormal tip pitch 45° and more, and
 large blade area. In a large pitch angle so much energy is
 wasted, not in dynamic thrust, but in transverse upsetting
 torque. On no propeller out of dozens and dozens that I<span class="pagenum"><a name="Page_77" id="Page_77">[77]</a></span>
-have tested have I ever found a tip-pitch of more than 35°
+have tested have I ever found a tip-pitch of more than 35°
 give a good dynamic thrust; and for length of flight
 velocity due to dynamic thrust must be given due weight,
 as well as the duration of running down of the rubber
 motor.</p>
 
-<p>§ 24. Of built up or carved out and twisted wooden
+<p>§ 24. Of built up or carved out and twisted wooden
 propellers, the former give the better result; the latter have
 an advantage, however, in sometimes weighing less.</p>
 
@@ -3050,7 +3011,7 @@ an advantage, however, in sometimes weighing less.</p>
 THE CENTRE OF PRESSURE</b>.</p>
 
 
-<p>§ 1. Passing on now to the study of an aeroplane actually
+<p>§ 1. Passing on now to the study of an aeroplane actually
 in the air, there are two forces acting on it, the upward
 lift due to the air (i.e. to the movement of the aeroplane
 supposed to be continually advancing on to fresh, undisturbed
@@ -3094,12 +3055,12 @@ A drop in the wind causes exactly an opposite effect.</p>
 <span class="caption smcap">Fig. 42.</span>
 </div>
 
-<p>§ 2. The danger lies in "oscillations" being set up in the
+<p>§ 2. The danger lies in "oscillations" being set up in the
 line of flight due to changes in the position of the centre of
 pressure. Hence the device of an elevator or horizontal
 tail for the purpose of damping out such oscillations.</p>
 
-<p>§ 3. But the aerofoil surface is not flat, owing to the
+<p>§ 3. But the aerofoil surface is not flat, owing to the
 increased "lift" given by arched surfaces, and a much more
 complicated set of phenomena then takes place, the centre
 of pressure moving forward until a certain critical angle of<span class="pagenum"><a name="Page_80" id="Page_80">[80]</a></span>
@@ -3118,7 +3079,7 @@ angles, and especially to determine at what angle (about) this
 <span class="caption smcap">Fig. 43.</span>
 </div>
 
-<p>§ 4. Natural automatic stability (the only one possible so
+<p>§ 4. Natural automatic stability (the only one possible so
 far as models are concerned) necessitates permanent or a
 permanently recurring coincidence (to coin a phrase) of the
 centre of gravity and the centre of pressure: the former is,
@@ -3126,7 +3087,7 @@ of course, totally unaffected by the vagaries of the latter,
 any shifting of which produces a couple tending to destroy
 equilibrium.</p>
 
-<p>§ 5. As to the best form of camber (for full sized machine)
+<p>§ 5. As to the best form of camber (for full sized machine)
 possibly more is known on this point than on any other in
 the whole of aeronautics.<span class="pagenum"><a name="Page_81" id="Page_81">[81]</a></span></p>
 
@@ -3153,7 +3114,7 @@ aerocurve, or curvature of the planes, is at what angle to
 set the cambered surface to the line of flight. This brings
 us to the question of the&mdash;</p>
 
-<p>§ 6. <b>Dipping Front Edge.</b>&mdash;The leading or front
+<p>§ 6. <b>Dipping Front Edge.</b>&mdash;The leading or front
 edge is not tangential to the line of flight, but to a relative
 upward wind. It is what is known as the "cyclic up-current,"
 which exists in the neighbourhood of the entering edge.
@@ -3186,22 +3147,22 @@ best determined by experiment on the model in question.</p>
 
 <p>But <i>if at any angle, that angle either way should be a very
 small one</i>. If you wish to be very scientific you can give
-the underside of the front edge a negative angle of 5° to 7°
+the underside of the front edge a negative angle of 5° to 7°
 for about one-eighth of the total length of the section, after
 that a positive angle, gradually increasing until you finally
-finish up at the trailing edge with one of 4°. Also, the
+finish up at the trailing edge with one of 4°. Also, the
 form of cambered surface should be a paraboloid&mdash;not arc
 or arc of circles. The writer does not recommend such an
 angle, but prefers an attitude similar to that adopted in the
 Wright machine, as in Fig. 47.</p>
 
-<p>§ 7. Apart from the attitude of the aerocurve: <i>the greatest
+<p>§ 7. Apart from the attitude of the aerocurve: <i>the greatest
 depth of the camber should be at one-third of the length of the</i><span class="pagenum"><a name="Page_83" id="Page_83">[83]</a></span>
 <i>section from the front edge, and the total depth measured from
 the top surface to the chord at this point should not be more
 than one-seventeenth of the length of section</i>.</p>
 
-<p>§ 8. It is the greatest mistake in model aeroplanes to
+<p>§ 8. It is the greatest mistake in model aeroplanes to
 make the camber otherwise than very slight (in the case of
 surfaced aerofoils the resistance is much increased), and
 aerofoils with anything but a <i>very slight</i> arch are liable to
@@ -3218,11 +3179,11 @@ of its chord to the line of flight, its altitude, etc.,
 are not the only important matters one must consider in the
 case of the aerofoil, we must also consider&mdash;</p>
 
-<p>§ 9. Its <b>Aspect Ratio</b>, i.e. the ratio of the span
+<p>§ 9. Its <b>Aspect Ratio</b>, i.e. the ratio of the span
 (length) of the aerofoil to the chord&mdash;usually expressed by
-span/chord. In the Farman machine this ratio is 5·4;
-Blériot, 4·3; Short, 6 to 7·5; Roe triplane, 7·5; a Clark
-flyer, 9·6.</p>
+span/chord. In the Farman machine this ratio is 5·4;
+Blériot, 4·3; Short, 6 to 7·5; Roe triplane, 7·5; a Clark
+flyer, 9·6.</p>
 
 <p>Now the higher the aspect ratio the greater should be
 the efficiency. Air escaping by the sides represents loss, and
@@ -3246,13 +3207,13 @@ has a higher aspect ratio than a monoplane, and a triplane
 (see above) a higher ratio still.</p>
 
 <p>It will be noticed the Clark model given has a considerably
-higher aspect ratio, viz. 9·6. And even this can
+higher aspect ratio, viz. 9·6. And even this can
 be exceeded.</p>
 
 <p><i>An aspect ratio of</i> 10:1 <i>or even</i> 12:1 <i>should be used if
 possible.</i><a name="FNanchor_37_37" id="FNanchor_37_37"></a><a href="#Footnote_37_37" class="fnanchor">[37]</a></p>
 
-<p>§ 10. <b>Constant or Varying Camber.</b>&mdash;Some model
+<p>§ 10. <b>Constant or Varying Camber.</b>&mdash;Some model
 makers vary the camber of their aerofoils, making them
 almost flat in some parts, with considerable camber in others;
 the tendency in some cases being to flatten the central portions
@@ -3269,7 +3230,7 @@ assumes a natural camber, more or less, when driven horizontally
 through the air. Reference has been made to a
 reversal of the<span class="pagenum"><a name="Page_85" id="Page_85">[85]</a></span>&mdash;</p>
 
-<p>§ 11. <b>Centre of Pressure on Arched Surfaces.</b>&mdash;Wilbur
+<p>§ 11. <b>Centre of Pressure on Arched Surfaces.</b>&mdash;Wilbur
 Wright in his explanation of this reversal says:
 "This phenomenon is due to the fact that at small angles
 the wind strikes the forward part of the aerofoil surface on
@@ -3278,8 +3239,8 @@ altogether ceases to lift, instead of being the most effective
 part of all." The whole question hangs on the value of the
 critical angle at which this reversal takes place; some
 experiments made by Mr. M.B. Sellers in 1906 (published
-in "Flight," May 14, 1910) place this angle between 16°
-and 20°. This angle is much above that used in model
+in "Flight," May 14, 1910) place this angle between 16°
+and 20°. This angle is much above that used in model
 aeroplanes, as well as in actual full-sized machines. But
 the equilibrium of the model might be upset, not by a
 change of attitude on its part, but on that of the wind, or
@@ -3301,7 +3262,7 @@ would show. Further experiments are much needed.</p>
 CONSTRUCTION</b>.</p>
 
 
-<p>§ 1. The choice of materials for model aeroplane construction
+<p>§ 1. The choice of materials for model aeroplane construction
 is more or less limited, if the best results are to be
 obtained. The lightness absolutely essential to success
 necessitates&mdash;in addition to skilful building and best disposition
@@ -3309,7 +3270,7 @@ of the materials&mdash;materials of no undue weight
 relative to their strength, of great elasticity, and especially
 of great resilience (capacity to absorb shock without injury).</p>
 
-<p>§ 2. <b>Bamboo.</b>&mdash;Bamboo has per pound weight a greater
+<p>§ 2. <b>Bamboo.</b>&mdash;Bamboo has per pound weight a greater
 resilience than any other suitable substance (silk and rubber
 are obviously useless as parts of the <i>framework</i> of an aeroplane).
 On full-sized machines the difficulty of making sufficiently
@@ -3344,12 +3305,12 @@ such as aluminium. Thin thread, or silk, is preferable to
 very thin wire for lashing purpose, as the latter "gives" too
 much, and cuts into the fibres of the wood as well.</p>
 
-<p>§ 3. <b>Ash</b>, <b>Spruce</b>, <b>Whitewood</b> are woods that are
+<p>§ 3. <b>Ash</b>, <b>Spruce</b>, <b>Whitewood</b> are woods that are
 also much used by model makers. Many prefer the last
 named owing to its uniform freedom from knots and ease
 with which it can be worked. It is stated 15 per cent. additional
 strength can be imparted by using hot size and
-allowing it to soak into the wood at an increase only of 3·7
+allowing it to soak into the wood at an increase only of 3·7
 per cent. of weight. It is less than half the weight of
 bamboo, but has a transverse rupture of only 7,900 lb. per
 sq. in. compared to 22,500 in the case of bamboo tubing
@@ -3367,8 +3328,8 @@ should be so treated when in the structure that it cannot
 absorb moisture.</p>
 
 <p>If we take the resilience of ash as 1, then (according to
-Haswell) relative resilience of beech is 0·86, and spruce
-0·64.</p>
+Haswell) relative resilience of beech is 0·86, and spruce
+0·64.</p>
 
 <p>The strongest of woods has a weight when well seasoned
 of about 40 lb. per cub. ft. and a tenacity of about 10,000 lb.
@@ -3380,7 +3341,7 @@ per sq. in.</p>
 A very effective French Toy Monoplane.</span>
 </div>
 
-<p>§ 4. <b>Steel.</b>&mdash;Ash has a transverse rupture of 14,300 lb.
+<p>§ 4. <b>Steel.</b>&mdash;Ash has a transverse rupture of 14,300 lb.
 per sq. in., steel tubing (thickness = 1/30 its diameter) 100,000
 lb. per sq. in. Ash weighs per cub. ft. 47 lb., steel 490.
 Steel being more than ten times as heavy as ash&mdash;but a
@@ -3391,7 +3352,7 @@ has a transverse rupture of 22,500 lb. per sq. in., and a
 weight of 55 lb. per cub. ft.</p>
 
 <p>Steel then is nine times as heavy as bamboo&mdash;and has a
-transverse rupture stress 4·4 times as great. In comparing
+transverse rupture stress 4·4 times as great. In comparing
 these three substances it must be carefully borne in mind
 that lightness and strength are not the only things that
 have to be provided for in model aeroplane building; there
@@ -3412,9 +3373,9 @@ of accurate thickness throughout, the price being about
 <p>Although suitable steel tubing is not yet procurable under
 ordinary circumstances, umbrella steel is.</p>
 
-<p>§ 5. <b>Umbrella Section Steel</b> is a section 5/32 in. by
-1/8 in. deep, 6 ft. long weighing 2·1 oz., and a section 3/32 in.
-across the base by 1/8 in. deep, 6 ft. long weighing 1·95 oz.</p>
+<p>§ 5. <b>Umbrella Section Steel</b> is a section 5/32 in. by
+1/8 in. deep, 6 ft. long weighing 2·1 oz., and a section 3/32 in.
+across the base by 1/8 in. deep, 6 ft. long weighing 1·95 oz.</p>
 
 <p>It is often stated that umbrella ribs are too heavy&mdash;but
 this entirely depends on the length you make use of, in lengths
@@ -3429,7 +3390,7 @@ employed&mdash;the front and ends of the aerofoil are of umbrella
 steel, the trailing edge of steel wire, comparatively thin, kept
 taut by steel wire stays.</p>
 
-<p>§ 6. <b>Steel Wire.</b>&mdash;Tensile strength about 300,000 lb.
+<p>§ 6. <b>Steel Wire.</b>&mdash;Tensile strength about 300,000 lb.
 per sq. in. For the aerofoil framework of small models and
 for all purposes of staying, or where a very strong and light
 tension is required, this substance is invaluable. Also for
@@ -3438,12 +3399,12 @@ for skids and shock absorber&mdash;also for hooks to hold the
 rubber motor strands, etc. No model is complete without it
 in some form or another.</p>
 
-<p>§ 7. <b>Silk.</b>&mdash;This again is a <i>sine qua non</i>. Silk is the
+<p>§ 7. <b>Silk.</b>&mdash;This again is a <i>sine qua non</i>. Silk is the
 strongest of all organic substances for certain parts of aeroplane
 construction. It has, in its best form, a specific gravity
-of 1·3, and is three times as strong as linen, and twice as strong
+of 1·3, and is three times as strong as linen, and twice as strong
 in the thread as hemp. Its finest fibres have a section of from
-0·0010 to 0·0015 in diameter. It will sustain about 35,000
+0·0010 to 0·0015 in diameter. It will sustain about 35,000
 lb. per sq. in. of its cross section; and its suspended fibre
 should carry about 150,000 ft. of its own material. This is
 six times the same figure for aluminium, and equals about
@@ -3457,7 +3418,7 @@ Several such are on the market. Hart's "fabric" and
 due regard to this and to its very high tensile strength
 it is superior to even steel wire stays.</p>
 
-<p>§ 8. <b>Aluminium and Magnalium.</b>&mdash;Two substances
+<p>§ 8. <b>Aluminium and Magnalium.</b>&mdash;Two substances
 about which a great deal has been heard in connection with
 model aeroplaning; but the writer does not recommend
 their use save in the case of fittings for scale models, not<span class="pagenum"><a name="Page_91" id="Page_91">[91]</a></span>
@@ -3472,7 +3433,7 @@ air travel is again less as in the case of wood. In fact,
 steel scores all round. Weight of magnalium : weight of
 aluminium :: 8:9.</p>
 
-<p>§ 9. <b>Alloys.</b>&mdash;During recent years scores, hundreds,
+<p>§ 9. <b>Alloys.</b>&mdash;During recent years scores, hundreds,
 possibly thousands of different alloys have been tried and
 experimented on, but steel still easily holds its own. It is
 no use a substance being lighter than another volume for
@@ -3480,7 +3441,7 @@ volume, it must be <i>lighter and stronger weight for weight</i>, to be
 superior for aeronautical purpose, and if the difference be but
 slight, question of <i>bulk</i> may decide it as offering <i>less resistance</i>.</p>
 
-<p>§ 10. <b>Sheet Ebonite.</b>&mdash;This substance is sometimes
+<p>§ 10. <b>Sheet Ebonite.</b>&mdash;This substance is sometimes
 useful for experiments with small propellers, for it can be
 bent and moulded in hot water, and when cold sets and
 keeps its shape. <i>Vulcanized fibre</i> can be used for same
@@ -3523,7 +3484,7 @@ the latter, are not without their uses.</p>
 AEROPLANES</b>.</p>
 
 
-<p>§ 1. The chief difficulty in the designing and building
+<p>§ 1. The chief difficulty in the designing and building
 of model aeroplanes is to successfully combat the conflicting
 interests contained therein. Weight gives stability, but
 requires extra supporting surface or a higher speed, i.e. more
@@ -3545,7 +3506,7 @@ general rules and features which if not adhered to and carefully
 carried out, or as carefully avoided, will cause endless
 trouble and failure.</p>
 
-<p>§ 2. In constructing a model aeroplane, or, indeed, any
+<p>§ 2. In constructing a model aeroplane, or, indeed, any
 piece of aerial apparatus, it is very important not to interrupt
 the continuity of any rib, tube, spar, etc., by drilling holes
 or making too thinned down holding places; if such be done,
@@ -3553,19 +3514,19 @@ additional strength by binding (with thread, not wire), or<span class="pagenum">
 by slipping a small piece of slightly larger tube over the
 other, must be imparted to the apparatus.</p>
 
-<p>§ 3. Begin by making a simple monoplane, and afterwards
+<p>§ 3. Begin by making a simple monoplane, and afterwards
 as you gain skill and experience proceed to construct
 more elaborate and scientific models.</p>
 
-<p>§ 4. Learn to solder&mdash;if you do not know how to&mdash;it is
+<p>§ 4. Learn to solder&mdash;if you do not know how to&mdash;it is
 absolutely essential.</p>
 
-<p>§ 5. Do not construct models (intended for actual flight)
+<p>§ 5. Do not construct models (intended for actual flight)
 with a tractor screw-main plane in front and tail (behind).
 Avoid them as you would the plague. Allusion has already
 been made in the Introduction to the difficulty of getting
 the centre of gravity sufficiently forward in the case of
-Blériot models; again with the main aerofoil in front, it is
+Blériot models; again with the main aerofoil in front, it is
 this aerofoil and not the balancing elevator, or tail, that <i>first</i>
 encounters the upsetting gust, and the effect of such a gust
 acting first on the larger surface is often more than the
@@ -3588,14 +3549,14 @@ resistance, the model generally running in such air&mdash;the slip
 of the screw is reduced to a corresponding degree&mdash;may even
 vanish altogether, and what is known as negative slip occur.<span class="pagenum"><a name="Page_95" id="Page_95">[95]</a></span></p>
 
-<p>§ 6. Wooden or metal aerofoils are more efficient than
+<p>§ 6. Wooden or metal aerofoils are more efficient than
 fabric covered ones. But they are only satisfactory in the
 smaller sizes, owing, for one thing, to the smash with which
 they come to the ground. This being due to the high
 speed necessary to sustain their weight. For larger-sized
 models fabric covered aerofoils should be used.</p>
 
-<p>§ 7. As to the shape of such, only three need be considered&mdash;the
+<p>§ 7. As to the shape of such, only three need be considered&mdash;the
 (<i>a</i>) rectangular, (<i>b</i>) the elongated ellipse,
 (<i>c</i>) the chamfered rear edge.</p>
 
@@ -3604,7 +3565,7 @@ models fabric covered aerofoils should be used.</p>
 <span class="caption"><span class="smcap">Fig. 48.</span>&mdash;(a), (b), (c).</span>
 </div>
 
-<p>§ 8. The stretching of the fabric on the aerofoil framework
+<p>§ 8. The stretching of the fabric on the aerofoil framework
 requires considerable care, especially when using silk.
 It is quite possible, even in models of 3 ft. to 4 ft. spread,
 to do without "ribs," and still obtain a fairly correct aerocurve,
@@ -3643,7 +3604,7 @@ very useful method of fastening, since it acts as an excellent<span class="pagen
 shock absorber, and "gives" when required, and yet
 possesses quite sufficient practical rigidity.</p>
 
-<p>§ 9. Flexible joints are an advantage in a biplane;
+<p>§ 9. Flexible joints are an advantage in a biplane;
 these can be made by fixing wire hooks and eyes to the ends of
 the "struts," and holding them in position by binding with
 silk or thread. Rigidity is obtained by use of steel wire
@@ -3655,12 +3616,12 @@ stays or thin silk cord.</p>
 Showing the position of C. of G., or point of support.</span>
 </div>
 
-<p>§ 10. Owing to the extra weight and difficulties of construction
+<p>§ 10. Owing to the extra weight and difficulties of construction
 on so small a scale it is not desirable to use
 "double surface" aerofoils except on large size power-driven
 models.</p>
 
-<p>§ 11. It is a good plan not to have the rod or tube
+<p>§ 11. It is a good plan not to have the rod or tube
 carrying the rubber motor connected with the outrigger
 carrying the elevator, because the torque of the rubber tends<span class="pagenum"><a name="Page_98" id="Page_98">[98]</a></span>
 to twist the carrying framework, and interferes with the
@@ -3685,7 +3646,7 @@ cane. Aerofoil covering nainsook.
 </span>
 </div>
 
-<p>§ 12. Some builders place the rubber motor above the
+<p>§ 12. Some builders place the rubber motor above the
 rod, or bow frame carrying the aerofoils, etc., the idea
 being that the pull of the rubber distorts the frame in such<span class="pagenum"><a name="Page_99" id="Page_99">[99]</a></span>
 a manner as to "lift" the elevator, and so cause the machine
@@ -3705,7 +3666,7 @@ propellers.
 </span>
 </div>
 
-<p>§ 13. In the Clarke models with the small front plane,
+<p>§ 13. In the Clarke models with the small front plane,
 the centre of pressure is slightly in front of the main plane.</p>
 
 <p>The balancing point of most models is generally slightly
@@ -3730,7 +3691,7 @@ catalogue on Model Aviation</i>]</span>
 </div>
 <p><span class="pagenum"><a name="Page_101" id="Page_101">[101]</a></span></p>
 
-<p>§ 14. The elevator (or tail) should be of the non-lifting
+<p>§ 14. The elevator (or tail) should be of the non-lifting
 type&mdash;in other words, the entire weight should be carried
 by the main aerofoil or aerofoils; the elevator being used
 simply as a balancer.<a name="FNanchor_39_39" id="FNanchor_39_39"></a><a href="#Footnote_39_39" class="fnanchor">[39]</a> If the machine be so constructed
@@ -3752,7 +3713,7 @@ thrust, and stay.<br />
 Model Aviation.</i>]</span>
 </div>
 
-<p>§ 15. In actual flying models "skids" should be used
+<p>§ 15. In actual flying models "skids" should be used
 and not "wheels"; the latter to be of any real use must
 be of large diameter, and the weight is prohibitive. Skids<span class="pagenum"><a name="Page_102" id="Page_102">[102]</a></span>
 can be constructed of cane, imitation whalebone, steel watch
@@ -3761,7 +3722,7 @@ better than imitation whalebone, but steel pianoforte wire
 best of all. For larger sized models bamboo is also suitable,
 as also ash or strong cane.</p>
 
-<p>§ 16. Apart from or in conjunction with skids we have
+<p>§ 16. Apart from or in conjunction with skids we have
 what are termed "shock absorbers" to lessen the shock on
 landing&mdash;the same substances can be used&mdash;steel wire in the
 form of a loop is very effectual; whalebone and steel springs
@@ -3771,7 +3732,7 @@ part front landing as well as a direct front landing. For
 this purpose they should be lashed to the main frame by
 thin indiarubber cord.</p>
 
-<p>§ 17. In the case of a biplane model the "gap" must
+<p>§ 17. In the case of a biplane model the "gap" must
 not be less than the "chord"&mdash;preferably greater.</p>
 
 <p>In a double monoplane (of the Langley type) there is
@@ -3789,7 +3750,7 @@ this is not by any means essential. If the propeller revolve
 clockwise, place it towards the right hand of the machine,
 and vice versa.</p>
 
-<p>§ 18. In designing a model to fly the longest possible
+<p>§ 18. In designing a model to fly the longest possible
 distance the monoplane type should be chosen, and when
 desiring to build one that shall remain the longest time in<span class="pagenum"><a name="Page_103" id="Page_103">[103]</a></span>
 the air the biplane or triplane type should be adopted.<a name="FNanchor_40_40" id="FNanchor_40_40"></a><a href="#Footnote_40_40" class="fnanchor">[40]</a>
@@ -3808,8 +3769,8 @@ length of the strands should be such as to render possible at
 least a thousand turns.</p>
 
 <p>The propellers should be of large diameter and pitch
-(not less than 35° at the tips), of curved shape, as advocated
-in §&nbsp;22 ch. v.; the aerofoil surface of as high an aspect
+(not less than 35° at the tips), of curved shape, as advocated
+in §&nbsp;22 ch. v.; the aerofoil surface of as high an aspect
 ratio as possible, and but slight camber if any; this is a very
 difficult question, the question of camber, and the writer
 feels bound to admit he has obtained as long flights with
@@ -3827,7 +3788,7 @@ in a straight course, combined with a rudder and universally
 jointed elevator.</p>
 
 <p>The manner of winding up the propellers has already
-been referred to (<i>see</i> chap. iii., §&nbsp;9). A winder is essential.</p>
+been referred to (<i>see</i> chap. iii., §&nbsp;9). A winder is essential.</p>
 
 <p>Another form of aerofoil is one of wood (as in Clarke's
 flyers) or metal, such a machine relying more on the swiftness
@@ -3853,7 +3814,7 @@ inclined to think that from 5 oz. to 10 oz. is likely to prove
 the most suitable. It is not too large to experiment with
 without difficulty, nor is it so small as to require the skill of
 a jeweller almost to build the necessary mechanism. The
-propeller speed has already been discussed (<i>see</i> ch. v., §&nbsp;15).
+propeller speed has already been discussed (<i>see</i> ch. v., §&nbsp;15).
 The model will, of course, be flown with the wind. The
 <i>total</i> length of the model should be at least twice the span
 of the main aerofoil.</p>
@@ -3867,7 +3828,7 @@ of the main aerofoil.</p>
 <p class="cen"><b>THE STEERING OF THE MODEL</b>.</p>
 
 
-<p>§ 1. Of all the various sections of model aeroplaning
+<p>§ 1. Of all the various sections of model aeroplaning
 that which is the least satisfactory is the above.</p>
 
 <p>The torque of the propeller naturally exerts a twisting
@@ -3878,7 +3839,7 @@ the screw be a right or left handed one. There are various
 devices by which the torque may be (approximately) got
 rid of.</p>
 
-<p>§ 2. In the case of a monoplane, by not placing the rod
+<p>§ 2. In the case of a monoplane, by not placing the rod
 carrying the rubber motor in the exact centre of the main
 aerofoil, but slightly to one side, the exact position to be
 determined by experiment.</p>
@@ -3888,7 +3849,7 @@ rod in the centre, but placing the bracket carrying the bearing
 in which the propeller shaft runs at right angles horizontally
 to the rod to obtain the same effect.</p>
 
-<p>§ 3. The most obvious solution of the problem is to use
+<p>§ 3. The most obvious solution of the problem is to use
 <i>two</i> equal propellers (as in the Wright biplane) of equal
 and opposite pitch, driven by two rubber motors of equal
 strength.</p>
@@ -3928,7 +3889,7 @@ fact, it is no solution at all.<a name="FNanchor_45_45" id="FNanchor_45_45"></a>
 and consequent tilting of the aeroplane is not the only cause
 at work diverting the machine from its course.</p>
 
-<p>§ 4. As it progresses through the air it is constantly<span class="pagenum"><a name="Page_107" id="Page_107">[107]</a></span>
+<p>§ 4. As it progresses through the air it is constantly<span class="pagenum"><a name="Page_107" id="Page_107">[107]</a></span>
 meeting air currents of varying velocity and direction, all
 tending to make the model deviate more or less from its
 course; the best way, in fact, the only way, to successfully
@@ -3939,7 +3900,7 @@ of twenty to thirty miles an hour, attainable only in models
 (petrol or steam driven) or by means of wooden or metal
 aerofoils.</p>
 
-<p>§ 5. Amongst devices used for horizontal steering are
+<p>§ 5. Amongst devices used for horizontal steering are
 vertical "<span class="smcap">FINS</span>." These should be placed in the rear above
 the centre of gravity. They should not be large, and can
 be made of fabric tightly stretched over a wire frame, or of
@@ -3951,19 +3912,19 @@ medium. The frame carrying the pivot and fin should be
 made to slide along the rod or backbone of the model in
 order to find the most efficient position.</p>
 
-<p>§ 6. Steering may also be attempted by means of little
+<p>§ 6. Steering may also be attempted by means of little
 balancing tips, or ailerons, fixed to or near the main aerofoil,
 and pivoted (either centrally or otherwise) in such a manner
 that they can be rotated one in one direction (tilted) and
 the other in the other (dipped), so as to raise one side and
 depress the other.</p>
 
-<p>§ 7. The model can also be steered by giving it a cant to
+<p>§ 7. The model can also be steered by giving it a cant to
 one side by weighting the tip of the aerofoil on that side on
 which it is desired it should turn, but this method is both
 clumsy and "weighty."</p>
 
-<p>§ 8. Another way is by means of the elevator; and this
+<p>§ 8. Another way is by means of the elevator; and this
 method, since it entails no additional surfaces entailing extra
 resistance and weight, is perhaps the most satisfactory of all.<span class="pagenum"><a name="Page_108" id="Page_108">[108]</a></span></p>
 
@@ -3972,15 +3933,15 @@ of universal joint, in order that it may not only be "tipped"
 or "dipped," but also canted sideways for horizontal
 steering.</p>
 
-<p>§ 9. A vertical fin in the rear, or something in the nature
+<p>§ 9. A vertical fin in the rear, or something in the nature
 of a "keel," i.e. a vertical fin running down the backbone
 of the machine, greatly assists this movement.</p>
 
-<p>If the model be of the tractor screw and tail (Blériot)
+<p>If the model be of the tractor screw and tail (Blériot)
 type, then the above remarks <i>re</i> elevator apply <i>mutatis
 mutandis</i> to the tail.</p>
 
-<p>§ 10. It is of the most vital importance that the propeller
+<p>§ 10. It is of the most vital importance that the propeller
 torque should be, as far as possible, correctly balanced.
 This can be tested by balancing the model transversely on a
 knife edge, winding up the propeller, and allowing it to run
@@ -4011,10 +3972,10 @@ diameter to be equally efficient.</p>
 <p class="cen"><b>THE LAUNCHING OF THE MODEL</b>.</p>
 
 
-<p>§ 1. Generally speaking, the model should be launched
+<p>§ 1. Generally speaking, the model should be launched
 into the air <i>against the wind</i>.</p>
 
-<p>§ 2. It should (theoretically) be launched into the air
+<p>§ 2. It should (theoretically) be launched into the air
 with a velocity equal to that with which it flies. If it
 launch with a velocity in excess of that it becomes at once
 unstable and has to "settle down" before assuming its
@@ -4028,7 +3989,7 @@ such as the well-known Clarke flyers, require to be practically
 <p>Other fabric-covered models capable of sustentation
 at a velocity of 8 to 10 miles an hour, may just be "released."</p>
 
-<p>§ 3. Light "featherweight" models designed for long
+<p>§ 3. Light "featherweight" models designed for long
 flights when travelling with the wind should be launched
 with it. They will not advance into it&mdash;if there be anything
 of a breeze&mdash;but, if well designed, just "hover," finally
@@ -4037,12 +3998,12 @@ of apparatus have been designed to mechanically launch the
 model into the air. Fig. 50 is an illustration of a very
 simple but effective one.</p>
 
-<p>§ 4. For large size power-driven models, unless provided
+<p>§ 4. For large size power-driven models, unless provided
 with a chassis and wheels to enable them to run along and<span class="pagenum"><a name="Page_110" id="Page_110">[110]</a></span>
 rise from the ground under their own power, the launching
 is a problem of considerable difficulty.</p>
 
-<p>§ 5. In the case of rubber-driven models desired to run
+<p>§ 5. In the case of rubber-driven models desired to run
 along and rise from the ground under their own power, this
 rising must be accomplished quickly and in a short space.
 A model requiring a 50 ft. run is useless, as the motor would
@@ -4058,7 +4019,7 @@ its velocity of sustentation must be a low one.</p>
 [<i>Reproduced by permission from the &quot;Model Engineer.&quot;</i>]</span>
 </div>
 
-<p>§ 6. It will not do to tip up the elevator to a large angle
+<p>§ 6. It will not do to tip up the elevator to a large angle
 to make it rise quickly, because when once off the ground
 the angle of the elevator is wrong for actual flight and the
 model will probably turn a somersault and land on its back.
@@ -4073,17 +4034,17 @@ at a comparatively large angle while the model is on the
 ground, but allowing of this angle being reduced when free
 flight is commenced.</p>
 
-<p>§ 7. The propeller most suitable to "get the machine off
+<p>§ 7. The propeller most suitable to "get the machine off
 the ground" is one giving considerable statical thrust. A
 small propeller of fine pitch quickly starts a machine, but
 is not, of course, so efficient when the model is in actual
 flight. A rubber motor is not at all well adapted for the
 purpose just discussed.</p>
 
-<p>§ 8. Professor Kress uses a polished plank (down which
+<p>§ 8. Professor Kress uses a polished plank (down which
 the models slip on cane skids) to launch his models.</p>
 
-<p>§ 9. When launching a twin-screw model the model
+<p>§ 9. When launching a twin-screw model the model
 should be held by each propeller, or to speak more correctly,
 the two brackets holding the bearings in which the propeller
 shafts run should be held one in each hand in such a way,
@@ -4095,13 +4056,13 @@ horizontal position is attained, and boldly push the machine
 into the air (moving forward if necessary) and release both
 brackets and screws simultaneously.<span class="pagenum"><a name="Page_112" id="Page_112">[112]</a></span><a name="FNanchor_46_46" id="FNanchor_46_46"></a><a href="#Footnote_46_46" class="fnanchor">[46]</a></p>
 
-<p>§ 10. In launching a model some prefer to allow the
+<p>§ 10. In launching a model some prefer to allow the
 propellers to revolve for a few moments (a second, say)
 <i>before</i> actually launching, contending that this gives a steadier
 initial flight. This is undoubtedly the case, see note on
 page 111.</p>
 
-<p>§ 11. In any case, unless trying for a height prize, do
+<p>§ 11. In any case, unless trying for a height prize, do
 not point the nose of the machine right up into the air
 with the idea that you will thereby obtain a better flight.</p>
 
@@ -4123,22 +4084,22 @@ be overthrown.</p>
 <p class="cen"><b>HELICOPTER MODELS</b>.</p>
 
 
-<p>§ 1. There is no difficulty whatever about making successful
+<p>§ 1. There is no difficulty whatever about making successful
 model helicopters, whatever there may be about full-sized
 machines.</p>
 
-<p>§ 2. The earliest flying models were helicopters. As
+<p>§ 2. The earliest flying models were helicopters. As
 early as 1796 Sir George Cayley constructed a perfectly
 successful helicopter model (see ch. iii.); it should be
 noticed the screws were superimposed and rotated in opposite
 directions.</p>
 
-<p>§ 3. In 1842 a Mr. Phillips constructed a successful power-driven
+<p>§ 3. In 1842 a Mr. Phillips constructed a successful power-driven
 model helicopter. The model was made entirely of
 metal, and when complete and charged weighed 2 lb. It
 consisted of a boiler or steam generator and four fans supported
 between eight arms. The fans had an inclination
-to the horizon of 20°, and through the arms the steam
+to the horizon of 20°, and through the arms the steam
 rushed on the principle of Hero's engines (Barker's Mill
 Principle probably). By the escape of steam from the arms
 the fans were caused to revolve with immense energy, so
@@ -4155,7 +4116,7 @@ the first model actuated by steam which actually flew.</p>
 
 <p>The helicopter is but a particular phase of the aeroplane.</p>
 
-<p>§ 4. The simplest form of helicopter is that in which
+<p>§ 4. The simplest form of helicopter is that in which
 the torque of the propeller is resisted by a vertical loose
 fabric plane, so designed as itself to form a propeller, rotating
 in the opposite direction. These little toys can be bought
@@ -4170,7 +4131,7 @@ rotating propellers for lifting purposes.</p>
 <span class="caption smcap">Fig. 51.&mdash;Incorrect Way of Arranging Screws.</span>
 </div>
 
-<p>§ 5. There is one essential point that must be carefully
+<p>§ 5. There is one essential point that must be carefully
 attended to, and that is, <i>that the horizontal propulsive thrust
 must be in the same plane as the vertical lift</i>, or the only effect
 will be to cause our model to turn somersaults. I speak from
@@ -4181,13 +4142,13 @@ a horizontal direction their "lifting" powers will be materially
 increased, as they will (like an ordinary aeroplane) be
 advancing on to fresh undisturbed air.</p>
 
-<p>§ 6. I have not for ordinary purposes advocated very
+<p>§ 6. I have not for ordinary purposes advocated very
 light weight wire framework fabric-covered screws, but in a
 case like this where the thrust from the propeller has to be
 more than the total weight of the machine, these might
 possibly be used with advantage.</p>
 
-<p>§ 7. Instead of using two long vertical rods as well as
+<p>§ 7. Instead of using two long vertical rods as well as
 one long horizontal one for the rubber strands, we might
 dispense with the two vertical ones altogether and use light
 gearing to turn the torque action through a right angle for
@@ -4203,7 +4164,7 @@ weight.</p>
 A, B, C = Screws.</span>
 </div>
 
-<p>§ 8. The model would require something in the nature
+<p>§ 8. The model would require something in the nature
 of a vertical fin or keel to give the sense of direction. Four
 propellers, two for "lift" and two for "drift," would
 undoubtedly be a better arrangement.</p>
@@ -4308,7 +4269,7 @@ be that, and may be very valuable.<span class="pagenum"><a name="Page_117" id="P
 
 <p class="cen"><b>MODEL FLYING COMPETITIONS</b>.</p>
 
-<p>§ 1. From time to time flying competitions are arranged
+<p>§ 1. From time to time flying competitions are arranged
 for model aeroplanes. Sometimes these competitions are
 entirely open, but more generally they are arranged by local
 clubs with both closed and open events.</p>
@@ -4348,7 +4309,7 @@ may be offered&mdash;</p>
 
 <p>The models are divided into classes:&mdash;</p>
 
-<p>§ 2. <i>Aero Models Association's Classification, etc.</i></p>
+<p>§ 2. <i>Aero Models Association's Classification, etc.</i></p>
 <table border="0" cellpadding="4" cellspacing="0" summary="">
 <tr><td align="center">A.</td><td align="center">Models of</td><td align="center">1 sq. ft.</td><td align="center">surface</td><td align="center">and</td><td align="center">under.</td></tr>
 <tr><td align="center">B.</td><td align="center">"</td><td align="center">2 sq. ft.</td><td align="center">"</td><td align="center"></td><td align="center">"</td></tr>
@@ -4412,7 +4373,7 @@ over some indicated point.</p>
 
 <p>The models are practically always launched by hand.</p>
 
-<p>§ 3. Those who desire to win prizes at such competitions
+<p>§ 3. Those who desire to win prizes at such competitions
 would do well to keep the following points well in mind.<span class="pagenum"><a name="Page_122" id="Page_122">[122]</a></span></p>
 
 <p>1. The distance is always measured in a straight line.
@@ -4490,7 +4451,7 @@ your model be a biplane, or the number of flights may be
 restricted to the number "one."</p>
 
 <p>12. Since the best "gliding" angle and "flying" angle
-are not the same, being, say, 7° in the former case and 1°-3°,
+are not the same, being, say, 7° in the former case and 1°-3°,
 say, in the latter, an adjustable angle might in some
 cases be advantageous.</p>
 
@@ -4522,58 +4483,58 @@ flights required for <span class="smcap">C</span>.</p>
 
 
 <h2>USEFUL NOTES, TABLES,<br />
-FORMULÆ, ETC.</h2>
+FORMULÆ, ETC.</h2>
 
 
-<p class="cen">§ 1. <span class="smcap">Comparative Velocities.</span></p>
+<p class="cen">§ 1. <span class="smcap">Comparative Velocities.</span></p>
 
 <table border="0" cellpadding="2" cellspacing="0" summary="">
 <tr><td align="center">Miles per hr.</td><td align="center"></td><td align="center">Feet per sec.</td><td align="center"></td><td align="center">Metres per sec.</td></tr>
-<tr><td align="center">10</td><td align="center">=</td><td align="center">14·7</td><td align="center">=</td><td align="center">4·470</td></tr>
-<tr><td align="center">15</td><td align="center">=</td><td align="center">22</td><td align="center">=</td><td align="center">6·705</td></tr>
-<tr><td align="center">20</td><td align="center">=</td><td align="center">29·4</td><td align="center">=</td><td align="center">8·940</td></tr>
-<tr><td align="center">25</td><td align="center">=</td><td align="center">36·7</td><td align="center">=</td><td align="center">11·176</td></tr>
-<tr><td align="center">30</td><td align="center">=</td><td align="center">44</td><td align="center">=</td><td align="center">13·411</td></tr>
-<tr><td align="center">35</td><td align="center">=</td><td align="center">51·3</td><td align="center">=</td><td align="center">15·646</td></tr>
+<tr><td align="center">10</td><td align="center">=</td><td align="center">14·7</td><td align="center">=</td><td align="center">4·470</td></tr>
+<tr><td align="center">15</td><td align="center">=</td><td align="center">22</td><td align="center">=</td><td align="center">6·705</td></tr>
+<tr><td align="center">20</td><td align="center">=</td><td align="center">29·4</td><td align="center">=</td><td align="center">8·940</td></tr>
+<tr><td align="center">25</td><td align="center">=</td><td align="center">36·7</td><td align="center">=</td><td align="center">11·176</td></tr>
+<tr><td align="center">30</td><td align="center">=</td><td align="center">44</td><td align="center">=</td><td align="center">13·411</td></tr>
+<tr><td align="center">35</td><td align="center">=</td><td align="center">51·3</td><td align="center">=</td><td align="center">15·646</td></tr>
 </table>
 
 
-<p>§ 2.<span style="margin-left:15em;">   A metre = 39·37079 inches</span>.</p>
+<p>§ 2.<span style="margin-left:15em;">   A metre = 39·37079 inches</span>.</p>
 
 
 <p class="noin"><i>In order to convert</i>&mdash;</p>
 <table border="0" cellpadding="2" cellspacing="0" summary="">
-<tr><td align="center">Metres into&nbsp;</td><td align="center">inches</td><td align="center">&nbsp;multiply by</td><td align="center">39·37</td></tr>
-<tr><td align="center">"</td><td align="center">feet</td><td align="center">"</td><td align="center">3·28</td></tr>
-<tr><td align="center">"</td><td align="center">yards</td><td align="center">"</td><td align="center">1·09</td></tr>
-<tr><td align="center">"</td><td align="center">miles</td><td align="center">"</td><td align="center">0·0006214</td></tr>
+<tr><td align="center">Metres into&nbsp;</td><td align="center">inches</td><td align="center">&nbsp;multiply by</td><td align="center">39·37</td></tr>
+<tr><td align="center">"</td><td align="center">feet</td><td align="center">"</td><td align="center">3·28</td></tr>
+<tr><td align="center">"</td><td align="center">yards</td><td align="center">"</td><td align="center">1·09</td></tr>
+<tr><td align="center">"</td><td align="center">miles</td><td align="center">"</td><td align="center">0·0006214</td></tr>
 </table>
 
 <table border="0" cellpadding="2" cellspacing="0" summary="">
-<tr><td align="center">Miles per&nbsp;</td><td align="right">hour into&nbsp;</td><td align="center">ft. per min.&nbsp;</td><td align="center">multiply by</td><td align="center">88·0</td></tr>
-<tr><td align="center">"</td><td align="right">min. into&nbsp;</td><td align="center">ft. per sec.</td><td align="center">"</td><td align="center">88·0</td></tr>
-<tr><td align="center">"</td><td align="right">hr. into&nbsp;</td><td align="center">kilometres per hr.</td><td align="center">"</td><td align="center">1·6093</td></tr>
-<tr><td align="center">"</td><td align="center">"</td><td align="center">metres per sec.</td><td align="center">"</td><td align="center">0·44702</td></tr>
-<tr><td align="right" colspan="2">Pounds into&nbsp;</td><td align="center">grammes</td><td align="center">"</td><td align="center">453·593</td></tr>
-<tr><td></td><td align="center">"</td><td align="center">kilogrammes</td><td align="center">"</td><td align="center">0·4536</td></tr>
+<tr><td align="center">Miles per&nbsp;</td><td align="right">hour into&nbsp;</td><td align="center">ft. per min.&nbsp;</td><td align="center">multiply by</td><td align="center">88·0</td></tr>
+<tr><td align="center">"</td><td align="right">min. into&nbsp;</td><td align="center">ft. per sec.</td><td align="center">"</td><td align="center">88·0</td></tr>
+<tr><td align="center">"</td><td align="right">hr. into&nbsp;</td><td align="center">kilometres per hr.</td><td align="center">"</td><td align="center">1·6093</td></tr>
+<tr><td align="center">"</td><td align="center">"</td><td align="center">metres per sec.</td><td align="center">"</td><td align="center">0·44702</td></tr>
+<tr><td align="right" colspan="2">Pounds into&nbsp;</td><td align="center">grammes</td><td align="center">"</td><td align="center">453·593</td></tr>
+<tr><td></td><td align="center">"</td><td align="center">kilogrammes</td><td align="center">"</td><td align="center">0·4536</td></tr>
 </table>
 
 
-<p>§ <ins class="mycorr" title='Correction: text was "8"'>3</ins>. Total surface of a cylinder = circumference of base
-× height + 2 area of base.<span class="pagenum"><a name="Page_126" id="Page_126">[126]</a></span></p>
+<p>§ <ins class="mycorr" title='Correction: text was "8"'>3</ins>. Total surface of a cylinder = circumference of base
+× height + 2 area of base.<span class="pagenum"><a name="Page_126" id="Page_126">[126]</a></span></p>
 
-<p>Area of a circle = square of diameter × 0·7854.</p>
+<p>Area of a circle = square of diameter × 0·7854.</p>
 
-<p>Area of a circle = square of rad. × 3·14159.</p>
+<p>Area of a circle = square of rad. × 3·14159.</p>
 
-<p>Area of an ellipse = product of axes × 0·7854.</p>
+<p>Area of an ellipse = product of axes × 0·7854.</p>
 
-<p>Circumference of a circle = diameter × 3·14159.</p>
+<p>Circumference of a circle = diameter × 3·14159.</p>
 
-<p>Solidity of a cylinder = height × area of base.</p>
+<p>Solidity of a cylinder = height × area of base.</p>
 
-<p>Area of a circular ring = sum of diameters × difference
-of diameters × 0·7854.</p>
+<p>Area of a circular ring = sum of diameters × difference
+of diameters × 0·7854.</p>
 
 <p>For the area of a sector of a circle the rule is:&mdash;As
 360 : number of degrees in the angle of the sector :: area
@@ -4587,72 +4548,72 @@ chord.</p>
 <p>The areas of corresponding figures are as the squares of
 corresponding lengths.</p>
 
-<p>§ 4. </p>
+<p>§ 4. </p>
 <table border="0" cellpadding="2" cellspacing="0" summary="">
-<tr><td align="left">1 mile</td><td align="left">=</td><td align="left">1·609 kilometres.</td></tr>
+<tr><td align="left">1 mile</td><td align="left">=</td><td align="left">1·609 kilometres.</td></tr>
 <tr><td align="left">1 kilometre</td><td align="left">=</td><td align="left">1093 yards.</td></tr>
-<tr><td align="left">1 oz.</td><td align="left">=</td><td align="left">28·35 grammes.</td></tr>
-<tr><td align="left">1 lb.</td><td align="left">=</td><td align="left">453·59  &nbsp;&nbsp;&nbsp;"</td></tr>
-<tr><td align="left">1 lb.</td><td align="left">=</td><td align="left">0·453 kilogrammes.</td></tr>
-<tr><td align="left">28 lb.</td><td align="left">=</td><td align="left">12·7  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"</td></tr>
-<tr><td align="left">112 lb.</td><td align="left">=</td><td align="left">50·8 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"</td></tr>
+<tr><td align="left">1 oz.</td><td align="left">=</td><td align="left">28·35 grammes.</td></tr>
+<tr><td align="left">1 lb.</td><td align="left">=</td><td align="left">453·59  &nbsp;&nbsp;&nbsp;"</td></tr>
+<tr><td align="left">1 lb.</td><td align="left">=</td><td align="left">0·453 kilogrammes.</td></tr>
+<tr><td align="left">28 lb.</td><td align="left">=</td><td align="left">12·7  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"</td></tr>
+<tr><td align="left">112 lb.</td><td align="left">=</td><td align="left">50·8 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"</td></tr>
 <tr><td align="left">2240 lb.</td><td align="left">=</td><td align="left">1016 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"</td></tr>
-<tr><td align="left">1 kilogram</td><td align="left">=</td><td align="left">2·2046 lb.</td></tr>
-<tr><td align="left">1 gram</td><td align="left">=</td><td align="left">0·0022 lb.</td></tr>
+<tr><td align="left">1 kilogram</td><td align="left">=</td><td align="left">2·2046 lb.</td></tr>
+<tr><td align="left">1 gram</td><td align="left">=</td><td align="left">0·0022 lb.</td></tr>
 <tr><td align="left">1 sq. in.</td><td align="left">=</td><td align="left">645 sq. millimetres.</td></tr>
-<tr><td align="left">1 sq. ft.</td><td align="left">=</td><td align="left">0·0929 sq. metres.</td></tr>
-<tr><td align="left">1 sq. yard</td><td align="left">=</td><td align="left">0·836 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; "</td></tr>
-<tr><td align="left">1 sq. metre</td><td align="left">=</td><td align="left">10·764 sq. ft.</td></tr>
+<tr><td align="left">1 sq. ft.</td><td align="left">=</td><td align="left">0·0929 sq. metres.</td></tr>
+<tr><td align="left">1 sq. yard</td><td align="left">=</td><td align="left">0·836 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; "</td></tr>
+<tr><td align="left">1 sq. metre</td><td align="left">=</td><td align="left">10·764 sq. ft.</td></tr>
 </table>
 
 
-<p>§ 5. One atmosphere = 14·7 lb. per sq. in. = 2116 lb.
+<p>§ 5. One atmosphere = 14·7 lb. per sq. in. = 2116 lb.
 per sq. ft. = 760 millimetres of mercury.<span class="pagenum"><a name="Page_127" id="Page_127">[127]</a></span></p>
 
-<p>A column of water 2·3 ft. high corresponds to a pressure
+<p>A column of water 2·3 ft. high corresponds to a pressure
 of 1 lb. per sq. in.</p>
 
 <p>1 H.P. = 33,000 ft.-lb. per min. = 746 watts.</p>
 
-<p>Volts × amperes = watts.</p>
+<p>Volts × amperes = watts.</p>
 
-<p>&#960; = 3·1416. &nbsp;&nbsp; <i>g</i> = 32·182 ft. per sec. at London.</p>
+<p>&#960; = 3·1416. &nbsp;&nbsp; <i>g</i> = 32·182 ft. per sec. at London.</p>
 
-<p class="cen">§ 6. <span class="smcap">Table of Equivalent Inclinations.</span></p>
+<p class="cen">§ 6. <span class="smcap">Table of Equivalent Inclinations.</span></p>
 
 <table border="0" cellpadding="2" cellspacing="0" summary="" style="text-align:center;">
 <tr><td colspan="3">Rise.</td><td colspan="3" style="padding-left:1em;">Angle in Degs.</td></tr>
-<tr><td align="left">1</td><td>in</td><td align="right">30</td><td>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td><td align="right">1·91</td><td>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">25</td><td></td><td align="right">2·29</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">20</td><td></td><td align="right">2·87</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">18</td><td></td><td align="right">3·18</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">16</td><td></td><td align="right">3·58</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">14</td><td></td><td align="right">4·09</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">12</td><td></td><td align="right">4·78</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">10</td><td></td><td align="right">5·73</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">9</td><td></td><td align="right">6·38</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">8</td><td></td><td align="right">7·18</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">7</td><td></td><td align="right">8·22</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">6</td><td></td><td align="right">9·6&nbsp;&nbsp;</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">5</td><td></td><td align="right">11·53</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">4</td><td></td><td align="right">14·48</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">3</td><td></td><td align="right">19·45</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">2</td><td></td><td align="right">30·00</td><td></td></tr>
-<tr><td align="left">1</td><td>"</td><td align="right">&#8730;2</td><td></td><td align="right">45·00</td><td></td></tr>
+<tr><td align="left">1</td><td>in</td><td align="right">30</td><td>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td><td align="right">1·91</td><td>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">25</td><td></td><td align="right">2·29</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">20</td><td></td><td align="right">2·87</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">18</td><td></td><td align="right">3·18</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">16</td><td></td><td align="right">3·58</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">14</td><td></td><td align="right">4·09</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">12</td><td></td><td align="right">4·78</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">10</td><td></td><td align="right">5·73</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">9</td><td></td><td align="right">6·38</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">8</td><td></td><td align="right">7·18</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">7</td><td></td><td align="right">8·22</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">6</td><td></td><td align="right">9·6&nbsp;&nbsp;</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">5</td><td></td><td align="right">11·53</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">4</td><td></td><td align="right">14·48</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">3</td><td></td><td align="right">19·45</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">2</td><td></td><td align="right">30·00</td><td></td></tr>
+<tr><td align="left">1</td><td>"</td><td align="right">&#8730;2</td><td></td><td align="right">45·00</td><td></td></tr>
 </table>
 
 
-<p class="cen">§ 7. <span class="smcap">Table of Skin Friction.</span><br />
+<p class="cen">§ 7. <span class="smcap">Table of Skin Friction.</span><br />
 Per sq. ft. for various speeds and surface lengths.</p>
 
 <table class="data" cellpadding="2" cellspacing="0" summary="">
 <tr class="bb bt"><td align="center">Velocity of Wind</td><td align="center">1 ft. Plane</td><td align="center">2 ft. Plane</td><td align="center">4 ft. Plane</td><td align="center">8 ft. Plane</td></tr>
-<tr><td align="center">10</td><td align="center">·00112</td><td align="center">·00105</td><td align="center">·00101</td><td align="center">·000967</td></tr>
-<tr><td align="center">15</td><td align="center">·00237</td><td align="center">·00226</td><td align="center">·00215</td><td align="center">·00205</td></tr>
-<tr><td align="center">20</td><td align="center">·00402</td><td align="center">·00384</td><td align="center">·00365</td><td align="center">·00349</td></tr>
-<tr><td align="center">25</td><td align="center">·00606</td><td align="center">·00579</td><td align="center">·00551</td><td align="center">·00527</td></tr>
-<tr><td align="center">30</td><td align="center">·00850</td><td align="center">·00810</td><td align="center">·00772</td><td align="center">·00736</td></tr>
-<tr class="bb"><td align="center">35</td><td align="center">·01130</td><td align="center">·0108&nbsp;&nbsp;</td><td align="center">·0103&nbsp;&nbsp;</td><td align="center">·0098&nbsp;&nbsp;</td></tr>
+<tr><td align="center">10</td><td align="center">·00112</td><td align="center">·00105</td><td align="center">·00101</td><td align="center">·000967</td></tr>
+<tr><td align="center">15</td><td align="center">·00237</td><td align="center">·00226</td><td align="center">·00215</td><td align="center">·00205</td></tr>
+<tr><td align="center">20</td><td align="center">·00402</td><td align="center">·00384</td><td align="center">·00365</td><td align="center">·00349</td></tr>
+<tr><td align="center">25</td><td align="center">·00606</td><td align="center">·00579</td><td align="center">·00551</td><td align="center">·00527</td></tr>
+<tr><td align="center">30</td><td align="center">·00850</td><td align="center">·00810</td><td align="center">·00772</td><td align="center">·00736</td></tr>
+<tr class="bb"><td align="center">35</td><td align="center">·01130</td><td align="center">·0108&nbsp;&nbsp;</td><td align="center">·0103&nbsp;&nbsp;</td><td align="center">·0098&nbsp;&nbsp;</td></tr>
 </table>
 
 <p><span class="pagenum"><a name="Page_128" id="Page_128">[128]</a></span></p>
@@ -4661,7 +4622,7 @@ Per sq. ft. for various speeds and surface lengths.</p>
 equation</p>
 
 <p class="cen"><ins class="mycorr" title="Correction: See Transcriber's Note at end of text">
-<i>f</i> = 0·00000778<i>l</i><sup>&nbsp;-0·07</sup><i>v</i><sup>1·85</sup><br /></ins></p>
+<i>f</i> = 0·00000778<i>l</i><sup>&nbsp;-0·07</sup><i>v</i><sup>1·85</sup><br /></ins></p>
 
 <p class="noin">Where <i>f</i> = skin friction per sq. ft.; <i>l</i> = length of surface;
 <i>v</i> = velocity in feet per second.</p>
@@ -4670,7 +4631,7 @@ equation</p>
 twelve to fourteen times the skin friction; in a racing
 monoplane from six to eight times.</p>
 
-<p class="cen">§ 8. <span class="smcap">Table I.&mdash;(Metals).</span></p>
+<p class="cen">§ 8. <span class="smcap">Table I.&mdash;(Metals).</span></p>
 
 <table class="data" cellpadding="4" cellspacing="0" summary="">
 <tr class="cen bb bt">
@@ -4679,47 +4640,47 @@ monoplane from six to eight times.</p>
 <td>Elasticity E[A]</td>
 <td>Tenacity<br />per sq. in.</td>
 </tr>
-<tr><td>Magnesium</td><td align="center">1·74</td><td align="center"></td>
+<tr><td>Magnesium</td><td align="center">1·74</td><td align="center"></td>
 <td align="right">22,000-<br />32,000&nbsp;</td>
 </tr>
 <tr><td>Magnalium[B]</td>
-<td align="center">2·4-2·57</td>
-<td align="center">10·2</td>
+<td align="center">2·4-2·57</td>
+<td align="center">10·2</td>
 <td></td>
 </tr>
 <tr><td>Aluminium-<br />Copper[C]</td>
-<td align="center">2·82</td>
+<td align="center">2·82</td>
 <td align="center"></td>
 <td align="right">54,773&nbsp;</td>
 </tr>
 <tr><td align="left">Aluminium</td>
-<td align="center">2·6</td>
-<td align="center">11·1</td>
+<td align="center">2·6</td>
+<td align="center">11·1</td>
 <td align="right">26,535&nbsp;</td>
 </tr>
 <tr>
 <td align="left">Iron</td>
-<td align="center">7·7 (about)</td>
+<td align="center">7·7 (about)</td>
 <td align="center">29</td>
 <td align="right">54,000&nbsp;</td>
 </tr>
 <tr><td align="left">Steel</td>
-<td align="center">7·8 (about)</td>
+<td align="center">7·8 (about)</td>
 <td align="center">32</td>
 <td align="right">100,000&nbsp;</td>
 </tr>
 <tr><td align="left">Brass</td>
-<td align="center">7·8-8·4</td>
+<td align="center">7·8-8·4</td>
 <td align="center">15</td>
 <td align="right">17,500&nbsp;</td>
 </tr>
 <tr><td align="left">Copper</td>
-<td align="center">8·8</td>
+<td align="center">8·8</td>
 <td align="center">36</td>
 <td align="right">33,000&nbsp;</td>
 </tr>
 <tr  class="bb"><td align="left">Mild Steel</td>
-<td align="center">7·8</td>
+<td align="center">7·8</td>
 <td align="center">30</td>
 <td align="right">60,000&nbsp;</td>
 </tr>
@@ -4730,54 +4691,54 @@ monoplane from six to eight times.</p>
 [C] Aluminium 94 per cent., copper 6 per cent. (the best percentage), a 6
 per cent. alloy thereby doubles the tenacity of pure aluminium with but 5 per cent. increase of density.</p>
 
-<p class="cen">§ 9. <span class="smcap">Table II.&mdash;Wind Pressures.</span></p>
+<p class="cen">§ 9. <span class="smcap">Table II.&mdash;Wind Pressures.</span></p>
 
 <p class="cen"><i>p</i> = <i>kv</i><sup>2</sup>.<br /></p>
 
-<p><i>k</i> coefficient (mean value taken) ·003 (miles per hour)
-= 0·0016 ft. per second. <i>p</i> = pressure in lb. per sq. ft.
+<p><i>k</i> coefficient (mean value taken) ·003 (miles per hour)
+= 0·0016 ft. per second. <i>p</i> = pressure in lb. per sq. ft.
 <i>v</i> = velocity of wind.</p>
 
 <table border="0" cellpadding="4" cellspacing="0" summary="">
 <tr><td align="center">Miles per hr.</td><td align="center">Ft. per sec.</td><td align="center">Lb. per sq. ft.</td></tr>
-<tr><td align="center">10</td><td align="center">14·7</td><td align="center">0·300</td></tr>
-<tr><td align="center">12</td><td align="center">17·6</td><td align="center">0·432</td></tr>
-<tr><td align="center">14</td><td align="center">20·5</td><td align="center">0·588</td></tr>
-<tr><td align="center">16</td><td align="center">23·5</td><td align="center">0·768</td></tr>
+<tr><td align="center">10</td><td align="center">14·7</td><td align="center">0·300</td></tr>
+<tr><td align="center">12</td><td align="center">17·6</td><td align="center">0·432</td></tr>
+<tr><td align="center">14</td><td align="center">20·5</td><td align="center">0·588</td></tr>
+<tr><td align="center">16</td><td align="center">23·5</td><td align="center">0·768</td></tr>
 </table>
 
 <p><span class="pagenum"><a name="Page_129" id="Page_129">[129]</a></span></p>
 
 <table border="0" cellpadding="4" cellspacing="0" summary="">
 <tr><td align="center">Miles per hr.</td><td align="center">Ft. per sec.</td><td align="center">Lb. per sq. ft.</td></tr>
-<tr><td align="center">18</td><td align="center">26·4</td><td align="center">0·972</td></tr>
-<tr><td align="center">20</td><td align="center">29·35</td><td align="center">1·200</td></tr>
-<tr><td align="center">25</td><td align="center">36·7</td><td align="center">1·875</td></tr>
-<tr><td align="center">30</td><td align="center">43·9</td><td align="center">2·700</td></tr>
-<tr><td align="center">35</td><td align="center">51·3</td><td align="center">3·675</td></tr>
+<tr><td align="center">18</td><td align="center">26·4</td><td align="center">0·972</td></tr>
+<tr><td align="center">20</td><td align="center">29·35</td><td align="center">1·200</td></tr>
+<tr><td align="center">25</td><td align="center">36·7</td><td align="center">1·875</td></tr>
+<tr><td align="center">30</td><td align="center">43·9</td><td align="center">2·700</td></tr>
+<tr><td align="center">35</td><td align="center">51·3</td><td align="center">3·675</td></tr>
 </table>
 
-<p>§ 10. Representing normal pressure on a plane surface
-by 1; pressure on a rod (round section) is 0·6; on a
-symmetrical elliptic cross section (axes 2:1) is 0·2 (approx.).
+<p>§ 10. Representing normal pressure on a plane surface
+by 1; pressure on a rod (round section) is 0·6; on a
+symmetrical elliptic cross section (axes 2:1) is 0·2 (approx.).
 Similar shape, but axes 6:1, and edges sharpened (<i>see</i>
-ch. ii., §&nbsp;5), is only 0·05, or 1/20, and for the body of
-minimum resistance (<i>see</i> ch. ii., §&nbsp;4) about 1/24.</p>
+ch. ii., §&nbsp;5), is only 0·05, or 1/20, and for the body of
+minimum resistance (<i>see</i> ch. ii., §&nbsp;4) about 1/24.</p>
 
-<p class="cen">§ 11. <span class="smcap">Table III.&mdash;Lift and Drift.</span></p>
+<p class="cen">§ 11. <span class="smcap">Table III.&mdash;Lift and Drift.</span></p>
 
 <p>On a well shaped aerocurve or correctly designed
-cambered surface. Aspect ratio 4·5.</p>
+cambered surface. Aspect ratio 4·5.</p>
 
 <table border="0" cellpadding="4" cellspacing="0" summary="">
 <tr><td align="center">Inclination.</td><td align="center">Ratio Lift to Drift.</td></tr>
-<tr><td align="center">0°</td><td align="center">19:1</td></tr>
-<tr><td align="center">2·87°</td><td align="center">15:1</td></tr>
-<tr><td align="center">3·58°</td><td align="center">16:1</td></tr>
-<tr><td align="center">4·09°</td><td align="center">14:1</td></tr>
-<tr><td align="center">4·78°</td><td align="center">12:1</td></tr>
-<tr><td align="center">5·73°</td><td align="center">9·6:1</td></tr>
-<tr><td align="center">7·18°</td><td align="center">7·9:1</td></tr>
+<tr><td align="center">0°</td><td align="center">19:1</td></tr>
+<tr><td align="center">2·87°</td><td align="center">15:1</td></tr>
+<tr><td align="center">3·58°</td><td align="center">16:1</td></tr>
+<tr><td align="center">4·09°</td><td align="center">14:1</td></tr>
+<tr><td align="center">4·78°</td><td align="center">12:1</td></tr>
+<tr><td align="center">5·73°</td><td align="center">9·6:1</td></tr>
+<tr><td align="center">7·18°</td><td align="center">7·9:1</td></tr>
 </table>
 
 <p>Wind velocity 40 miles per hour. (The above deduced
@@ -4787,7 +4748,7 @@ from some experiments of Sir Hiram Maxim.)</p>
 should lift 21 oz. to 24 oz. per sq. ft.<span class="pagenum"><a name="Page_130" id="Page_130">[130]</a></span></p>
 
 
-<p class="cen">§ 12. <span class="smcap">Table IV.&mdash;Lift and Drift.</span></p>
+<p class="cen">§ 12. <span class="smcap">Table IV.&mdash;Lift and Drift.</span></p>
 
 <p>On a plane aerofoil.</p>
 
@@ -4795,16 +4756,16 @@ should lift 21 oz. to 24 oz. per sq. ft.<span class="pagenum"><a name="Page_130"
 
 <table border="0" cellpadding="4" cellspacing="0" summary="">
 <tr><td align="center">Inclination.</td><td align="center">Ratio Lift to Drift.</td></tr>
-<tr><td align="center">1°</td><td align="center">58·3:1</td></tr>
-<tr><td align="center">2°</td><td align="center">29·2:1</td></tr>
-<tr><td align="center">3°</td><td align="center">19·3:1</td></tr>
-<tr><td align="center">4°</td><td align="center">14·3:1</td></tr>
-<tr><td align="center">5°</td><td align="center">11·4:1</td></tr>
-<tr><td align="center">6°</td><td align="center">9·5:1</td></tr>
-<tr><td align="center">7°</td><td align="center">8·0:1</td></tr>
-<tr><td align="center">8°</td><td align="center">7·0:1</td></tr>
-<tr><td align="center">9°</td><td align="center">6·3:1</td></tr>
-<tr><td align="center">10°</td><td align="center">5·7:1</td></tr>
+<tr><td align="center">1°</td><td align="center">58·3:1</td></tr>
+<tr><td align="center">2°</td><td align="center">29·2:1</td></tr>
+<tr><td align="center">3°</td><td align="center">19·3:1</td></tr>
+<tr><td align="center">4°</td><td align="center">14·3:1</td></tr>
+<tr><td align="center">5°</td><td align="center">11·4:1</td></tr>
+<tr><td align="center">6°</td><td align="center">9·5:1</td></tr>
+<tr><td align="center">7°</td><td align="center">8·0:1</td></tr>
+<tr><td align="center">8°</td><td align="center">7·0:1</td></tr>
+<tr><td align="center">9°</td><td align="center">6·3:1</td></tr>
+<tr><td align="center">10°</td><td align="center">5·7:1</td></tr>
 </table>
 
 
@@ -4812,7 +4773,7 @@ should lift 21 oz. to 24 oz. per sq. ft.<span class="pagenum"><a name="Page_130"
 
 <p>A useful formula for a single plane surface. P = pressure
 supporting the plane in pounds per square foot, <i>k</i> a
-constant = 0·003 in miles per hour, <i>d</i> = the density of
+constant = 0·003 in miles per hour, <i>d</i> = the density of
 the air.</p>
 
 <p>A = the area of the plane, V relative velocity of translation
@@ -4831,7 +4792,7 @@ sustentation diminishes with the speed, the work of penetration
 varies as the cube of the speed.<span class="pagenum"><a name="Page_131" id="Page_131">[131]</a></span></p>
 
 
-<p class="cen">§ 13. <span class="smcap">Table V.&mdash;Timber.</span></p>
+<p class="cen">§ 13. <span class="smcap">Table V.&mdash;Timber.</span></p>
 
 <table border="1" cellpadding="4" cellspacing="0" summary="">
 <tr><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center">Relative</td></tr>
@@ -4839,29 +4800,29 @@ varies as the cube of the speed.<span class="pagenum"><a name="Page_131" id="Pag
 <tr><td align="center"></td><td align="center"></td><td align="center">Weight</td><td align="center">Strength per</td><td align="center">Breaking</td><td align="center">Relative</td><td align="center">Elasticity</td><td align="center">Bending</td></tr>
 <tr><td align="center">Material</td><td align="center">Specific</td><td align="center">per</td><td align="center">Sq. In.</td><td align="center">Load (Lb.)</td><td align="center">Resilience</td><td align="center">in Millions</td><td align="center">Strength</td></tr>
 <tr><td align="center"></td><td align="center">Gravity</td><td align="center">Cub. Ft.</td><td align="center">in Lb.</td><td align="center">Span</td><td align="center">in Bending</td><td align="center">of Lb. per</td><td align="center">compared</td></tr>
-<tr><td align="center"> </td><td align="center"></td><td align="center">in Lb.</td><td align="center"></td><td align="center">1' × 1"</td><td align="center"></td><td align="center">Sq. In. for</td><td align="center">with</td></tr>
-<tr><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center">× 1"</td><td align="center"></td><td align="center">Bending</td><td align="left">Weight</td></tr>
-<tr><td align="center">Ash</td><td align="center">·79</td><td align="center">43-52</td><td align="center">14,000-17,000</td><td align="center">622</td><td align="center">4·69</td><td align="center">1·55</td><td align="center">13·0</td></tr>
-<tr><td align="center">Bamboo</td><td align="center"></td><td align="center">25[A]</td><td align="center">6300[A]</td><td align="center"></td><td align="center">3·07</td><td align="center">3·20</td><td align="center"></td></tr>
-<tr><td align="center">Beech</td><td align="center">·69</td><td align="center">43</td><td align="center">10,000-12,000</td><td align="center">850</td><td align="center"></td><td align="center">1·65</td><td align="center">19·8</td></tr>
-<tr><td align="center">Birch</td><td align="center">·71</td><td align="center">45</td><td align="center">15,000</td><td align="center">550</td><td align="center"></td><td align="center">3·28</td><td align="center">12·2</td></tr>
-<tr><td align="center">Box</td><td align="center">1·28</td><td align="center">80</td><td align="center">20,000-23,000</td><td align="center">815</td><td align="center"></td><td align="center"></td><td align="center">10·2</td></tr>
-<tr><td align="center">Cork</td><td align="center">·24</td><td align="center">15</td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td></tr>
+<tr><td align="center"> </td><td align="center"></td><td align="center">in Lb.</td><td align="center"></td><td align="center">1' × 1"</td><td align="center"></td><td align="center">Sq. In. for</td><td align="center">with</td></tr>
+<tr><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center">× 1"</td><td align="center"></td><td align="center">Bending</td><td align="left">Weight</td></tr>
+<tr><td align="center">Ash</td><td align="center">·79</td><td align="center">43-52</td><td align="center">14,000-17,000</td><td align="center">622</td><td align="center">4·69</td><td align="center">1·55</td><td align="center">13·0</td></tr>
+<tr><td align="center">Bamboo</td><td align="center"></td><td align="center">25[A]</td><td align="center">6300[A]</td><td align="center"></td><td align="center">3·07</td><td align="center">3·20</td><td align="center"></td></tr>
+<tr><td align="center">Beech</td><td align="center">·69</td><td align="center">43</td><td align="center">10,000-12,000</td><td align="center">850</td><td align="center"></td><td align="center">1·65</td><td align="center">19·8</td></tr>
+<tr><td align="center">Birch</td><td align="center">·71</td><td align="center">45</td><td align="center">15,000</td><td align="center">550</td><td align="center"></td><td align="center">3·28</td><td align="center">12·2</td></tr>
+<tr><td align="center">Box</td><td align="center">1·28</td><td align="center">80</td><td align="center">20,000-23,000</td><td align="center">815</td><td align="center"></td><td align="center"></td><td align="center">10·2</td></tr>
+<tr><td align="center">Cork</td><td align="center">·24</td><td align="center">15</td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td></tr>
 <tr><td align="center">Fir (Norway</td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td></tr>
-<tr><td align="center">Spruce)</td><td align="center">·51</td><td align="center">32</td><td align="center">9,000-11,000</td><td align="center">450</td><td align="center">3·01</td><td align="center">1·70</td><td align="center">14·0</td></tr>
+<tr><td align="center">Spruce)</td><td align="center">·51</td><td align="center">32</td><td align="center">9,000-11,000</td><td align="center">450</td><td align="center">3·01</td><td align="center">1·70</td><td align="center">14·0</td></tr>
 <tr><td align="center">American</td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td></tr>
-<tr><td align="center">Hickory</td><td align="center"></td><td align="center">49</td><td align="center">11,000</td><td align="center">800</td><td align="center">3·47</td><td align="center">2·40</td><td align="center">16·3</td></tr>
+<tr><td align="center">Hickory</td><td align="center"></td><td align="center">49</td><td align="center">11,000</td><td align="center">800</td><td align="center">3·47</td><td align="center">2·40</td><td align="center">16·3</td></tr>
 <tr><td align="center">Honduras</td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td></tr>
-<tr><td align="center">Mahogany</td><td align="center">·56</td><td align="center">35</td><td align="center">20,000</td><td align="center">750</td><td align="center">3·40</td><td align="center">1·60</td><td align="center">21·4</td></tr>
-<tr><td align="center">Maple</td><td align="center">·68</td><td align="center">44</td><td align="center">10,600</td><td align="center">750</td><td align="center"></td><td align="center"></td><td align="center">17·0</td></tr>
+<tr><td align="center">Mahogany</td><td align="center">·56</td><td align="center">35</td><td align="center">20,000</td><td align="center">750</td><td align="center">3·40</td><td align="center">1·60</td><td align="center">21·4</td></tr>
+<tr><td align="center">Maple</td><td align="center">·68</td><td align="center">44</td><td align="center">10,600</td><td align="center">750</td><td align="center"></td><td align="center"></td><td align="center">17·0</td></tr>
 <tr><td align="center">American White</td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td></tr>
-<tr><td align="center">Pine</td><td align="center">·42</td><td align="center">25</td><td align="center">11,800</td><td align="center">450</td><td align="center">2·37</td><td align="center">1·39</td><td align="center">18·0</td></tr>
-<tr><td align="center">Lombardy Poplar</td><td align="center"></td><td align="center">24</td><td align="center">7,000</td><td align="center">550</td><td align="center">2·89</td><td align="center">0·77</td><td align="center">22·9</td></tr>
+<tr><td align="center">Pine</td><td align="center">·42</td><td align="center">25</td><td align="center">11,800</td><td align="center">450</td><td align="center">2·37</td><td align="center">1·39</td><td align="center">18·0</td></tr>
+<tr><td align="center">Lombardy Poplar</td><td align="center"></td><td align="center">24</td><td align="center">7,000</td><td align="center">550</td><td align="center">2·89</td><td align="center">0·77</td><td align="center">22·9</td></tr>
 <tr><td align="center">American Yellow</td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td></tr>
-<tr><td align="center">Poplar</td><td align="center"></td><td align="center">44</td><td align="center">10,000</td><td align="center"></td><td align="center">3·63</td><td align="center">1·40</td><td align="center"></td></tr>
-<tr><td align="center">Satinwood</td><td align="center">·96</td><td align="center">60</td><td align="center"></td><td align="center">1,033</td><td align="center"></td><td align="center"></td><td align="center">17·2</td></tr>
-<tr><td align="center">Spruce</td><td align="center">·50</td><td align="center">31</td><td align="center">12,400</td><td align="center">450</td><td align="center"></td><td align="center"></td><td align="center">14·5</td></tr>
-<tr><td align="center">Tubular Ash,<i>t</i> =1/8 <i>d</i></td><td align="center"></td><td align="center">47</td><td align="center"></td><td align="center"></td><td align="center">3·50</td><td align="center">1·55</td><td align="center"></td></tr>
+<tr><td align="center">Poplar</td><td align="center"></td><td align="center">44</td><td align="center">10,000</td><td align="center"></td><td align="center">3·63</td><td align="center">1·40</td><td align="center"></td></tr>
+<tr><td align="center">Satinwood</td><td align="center">·96</td><td align="center">60</td><td align="center"></td><td align="center">1,033</td><td align="center"></td><td align="center"></td><td align="center">17·2</td></tr>
+<tr><td align="center">Spruce</td><td align="center">·50</td><td align="center">31</td><td align="center">12,400</td><td align="center">450</td><td align="center"></td><td align="center"></td><td align="center">14·5</td></tr>
+<tr><td align="center">Tubular Ash,<i>t</i> =1/8 <i>d</i></td><td align="center"></td><td align="center">47</td><td align="center"></td><td align="center"></td><td align="center">3·50</td><td align="center">1·55</td><td align="center"></td></tr>
 </table>
 
 
@@ -4870,7 +4831,7 @@ varies as the cube of the speed.<span class="pagenum"><a name="Page_131" id="Pag
 
 <p><span class="pagenum"><a name="Page_132" id="Page_132">[132]</a></span></p>
 
-<p>§ 14.&mdash;<b>Formula connecting the Weight Lifted
+<p>§ 14.&mdash;<b>Formula connecting the Weight Lifted
 in Pounds per Square Foot and the Velocity.</b>&mdash;The
 empirical formula</p>
 
@@ -4879,8 +4840,8 @@ empirical formula</p>
 <blockquote><p>
 Where W   = weight lifted in lb. per sq. ft.<br />
 <span style="margin-left: 3em;">V&nbsp;  = velocity in ft. per sec.</span><br />
-<span style="margin-left: 3em;">C&nbsp;  = a constant = 0·025.</span><br />
-<span style="margin-left: 3em;"><i>g</i> = 32·2, or 32 approx.</span><br />
+<span style="margin-left: 3em;">C&nbsp;  = a constant = 0·025.</span><br />
+<span style="margin-left: 3em;"><i>g</i> = 32·2, or 32 approx.</span><br />
 </p></blockquote>
 
 <p>may be used for a thoroughly efficient model. This gives
@@ -4891,13 +4852,13 @@ Where W   = weight lifted in lb. per sq. ft.<br />
 <tr><td align="center">21 oz.</td><td align="center">"</td><td align="center">"</td><td align="center">30</td><td align="center">"</td></tr>
 <tr><td align="center">6 oz.</td><td align="center">"</td><td align="center">"</td><td align="center">15</td><td align="center">"</td></tr>
 <tr><td align="center">4 oz.</td><td align="center">"</td><td align="center">"</td><td align="center">12</td><td align="center">"</td></tr>
-<tr><td align="center">2·7 oz.</td><td align="center">"</td><td align="center">"</td><td align="center">10</td><td align="center">"</td></tr>
+<tr><td align="center">2·7 oz.</td><td align="center">"</td><td align="center">"</td><td align="center">10</td><td align="center">"</td></tr>
 </table>
 
 <p>Remember the results work out in feet per second. To
 convert (approximately) into miles per hour multiply by 2/3.</p>
 
-<p>§ 15. <b>Formula connecting Models of Similar
+<p>§ 15. <b>Formula connecting Models of Similar
 Design, but Different Weights.</b></p>
 
 <p class="cen">D &#8733;&#8730;W.</p>
@@ -4917,7 +4878,7 @@ but not too much reliance must be placed on the above.
 The record for a 1 oz. model to date is over 300 yards
 (with the wind, of course), say 750 ft. in calm air.</p>
 
-<p>§ 16. <b>Power and Speed.</b>&mdash;The following formula,
+<p>§ 16. <b>Power and Speed.</b>&mdash;The following formula,
 given by Mr. L. Blin Desbleds, between these is&mdash;</p>
 
 <p class="cen"><span style="font-size:large;">
@@ -4940,7 +4901,7 @@ power 2<span style="font-size:large;"><sup>3</sup>/<sub>8</sub></span> times as
 of minimum power" being the speed at which the aeroplane
 must travel for the minimum expenditure of power.</p>
 
-<p>§ 17. The thrust of the propeller has evidently to balance
+<p>§ 17. The thrust of the propeller has evidently to balance
 the</p>
 
 <blockquote><p class="noin">Aerodynamic resistance                        = R<br />
@@ -4961,12 +4922,12 @@ by R + S is a minimum when</p>
 to give. Now supposing the propeller's efficiency to be
 80 per cent., then P&mdash;the minimum propulsion power</p>
 
-<p class="cen">= <span style="font-size:large;"><sup>4</sup>/<sub>3</sub></span>R × <span style="font-size:large;"><sup>100</sup>/<sub>80</sub></span> × <span style="font-size:large;"><sup>100</sup>/<sub>75 </sub></span>× <i>v</i>.</p>
+<p class="cen">= <span style="font-size:large;"><sup>4</sup>/<sub>3</sub></span>R × <span style="font-size:large;"><sup>100</sup>/<sub>80</sub></span> × <span style="font-size:large;"><sup>100</sup>/<sub>75 </sub></span>× <i>v</i>.</p>
 
 <p>Where 25 per cent. is the slip of the screw, <i>v</i> the velocity
 of the aeroplane.</p>
 
-<p>§ 18. <b>To determine experimentally the Static
+<p>§ 18. <b>To determine experimentally the Static
 Thrust of a Propeller.</b>&mdash;Useful for models intended to
 raise themselves from the ground under their own power,
 and for helicopters.</p>
@@ -5015,20 +4976,20 @@ driven by 56 watts.</p>
 
 <p>at the observed number of revolutions per minute.</p>
 
-<p>§ 19. N.B.&mdash;The h.p. required to drive a propeller varies
+<p>§ 19. N.B.&mdash;The h.p. required to drive a propeller varies
 as the cube of the revolutions.</p>
 
 <p><i>Proof.</i>&mdash;Double the speed of the screw, then it strikes
 the air twice as hard; it also strikes twice as much air, and
 the motor has to go twice as fast to do it.</p>
 
-<p>§ 20. To compare one model with another the formula</p>
+<p>§ 20. To compare one model with another the formula</p>
 
-<p class="cen"><span style="font-size:large;"><sup>Weight × velocity (in ft. per sec.)</sup>/<sub>horse-power</sub></span></p>
+<p class="cen"><span style="font-size:large;"><sup>Weight × velocity (in ft. per sec.)</sup>/<sub>horse-power</sub></span></p>
 
 <p>is sometimes useful.</p>
 
-<p>§ 21. <b>A Horse-power</b> is 33,000 lb. raised one foot in
+<p>§ 21. <b>A Horse-power</b> is 33,000 lb. raised one foot in
 one minute, or 550 lb. one foot in one second.</p>
 
 <p>A clockwork spring raised 1 lb. through 4&frac12; ft. in 3
@@ -5038,33 +4999,33 @@ seconds. What is its h.p.?</p>
 is   1 lb.    "       90 ft.  " 1 minute.</p>
 
 <p class="cen">&#8756;  Work done is 90 ft.-lb.<br />
-= <span style="font-size:large;"><sup>90</sup>/<sub>33000</sub></span> = 0·002727 h.p.</p>
+= <span style="font-size:large;"><sup>90</sup>/<sub>33000</sub></span> = 0·002727 h.p.</p>
 <p><span class="pagenum"><a name="Page_136" id="Page_136">[136]</a></span></p>
 
 <p>The weight of the spring was 6&frac34; oz. (this is taken from
 an actual experiment), i.e. this motor develops power at the
-rate of 0·002727 h.p. for 3&frac12; seconds only.</p>
+rate of 0·002727 h.p. for 3&frac12; seconds only.</p>
 
-<p>§ 22. <b>To Ascertain the H.P. of a Rubber Motor.</b>
+<p>§ 22. <b>To Ascertain the H.P. of a Rubber Motor.</b>
 Supposing a propeller wound up to 250 turns to run down
 in 15 seconds, i.e. at a mean speed of 1200 revolutions per
 minute or 20 per second. Suppose the mean thrust to be
 2 oz., and let the pitch of the propeller be 1 foot. Then
 the number of foot-pounds of energy developed</p>
 
-<p class="cen">= <span style="font-size:larger;"><sup>2 oz. × 1200 revols. × 1 ft. (pitch)</sup> / <sub>16 oz.</sub></span></p>
+<p class="cen">= <span style="font-size:larger;"><sup>2 oz. × 1200 revols. × 1 ft. (pitch)</sup> / <sub>16 oz.</sub></span></p>
 
 <p class="noin">= 150 ft.-lb. per minute.</p>
 <p>But the rubber motor runs down in 15 seconds.<br />
 &#8756; Energy really developed is</p>
 
-<p class="cen">= <span style="font-size:larger;"><sup>150 × 15</sup> / <sub>60</sub></span> = 37·5 ft.-lb.</p>
+<p class="cen">= <span style="font-size:larger;"><sup>150 × 15</sup> / <sub>60</sub></span> = 37·5 ft.-lb.</p>
 
 
-<p>The motor develops power at rate of <span style="font-size:larger;"><sup>150</sup>/<sub>33000</sub></span> = 0·004545
+<p>The motor develops power at rate of <span style="font-size:larger;"><sup>150</sup>/<sub>33000</sub></span> = 0·004545
 h.p., but for 15 seconds only.</p>
 
-<p>§ 23. <b>Foot-pounds of Energy in a Given Weight
+<p>§ 23. <b>Foot-pounds of Energy in a Given Weight
 of Rubber</b> (experimental determination of).</p>
 
 <table border="0" cellpadding="4" cellspacing="0" summary="">
@@ -5074,8 +5035,8 @@ of Rubber</b> (experimental determination of).</p>
 </table>
 
 <blockquote><p class="noin">12 oz. were raised 19 ft. in 5 seconds.<br />
-i.e. &frac34; lb. was raised 19 × 12 ft. in 1 minute.<br />
-i.e. 1 lb. was raised 19 × 3 × 3 ft. in 1 minute.<br />
+i.e. &frac34; lb. was raised 19 × 12 ft. in 1 minute.<br />
+i.e. 1 lb. was raised 19 × 3 × 3 ft. in 1 minute.<br />
 = 171 ft. in 1 minute.</p></blockquote>
 
 <p class="noin">i.e. 171 ft.-lb. of energy per minute. But actual time was
@@ -5095,17 +5056,17 @@ at the end of the experiment. Now allowing for friction,
 etc. being the same as on an actual model, we can take &frac34; of
 a ft.-lb. for the unwound amount and estimate the total
 energy as 15 ft.-lb. as a minimum. The energy actually
-developed being at the rate of 0·0055 h.p., or <sup>1</sup>/<sub>200</sub> of a h.p.
+developed being at the rate of 0·0055 h.p., or <sup>1</sup>/<sub>200</sub> of a h.p.
 if supposed uniform.</p>
 
-<p>§ 24. The actual energy derivable from 1 lb. weight of
+<p>§ 24. The actual energy derivable from 1 lb. weight of
 rubber is stated to be 300 ft.-lb. On this basis 2-<sup>7</sup>/<sub>16</sub> oz.
-should be capable of giving 45·7 ft.-lb. of energy, i.e. three
+should be capable of giving 45·7 ft.-lb. of energy, i.e. three
 times the amount given above. Now the motor-rubber not
 lubricated was only given 200 turns&mdash;lubricated 400 could
 have been given it, 600 probably before rupture&mdash;and the
 energy then derivable would certainly have been approximating
-to 45 ft.-lb., i.e. 36·25. Now on the basis of 300
+to 45 ft.-lb., i.e. 36·25. Now on the basis of 300
 ft.-lb. per lb. a weight of &frac12; oz. (the amount of rubber
 carried in "one-ouncers") gives 9 ft.-lb. of energy. Now
 assuming the gliding angle (including weight of propellers)
@@ -5116,7 +5077,7 @@ vertically. Now 9 ft.-lb. of energy will lift 1 oz. 154 ft.
 Therefore theoretically it will drive it a distance (in yards)
 of</p>
 
-<p class="cen"><span style="font-size:larger;"><sup>8 × 154</sup>/<sub>3</sub></span> = 410·6 yards.</p>
+<p class="cen"><span style="font-size:larger;"><sup>8 × 154</sup>/<sub>3</sub></span> = 410·6 yards.</p>
 <p><span class="pagenum"><a name="Page_138" id="Page_138">[138]</a></span></p>
 
 <p>Now the greatest distance that a 1 oz. model has flown
@@ -5134,26 +5095,26 @@ method of working out.</p>
 <p>Mr. T.W.K. Clarke informs me that in his one-ouncers
 the gliding angle is about 1 in 5.</p>
 
-<p>§ 25. <b>To Test Different Motors or Different
+<p>§ 25. <b>To Test Different Motors or Different
 Powers of the Same Kind of Motor.</b>&mdash;Test them on
 the same machine, and do not use different motors or different
 powers on different machines.</p>
 
-<p>§ 26. <b>Efficiency of a Model.</b>&mdash;The efficiency of a
+<p>§ 26. <b>Efficiency of a Model.</b>&mdash;The efficiency of a
 model depends on the weight carried per h.p.</p>
 
-<p>§ 27. <b>Efficiency of Design.</b>&mdash;The efficiency of some
+<p>§ 27. <b>Efficiency of Design.</b>&mdash;The efficiency of some
 particular design depends on the amount of supporting surface
 necessary at a given speed.</p>
 
-<p>§ 28. <b>Naphtha Engines</b>, that is, engines made on
+<p>§ 28. <b>Naphtha Engines</b>, that is, engines made on
 the principle of the steam engine, but which use a light
 spirit of petrol or similar agent in their generator instead
 of water with the same amount of heat, will develop
 twice as much energy as in the case of the ordinary steam
 engine.</p>
 
-<p>§ 29.<b>Petrol Motors.</b></p>
+<p>§ 29.<b>Petrol Motors.</b></p>
 
 <table border="0" cellpadding="4" cellspacing="0" summary="">
 <tr><td align="center">Horse-power.</td><td align="center">No. of Cylinders.</td><td align="left">Weight.</td></tr>
@@ -5164,12 +5125,12 @@ engine.</p>
 
 <p><span class="pagenum"><a name="Page_139" id="Page_139">[139]</a></span></p>
 
-<p>§ 30. <b>The Horse-power of Model Petrol
+<p>§ 30. <b>The Horse-power of Model Petrol
 Motors.</b>&mdash;Formula for rating of the above.</p>
 
 <p class="cen">(R.P.M. = revolutions per minute.)<br />
 
-H.P. = <span style="font-size:larger;"><sup>(Bore)</sup><sup>2 × stroke × no. of cylinders × R.P.M.</sup>/<sub>12,000</sub></span></p>
+H.P. = <span style="font-size:larger;"><sup>(Bore)</sup><sup>2 × stroke × no. of cylinders × R.P.M.</sup>/<sub>12,000</sub></span></p>
 
 <p>If the right-hand side of the equation gives a less h.p.
 than that stated for some particular motor, then it follows
@@ -5180,11 +5141,11 @@ that the h.p. of the motor has been over-estimated.</p>
 <span class="caption smcap">Fig. 56.</span>
 </div>
 
-<p>§ 30A. <b>Relation between Static Thrust of Propeller
+<p>§ 30A. <b>Relation between Static Thrust of Propeller
 and Total Weight of Model.</b>&mdash;The thrust
 should be approx. = &frac14; of the weight.<span class="pagenum"><a name="Page_140" id="Page_140">[140]</a></span></p>
 
-<p>§ 31. <b>How to find the Height of an Inaccessible
+<p>§ 31. <b>How to find the Height of an Inaccessible
 Object by Means of Three Observations taken on
 the Ground (supposed flat) in the same Straight
 Line.</b>&mdash;Let A, C, B be the angular elevations of the object
@@ -5196,7 +5157,7 @@ we have (see Fig. 56)</p>
 <p class="cen">
 <i>h</i><span style="font-size:larger;"><sup>2</sup></span> = <span style="font-size:larger;"><sup><i>abc</i></sup>/<sub>(<i>a</i> cot<sup>2</sup>A - <i>c</i> cot<sup>2</sup>C + <i>b</i> cot<sup>2</sup>B)</sub></span>.</p>
 
-<p>§ 32. <b>Formula</b> for calculating the I.H.P. (indicated
+<p>§ 32. <b>Formula</b> for calculating the I.H.P. (indicated
 horse-power) of a single-cylinder double-acting steam-engine.</p>
 
 <p>Indicated h.p. means the h.p. actually exerted by the
@@ -5204,7 +5165,7 @@ steam in the cylinder without taking into account engine
 friction. Brake h.p. or effective h.p. is the actual h.p.
 delivered by the crank shaft of the engine.</p>
 
-<p class="cen">I.H.P. = <span style="font-size:larger;"><sup>2 × S × R × A × P</sup>/<sub>33,000</sub></span>.</p>
+<p class="cen">I.H.P. = <span style="font-size:larger;"><sup>2 × S × R × A × P</sup>/<sub>33,000</sub></span>.</p>
 <p class="noin">Where    <span style="margin-left: 1.7em;">S = stroke in feet.</span><br />
 <span style="margin-left: 4.5em;">R = revolutions per minute.</span><br />
 <span style="margin-left: 4.5em;">A = area of piston in inches.</span><br />
@@ -5220,19 +5181,19 @@ table.<span class="pagenum"><a name="Page_141" id="Page_141">[141]</a></span></p
 
 <table border="1" cellpadding="4" cellspacing="0" summary="">
 <tr><td align="center">Cut-off</td><td align="center">Constant</td><td align="center">Cut-off</td><td align="center">Constant</td><td align="center">Cut-off</td><td align="center">Constant</td></tr>
-<tr><td align="center"><sup>1</sup>/<sub>6</sub></td><td align="center">·566</td><td align="center"><sup>3</sup>/<sub>8</sub></td><td align="center">·771</td><td align="center"><sup>2</sup>/<sub>3</sub></td><td align="center">·917</td></tr>
-<tr><td align="center"><sup>1</sup>/<sub>5</sub></td><td align="center">·603</td><td align="center">·4</td><td align="center">·789</td><td align="center">·7</td><td align="center">·926</td></tr>
-<tr><td align="center">&frac14;</td><td align="center">·659</td><td align="center">&frac12;</td><td align="center">·847</td><td align="center">&frac34;</td><td align="center">·937</td></tr>
-<tr><td align="center">·3</td><td align="center">·708</td><td align="center">·6</td><td align="center">·895</td><td align="center">·8</td><td align="center">·944</td></tr>
-<tr><td align="center"><sup>1</sup>/<sub>3</sub></td><td align="center">·743</td><td align="center"><sup>5</sup>/<sub>8</sub></td><td align="center">·904</td><td align="center"><sup>7</sup>/<sub>8</sub></td><td align="center">·951</td></tr>
+<tr><td align="center"><sup>1</sup>/<sub>6</sub></td><td align="center">·566</td><td align="center"><sup>3</sup>/<sub>8</sub></td><td align="center">·771</td><td align="center"><sup>2</sup>/<sub>3</sub></td><td align="center">·917</td></tr>
+<tr><td align="center"><sup>1</sup>/<sub>5</sub></td><td align="center">·603</td><td align="center">·4</td><td align="center">·789</td><td align="center">·7</td><td align="center">·926</td></tr>
+<tr><td align="center">&frac14;</td><td align="center">·659</td><td align="center">&frac12;</td><td align="center">·847</td><td align="center">&frac34;</td><td align="center">·937</td></tr>
+<tr><td align="center">·3</td><td align="center">·708</td><td align="center">·6</td><td align="center">·895</td><td align="center">·8</td><td align="center">·944</td></tr>
+<tr><td align="center"><sup>1</sup>/<sub>3</sub></td><td align="center">·743</td><td align="center"><sup>5</sup>/<sub>8</sub></td><td align="center">·904</td><td align="center"><sup>7</sup>/<sub>8</sub></td><td align="center">·951</td></tr>
 </table>
 
 
-<p>Rule.&mdash;"Add 14·7 to gauge pressure of boiler, this
+<p>Rule.&mdash;"Add 14·7 to gauge pressure of boiler, this
 giving 'absolute steam pressure,' multiply this sum by the
 number opposite the fraction representing the point of cut-off
 in the cylinder in accompanying table. Subtract 17
-from the product and multiply the remainder by 0·9. The
+from the product and multiply the remainder by 0·9. The
 result will be very nearly the M.E.P." (R.M. de Vignier.)</p>
 
 
@@ -5298,12 +5259,12 @@ Model Flyers.</span>
 </div>
 
 <p>For illustrations, etc., of the Fleming-Williams model,
-<i>see</i> ch. v., §&nbsp;23.</p>
+<i>see</i> ch. v., §&nbsp;23.</p>
 
 <p>(Fig. 60.) This is another well-constructed and efficient
 model, the shape and character of the aerofoil surfaces much
 resembling those of the French toy monoplane AL-MA (see
-§&nbsp;4, ch. vii.), but they are supported and held in position by
+§&nbsp;4, ch. vii.), but they are supported and held in position by
 quite a different method, a neat little device enabling the front
 plane to become partly detached on collision with any obstacle.
 The model is provided with a keel (below the centre of gravity),
@@ -5384,7 +5345,7 @@ GREAT WINDMILL STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.</p>
 
 <div class="footnote"><p><a name="Footnote_1_1" id="Footnote_1_1"></a><a href="#FNanchor_1_1"><span class="label">[1]</span></a> The smallest working steam engine that the writer has ever
 heard of has a net weight of 4 grains. One hundred such engines
-would be required to weigh one ounce. The bore being 0·03 in., and
+would be required to weigh one ounce. The bore being 0·03 in., and
 stroke<sup>1</sup>/<sub>32</sub> of an inch, r.p.m. 6000 per min., h.p. developed<sup>1</sup>/<sub>489000</sub>
 ("Model Engineer," July 7, 1910). When working it hums like
 a bee.</p></div>
@@ -5442,7 +5403,7 @@ mechanical help available.</p></div>
 <div class="footnote"><p><a name="Footnote_21_21" id="Footnote_21_21"></a><a href="#FNanchor_21_21"><span class="label">[21]</span></a> Model Steam Turbines. "Model Engineer" Series, No. 13,
 price 6<i>d.</i></p></div>
 
-<div class="footnote"><p><a name="Footnote_22_22" id="Footnote_22_22"></a><a href="#FNanchor_22_22"><span class="label">[22]</span></a> See Introduction, note to §&nbsp;1.</p></div>
+<div class="footnote"><p><a name="Footnote_22_22" id="Footnote_22_22"></a><a href="#FNanchor_22_22"><span class="label">[22]</span></a> See Introduction, note to §&nbsp;1.</p></div>
 
 <div class="footnote"><p><a name="Footnote_23_23" id="Footnote_23_23"></a><a href="#FNanchor_23_23"><span class="label">[23]</span></a> The voltage, etc., is not stated.</p></div>
 
@@ -5452,9 +5413,9 @@ one in front and the other behind. Equally good flights have also
 been obtained with the two propellers behind, one revolving in the
 immediate rear of the other. Flying, of course, with the wind, <i>weight</i>
 is of paramount importance in these little models, and in both these
-cases the "single stick" can be made use of. <i>See also</i> ch. iv., §&nbsp;28.</p></div>
+cases the "single stick" can be made use of. <i>See also</i> ch. iv., §&nbsp;28.</p></div>
 
-<div class="footnote"><p><a name="Footnote_25_25" id="Footnote_25_25"></a><a href="#FNanchor_25_25"><span class="label">[25]</span></a> <i>See also</i> ch. viii., §&nbsp;5.</p></div>
+<div class="footnote"><p><a name="Footnote_25_25" id="Footnote_25_25"></a><a href="#FNanchor_25_25"><span class="label">[25]</span></a> <i>See also</i> ch. viii., §&nbsp;5.</p></div>
 
 <div class="footnote"><p><a name="Footnote_26_26" id="Footnote_26_26"></a><a href="#FNanchor_26_26"><span class="label">[26]</span></a> Save in case of some models with fabric-covered propellers.
 Some dirigibles are now being fitted with four-bladed wooden
@@ -5464,27 +5425,27 @@ screws.</p></div>
 
 <div class="footnote"><p><a name="Footnote_28_28" id="Footnote_28_28"></a><a href="#FNanchor_28_28"><span class="label">[28]</span></a> Vide Equivalent Inclinations&mdash;Table of.</p></div>
 
-<div class="footnote"><p><a name="Footnote_29_29" id="Footnote_29_29"></a><a href="#FNanchor_29_29"><span class="label">[29]</span></a> One in 3 or 0·333 is the <i>sine</i> of the angle; similarly if the angle
-were 30° the sine would be 0·5 or &frac12;, and the theoretical distance
+<div class="footnote"><p><a name="Footnote_29_29" id="Footnote_29_29"></a><a href="#FNanchor_29_29"><span class="label">[29]</span></a> One in 3 or 0·333 is the <i>sine</i> of the angle; similarly if the angle
+were 30° the sine would be 0·5 or &frac12;, and the theoretical distance
 travelled one-half.</p></div>
 
 <div class="footnote"><p><a name="Footnote_30_30" id="Footnote_30_30"></a><a href="#FNanchor_30_30"><span class="label">[30]</span></a> <i>Flat-Faced Blades.</i>&mdash;If the blade be not hollow-faced&mdash;and we
 consider the screw as an inclined plane and apply the Duchemin
 formula to it&mdash;the velocity remaining the same, the angle of maximum
-thrust is 35&frac14;°. Experiments made with such screws confirm this.</p></div>
+thrust is 35&frac14;°. Experiments made with such screws confirm this.</p></div>
 
 <div class="footnote"><p><a name="Footnote_31_31" id="Footnote_31_31"></a><a href="#FNanchor_31_31"><span class="label">[31]</span></a> Cavitation is when the high speed of the screw causes it to
 carry round a certain amount of the medium with it, so that the
 blades strike no undisturbed, or "solid," air at all, with a proportionate
 decrease in thrust.</p></div>
 
-<div class="footnote"><p><a name="Footnote_32_32" id="Footnote_32_32"></a><a href="#FNanchor_32_32"><span class="label">[32]</span></a> In the Wright machine r.p.m. = 450; in Blériot XI. r.p.m. =
+<div class="footnote"><p><a name="Footnote_32_32" id="Footnote_32_32"></a><a href="#FNanchor_32_32"><span class="label">[32]</span></a> In the Wright machine r.p.m. = 450; in Blériot XI. r.p.m. =
 1350.</p></div>
 
 <div class="footnote"><p><a name="Footnote_33_33" id="Footnote_33_33"></a><a href="#FNanchor_33_33"><span class="label">[33]</span></a> Such propellers, however, require a considerable amount of
 rubber.</p></div>
 
-<div class="footnote"><p><a name="Footnote_34_34" id="Footnote_34_34"></a><a href="#FNanchor_34_34"><span class="label">[34]</span></a> But <i>see also</i> §&nbsp;22.</p></div>
+<div class="footnote"><p><a name="Footnote_34_34" id="Footnote_34_34"></a><a href="#FNanchor_34_34"><span class="label">[34]</span></a> But <i>see also</i> §&nbsp;22.</p></div>
 
 <div class="footnote"><p><a name="Footnote_35_35" id="Footnote_35_35"></a><a href="#FNanchor_35_35"><span class="label">[35]</span></a> "Flight," March 10, 1910. (Illustration reproduced by permission.)</p></div>
 
@@ -5761,7 +5722,7 @@ diary</td>
 Hoskins</span>. Seventh edition, 52 pp. fcap. 8vo. (<i>1901</i>)</td>
 <td class="anet"></td>
 <td class="aprice">1&nbsp;&nbsp;6</td></tr>
-<tr><td class="atitle"><b>A Handbook of Formulæ, Tables, and Memoranda</b>,
+<tr><td class="atitle"><b>A Handbook of Formulæ, Tables, and Memoranda</b>,
 for Architectural Surveyors and others
 engaged in Building. By <span class="smcap">J.T. Hurst</span>. Fifteenth
 edition, 512 pp. royal 32mo, roan. (<i>1905</i>)</td>
@@ -5896,7 +5857,7 @@ Third edition, 201 pp. 18mo, boards. (<i>New York,
 1905</i>)</td>
 <td class="anet"><i>net</i></td>
 <td class="aprice">2&nbsp;&nbsp;0</td></tr>
-<tr><td class="atitle"><b>New Formulæ for the Loads and Deflections</b> of
+<tr><td class="atitle"><b>New Formulæ for the Loads and Deflections</b> of
 Solid Beams and Girders. By <span class="smcap">W. Donaldson</span>.
 Second edition, 8vo. (<i>1872</i>)</td>
 <td class="anet"></td>
@@ -6146,7 +6107,7 @@ and <span class="smcap">O. Chadwick</span>. Second edition, royal 8vo.</td></tr>
 <tr><td class="atitle sub">Part II. Fully illustrated, 334 pp. (<i>1906</i>)</td>
 <td class="anet"></td>
 <td class="aprice">10&nbsp;&nbsp;6</td></tr>
-<tr><td class="atitle"><b>A Pocket Book of Useful Formulæ and Memoranda,</b>
+<tr><td class="atitle"><b>A Pocket Book of Useful Formulæ and Memoranda,</b>
 for Civil and Mechanical Engineers. By
 Sir <span class="smcap">G.L. Molesworth</span> and <span class="smcap">H.B. Molesworth</span>.
 With an Electrical Supplement by <span class="smcap">W.H. Molesworth</span>.
@@ -6654,7 +6615,7 @@ By <span class="smcap">J.T. Sprague</span>. Third edition, 109 illus.
 York, 1892</i>)</td>
 <td class="anet"><i>net</i></td>
 <td class="aprice">3&nbsp;&nbsp;6</td></tr>
-<tr><td class="atitle"><b>Röntgen Rays</b> and Phenomena of the Anode and
+<tr><td class="atitle"><b>Röntgen Rays</b> and Phenomena of the Anode and
 Cathode. By <span class="smcap">E.P. Thompson</span> and <span class="smcap">W.A.
 Anthony</span>. 105 illus. 204 pp. 8vo. (<i>New York</i>,
 <i>1896</i>)</td>
@@ -6891,25 +6852,25 @@ MACHINERY.</h3>
 
 <table class="booklist" summary="">
 <tr><td class="atitle"><b>Pumps:</b> Historically, Theoretically and Practically
-Considered. By <span class="smcap">P.R. Björling</span>. Second edition,
+Considered. By <span class="smcap">P.R. Björling</span>. Second edition,
 156 illus. 234 pp. crown 8vo. (<i>1895</i>)</td>
 <td class="anet"></td>
 <td class="aprice">7&nbsp;&nbsp;6</td></tr>
-<tr><td class="atitle"><b>Pump Details.</b> By <span class="smcap">P.R. Björling</span>. 278 illus.
+<tr><td class="atitle"><b>Pump Details.</b> By <span class="smcap">P.R. Björling</span>. 278 illus.
 211 pp. crown 8vo. (<i>1892</i>)</td>
 <td class="anet"></td>
 <td class="aprice">7&nbsp;&nbsp;6</td></tr>
 <tr><td class="atitle"><b>Pumps and Pump Motors:</b> A Manual for the use
-of Hydraulic Engineers. By <span class="smcap">P.R. Björling</span>.
+of Hydraulic Engineers. By <span class="smcap">P.R. Björling</span>.
 Two vols. 261 plates, 369 pp. royal 4to. (<i>1895</i>).</td>
 <td class="anet"><i>net</i></td>
 <td class="aprice">1&nbsp;&nbsp;10&nbsp;&nbsp;0</td></tr>
 <tr><td class="atitle"><b>Practical Handbook on Pump Construction.</b>
-By <span class="smcap">P.R. Björling</span>. Second edition, 9 plates,
+By <span class="smcap">P.R. Björling</span>. Second edition, 9 plates,
 90 pp. crown 8vo. (<i>1904</i>)</td>
 <td class="anet"></td>
 <td class="aprice">5&nbsp;&nbsp;0</td></tr>
-<tr><td class="atitle"><b>Water or Hydraulic Motors.</b> By <span class="smcap">P.R. Björling</span>.
+<tr><td class="atitle"><b>Water or Hydraulic Motors.</b> By <span class="smcap">P.R. Björling</span>.
 206 illus. 287 pp. crown 8vo. (<i>1903</i>)</td>
 <td class="anet"></td>
 <td class="aprice">9&nbsp;&nbsp;0</td></tr>
@@ -6952,7 +6913,7 @@ Water-wheels.</b> By <span class="smcap">W. Donaldson</span>. 13 illus.
 94 pp. 8vo. (<i>1876</i>)</td>
 <td class="anet"></td>
 <td class="aprice">5&nbsp;&nbsp;0</td></tr>
-<tr><td class="atitle"><b>Practical Hydrostatics and Hydrostatic Formulæ.</b>
+<tr><td class="atitle"><b>Practical Hydrostatics and Hydrostatic Formulæ.</b>
 By <span class="smcap">E.S. Gould</span>. 27 illus. 114 pp. 18mo, boards.
 (<i>New York, 1903</i>)</td>
 <td class="anet"><i>net</i></td>
@@ -6973,7 +6934,7 @@ at side for ready reference. By <span class="smcap">A.E. Silk</span>.
 63 pp. crown 8vo. (<i>1899</i>)</td>
 <td class="anet"></td>
 <td class="aprice">5&nbsp;&nbsp;0</td></tr>
-<tr><td class="atitle"><b>Simple Hydraulic Formulæ.</b> By <span class="smcap">T.W. Stone</span>.
+<tr><td class="atitle"><b>Simple Hydraulic Formulæ.</b> By <span class="smcap">T.W. Stone</span>.
 9 plates, 98 pp. crown 8vo. (<i>1881</i>)</td>
 <td class="anet"></td>
 <td class="aprice">4&nbsp;&nbsp;0</td></tr>
@@ -7081,7 +7042,7 @@ Sanitary Glazes. (<i>1908</i>)</td>
 Speyers</span>. 224 pp. demy 8vo. (<i>New York, 1898</i>)</td>
 <td class="anet"></td>
 <td class="aprice">9&nbsp;&nbsp;0</td></tr>
-<tr><td class="atitle"><b>Spons' Encyclopædia of the Industrial Arts,</b>
+<tr><td class="atitle"><b>Spons' Encyclopædia of the Industrial Arts,</b>
 Manufactures and Commercial Products.
 1500 illus. 2100 pp. super-royal 8vo. (<i>1882</i>)
 In 2 Vols. cloth</td>
@@ -7132,7 +7093,7 @@ Buckley</span>. Second edition, with coloured maps
 and plans. 336 pp. 4to, cloth. (<i>1905</i>)</td>
 <td class="anet"><i>net</i></td>
 <td class="aprice">2&nbsp;&nbsp;2&nbsp;&nbsp;0</td></tr>
-<tr><td class="atitle"><b>Facts, Figures, and Formulæ for Irrigation
+<tr><td class="atitle"><b>Facts, Figures, and Formulæ for Irrigation
 Engineers.</b> By <span class="smcap">R.B. Buckley</span>. With illus.
 239 pp. large 8vo. (<i>1908</i>)</td>
 <td class="anet"><i>net</i></td>
@@ -8089,7 +8050,7 @@ Wood</span>. Fifth edition, 92 illus. 266 pp. 12mo.
 Mounted on linen in cloth covers. (<i>1908</i>)</td>
 <td class="anet"><i>net</i></td>
 <td class="aprice">3&nbsp;&nbsp;0</td></tr>
-<tr><td class="atitle"><b>Formulæ for Railway Crossings and Switches.</b>
+<tr><td class="atitle"><b>Formulæ for Railway Crossings and Switches.</b>
 By <span class="smcap">J. Glover</span>. 9 illus. 28 pp. royal 32mo. (<i>1896</i>)</td>
 <td class="anet"></td>
 <td class="aprice">2 6<span class="pagenum">[44]</span></td></tr>
@@ -8341,7 +8302,7 @@ Hot Water.</b> By <span class="smcap">F. Dye</span>. 192 illus. 319 pp.
 <span class="smcap">J.H. Kinealy</span>. Small folio. (<i>New York</i>)</td>
 <td class="anet"></td>
 <td class="aprice">4&nbsp;&nbsp;6</td></tr>
-<tr><td class="atitle"><b>Formulæ and Tables for Heating.</b> By <span class="smcap">J.H.
+<tr><td class="atitle"><b>Formulæ and Tables for Heating.</b> By <span class="smcap">J.H.
 Kinealy</span>. 18 illus. 53 pp. 8vo. (<i>New York, 1899</i>)</td>
 <td class="anet"></td>
 <td class="aprice">3&nbsp;&nbsp;6</td></tr>
@@ -8860,7 +8821,7 @@ the following celebrated Aeroplanes.</b></p>
 Herring-Curtis</b>.</p>
 
 <p style="padding-left:4em; text-indent:-4em;"><b>Monoplanes;&mdash;Rep, Antoinette, Santos Dumont,
-and Blériot</b>.</p>
+and Blériot</b>.</p>
 
 <p><b>Each of these machines are here shown in
 End View, Plan and Elevation</b>.</p>
@@ -9009,16 +8970,16 @@ If they do not display properly, you may have an incompatible browser or unavail
 Make sure that the browser's "character set" or "file encoding" is set to Unicode (UTF-8).
 You may also need to change your browser's default font.</p>
 
-<p>The fractions ¼, ½ and ¾ are represented using single characters,
+<p>The fractions ¼, ½ and ¾ are represented using single characters,
 but other fractions use the / and - symbols, e.g. 3/8 or 2-5/8.</p>
 
-<p>The skin friction formulæ given on pages 11 and 128 have been corrected
-by comparison with other sources. Respectively, the formulæ were
+<p>The skin friction formulæ given on pages 11 and 128 have been corrected
+by comparison with other sources. Respectively, the formulæ were
 originally printed as</p>
 <p class="cen">
-<i>f</i> = 0·00000778<i>l</i><sup>&nbsp;9·3</sup><i>v</i><sup>1·85</sup><br />
+<i>f</i> = 0·00000778<i>l</i><sup>&nbsp;9·3</sup><i>v</i><sup>1·85</sup><br />
 and<br />
-<i>f</i> = 0·00000778<i>l</i> - <sup>00·7</sup><i>v</i><sup>1·85</sup>
+<i>f</i> = 0·00000778<i>l</i> - <sup>00·7</sup><i>v</i><sup>1·85</sup>
 </p>
 
 <p>The remaining corrections made are indicated by red dotted lines under the
@@ -9029,388 +8990,6 @@ will be displayed.</p>
 
 </div>
 
-
-
-
-
-
-
-
-<pre>
-
-
-
-
-
-End of the Project Gutenberg EBook of The Theory and Practice of Model
-Aeroplaning, by V. E. Johnson
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+<div>*** END OF THE PROJECT GUTENBERG EBOOK 41135 ***</div>
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-The Project Gutenberg EBook of The Theory and Practice of Model Aeroplaning, by
-V. E. Johnson
-
-This eBook is for the use of anyone anywhere at no cost and with
-almost no restrictions whatsoever.  You may copy it, give it away or
-re-use it under the terms of the Project Gutenberg License included
-with this eBook or online at www.gutenberg.org/license
-
-
-Title: The Theory and Practice of Model Aeroplaning
-
-Author: V. E. Johnson
-
-Release Date: October 21, 2012 [EBook #41135]
-
-Language: English
-
-Character set encoding: ASCII
-
-*** START OF THIS PROJECT GUTENBERG EBOOK THE THEORY AND PRACTICE ***
-
-
-
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-Produced by Chris Curnow, Mark Young and the Online
-Distributed Proofreading Team at http://www.pgdp.net (This
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-
-[Illustration: THE MOST IMPORTANT "TOOL" IN THE BUILDING OF MODEL
-AEROPLANES.
-
-[_Illustration by permission from_ MESSRS. A. GALLENKAMP & CO'S.
-CHEMICAL CATALOGUE.]]
-
-
-
-
-    THE THEORY AND PRACTICE
-    OF
-    MODEL AEROPLANING
-
-    BY
-    V.E. JOHNSON, M.A.
-
-    AUTHOR OF
-    'THE BEST SHAPE FOR AN AIRSHIP,' 'SOARING FLIGHT,'
-    'HOW TO ADVANCE THE SCIENCE OF AERONAUTICS,'
-    'HOW TO BUILD A MODEL AEROPLANE,' ETC.
-
-    "Model Aeroplaning is an Art in itself"
-
-    [Illustration]
-
-    London
-    E. & F.N. SPON, LTD., 57 HAYMARKET
-
-    New York
-    SPON & CHAMBERLAIN, 123 LIBERTY STREET
-
-    1910
-
-
-
-
-PREFACE
-
-
-The object of this little book is not to describe how to construct
-some particular kind of aeroplane; this has been done elsewhere: but
-to narrate in plain language the general practice and principles of
-model aeroplaning.
-
-There is a _science_ of model aeroplaning--just as there is a science
-of model yachting and model steam and electric traction, and an
-endeavour is made in the following pages to do in some measure for
-model aeroplanes what has already been done for model yachts and
-locomotives. To achieve the best results, theory and practice must go
-hand in hand.
-
-From a series of carefully conducted experiments empirical formulae can
-be obtained which, combined later with mathematical induction and
-deduction, may lead, not only to a more accurate and generalized law
-than that contained in the empirical formula, but to valuable
-deductions of a totally new type, embodying some general law hitherto
-quite unknown by experimentalists, which in its turn may serve as a
-foundation or stepping stone for suggesting other experiments and
-empirical formulae which may be of especial importance, to be treated
-in _their_ turn like their predecessor. By "especial importance," I
-mean not only to "model," but "Aeroplaning" generally.
-
-As to the value of experiments on or with models with respect to
-full-sized machines, fifteen years ago I held the opinion that they
-were a very doubtful factor. I have since considerably modified that
-view, and now consider that experiments with models--if properly
-carried out, and given due, not _undue_, weight--both can and will be
-of as much use to the science of Aeronautics as they have already
-proved themselves to be in that of marine engineering.
-
-The subject of model propellers and motors has been somewhat fully
-dealt with, as but little has been published (in book form, at any
-rate) on these all-important departments. On similar grounds the
-reasons why and how a model aeroplane flies have been practically
-omitted, because these have been dealt with more or less in every book
-on heavier-than-air machines.
-
-Great care has been exercised in the selection of matter, and in the
-various facts stated herein; in most cases I have personally verified
-them; great pains have also been exercised to exclude not only
-misleading, but also doubtful matter. I have no personal axe to grind
-whatever, nor am I connected either directly or indirectly with any
-firm of aeroplane builders, model or otherwise.
-
-The statements contained in these pages are absolutely free from bias
-of any kind, and for them I am prepared to accept full responsibility.
-
-I have to thank Messrs. A.W. GAMAGE (Holborn) for the use of various
-model parts for testing purposes, and also for the use of various
-electros from their modern Aviation Catalogue; also Messrs. T.W.K.
-CLARKE & CO., of Kingston-on-Thames. For the further use of electros,
-and for permission to reproduce illustrations which have previously
-appeared in their papers, I must express my acknowledgment and thanks
-to the publishers of the "Model Engineer," "Flight," and the "Aero."
-Corrections and suggestions of any kind will be gratefully received,
-and duly acknowledged.
-
-    V.E. JOHNSON.
-
-
-
-
-CONTENTS
-
-
-    INTRODUCTION.
-                                                                   PAGE
-
-    Sec.Sec. 1-5. The two classes of models--First requisite of a model
-    aeroplane. Sec. 6. An art in itself. Sec. 7. The leading principle      1
-
-
-    CHAPTER I.
-
-    THE QUESTION OF WEIGHT.
-
-    Sec.Sec. 1-2. Its primary importance both in rubber and
-    power-driven models--Professor Langley's experiences. Sec. 3.
-    Theoretical aspect of the question. Sec. 4. Means whereby more
-    weight can be carried--How to obtain maximum strength with
-    minimum weight. Sec. 5. Heavy models versus light ones               4
-
-
-    CHAPTER II.
-
-    THE QUESTION OF RESISTANCE.
-
-    Sec. 1. The chief function of a model in the medium in which it
-    travels. Sec. 2. Resistance considered as load percentage. Sec. 3.
-    How made up. Sec. 4. The shape of minimum resistance. Sec. 5. The
-    case of rubber-driven models. Sec. 6. The aerofoil
-    surface--Shape and material as affecting this question. Sec. 7.
-    Skin friction--Its coefficient. Sec. 8. Experimental proofs of
-    its existence and importance                                      7
-
-
-    CHAPTER III.
-
-    THE QUESTION OF BALANCE.
-
-    Sec. 1. automatic stability essential in a flying model. Sec. 2.
-    theoretical researches on this question. Sec.Sec. 3-6. a brief
-    summary of the chief conclusions arrived at--remarks on and
-    deductions from the same--conditions for automatic stability.
-    Sec. 7. theory and practice--stringfellow--penaud--tatin--the
-    question of fins--clarke's models--some further
-    considerations. Sec. 8. longitudinal stability. Sec. 9. transverse
-    stability. Sec. 10. the dihedral angle. Sec. 11. different forms of
-    the latter. Sec. 12. the "upturned" tip. Sec. 13. the most
-    efficient section                                                13
-
-
-    CHAPTER IV.
-
-    THE MOTIVE POWER.
-
-    SECTION I.--RUBBER MOTORS.
-
-    Sec. 1. Some experiments with rubber cord. Sec. 2. Its extension
-    under various weights. Sec. 3. The laws of elongation
-    (stretching)--Permanent set. Sec. 4. Effects of elongation on
-    its volume. Sec. 5. "Stretched-twisted" rubber cord--Torque
-    experiments with rubber strands of varying length and number.
-    Sec. 6. Results plotted as graphs--Deductions--Various
-    relations--How to obtain the most efficient
-    results--Relations between the torque and the number of
-    strands, and between the length of the strands and their
-    number. Sec. 7. Analogy between rubber and "spring"
-    motors--Where it fails to hold. Sec. 8. Some further practical
-    deductions. Sec. 9. The number of revolutions that can be given
-    to rubber motors. Sec. 10. The maximum number of turns. Sec. 11.
-    "Lubricants" for rubber. Sec. 12. Action of copper upon rubber.
-    Sec. 12A. Action of water, etc. Sec. 12B. How to preserve rubber.
-    Sec. 13. To test rubber. Sec. 14. The shape of the section. Sec. 15.
-    Size of section. Sec. 16. Geared rubber motors. Sec. 17. The only
-    system worth consideration--Its practical difficulties. Sec. 18.
-    Its advantages                                                   24
-
-    SECTION II.--OTHER FORMS OF MOTORS.
-
-    Sec. 18A. _Spring motors_; their inferiority to rubber. Sec. 18B.
-    The most efficient form of spring motor. Sec. 18C. _Compressed
-    air motors_--A fascinating form of motor, "on paper." Sec. 18D.
-    The pneumatic drill--Application to a model aeroplane--Length
-    of possible flight. Sec. 18E. The pressure in motor-car tyres.
-    Sec. 19. Hargraves' compressed air models--The best results
-    compared with rubber motors. Sec. 20. The effect of heating the
-    air in its passage from the reservoir to the motor--The great
-    gain in efficiency thereby attained--Liquid air--Practical
-    drawbacks to the compressed-air motor. Sec. 21. Reducing
-    valves--Lowest working pressure. Sec. 22. The inferiority of
-    this motor compared with the steam engine. Sec. 22A. Tatin's
-    air-compressed motor. Sec. 23. _Steam engine_--Steam engine
-    model--Professor Langley's models--His experiment with
-    various forms of motive power--Conclusions arrived at. Sec. 24.
-    His steam engine models--Difficulties and failures--and final
-    success--The "boiler" the great difficulty--His model
-    described. Sec. 25. The use of spirit or some very volatile
-    hydrocarbon in the place of water. Sec. 26. Steam turbines.
-    Sec. 27. Relation between "difficulty in construction" and the
-    "size of the model." Sec. 28. Experiments in France. Sec. 29.
-    _Petrol motors._--But few successful models. Sec. 30. Limit to
-    size. Sec. 31. Stanger's successful model described and
-    illustrated. Sec. 32. One-cylinder petrol motors. Sec. 33.
-    _Electric motors_                                                39
-
-
-    CHAPTER V.
-
-    PROPELLERS OR SCREWS.
-
-    Sec. 1. The position of the propeller. Sec. 2. The number of
-    blades. Sec. 3. Fan _versus_ propeller. Sec. 4. The function of a
-    propeller. Sec. 5. The pitch. Sec. 6. Slip. Sec. 7. Thrust. Sec. 8. Pitch
-    coefficient (or ratio). Sec. 9. Diameter. Sec. 10. Theoretical
-    pitch. Sec. 11. Uniform pitch. Sec. 12. How to ascertain the pitch
-    of a propeller. Sec. 13. Hollow-faced blades. Sec. 14. Blade area.
-    Sec. 15. Rate of rotation. Sec. 16. Shrouding. Sec. 17. General
-    design. Sec. 18. The shape of the blades. Sec. 19. Their general
-    contour--Propeller design--How to design a propeller. Sec. 20.
-    Experiments with propellers--Havilland's design for
-    experiments--The author experiments on dynamic thrust and
-    model propellers generally. Sec. 21. Fabric-covered screws.
-    Sec. 22. Experiments with twin propellers. Sec. 23. The Fleming
-    Williams propeller. Sec. 24. Built-up _v._ twisted wooden
-    propellers                                                       52
-
-
-    CHAPTER VI.
-
-    THE QUESTION OF SUSTENTATION.
-    THE CENTRE OF PRESSURE.
-
-    Sec. 1. The centre of pressure--Automatic stability. Sec. 2.
-    Oscillations. Sec. 3. Arched surfaces and movements of the
-    centre of pressure--Reversal. Sec. 4. The centre of gravity and
-    the centre of pressure. Sec. 5. Camber. Sec. 6. Dipping front
-    edge--Camber--The angle of incidence and camber--Attitude of
-    the Wright machine. Sec. 7. The most efficient form of camber.
-    Sec. 8. The instability of a deeply cambered surface. Sec. 9.
-    Aspect ratio. Sec. 10. Constant or varying camber. Sec. 11. Centre
-    of pressure on arched surfaces                                   78
-
-
-    CHAPTER VII.
-
-    MATERIALS FOR AEROPLANE
-    CONSTRUCTION.
-
-    Sec. 1. The choice strictly limited. Sec. 2. Bamboo. Sec. 3.
-    Ash--spruce-- whitewood--poplar. Sec. 4. Steel. Sec. 5. Umbrella
-    section steel. Sec. 6. Steel wire. Sec. 7. Silk. Sec. 8. Aluminium and
-    magnalium. Sec. 9. Alloys. Sec. 10. Sheet ebonite--Vulcanized
-    fibre--Sheet celluloid--Mica                                     86
-
-
-    CHAPTER VIII.
-
-    HINTS ON THE BUILDING OF MODEL
-    AEROPLANES.
-
-    Sec. 1. The chief difficulty to overcome. Sec. 2. General
-    design--The principle of continuity. Sec. 3. Simple monoplane.
-    Sec. 4. Importance of soldering. Sec. 5. Things to avoid. Sec. 6.
-    Aerofoil of metal--wood--or fabric. Sec. 7. Shape of aerofoil.
-    Sec. 8. How to camber an aerocurve without ribs. Sec. 9. Flexible
-    joints. Sec. 10. Single surfaces. Sec. 11. The rod or tube carrying
-    the rubber motor. Sec. 12. Position of the rubber. Sec. 13. The
-    position of the centre of pressure. Sec. 14. Elevators and
-    tails. Sec. 15. Skids _versus_ wheels--Materials for skids.
-    Sec. 16. Shock absorbers, how to attach--Relation between the
-    "gap" and the "chord"                                            93
-
-
-    CHAPTER IX.
-
-    THE STEERING OF THE MODEL.
-
-    Sec. 1. A problem of great difficulty--Effects of propeller
-    torque. Sec. 2. How obviated. Sec. 3. The two-propeller
-    solution--The reason why it is only a partial success. Sec. 4.
-    The _speed_ solution. Sec. 5. Vertical fins. Sec. 6. Balancing tips
-    or ailerons. Sec. 7. Weighting. Sec. 8. By means of transversely
-    canting the elevator. Sec. 9. The necessity for some form of
-    "keel"                                                          105
-
-
-    CHAPTER X.
-
-    THE LAUNCHING OF THE MODEL.
-
-    Sec. 1. The direction in which to launch them. Sec. 2. The
-    velocity--wooden aerofoils and fabric-covered
-    aerofoils--Poynter's launching apparatus. Sec. 3. The launching
-    of very light models. Sec. 4. Large size and power-driven
-    models. Sec. 5. Models designed to rise from the
-    ground--Paulhan's prize model. Sec. 6. The setting of the
-    elevator. Sec. 7. The most suitable propeller for this form of
-    model. Sec. 8. Professor Kress' method of launching. Sec. 9. How to
-    launch a twin screw model. Sec. 10. A prior revolution of the
-    propellers. Sec. 11. The best angle at which to launch a model     109
-
-
-    CHAPTER XI.
-
-    HELICOPTER MODELS.
-
-    Sec. 1. Models quite easy to make. Sec. 2. Sir George Cayley's
-    helicopter model. Sec. 3. Phillips' successful power-driven
-    model. Sec. 4. Toy helicopters. Sec. 5. Incorrect and correct way
-    of arranging the propellers. Sec. 6. Fabric covered screws. Sec. 7.
-    A design to obviate weight. Sec. 8. The question of a fin or
-    keel.                                                           113
-
-
-    CHAPTER XII.
-
-    EXPERIMENTAL RECORDS                                            116
-
-
-    CHAPTER XIII.
-
-    MODEL FLYING COMPETITIONS.
-
-    Sec. 1. A few general details concerning such. Sec. 2. Aero Models
-    Association's classification, etc. Sec. 3. Various points to be
-    kept in mind when competing                                     119
-
-
-    CHAPTER XIV.
-
-    USEFUL NOTES, TABLES, FORMULAE, ETC.
-
-    Sec. 1. Comparative velocities. Sec. 2. Conversions. Sec. 3. Areas of
-    various shaped surfaces. Sec. 4. French and English measures.
-    Sec. 5. Useful data. Sec. 6. Table of equivalent inclinations. Sec. 7.
-    Table of skin friction. Sec. 8. Table I. (metals). Sec. 9. Table
-    II. (wind pressures). Sec. 10. Wind pressure on various shaped
-    bodies. Sec. 11. Table III. (lift and drift) on a cambered
-    surface. Sec. 12. Table IV. (lift and drift)--On a plane
-    aerofoil--Deductions. Sec. 13. Table V. (timber). Sec. 14. Formula
-    connecting weight lifted and velocity. Sec. 15. Formula
-    connecting models of similar design but different weights.
-    Sec. 16. Formula connecting power and speed. Sec. 17. Propeller
-    thrust. Sec. 18. To determine experimentally the static thrust
-    of a propeller. Sec. 19. Horse-power and the number of
-    revolutions. Sec. 20. To compare one model with another. Sec. 21.
-    Work done by a clockwork spring motor. Sec. 22. To ascertain the
-    horse-power of a rubber motor. Sec. 23. Foot-pounds of energy in
-    a given weight of rubber--Experimental determination of.
-    Sec. 24. Theoretical length of flight. Sec. 25. To test different
-    motors. Sec. 26. Efficiency of a model. Sec. 27. Efficiency of
-    design. Sec. 28. Naphtha engines. Sec. 29. Horse-power and weight
-    of model petrol motors. Sec. 30. Formula for rating the same.
-    Sec. 30A. Relation between static thrust of propeller and total
-    weight of model. Sec. 31. How to find the height of an
-    inaccessible object (kite, balloon, etc.). Sec. 32. Formula for
-    I.H.P. of model steam engines                                   125
-
-    APPENDIX A. Some models which have won medals at open
-    competitions                                                    143
-
-
-
-
-GLOSSARY OF TERMS USED IN MODEL AEROPLANING.
-
-
-_Aeroplane._ A motor-driven flying machine which relies upon surfaces
-for its support in the air.
-
-_Monoplane_ (single). An aeroplane with one pair of outstretched
-wings.
-
-_Aerofoil._ These outstretched wings are often called aerofoil
-surfaces. One pair of wings forming one aerofoil surface.
-
-_Monoplane_ (double). An aeroplane with two aerofoils, one behind the
-other or two main planes, tandem-wise.
-
-_Biplane._ An aeroplane with two aerofoils, one below the other, or
-having two main planes superposed.
-
-_Triplane._ An aeroplane having three such aerofoils or three such
-main planes.
-
-_Multiplane._ Any such machine having more than three of the above.
-
-_Glider._ A motorless aeroplane.
-
-_Helicopter._ A flying machine in which propellers are employed to
-raise the machine in the air by their own unaided efforts.
-
-_Dihedral Angle._ A dihedral angle is an angle made by two surfaces
-that do not lie in the same plane, i.e. when the aerofoils are
-arranged V-shaped. It is better, however, to somewhat extend this
-definition, and not to consider it as necessary that the two surfaces
-_do_ actually meet, but would do so if produced thus in figure. BA and
-CD are still dihedrals, sometimes termed "upturned tips."
-
-[Illustration: Dihedrals.]
-
-_Span_ is the distance from tip to tip of the main supporting surface
-measured transversely (across) the line of flight.
-
-_Camber_ (a slight arching or convexity upwards). This term denotes
-that the aerofoil has such a curved transverse section.
-
-_Chord_ is the distance between the entering (or leading) edge of the
-main supporting surface (aerofoil) and the trailing edge of the same;
-also defined as the fore and aft dimension of the main planes measured
-in a straight line between the leading and trailing edges.
-
-                       span
-    _Aspect Ratio_ is -----
-                      chord
-
-_Gap_ is the vertical distance between one aerofoil and the one which
-is immediately above it.
-
-(The gap is usually made equal to the chord).
-
-_Angle of Incidence._ The angle of incidence is the angle made by the
-chord with the line of flight.
-
-[Illustration:
-
-  AB = chord.            AB = cambered surface.
-  SP = line of flight.  ASP = {alpha} = L of incidence.]
-
-_Width._ The width of an aerofoil is the distance from the front to
-the rear edge, allowing for camber.
-
-_Length._ This term is usually applied to the machine as a whole, from
-the front leading edge of elevator (or supports) to tip of tail.
-
-_Arched._ This term is usually applied to aerofoil surfaces which dip
-downwards like the wings of a bird. The curve in this case being at
-right angles to "camber." A surface can, of course, be both cambered
-and arched.
-
-_Propeller._ A device for propelling or pushing an aeroplane forward
-or for raising it vertically (lifting screw).
-
-_Tractor Screw._ A device for pulling the machine (used when the
-propeller is placed in the front of the machine).
-
-_Keel._ A vertical plane or planes (usually termed "fins") arranged
-longitudinally for the purposes of stability and steering.
-
-_Tail._ The plane, or group of planes, at the rear end of an
-aeroplane for the purpose chiefly of giving longitudinal stability. In
-such cases the tail is normally (approx.) horizontal, but not
-unfrequently vertical tail-pieces are fitted as well for steering
-(transversely) to the right or left, or the entire tail may be twisted
-for the purpose of transverse stability (vide _Elevator_). Such
-appendages are being used less and less with the idea of giving actual
-support.
-
-_Rudder_ is the term used for the vertical plane, or planes, which are
-used to steer the aeroplane sideways.
-
-_Warping._ The flexing or bending of an aerofoil out of its normal
-shape. The rear edges near the tips of the aerofoil being dipped or
-tilted respectively, in order to create a temporary difference in
-their inclinations to the line of flight. Performed in conjunction
-with rudder movements, to counteract the excessive action of the
-latter.
-
-_Ailerons_ (also called "righting-tips," "balancing-planes," etc.).
-Small aeroplanes in the vicinity of the tips of the main aerofoil for
-the purpose of assisting in the maintenance of equilibrium or for
-steering purposes either with or without the assistance of the rudder.
-
-_Elevator._ The plane, or planes, in front of the main aerofoil used
-for the purpose of keeping the aeroplane on an even keel, or which
-cause (by being tilted or dipped) the aeroplane to rise or fall (vide
-_Tail_).
-
-
-
-
-MODEL AEROPLANING
-
-
-
-
-INTRODUCTION.
-
-
-Sec. 1. Model Aeroplanes are primarily divided into two classes: first,
-models intended before all else to be ones that shall _fly_; secondly,
-_models_, using the word in its proper sense of full-sized machines.
-Herein model aeroplanes differ from model yachts and model
-locomotives. An extremely small model locomotive _built to scale_ will
-still _work_, just as a very small yacht built to scale will _sail_;
-but when you try to build a scale model of an "Antoinette" monoplane,
-_including engine_, it cannot be made to fly unless the scale be a
-very large one. If, for instance, you endeavoured to make a 1/10 scale
-model, your model petrol motor would be compelled to have eight
-cylinders, each 0.52 bore, and your magneto of such size as easily to
-pass through a ring half an inch in diameter. Such a model could not
-possibly work.[1]
-
-    _Note._--Readers will find in the "Model Engineer" of June 16,
-    1910, some really very fine working drawings of a prize-winning
-    Antoinette monoplane model.
-
-Sec. 2. Again, although the motor constitutes the _chief_, it is by no
-means the sole difficulty in _scale_ model aeroplane building. To
-reproduce to scale at _scale weight_, or indeed anything approaching it,
-_all_ the _necessary_--in the case of a full-sized machine--framework is
-not possible in a less than 1/5 scale.
-
-Sec. 3. Special difficulties occur in the case of any prototype taken.
-For instance, in the case of model Bleriots it is extremely difficult
-to get the centre of gravity sufficiently forward.
-
-Sec. 4. Scale models of actual flying machines _that will fly_ mean
-models _at least_ 10 or 12 feet across, and every other dimension in
-like proportion; and it must always be carefully borne in mind that
-the smaller the scale the greater the difficulties, but not in the
-same proportion--it would not be _twice_ as difficult to build a
-1/4-in. scale model as a 1/2-in., but _four_, _five_ or _six_ times as
-difficult.
-
-Sec. 5. Now, the _first_ requirement of a model aeroplane, or flying
-machine, is that it shall FLY.
-
-As will be seen later on--unless the machine be of large size, 10 feet
-and more spread--the only motor at our disposal is the motor of
-twisted rubber strands, and this to be efficient requires to be long,
-and is of practically uniform weight throughout; this alone alters the
-entire _distribution of weight_ on the machine and makes:
-
-Sec. 6. "=Model Aeroplaning an Art in itself=," and as such we propose to
-consider it in the following pages.
-
-We have said that the first requisite of a model aeroplane is that it
-shall fly, but there is no necessity, nor is it indeed always to be
-desired, that this should be its only one, unless it be built with the
-express purpose of obtaining a record length of flight. For ordinary
-flights and scientific study what is required is a machine in which
-minute detail is of secondary importance, but which does along its
-main lines "_approximate_ to the real thing."
-
-Sec. 7. Simplicity should be the first thing aimed at--simplicity means
-efficiency, it means it in full-sized machines, still more does it
-mean it in models--and this very question of simplicity brings us to
-that most important question of all, namely, the question of _weight_.
-
-FOOTNOTE:
-
-[1] The smallest working steam engine that the writer has ever heard
-of has a net weight of 4 grains. One hundred such engines would be
-required to weigh one ounce. The bore being 0.03 in., and stroke 1/32
-of an inch, r.p.m. 6000 per min., h.p. developed 1/489000 ("Model
-Engineer," July 7, 1910). When working it hums like a bee.
-
-
-
-
-CHAPTER I.
-
-THE QUESTION OF WEIGHT.
-
-
-Sec. 1. The following is an extract from a letter that appeared in the
-correspondence columns of "The Aero."[2]
-
-"To give you some idea how slight a thing will make a model behave
-badly, I fitted a skid to protect the propeller underneath the
-aeroplane, and the result in retarding flight could be seen very
-quickly, although the weight of the skid was almost nil.[3] To all
-model makers who wish to make a success I would say, strip all that
-useless and heavy chassis off, cut down the 'good, honest stick' that
-you have for a backbone to half its thickness, stay it with wire if it
-bends under the strain of the rubber, put light silk on the planes,
-and use an aluminium[4] propeller. The result will surpass all
-expectations."
-
-Sec. 2. The above refers, of course, to a rubber-motor driven model. Let
-us turn to a steam-driven prototype. I take the best known example of
-all, Professor Langley's famous model. Here is what the professor has
-to say on the question[5]:--
-
-"Every bit of the machinery had to be constructed with scientific
-accuracy. It had to be tested again and again. The difficulty of
-getting the machine light enough was such that every part of it had to
-be remade several times. It would be in full working order when
-something would give way, and this part would have to be strengthened.
-This caused additional weight, and necessitated cutting off so much
-weight from some other part of the machinery. At times the difficulty
-seemed almost heartbreaking; but I went on, piece by piece and atom by
-atom, until I at last succeeded in getting all the parts of the right
-strength and proportion."
-
-How to obtain the maximum strength with the minimum of weight is one
-of the, if not the most, difficult problems which the student has to
-solve.
-
-Sec. 3. The theoretical reason why _weight_ is such an all-important item
-in model aeroplaning, much more so than in the case of full-size
-machines, is that, generally speaking, such models do not fly fast
-enough to possess a high weight carrying capacity. If you increase the
-area of the supporting surface you increase also the resistance, and
-thereby diminish the speed, and are no better off than before. The
-only way to increase the weight carrying capacity of a model is to
-increase its speed. This point will be recurred to later on. One of
-Mr. T.W.K. Clarke's well-known models, surface area 11/4 sq. ft.,
-weight 11/4 lb., is stated to have made a flight of 300 yards
-carrying 6 oz. of lead. This works out approximately at 21 oz. per sq.
-ft.
-
-The velocity (speed) is not stated, but some earlier models by the
-same designer, weight 11/2 lb., supporting area 11/2 sq. ft., i.e.,
-at rate of 16 oz. per sq. ft., travelled at a rate of 37 ft. per
-second, or 25 miles an hour.
-
-The velocity of the former, therefore, would certainly not be less
-than 30 miles an hour.
-
-Sec. 4. Generally speaking, however, models do not travel at anything
-like this velocity, or carry anything like this weight per sq. ft.
-
-An average assumption of 13 to 15 miles an hour does nor err on the
-minimum side. Some very light fabric covered models have a speed of
-less than even 10 miles an hour. Such, of course, cannot be termed
-efficient models, and carry only about 3 oz. per sq. ft. Between these
-two types--these two extremes--somewhere lies the "Ideal Model."
-
-The maximum of strength with the minimum of weight can be obtained
-only:--
-
-1. By a knowledge of materials.
-
-2. Of how to combine those materials in a most efficient and skilful
-manner.
-
-3. By a constant use of the balance or a pair of scales, and noting
-(in writing) the weight and result of every trial and every experiment
-in the alteration and change of material used. WEIGH EVERYTHING.
-
-Sec. 5. The reader must not be misled by what has been said, and think
-that a model must not weigh anything if it is to fly well. A heavy
-model will fly much better against the wind than a light one, provided
-that the former _will_ fly. To do this it must fly _fast_. To do this
-again it must be well powered, and offer the minimum of resistance to
-the medium through which it moves. This means its aerofoil
-(supporting) surfaces must be of polished wood or metal. This point
-brings us to the question of Resistance, which we will now consider.
-
-FOOTNOTES:
-
-[2] "Aero," May 3, 1910.
-
-[3] Part of this retardation was, of course, "increased resistance."
-
-[4] Personally I do not recommend aluminium.--V.E.J.
-
-[5] "Aeronautical Journal," January 1897, p. 7.
-
-
-
-
-CHAPTER II.
-
-THE QUESTION OF RESISTANCE.
-
-
-Sec. 1. It is, or should be, the function of an aeroplane--model or
-otherwise--to pass through the medium in which it travels in such a
-manner as to leave that medium in as motionless a state as possible,
-since all motion of the surrounding air represents so much power
-wasted.
-
-Every part of the machine should be so constructed as to move through
-the air with the minimum of disturbance and resistance.
-
-Sec. 2. The resistance, considered as a percentage of the load itself,
-that has to be overcome in moving a load from one place to another,
-is, according to Mr. F.W. Lanchester, 121/2 per cent. in the case of
-a flying machine, and 0.1 per cent. in the case of a cargo boat, and
-of a solid tyre motor car 3 per cent., a locomotive 1 per cent. Four
-times at least the resistance in the case of aerial locomotion has to
-be overcome to that obtained from ordinary locomotion on land. The
-above refer, of course, to full-sized machines; for a model the
-resistance is probably nearer 14 or 15 per cent.
-
-Sec. 3. This resistance is made up of--
-
-    1. Aerodynamic resistance.
-    2. Head resistance.
-    3. Skin-friction (surface resistance).
-
-The first results from the necessity of air supporting the model
-during flight.
-
-The second is the resistance offered by the framework, wires, edges of
-aerofoils, etc.
-
-The third, skin-friction or surface resistance, is very small at low
-velocities, but increases as the square of the velocity. To reduce the
-resistance which it sets up, all surfaces used should be as smooth as
-possible. To reduce the second, contours of ichthyoid, or fish-like,
-form should be used, so that the resultant stream-line flow of the
-medium shall keep in touch with the surface of the body.
-
-Sec. 4. As long ago as 1894 a series of experiments were made by the
-writer[6] to solve the following problem: given a certain length and
-breadth, to find the shape which will offer the least resistance. The
-experiments were made with a whirling table 40 ft. in diameter, which
-could be rotated so that the extremity of the arm rotated up to a
-speed of 45 miles an hour. The method of experimenting was as follows:
-The bodies (diam. 4 in.) were balanced against one another at the
-extremity of the arm, being so balanced that their motions forward and
-backward were parallel. Provision was made for accurately balancing
-the parallel scales on which the bodies were suspended without
-altering the resistance offered by the apparatus to the air. Two
-experiments at least (to avoid error) were made in each case, the
-bodies being reversed in the second experiment, the top one being put
-at the bottom, and _vice versa_. The conclusions arrived at were:--
-
-For minimum (head) resistance a body should have--
-
-1. Its greatest diameter two-fifths of its entire length from its
-head.
-
-2. Its breadth and its depth in the proportion of four to three.
-
-3. Its length at least from five to nine times its greatest breadth
-(nine being better than five).
-
-4. A very tapering form of stern, the actual stern only being of just
-sufficient size to allow of the propeller shaft passing through. In
-the case of twin propellers some slight modification of the stern
-would be necessary.
-
-5. Every portion of the body in contact with the fluid to be made as
-smooth as possible.
-
-6. A body of such shape gives at most only _one-twentieth_ the
-resistance offered by a flat disk of similar maximum sectional area.
-
-_Results since fully confirmed._
-
-[Illustration: FIG. 1.--SHAPE OF LEAST RESISTANCE.]
-
-The design in Fig. 2 is interesting, not only because of its probable
-origin, but because of the shape of the body and arrangement of the
-propellers; no rudder is shown, and the long steel vertical mast
-extending both upwards and downwards through the centre would render
-it suitable only for landing on water.
-
-Sec. 5. In the case of a rubber-driven model, there is no containing body
-part, so to speak, a long thin stick, or tubular construction if
-preferred, being all that is necessary.
-
-The long skein of elastic, vibrating as well as untwisting as it
-travels with the machine through the air, offers some appreciable
-resistance, and several experimenters have _enclosed_ it in a light
-tube made of _very thin_ veneer wood rolled and glued, or paper even
-may be used; such tubes can be made very light, and possess
-considerable rigidity, especially longitudinally. If the model be a
-biplane, then all the upright struts between the two aerofoils should
-be given a shape, a vertical section of which is shown in Fig. 3.
-
-Sec. 6. In considering this question of resistance, the substance of
-which the aerofoil surface is made plays a very important part, as
-well as whether that surface be plane or curved. For some reason not
-altogether easy to determine, fabric-covered planes offer
-_considerably_ more resistance than wooden or metal ones. That they
-should offer _more_ resistance is what common sense would lead one to
-expect, but hardly to the extent met with in actual practice.
-
-[Illustration: FIG. 2.--DESIGN FOR AN AEROPLANE MODEL (POWER DRIVEN).
-
-This design is attributed to Professor Langley.]
-
-_Built up fabric-covered aeroplanes[7] gain in lightness, but lose in
-resistance._ In the case of curved surfaces this difference is
-considerably more; one reason, undoubtedly, is that in a built up
-model surface there is nearly always a tendency to make this curvature
-excessive, and much more than it should be. Having called attention to
-this under the head of resistance, we will leave it now to recur to it
-later when considering the aerofoil proper.
-
-[Illustration: FIG. 3.--HORIZONTAL SECTION OF VERTICAL STRUT
-(ENLARGED.)]
-
-Sec. 7. Allusion has been made in this chapter to skin friction, but no
-value given for its coefficient.[8] Lanchester's value for planes from
-1/2 to 11/2 sq. ft. in area, moving about 20 to 30 ft. per second, is
-
-    0.009 to 0.015.
-
-Professor Zahm (Washington) gives 0.0026 lb. per sq. ft. at 25 ft. per
-second, and at 37 ft. per second, 0.005, and the formula
-
-    _f_ = 0.00000778_l_^{.93}_v_^{1.85}
-
-_f_ being the average friction in lb. per sq. in., _l_ the length in
-feet, and _v_ the velocity in ft. per second. He also experimented
-with various kinds of surfaces, some rough, some smooth, etc.
-
-His conclusion is:--"All even surfaces have approximately the same
-coefficient of skin friction. Uneven surfaces have a greater
-coefficient." All formulae on skin friction must at present be accepted
-with reserve.
-
-Sec. 8. The following three experiments, however, clearly prove its
-_existence_, and _that it has considerable effect_:--
-
-1. A light, hollow celluloid ball, supported on a stream of air
-projected upwards from a jet, rotates in one direction or the other as
-the jet is inclined to the left or to the right. (F.W. Lanchester.)
-
-2. When a golf ball (which is rough) is hit so as to have considerable
-underspin, its range is increased from 135 to 180 yards, due entirely
-to the greater frictional resistance to the air on that side on which
-the whirl and the progressive motion combine. (Prof. Tait.)
-
-3. By means of a (weak) bow a golf ball can be made to move point
-blank to a mark 30 yards off, provided the string be so adjusted as to
-give a good underspin; adjust the string to the centre of the ball,
-instead of catching it below, and the drop will be about 8 ft. (Prof.
-Tait.)
-
-FOOTNOTES:
-
-[6] _Vide_ "Invention," Feb. 15, 22, and 29, 1896.
-
-[7] Really aerofoils, since we are considering only the supporting
-surface.
-
-[8] I.e., to express it as a decimal fraction of the resistance,
-encountered by the same plane when moving "face" instead of "edge" on.
-
-
-
-
-CHAPTER III.
-
-THE QUESTION OF BALANCE.
-
-
-Sec. 1. It is perfectly obvious for successful flight that any model
-flying machine (in the absence of a pilot) must possess a high degree
-of automatic stability. The model must be so constructed as to be
-naturally stable, _in the medium through which it is proposed to drive
-it_. The last remark is of the greatest importance, as we shall see.
-
-Sec. 2. In connexion with this same question of automatic stability, the
-question must be considered from the theoretical as well as from the
-practical side, and the labours and researches of such men as
-Professors Brian and Chatley, F.W. Lanchester, Captain Ferber,
-Mouillard and others must receive due weight. Their work cannot yet be
-fully assessed, but already results have been arrived at far more
-important than are generally supposed.
-
-The following are a few of the results arrived at from theoretical
-considerations; they cannot be too widely known.
-
-(A) Surfaces concave on the under side are not stable unless some form
-of balancing device (such as a tail, etc.) is used.
-
-(B) If an aeroplane is in equilibrium and moving uniformly, it is
-necessary for stability that it shall tend towards a condition of
-equilibrium.
-
-(C) In the case of "oscillations" it is absolutely necessary for
-stability that these oscillations shall decrease in amplitude, in
-other words, be damped out.
-
-(D) In aeroplanes in which the dihedral angle is excessive or the
-centre of gravity very low down, a dangerous pitching motion is quite
-likely to be set up. [Analogy in shipbuilding--an increase in the
-metacentre height while increasing the stability in a statical sense
-causes the ship to do the same.]
-
-(E) The propeller shaft should pass through the centre of gravity of
-the machine.
-
-(F) The front planes should be at a greater angle of inclination than
-the rear ones.
-
-(G) The longitudinal stability of an aeroplane grows much less when
-the aeroplane commences to rise, a monoplane becoming unstable when
-the angle of ascent is greater than the inclination of the main
-aerofoil to the horizon.
-
-(H) Head resistance increases stability.
-
-(I) Three planes are more stable than two. [Elevator--main
-aerofoil--horizontal rudder behind.]
-
-(J) When an aeroplane is gliding (downwards) stability is greater than
-in horizontal flight.
-
-(K) A large moment of inertia is inimical (opposed) to stability.
-
-(M) Aeroplanes (naturally) stable up to a certain velocity (speed) may
-become unstable when moving beyond that speed. [Possible explanation.
-The motion of the air over the edges of the aerofoil becomes
-turbulent, and the form of the stream lines suddenly changes.
-Aeroplane also probably becomes deformed.]
-
-(N) In a balanced glider for stability a separate surface at a
-negative angle to the line of flight is essential. [Compare F.]
-
-(O) A keel surface should be situated well above and behind the centre
-of gravity.
-
-(P) An aeroplane is a conservative system, and stability is greatest
-when the kinetic energy is a maximum. [Illustration, the pendulum.]
-
-Sec. 3. Referring to A. Models with a plane or flat surface are not
-unstable, and will fly well without a tail; such a machine is called a
-simple monoplane.
-
-[Illustration: FIG. 4.--ONE OF MR. BURGE WEBB'S SIMPLE MONOPLANES.
-
-Showing balance weight A (movable), and also his winding-up gear--a
-very handy device.]
-
-
-Sec. 4. Referring to D. Many model builders make this mistake, i.e., the
-mistake of getting as low a centre of gravity as possible under the
-quite erroneous idea that they are thereby increasing the stability of
-the machine. Theoretically the _centre of gravity should be the centre
-of head resistance, as also the centre of pressure_.
-
-In practice some prefer to put the centre of gravity in models
-_slightly_ above the centre of head resistance, the reason being that,
-generally speaking, wind gusts have a "lifting" action on the machine.
-It must be carefully borne in mind, however, that if the centre of
-wind pressure on the aerofoil surface and the centre of gravity do not
-coincide, no matter at what point propulsive action be applied, it can
-be proved by quite elementary mechanics that such an arrangement,
-known as "acentric," produces a couple tending to upset the machine.
-
-This action is the probable cause of many failures.
-
-[Illustration: FIG. 5.--THE STRINGFELLOW MODEL MONOPLANE OF 1848.]
-
-Sec. 5. Referring to E. If the propulsive action does not pass through
-the centre of gravity the system again becomes "acentric." Even
-supposing condition D fulfilled, and we arrive at the following most
-important result, viz., that for stability:--
-
-THE CENTRES OF GRAVITY, OF PRESSURE, OF HEAD RESISTANCE, SHOULD BE
-COINCIDENT, AND THE PROPULSIVE ACTION OF THE PROPELLER PASS THROUGH
-THIS SAME POINT.
-
-[Illustration: FIG. 6.--THE STRINGFELLOW MODEL TRIPLANE OF 1868.]
-
-Sec. 6. Referring to F and N--the problem of longitudinal stability.
-There is one absolutely essential feature not mentioned in F or N, and
-that is for automatic longitudinal stability _the two surfaces, the
-aerofoil proper and the balancer_ (elevator or tail, or both), _must
-be separated by some considerable distance, a distance not less than
-four times the width of the main aerofoil_.[9] More is better.
-
-[Illustration: FIG. 7. _PENAUD 1871_]
-
-Sec. 7. With one exception (Penaud) early experimenters with model
-aeroplanes had not grasped this all-important fact, and their models
-would not fly, only make a series of jumps, because they failed to
-balance longitudinally. In Stringfellow's and Tatin's models the main
-aerofoil and balancer (tail) are practically contiguous.
-
-Penaud in his rubber-motored models appears to have fully realised
-this (_vide_ Fig. 7), and also the necessity for using long strands of
-rubber. Some of his models flew 150 ft., and showed considerable
-stability.
-
-[Illustration: FIG. 8.--TATIN'S AEROPLANE (1879).
-
-Surface 0.7 sq. metres, total weight 1.75 kilogrammes, velocity of
-sustentation 8 metres a second. Motor, compressed air (for description
-see Sec. 23, ch. iv). Revolved round and round a track tethered to a post
-at the centre. In one of its jumps it cleared the head of a
-spectator.]
-
-With three surfaces one would set the elevator at a slight plus angle,
-main aerofoil horizontal (neither positive nor negative), and the tail
-at a corresponding negative angle to the positive one of the elevator.
-
-Referring to O.[10] One would naturally be inclined to put a keel
-surface--or, in other words, vertical fins--beneath the centre of
-gravity, but D shows us this may have the opposite effect to what we
-might expect.
-
-In full-sized machines, those in which the distance between the main
-aerofoil and balancers is considerable (like the Farman) show
-considerable automatic longitudinal stability, and those in which it
-is short (like the Wright) are purposely made so with the idea of
-doing away with it, and rendering the machine quicker and more
-sensitive to personal control. In the case of the Stringfellow and
-Tatin models we have the extreme case--practically the bird entirely
-volitional and personal--which is the opposite in every way to what we
-desire on a model under no personal or volitional control at all.
-
-[Illustration: FIG. 9.--CLARK'S MODEL FLYER.
-
-Main aerofoil set at a slight negative angle. Dihedral angles on both
-aerofoils.]
-
-The theoretical conditions stated in F and N are fully borne out in
-practice.
-
-And since a curved aerofoil even when set at a _slight_ negative
-angle has still considerable powers of sustentation, it is possible to
-give the main aerofoil a slight negative angle and the elevator a
-slight positive one. This fact is of the greatest importance, since it
-enables us to counteract the effect of the travel of the "centre of
-pressure."[11]
-
-[Illustration: FIG. 10.--LARGE MODEL MONOPLANE.
-
-Designed and constructed by the author, with vertical fin (no dihedral
-angle). With a larger and more efficient propeller than the one here
-shown some excellent flights were obtained. Constructed of bamboo and
-nainsook. Stayed with steel wire.]
-
-Sec. 8. Referring to I. This, again, is of primary importance in
-longitudinal stability. The Farman machine has three such
-planes--elevator, main aerofoil, tail the Wright originally had _not_,
-but is now being fitted with a tail, and experiments on the
-Short-Wright biplane have quite proved its stabilising efficiency.
-
-The three plane (triple monoplane) in the case of models has been
-tried, but possesses no advantage so far over the double monoplane
-type. The writer has made many experiments with vertical fins, and has
-found the machine very stable, even when the fin or vertical keel is
-placed some distance above the centre of gravity.
-
-Sec. 9. The question of transverse (side to side) stability at once
-brings us to the question of the dihedral angle, practically similar
-in its action to a flat plane with vertical fins.
-
-[Illustration: FIG. 11.--SIR GEORGE CAYLEY'S FLYING MACHINE.
-
-Eight feathers, two corks, a thin rod, a piece of whalebone, and a
-piece of thread.]
-
-Sec. 10. The setting up of the front surface at an angle to the rear, or
-the setting of these at corresponding compensatory angles already
-dealt with, is nothing more nor less than the principle of the
-dihedral angle for longitudinal stability.
-
-[Illustration: FIG. 12.--VARIOUS FORMS OF DIHEDRALS.]
-
-As early as the commencement of last century Sir George Cayley (a
-man more than a hundred years ahead of his times) was the first to
-point out that two planes at a dihedral angle constitute a basis of
-stability. For, on the machine heeling over, the side which is
-required to rise gains resistance by its new position, and that which
-is required to sink loses it.
-
-Sec. 11. The dihedral angle principle may take many forms.
-
-As in Fig. 12 _a_ is a monoplane, the rest biplanes. The angles and
-curves are somewhat exaggerated. It is quite a mistake to make the
-angle excessive, the "lift" being thereby diminished. A few degrees
-should suffice.
-
-Whilst it is evident enough that transverse stability is promoted by
-making the sustaining surface trough-shaped, it is not so evident what
-form of cross section is the most efficient for sustentation and
-equilibrium combined.
-
-[Illustration: FIG. 13.]
-
-It is evident that the righting moment of a unit of surface of an
-aeroplane is greater at the outer edge than elsewhere, owing to the
-greater lever arm.
-
-Sec. 12. The "upturned tip" dihedral certainly appears to have the
-advantage.
-
-_The outer edges of the aerofoil then should be turned upward for the
-purpose of transverse stability, while the inner surface should remain
-flat or concave for greater support._
-
-Sec. 13. The exact most favourable outline of transverse section for
-stability, steadiness and buoyancy has not yet been found; but the
-writer has found the section given in Fig. 13, a very efficient one.
-
-FOOTNOTES:
-
-[9] If the width be not uniform the mean width should be taken.
-
-[10] This refers, of course, to transverse stability.
-
-[11] See ch. vi.
-
-
-
-
-CHAPTER IV.
-
-THE MOTIVE POWER.
-
-
-SECTION I.--RUBBER MOTORS.
-
-Sec. 1. Some forty years have elapsed since Penaud first used elastic
-(rubber) for model aeroplanes, and during that time no better
-substitute (in spite of innumerable experiments) has been found. Nor
-for the smaller and lighter class of models is there any likelihood of
-rubber being displaced. Such being the case, a brief account of some
-experiments on this substance as a motive power for the same may not
-be without interest. The word _elastic_ (in science) denotes: _the
-tendency which a body has when distorted to return to its original
-shape_. Glass and ivory (within certain limits) are two of the most
-elastic bodies known. But the limits within which most bodies can be
-distorted (twisted or stretched, or both) without either fracture or a
-LARGE _permanent_ alteration of shape is very small. Not so rubber--it
-far surpasses in this respect even steel springs.
-
-Sec. 2. Let us take a piece of elastic (rubber) cord, and stretch it with
-known weights and observe carefully what happens. We shall find that,
-first of all: _the extension is proportional to the weight
-suspended_--but soon we have an _increasing_ increase of extension. In
-one experiment made by the writer, when the weights were removed the
-rubber cord remained 1/8 of an inch longer, and at the end of an hour
-recovered itself to the extent of 1/16, remaining finally permanently
-1/16 of an inch longer. Length of elastic cord used in this experiment
-8-1/8 inches, 3/16 of an inch thick. Suspended weights, 1 oz. up to 64
-oz. Extension from 1/4 inch up to 24-5/8 inches. Graph drawn in Fig.
-14, No. B abscissae extension in eighths of an inch, ordinates weights
-in ounces. So long as the graph is a straight line it shows the
-extension is proportional to the suspended weight; afterwards in
-excess.
-
-[Illustration: FIG. 14.--WEIGHT AND EXTENSION.
-
-B, rubber 3/16 in. thick; C, 2/16 in. thick; D, 1/16 in. thick. A,
-theoretical line if extension were proportional to weight.]
-
-In this experiment we have been able to stretch (distort) a piece of
-rubber to more than three times its original length, and afterwards it
-finally returns to almost its original length: not only so, a piece of
-rubber cord can be stretched to eight or nine times its original
-length without fracture. Herein lies its supreme advantage over steel
-or other springs. Weight for weight more energy can be got or more
-work be done by stretched (or twisted, or, to speak more correctly, by
-stretched-twisted) rubber cord than from any form of steel spring.[12]
-It is true it is stretched--twisted--far beyond what is called the
-"elastic limit," and its efficiency falls off, but with care not
-nearly so quickly as is commonly supposed, but in spite of this and
-other drawbacks its advantages far more than counterbalance these.
-
-Sec. 3. Experimenting with cords of varying thickness we find that: _the
-extension is inversely proportional to the thickness_. If we leave a
-weight hanging on a piece of rubber cord (stretched, of course, beyond
-its "elastic limit") we find that: _the cord continues to elongate as
-long as the weight is left on_. For example: a 1 lb. weight hung on a
-piece of rubber cord, 8-1/8 inches long and 1/8 of an inch thick,
-stretched it--at first--61/4 inches; after two minutes this had
-increased to 6-5/8 (3/8 of an inch more). One hour later 1/8 of an
-inch more, and sixteen hours later 1/8 of an inch more, i.e. a sixteen
-hours' hang produced an additional extension of 3/4 of an inch. On a
-thinner cord (half the thickness) same weight produced _an additional
-extension_ (_after_ 14 _hours_) _of _10-3/8 _in_.
-
-N.B.--An elastic cord or spring balance should never have a weight
-left permanently on it--or be subjected to a distorting force for a
-longer time than necessary, or it will take a "permanent set," and not
-return to even approximately its original length or form.
-
-In a rubber cord the extension is _directly proportional to the
-length_ as well as _inversely proportional to the thickness and to the
-weight suspended_--true only within the limits of elasticity.
-
-[Illustration: FIG. 15.--EXTENSION AND INCREASE IN VOLUME.]
-
-Sec. 4. =When a Rubber Cord is stretched there is an Increase of
-Volume.=--On stretching a piece of rubber cord to _twice_ its
-original (natural) length, we should perhaps expect to find that the
-string would only be _half_ as thick, as would be the case if the
-volume remained the same. Performing the experiment, and measuring the
-cord as accurately as possible with a micrometer, measuring to the
-one-thousandth of an inch, we at once perceive that this is not the
-case, being about _two-thirds_ of its former volume.
-
-Sec. 5. In the case of rubber cord used for a motive power on model
-aeroplanes, the rubber is _both_ twisted and stretched, but chiefly
-the latter.
-
-Thirty-six strands of rubber, weight about 56 grammes, at 150 turns
-give a torque of 4 oz. on a 5-in. arm, but an end thrust, or end pull,
-of about 31/2 lb. (Ball bearings, or some such device, can be used to
-obviate this end thrust when desirable.) A series of experiments
-undertaken by the writer on the torque produced by twisted rubber
-strands, varying in number, length, etc., and afterwards carefully
-plotted out in graph form, have led to some very interesting and
-instructive results. Ball bearings were used, and the torque, measured
-in eighths of an ounce, was taken (in each case) from an arm 5 in. in
-length.
-
-The following are the principal results arrived at. For graphs, see
-Fig. 16.
-
-Sec. 6. A. Increasing the number of (rubber) strands by _one-half_
-(length and thickness of rubber remaining constant) increases the
-torque (unwinding tendency) _twofold_, i.e., doubles the motive power.
-
-B. _Doubling_ the number of strands increases the torque _more than
-three times_--about 3-1/3 times, 3 times up to 100 turns, 31/2 times
-from 100 to 250 turns.
-
-C. _Trebling_ the number of strands increases the torque at least
-_seven times_.
-
-The increased _size_ of the coils, and thereby _increased_ extension,
-explains this result. As we increase the number of strands, the
-_number_ of twists or turns that can be given it becomes less.
-
-D. _Doubling_ the number of strands (length, etc., remaining
-constant) _diminishes_ the number of turns by _one-third to
-one-half_. (In few strands one-third, in 30 and over one-half.)
-
-[Illustration: FIG. 16.--TORQUE GRAPHS OF RUBBER MOTORS.
-
-    Abscissae = Turns. Ordinates = Torque measured in 1/16 of an oz.
-    Length of arm, 5 in.
-
-    A.  38 strands of new rubber, 2 ft. 6 in. long; 58 grammes weight.
-    B.  36 strands, 2 ft. 6 in. long; end thrust at 150 turns, 31/2 lb.
-    C.  32 strands, 2 ft. 6 in. long.
-    D.  24    "        "        "
-    E.  18    "        "        "     weight 28 grammes.
-    F.  12    "     1 ft. 3 in. long
-    G.  12    "     2 ft. 6 in. long.]
-
-E. If we halve the length of the rubber strands, keeping the _number_
-of strands the same, the torque is but slightly increased for the
-first 100 turns; at 240 turns it is double. But the greater number of
-turns--in ratio of about 2:1--that can be given the longer strand much
-more than compensates for this.
-
-F. No arrangement of the strands, _per se_, gets more energy (more
-motive power) out of them than any other, but there are special
-reasons for making the strands--
-
-G. As long and as few in number as possible.
-
-1. More turns can be given it.
-
-2. It gives a far more even torque. Twelve strands 2 ft. 6 in. long
-give practically a line of small constant angle. Thirty-six strands
-same length a much steeper angle, with considerable variations.
-
-A very good result, which the writer has verified in practice, paying
-due regard to _both_ propeller and motor, is to make--
-
-H. _The length of the rubber strands twice[13] in feet the number of
-the strands in inches_,[14] e.g., if the number of strands is 12 their
-length should be 2 ft., if 18, 3 ft., and so on.
-
-Sec. 7. Experiments with 32 to 38 strands 2 ft. 6 in. long give a torque
-curve almost precisely similar to that obtained from experiments made
-with flat spiral steel springs, similar to those used in watches and
-clocks; and, as we know, the torque given by such springs is very
-uneven, and has to be equalised by use of a fusee, or some such
-device. In the case of such springs it must not be forgotten that the
-turning moment (unwinding tendency) is NOT proportional to the amount
-of winding up, this being true only in the "balance" springs of
-watches, etc., where _both_ ends of the spring are rigidly fastened.
-
-In the case of SPRING MOTORS.[15]
-
-I. The turning moment (unwinding tendency) is proportional to the
-difference between the angle of winding and yielding, proportional to
-the moment of inertia of its section, i.e., to the breadth and the
-cube of its thickness, also proportional to the modulus of elasticity
-of the substance used, and inversely proportional to the length of the
-strip.
-
-Sec. 8. Referring back to A, B, C, there are one or two practical
-deductions which should be carefully noted.
-
-Supposing we have a model with one propeller and 36 strands of
-elastic. If we decide to fit it with twin screws, then, other reasons
-apart, we shall require two sets of strands of more than 18 in number
-each to have the same motive power (27 if the same torque be
-required).[16] This is an important point, and one not to be lost
-sight of when thinking of using two propellers.
-
-Experiments on--
-
-Sec.9. =The Number of Revolutions= (turns) =that can be given to Rubber
-Motors= led to interesting results, e.g., the number of turns to
-produce a double knot in the cord from end to end were, in the case of
-rubber, one yard long:--
-
-    No. of Strands.   No. of Turns.  No. of Strands. No. of Turns.
-            4             440              16            200
-            8             310              28            170
-           12             250
-
-It will be at once noticed that the greater the number of rubber
-strands used in a given length, the fewer turns will it stand in
-proportion. For instance, 8 strands double knot at 310, and 4 at 440
-(and not at 620), 16 at 200, and 8 at 310 (and not 400), and so on.
-The reason, of course, is the more the strands the greater the
-distance they have to travel round themselves.
-
-Sec. 10. =The Maximum Number of Turns.=--As to the maximum number of
-permissible turns, rubber has rupture stress of 330 lb. per sq. in.,
-_but a very high permissible stress_, as much as 80 per cent. The
-resilience (power of recovery after distortion) in tension of rubber
-is in considerable excess of any other substance, silk being the only
-other substance which at all approaches it in this respect, the ratio
-being about 11 : 9. The resilience of steel spiral spring is very
-slight in comparison.
-
-A rubber motor in which the double knot is not exceeded by more than
-100 turns (rubber one yard in length) should last a good time. When
-trying for a record flight, using new elastic, as many as even 500 or
-600 or even more turns have been given in the case of 32-36 strands a
-yard in length; but such a severe strain soon spoils the rubber.
-
-Sec. 11. =On the Use of "Lubricants."=--One of the drawbacks to rubber is
-that if it be excessively strained it soon begins to break up. One of
-the chief causes of this is that the strands stick together--they
-should always be carefully separated, if necessary, after a
-flight--and an undue strain is thereby cast on certain parts. Apart
-also from this the various strands are not subject to the same
-tension. It has been suggested that if some means could be devised to
-prevent this, and allow the strands to slip over one another, a
-considerable increase of power might result. It must, however, be
-carefully borne in mind that anything of an oily or greasy nature has
-an injurious effect on the rubber, and must be avoided at all costs.
-Benzol, petroleum, ether, volatile oils, turpentine, chloroform,
-naphtha, vaseline, soap, and all kinds of oil must be carefully
-avoided, as they soften the rubber, and reduce it more or less to the
-consistence of a sticky mass. The only oil which is said to have no
-action on rubber, or practically none, is castor oil; all the same, I
-do not advise its use as a lubricant.
-
-There are three only which we need consider:--
-
-    1. Soda and water.
-    2. French chalk.
-    3. Pure redistilled glycerine.
-
-The first is perfectly satisfactory when freshly applied, but soon
-dries up and evaporates.
-
-The second falls off; and unless the chalk be of the softest kind,
-free from all grit and hard particles, it will soon do more harm than
-good.
-
-The third, glycerine, is for ordinary purposes by far the best, and
-has a beneficial rather than a deleterious effect on the rubber; but
-it must be _pure_. The redistilled kind, free from all traces of
-arsenic, grease, etc., is the only kind permissible. It does not
-evaporate, and a few drops, comparatively speaking, will lubricate
-fifty or sixty yards of rubber.
-
-Being of a sticky or tacky nature it naturally gathers up dust and
-particles of dirt in course of time. To prevent these grinding into
-the rubber, wash it from time to time in warm soda, and warm and apply
-fresh glycerine when required.
-
-Glycerine, unlike vaseline (a product of petroleum), is not a grease;
-it is formed from fats by a process known as _saponification_, or
-treatment of the oil with caustic alkali, which decomposes the
-compound, forming an alkaline stearate (soap), and liberating the
-glycerine which remains in solution when the soap is separated by
-throwing in common salt. In order to obtain pure glycerine, the fat
-can be decomposed by lead oxide, the glycerine remaining in solution,
-and the lead soap or plaster being precipitated.
-
-By using glycerine as a lubricant the number of turns that can be
-given a rubber motor is greatly increased, and the coils slip over one
-another freely and easily, and prevent the throwing of undue strain on
-some particular portion, and absolutely prevent the strands from
-sticking together.
-
-Sec. 12. =The Action of Copper upon Rubber.=--Copper, whether in the form
-of the metal, the oxides, or the soluble salts, has a marked injurious
-action upon rubber.
-
-In the case of metallic copper this action has been attributed to
-oxidation induced by the dissolved oxygen in the copper. In working
-drawings for model aeroplanes I have noticed designs in which the
-hooks on which the rubber strands were to be stretched were made of
-_copper_. In no case should the strands be placed upon bare metal. I
-always cover mine with a piece of valve tubing, which can easily be
-renewed from time to time.
-
-Sec. 12A. =The Action of Water, etc., on Rubber.=--Rubber is quite
-insoluble in water; but it must not be forgotten that it will absorb
-about 25 per cent. into its pores after soaking for some time.
-
-Ether, chloroform, carbon-tetrachloride, turpentine, carbon
-bi-sulphide, petroleum spirit, benzene and its homologues found in
-coal-tar naphtha, dissolve rubber readily. Alcohol is absorbed by
-rubber, but is not a solvent of it.
-
-Sec. 12B. =How to Preserve Rubber.=--In the first place, in order that it
-shall be _possible_ to preserve and keep rubber in the best condition
-of efficiency, it is absolutely essential that the rubber shall be,
-when obtained, fresh and of the best kind. Only the best Para rubber
-should be bought; to obtain it fresh it should be got in as large
-quantities as possible direct from a manufacturer or reliable rubber
-shop. The composition of the best Para rubber is as follows:--Carbon,
-87.46 per cent.; hydrogen, 12.00 per cent.; oxygen and ash, 0.54 per
-cent.
-
-In order to increase its elasticity the pure rubber has to be
-vulcanised before being made into the sheet some sixty or eighty yards
-in length, from which the rubber threads are cut; after vulcanization
-the substance consists of rubber plus about 3 per cent. of sulphur.
-Now, unfortunately, the presence of the sulphur makes the rubber more
-prone to atmospheric oxidation. Vulcanized rubber, compared to pure
-rubber, has then but a limited life. It is to this process of
-oxidation that the more or less rapid deterioration of rubber is due.
-
-To preserve rubber it should be kept from the sun's rays, or, indeed,
-any actinic rays, in a cool, airy place, and subjected to as even a
-temperature as possible. Great extremes of temperature have a very
-injurious effect on rubber, and it should be washed from time to time
-in warm soda water. It should be subjected to no tension or
-compression.
-
-Deteriorated rubber is absolutely useless for model aeroplanes.
-
-Sec. 13. =To Test Rubber.=--Good elastic thread composed of pure Para
-rubber and sulphur should, if properly made, stretch to seven times
-its length, and then return to its original length. It should also
-possess a stretching limit at least ten times its original length.
-
-As already stated, the threads or strands are cut from sheets; these
-threads can now be cut fifty to the inch. For rubber motors a very
-great deal so far as length of life depends on the accuracy and skill
-with which the strands are cut. When examined under a microscope (not
-too powerful) the strands having the least ragged edge, i.e., the best
-cut, are to be preferred.
-
-Sec. 14. =The Section--Strip or Ribbon versus Square.=--In section the
-square and not the ribbon or strip should be used. The edge of the
-strip I have always found more ragged under the microscope than the
-square. I have also found it less efficient. Theoretically no doubt a
-round section would be best, but none such (in small sizes) is on the
-market. Models have been fitted with a tubular section, but such
-should on no account be used.
-
-Sec. 15. =Size of the Section.=--One-sixteenth or one-twelfth is the best
-size for ordinary models; personally, I prefer the thinner. If more
-than a certain number of strands are required to provide the necessary
-power, a larger size should be used. It is not easy to say _what_ this
-number is, but fifty may probably be taken as an outside limit.
-Remember the size increases by area section; twice the _sectional_
-height and breadth means four times the rubber.
-
-Sec. 16. =Geared Rubber Motors.=--It is quite a mistake to suppose that
-any advantage can be obtained by using a four to one gearing, say; all
-that you do obtain is one-fourth of the power minus the increased
-friction, minus the added weight. This presumes, of course, you make
-no alteration in your rubber strands.
-
-Gearing such as this means _short_ rubber strands, and such are not to
-be desired; in any case, there is the difficulty of increased friction
-and added weight to overcome. It is true by splitting up your rubber
-motor into two sets of strands instead of one you can obtain more
-turns, but, as we have seen, you must increase the number of strands
-to get the same thrust, and you have this to counteract any advantage
-you gain as well as added weight and friction.
-
-Sec. 17. The writer has tried endless experiments with all kinds of
-geared rubber motors, and the only one worth a moment's consideration
-is the following, viz., one in which two gear wheels--same size,
-weight, and number of teeth--are made use of, the propeller being
-attached to the axle of one of them, and the same number of strands
-are used on each axle. The success or non-success of this motor
-depends entirely on the method used in its construction. At first
-sight it may appear that no great skill is required in the
-construction of such a simple piece of apparatus. No greater mistake
-could be made. It is absolutely necessary that _the friction and
-weight be reduced to a minimum_, and the strength be a maximum. The
-torque of the rubber strands on so short an arm is very great.
-
-Ordinary light brass cogwheels will not stand the strain.
-
-A. The cogwheels should be of steel[17] and accurately cut of diameter
-sufficient to separate the two strands the requisite distance, _but no
-more_.
-
-B. The weight must be a minimum. This is best attained by using solid
-wheels, and lightening by drilling and turning.
-
-C. The friction must be a minimum. Use the lightest ball bearings
-obtainable (these weigh only 0.3 gramme), adjust the wheels so that
-they run with the greatest freedom, but see that the teeth overlap
-sufficiently to stand the strain and slight variations in direction
-without fear of slipping. Shallow teeth are useless.
-
-D. Use vaseline on the cogs to make them run as easily as possible.
-
-[Illustration: FIG. 17.--GEARED RUBBER MOTOR.
-
-Designed and constructed by the writer. For description of the model,
-etc., see Appendix.]
-
-E. The material of the containing framework must be of maximum
-strength and minimum lightness. Construct it of minimum size, box
-shaped, use the thinnest tin (really tinned sheet-iron) procurable,
-and lighten by drilling holes, not too large, all over it. Do not use
-aluminium or magnalium. Steel, could it be procured thin enough, would
-be better still.
-
-F. Use steel pianoforte wire for the spindles, and hooks for the
-rubber strands, using as thin wire as will stand the strain.
-
-Unless these directions are carefully carried out no advantage will be
-gained--the writer speaks from experience. The requisite number of
-rubber strands to give the best result must be determined by
-experiment.
-
-Sec. 18. One advantage in using such a motor as this is that the two
-equal strands untwisting in opposite directions have a decided
-steadying effect on the model, similar almost to the case in which two
-propellers are used.
-
-The "best" model flights that the writer has achieved have been
-obtained with a motor of this description.[18]
-
-In the case of twin screws two such gearings can be used, and the
-rubber split up into four strands. The containing framework in this
-case can be simply light pieces of tubing let into the wooden
-framework, or very light iron pieces fastened thereto.
-
-Do not attempt to split up the rubber into more than two strands to
-each propeller.
-
-
-SECTION II.--OTHER FORMS OF MOTORS.
-
-Sec. 18A. =Spring Motors.=--This question has already been dealt with
-more or less whilst dealing with rubber motors, and the superiority of
-the latter over the former pointed out. Rubber has a much greater
-superiority over steel or other springs, because in stretch-twisted
-rubber far more energy can be stored up weight for weight. One pound
-weight of elastic can be made to store up some 320 ft.-lb. of energy,
-and steel only some 65 lb. And in addition to this there is the
-question of gearing, involving extra weight and friction; that is, if
-flat steel springs similar to those used in clockwork mechanism be
-made use of, as is generally the case. The only instance in which such
-springs are of use is for the purpose of studying the effects of
-different distributions of weight on the model, and its effect on the
-balance of the machine; but effects such as this can be brought about
-without a change of motor.
-
-Sec. 18B. A more efficient form of spring motor, doing away with gearing
-troubles, is to use a long spiral spring (as long as the rubber
-strands) made of medium-sized piano wire, similar in principle to
-those used in some roller-blinds, but longer and of thinner steel.
-
-The writer has experimented with such, as well as scores of other
-forms of spring motors, but none can compare with rubber.
-
-The long spiral form of steel spring is, however, much the best.
-
-Sec. 18C. =Compressed Air Motors.=--This is a very fascinating form of
-motor, on paper, and appears at first sight the ideal form. It is so
-easy to write: "Its weight is negligible, and it can be provided free
-of cost; all that is necessary is to work a bicycle pump for as many
-minutes as the motor is desired to run. This stored-up energy can be
-contained in a mere tube, of aluminium or magnalium, forming the
-central rib of the machine, and the engine mechanism necessary for
-conveying this stored-up energy to the revolving propeller need weigh
-only a few ounces." Another writer recommends "a pressure of 300 lb."
-
-Sec. 18D. A pneumatic drill generally works at about 80 lb. pressure,
-and when developing 1 horse-power, uses about 55 cubic ft. of free air
-per minute. Now if we apply this to a model aeroplane of average size,
-taking a reservoir 3 ft. long by 11/2 in. internal diameter, made of
-magnalium, say--steel would, of course, be much better--the weight of
-which would certainly not be less than 4 oz., we find that at 80 lb.
-pressure such a motor would use
-
-    55/Horse Power (H.P.)
-
-cub. ft. per minute.
-
-Now 80 lb. is about 51/2 atmospheres, and the cubical contents of the
-above motor some 63 cub. in. The time during which such a model would
-fly depends on the H.P. necessary for flight; but a fair allowance
-gives a flight of from 10 to 30 sec. I take 80 lb. pressure as a fair
-practical limit.
-
-Sec. 18E. The pressure in a motor-car tyre runs from 40 to 80 lb.,
-usually about 70 lb. Now 260 strokes are required with an ordinary
-inflator to obtain so low a pressure as 70 lb., and it is no easy job,
-as those who have done it know.
-
-Sec. 19. Prior to 1893 Mr. Hargraves (of cellular kite fame) studied the
-question of compressed-air motors for model flying machines. His motor
-was described as a marvel of simplicity and lightness, its cylinder
-was made like a common tin can, the cylinder covers cut from sheet tin
-and pressed to shape, the piston and junk rings of ebonite.
-
-One of his receivers was 23-3/8 in. long, and 5.5 in. diameter, of
-aluminium plate 0.2 in. thick, 3/8 in. by 1/8 in. riveting strips were
-insufficient to make tight joints; it weighed 26 oz., and at 80 lb.
-water pressure one of the ends blew out, the fracture occurring at the
-bend of the flange, and not along the line of rivets. The receiver
-which was successful being apparently a tin-iron one; steel tubing was
-not to be had at that date in Sydney. With a receiver of this
-character, and the engine referred to above, a flight of 343 ft. was
-obtained, this flight being the best. (The models constructed by him
-were not on the aeroplane, but ornithoptere, or wing-flapping
-principle.) The time of flight was 23 _seconds_, with 541/2 double
-vibrations of the engines. The efficiency of this motor was estimated
-to be 29 per cent.
-
-Sec. 20. By using compressed air, and heating it in its passage to the
-cylinder, far greater efficiency can be obtained. Steel cylinders can
-be obtained containing air under the enormous pressure of 120
-atmospheres.[19] This is practically liquid air. A 20-ft. cylinder
-weighs empty 23 lb. The smaller the cylinder the less the
-proportionate pressure that it will stand; and supposing a small steel
-cylinder, produced of suitable form and weight, and capable of
-withstanding with safety a pressure of from 300 to 600 lb. per sq.
-in., or from 20 to 40 atmospheres. The most economical way of working
-would be to admit the air from the reservoir directly to the motor
-cylinders; but this would mean a very great range in the initial
-working pressure, entailing not-to-be-thought-of weight in the form of
-multi-cylinder compound engines, variable expansion gear, etc.
-
-Sec. 21. This means relinquishing the advantages of the high initial
-pressure, and the passing of the air through a reducing valve, whereby
-a constant pressure, say, of 90 to 150, according to circumstances,
-could be maintained. By a variation in the ratio of expansion the air
-could be worked down to, say, 30 lb.
-
-The initial loss entailed by the use of a reducing valve may be in a
-great measure restored by heating the air before using it in the motor
-cylinders; by heating it to a temperature of only 320 deg.F., by means of
-a suitable burner, the volume of air is increased by one half, the
-consumption being reduced in the same proportion; the consumption of
-air used in this way being 24 lb. per indicated horse-power per hour.
-But this means extra weight in the form of fuel and burners, and what
-we gain in one way we lose in another. It is, of course, desirable
-that the motor should work at as low a pressure as possible, since as
-the store of air is used up the pressure in the reservoir falls, until
-it reaches a limit below which it cannot usefully be employed. The air
-then remaining is dead and useless, adding only to the weight of the
-aeroplane.
-
-Sec. 22. From calculations made by the writer the _entire_ weight of a
-compressed-air model motor plant would be at least _one-third_ the
-weight of the aeroplane, and on a small scale probably one-half, and
-cannot therefore hold comparison with the _steam engine_ discussed in
-the next paragraph. In concluding these remarks on compressed-air
-motors, I do not wish to dissuade anyone from trying this form of
-motor; but they must not embark on experiments with the idea that
-anything useful or anything superior to results obtained with
-infinitely less expense by means of rubber can be brought to pass with
-a bicycle pump, a bit of magnalium tube, and 60 lb. pressure.
-
-Sec. 22A. In Tatin's air-compressed motor the reservoir weighed 700
-grammes, and had a capacity of 8 litres. It was tested to withstand a
-pressure of 20 atmospheres, but was worked only up to seven. The
-little engine attached thereto weighed 300 grammes, and developed a
-motive power of 2 kilogram-metres per second (_see_ ch. iii.).
-
-Sec. 23. =Steam-Driven Motors.=--Several successful steam-engined model
-aeroplanes have been constructed, the most famous being those of
-Professor Langley.
-
-Having constructed over 30 modifications of rubber-driven models, and
-experimented with compressed air, carbonic-acid gas, electricity, and
-other methods of obtaining energy, he finally settled upon the steam
-engine (the petrol motor was not available at that time, 1893). After
-many months' work it was found that the weight could not be reduced
-below 40 lb., whilst the engine would only develop 1/2 H.P., and
-finally the model was condemned. A second apparatus to be worked by
-compressed air was tried, but the power proved insufficient. Then came
-another with a carbonic-acid gas engine. Then others with various
-applications of electricity and gas, etc., but the steam engine was
-found most suitable; yet it seemed to become more and more doubtful
-whether it could ever be made sufficiently light, and whether the
-desired end could be attained at all. The chief obstacle proved not to
-be with the engines, which were made surprisingly light after
-sufficient experiment. _The great difficulty was to make a boiler of
-almost no weight which would give steam enough._
-
-Sec. 24. At last a satisfactory boiler and engine were produced.
-
-The engine was of 1 to 11/2 H.P., total weight (including moving
-parts) 26 oz. The cylinders, two in number, had each a diameter of
-11/4 in., and piston stroke 2 in.
-
-The boiler, with its firegrate, weighed a little over 5 lb. It
-consisted of a continuous helix of copper tubing, 3/8 in. external
-diameter, the diameter of the coil being 3 in. altogether. Through the
-centre of this was driven the blast from an "AElopile," a modification
-of the naphtha blow-torch used by plumbers, the flame of which is
-about 2000 deg. F.[20] The pressure of steam issuing into the engines
-varied from 100 to 150 lb. per sq. in.; 4 lb. weight of water and
-about 10 oz. of naphtha could be carried. The boiler evaporated 1 lb.
-of water per minute.
-
-The twin propellers, 39 in. in diam., pitch 11/4, revolved from 800
-to 1000 a minute. The entire aeroplane was 15 ft. in length, the
-aerofoils from tip to tip about 14 ft., and the total weight slightly
-less than 30 lb., of which _one-fourth was contained in the
-machinery_. Its flight was a little over half a mile in length, and of
-11/2 minutes' duration. Another model flew for about three-quarters
-of a mile, at a rate of about 30 miles an hour.
-
-It will be noted that engine, generator, etc., work out at about 7 lb.
-per H.P. Considerable advance has been made in the construction of
-light and powerful model steam engines since Langley's time, chiefly
-in connexion with model hydroplanes, and a pressure of from 500 to 600
-lb. per sq. in. has been employed; the steam turbine has been brought
-to a high state of perfection, and it is now possible to make a model
-De Laval turbine of considerable power weighing almost next to
-nothing,[21] the real trouble, in fact the only one, being the steam
-generator. An economization of weight means a waste of steam, of which
-models can easily spend their only weight in five minutes.
-
-Sec. 25. One way to economize without increased weight in the shape of a
-condenser is to use spirit (methylated spirit, for instance) for both
-fuel and boiler, and cause the exhaust from the engines to be ejected
-on to the burning spirit, where it itself serves as fuel. By using
-spirit, or some very volatile hydrocarbon, instead of water, we have a
-further advantage from the fact that such vaporize at a much lower
-temperature than water.
-
-Sec. 26. When experimenting with an engine of the turbine type we must
-use a propeller of small diameter and pitch, owing to the very high
-velocity at which such engines run.
-
-Anyone, however, who is not an expert on such matters would do well to
-leave such motors alone, as the very highest technical skill, combined
-with many preliminary disappointments and trials, are sure to be
-encountered before success is attained.
-
-Sec. 27. And the smaller the model the more difficult the problem--halve
-your aeroplane, and your difficulties increase anything from fourfold
-to tenfold.
-
-The boiler would in any case be of the flash type of either copper or
-steel tubing (the former for safety), with a magnalium container for
-the spirit, and a working pressure of from 150 to 200 lb. per sq. in.
-Anything less than this would not be worth consideration.
-
-Sec. 28. Some ten months after Professor Langley's successful model
-flights (1896), experiments were made in France at Carquenez, near
-Toulon. The total weight of the model aeroplane in this case was 70
-lb.; the engine power a little more than 1 H.P. Twin screws were
-used--_one in front and one behind_. The maximum velocity obtained was
-40 miles per hour; but the length of run only 154 yards, and duration
-of flight only a few seconds. This result compares very poorly with
-Langley's distance (of best flight), nearly one mile, duration 1 min.
-45 sec. The maximum velocity was greater--30 to 40 miles per hour. The
-total breadth of this large model was rather more than 6 metres, and
-the surface a little more than 8 sq. metres.
-
-Sec. 29. =Petrol Motors.=--Here it would appear at first thought is the
-true solution of the problem of the model aeroplane motor. Such a
-motor has solved the problem of aerial locomotion, as the steam engine
-solved that of terrestrial and marine travel, both full sized and
-model; and if in the case of full sized machines, then why not models.
-
-[Illustration: FIG. 18.--MR. STANGER'S MODEL IN FULL FLIGHT.]
-
-[Illustration: FIG. 19.--MR. STANGER'S PETROL-DRIVEN MODEL AEROPLANE.
-
-(_Illustrations by permission from electros supplied by the "Aero."_)]
-
-Sec. 30. The exact size of the smallest _working_ model steam engine that
-has been made I do not know,[22] but it is or could be surprisingly
-small; not so the petrol motor--not one, that is, that would _work_.
-The number of petrol motor-driven model aeroplanes that have actually
-flown is very small. Personally I only know of one, viz., Mr. D.
-Stanger's, exhibited at the aero exhibition at the Agricultural Hall
-in 1908.
-
-[Illustration: FIG. 20.--MR. STANGER'S MODEL PETROL ENGINE.]
-
-[Illustration: FIG. 21.--MR. STANGER'S MODEL PETROL ENGINE.]
-
-    In Fig. 21 the motor is in position on the aeroplane. Note
-    small carburettor. In Fig. 20 an idea of the size of engine may
-    be gathered by comparing it with the ordinary sparking-plug
-    seen by the side, whilst to the left of this is one of the
-    special plugs used on this motor. (_Illustrations by permission
-    from electros supplied by the "Aero."_)
-
-Sec. 31. The following are the chief particulars of this interesting
-machine:--The engine is a four-cylinder one, and weighs (complete with
-double carburetter and petrol tank) 51/2 lb., and develops 11/4 H.P.
-at 1300 revolutions per minute.
-
-[Illustration: FIG. 22.--ONE-CYLINDER PETROL MOTOR.
-
-(_Electro from Messrs. A.W. Gamage's Aviation Catalogue._)]
-
-The propeller, 29 in. in diam. and 36 in. in pitch, gives a static
-thrust of about 7 lb. The machine has a spread of 8 ft. 2 in., and is
-6 ft. 10 in. in length. Total weight 21 lb. Rises from the ground when
-a speed of about 16 miles an hour is attained. A clockwork
-arrangement automatically stops the engine. The engine air-cooled. The
-cylinder of steel, cast-iron heads, aluminium crank-case, double float
-feed carburetter, ignition by single coil and distributor. The
-aeroplane being 7 ft. 6 in. long, and having a span 8 ft.
-
-Sec. 32. =One-cylinder Petrol Motors.=--So far as the writer is aware no
-success has as yet attended the use of a single-cylinder petrol motor
-on a model aeroplane. Undoubtedly the vibration is excessive; but this
-should not be an insuperable difficulty. It is true it is heavier in
-proportion than a two-cylinder one, and not so efficient; and so far
-has not proved successful. The question of vibration on a model
-aeroplane is one of considerable importance. A badly balanced
-propeller even will seriously interfere with and often greatly curtail
-the length of flight.
-
-Sec. 33. =Electric Motors.=--No attempt should on any account be made to
-use electric motors for model aeroplanes. They are altogether too
-heavy, apart even from the accumulator or source of electric energy,
-for the power derivable from them. To take an extreme case, and
-supposing we use a 2-oz. electric motor capable of driving a propeller
-giving a static thrust of 3 oz.,[23] on weighing one of the smallest
-size accumulators without case, etc., I find its weight is 41/2 oz.
-One would, of course, be of no use; at least three would be required,
-and they would require practically short circuiting to give sufficient
-amperage (running them down, that is, in some 10 to 15 seconds). Total
-weight, 1 lb. nearly. Now from a _pound_ weight of rubber one could
-obtain a thrust of _pounds_, not ounces. For scale models not intended
-for actual flight, of course, electric motors have their uses.
-
-FOOTNOTES:
-
-[12] Also there is no necessity for gearing.
-
-[13] In his latest models the writer uses strands even three times and
-not twice as long, viz. fourteen strands 43 in. long.
-
-[14] This refers to 1/16 in. square sectioned rubber.
-
-[15] Of uniform breadth and thickness.
-
-[16] In practice I find not quite so high a proportion as this is
-always necessary.
-
-[17] Steel pinion wire is very suitable.
-
-[18] See Appendix.
-
-[19] As high a pressure as 250 atmospheres has been used.
-
-[20] There was a special pump keeping the water circulating rapidly
-through the boiler, the intense heat converting some of it into steam
-as it flowed. The making of this boiler alone consumed months of work;
-the entire machine taking a year to construct, with the best
-mechanical help available.
-
-[21] Model Steam Turbines. "Model Engineer" Series, No. 13, price
-6_d._
-
-[22] See Introduction, note to Sec. 1.
-
-[23] The voltage, etc., is not stated.
-
-
-
-
-CHAPTER V.
-
-PROPELLERS OR SCREWS.
-
-
-Sec. 1. The design and construction of propellers, more especially the
-former, is without doubt one of the most difficult parts of model
-aeroplaning.
-
-With elastic or spring driven models the problem is more complicated
-than for models driven by petrol or some vaporized form of liquid
-fuel; and less reliable information is to hand. The problem of
-_weight_, unfortunately, is of primary importance.
-
-We will deal with these points in due course; to begin with let us
-take:--
-
-
-THE POSITION OF THE PROPELLER.
-
-In model aeroplanes the propeller is usually situated either in front
-or in the rear of the model; in the former case it is called a TRACTOR
-SCREW, i.e., it pulls instead of pushes.
-
-As to the merits of the two systems with respect to the tractor, there
-is, we know, in the case of models moving through water a distinct
-advantage in placing the propeller behind, and using a pushing or
-propulsive action, on account of the frictional "wake" created behind
-the boat, and which causes the water to flow after the vessel, but at
-a lesser velocity.
-
-In placing the propeller behind, we place it in such a position as to
-act upon and make use of this phenomenon, the effect of the propeller
-being to bring this following wake to rest. Theoretically a boat,
-model or otherwise, can be propelled with less horse-power than it can
-be towed. But with respect to aeroplanes, apart altogether from the
-difference of medium, there is _at present_ a very considerable
-difference of _form_, an aeroplane, model or otherwise, bearing at
-present but little resemblance to the hull of a boat.
-
-Undoubtedly there is a frictional wake in the case of aeroplanes,
-possibly quite as much in proportion as in the case of a boat,
-allowing for difference of medium. Admitting, then, that this wake
-does exist, it follows that a propulsive screw is better than a
-tractor. In a matter of this kind constructional considerations, or
-"ease of launching," and "ability to land without damage," must be
-given due weight.
-
-In the case of model aeroplanes constructional details incline the
-balance neither one way nor the other; but "ease in launching" and
-"ability to land without damage" weigh the balance down most decidedly
-in favour of a driving or propulsive screw.
-
-In the case of full-sized monoplanes constructional details had most
-to do with the use of tractors; but monoplanes are now being built
-with propulsive screws.[24]
-
-In the case of models, not models of full-sized machines, but actual
-model flyers, the writer considers propulsive screws much the
-best.[25]
-
-In no case should the propeller be placed in the centre of the model,
-or in such a position as to _shorten the strands of the elastic
-motor_, if good flights are desired.
-
-In the case of petrol or similar driven models the position of the
-propeller can be safely copied from actual well-recognised and
-successful full-sized machines.
-
-Sec. 2. =The Number of Blades.=--Theoretically the number of blades does
-not enter into consideration. The mass of air dealt with by the
-propeller is represented by a cylinder of indefinite length, whose
-diameter is the same as that of the screw, and the rate at which this
-cylinder is projected to the rear depends theoretically upon the pitch
-and revolutions (per minute, say) of the propeller and not the number
-of blades. Theoretically one blade (helix incomplete) would be
-sufficient, but such a screw would not "balance," and balance is of
-primary importance; the minimum number of blades which can be used is
-therefore _two_.
-
-In marine models three blades are considered best, as giving a better
-balance.
-
-In the case of their aerial prototypes the question of _weight_ has
-again to be considered, and two blades is practically the invariable
-custom.[26] Here, again, constructional considerations again come to
-the fore, and in the case of wooden propellers one of two blades is of
-far more easy construction than one of three.
-
-By increasing the number of blades the "thrust" is, of course, more
-evenly distributed over a larger area, but the weight is considerably
-increased, and in models a greater advantage is gained by keeping down
-the weight than might follow from the use of more blades.
-
-Sec. 3. =Fan versus Propeller.=--It must always be most carefully borne
-in mind that a fan (ventilating) and a propeller are not the same
-thing. Because many blades are found in practice to be efficient in
-the case of the former, it is quite wrong to assume that the same
-conclusion holds in the case of the latter.
-
-By increasing the number of blades the skin friction due to the
-resistance that has to be overcome in rotating the propeller through
-the air is added to.
-
-Moreover a fan is stationary, whilst a propeller is constantly
-_advancing_ as well as _rotating_ through the air.
-
-The action of a fan blower is to move a small quantity of air at a
-high velocity; whereas the action of a propeller is, or should be, to
-move _a large quantity of air at a small velocity_, for the function
-of a screw is to create thrust. Operating on a yielding fluid medium
-this thrust will evidently be in proportion to the mass of fluid
-moved, and also to the velocity at which it is put in motion.
-
-But the power consumed in putting this mass of fluid in motion is
-proportional to the mass and to the _square_ of the velocity at which
-it moves. From this it follows, as stated above, that in order to
-obtain a given thrust with the least loss of power, the mass of fluid
-acted on should be as large as possible, and the velocity imparted to
-it as little as possible.
-
-A fan requires to be so designed as to create a thrust when stationary
-(static thrust), and a propeller whilst moving through the air
-(dynamic thrust).
-
-Sec. 4. =The Function of a Propeller= is to produce dynamic thrust; and
-the great advantage of the use of a propeller as a thrusting or
-propulsive agent is that its surface is always active. It has no
-_dead_ points, and its motion is continuous and not reciprocating, and
-it requires no special machinery or moving parts in its construction
-and operation.
-
-Sec. 5. =The Pitch= of a propeller or screw is the linear distance a
-screw moves, backwards or forwards, in one complete revolution. This
-distance is purely a theoretical one. When, for instance, a screw is
-said to have a pitch of 1 ft., or 12 in., it means that the model
-would advance 1 ft. through the air for each revolution of the screw,
-provided that the propeller blade were mounted in _solid_ guides, like
-a nut on a bolt with one thread per foot. In a yielding fluid such as
-water or air it does not practically advance this distance, and hence
-occurs what is known as--
-
-Sec. 6. =Slip=, which may be defined as the distance which ought to be
-traversed, but which is lost through imperfections in the propelling
-mechanism; or it may be considered as power which should have been
-used in driving the model forward. In the case of a locomotive running
-on dry rails nothing is lost in slip, there being none. In the case of
-a steamer moored and her engines set going, or of an aeroplane held
-back prior to starting, all the power is used in slip, i.e. in putting
-the fluid in motion, and none is used in propulsion.
-
-Supposing the propeller on our model has a pitch of 1 ft., and we give
-the elastic motor 100 turns, theoretically the model should travel 100
-ft. in calm air before the propeller is run down; no propeller yet
-designed will do this. Supposing the actual length 77 ft., 23 per
-cent. has been lost in "slip." For this to be actually correct the
-propeller must stop at the precise instant when the machine comes to
-ground.
-
-Taking "slip" into account, then--
-
-_The speed of the model in feet per minute = pitch (in feet) x
-revolutions per minute -- slip (feet per minute)._
-
-This slip wants to be made small--just how small is not yet known.
-
-If made too small then the propeller will not be so efficient, or, at
-any rate, such is the conclusion come to in marine propulsion, where
-it is found for the most economical results to be obtained that the
-slip should be from 10 to 20 per cent.
-
-In the case of aerial propellers a slip of 25 per cent. is quite good,
-40 per cent. bad; and there are certain reasons for assuming that
-possibly about 15 per cent. may be the best.
-
-Sec. 7. It is true that slip represents energy lost; but some slip is
-essential, because without slip there could be no "thrust," this same
-thrust being derived from the reaction of the volume of air driven
-backwards.
-
-The thrust is equal to--
-
-_Weight of mass of air acted on per second x slip velocity in feet per
-second._
-
-In the case of an aeroplane advancing through the air it might be
-thought that the thrust would be less. Sir Hiram Maxim found, however,
-as the result of his experiments that the thrust with a propeller
-travelling through the air at a velocity of 40 miles an hour was the
-same as when stationary, the r.p.m. remaining constant throughout. The
-explanation is that when travelling the propeller is continually
-advancing on to "undisturbed" air, the "slip" velocity is reduced, but
-the undisturbed air is equivalent to acting upon a greater mass of
-air.
-
-Sec. 8. =Pitch Coefficient or Pitch Ratio.=--If we divide the pitch of a
-screw by its diameter we obtain what is known as pitch coefficient or
-ratio.
-
-The mean value of eighteen pitch coefficients of well-known full-sized
-machines works out at 0.62, which, as it so happens, is exactly the
-same as the case of the Farman machine propeller considered alone,
-this ratio varying from 0.4 to 1.2; in the case of the Wright's
-machine it is (probably) 1. The efficiency of their propeller is
-admitted on all hands. Their propeller is, of course, a slow-speed
-propeller, 450 r.p.m. The one on the Bleriot monoplane (Bleriot XI.)
-pitch ratio 0.4, r.p.m. 1350.
-
-In marine propulsion the pitch ratio is generally 1.3 for a slow-speed
-propeller, decreasing to 0.9 for a high-speed one. In the case of
-rubber-driven model aeroplanes the pitch ratio is often carried much
-higher, even to over 3.
-
-Mr. T.W.K. Clarke recommends a pitch angle of 45 deg., or less, at the
-tips, and a pitch ratio of 3-1/7 (with an angle of 45 deg.). Within limits
-the higher the pitch ratio the better the efficiency. The higher the
-pitch ratio the slower may be the rate of revolution. Now in a rubber
-motor we do not want the rubber to untwist (run out) too quickly; with
-too fine a pitch the propeller "races," or does something remarkably
-like it. It certainly revolves with an abnormally high percentage of
-slip. And for efficiency it is certainly desirable to push this ratio
-to its limit; but there is also the question of the
-
-Sec. 9. =Diameter.=--"The diameter (says Mr. T.W.K. Clarke) should be
-equal to one-quarter the span of the machine."
-
-If we increase the diameter we shall decrease the pitch ratio. From
-experiments which the writer has made he prefers a lower pitch ratio
-and increased diameter, viz. a pitch ratio of 1.5, and a diameter of
-one-third to even one-half the span, or even more.[27] Certainly not
-less than one-third. Some model makers indulge in a large pitch ratio,
-angle, diameter, and blade area as well, but such a course is not to
-be recommended.
-
-Sec. 10. =Theoretical Pitch.=--Theoretically the pitch (from boss to
-tip) should at all points be the same; the boss or centre of the blade
-at right angles to the plane of rotation, and the angle decreasing as
-one approaches the tips. This is obvious when one considers that the
-whole blade has to move forward the same amount. In the diagrams Figs.
-23 and 24 the tip A of the propeller travels a distance = 2 {pi} R every
-revolution. At a point D on the blade, distant _r_ from the centre,
-the distance is 2 {pi} _r_. In both instances the two points must advance
-a distance equal to the pitch, i.e. the distance represented by P O.
-
-[Illustration: FIG. 23.]
-
-[Illustration: FIG. 24.
-
-A O = 2 {pi} R; D O = 2 {pi} _r_.]
-
-A will move along A P, B along B P, and so on. The angles at the
-points A, B, C ... (Fig. 24), showing the angles at which the
-corresponding parts of the blade at A, B, C ... in Fig. 23 must be set
-in order that a uniform pitch may be obtained.
-
-Sec. 11. If the pitch be not uniform then there will be some portions of
-the blade which will drag through the air instead of affording useful
-thrust, and others which will be doing more than they ought, putting
-air in motion which had better be left quiet. This uniform total pitch
-for all parts of the propeller is (as already stated) a decreasing
-rate of pitch from the centre to the edge. With a total pitch of 5
-ft., and a radius of 4 ft., and an angle at the circumference of 6 deg.,
-then the angle of pitch at a point midway between centre and
-circumference should be 12 deg., in order that the total pitch may be the
-same at all parts.
-
-Sec. 12. =To Ascertain the Pitch of a Propeller.=--Take any point on one
-of the blades, and carefully measure the inclination of the blade at
-that point to the plane of rotation.
-
-If the angle so formed be about 19 deg. (19.45),[28] i.e., 1 in 3, and the
-point 5 in. from the centre, then every revolution this point will
-travel a distance
-
-    2 {pi} _r_ = 2 x 22/7 x 5 = 31.34.
-
-Now since the inclination is 1 in 3,[29] the propeller will travel
-forward theoretically one-third of this distance, or
-
-    31.43/3 = 10.48 = 101/2 in. approx.
-
-Similarly any other case may be dealt with. If the propeller have a
-uniform _constant angle_ instead of a uniform pitch, then the pitch
-may be calculated at a point about one-third the length of the blade
-from the tip.
-
-Sec. 13. =Hollow-Faced Blades.=[30]--It must always be carefully borne
-in mind that a propeller is nothing more nor less than a particular
-form of aeroplane specially designed to travel a helical path. It
-should, therefore, be hollow faced and partake of the "stream line"
-form, a condition not fulfilled if the face of the blade be flat--such
-a surface cutting into the air with considerable shock, and by no
-means creating as little undesirable motion in the surrounding medium
-as possible.
-
-It must not be forgotten that a curved face blade has of necessity an
-increasing pitch from the cutting to the trailing edge (considering,
-of course, any particular section). In such a case the pitch is the
-_mean effective pitch_.
-
-Sec. 14. =Blade Area.=--We have already referred to the fact that the
-function of a propeller is to produce dynamic thrust--to drive the
-aeroplane forward by driving the air backwards. At the same time it is
-most desirable for efficiency that the air should be set in motion as
-little as possible, this being so much power wasted; to obtain the
-greatest reaction or thrust the greatest possible volume of air should
-be accelerated to the smallest velocity.
-
-In marine engineering in slow-speed propellers (where cavitation[31]
-does not come in) narrow blades are usually used. In high-speed marine
-propellers (where cavitation is liable to occur) the projected area of
-the blades is sometimes as much as 0.6 of the total disk area. In the
-case of aerial propellers, where cavitation does not occur, or not
-unless the velocity be a very high one (1500 or more a minute), narrow
-blades are the best. Experiments in marine propulsion also show that
-the thrust depends more on the disk area than on the width of the
-blades. All the facts tend to show that for efficiency the blades of
-the propeller should be narrow, in order that the air may not be acted
-on for too long a time, and so put too much in motion, and the blades
-be so separated that one blade does not disturb the molecules of air
-upon which the next following one must act. Both in the case of marine
-and aerial propellers multiplicity of blades (i.e. increased blade
-area) tends to inefficiency of action, apart altogether from the
-question of weight and constructional difficulties. The question of
-increasing pitch in the case of hollow-faced blades, considered in the
-last paragraph, has a very important bearing on the point we are
-considering. To make a wide blade under such circumstances would be to
-soon obtain an excessive angle.
-
-In the case of a flat blade the same result holds, because the air has
-by the contact of its molecules with the "initial minimum width" been
-already accelerated up to its final velocity, and further area is not
-only wasted, but inimical to good flights, being our old bugbear
-"weight in excess."
-
-Requisite strength and stiffness, of course, set a limit on the final
-narrowness of the blades, apart from other considerations.
-
-Sec. 15. The velocity with which the propeller is rotated has also an
-important bearing on this point; but a higher speed than 900 r.p.m.
-does not appear desirable, and even 700 or less is generally
-preferable.[32] In case of twin-screw propellers, with an angle at the
-tips of 40 deg. to 45 deg., as low a velocity of 500 or even less would be
-still better.[33]
-
-Sec. 16. =Shrouding.=--No improvement whatever is obtained by the use of
-any kind of shrouding or ring round the propeller tips, or by
-corrugating the surface of the propeller, or by using cylindrical or
-cone-shaped propeller chamber or any kind of air guide either before
-or after the propeller; allow it to revolve in as free an air-feed as
-possible, the air does not fly off under centrifugal force, but is
-powerfully sucked inwards in a well-designed propeller.
-
-[Illustration: FIG. 25.
-
-A TUBE OF AIR.]
-
-[Illustration: FIG. 26.
-
-A CYLINDER OF AIR.]
-
-Sec. 17. =General Design.=--The propeller should be so constructed as to
-act upon a tube and not a "cylinder" of air. Many flying toys
-(especially the French ones) are constructed with propellers of the
-cylinder type. Ease of manufacture and the contention that those
-portions of the blades adjacent to the boss do little work, and a
-slight saving in weight, are arguments that can be urged in their
-favour. But all the central cut away part offers resistance in the
-line of travel, instead of exerting its proportionate propulsive
-power, and their efficiency is affected by such a practice.
-
-Sec. 18. A good =Shape= for the blades[34] is rectangular with rounded
-corners; the radius of the circle for rounding off the corners may be
-taken as about one-quarter of the width of the blade. The shape is not
-_truly rectangular, for the width of this rectangular at (near) the
-boss should be one-half the width at the tip_.
-
-The thickness should diminish uniformly from the boss to the tip. (In
-models the thickness should be as little as is consistent with
-strength to keep down the weight). _The pitch uniform and large._
-
-[Illustration: FIG. 27.--O T = 1/3 O P.]
-
-Sec. 19. =The Blades, two in number=, and hollow faced--the maximum
-concavity being one-third the distance from the entering to the
-trailing edge; the ratio of A T to O P (the width) being 0.048 or 1 :
-21, these latter considerations being founded on the analogy between a
-propeller and the aerofoil surface. (If the thickness be varied from
-the entering to the trailing edge the greatest thickness should be
-towards the former.) The convex surface of the propeller must be taken
-into account, in fact, it is no less important than the concave, and
-the entire surface must be given a true "stream line" form.
-
-[Illustration: FIG. 28.]
-
-[Illustration: FIG. 29.]
-
-If the entering and trailing edge be not both straight, but one be
-curved as in Fig. 28, then the straight edge must be made the
-_trailing_ edge. And if both be curved as in Fig. 29, then the
-_concave_ edge must be the trailing edge.
-
-Sec. 19. =Propeller Design.=--To design a propeller, proceed as follows.
-Suppose the diameter 14 in. and the pitch three times the diameter,
-i.e. 52 in. (See Fig. 30.)
-
-Take one-quarter scale, say. Draw a centre line A B of convenient
-length, set of half the pitch 52 in. -- 1/4 scale = 51/4 in. = C - D.
-Draw lines through C and D at right angles to C D.
-
-With a radius equal to half the diameter (i.e. in this case 13/4 in.)
-of the propeller, describe a semicircle E B F and complete the
-parallelogram F H G E. Divide the semicircle into a number of equal
-parts; twelve is a convenient number to take, then each division
-subtends an angle of 15 deg. at the centre D.
-
-Divide one of the sides E G into the same number of equal parts
-(twelve) as shown. Through these points draw lines parallel to F E or
-H G.
-
-And through the twelve points of division on the semicircle draw lines
-parallel to F H or E G as shown. The line drawn through the successive
-intersections of these lines is the path of the tip of the blade
-through half a revolution, viz. the line H S O T E.
-
-S O T X gives the angle at the tip of the blades = 44 deg..
-
-Let the shape of the blade be rectangular with rounded corners, and
-let the breadth at the tip be twice that at the boss.
-
-Then the area (neglecting the rounded off corners) is 101/2 sq. in.
-
-[Illustration: FIG. 30.--PROPELLER DESIGN.
-
-One quarter scale. Diameter 14 in. Pitch 52 in. Angle at tip 44 deg..]
-
-The area being that of a rectangle 7 in. x 1 in. = 7 sq. in. plus area
-of two triangles, base 1/2 in., height 7 in. Now area of triangle =
-half base x height. Therefore area of both triangles = 1/2 in. x 7
-in. = 31/2 sq. in. Now the area of the disc swept out by the
-propeller is
-
-    {pi}/4 x (diam.) squared  ({pi} = 22/7)
-
-[Illustration: FIG. 31.--PROPELLER DESIGN.
-
-Scale one-eighth for A B and B C; but sections of blade are
-full-sized.]
-
-And if _d_ A _r_ = the "disc area ratio" we have
-
-    (_d_ A _r_) x {pi}/4 x (14) squared = area of blade = 101/2,
-
-whence _d_ A _r_ = 0.07 about.
-
-[Illustration: FIG. 32.]
-
-[Illustration: FIG. 33.]
-
-In Fig. 31 set off A B equal to the pitch of the propeller (42 in.),
-one-eighth scale. Set off B C at right angles to A B and equal to
-
-    {pi} x diameter = 22/7 x 14 = 44 in. to scale 51/2 in.
-
-Divide B C into a convenient number of equal parts in the figure; five
-only are taken, D, E, F, G, H; join A D, A E, A F, A G, A H and
-produce them; mark off distances P O, S R, Y T ... equal to the width
-of the blade at these points (H P = H O; G S = G R ...) and sketch in
-the sections of blade as desired. In the figure the greatest concavity
-of the blade is supposed to be one-third the distances P O, S R ...
-from PS.... The concavity is somewhat exaggerated. The angles A H B, A
-G B, A F B ... represent the pitch angle at the points H, G, F ... of
-the blade.
-
-Similarly any other design may be dealt with; in a propeller of 14 in.
-diameter the diameter of the "boss" should not be more than 10/16 in.
-
-Sec. 20. =Experiments with Propellers.=--The propeller design shown in
-Figs. 32 and 33, due to Mr. G. de Havilland,[35] is one very suitable
-for experimental purposes. A single tube passing through a T-shaped
-boss forms the arms. On the back of the metal blade are riveted four
-metallic clips; these clips being tightened round the arm by
-countersunk screws in the face of the blade.
-
-The tube and clips, etc., are all contained with the back covering of
-the blade, as shown in Fig. 35, if desired, the blade then practically
-resembling a wooden propeller. The construction, it will be noticed,
-allows of the blade being set at any angle, constant or otherwise;
-also the pitch can be constant or variable as desired, and any "shape"
-of propeller can be fitted.
-
-The advantage of being able to _twist_ the blade (within limits) on
-the axis is one not to be underestimated in experimental work.
-
-[Illustration: FIG. 34.--THE AUTHOR'S PROPELLER TESTING APPARATUS.]
-
-With a view to ascertain some practical and reliable data with respect
-to the _dynamic_, or actual thrust given when moving through free air
-at the velocity of actual travel, the author experimented with the
-apparatus illustrated in Figs. 34 and 35, which is so simple and
-obvious as to require scarcely any explanation.
-
-The wires were of steel, length not quite 150 ft., fitted with wire
-strainers for equalising tension, and absolutely free from "kinks."
-As shown most plainly in Fig. 35, there were two parallel wires
-sufficiently far apart for the action of one propeller not to affect
-the other. Calling these two wires A and B, and two propellers _x_ and
-_y_, then _x_ is first tried on A and _y_ on B. Results carefully
-noted.
-
-[Illustration: FIG. 35.--PROPELLER TESTING.
-
-Showing distance separating the two wires.]
-
-Then _x_ is tried on B and _y_ on A, and the results again carefully
-noted. If the results confirm one another, the power used in both
-cases being the same, well and good; if not, adjustments, etc., are
-made in the apparatus until satisfactory results are obtained. This
-was done when the propellers "raced" one against the other. At other
-times one wire only was made use of, and the time and distance
-traversed was noted in each case. Propellers were driven through
-smoke, and with silk threads tied to a light framework slightly larger
-than their disc area circumference. Results of great interest were
-arrived at. These results have been assumed in much that has been said
-in the foregoing paragraphs.
-
-[Illustration: FIG. 36.--ONE GROUP OF PROPELLERS TESTED BY THE AUTHOR.]
-
-Briefly put, these results showed:--
-
-1. The inefficiency of a propeller of the fan blower or of the static
-thrust type.
-
-2. The advantage of using propellers having hollow-faced blades and
-large diameter.
-
-3. That diameter was more useful than blade area, i.e. given a certain
-quantity (weight) of wood, make a long thin blade and not a shorter
-one of more blade area--blade area, i.e., as proportionate to its
-corresponding disc area.
-
-4. That the propeller surface should be of true stream-line form.
-
-5. That it should act on a cylinder and not tubes of air.
-
-6. That a correctly designed and proportioned propeller was just as
-efficacious in a small size of 9 in. to 28 in. as a full-sized
-propeller on a full-sized machine.
-
-[Illustration: FIG. 37.--AN EFFICIENT PROPELLER, BUT RATHER HEAVY.
-
-Ball bearings, old and new. Note difference in sizes and weights.
-Propeller, 14 in. diam.; weight 36 grammes.]
-
-A propeller of the static-thrust type was, of course, "first off,"
-sometimes 10 ft. or 12 ft. ahead, or even more; but the correctly
-designed propeller gradually gathered up speed and acceleration, just
-as the other fell off and lost it, and finally the "dynamic" finished
-along its corresponding wire far ahead of the "static," sometimes
-twice as far, sometimes six times. "Freak" propellers were simply not
-in it.
-
-[Illustration: FIG. 38.--"VENNA" PROPELLER.
-
-A 20 per cent. more efficient propeller than that shown in Fig. 41; 14
-per cent. lighter; 6 per cent. better in dynamic thrust--14 in. diam.;
-weight 31 grammes.]
-
-Metal propellers of constant angle, as well as wooden ones of uniform
-(constant) pitch, were tested; the former gave good results, but not
-so good as the latter.
-
-The best angle of pitch (at the tip) was found to be from 20 deg. to 30 deg..
-
-In all cases when the slip was as low as 25 per cent., or even
-somewhat less, nearly 20 per cent., a distinct "back current" of air
-was given out by the screw. This "slip stream," as it is caused, is
-absolutely necessary for efficiency.
-
-Sec. 21. =Fabric-covered= screws did not give very efficient results; the
-only point in their use on model aeroplanes is their extreme
-lightness. Two such propellers of 6 in. diameter can be made to weigh
-less than 1/5 oz. the pair; but wooden propellers (built-up principle)
-have been made 5 in. diameter and 1/12 oz. in weight.
-
-Sec. 22. Further experiments were made with twin screws mounted on model
-aeroplanes. In one case two propellers, both turning in the _same_
-direction, were mounted (without any compensatory adjustment for
-torque) on a model, total weight 11/2 lb. Diameter of each propeller
-14 in.; angle of blade at tip 25 deg.. The result was several good
-flights--the model (_see_ Fig. 49c) was slightly unsteady across the
-wind, that was all.
-
-In another experiment two propellers of same diameter, pitch, etc.,
-but of shape similar to those shown in Figs. 28 and 29, were tried as
-twin propellers on the same machine. The rubber motors were of equal
-weight and strength.
-
-The model described circled to the right or left according to the
-position of the curved-shaped propeller, whether on the left or right
-hand, thereby showing its superiority in dynamic thrust. Various
-alterations were made, but always with the same result. These
-experiments have since been confirmed, and there seems no doubt that
-the double-curved shaped blade _is_ superior. (See Fig. 39.)
-
-Sec. 23. =The Fleming-Williams Propeller.=--A chapter on propellers would
-scarcely be complete without a reference to the propeller used on a
-machine claiming a record of over a quarter of a mile. This form of
-propeller, shown in the group in Fig. 36 (top right hand), was found
-by the writer to be extremely deficient in dynamic thrust, giving the
-worst result of any shown there.
-
-[Illustration: FIG. 39.--CURVED DOUBLE PROPELLER.
-
-The most efficient type yet tested by the writer, when the blade is
-made hollow-faced. When given to the writer to test it was flat-faced
-on one side.]
-
-[Illustration: FIG. 40.--THE FLEMING-WILLIAMS MODEL.]
-
-It possesses large blade area, large pitch angle--more than 45 deg. at the
-tip--and large diameter. These do not combine to propeller efficiency
-or to efficient dynamic thrust; but they do, of course, combine to
-give the propeller a very slow rotational velocity. Provided they give
-_sufficient_ thrust to cause the model to move through the air at a
-velocity capable of sustaining it, a long flight may result, not
-really owing to true efficiency on the part of the propellers,[36] but
-owing to the check placed on their revolutions per minute by their
-abnormal pitch angle, etc. The amount of rubber used is very great for
-a 10 oz. model, namely, 34 strands of 1/16 in. square rubber to each
-propeller, i.e. 68 strands in all.
-
-[Illustration: FIG. 41.--THE SAME IN FLIGHT.
-
-(_Reproduced by permission from "The Aero."_)]
-
-On the score of efficiency, when it is desired to make a limited
-number of turns give the longest flight (which is the problem one
-always has to face when using a rubber motor) it is better to make use
-of an abnormal diameter, say, more than half the span, and using a tip
-pitch angle of 25 deg., than to make use of an abnormal tip pitch 45 deg. and
-more, and large blade area. In a large pitch angle so much energy is
-wasted, not in dynamic thrust, but in transverse upsetting torque. On
-no propeller out of dozens and dozens that I have tested have I ever
-found a tip-pitch of more than 35 deg. give a good dynamic thrust; and for
-length of flight velocity due to dynamic thrust must be given due
-weight, as well as the duration of running down of the rubber motor.
-
-Sec. 24. Of built up or carved out and twisted wooden propellers, the
-former give the better result; the latter have an advantage, however,
-in sometimes weighing less.
-
-FOOTNOTES:
-
-[24] _Note._--Since the above was written some really remarkable
-flights have been obtained with a 1 oz. model having two screws, one
-in front and the other behind. Equally good flights have also been
-obtained with the two propellers behind, one revolving in the
-immediate rear of the other. Flying, of course, with the wind,
-_weight_ is of paramount importance in these little models, and in
-both these cases the "single stick" can be made use of. _See also_ ch.
-iv., Sec. 28.
-
-[25] _See also_ ch. viii., Sec. 5.
-
-[26] Save in case of some models with fabric-covered propellers. Some
-dirigibles are now being fitted with four-bladed wooden screws.
-
-[27] Vide Appendix.
-
-[28] Vide Equivalent Inclinations--Table of.
-
-[29] One in 3 or 0.333 is the _sine_ of the angle; similarly if the
-angle were 30 deg. the sine would be 0.5 or 1/2, and the theoretical
-distance travelled one-half.
-
-[30] _Flat-Faced Blades._--If the blade be not hollow-faced--and we
-consider the screw as an inclined plane and apply the Duchemin formula
-to it--the velocity remaining the same, the angle of maximum thrust is
-351/4 deg.. Experiments made with such screws confirm this.
-
-[31] Cavitation is when the high speed of the screw causes it to carry
-round a certain amount of the medium with it, so that the blades
-strike no undisturbed, or "solid," air at all, with a proportionate
-decrease in thrust.
-
-[32] In the Wright machine r.p.m. = 450; in Bleriot XI. r.p.m. = 1350.
-
-[33] Such propellers, however, require a considerable amount of
-rubber.
-
-[34] But _see also_ Sec. 22.
-
-[35] "Flight," March 10, 1910. (Illustration reproduced by
-permission.)
-
-[36] According to the author's views on the subject.
-
-
-
-
-CHAPTER VI.
-
-THE QUESTION OF SUSTENTATION THE CENTRE OF PRESSURE.
-
-
-Sec. 1. Passing on now to the study of an aeroplane actually in the air,
-there are two forces acting on it, the upward lift due to the air
-(i.e. to the movement of the aeroplane supposed to be continually
-advancing on to fresh, undisturbed _virgin_ air), and the force due to
-the weight acting vertically downwards. We can consider the resultant
-of all the upward sustaining forces as acting at a single point--that
-point is called the "Centre of Pressure."
-
-Suppose A B a vertical section of a flat aerofoil, inclined at a small
-angle _a_ to the horizon C, the point of application of the resultant
-upward 'lift,' D the point through which the weight acts vertically
-downwards. Omitting for the moment the action of propulsion, if these
-two forces balance there will be equilibrium; but to do this they must
-pass through the same point, but as the angle of inclination varies,
-so does the centre of pressure, and some means must be employed
-whereby if C and D coincide at a certain angle the aeroplane will come
-back to the correct angle of balance if the latter be altered.
-
-In a model the means must be automatic. Automatic stability depends
-for its action upon the movement of the centre of pressure when the
-angle of incidence varies. When the angle of incidence increases the
-centre of pressure moves backwards towards the rear of the aerofoil,
-and vice versa.
-
-Let us take the case when steady flight is in progress and C and D are
-coincident, suppose the velocity of the wind suddenly to
-increase--increased lifting effect is at once the result, and the fore
-part of the machine rises, i.e. the angle of incidence increases and
-the centre of pressure moves back to some point in the rear of C D.
-The weight is now clearly trying to pull the nose of the aeroplane
-down, and the "lift" tending to raise the tail. The result being an
-alteration of the angle of incidence, or angle of attack as it is
-called, until it resumes its original position of equilibrium. A drop
-in the wind causes exactly an opposite effect.
-
-[Illustration: FIG. 42.]
-
-Sec. 2. The danger lies in "oscillations" being set up in the line of
-flight due to changes in the position of the centre of pressure. Hence
-the device of an elevator or horizontal tail for the purpose of
-damping out such oscillations.
-
-Sec. 3. But the aerofoil surface is not flat, owing to the increased
-"lift" given by arched surfaces, and a much more complicated set of
-phenomena then takes place, the centre of pressure moving forward
-until a certain critical angle of incidence is reached, and after
-this a reversal takes place, the centre of pressure then actually
-moving backwards.
-
-The problem then consists in ascertaining the most efficient aerocurve
-to give the greatest "lift" with the least "drift," and, having found
-it, to investigate again experimentally the movements of the centre of
-pressure at varying angles, and especially to determine at what angle
-(about) this "reversal" takes place.
-
-[Illustration: FIG. 43.]
-
-Sec. 4. Natural automatic stability (the only one possible so far as
-models are concerned) necessitates permanent or a permanently
-recurring coincidence (to coin a phrase) of the centre of gravity and
-the centre of pressure: the former is, of course, totally unaffected
-by the vagaries of the latter, any shifting of which produces a couple
-tending to destroy equilibrium.
-
-Sec. 5. As to the best form of camber (for full sized machine) possibly
-more is known on this point than on any other in the whole of
-aeronautics.
-
-In Figs. 44 and 45 are given two very efficient forms of cambered
-surfaces for models.
-
-[Illustration: FIG. 44.--AN EFFICIENT FORM OF CAMBER.
-
-  B D Maximum Altitude.        A C Chord.
-  Ratio of B D: A C :: 1:17.   A D 1/3 of A C.]
-
-[Illustration: FIG. 45.--ANOTHER EFFICIENT FORM.
-
-Ratio of B D to A C 1 to 17. AD rather more than 1/4 of A C.]
-
-The next question, after having decided the question of aerocurve, or
-curvature of the planes, is at what angle to set the cambered surface
-to the line of flight. This brings us to the question of the--
-
-Sec. 6. =Dipping Front Edge.=--The leading or front edge is not
-tangential to the line of flight, but to a relative upward wind. It is
-what is known as the "cyclic up-current," which exists in the
-neighbourhood of the entering edge. Now, as we have stated before, it
-is of paramount importance that the aerofoil should receive the air
-with as little shock as possible, and since this up-current does
-really exist to do this, it must travel through the air with a dipping
-front edge. The "relative wind" (the only one with which we are
-concerned) _is_ thereby met tangentially, and as it moves onward
-through the air the cambered surface (or aerocurve) gradually
-transforms this upward trend into a downward wake, and since by
-Newton's law, "Action and reaction are equal and opposite," we have
-an equal and opposite upward reaction.
-
-We now know that the top (or convex side) of the cambered surface is
-practically almost as important as the underneath or concave side in
-bringing this result about.
-
-The exact amount of "dipping edge," and the exact angle at which the
-chord of the aerocurve, or cambered surface, should be set to the line
-of flight--whether at a positive angle, at no angle, or at a negative
-angle--is one best determined by experiment on the model in question.
-
-[Illustration: FIG. 46.]
-
-But _if at any angle, that angle either way should be a very small
-one_. If you wish to be very scientific you can give the underside of
-the front edge a negative angle of 5 deg. to 7 deg. for about one-eighth of
-the total length of the section, after that a positive angle,
-gradually increasing until you finally finish up at the trailing edge
-with one of 4 deg.. Also, the form of cambered surface should be a
-paraboloid--not arc or arc of circles. The writer does not recommend
-such an angle, but prefers an attitude similar to that adopted in the
-Wright machine, as in Fig. 47.
-
-Sec. 7. Apart from the attitude of the aerocurve: _the greatest depth of
-the camber should be at one-third of the length of the section from
-the front edge, and the total depth measured from the top surface to
-the chord at this point should not be more than one-seventeenth of the
-length of section_.
-
-Sec. 8. It is the greatest mistake in model aeroplanes to make the camber
-otherwise than very slight (in the case of surfaced aerofoils the
-resistance is much increased), and aerofoils with anything but a _very
-slight_ arch are liable to be very unstable, for the aerocurve has
-always a decided tendency to "follow its own curve."
-
-[Illustration: FIG. 47.--ATTITUDE OF WRIGHT MACHINE.]
-
-The nature of the aerocurve, its area, the angle of inclination of its
-chord to the line of flight, its altitude, etc., are not the only
-important matters one must consider in the case of the aerofoil, we
-must also consider--
-
-Sec. 9. Its =Aspect Ratio=, i.e. the ratio of the span (length) of the
-aerofoil to the chord--usually expressed by span/chord. In the Farman
-machine this ratio is 5.4; Bleriot, 4.3; Short, 6 to 7.5; Roe
-triplane, 7.5; a Clark flyer, 9.6.
-
-Now the higher the aspect ratio the greater should be the efficiency.
-Air escaping by the sides represents loss, and the length of the sides
-should be kept short. A broader aerofoil means a steeper angle of
-inclination, less stability, unnecessary waste of power, and is
-totally unsuited for a model--to say nothing of a full-sized machine.
-
-In models this aspect ratio may with advantage be given a higher value
-than in full-sized machines, where it is well known a practical safe
-constructional limit is reached long before theory suggests the
-limit. The difficulty consists in constructing models having a very
-high aspect ratio, and yet possessing sufficient strength and
-lightness for successful flight. It is in such a case as this where
-the skill and ingenuity of the designer and builder come in.
-
-It is this very question of aspect ratio which has given us the
-monoplane, the biplane, and the triplane. A biplane has a higher
-aspect ratio than a monoplane, and a triplane (see above) a higher
-ratio still.
-
-It will be noticed the Clark model given has a considerably higher
-aspect ratio, viz. 9.6. And even this can be exceeded.
-
-_An aspect ratio of_ 10:1 _or even_ 12:1 _should be used if
-possible._[37]
-
-Sec. 10. =Constant or Varying Camber.=--Some model makers vary the camber
-of their aerofoils, making them almost flat in some parts, with
-considerable camber in others; the tendency in some cases being to
-flatten the central portions of the aerofoil, and with increasing
-camber towards the tips. In others the opposite is done. The writer
-has made a number of experiments on this subject, but cannot say he
-has arrived at any very decisive results, save that the camber should
-in all cases be (as stated before) very slight, and so far as his
-experiments do show anything, they incline towards the further
-flattening of the camber in the end portions of the aerofoil. It must
-not be forgotten that a flat-surfaced aerofoil, constructed as it is
-of more or less elastic materials, assumes a natural camber, more or
-less, when driven horizontally through the air. Reference has been
-made to a reversal of the--
-
-Sec. 11. =Centre of Pressure on Arched Surfaces.=--Wilbur Wright in his
-explanation of this reversal says: "This phenomenon is due to the fact
-that at small angles the wind strikes the forward part of the aerofoil
-surface on the upper side instead of the lower, and thus this part
-altogether ceases to lift, instead of being the most effective part of
-all." The whole question hangs on the value of the critical angle at
-which this reversal takes place; some experiments made by Mr. M.B.
-Sellers in 1906 (published in "Flight," May 14, 1910) place this angle
-between 16 deg. and 20 deg.. This angle is much above that used in model
-aeroplanes, as well as in actual full-sized machines. But the
-equilibrium of the model might be upset, not by a change of attitude
-on its part, but on that of the wind, or both combined. By giving (as
-already advised) the aerofoil a high aspect ratio we limit the travel
-of the centre of pressure, for a high aspect ratio means, as we have
-seen, a short chord; and this is an additional reason for making the
-aspect ratio as high as practically possible. The question is, is the
-critical angle really as high as Mr. Seller's experiments would show.
-Further experiments are much needed.
-
-FOOTNOTES:
-
-[37] Nevertheless some models with a very low aspect ratio make good
-flyers, owing to their extreme lightness.
-
-
-
-
-CHAPTER VII.
-
-MATERIALS FOR AEROPLANE CONSTRUCTION.
-
-
-Sec. 1. The choice of materials for model aeroplane construction is more
-or less limited, if the best results are to be obtained. The lightness
-absolutely essential to success necessitates--in addition to skilful
-building and best disposition of the materials--materials of no undue
-weight relative to their strength, of great elasticity, and especially
-of great resilience (capacity to absorb shock without injury).
-
-Sec. 2. =Bamboo.=--Bamboo has per pound weight a greater resilience than
-any other suitable substance (silk and rubber are obviously useless as
-parts of the _framework_ of an aeroplane). On full-sized machines the
-difficulty of making sufficiently strong connections and a liability
-to split, in the larger sizes, are sufficient reasons for its not
-being made more use of; but it makes an almost ideal material for
-model construction. The best part to use (split out from the
-centrepiece) is the strip of tough wood immediately below the hard
-glazed surface. For struts, spars, and ribs it can be used in this
-manner, and for the long strut supporting the rubber motor an entire
-tube piece should be used of the requisite strength required; for an
-ordinary rubber motor (one yard long), 30 to 50 strands, this should
-be a piece 3/8 in. in diameter, and weight about 5/8 oz. per ft.
-_Bamboo may be bent_ by either the "dry" heat from a spirit lamp or
-stove, or it may be steamed, the latter for preference, as there is
-no danger of "scorching" the fibres on the inside of the bend. When
-bent (as in the case of other woods) it should be bound on to a
-"former" having a somewhat greater curvature than the curve required,
-because when cool and dry it will be sure to "go back" slightly. It
-must be left on the former till quite dry. When bending the "tube"
-entire, and not split portions thereof, it should be immersed in very
-hot, or even boiling, water for some time before steaming. The really
-successful bending of the tube _en bloc_ requires considerable
-patience and care.
-
-Bamboo is inclined to split at the ends, and some care is required in
-making "joints." The ribs can be attached to the spars by lashing them
-to thin T strips of light metal, such as aluminium. Thin thread, or
-silk, is preferable to very thin wire for lashing purpose, as the
-latter "gives" too much, and cuts into the fibres of the wood as well.
-
-Sec. 3. =Ash=, =Spruce=, =Whitewood= are woods that are also much used by
-model makers. Many prefer the last named owing to its uniform freedom
-from knots and ease with which it can be worked. It is stated 15 per
-cent. additional strength can be imparted by using hot size and
-allowing it to soak into the wood at an increase only of 3.7 per cent.
-of weight. It is less than half the weight of bamboo, but has a
-transverse rupture of only 7,900 lb. per sq. in. compared to 22,500 in
-the case of bamboo tubing (thickness one-eighth diameter) and a
-resilience per lb. weight of slightly more than one half. Some model
-makers advocate the use of =poplar= owing to its extreme lightness
-(about the same as whitewood), but its strength is less in the ratio
-of about 4:3; its resilience is very slightly more. It must be
-remembered that wood of the same kind can differ much as to its
-strength, etc., owing to what part of the tree it may have been cut
-from, the manner in which it may have been seasoned, etc. For model
-aeroplanes all wood used should have been at least a year in
-seasoning, and should be so treated when in the structure that it
-cannot absorb moisture.
-
-If we take the resilience of ash as 1, then (according to Haswell)
-relative resilience of beech is 0.86, and spruce 0.64.
-
-The strongest of woods has a weight when well seasoned of about 40 lb.
-per cub. ft. and a tenacity of about 10,000 lb. per sq. in.
-
-[Illustration: FIG. 47A.--"AEROPLANE ALMA."
-
-A very effective French Toy Monoplane.]
-
-Sec. 4. =Steel.=--Ash has a transverse rupture of 14,300 lb. per sq. in.,
-steel tubing (thickness = 1/30 its diameter) 100,000 lb. per sq. in.
-Ash weighs per cub. ft. 47 lb., steel 490. Steel being more than ten
-times as heavy as ash--but a transverse rupture stress seven times as
-high.
-
-Bamboo in tube form, thickness one-third of diameter, has a
-transverse rupture of 22,500 lb. per sq. in., and a weight of 55 lb.
-per cub. ft.
-
-Steel then is nine times as heavy as bamboo--and has a transverse
-rupture stress 4.4 times as great. In comparing these three substances
-it must be carefully borne in mind that lightness and strength are not
-the only things that have to be provided for in model aeroplane
-building; there is the question of _resistance_--we must offer as
-small a cross-section to moving through the air as possible.
-
-Now while ash or bamboo and certain other timbers may carry a higher
-load per unit of weight than steel, they will present about three to
-three and a half times the cross-section, and this produces a serious
-obstacle, while otherwise meeting certain requirements that are most
-desirable. Steel tubing of sufficiently small bore is not, so far as
-the writer knows, yet on the market in England. In France very thin
-steel tubes are made of round, oval, hexagon, etc., shape, and of
-accurate thickness throughout, the price being about 18s. a lb.
-
-Although suitable steel tubing is not yet procurable under ordinary
-circumstances, umbrella steel is.
-
-Sec. 5. =Umbrella Section Steel= is a section 5/32 in. by 1/8 in. deep, 6
-ft. long weighing 2.1 oz., and a section 3/32 in. across the base by
-1/8 in. deep, 6 ft. long weighing 1.95 oz.
-
-It is often stated that umbrella ribs are too heavy--but this entirely
-depends on the length you make use of, in lengths of 25 in. for small
-aerofoils made from such lengths it is so; but in lengths of 48 in.
-(two such lengths joined together) the writer has used it with great
-success; often making use of it now in his larger models; the
-particular size used by him weighs 131/2 grammes, to a length of 25
-in. He has never had one of these aerofoils break or become
-kinked--thin piano wire is used to stay them and also for spars when
-employed--the front and ends of the aerofoil are of umbrella steel,
-the trailing edge of steel wire, comparatively thin, kept taut by
-steel wire stays.
-
-Sec. 6. =Steel Wire.=--Tensile strength about 300,000 lb. per sq. in. For
-the aerofoil framework of small models and for all purposes of
-staying, or where a very strong and light tension is required, this
-substance is invaluable. Also for framework of light fabric covered
-propellers as well as for skids and shock absorber--also for hooks to
-hold the rubber motor strands, etc. No model is complete without it in
-some form or another.
-
-Sec. 7. =Silk.=--This again is a _sine qua non_. Silk is the strongest of
-all organic substances for certain parts of aeroplane construction. It
-has, in its best form, a specific gravity of 1.3, and is three times
-as strong as linen, and twice as strong in the thread as hemp. Its
-finest fibres have a section of from 0.0010 to 0.0015 in diameter. It
-will sustain about 35,000 lb. per sq. in. of its cross section; and
-its suspended fibre should carry about 150,000 ft. of its own
-material. This is six times the same figure for aluminium, and equals
-about 75,000 lb. steel tenacity, and 50 more than is obtained with
-steel in the form of watch springs or wire. For aerofoil surface no
-substance can compare with it. But it must be used in the form of an
-"oiled" or specially treated silk. Several such are on the market.
-Hart's "fabric" and "radium" silk are perhaps the best known. Silk
-weighs 62 lb. per cub. ft., steel has, we have seen, 490 lb., thus
-paying due regard to this and to its very high tensile strength it is
-superior to even steel wire stays.
-
-Sec. 8. =Aluminium and Magnalium.=--Two substances about which a great
-deal has been heard in connection with model aeroplaning; but the
-writer does not recommend their use save in the case of fittings for
-scale models, not actual flyers, unless especially light ones meant
-to fly with the wind. Neither can compare with steel. Steel, it is
-true, is three times as heavy as aluminium, but it has four or five
-times its strength; and whereas aluminium and magnalium may with
-safety be given a permissible breaking strength of 60 per cent. and 80
-per cent. respectively, steel can easily be given 80 per cent. Being
-also less in section, resistance to air travel is again less as in the
-case of wood. In fact, steel scores all round. Weight of magnalium :
-weight of aluminium :: 8:9.
-
-Sec. 9. =Alloys.=--During recent years scores, hundreds, possibly
-thousands of different alloys have been tried and experimented on, but
-steel still easily holds its own. It is no use a substance being
-lighter than another volume for volume, it must be _lighter and
-stronger weight for weight_, to be superior for aeronautical purpose,
-and if the difference be but slight, question of _bulk_ may decide it
-as offering _less resistance_.
-
-Sec. 10. =Sheet Ebonite.=--This substance is sometimes useful for
-experiments with small propellers, for it can be bent and moulded in
-hot water, and when cold sets and keeps its shape. _Vulcanized fibre_
-can be used for same purpose. _Sheet celluloid_ can be used in the
-same way, but in time it becomes brittle and shrinks. _Mica_ should be
-avoided. _Jointless cane_ in various sizes is a very useful
-material--the main aerofoil can be built of it, and it is useful for
-skids, and might be made more use of than it is.[38] _Three ply wood_,
-from 1/50 in. in thickness, is now on the market. Four or five ply
-wood can also be obtained. To those desiring to build models having
-wooden aerofoils such woods offer the advantage of great strength and
-extreme lightness.
-
-Referring to Table V. (Timber) at the end of the book, apparently the
-most suitable wood is Lombardy poplar; but its light weight means
-increased bulk, i.e. additional air resistance. Honduras mahogany is
-really a better all-round wood, and beech is not far behind.
-
-Resilience is an important factor. Ash heads the list; but mahogany's
-factor is also good, and in other respects superior.
-
-Lombardy poplar ought to be a very good wood for propellers, owing to
-its lightness and the ease with which it can be worked.
-
-_Hollow reeds_, and even _porcupine quills_, have been pressed into
-the service of the model maker, and owing to their great strength and
-extreme lightness, more especially the latter, are not without their
-uses.
-
-FOOTNOTES:
-
-[38] The chief advantage of cane--its want of stiffness, or facility
-in bending--is for some parts of the machine its chief disadvantage,
-where stiffness with resilience is most required.
-
-
-
-
-CHAPTER VIII.
-
-HINTS ON THE BUILDING OF MODEL AEROPLANES.
-
-
-Sec. 1. The chief difficulty in the designing and building of model
-aeroplanes is to successfully combat the conflicting interests
-contained therein. Weight gives stability, but requires extra
-supporting surface or a higher speed, i.e. more power, i.e. more
-weight. Inefficiency in one part has a terrible manner of repeating
-itself; for instance, suppose the aerofoil surface inefficient--badly
-designed--this means more resistance; more resistance means more
-power, i.e. weight, i.e. more surface, and so on _ad infinitum_.
-
-It is because of circumstances like the above that it is so difficult
-to _design_ really good and efficient flying models; the actual
-building of them is not so difficult, but few tools are required, none
-that are expensive or difficult to use.
-
-In the making of any particular model there are special points that
-require special attention; but there are certain general rules and
-features which if not adhered to and carefully carried out, or as
-carefully avoided, will cause endless trouble and failure.
-
-Sec. 2. In constructing a model aeroplane, or, indeed, any piece of
-aerial apparatus, it is very important not to interrupt the continuity
-of any rib, tube, spar, etc., by drilling holes or making too thinned
-down holding places; if such be done, additional strength by binding
-(with thread, not wire), or by slipping a small piece of slightly
-larger tube over the other, must be imparted to the apparatus.
-
-Sec. 3. Begin by making a simple monoplane, and afterwards as you gain
-skill and experience proceed to construct more elaborate and
-scientific models.
-
-Sec. 4. Learn to solder--if you do not know how to--it is absolutely
-essential.
-
-Sec. 5. Do not construct models (intended for actual flight) with a
-tractor screw-main plane in front and tail (behind). Avoid them as you
-would the plague. Allusion has already been made in the Introduction
-to the difficulty of getting the centre of gravity sufficiently
-forward in the case of Bleriot models; again with the main aerofoil in
-front, it is this aerofoil and not the balancing elevator, or tail,
-that _first_ encounters the upsetting gust, and the effect of such a
-gust acting first on the larger surface is often more than the
-balancer can rectify in time to avert disaster. The proper place for
-the propeller is behind, in the wake of the machine. If the screw be
-in front the backwash from it strikes the machine and has a decidedly
-retarding action. It is often contended that it drives the air at an
-increased velocity under (and over) the main aerofoil, and so gives a
-greater lifting effect. But for proper lifting effect which it can
-turn without effort into air columns of proper stream line form what
-the aerofoil requires is undisturbed air--not propeller backwash.
-
-The rear of the model is the proper place for the propeller, in the
-centre of greatest air disturbance; in such a position it will recover
-a portion of the energy lost in imparting a forward movement to the
-air, caused by the resistance, the model generally running in such
-air--the slip of the screw is reduced to a corresponding degree--may
-even vanish altogether, and what is known as negative slip occur.
-
-Sec. 6. Wooden or metal aerofoils are more efficient than fabric covered
-ones. But they are only satisfactory in the smaller sizes, owing, for
-one thing, to the smash with which they come to the ground. This being
-due to the high speed necessary to sustain their weight. For
-larger-sized models fabric covered aerofoils should be used.
-
-Sec. 7. As to the shape of such, only three need be considered--the (_a_)
-rectangular, (_b_) the elongated ellipse, (_c_) the chamfered rear
-edge.
-
-[Illustration: FIG. 48.--(_a_), (_b_), (_c_).]
-
-Sec. 8. The stretching of the fabric on the aerofoil framework requires
-considerable care, especially when using silk. It is quite possible,
-even in models of 3 ft. to 4 ft. spread, to do without "ribs," and
-still obtain a fairly correct aerocurve, if the material be stretched
-on in a certain way. It consists in getting a correct longitudinal and
-transverse tension. We will illustrate it by a simple case. Take a
-piece of thickish steel pianoforte wire, say, 18 in. long, bend it
-round into a circle, allowing 1/2 in. to 1 in. to overlap, tin and
-solder, bind this with soft very thin iron wire, and again solder
-(always use as little solder as possible). Now stitch on to this a
-piece of nainsook or silk, deforming the circle as you do so until it
-has the accompanying elliptical shape. The result is one of double
-curvature; the transverse curve (dihedral angle) can be regulated by
-cross threads or wires going from A to B and C to D.
-
-[Illustration: FIG. 49.]
-
-[Illustration: FIG. 49A.--MR. T.W.K. CLARKE'S 1 OZ. MODEL.]
-
-The longitudinal curve on the camber can be regulated by the original
-tension given to it, and by the manner of its fixing to the main
-framework. Suitable wire projections or loops should be bound to it by
-wire, and these fastened to the main framework by binding with _thin_
-rubber cord, a very useful method of fastening, since it acts as an
-excellent shock absorber, and "gives" when required, and yet
-possesses quite sufficient practical rigidity.
-
-Sec. 9. Flexible joints are an advantage in a biplane; these can be made
-by fixing wire hooks and eyes to the ends of the "struts," and holding
-them in position by binding with silk or thread. Rigidity is obtained
-by use of steel wire stays or thin silk cord.
-
-[Illustration: FIG. 49B.--MR. T.W.K. CLARKE'S 1 OZ. MODEL.
-
-Showing the position of C. of G., or point of support.]
-
-Sec. 10. Owing to the extra weight and difficulties of construction on so
-small a scale it is not desirable to use "double surface" aerofoils
-except on large size power-driven models.
-
-Sec. 11. It is a good plan not to have the rod or tube carrying the
-rubber motor connected with the outrigger carrying the elevator,
-because the torque of the rubber tends to twist the carrying
-framework, and interferes with the proper and correct action of the
-elevator. If it be so connected the rod must be stayed with piano
-wire, both longitudinally (to overcome the pull which we know is very
-great), and also laterally, to overcome the torque.
-
-[Illustration: FIG. 49C.--A LARGE MODEL AEROPLANE.
-
-Shown without rubber or propellers. Designed and constructed by the
-writer. As a test it was fitted with two 14 in. propellers revolving
-in the _same_ direction, and made some excellent flights under these
-conditions, rolling slightly across the wind, but otherwise keeping
-quite steady. Total weight, 11/2 lb.; length, 6 ft.; span of main
-aerofoil, 5 ft. Constructed of bamboo, cane, and steel wire. Front
-skids steel wire. Back skids cane. Aerofoil covering nainsook.]
-
-
-Sec. 12. Some builders place the rubber motor above the rod, or bow frame
-carrying the aerofoils, etc., the idea being that the pull of the
-rubber distorts the frame in such a manner as to "lift" the elevator,
-and so cause the machine to rise rapidly in the air. This it does; but
-the model naturally drops badly at the finish and spoils the effect.
-It is not a principle that should be copied.
-
-[Illustration: FIG. 49D.--A VERY LIGHT WEIGHT MODEL.
-
-Constructed by the author. Provided with twin propellers of a modified
-Fleming-Williams type. This machine flew well when provided with an
-abnormal amount of rubber, owing to the poor dynamic thrust given by
-the propellers.]
-
-Sec. 13. In the Clarke models with the small front plane, the centre of
-pressure is slightly in front of the main plane.
-
-The balancing point of most models is generally slightly in front, or
-just within the front edge of the main aerofoil. The best plan is to
-adjust the rod carrying the rubber motor and propeller until the best
-balance is obtained, then hang up the machine to ascertain the centre
-of gravity, and you will have (approximately) the centre of pressure.
-
-[Illustration: FIG. 49E.--USEFUL FITTINGS FOR MODELS.
-
-1. Rubber tyred wheels. 2. Ball-bearing steel axle shafts. 3. Brass wire
-strainers with steel screws; breaking strain 200 lb. 4. Magnalium
-tubing. 5. Steel eyebolt. 6. Aluminium "T" joint. 7. Aluminium "L"
-piece. 8. Brass brazed fittings. 9. Ball-bearing thrust. 10. Flat
-aluminium "L" piece. (_The above illustrations taken (by permission)
-from Messrs. Gamage's catalogue on Model Aviation._)]
-
-Sec. 14. The elevator (or tail) should be of the non-lifting type--in
-other words, the entire weight should be carried by the main aerofoil
-or aerofoils; the elevator being used simply as a balancer.[39] If the
-machine be so constructed that part of the weight be carried by the
-elevator, then either it must be large (in proportion) or set up at a
-large angle to carry it. Both mean considerably more resistance--which
-is to be avoided. In practice this means the propeller being some
-little distance in rear of the main supporting surface.
-
-[Illustration: FIG. 49F.--USEFUL FITTINGS FOR MODELS.
-
-11. Aluminium ball thrust and racket. 12. Ball-bearing propeller,
-thrust, and stay.
-
-(_The above illustrations taken (by permission) from Messrs. Gamage's
-catalogue on Model Aviation._)]
-
-Sec. 15. In actual flying models "skids" should be used and not "wheels";
-the latter to be of any real use must be of large diameter, and the
-weight is prohibitive. Skids can be constructed of cane, imitation
-whalebone, steel watch or clock-spring, steel pianoforte wire. Steel
-mainsprings are better than imitation whalebone, but steel pianoforte
-wire best of all. For larger sized models bamboo is also suitable, as
-also ash or strong cane.
-
-Sec. 16. Apart from or in conjunction with skids we have what are termed
-"shock absorbers" to lessen the shock on landing--the same substances
-can be used--steel wire in the form of a loop is very effectual;
-whalebone and steel springs have a knack of snapping. These shock
-absorbers should be so attached as to "give all ways" for a part side
-and part front landing as well as a direct front landing. For this
-purpose they should be lashed to the main frame by thin indiarubber
-cord.
-
-Sec. 17. In the case of a biplane model the "gap" must not be less than
-the "chord"--preferably greater.
-
-In a double monoplane (of the Langley type) there is considerable
-"interference," i.e. the rear plane is moving in air already acted on
-by the front one, and therefore moving in a downward direction. This
-means decreased efficiency. It can be overcome, more or less, by
-varying the dihedral angle at which the two planes are set; but cannot
-be got rid of altogether, or by placing them far apart. In biplanes
-not possessing a dihedral angle--the propeller can be placed
-_slightly_ to one side--in order to neutralise the torque of the
-propeller--the best portion should be found by experiment--unless the
-pitch be very large; with a well designed propeller this is not by any
-means essential. If the propeller revolve clockwise, place it towards
-the right hand of the machine, and vice versa.
-
-Sec. 18. In designing a model to fly the longest possible distance the
-monoplane type should be chosen, and when desiring to build one that
-shall remain the longest time in the air the biplane or triplane type
-should be adopted.[40] For the longest possible flight twin propellers
-revolving in opposite directions[41] are essential. To take a concrete
-case--one of the writer's models weighed complete with a single
-propeller 81/2 oz. It was then altered and fitted with two propellers
-(same diameter and weight); this complete with double rubber weighed
-101/4 oz. The advantage double the power. Weight increased only 20
-per cent., resistance about 10 per cent., total 30 per cent. Gain 70
-per cent. Or if the method of gearing advocated (see Geared Motors) be
-adopted then we shall have four bunches of rubber instead of two, and
-can thereby obtain so many more turns.[42] The length of the strands
-should be such as to render possible at least a thousand turns.
-
-The propellers should be of large diameter and pitch (not less than
-35 deg. at the tips), of curved shape, as advocated in Sec. 22 ch. v.; the
-aerofoil surface of as high an aspect ratio as possible, and but
-slight camber if any; this is a very difficult question, the question
-of camber, and the writer feels bound to admit he has obtained as long
-flights with surfaces practically flat, but which do, of course,
-camber slightly in a suitable wind, as with stiffer cambered surfaces.
-
-Wind cambered surfaces are, however, totally unsuitable in gusty
-weather, when the wind has frequently a downward trend, which has the
-effect of cambering the surface the wrong way about, and placing the
-machine flat on the ground. Oiled or specially prepared silk of the
-lightest kind should be used for surfacing the aerofoils. Some form of
-keel, or fin, is essential to assist in keeping the machine in a
-straight course, combined with a rudder and universally jointed
-elevator.
-
-The manner of winding up the propellers has already been referred to
-(_see_ chap. iii., Sec. 9). A winder is essential.
-
-Another form of aerofoil is one of wood (as in Clarke's flyers) or
-metal, such a machine relying more on the swiftness of its flight than
-on its duration. In this the gearing would possibly not be so
-advantageous--but experiment alone could decide.
-
-The weight of the machine would require to be an absolute minimum, and
-everything not absolutely essential omitted.
-
-It is quite possible to build a twin-screw model on one central stick
-alone; but the isosceles triangular form of framework, with two
-propellers at the base corners, and the rubber motors running along
-the two sides and terminating at the vertex, is preferred by most
-model makers. It entails, of course, extra weight. A light form of
-skid, made of steel pianoforte wire, should be used. As to the weight
-and size of the model, the now famous "one-ouncers" have made some
-long flights of over 300 yards[43]; but the machine claiming the
-record, half a mile,[44] weighs about 10 oz. And apart from this
-latter consideration altogether the writer is inclined to think that
-from 5 oz. to 10 oz. is likely to prove the most suitable. It is not
-too large to experiment with without difficulty, nor is it so small as
-to require the skill of a jeweller almost to build the necessary
-mechanism. The propeller speed has already been discussed (_see_ ch.
-v., Sec. 15). The model will, of course, be flown with the wind. The
-_total_ length of the model should be at least twice the span of the
-main aerofoil.
-
-FOOTNOTES:
-
-[39] This is a good plan--not a rule. Good flying models can, of
-course, be made in which this does not hold.
-
-[40] This is in theory only: in practice the monoplane holds both
-records.
-
-[41] The best position for the propellers appears to be one in front
-and one behind, when extreme lightness is the chief thing desired.
-
-[42] Because the number of strands of rubber in each bunch will be
-much less.
-
-[43] Mr. Burge Webb claims a record of 500 yards for one of his.
-
-[44] Flying, of course, with the wind. _Note._--In the "Model
-Engineer" of July 7, 1910, will be found an interesting account (with
-illustrations) of Mr. W.G. Aston's 1 oz. model, which has remained in
-the air for over a minute.
-
-
-
-
-CHAPTER IX.
-
-THE STEERING OF THE MODEL.
-
-
-Sec. 1. Of all the various sections of model aeroplaning that which is
-the least satisfactory is the above.
-
-The torque of the propeller naturally exerts a twisting or tilting
-effect upon the model as a whole, the effect of which is to cause it
-to fly in (roughly speaking) a circular course, the direction
-depending on whether the pitch of the screw be a right or left handed
-one. There are various devices by which the torque may be
-(approximately) got rid of.
-
-Sec. 2. In the case of a monoplane, by not placing the rod carrying the
-rubber motor in the exact centre of the main aerofoil, but slightly to
-one side, the exact position to be determined by experiment.
-
-In a biplane the same result is obtained by keeping the rod in the
-centre, but placing the bracket carrying the bearing in which the
-propeller shaft runs at right angles horizontally to the rod to obtain
-the same effect.
-
-Sec. 3. The most obvious solution of the problem is to use _two_ equal
-propellers (as in the Wright biplane) of equal and opposite pitch,
-driven by two rubber motors of equal strength.
-
-Theoretically this idea is perfect. In practice it is not so. It is
-quite possible, of course, to use two rubber motors of an equal number
-of strands (equality should be first tested by _weighing_). It should
-be possible to obtain two propellers of equal and opposite pitch,
-etc., and it is also possible to give the rubber motors the same
-number of turns. In practice one is always wound up before the other.
-This is the first mistake. They should be wound up _at the same time_,
-using a double winder made for the purpose.
-
-The fact that this is _not_ done is quite sufficient to give an
-unequal torsion. The friction in both cases must also be exactly
-equal. Both propellers must be released at exactly the same instant.
-
-Supposing _all_ these conditions fulfilled (in practice they never
-are), supposing also the propellers connected by gearing (prohibitive
-on account of the weight), and the air quite calm (which it never is),
-then the machine should and undoubtedly would _fly straight_.
-
-For steering purposes by winding up one propeller _many more times_
-than the other, the aeroplane can generally speaking be steered to the
-right or left; but from what I have both seen and tried twin-screw
-model aeroplanes are _not_ the success they are often made out to be,
-and they are much more troublesome to deal with, in spite of what some
-say to the contrary.
-
-The solution of the problem of steering by the use of two propellers
-is only partially satisfactory and reliable, in fact, it is no
-solution at all.[45] The torque of the propeller and consequent
-tilting of the aeroplane is not the only cause at work diverting the
-machine from its course.
-
-Sec. 4. As it progresses through the air it is constantly meeting air
-currents of varying velocity and direction, all tending to make the
-model deviate more or less from its course; the best way, in fact, the
-only way, to successfully overcome such is by means of _speed_, by
-giving the aeroplane a high velocity, not of ten or twelve to fifteen
-miles an hour, as is usual in built up fabric-covered aerofoils, but a
-velocity of twenty to thirty miles an hour, attainable only in models
-(petrol or steam driven) or by means of wooden or metal aerofoils.
-
-Sec. 5. Amongst devices used for horizontal steering are vertical "FINS."
-These should be placed in the rear above the centre of gravity. They
-should not be large, and can be made of fabric tightly stretched over
-a wire frame, or of a piece of sheet magnalium or aluminium, turning
-on a pivot at the front edge, adjustment being made by simply twisting
-the fin round to the desired angle. As to the size, think of rudder
-and the size of a boat, but allow for the difference of medium. The
-frame carrying the pivot and fin should be made to slide along the rod
-or backbone of the model in order to find the most efficient position.
-
-Sec. 6. Steering may also be attempted by means of little balancing tips,
-or ailerons, fixed to or near the main aerofoil, and pivoted (either
-centrally or otherwise) in such a manner that they can be rotated one
-in one direction (tilted) and the other in the other (dipped), so as
-to raise one side and depress the other.
-
-Sec. 7. The model can also be steered by giving it a cant to one side by
-weighting the tip of the aerofoil on that side on which it is desired
-it should turn, but this method is both clumsy and "weighty."
-
-Sec. 8. Another way is by means of the elevator; and this method, since
-it entails no additional surfaces entailing extra resistance and
-weight, is perhaps the most satisfactory of all.
-
-It is necessary that the elevator be mounted on some kind of universal
-joint, in order that it may not only be "tipped" or "dipped," but also
-canted sideways for horizontal steering.
-
-Sec. 9. A vertical fin in the rear, or something in the nature of a
-"keel," i.e. a vertical fin running down the backbone of the machine,
-greatly assists this movement.
-
-If the model be of the tractor screw and tail (Bleriot) type, then the
-above remarks _re_ elevator apply _mutatis mutandis_ to the tail.
-
-Sec. 10. It is of the most vital importance that the propeller torque
-should be, as far as possible, correctly balanced. This can be tested
-by balancing the model transversely on a knife edge, winding up the
-propeller, and allowing it to run down, and adjusting matters until
-the torque and compensatory apparatus balance. As the torque varies
-the mean should be used.
-
-In the case of twin propellers, suspend the model by its centre of
-gravity, wind up the propellers, and when running down if the model is
-drawn forward without rotation the thrust is equal; if not adjustment
-must be made till it does. The easiest way to do this _may_ be by
-placing one propeller, the one giving the greater thrust, slightly
-nearer the centre.
-
-In the case of two propellers rotating in opposite directions (by
-suitable gearing) on the common centre of two axes, one of the axes
-being, of course, hollow, and turning on the other--the rear propeller
-working in air already driven back by the other will require a coarser
-pitch or larger diameter to be equally efficient.
-
-FOOTNOTE:
-
-[45] These remarks apply to rubber driven motors. In the case of
-two-power driven propellers in which the power was automatically
-adjusted, say, by a gyroscope as in the case of a torpedo--and the
-_speed_ of each propeller varied accordingly--the machine could, of
-course, be easily steered by such means; but the model to carry such
-power and appliances would certainly weigh from 40 lb. to 60 lb.
-
-
-
-
-CHAPTER X.
-
-THE LAUNCHING OF THE MODEL.
-
-
-Sec. 1. Generally speaking, the model should be launched into the air
-_against the wind_.
-
-Sec. 2. It should (theoretically) be launched into the air with a
-velocity equal to that with which it flies. If it launch with a
-velocity in excess of that it becomes at once unstable and has to
-"settle down" before assuming its normal line of flight. If the
-velocity be insufficient, it may be unable to "pick up" its requisite
-velocity in time to prevent its falling to the ground. Models with
-wooden aerofoils and a high aspect ratio designed for swift flying,
-such as the well-known Clarke flyers, require to be practically
-"hurled" into the air.
-
-Other fabric-covered models capable of sustentation at a velocity of 8
-to 10 miles an hour, may just be "released."
-
-Sec. 3. Light "featherweight" models designed for long flights when
-travelling with the wind should be launched with it. They will not
-advance into it--if there be anything of a breeze--but, if well
-designed, just "hover," finally sinking to earth on an even keel. Many
-ingenious pieces of apparatus have been designed to mechanically
-launch the model into the air. Fig. 50 is an illustration of a very
-simple but effective one.
-
-Sec. 4. For large size power-driven models, unless provided with a
-chassis and wheels to enable them to run along and rise from the
-ground under their own power, the launching is a problem of
-considerable difficulty.
-
-Sec. 5. In the case of rubber-driven models desired to run along and rise
-from the ground under their own power, this rising must be
-accomplished quickly and in a short space. A model requiring a 50 ft.
-run is useless, as the motor would be practically run out by that
-time. Ten or twelve feet is the limit; now, in order to rise quickly
-the machine must be light and carry considerable surface, or, in other
-words, its velocity of sustentation must be a low one.
-
-[Illustration: FIG. 50.--MR. POYNTER'S LAUNCHING APPARATUS.
-
-(_Reproduced by permission from the "Model Engineer."_)]
-
-Sec. 6. It will not do to tip up the elevator to a large angle to make it
-rise quickly, because when once off the ground the angle of the
-elevator is wrong for actual flight and the model will probably turn a
-somersault and land on its back. I have often seen this happen. If the
-elevator be set at an increased angle to get it to rise quickly, then
-what is required is a little mechanical device which sets the elevator
-at its proper flight angle when it leaves the ground. Such a device
-does not present any great mechanical difficulties; and I leave it to
-the mechanical ingenuity of my readers to devise a simple little
-device which shall maintain the elevator at a comparatively large
-angle while the model is on the ground, but allowing of this angle
-being reduced when free flight is commenced.
-
-Sec. 7. The propeller most suitable to "get the machine off the ground"
-is one giving considerable statical thrust. A small propeller of fine
-pitch quickly starts a machine, but is not, of course, so efficient
-when the model is in actual flight. A rubber motor is not at all well
-adapted for the purpose just discussed.
-
-Sec. 8. Professor Kress uses a polished plank (down which the models slip
-on cane skids) to launch his models.
-
-Sec. 9. When launching a twin-screw model the model should be held by
-each propeller, or to speak more correctly, the two brackets holding
-the bearings in which the propeller shafts run should be held one in
-each hand in such a way, of course, as to prevent the propellers from
-revolving. Hold the machine vertically downwards, or, if too large for
-this, allow the nose to rest slightly on the ground; raise (or swing)
-the machine up into the air until a little more than horizontal
-position is attained, and boldly push the machine into the air (moving
-forward if necessary) and release both brackets and screws
-simultaneously.[46]
-
-Sec. 10. In launching a model some prefer to allow the propellers to
-revolve for a few moments (a second, say) _before_ actually launching,
-contending that this gives a steadier initial flight. This is
-undoubtedly the case, see note on page 111.
-
-Sec. 11. In any case, unless trying for a height prize, do not point the
-nose of the machine right up into the air with the idea that you will
-thereby obtain a better flight.
-
-Launch it horizontally, or at a very small angle of inclination. When
-requiring a model to run along a field or a lawn and rise therefrom
-this is much facilitated by using a little strip of smooth oilcloth on
-which it can run. Remember that swift flying wooden and metal models
-require a high initial velocity, particularly if of large size and
-weight. If thrown steadily and at the proper angle they can scarcely
-be overthrown.
-
-FOOTNOTE:
-
-[46] Another and better way--supposing the model constructed with a
-central rod, or some suitable holdfast (this should be situated at the
-centre of gravity of the machine) by which it can be held in one
-hand--is to hold the machine with both hands above the head, the right
-hand grasping it ready to launch it, and the left holding the two
-propellers. Release the propellers and allow them a brief interval
-(about half a second) to start. Then launch boldly into the air. The
-writer has easily launched 11/2 lb. models by this means, even in a
-high wind. Never launch a model by one hand only.
-
-
-
-
-CHAPTER XI.
-
-HELICOPTER MODELS.
-
-
-Sec. 1. There is no difficulty whatever about making successful model
-helicopters, whatever there may be about full-sized machines.
-
-Sec. 2. The earliest flying models were helicopters. As early as 1796 Sir
-George Cayley constructed a perfectly successful helicopter model (see
-ch. iii.); it should be noticed the screws were superimposed and
-rotated in opposite directions.
-
-Sec. 3. In 1842 a Mr. Phillips constructed a successful power-driven
-model helicopter. The model was made entirely of metal, and when
-complete and charged weighed 2 lb. It consisted of a boiler or steam
-generator and four fans supported between eight arms. The fans had an
-inclination to the horizon of 20 deg., and through the arms the steam
-rushed on the principle of Hero's engines (Barker's Mill Principle
-probably). By the escape of steam from the arms the fans were caused
-to revolve with immense energy, so much so that the model rose to an
-immense altitude and flew across two fields before it alighted. The
-motive power employed was obtained from the combustion of charcoal,
-nitre and gypsum, as used in the original fire annihilator; the
-products of combustion mixing with water in the boiler and forming
-gas-charged steam, which was delivered at high pressure from the
-extremities of the eight arms.[47] This model and its flight (fully
-authenticated) is full of interest and should not be lost sight of, as
-in all probability being the first model actuated by steam which
-actually flew.
-
-The helicopter is but a particular phase of the aeroplane.
-
-Sec. 4. The simplest form of helicopter is that in which the torque of
-the propeller is resisted by a vertical loose fabric plane, so
-designed as itself to form a propeller, rotating in the opposite
-direction. These little toys can be bought at any good toy shop from
-about 6_d._ to 1_s._ Supposing we desire to construct a helicopter of
-a more ambitious and scientific character, possessing a vertically
-rotating propeller or propellers for horizontal propulsion, as well as
-horizontally rotating propellers for lifting purposes.
-
-[Illustration: FIG. 51.--INCORRECT WAY OF ARRANGING SCREWS.]
-
-Sec. 5. There is one essential point that must be carefully attended to,
-and that is, _that the horizontal propulsive thrust must be in the
-same plane as the vertical lift_, or the only effect will be to cause
-our model to turn somersaults. I speak from experience.
-
-When the horizontally revolving propellers are driven in a horizontal
-direction their "lifting" powers will be materially increased, as they
-will (like an ordinary aeroplane) be advancing on to fresh undisturbed
-air.
-
-Sec. 6. I have not for ordinary purposes advocated very light weight wire
-framework fabric-covered screws, but in a case like this where the
-thrust from the propeller has to be more than the total weight of the
-machine, these might possibly be used with advantage.
-
-Sec. 7. Instead of using two long vertical rods as well as one long
-horizontal one for the rubber strands, we might dispense with the two
-vertical ones altogether and use light gearing to turn the torque
-action through a right angle for the lifting screws, and use three
-separate horizontal rubber strands for the three propellers on a
-suitable light horizontal framework. Such should result in a
-considerable saving of weight.
-
-[Illustration: FIG. 52.--CORRECT MANNER. A, B, C = Screws.]
-
-Sec. 8. The model would require something in the nature of a vertical fin
-or keel to give the sense of direction. Four propellers, two for
-"lift" and two for "drift," would undoubtedly be a better
-arrangement.
-
-FOOTNOTE:
-
-[47] Report on First Exhibition of Aeronautical Society of Great
-Britain, held at Crystal Palace, June 1868.
-
-
-
-
-CHAPTER XII.
-
-EXPERIMENTAL RECORDS.
-
-
-A model flying machine being a scientific invention and not a toy,
-every devotee to the science should make it his or her business to
-keep, as far as they are able, accurate and scientific records. For by
-such means as this, and the making known of the same, can a _science_
-of model aeroplaning be finally evolved. The following experimental
-entry forms, left purposely blank to be filled in by the reader, are
-intended as suggestions only, and can, of course, be varied at the
-reader's discretion. When you _have_ obtained carefully established
-data, do not keep them to yourself, send them along to one of the
-aeronautical journals. Do not think them valueless; if carefully
-arranged they cannot be that, and may be very valuable.
-
-
-EXPERIMENTAL DATA.
-
-  FORM I.
-
-  Column Headings:
-
-  A:  Model
-  B:  Weight
-  C:  Area of Supporting Surface
-  D:  Aspect Ratio
-  E:  Average Length of Flight in Feet
-  F:  Maximum Flight
-  G:  Time of Flight, A. average
-  H:  M. maximum
-  I:  Kind and Direction of Wind
-  J:  Camber
-  K:  Angle of Inclination of Main Aerofoil to Line of Flight
-
-  -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
-    A  |  B  |  C  |  D  |  E  |  F  |  G  |  H  |  I  |  J  |  K
-  -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
-       |     |     |     |     |     |  A  |  M  |     |     |
-    1  |     |     |     |     |     |     |     |     |     |
-    2  |     |     |     |     |     |     |     |     |     |
-    3  |     |     |     |     |     |     |     |     |     |
-    4  |     |     |     |     |     |     |     |     |     |
-    5  |     |     |     |     |     |     |     |     |     |
-    6  |     |     |     |     |     |     |     |     |     |
-    7  |     |     |     |     |     |     |     |     |     |
-    8  |     |     |     |     |     |     |     |     |     |
-    9  |     |     |     |     |     |     |     |     |     |
-   10  |     |     |     |     |     |     |     |     |     |
-   11  |     |     |     |     |     |     |     |     |     |
-   12  |     |     |     |     |     |     |     |     |     |
-       |     |     |     |     |     |     |     |     |     |
-  -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
-
-  FORM I.--_continued_.
-
-  Column Headings:
-
-  A: Model
-  B: Weight of (Rubber) Motor
-  C: Kind of Rubber, Flat, Square or Round
-  D: Lenght in Inches and Number of Strands
-  E: Number of Turns
-  F: Condition at End of Flight
-  G: Number of Propellers (No.) and Diameter (Diam.)
-  H: Number of Blades
-  I: Disc Area (DiscA.) and Pitch (Pitch)
-  J: Percentage of Slip
-  K: Thrust
-  L: Torque in Inche-Ounces
-
-  ----+----+----+-----+----+----+-----+----+-----+----+----+----+
-    A |  B |  C |  D  |  E |  F |  G  |  H |  I  |  J |  K |  L |
-  ----+----+----+-----+----+----+-----+----+-----+----+----+----+
-      |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
-    1 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
-    2 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
-    3 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
-    4 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
-    5 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
-    6 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
-    7 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
-    8 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
-    9 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
-   10 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
-   11 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
-   12 |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
-      |    |    |  |  |    |    |  |  |    |  |  |    |    |    |
-  ----+----+----+-----+----+----+-----+----+-----+----+----+----+
-
-
-
-
-CHAPTER XIII.
-
-MODEL FLYING COMPETITIONS.
-
-
-Sec. 1. From time to time flying competitions are arranged for model
-aeroplanes. Sometimes these competitions are entirely open, but more
-generally they are arranged by local clubs with both closed and open
-events.
-
-No two programmes are probably exactly alike, but the following may be
-taken as fairly representative:--
-
-1. Longest flight measured in a straight line (sometimes both with and
-against the wind).[48]
-
-2. Stability (both longitudinal and transverse).
-
-3. Longest glide when launched from a given height without power, but
-with motor and propeller attached.
-
-4. Steering.
-
-5. Greatest height.
-
-6. The best all-round model, including, in addition to the above,
-excellence in building.
-
-Generally so many "points" or marks are given for each test, and the
-model whose aggregate of points makes the largest total wins the
-prize; or more than one prize may be offered--
-
-One for the longest flight.
-
-One for the swiftest flight over a measured distance.
-
-One for the greatest height.
-
-One for stability and steering.
-
-And one for the best all-round model.
-
-The models are divided into classes:--
-
-Sec. 2. _Aero Models Association's Classification, etc._
-
-    A.   Models of 1 sq. ft. surface and under.
-    B.     "       2 sq. ft.     "       "
-    C.     "       4 sq. ft.     "       "
-    D.     "       8 sq. ft.     "       "
-    E.     "       over 8 sq. ft.
-
-All surfaces, whether vertical, horizontal, or otherwise, to be
-calculated together for the above classification.
-
-All round efficiency--marks or points as percentages:--
-
-    Distance              40 per cent.
-    Stability             35    "
-    Directional control   15    "
-    Gliding angle         10    "[49]
-
-Two prizes:--
-
-One for length of flight.
-
-One for all-round efficiency (marked as above).
-
-Every competitor to be allowed three trials in each competition, the
-best only to count.
-
-All flights to be measured in a straight line from the starting to the
-landing point.
-
-Repairs may be made during the competition at the direction of the
-judges.[50]
-
-There are one or two other points where flights are _not_ made with
-and against the wind. The competitors are usually requested to start
-their models from within a given circle of (say) six feet diameter,
-and fly them _in any direction_ they please.
-
-"Gliding angle" means that the model is allowed to fall from a height
-(say) of 20 ft.
-
-[Illustration: FIG. 53.--MODEL DESIGNED AND CONSTRUCTED BY THE AUTHOR
-FOR "GREATEST HEIGHT."
-
-A very lightly built model with a very low aspect ratio, and screw
-giving a very powerful dynamic thrust, and carrying rather a large
-amount of rubber. Climbs in left-handed spirals.]
-
-"Directional control," that the model is launched in some specified
-direction, and must pass as near as possible over some indicated
-point.
-
-The models are practically always launched by hand.
-
-Sec. 3. Those who desire to win prizes at such competitions would do well
-to keep the following points well in mind.
-
-1. The distance is always measured in a straight line. It is
-absolutely essential that your model should be capable of flying
-(approximately) straight. To see, as I have done, model after model
-fly quite 150 to 200 yards and finish within 50 yards of the
-starting-point (credited flight 50 yards) is useless, and a severe
-strain on one's temper and patience.
-
-[Illustration: FIG. 54.--THE GAMAGE CHALLENGE CUP.
-
-Open Competition for longest flight. Crystal Palace, July 27. Won by
-Mr. E.W. Twining.]
-
-[Illustration: FIG. 55.--MEDAL WON BY THE AUTHOR IN THE SAME
-COMPETITION.]
-
-2. Always enter more than one model, there nearly always is an
-entrance fee; never mind the extra shilling or so. Go in to win.
-
-3. It is not necessary that these models should be replicas of one
-another. On some days a light fabric-covered model might stand the
-best chance; on another day, a swift flying wooden or metal aerofoil.
-
-Against the wind the latter have an immense advantage; also if the day
-be a "gusty" one.[51]
-
-4. Always make it a point of arriving early on the ground, so that you
-can make some trial flights beforehand. Every ground has its local
-peculiarities of air currents, etc.
-
-5. Always be ready in time, or you may be disqualified. If you are
-flying a twin-screw model use a special winder, so that both
-propellers are wound up at the same time, and take a competent friend
-with you as assistant.
-
-6. For all-round efficiency nothing but a good all-round model, which
-can be absolutely relied on to make a dozen (approximately) equivalent
-flights, is any good.
-
-7. In an open distance competition, unless you have a model which you
-can rely on to make a _minimum_ flight of 200 yards, do not enter
-unless you know for certain that none of the "crack" flyers will be
-present.
-
-8. Do not neglect the smallest detail likely to lead to success; be
-prepared with spare parts, extra rubber, one or two handy tools, wire,
-thread, etc. Before a lecture, that prince of experimentalists,
-Faraday, was always careful to see that the stoppers of all the
-bottles were loose, so that there should be no delay or mishap.
-
-9. If the rating of the model be by "weight" (1 oz., 2 oz., 4 oz.,
-etc.) and not area, use a model weighing from 10 oz. to a pound.
-
-10. If there is a greatest height prize, a helicopter model should win
-it.[52] (The writer has attained an altitude of between three and four
-hundred feet with such.) The altitude was arrived at by observation,
-not guesswork.
-
-11. It is most important that your model should be able to "land"
-without damage, and, as far as possible, on an even keel; do not omit
-some form of "skid" or "shock-absorber" with the idea of saving
-weight, more especially if your model be a biplane, or the number of
-flights may be restricted to the number "one."
-
-12. Since the best "gliding" angle and "flying" angle are not the
-same, being, say, 7 deg. in the former case and 1 deg.-3 deg., say, in the latter,
-an adjustable angle might in some cases be advantageous.
-
-13. Never turn up at a competition with a model only just finished and
-practically untested which you have flown only on the morning of the
-competition, using old rubber and winding to 500 turns; result, a
-flight of 250 yards, say. Arrived on the competition ground you put on
-new rubber and wind to 750 turns, and expect a flight of a quarter of
-a mile at least; result 70 yards, _measured in a straight line_ from
-the starting-point.
-
-14. Directional control is the most difficult problem to overcome with
-any degree of success under all adverse conditions, and 15 per cent.,
-in the writer's opinion, is far too low a percentage; by directional I
-include flying in a straight line; personally I would mark for
-all-round efficiency: (A) distance and stability, 50 per cent.; (B)
-directional control, 30 per cent.; (C) duration of flight, 20 per
-cent. In A the competitor would launch his model _in any direction_;
-in B as directed by the judges. No separate flights required for C.
-
-FOOTNOTES:
-
-[48] The better way, undoubtedly, is to allow the competitor to choose
-his direction, the starting "circle" only to be fixed.
-
-[49] Or 10 per cent. for duration of flight.
-
-[50] In another competition, held under the rules and regulations of
-the Kite and Model Aeroplane Association for the best all-round model,
-open to the world, for machines not under 2 sq. ft. of surface, the
-tests (50 marks for each) were:--A. Longest flight in a straight line.
-B. Circular flight to the right. C. Circular flight to the left. D.
-Stability and landing after a flight. E. Excellence in building of the
-model.
-
-[51] On the assumption that the model will fly straight.
-
-[52] If permitted to enter; if not see Fig. 53.
-
-
-
-
-CHAPTER XIV.
-
-USEFUL NOTES, TABLES, FORMULAE, ETC.
-
-
-Sec. 1. COMPARATIVE VELOCITIES.
-
-    Miles per hr.    Feet per sec.     Metres per sec.
-         10       =     14.7        =      4.470
-         15       =     22          =      6.705
-         20       =     29.4        =      8.940
-         25       =     36.7        =     11.176
-         30       =     44          =     13.411
-         35       =     51.3        =     15.646
-
-Sec. 2. A metre = 39.37079 inches.
-
-    _In order to convert_:--
-               Metres into inches multiply by 39.37
-                     "     feet        "       3.28
-                     "     yards       "       1.09
-                     "     miles       "       0.0006214
-    Miles per hour into ft. per min. multiply by 88.0
-         "    min.      "       sec.      "      88.0
-         "    hr. into kilometres per hr. "       1.6093
-         "       "     metres per sec.    "       0.44702
-         Pounds into grammes multiply by 453.593
-             "       kilogrammes   "       0.4536
-
-Sec. 8. Total surface of a cylinder = circumference of base x height + 2
-area of base.
-
-Area of a circle = square of diameter x 0.7854.
-
-Area of a circle = square of rad. x 3.14159.
-
-Area of an ellipse = product of axes x 0.7854.
-
-Circumference of a circle = diameter x 3.14159.
-
-Solidity of a cylinder = height x area of base.
-
-Area of a circular ring = sum of diameters x difference of diameters x
-0.7854.
-
-For the area of a sector of a circle the rule is:--As 360 : number of
-degrees in the angle of the sector :: area of the sector : area of
-circle.
-
-To find the area of a segment less than a semicircle:--Find the area
-of the sector which has the same arc, and subtract the area of the
-triangle formed by the radii and the chord.
-
-The areas of corresponding figures are as the squares of corresponding
-lengths.
-
-  Sec. 4.  1 mile     =   1.609 kilometres.
-        1 kilometre   =   1093 yards.
-        1 oz.         =   28.35 grammes.
-        1 lb.         =   453.59   "
-        1 lb.         =   0.453 kilogrammes.
-        28 lb.        =   12.7       "
-        112 lb.       =   50.8       "
-        2240 lb.      =   1016       "
-        1 kilogram    =   2.2046 lb.
-        1 gram        =   0.0022 lb.
-        1 sq. in.     =   645 sq. millimetres.
-        1 sq. ft.     =   0.0929 sq. metres.
-        1 sq. yard    =   0.836      "
-        1 sq. metre   =   10.764 sq. ft.
-
-Sec. 5. One atmosphere = 14.7 lb. per sq. in. = 2116 lb. per sq. ft. =
-760 millimetres of mercury.
-
-A column of water 2.3 ft. high corresponds to a pressure of 1 lb. per
-sq. in.
-
-1 H.P. = 33,000 ft.-lb. per min. = 746 watts.
-
-Volts x amperes = watts.
-
-{pi} = 3.1416. _g_ = 32.182 ft. per sec. at London.
-
-Sec. 6. TABLE OF EQUIVALENT INCLINATIONS.
-
-     Rise.            Angle in Degs.
-    1 in 30               1.91
-    1 "  25               2.29
-    1 "  20               2.87
-    1 "  18               3.18
-    1 "  16               3.58
-    1 "  14               4.09
-    1 "  12               4.78
-    1 "  10               5.73
-    1 "   9               6.38
-    1 "   8               7.18
-    1 "   7               8.22
-    1 "   6               9.6
-    1 "   5              11.53
-    1 "   4              14.48
-    1 "   3              19.45
-    1 "   2              30.00
-    1 " {square root}2   45.00
-
-Sec. 7. TABLE OF SKIN FRICTION.
-
-Per sq. ft. for various speeds and surface lengths.
-
-  -----------------+-------------+-------------+-------------+------------
-  Velocity of Wind | 1 ft. Plane | 2 ft. Plane | 4 ft. Plane | 8 ft. Plane
-  -----------------+-------------+-------------+-------------+------------
-         10        |   .00112    |   .00105    |   .00101    |   .000967
-         15        |   .00237    |   .00226    |   .00215    |   .00205
-         20        |   .00402    |   .00384    |   .00365    |   .00349
-         25        |   .00606    |   .00579    |   .00551    |   .00527
-         30        |   .00850    |   .00810    |   .00772    |   .00736
-         35        |   .01130    |   .0108     |   .0103     |   .0098
-  -----------------+-------------+-------------+-------------+------------
-
-This table is based on Dr. Zahm's experiments and the equation
-
-    _f_ = 0.00000778_l_^{-0.07}_v_^{1.85}
-
-Where _f_ = skin friction per sq. ft.; _l_ = length of surface; _v_ =
-velocity in feet per second.
-
-In a biplane model the head resistance is probably from twelve to
-fourteen times the skin friction; in a racing monoplane from six to
-eight times.
-
-Sec. 8. TABLE I.--(METALS).
-
-  --------------+------------+-----------------+-------------
-     Material   |  Specific  | Elasticity E[A] |  Tenacity
-                |  Gravity   |                 | per sq. in.
-  --------------+------------+-----------------+-------------
-  Magnesium     |    1.74    |                 |   {22,000-
-                |            |                 |   {32,000
-  Magnalium[B]  |  2.4-2.57  |      10.2       |
-  Aluminium- }  |            |                 |
-    Copper[C]}  |    2.82    |                 |    54,773
-  Aluminium     |    2.6     |      11.1       |    26,535
-  Iron          | 7.7 (about)|       29        |    54,000
-  Steel         | 7.8 (about)|       32        |   100,000
-  Brass         |  7.8-8.4   |       15        |    17,500
-  Copper        |    8.8     |       36        |    33,000
-  Mild Steel    |    7.8     |       30        |    60,000
-                |            |                 |
-  --------------+------------+-----------------+-------------
-  [A] E in millions of lb. per sq. in.
-  [B] Magnalium is an alloy of magnesium and aluminium.
-  [C] Aluminium 94 per cent., copper 6 per cent. (the best
-      percentage), a 6 per cent. alloy thereby doubles the
-      tenacity of pure aluminium with but 5 per cent.
-      increase of density.
-  --------------+------------+-----------------+-------------
-
-Sec. 9. TABLE II.--WIND PRESSURES.
-
-    _p_ = _kv squared_.
-
-_k_ coefficient (mean value taken) .003 (miles per hour) = 0.0016 ft.
-per second. _p_ = pressure in lb. per sq. ft. _v_ = velocity of wind.
-
-    Miles per hr.   Ft. per sec.   Lb. per sq. ft.
-         10             14.7          0.300
-         12             17.6          0.432
-         14             20.5          0.588
-         16             23.5          0.768
-         18             26.4          0.972
-         20             29.35         1.200
-         25             36.7          1.875
-         30             43.9          2.700
-         35             51.3          3.675
-
-Sec. 10. Representing normal pressure on a plane surface by 1; pressure
-on a rod (round section) is 0.6; on a symmetrical elliptic cross
-section (axes 2:1) is 0.2 (approx.). Similar shape, but axes 6:1, and
-edges sharpened (_see_ ch. ii., Sec. 5), is only 0.05, or 1/20, and for
-the body of minimum resistance (_see_ ch. ii., Sec. 4) about 1/24.
-
-Sec. 11. TABLE III.--LIFT AND DRIFT.
-
-On a well shaped aerocurve or correctly designed cambered surface.
-Aspect ratio 4.5.
-
-    Inclination.   Ratio Lift to Drift.
-           0 deg.            19:1
-        2.87 deg.            15:1
-        3.58 deg.            16:1
-        4.09 deg.            14:1
-        4.78 deg.            12:1
-        5.73 deg.           9.6:1
-        7.18 deg.           7.9:1
-
-Wind velocity 40 miles per hour. (The above deduced from some
-experiments of Sir Hiram Maxim.)
-
-At a velocity of 30 miles an hour a good aerocurve should lift 21 oz.
-to 24 oz. per sq. ft.
-
-
-Sec. 12. TABLE IV.--LIFT AND DRIFT.
-
-On a plane aerofoil.
-
-    N = P(2 sin {alpha}/1 + sin squared {alpha})
-
-    Inclination.   Ratio Lift to Drift.
-         1 deg.              58.3:1
-         2 deg.              29.2:1
-         3 deg.              19.3:1
-         4 deg.              14.3:1
-         5 deg.              11.4:1
-         6 deg.               9.5:1
-         7 deg.               8.0:1
-         8 deg.               7.0:1
-         9 deg.               6.3:1
-        10 deg.               5.7:1
-
-    P = 2_kd_ AV squared sin {alpha}.
-
-A useful formula for a single plane surface. P = pressure supporting
-the plane in pounds per square foot, _k_ a constant = 0.003 in miles
-per hour, _d_ = the density of the air.
-
-A = the area of the plane, V relative velocity of translation through
-the air, and {alpha} the angle of flight.
-
-Transposing we have
-
-    AV squared = P/(2_kd_ sin {alpha})
-
-If P and {alpha} are constants; then AV squared = a constant or area is
-inversely as velocity squared. Increase of velocity meaning diminished
-supporting surface (_and so far as supporting surface goes_), diminished
-resistance and skin friction. It must be remembered, however, that while
-the work of sustentation diminishes with the speed, the work of
-penetration varies as the cube of the speed.
-
-
-Sec. 13. TABLE V.--TIMBER.
-
-  Column Headings:
-
-  A. Material
-  B. Specific Gravity
-  C. Weight per Cub. Ft. in Lb.
-  D. Strength per Sq. In. in Lb.
-  E. Ultimate Breaking Load (Lb.) span 1' x 1" x 1"
-  F. Relative Resilience in Bending
-  G. Modulus of Elasticity in millions of Lb. per Sq. In. for Bending
-  H. Relative Value. Bending Strength compared with Weight
-
-  ---------------+-----+-------+-------------+-------+-----+-----+----
-    A            |B    | C     |  D          |E      |F    |G    | H
-  ---------------+-----+-------+-------------+-------+-----+-----+----
-  Ash            | .79 | 43-52 |14,000-17,000| 622   |4.69 |1.55 |13.0
-  Bamboo         |     |  25[A]|    6300[53] |       |3.07 |3.20 |
-  Beech          | .69 |  43   |10,000-12,000| 850   |     |1.65 |19.8
-  Birch          | .71 |  45   |   15,000    | 550   |     |3.28 |12.2
-  Box            |1.28 |  80   |20,000-23,000| 815   |     |     |10.2
-  Cork           | .24 |  15   |             |       |     |     |
-  Fir (Norway    |     |       |             |       |     |     |
-    Spruce)      | .51 |  32   | 9,000-11,000| 450   |3.01 |1.70 |14.0
-  American       |     |       |             |       |     |     |
-    Hickory      |     |  49   |   11,000    | 800   |3.47 |2.40 |16.3
-  Honduras       |     |       |             |       |     |     |
-    Mahogany     | .56 |  35   |   20,000    | 750   |3.40 |1.60 |21.4
-  Maple          | .68 |  44   |   10,600    | 750   |     |     |17.0
-  American White |     |       |             |       |     |     |
-    Pine         | .42 |  25   |   11,800    | 450   |2.37 |1.39 |18.0
-  Lombardy Poplar|     |  24   |    7,000    | 550   |2.89 | 0.77|22.9
-  American Yellow|     |       |             |       |     |     |
-    Poplar       |     |  44   |   10,000    |       |3.63 |1.40 |
-  Satinwood      | .96 |  60   |             |1,033  |     |     |17.2
-  Spruce         | .50 |  31   |   12,400    | 450   |     |     |14.5
-  Tubular Ash,   |     |       |             |       |     |     |
-   _t_ = 1/8 _d_ |     |  47   |             |       |3.50 |1.55 |
-  ---------------+-----+-------+-------------+-------+-----+-----+----
-
-                         _t_ = thickness: _d_ = diameter.
-
-  [A] Given elsewhere as 55 and 22,500 (_t_ = 1/3_d_), evidently
-  regarded as solid.
-
-Sec. 14.--=Formula connecting the Weight Lifted in Pounds per Square Foot
-and the Velocity.=--The empirical formula
-
-    W = (V squaredC)/_g_
-
-    Where W   = weight lifted in lb. per sq. ft.
-          V   = velocity in ft. per sec.
-          C   = a constant = 0.025.
-          _g_ = 32.2, or 32 approx.
-
-may be used for a thoroughly efficient model. This gives
-(approximately)
-
-      1 lb. per sq. ft. lift at 25 miles an hour.
-     21 oz.     "        "      30       "
-      6 oz.     "        "      15       "
-      4 oz.     "        "      12       "
-    2.7 oz.     "        "      10       "
-
-Remember the results work out in feet per second. To convert
-(approximately) into miles per hour multiply by 2/3.
-
-Sec. 15. =Formula connecting Models of Similar Design, but Different
-Weights.=
-
-    D {proportional to} {square root}W.
-
-or in models of _similar design_ the distances flown are proportional
-to the square roots of the weights. (Derived from data obtained from
-Clarke's flyers.)
-
-For models from 1 oz. to 24-30 oz. the formula appears to hold very
-well. For heavier models it appears to give the heavier model rather
-too great a distance.
-
-Since this was deduced a 1 oz. Clarke model of somewhat similar design
-but longer rubber motor has flown 750 ft. at least; it is true the
-design is not, strictly speaking, similar, but not too much reliance
-must be placed on the above. The record for a 1 oz. model to date is
-over 300 yards (with the wind, of course), say 750 ft. in calm air.
-
-Sec. 16. =Power and Speed.=--The following formula, given by Mr. L. Blin
-Desbleds, between these is--
-
-    W/W{0} = (3_v{0}_)/(4_v_) + 1/4(_v_/_v{0}_) cubed.
-
-    Where   _v{0}_ = speed of minimum power
-              W{0} = work done at speed _v{0}_.
-                 W = work done at speed _v_.
-
-Making _v_ = 2_v{0}_, i.e. doubling the speed of minimum power, and
-substituting, we have finally
-
-    W = (2-3/8)W{0}
-
-i.e. the speed of an aeroplane can be doubled by using a power 2-3/8
-times as great as the original one. The "speed of minimum power" being
-the speed at which the aeroplane must travel for the minimum
-expenditure of power.
-
-Sec. 17. The thrust of the propeller has evidently to balance the
-
-    Aerodynamic resistance                        = R
-    The head resistance (including skin friction) = S
-
-Now according to Renard's theorem, the power absorbed by R + S is a
-minimum when
-
-    S = R/3.
-
-Having built a model, then, in which the total resistance
-
-    = (4/3)R.
-
-This is the thrust which the propeller should be designed to give. Now
-supposing the propeller's efficiency to be 80 per cent., then P--the
-minimum propulsion power
-
-    = (4/3)R x 100/80 x 100/75 x _v_.
-
-Where 25 per cent. is the slip of the screw, _v_ the velocity of the
-aeroplane.
-
-Sec. 18. =To determine experimentally the Static Thrust of a
-Propeller.=--Useful for models intended to raise themselves from the
-ground under their own power, and for helicopters.
-
-The easiest way to do this is as follows: Mount the propeller on the
-shaft of an electric motor, of sufficient power to give the propeller
-1000 to 1500 revolutions per minute; a suitable accumulator or other
-source of electric energy will be required, a speedometer or speed
-counter, also a voltmeter and ammeter.
-
-Place the motor in a pair of scales or on a suitable spring balance
-(the former is preferable), the axis of the motor vertical, with the
-propeller attached. Rotate the propeller so that the air current is
-driven _upwards_. When the correct speed (as indicated by the speed
-counter) has been attained, notice the difference in the readings if a
-spring balance be used, or, if a pair of scales, place weights in the
-scale pan until the downward thrust of the propeller is exactly
-balanced. This gives you the thrust in ounces or pounds.
-
-Note carefully the voltage and amperage, supposing it is 8 volts and
-10 amperes = 80 watts.
-
-Remove the propeller and note the volts and amperes consumed to run
-the motor alone, i.e. to excite itself, and overcome friction and air
-resistance; suppose this to be 8 volts and 2 amperes = 16; the
-increased load when the propeller is on is therefore
-
-    80 - 16 = 64 watts.
-
-All this increased power is not, however, expended on the propeller.
-
-The lost power in the motor increases as C squaredR.
-
-R = resistance of armature and C = current. If we deduct 10 per cent.
-for this then the propeller is actually driven by 56 watts.
-
-Now 746 watts = 1 h.p.
-
-    {therefore} 56/746 = 1/13 h.p. approx.
-
-at the observed number of revolutions per minute.
-
-Sec. 19. N.B.--The h.p. required to drive a propeller varies as the cube
-of the revolutions.
-
-_Proof._--Double the speed of the screw, then it strikes the air twice
-as hard; it also strikes twice as much air, and the motor has to go
-twice as fast to do it.
-
-Sec. 20. To compare one model with another the formula
-
-    Weight x velocity (in ft. per sec.)/horse-power
-
-is sometimes useful.
-
-Sec. 21. =A Horse-power= is 33,000 lb. raised one foot in one minute, or
-550 lb. one foot in one second.
-
-A clockwork spring raised 1 lb. through 41/2 ft. in 3 seconds. What
-is its h.p.?
-
-         1 lb. through 41/2 ft. in 3 seconds
-    is   1 lb.    "    90 ft.  " 1 minute.
-
-          {therefore} Work done is 90 ft.-lb.
-           = 90/33000 = 0.002727 h.p.
-
-The weight of the spring was 63/4 oz. (this is taken from an actual
-experiment), i.e. this motor develops power at the rate of 0.002727
-h.p. for 31/2 seconds only.
-
-Sec. 22. =To Ascertain the H.P. of a Rubber Motor.= Supposing a propeller
-wound up to 250 turns to run down in 15 seconds, i.e. at a mean speed
-of 1200 revolutions per minute or 20 per second. Suppose the mean
-thrust to be 2 oz., and let the pitch of the propeller be 1 foot. Then
-the number of foot-pounds of energy developed
-
-    = (2 oz. x 1200 revols. x 1 ft. (pitch)) / 16 oz.
-
-= 150 ft.-lb. per minute.
-
-But the rubber motor runs down in 15 seconds.
-
-    {therefore} Energy really developed is
-
-          = (150 x 15) / 60 = 37.5 ft.-lb.
-
-The motor develops power at rate of 150/33000 = 0.004545 h.p., but for
-15 seconds only.
-
-Sec. 23. =Foot-pounds of Energy in a Given Weight of Rubber=
-(experimental determination of).
-
-         Length of rubber    36 yds.
-         Weight     "        2-7/16 oz.
-         Number of turns     = 200.
-
-    12 oz. were raised 19 ft. in 5 seconds.
-    i.e. 3/4 lb. was raised 19 x 12 ft. in 1 minute.
-    i.e. 1 lb. was raised 19 x 3 x 3 ft. in 1 minute.
-                               = 171 ft. in 1 minute.
-
-i.e. 171 ft.-lb. of energy per minute. But actual time was 5 seconds.
-
-{therefore} Actual energy developed by 2-7/16 oz. of rubber of 36
-yards, i.e. 36 strands 1 yard each at 200 turns is
-
-    = 171/12 ft.-lb.
-
-    = 141/4 ft.-lb.
-
-This allows nothing for friction or turning the axle on which the cord
-was wound. Ball bearings were used; but the rubber was not new and
-twenty turns were still unwound at the end of the experiment. Now
-allowing for friction, etc. being the same as on an actual model, we
-can take 3/4 of a ft.-lb. for the unwound amount and estimate the
-total energy as 15 ft.-lb. as a minimum. The energy actually developed
-being at the rate of 0.0055 h.p., or 1/200 of a h.p. if supposed
-uniform.
-
-Sec. 24. The actual energy derivable from 1 lb. weight of rubber is
-stated to be 300 ft.-lb. On this basis 2-7/16 oz. should be capable of
-giving 45.7 ft.-lb. of energy, i.e. three times the amount given
-above. Now the motor-rubber not lubricated was only given 200
-turns--lubricated 400 could have been given it, 600 probably before
-rupture--and the energy then derivable would certainly have been
-approximating to 45 ft.-lb., i.e. 36.25. Now on the basis of 300
-ft.-lb. per lb. a weight of 1/2 oz. (the amount of rubber carried in
-"one-ouncers") gives 9 ft.-lb. of energy. Now assuming the gliding
-angle (including weight of propellers) to be 1 in 8; a perfectly
-efficient model should be capable of flying eight times as great a
-distance in a horizontal direction as the energy in the rubber motor
-would lift it vertically. Now 9 ft.-lb. of energy will lift 1 oz. 154
-ft. Therefore theoretically it will drive it a distance (in yards) of
-
-    (8 x 154)/3 = 410.6 yards.
-
-Now the greatest distance that a 1 oz. model has flown in perfectly
-calm air (which never exists) is not known. Flying with the wind 500
-yards is claimed. Admitting this what allowance shall we make for the
-wind; supposing we deduct half this, viz. 250 yards. Then, on this
-assumption, the efficiency of this "one ouncer" works out (in
-perfectly still air) at 61 per cent.
-
-The gliding angle assumption of 1 in 8 is rather a high one, possibly
-too high; all the writer desires to show is the method of working out.
-
-Mr. T.W.K. Clarke informs me that in his one-ouncers the gliding
-angle is about 1 in 5.
-
-Sec. 25. =To Test Different Motors or Different Powers of the Same Kind
-of Motor.=--Test them on the same machine, and do not use different
-motors or different powers on different machines.
-
-Sec. 26. =Efficiency of a Model.=--The efficiency of a model depends on
-the weight carried per h.p.
-
-Sec. 27. =Efficiency of Design.=--The efficiency of some particular
-design depends on the amount of supporting surface necessary at a
-given speed.
-
-Sec. 28. =Naphtha Engines=, that is, engines made on the principle of the
-steam engine, but which use a light spirit of petrol or similar agent
-in their generator instead of water with the same amount of heat, will
-develop twice as much energy as in the case of the ordinary steam
-engine.
-
-Sec. 29.=Petrol Motors.=
-
-    Horse-power.     No. of Cylinders.   Weight.
-        1/4                Single          41/2 lb.
-        1/2 to 3/4             "             61/2  "
-        11/2               Double          9   "
-
-Sec. 30. =The Horse-power of Model Petrol Motors.=--Formula for rating of
-the above.
-
-    (R.P.M. = revolutions per minute.)
-
-    H.P. = ((Bore) squared x stroke x no. of cylinders x R.P.M.)/12,000
-
-If the right-hand side of the equation gives a less h.p. than that
-stated for some particular motor, then it follows that the h.p. of the
-motor has been over-estimated.
-
-[Illustration: FIG. 56.]
-
-Sec. 30A. =Relation between Static Thrust of Propeller and Total Weight
-of Model.=--The thrust should be approx. = 1/4 of the weight.
-
-Sec. 31. =How to find the Height of an Inaccessible Object by Means of
-Three Observations taken on the Ground (supposed flat) in the same
-Straight Line.=--Let A, C, B be the angular elevations of the object
-D, as seen from these points, taken in the same straight line. Let the
-distances B C, C A and A B be _a_, _b_, _c_ respectively. And let
-required height P D = _h_; then by trigonometry we have (see Fig. 56)
-
-    _h squared_ = _abc_/(_a_ cot squaredA - _c_ cot squaredC + _b_ cot squaredB).
-
-Sec. 32. =Formula= for calculating the I.H.P. (indicated horse-power) of
-a single-cylinder double-acting steam-engine.
-
-Indicated h.p. means the h.p. actually exerted by the steam in the
-cylinder without taking into account engine friction. Brake h.p. or
-effective h.p. is the actual h.p. delivered by the crank shaft of the
-engine.
-
-    I.H.P. = (2 x S x R x A x P)/33,000.
-
-    Where    S = stroke in feet.
-             R = revolutions per minute.
-             A = area of piston in inches.
-             P = mean pressure in lb. exerted per sq. in. on the piston.
-
-The only difficulty is the mean effective pressure; this can be found
-approximately by the following rule and accompanying table.
-
-
-TABLE VI.
-
-    ---------+----------+---------+----------+---------+---------
-     Cut-off | Constant | Cut-off | Constant | Cut-off | Constant
-    ---------+----------+---------+----------+---------+---------
-       1/6   |   .566   |   3/8   |   .771   |   2/3   |  .917
-       1/5   |   .603   |    .4   |   .789   |    .7   |  .926
-       1/4   |   .659   |   1/2   |   .847   |   3/4   |  .937
-        .3   |   .708   |    .6   |   .895   |    .8   |  .944
-       1/3   |   .743   |   5/8   |   .904   |   7/8   |  .951
-    ---------+----------+---------+----------+---------+---------
-
-Rule.--"Add 14.7 to gauge pressure of boiler, this giving 'absolute
-steam pressure,' multiply this sum by the number opposite the fraction
-representing the point of cut-off in the cylinder in accompanying
-table. Subtract 17 from the product and multiply the remainder by 0.9.
-The result will be very nearly the M.E.P." (R.M. de Vignier.)
-
-
-FOOTNOTE:
-
-[53] Given elsewhere as 55 and 22,500 (_t_ = 1/3 _d_), evidently
-regarded as solid.
-
-
-
-
-APPENDIX A.
-
-SOME MODELS WHICH HAVE WON MEDALS AT OPEN COMPETITIONS.
-
-
-[Illustration: FIG. 57.--THE G.P.B. SMITH MODEL.]
-
-The model shown in Fig. 57 has won more competition medals than any
-other. It is a thoroughly well designed[54] and well constructed
-model. Originally a very slow flyer, the design has been simplified,
-and although by no means a fast flyer, its speed has been much
-accelerated. Originally a one-propeller machine, it has latterly been
-fitted with twin propellers, with the idea of obtaining more
-directional control; but in the writer's opinion, speaking from
-personal observation, with but little, if any, success. The steering
-of the model is effected by canting the elevator. Originally the
-machine had ailerons for the purpose, but these were removed owing, I
-understand, to their retarding the speed of the machine.
-
-In every competition in which this machine has been entered it has
-always gained very high marks for stability.
-
-[Illustration: FIG. 58.--THE GORDON-JONES DIHEDRAL BIPLANE.]
-
-Up to the time of writing it has not been provided with anything in
-the nature of fins or rudder.
-
-Fig. 58 is a biplane very much after the type of the model just
-alluded to, but the one straight and one curved aerofoil surfaces are
-here replaced by two parallel aerofoils set on a dihedral angle. The
-large size of the propeller should be noted; with this the writer is
-in complete agreement. He has not unfortunately seen this model in
-actual flight.
-
-The scientifically designed and beautifully made models illustrated in
-Fig. 59 are so well known that any remarks on them appear
-superfluous. Their efficiency, so far as their supporting area goes,
-is of the highest, as much as 21 oz. per square foot having been
-carried.
-
-[Illustration: FIG. 59.--MESSRS. T.W.K. CLARKE AND CO.'S MODEL
-FLYERS.]
-
-For illustrations, etc., of the Fleming-Williams model, _see_ ch. v.,
-Sec. 23.
-
-(Fig. 60.) This is another well-constructed and efficient model, the
-shape and character of the aerofoil surfaces much resembling those of
-the French toy monoplane AL-MA (see Sec. 4, ch. vii.), but they are
-supported and held in position by quite a different method, a neat
-little device enabling the front plane to become partly detached on
-collision with any obstacle. The model is provided with a keel (below
-the centre of gravity), and rudder for steering; in fact, this machine
-especially claims certainty of directional control. The writer has
-seen a number of flights by this model, but it experiences, like other
-models, the greatest difficulty in keeping straight if the conditions
-be adverse.
-
-The model which will do this is, in his opinion, yet to be evolved.
-The small size of the propellers is, of course, in total disagreement
-with the author's ideas. All the same, the model is in many respects
-an excellent one, and has flown over 300 yards at the time of writing.
-
-[Illustration: FIG. 60.--THE DING SAYERS MONOPLANE.]
-
-More than a year ago the author made a number of models with
-triangular-shaped aerofoils, using umbrella ribs for the leading edge
-and steel piano wire for the trailing, but has latterly used aerofoils
-of the elongated ellipse shape.
-
-Fig. 61 is an illustration of one of the author's latest models which
-won a Bronze Medal at the Long Distance Open Competition, held at the
-Crystal Palace on July 27, 1910, the largest and most keenly contested
-competition held up to that date.
-
-The best and straightest flight against the wind was made by this
-model.
-
-On the morning of the competition a flight of about 320 yards
-(measured in a straight line) was made on Mitcham Common, the model
-being launched against the wind so as to gain altitude, and then
-flying away with the breeze behind the writer. Duration of flight 50
-seconds. The following are the chief particulars of the
-model:--Weight, 71/2 oz. Area of supporting surface, 1-1/3 sq. ft.
-Total length, 4 ft. Span of main aerofoil, 25 in. Aspect ratio, 4 : 1.
-Diameter of propeller, 14 in. Two strand geared rubber motor, carrying
-altogether 28 strands of 1/16 square rubber cord 43 in. long. The
-propeller was originally a Venna, but with the weight reduced by
-one-third, and considerable alteration made in its central contours.
-The front skid of steel pianoforte wire, the rear of jointless cane
-wire tipped; the rear skid was a necessity in order to protect the
-delicate gearing mechanism, the weight of which was reduced to a
-minimum.
-
-[Illustration: FIG. 61.--THE AUTHOR'S "GRASSHOPPER" MODEL.]
-
-The very large diameter of the propeller should be noted, being 56
-per cent. of the span. The fin, high above the centre of gravity, was
-so placed for transverse stability and direction. At the rear of the
-fin was a rudder. The small amount of rubber carried (for a long
-distance machine) should also be noted, especially when allowing for
-friction in gearing, etc.
-
-The central rod was a penny bamboo cane, the large aerofoil of
-jointless cane and Hart's fabric, and the front aerofoil of steel wire
-surfaced with the same material.
-
-
-LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, GREAT WINDMILL
-STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.
-
-FOOTNOTE:
-
-[54] The design is patented.
-
-
-
-
-    _October, 1910_
-
-A SHORT LIST OF
-
-SCIENTIFIC BOOKS
-
-PUBLISHED AND SOLD BY
-
-E. & F.N. SPON, Limited,
-
-57 Haymarket, London, S.W.
-
-SOLE ENGLISH AGENTS for the Books of--
-
-    MYRON C. CLARK, NEW YORK
-    THE BUSINESS CODE COMPANY, CHICAGO
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-
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-                                 PAGE
-    AERONAUTICS                    2
-    AGRICULTURE                    2
-    ARCHITECTURE                   3
-    ARTILLERY                      5
-    BRIDGES AND ROOFS              5
-    BUILDING                       3
-    CEMENT AND CONCRETE            7
-    CIVIL ENGINEERING              8
-    DICTIONARIES                  11
-    DOMESTIC ECONOMY              12
-    DRAWING                       13
-    ELECTRICAL ENGINEERING        14
-    FOREIGN EXCHANGE              19
-    GAS AND OIL ENGINES           20
-    GAS LIGHTING                  20
-    HISTORICAL; BIOGRAPHICAL      21
-    HOROLOGY                      22
-    HYDRAULICS                    22
-    INDUSTRIAL CHEMISTRY          24
-    IRRIGATION                    27
-    LOGARITHM TABLES              28
-    MANUFACTURES                  24
-    MARINE ENGINEERING            28
-    MATERIALS                     30
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-    MECHANICAL ENGINEERING        33
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-
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-    93 illus. 119 pp. 8vo. (_1903_)
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-    12 illus. 74 pp. crown 8vo, limp. (S. & C. SERIES, NO. 19.) (_1910_)
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-    CUMMINGS. 45 illus. 137 pp. 8vo. (_New York, 1908_) . ..
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-    =Notes on Design of Small Dynamo.= By GEORGE HALLIDAY. Second edition,
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-    crown 8vo. (_New York, 1906_)
-
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-    limp. (S. & C. SERIES, NO. 11.) (_New York, 1909_)
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-    (_1908_)
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-
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-    illus. 345 pp. crown 8vo. (_New York, 1907_)
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-
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-    WILLIAMS. 45 illus. 252 pp. 12mo. (_New York, 1903_)
-
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-    illus. 284 pp. crown 8vo. (_New York, 1908_)
-
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-    (_New York, 1905_)
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-    NO. 1.) (_New York, 1905_)
-
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-
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-
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-    =Experimenting with Induction Coils.= By N.H. SCHNEIDER. 26 illus. 73
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-
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-    =Study of Electricity for Beginners.= By N.H. SCHNEIDER. 54 illus. 88
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-
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-    13.) (_New York, 1902_)
-
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-    Translated from the French by J.A. BERLY. 62 illus. 202 pp. 8vo
-
-               9  0
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-    With additional notes by N.H. SCHNEIDER. 30 illus. 59 pp. crown 8vo,
-    sewed. (S. & C. SERIES, NO. 7.) (_New York, 1905_)
-
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-    Preface, by Prof. S.P. THOMPSON. 42 illus. 84 pp. crown 8vo
-
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-    =Electric Toy-Making.= By T.O. SLOANE. Fifteenth edition, 70 illus.
-    183 pp. crown 8vo. (_New York, 1903_)
-
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-
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-    =How to become a Successful Electrician.= By T.O. SLOANE. Third
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-    =Electricity:= its Theory, Sources and Applications. By J.T. SPRAGUE.
-    Third edition, 109 illus. 658 pp. crown 8vo. (_1892_)
-
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-    =Telegraphic Connections.= By C. THOM and W.H. JONES. 20 plates, 59
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-
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-
-    =Roentgen Rays= and Phenomena of the Anode and Cathode. By E.P.
-    THOMPSON and W.A. ANTHONY. 105 illus. 204 pp. 8vo. (_New York, 1896_)
-
-    _net_      4  6
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-    =Dynamo Electric Machinery.= By Prof. S.P. THOMPSON. Seventh edition,
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-    transparent paper for office use of Plate L from Dynamo Electric
-    Machinery, and measuring 25 in. by 16 in.
-
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-    =The Electromagnet.= By C.R. UNDERHILL. 67 illus. 159 pp. crown 8vo.
-    (_New York, 1903_)
-
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-    =Practical Guide to the Testing of Insulated Wires and Cables.= By
-    H.L. WEBB. Fifth edition, 38 illus. 118 pp. crown 8vo. (_New York,
-    1902_)
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-    Translated by WILLIAM FRANCIS. 269 pp. 18mo, boards. (_New York,
-    1891_)
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-    (_1900_)
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-    MECHANICAL ENGINEERING.
-
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-
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-    Practice in the United States. By J. BEGTRUP. 90 diagrams, 146 pp.
-    medium 8vo. (_New York, 1902_)
-
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-    COTTERILL. Third edition, 39 diagrams, 444 pp. 8vo. (_1896_)
-
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-    DAHLSTROM. Ninth edition fcap. 8vo. (_New York, 1902_)
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-
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-    KINEALY. Fourth edition, 106 illus. 259 pp. 8vo. (_New York,
-    1903_)
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-    =Centrifugal Fans.= By J.H. KINEALY. 33 illus. 206 pp. fcap.
-    8vo, leather. (_New York, 1905_)
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-
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-    PORTER. Sixth edition, 3 plates and 73 diagrams, 285 pp. 8vo.
-    (_1902_)
-
-               9  0
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-    =Practical Treatise on the Steam Engine.= By A. RIGG. Second
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-    =Power and its Transmission.= A Practical Handbook for the
-    Factory and Works Manager. By T.A. SMITH. 76 pp. fcap. 8vo.
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-    =Drawings for Medium Sized Repetition Work.= By R.D. SPINNEY.
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-    =Slide Valve Simply Explained.= By W.J. TENNANT. Revised by
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-    47 plates and 314 illus. 155 pp. Two vols. folio, half morocco.
-    (_1882_)
-
-            1 16  0
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-    =How to run Engines and Boilers.= By E.P. WATSON. Fifth
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-    =Position Diagram of Cylinder with Meyer Cut-off.= By W.H.
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-    =Practical Method of Designing Slide Valve Gearing.= By E.J.
-    WELCH. 69 diagrams, 283 pp. Crown 8vo. (_1890_)
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-    =Manual of Assaying Gold, Silver, Copper and Lead Ores.= By
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-    (_New York, 1907_)
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-    By A.G. CHARLETON. 82 illus. and numerous plans and tables, 648
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-    Prof. E. HULL. 157 pp. demy 8vo. (_1897_)
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-
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-    266 pp. 12mo. (_New York, 1908_)
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-    graphically. By J.H. HAISTE. On folding card for pocket use
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-    F.R. JOHNSON. 6 plates, 31 pp. crown 8vo. (_1896_)
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-    etc. By A. KENNEDY and R.W. HACKWOOD. 32mo
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-    Engineers. By B. STEWART. 55 illus. 98 pp. crown 8vo. (_1909_)
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-
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-    principal dimensions, 118 pp. oblong 8vo. (_1907_)
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-[Illustration]
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-    Lighting--Telegraphy and Telephony.
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-During 1908 and 1909 over 2800 Abstracts and References were included
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-       *       *       *       *       *
-
-
-  Transcriber's Notes
-
-  Obvious punctuation and spelling errors and inconsistent hyphenation
-  have been corrected.
-
-  Italic text is denoted by _underscores_ and bold text by =equal signs=.
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-  The OE ligature has been replaced by the separate characters.
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-  but other fractions use the / and - symbols, e.g. 3/8 or 2-5/8.
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-  The exponents 2 and 3 are represented using  squared and  cubed respectively, but
-  other exponents are indicated by the caret character, for example,
-  v^{1.85}
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-  Subscripts are simply enclosed in braces, e.g. W{0}.
-
-  Other symbols that cannot be represented have been replaced by words
-  in braces: {alpha}, {pi}, {therefore}, {square root} and
-  {proportional to}.
-
-  The skin friction formulae given on pages 11 and 128 have been corrected
-  by comparison with other sources. Respectively, the formulae were
-  originally printed as
-      _f_ = 0.00000778_l_^{9.3}_v_^{1.85}
-  and
-      _f_ = 0.00000778_l_ - ^{00.7}_v_^{1.85}
-
-  In ambiguous cases, the text has been left as it appears in the
-  original book.
-
-
-
-
-
-End of the Project Gutenberg EBook of The Theory and Practice of Model
-Aeroplaning, by V. E. Johnson
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