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diff --git a/41135-h/41135-h.htm b/41135-h/41135-h.htm index 69039c3..5b5a943 100644 --- a/41135-h/41135-h.htm +++ b/41135-h/41135-h.htm @@ -3,7 +3,7 @@ <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> <head> - <meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1" /> + <meta http-equiv="Content-Type" content="text/html;charset=UTF-8" /> <meta http-equiv="Content-Style-Type" content="text/css" /> <title> The Project Gutenberg eBook of The Theory and Practice of Model Aeroplaning, by V.E. Johnson @@ -113,46 +113,7 @@ td.sub {padding-left:6em;} </style> </head> <body> - - -<pre> - -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) - - - - - - -</pre> - +<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"> </td> <td class="tocpag"><small>PAGE</small></td> </tr><tr> -<td class="toctxt">§§ 1-5. The two classes of models—First requisite of a model -aeroplane. § 6. An art in itself. § 7. The leading principle</td> +<td class="toctxt">§§ 1-5. The two classes of models—First requisite of a model +aeroplane. § 6. An art in itself. § 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">§§ 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 +<td class="toctxt">§§ 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.</td> +minimum weight. § 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">§ 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 +<td class="toctxt">§ 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 +§ 7. Skin friction—Its coefficient. § 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">§ 1. Automatic stability essential in a flying model. § 2. -Theoretical researches on this question. §§ 3-6. A brief +<td class="toctxt">§ 1. Automatic stability essential in a flying model. § 2. +Theoretical researches on this question. §§ 3-6. A brief <span class="pagenum"><a name="Page_viii" id="Page_viii">[viii]</a></span>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 +stability. § 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 efficient section.</td> +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 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. § 13. The most efficient section.</td> </tr><tr> <td colspan="2" class="tocsec"><span class="smcap"><a href="#Section_I">Section I.</a>—Rubber Motors.</span></td> </tr><tr> -<td class="toctxt">§ 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 +<td class="toctxt">§ 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 +and number. § 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. § 12<span class="smcap">A</span>. Action of water, etc. -§ 12<span class="smcap">B</span>. 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. </td> +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. § 12<span class="smcap">A</span>. Action of water, etc. +§ 12<span class="smcap">B</span>. 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. </td> <td class="tocpag">24</td> </tr><tr> <td colspan="2" class="tocsec"><span class="smcap"><a href="#Section_II">Section II.</a>—Other Forms of Motors.</span></td> </tr><tr> -<td class="toctxt">§ 18<span class="smcap">A</span>. <i>Spring motors</i>; their inferiority to rubber. § 18<span class="smcap">B</span>. The -most efficient form of spring motor. § 18<span class="smcap">C</span>. <i>Compressed air -motors</i>—A fascinating form of motor, "on paper." § 18<span class="smcap">D</span>. +<td class="toctxt">§ 18<span class="smcap">A</span>. <i>Spring motors</i>; their inferiority to rubber. § 18<span class="smcap">B</span>. The +most efficient form of spring motor. § 18<span class="smcap">C</span>. <i>Compressed air +motors</i>—A fascinating form of motor, "on paper." § 18<span class="smcap">D</span>. The pneumatic drill—Application to a model aeroplane—Length -<span class="pagenum"><a name="Page_ix" id="Page_ix">[ix]</a></span>of possible flight. § 18<span class="smcap">E</span>. The pressure in motor-car -tyres. § 19. Hargraves' compressed air models—The best -results compared with rubber motors. § 20. The effect of +<span class="pagenum"><a name="Page_ix" id="Page_ix">[ix]</a></span>of possible flight. § 18<span class="smcap">E</span>. 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. § 22<span class="smcap">A</span>. Tatin's air-compressed motor. -§ 23. <i>Steam engine</i>—Steam engine model—Professor +motor. § 21. Reducing valves—Lowest working pressure. +§ 22. The inferiority of this motor compared with the +steam engine. § 22<span class="smcap">A</span>. Tatin's air-compressed motor. +§ 23. <i>Steam engine</i>—Steam engine model—Professor Langley's models—His experiment with various forms of -motive power—Conclusions arrived at. § 24. His steam +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. +§ 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. -<i>Petrol motors.</i>—But few successful models. § 30. Limit -to size. § 31. Stanger's successful model described and -illustrated. § 32. One-cylinder petrol motors. § 33. <i>Electric +"size of the model." § 28. Experiments in France. § 29. +<i>Petrol motors.</i>—But few successful models. § 30. Limit +to size. § 31. Stanger's successful model described and +illustrated. § 32. One-cylinder petrol motors. § 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">§ 1. The position of the propeller. § 2. The number of blades. -§ 3. Fan <i>versus</i> 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 +<td class="toctxt">§ 1. The position of the propeller. § 2. The number of blades. +§ 3. Fan <i>versus</i> 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 +§ 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 <i>v.</i> twisted +and model propellers generally. § 21. Fabric-covered +screws. § 22. Experiments with twin propellers. § 23. +The Fleming Williams propeller. § 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">§ 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 +<td class="toctxt">§ 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 of pressure on arched surfaces</td> +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 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">§ 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 +<td class="toctxt">§ 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.</td> <td class="tocpag">86</td> </tr><tr> @@ -434,16 +395,16 @@ fibre—Sheet celluloid—Mica.</td> </tr><tr> <td colspan="2" class="toctit">HINTS ON THE BUILDING OF MODEL AEROPLANES.</td> </tr><tr> -<td class="toctxt">§ 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 <i>versus</i> wheels—Materials for -skids. § 16. Shock absorbers, how to attach—Relation +<td class="toctxt">§ 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 <i>versus</i> wheels—Materials for +skids. § 16. Shock absorbers, how to attach—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">§ 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 <i>speed</i> -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".</td> +<td class="toctxt">§ 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 <i>speed</i> +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".</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">§ 1. The direction in which to launch them. § 2. The velocity—wooden +<td class="toctxt">§ 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. +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</td> +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</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">§ 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 +<td class="toctxt">§ 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.</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">§ 1. A few general details concerning such. § 2. Aero Models -Association's classification, etc. § 3. Various points to be +<td class="toctxt">§ 1. A few general details concerning such. § 2. Aero Models +Association's classification, etc. § 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">§ 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. +<td class="toctxt">§ 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 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. § 30<span class="smcap">A</span>. Relation +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 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. § 30<span class="smcap">A</span>. 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. § 31. How to find the height of an inaccessible +object (kite, balloon, etc.). § 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>—in the case of a full-sized machine—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—it would not be <i>twice</i> as difficult to build a ¼-in. scale model as a ½-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—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—simplicity +<p>§ 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 @@ -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—model +<p>§ 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 @@ -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, -12½ per cent. in the case of a flying machine, and 0·1 per +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 @@ -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—</p> +<p>§ 3. This resistance is made up of—</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 ½ to l½ 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> ·93</sup><i>v</i><sup>1·85</sup></ins> +<i>f</i> = 0·00000778<i>l</i><sup> ·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:—"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>:—</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—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.—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.—The Stringfellow Model Triplane of 1868.</span></span> </div> -<p>§ 6. Referring to F and N—the problem of longitudinal +<p>§ 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 <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.—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 § 23, ch. iv). Revolved +compressed air (for description 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.</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—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.—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—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>—but soon we have an @@ -1404,7 +1365,7 @@ 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 +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.—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>—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.—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, 3½ 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—</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:—</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>—As to +<p>§ 10. <b>The Maximum Number of Turns.</b>—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>—One of the +<p>§ 11. <b>On the Use of "Lubricants."</b>—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 @@ -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>—Copper, +<p>§ 12. <b>The Action of Copper upon Rubber.</b>—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>—Rubber +<p>§ 12<span class="smcap">A</span>. <b>The Action of Water, etc., on Rubber.</b>—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>—In the first +<p>§ 12B. <b>How to Preserve Rubber.</b>—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:—Carbon, 87·46 per cent.; hydrogen, 12·00 per -cent.; oxygen and ash, 0·54 per cent.</p> +as follows:—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>—Good elastic thread composed +<p>§ 13. <b>To Test Rubber.</b>—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—Strip or Ribbon versus +<p>§ 14. <b>The Section—Strip or Ribbon versus Square.</b>—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>—One-sixteenth or one-twelfth +<p>§ 15. <b>Size of the Section.</b>—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>—It is quite a mistake +<p>§ 16. <b>Geared Rubber Motors.</b>—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—same size, weight, and number of teeth—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—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>.—Other Forms of Motors</span>.</p> -<p>§ 18<span class="smcap">A</span>. <b>Spring Motors.</b>—This question has already +<p>§ 18<span class="smcap">A</span>. <b>Spring Motors.</b>—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>—This is a very +<p>§ 18<span class="smcap">C</span>. <b>Compressed Air Motors.</b>—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 54½ 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>—Several successful +<p>§ 23. <b>Steam-Driven Motors.</b>—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 1½ H.P., total weight (including @@ -2072,8 +2033,8 @@ each a diameter of 1¼ 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—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—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>—Here it would appear at first +<p>§ 29. <b>Petrol Motors.</b>—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 "Aero."]</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—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:—The engine is a four-cylinder one, and weighs (complete with double carburetter and petrol tank) 5½ lb., and develops 1¼ 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>—So far as the +<p>§ 32. <b>One-cylinder Petrol Motors.</b>—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>—No attempt should on any +<p>§ 33. <b>Electric Motors.</b>—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>—Theoretically the +<p>§ 2. <b>The Number of Blades.</b>—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>—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>—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—</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—</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— slip (feet per minute).</i></p> <p>This slip wants to be made small—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—</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>—If we +<p>§ 8. <b>Pitch Coefficient or Pitch Ratio.</b>—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>—"The diameter (says Mr. T. W.K. +<p>§ 9. <b>Diameter.</b>—"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>—Theoretically the pitch<span class="pagenum"><a name="Page_59" id="Page_59">[59]</a></span> +<p>§ 10. <b>Theoretical Pitch.</b>—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>—Take +<p>§ 12. <b>To Ascertain the Pitch of a Propeller.</b>—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 π <i>r</i> = 2 × 22/7 × 5 = 31·34.<br /> +2 π <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 = 10½ in. approx.<br /> +31·43/3 = 10·48 = 10½ 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>—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>—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>—We have already referred to the +<p>§ 14. <b>Blade Area.</b>—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 @@ -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>—No improvement whatever is <span class="pagenum"><a name="Page_63" id="Page_63">[63]</a></span>obtained +<p>§ 16. <b>Shrouding.</b>—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>—The propeller should be so +<p>§ 17. <b>General Design.</b>—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>—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—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>—To design a propeller, proceed +<p>§ 19. <b>Propeller Design.</b>—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 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.</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.—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 ½ 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 = ½ in. × 7 in. = 3½ 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 = ½ in. × 7 in. = 3½ sq. in. Now the area of the disc swept out by the propeller is</p> <p class="cen"> -π/4 × (diam.)<sup>2</sup> <span style="padding-left:3em;">(π = 22/7)</span> +π/4 × (diam.)<sup>2</sup> <span style="padding-left:3em;">(π = 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>) × π/4 × (14)<sup>2</sup> = area of blade = 10½,<br /> +(<i>d</i> A <i>r</i>) × π/4 × (14)<sup>2</sup> = area of blade = 10½,<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> -π × diameter = 22/7 × 14 = 44 in. to scale 5½ in.<br /> +π × diameter = 22/7 × 14 = 44 in. to scale 5½ 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>—The propeller +<p>§ 20. <b>Experiments with Propellers.</b>—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 1½ lb. Diameter of each propeller 14 in.; angle of -blade at tip 25°. The result was several good flights—the +blade at tip 25°. The result was several good flights—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>—A +<p>§ 23. <b>The Fleming-Williams Propeller.</b>—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—more -than 45° at the tip—and large diameter. These do not +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 <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—</p> -<p>§ 6. <b>Dipping Front Edge.</b>—The leading or front +<p>§ 6. <b>Dipping Front Edge.</b>—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—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—</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—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>—Some model +<p>§ 10. <b>Constant or Varying Camber.</b>—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>—</p> -<p>§ 11. <b>Centre of Pressure on Arched Surfaces.</b>—Wilbur +<p>§ 11. <b>Centre of Pressure on Arched Surfaces.</b>—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—in addition to skilful building and best disposition @@ -3309,7 +3270,7 @@ 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).</p> -<p>§ 2. <b>Bamboo.</b>—Bamboo has per pound weight a greater +<p>§ 2. <b>Bamboo.</b>—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>—Ash has a transverse rupture of 14,300 lb. +<p>§ 4. <b>Steel.</b>—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 @@ -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—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—but this entirely depends on the length you make use of, in lengths @@ -3429,7 +3390,7 @@ 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.</p> -<p>§ 6. <b>Steel Wire.</b>—Tensile strength about 300,000 lb. +<p>§ 6. <b>Steel Wire.</b>—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—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>—This again is a <i>sine qua non</i>. Silk is the +<p>§ 7. <b>Silk.</b>—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>—Two substances +<p>§ 8. <b>Aluminium and Magnalium.</b>—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>—During recent years scores, hundreds, +<p>§ 9. <b>Alloys.</b>—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>—This substance is sometimes +<p>§ 10. <b>Sheet Ebonite.</b>—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—if you do not know how to—it is +<p>§ 4. Learn to solder—if you do not know how to—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—the slip of the screw is reduced to a corresponding degree—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—the +<p>§ 7. As to the shape of such, only three need be considered—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>—(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—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—the same substances can be used—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"—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 § 22 ch. v.; the aerofoil surface of as high an aspect +(not less than 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 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., § 9). A winder is essential.</p> +been referred to (<i>see</i> chap. iii., § 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., § 15). +propeller speed has already been discussed (<i>see</i> ch. v., § 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—if there be anything of a breeze—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 "Model Engineer."</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.—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—</p> <p>The models are divided into classes:—</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>—</p> <table border="0" cellpadding="2" cellspacing="0" summary=""> -<tr><td align="center">Metres into </td><td align="center">inches</td><td align="center"> 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 </td><td align="center">inches</td><td align="center"> 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 </td><td align="right">hour into </td><td align="center">ft. per min. </td><td align="center">multiply by</td><td align="center">88·0</td></tr> -<tr><td align="center">"</td><td align="right">min. into </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 </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 </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 </td><td align="right">hour into </td><td align="center">ft. per min. </td><td align="center">multiply by</td><td align="center">88·0</td></tr> +<tr><td align="center">"</td><td align="right">min. into </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 </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 </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:—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 "</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 "</td></tr> -<tr><td align="left">112 lb.</td><td align="left">=</td><td align="left">50·8 "</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 "</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 "</td></tr> +<tr><td align="left">112 lb.</td><td align="left">=</td><td align="left">50·8 "</td></tr> <tr><td align="left">2240 lb.</td><td align="left">=</td><td align="left">1016 "</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 "</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 "</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>π = 3·1416. <i>g</i> = 32·182 ft. per sec. at London.</p> +<p>π = 3·1416. <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> </td><td align="right">1·91</td><td> </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 </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">√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> </td><td align="right">1·91</td><td> </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 </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">√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 </td><td align="center">·0103 </td><td align="center">·0098 </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 </td><td align="center">·0103 </td><td align="center">·0098 </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> -0·07</sup><i>v</i><sup>1·85</sup><br /></ins></p> +<i>f</i> = 0·00000778<i>l</i><sup> -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.—(Metals).</span></p> +<p class="cen">§ 8. <span class="smcap">Table I.—(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 </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 </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 </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 </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 </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 </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 </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 </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.—Wind Pressures.</span></p> +<p class="cen">§ 9. <span class="smcap">Table II.—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., § 5), is only 0·05, or 1/20, and for the body of -minimum resistance (<i>see</i> ch. ii., § 4) about 1/24.</p> +ch. ii., § 5), is only 0·05, or 1/20, and for the body of +minimum resistance (<i>see</i> ch. ii., § 4) about 1/24.</p> -<p class="cen">§ 11. <span class="smcap">Table III.—Lift and Drift.</span></p> +<p class="cen">§ 11. <span class="smcap">Table III.—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.—Lift and Drift.</span></p> +<p class="cen">§ 12. <span class="smcap">Table IV.—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.—Timber.</span></p> +<p class="cen">§ 13. <span class="smcap">Table V.—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.—<b>Formula connecting the Weight Lifted +<p>§ 14.—<b>Formula connecting the Weight Lifted in Pounds per Square Foot and the Velocity.</b>—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 = velocity in ft. per sec.</span><br /> -<span style="margin-left: 3em;">C = 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 = 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 ∝√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>—The following formula, +<p>§ 16. <b>Power and Speed.</b>—The following formula, given by Mr. L. Blin Desbleds, between these is—</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—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>—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.—The h.p. required to drive a propeller varies +<p>§ 19. N.B.—The h.p. required to drive a propeller varies as the cube of the revolutions.</p> <p><i>Proof.</i>—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 4½ 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">∴ 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 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.</p> +rate of 0·002727 h.p. for 3½ 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 /> ∴ 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. ¾ 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. ¾ 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 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 <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—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 +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) @@ -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>—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>—The efficiency of a +<p>§ 26. <b>Efficiency of a Model.</b>—The efficiency of a model depends on the weight carried per h.p.</p> -<p>§ 27. <b>Efficiency of Design.</b>—The efficiency of some +<p>§ 27. <b>Efficiency of Design.</b>—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>—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>—The thrust should be approx. = ¼ 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>—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">¼</td><td align="center">·659</td><td align="center">½</td><td align="center">·847</td><td align="center">¾</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">¼</td><td align="center">·659</td><td align="center">½</td><td align="center">·847</td><td align="center">¾</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.—"Add 14·7 to gauge pressure of boiler, this +<p>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 +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., § 23.</p> +<i>see</i> ch. v., § 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 -§ 4, ch. vii.), but they are supported and held in position by +§ 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 § 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 § 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., § 28.</p></div> +cases the "single stick" can be made use of. <i>See also</i> ch. iv., § 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., § 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., § 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—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 ½, 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 ½, 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>—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.</p></div> +thrust is 35¼Â°. 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> § 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> § 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 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 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 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 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 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 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 10 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 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 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 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 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 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 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 2 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 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 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 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;—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> 9·3</sup><i>v</i><sup>1·85</sup><br /> +<i>f</i> = 0·00000778<i>l</i><sup> 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. 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