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diff --git a/41135-0.txt b/41135-0.txt new file mode 100644 index 0000000..e3e9c5d --- /dev/null +++ b/41135-0.txt @@ -0,0 +1,8150 @@ +*** START OF THE PROJECT GUTENBERG EBOOK 41135 *** + +[Illustration: THE MOST IMPORTANT "TOOL" IN THE BUILDING OF MODEL +AEROPLANES. + +[_Illustration by permission from_ MESSRS. A. GALLENKAMP & CO'S. +CHEMICAL CATALOGUE.]] + + + + + THE THEORY AND PRACTICE + OF + MODEL AEROPLANING + + BY + V.E. JOHNSON, M.A. + + AUTHOR OF + 'THE BEST SHAPE FOR AN AIRSHIP,' 'SOARING FLIGHT,' + 'HOW TO ADVANCE THE SCIENCE OF AERONAUTICS,' + 'HOW TO BUILD A MODEL AEROPLANE,' ETC. + + "Model Aeroplaning is an Art in itself" + + [Illustration] + + London + E. & F.N. SPON, LTD., 57 HAYMARKET + + New York + SPON & CHAMBERLAIN, 123 LIBERTY STREET + + 1910 + + + + +PREFACE + + +The object of this little book is not to describe how to construct +some particular kind of aeroplane; this has been done elsewhere: but +to narrate in plain language the general practice and principles of +model aeroplaning. + +There is a _science_ of model aeroplaning--just as there is a science +of model yachting and model steam and electric traction, and an +endeavour is made in the following pages to do in some measure for +model aeroplanes what has already been done for model yachts and +locomotives. To achieve the best results, theory and practice must go +hand in hand. + +From a series of carefully conducted experiments empirical formulæ can +be obtained which, combined later with mathematical induction and +deduction, may lead, not only to a more accurate and generalized law +than that contained in the empirical formula, but to valuable +deductions of a totally new type, embodying some general law hitherto +quite unknown by experimentalists, which in its turn may serve as a +foundation or stepping stone for suggesting other experiments and +empirical formulæ which may be of especial importance, to be treated +in _their_ turn like their predecessor. By "especial importance," I +mean not only to "model," but "Aeroplaning" generally. + +As to the value of experiments on or with models with respect to +full-sized machines, fifteen years ago I held the opinion that they +were a very doubtful factor. I have since considerably modified that +view, and now consider that experiments with models--if properly +carried out, and given due, not _undue_, weight--both can and will be +of as much use to the science of Aeronautics as they have already +proved themselves to be in that of marine engineering. + +The subject of model propellers and motors has been somewhat fully +dealt with, as but little has been published (in book form, at any +rate) on these all-important departments. On similar grounds the +reasons why and how a model aeroplane flies have been practically +omitted, because these have been dealt with more or less in every book +on heavier-than-air machines. + +Great care has been exercised in the selection of matter, and in the +various facts stated herein; in most cases I have personally verified +them; great pains have also been exercised to exclude not only +misleading, but also doubtful matter. I have no personal axe to grind +whatever, nor am I connected either directly or indirectly with any +firm of aeroplane builders, model or otherwise. + +The statements contained in these pages are absolutely free from bias +of any kind, and for them I am prepared to accept full responsibility. + +I have to thank Messrs. A.W. GAMAGE (Holborn) for the use of various +model parts for testing purposes, and also for the use of various +electros from their modern Aviation Catalogue; also Messrs. T.W.K. +CLARKE & CO., of Kingston-on-Thames. For the further use of electros, +and for permission to reproduce illustrations which have previously +appeared in their papers, I must express my acknowledgment and thanks +to the publishers of the "Model Engineer," "Flight," and the "Aero." +Corrections and suggestions of any kind will be gratefully received, +and duly acknowledged. + + V.E. JOHNSON. + + + + +CONTENTS + + + INTRODUCTION. + PAGE + + §§ 1-5. The two classes of models--First requisite of a model + aeroplane. § 6. An art in itself. § 7. The leading principle 1 + + + CHAPTER I. + + THE QUESTION OF WEIGHT. + + §§ 1-2. Its primary importance both in rubber and + power-driven models--Professor Langley's experiences. § 3. + Theoretical aspect of the question. § 4. Means whereby more + weight can be carried--How to obtain maximum strength with + minimum weight. § 5. Heavy models versus light ones 4 + + + CHAPTER II. + + THE QUESTION OF RESISTANCE. + + § 1. The chief function of a model in the medium in which it + travels. § 2. Resistance considered as load percentage. § 3. + How made up. § 4. The shape of minimum resistance. § 5. The + case of rubber-driven models. § 6. The aerofoil + surface--Shape and material as affecting this question. § 7. + Skin friction--Its coefficient. § 8. Experimental proofs of + its existence and importance 7 + + + CHAPTER III. + + THE QUESTION OF BALANCE. + + § 1. automatic stability essential in a flying model. § 2. + theoretical researches on this question. §§ 3-6. a brief + summary of the chief conclusions arrived at--remarks on and + deductions from the same--conditions for automatic stability. + § 7. theory and practice--stringfellow--pénaud--tatin--the + 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 13 + + + CHAPTER IV. + + THE MOTIVE POWER. + + SECTION I.--RUBBER MOTORS. + + § 1. Some experiments with rubber cord. § 2. Its extension + under various weights. § 3. The laws of elongation + (stretching)--Permanent set. § 4. Effects of elongation on + its volume. § 5. "Stretched-twisted" rubber cord--Torque + experiments with rubber strands of varying length 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. + § 12A. Action of water, etc. § 12B. How to preserve rubber. + § 13. To test rubber. § 14. The shape of the section. § 15. + Size of section. § 16. Geared rubber motors. § 17. The only + system worth consideration--Its practical difficulties. § 18. + Its advantages 24 + + SECTION II.--OTHER FORMS OF MOTORS. + + § 18A. _Spring motors_; their inferiority to rubber. § 18B. + The most efficient form of spring motor. § 18C. _Compressed + air motors_--A fascinating form of motor, "on paper." § 18D. + The pneumatic drill--Application to a model aeroplane--Length + of possible flight. § 18E. The pressure in motor-car tyres. + § 19. Hargraves' compressed air models--The best results + compared with rubber motors. § 20. The effect of heating the + air in its passage from the reservoir to the motor--The great + gain in efficiency thereby attained--Liquid air--Practical + drawbacks to the compressed-air motor. § 21. Reducing + valves--Lowest working pressure. § 22. The inferiority of + this motor compared with the steam engine. § 22A. Tatin's + air-compressed motor. § 23. _Steam engine_--Steam engine + model--Professor Langley's models--His experiment with + various forms of motive power--Conclusions arrived at. § 24. + His steam engine models--Difficulties and failures--and final + success--The "boiler" the great difficulty--His model + described. § 25. The use of spirit or some very volatile + hydrocarbon in the place of water. § 26. Steam turbines. + § 27. Relation between "difficulty in construction" and the + "size of the model." § 28. Experiments in France. § 29. + _Petrol motors._--But few successful models. § 30. Limit to + size. § 31. Stanger's successful model described and + illustrated. § 32. One-cylinder petrol motors. § 33. + _Electric motors_ 39 + + + CHAPTER V. + + PROPELLERS OR SCREWS. + + § 1. The position of the propeller. § 2. The number of + blades. § 3. Fan _versus_ propeller. § 4. The function of a + propeller. § 5. The pitch. § 6. Slip. § 7. Thrust. § 8. Pitch + coefficient (or ratio). § 9. Diameter. § 10. Theoretical + pitch. § 11. Uniform pitch. § 12. How to ascertain the pitch + of a propeller. § 13. Hollow-faced blades. § 14. Blade area. + § 15. Rate of rotation. § 16. Shrouding. § 17. General + design. § 18. The shape of the blades. § 19. Their general + contour--Propeller design--How to design a propeller. § 20. + Experiments with propellers--Havilland's design for + experiments--The author experiments on dynamic thrust and + model propellers generally. § 21. Fabric-covered screws. + § 22. Experiments with twin propellers. § 23. The Fleming + Williams propeller. § 24. Built-up _v._ twisted wooden + propellers 52 + + + CHAPTER VI. + + THE QUESTION OF SUSTENTATION. + THE CENTRE OF PRESSURE. + + § 1. The centre of pressure--Automatic stability. § 2. + Oscillations. § 3. Arched surfaces and movements of the + centre of pressure--Reversal. § 4. The centre of gravity and + the centre of pressure. § 5. Camber. § 6. Dipping front + 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 78 + + + CHAPTER VII. + + MATERIALS FOR AEROPLANE + CONSTRUCTION. + + § 1. The choice strictly limited. § 2. Bamboo. § 3. + Ash--spruce-- whitewood--poplar. § 4. Steel. § 5. Umbrella + section steel. § 6. Steel wire. § 7. Silk. § 8. Aluminium and + magnalium. § 9. Alloys. § 10. Sheet ebonite--Vulcanized + fibre--Sheet celluloid--Mica 86 + + + CHAPTER VIII. + + HINTS ON THE BUILDING OF MODEL + AEROPLANES. + + § 1. The chief difficulty to overcome. § 2. General + design--The principle of continuity. § 3. Simple monoplane. + § 4. Importance of soldering. § 5. Things to avoid. § 6. + Aerofoil of metal--wood--or fabric. § 7. Shape of aerofoil. + § 8. How to camber an aerocurve without ribs. § 9. Flexible + joints. § 10. Single surfaces. § 11. The rod or tube carrying + the rubber motor. § 12. Position of the rubber. § 13. The + position of the centre of pressure. § 14. Elevators and + tails. § 15. Skids _versus_ wheels--Materials for skids. + § 16. Shock absorbers, how to attach--Relation between the + "gap" and the "chord" 93 + + + CHAPTER IX. + + THE STEERING OF THE MODEL. + + § 1. A problem of great difficulty--Effects of propeller + torque. § 2. How obviated. § 3. The two-propeller + solution--The reason why it is only a partial success. § 4. + The _speed_ solution. § 5. Vertical fins. § 6. Balancing tips + or ailerons. § 7. Weighting. § 8. By means of transversely + canting the elevator. § 9. The necessity for some form of + "keel" 105 + + + CHAPTER X. + + THE LAUNCHING OF THE MODEL. + + § 1. The direction in which to launch them. § 2. The + velocity--wooden aerofoils and fabric-covered + aerofoils--Poynter's launching apparatus. § 3. The launching + of very light models. § 4. Large size and power-driven + models. § 5. Models designed to rise from the + ground--Paulhan's prize model. § 6. The setting of the + elevator. § 7. The most suitable propeller for this form of + model. § 8. Professor Kress' method of launching. § 9. How to + launch a twin screw model. § 10. A prior revolution of the + propellers. § 11. The best angle at which to launch a model 109 + + + CHAPTER XI. + + HELICOPTER MODELS. + + § 1. Models quite easy to make. § 2. Sir George Cayley's + helicopter model. § 3. Phillips' successful power-driven + model. § 4. Toy helicopters. § 5. Incorrect and correct way + of arranging the propellers. § 6. Fabric covered screws. § 7. + A design to obviate weight. § 8. The question of a fin or + keel. 113 + + + CHAPTER XII. + + EXPERIMENTAL RECORDS 116 + + + CHAPTER XIII. + + MODEL FLYING COMPETITIONS. + + § 1. A few general details concerning such. § 2. Aero Models + Association's classification, etc. § 3. Various points to be + kept in mind when competing 119 + + + CHAPTER XIV. + + USEFUL NOTES, TABLES, FORMULÆ, ETC. + + § 1. Comparative velocities. § 2. Conversions. § 3. Areas of + various shaped surfaces. § 4. French and English measures. + § 5. Useful data. § 6. Table of equivalent inclinations. § 7. + Table of skin friction. § 8. Table I. (metals). § 9. Table + II. (wind pressures). § 10. Wind pressure on various shaped + bodies. § 11. Table III. (lift and drift) on a cambered + surface. § 12. Table IV. (lift and drift)--On a plane + aerofoil--Deductions. § 13. Table V. (timber). § 14. Formula + connecting weight lifted and velocity. § 15. Formula + 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. + § 30A. Relation between static thrust of propeller and total + weight of model. § 31. How to find the height of an + inaccessible object (kite, balloon, etc.). § 32. Formula for + I.H.P. of model steam engines 125 + + APPENDIX A. Some models which have won medals at open + competitions 143 + + + + +GLOSSARY OF TERMS USED IN MODEL AEROPLANING. + + +_Aeroplane._ A motor-driven flying machine which relies upon surfaces +for its support in the air. + +_Monoplane_ (single). An aeroplane with one pair of outstretched +wings. + +_Aerofoil._ These outstretched wings are often called aerofoil +surfaces. One pair of wings forming one aerofoil surface. + +_Monoplane_ (double). An aeroplane with two aerofoils, one behind the +other or two main planes, tandem-wise. + +_Biplane._ An aeroplane with two aerofoils, one below the other, or +having two main planes superposed. + +_Triplane._ An aeroplane having three such aerofoils or three such +main planes. + +_Multiplane._ Any such machine having more than three of the above. + +_Glider._ A motorless aeroplane. + +_Helicopter._ A flying machine in which propellers are employed to +raise the machine in the air by their own unaided efforts. + +_Dihedral Angle._ A dihedral angle is an angle made by two surfaces +that do not lie in the same plane, i.e. when the aerofoils are +arranged V-shaped. It is better, however, to somewhat extend this +definition, and not to consider it as necessary that the two surfaces +_do_ actually meet, but would do so if produced thus in figure. BA and +CD are still dihedrals, sometimes termed "upturned tips." + +[Illustration: Dihedrals.] + +_Span_ is the distance from tip to tip of the main supporting surface +measured transversely (across) the line of flight. + +_Camber_ (a slight arching or convexity upwards). This term denotes +that the aerofoil has such a curved transverse section. + +_Chord_ is the distance between the entering (or leading) edge of the +main supporting surface (aerofoil) and the trailing edge of the same; +also defined as the fore and aft dimension of the main planes measured +in a straight line between the leading and trailing edges. + + span + _Aspect Ratio_ is ----- + chord + +_Gap_ is the vertical distance between one aerofoil and the one which +is immediately above it. + +(The gap is usually made equal to the chord). + +_Angle of Incidence._ The angle of incidence is the angle made by the +chord with the line of flight. + +[Illustration: + + AB = chord. AB = cambered surface. + SP = line of flight. ASP = {alpha} = L of incidence.] + +_Width._ The width of an aerofoil is the distance from the front to +the rear edge, allowing for camber. + +_Length._ This term is usually applied to the machine as a whole, from +the front leading edge of elevator (or supports) to tip of tail. + +_Arched._ This term is usually applied to aerofoil surfaces which dip +downwards like the wings of a bird. The curve in this case being at +right angles to "camber." A surface can, of course, be both cambered +and arched. + +_Propeller._ A device for propelling or pushing an aeroplane forward +or for raising it vertically (lifting screw). + +_Tractor Screw._ A device for pulling the machine (used when the +propeller is placed in the front of the machine). + +_Keel._ A vertical plane or planes (usually termed "fins") arranged +longitudinally for the purposes of stability and steering. + +_Tail._ The plane, or group of planes, at the rear end of an +aeroplane for the purpose chiefly of giving longitudinal stability. In +such cases the tail is normally (approx.) horizontal, but not +unfrequently vertical tail-pieces are fitted as well for steering +(transversely) to the right or left, or the entire tail may be twisted +for the purpose of transverse stability (vide _Elevator_). Such +appendages are being used less and less with the idea of giving actual +support. + +_Rudder_ is the term used for the vertical plane, or planes, which are +used to steer the aeroplane sideways. + +_Warping._ The flexing or bending of an aerofoil out of its normal +shape. The rear edges near the tips of the aerofoil being dipped or +tilted respectively, in order to create a temporary difference in +their inclinations to the line of flight. Performed in conjunction +with rudder movements, to counteract the excessive action of the +latter. + +_Ailerons_ (also called "righting-tips," "balancing-planes," etc.). +Small aeroplanes in the vicinity of the tips of the main aerofoil for +the purpose of assisting in the maintenance of equilibrium or for +steering purposes either with or without the assistance of the rudder. + +_Elevator._ The plane, or planes, in front of the main aerofoil used +for the purpose of keeping the aeroplane on an even keel, or which +cause (by being tilted or dipped) the aeroplane to rise or fall (vide +_Tail_). + + + + +MODEL AEROPLANING + + + + +INTRODUCTION. + + +§ 1. Model Aeroplanes are primarily divided into two classes: first, +models intended before all else to be ones that shall _fly_; secondly, +_models_, using the word in its proper sense of full-sized machines. +Herein model aeroplanes differ from model yachts and model +locomotives. An extremely small model locomotive _built to scale_ will +still _work_, just as a very small yacht built to scale will _sail_; +but when you try to build a scale model of an "Antoinette" monoplane, +_including engine_, it cannot be made to fly unless the scale be a +very large one. If, for instance, you endeavoured to make a 1/10 scale +model, your model petrol motor would be compelled to have eight +cylinders, each 0·52 bore, and your magneto of such size as easily to +pass through a ring half an inch in diameter. Such a model could not +possibly work.[1] + + _Note._--Readers will find in the "Model Engineer" of June 16, + 1910, some really very fine working drawings of a prize-winning + Antoinette monoplane model. + +§ 2. Again, although the motor constitutes the _chief_, it is by no +means the sole difficulty in _scale_ model aeroplane building. To +reproduce to scale at _scale weight_, or indeed anything approaching it, +_all_ the _necessary_--in the case of a full-sized machine--framework is +not possible in a less than 1/5 scale. + +§ 3. Special difficulties occur in the case of any prototype taken. +For instance, in the case of model Blériots it is extremely difficult +to get the centre of gravity sufficiently forward. + +§ 4. Scale models of actual flying machines _that will fly_ mean +models _at least_ 10 or 12 feet across, and every other dimension in +like proportion; and it must always be carefully borne in mind that +the smaller the scale the greater the difficulties, but not in the +same proportion--it would not be _twice_ as difficult to build a +¼-in. scale model as a ½-in., but _four_, _five_ or _six_ times as +difficult. + +§ 5. Now, the _first_ requirement of a model aeroplane, or flying +machine, is that it shall FLY. + +As will be seen later on--unless the machine be of large size, 10 feet +and more spread--the only motor at our disposal is the motor of +twisted rubber strands, and this to be efficient requires to be long, +and is of practically uniform weight throughout; this alone alters the +entire _distribution of weight_ on the machine and makes: + +§ 6. "=Model Aeroplaning an Art in itself=," and as such we propose to +consider it in the following pages. + +We have said that the first requisite of a model aeroplane is that it +shall fly, but there is no necessity, nor is it indeed always to be +desired, that this should be its only one, unless it be built with the +express purpose of obtaining a record length of flight. For ordinary +flights and scientific study what is required is a machine in which +minute detail is of secondary importance, but which does along its +main lines "_approximate_ to the real thing." + +§ 7. Simplicity should be the first thing aimed at--simplicity means +efficiency, it means it in full-sized machines, still more does it +mean it in models--and this very question of simplicity brings us to +that most important question of all, namely, the question of _weight_. + +FOOTNOTE: + +[1] The smallest working steam engine that the writer has ever heard +of has a net weight of 4 grains. One hundred such engines would be +required to weigh one ounce. The bore being 0·03 in., and stroke 1/32 +of an inch, r.p.m. 6000 per min., h.p. developed 1/489000 ("Model +Engineer," July 7, 1910). When working it hums like a bee. + + + + +CHAPTER I. + +THE QUESTION OF WEIGHT. + + +§ 1. The following is an extract from a letter that appeared in the +correspondence columns of "The Aero."[2] + +"To give you some idea how slight a thing will make a model behave +badly, I fitted a skid to protect the propeller underneath the +aeroplane, and the result in retarding flight could be seen very +quickly, although the weight of the skid was almost nil.[3] To all +model makers who wish to make a success I would say, strip all that +useless and heavy chassis off, cut down the 'good, honest stick' that +you have for a backbone to half its thickness, stay it with wire if it +bends under the strain of the rubber, put light silk on the planes, +and use an aluminium[4] propeller. The result will surpass all +expectations." + +§ 2. The above refers, of course, to a rubber-motor driven model. Let +us turn to a steam-driven prototype. I take the best known example of +all, Professor Langley's famous model. Here is what the professor has +to say on the question[5]:-- + +"Every bit of the machinery had to be constructed with scientific +accuracy. It had to be tested again and again. The difficulty of +getting the machine light enough was such that every part of it had to +be remade several times. It would be in full working order when +something would give way, and this part would have to be strengthened. +This caused additional weight, and necessitated cutting off so much +weight from some other part of the machinery. At times the difficulty +seemed almost heartbreaking; but I went on, piece by piece and atom by +atom, until I at last succeeded in getting all the parts of the right +strength and proportion." + +How to obtain the maximum strength with the minimum of weight is one +of the, if not the most, difficult problems which the student has to +solve. + +§ 3. The theoretical reason why _weight_ is such an all-important item +in model aeroplaning, much more so than in the case of full-size +machines, is that, generally speaking, such models do not fly fast +enough to possess a high weight carrying capacity. If you increase the +area of the supporting surface you increase also the resistance, and +thereby diminish the speed, and are no better off than before. The +only way to increase the weight carrying capacity of a model is to +increase its speed. This point will be recurred to later on. One of +Mr. T.W.K. Clarke's well-known models, surface area 1¼ sq. ft., +weight 1¼ lb., is stated to have made a flight of 300 yards +carrying 6 oz. of lead. This works out approximately at 21 oz. per sq. +ft. + +The velocity (speed) is not stated, but some earlier models by the +same designer, weight 1½ lb., supporting area 1½ sq. ft., i.e., +at rate of 16 oz. per sq. ft., travelled at a rate of 37 ft. per +second, or 25 miles an hour. + +The velocity of the former, therefore, would certainly not be less +than 30 miles an hour. + +§ 4. Generally speaking, however, models do not travel at anything +like this velocity, or carry anything like this weight per sq. ft. + +An average assumption of 13 to 15 miles an hour does nor err on the +minimum side. Some very light fabric covered models have a speed of +less than even 10 miles an hour. Such, of course, cannot be termed +efficient models, and carry only about 3 oz. per sq. ft. Between these +two types--these two extremes--somewhere lies the "Ideal Model." + +The maximum of strength with the minimum of weight can be obtained +only:-- + +1. By a knowledge of materials. + +2. Of how to combine those materials in a most efficient and skilful +manner. + +3. By a constant use of the balance or a pair of scales, and noting +(in writing) the weight and result of every trial and every experiment +in the alteration and change of material used. WEIGH EVERYTHING. + +§ 5. The reader must not be misled by what has been said, and think +that a model must not weigh anything if it is to fly well. A heavy +model will fly much better against the wind than a light one, provided +that the former _will_ fly. To do this it must fly _fast_. To do this +again it must be well powered, and offer the minimum of resistance to +the medium through which it moves. This means its aerofoil +(supporting) surfaces must be of polished wood or metal. This point +brings us to the question of Resistance, which we will now consider. + +FOOTNOTES: + +[2] "Aero," May 3, 1910. + +[3] Part of this retardation was, of course, "increased resistance." + +[4] Personally I do not recommend aluminium.--V.E.J. + +[5] "Aeronautical Journal," January 1897, p. 7. + + + + +CHAPTER II. + +THE QUESTION OF RESISTANCE. + + +§ 1. It is, or should be, the function of an aeroplane--model or +otherwise--to pass through the medium in which it travels in such a +manner as to leave that medium in as motionless a state as possible, +since all motion of the surrounding air represents so much power +wasted. + +Every part of the machine should be so constructed as to move through +the air with the minimum of disturbance and resistance. + +§ 2. The resistance, considered as a percentage of the load itself, +that has to be overcome in moving a load from one place to another, +is, according to Mr. F.W. Lanchester, 12½ per cent. in the case of +a flying machine, and 0·1 per cent. in the case of a cargo boat, and +of a solid tyre motor car 3 per cent., a locomotive 1 per cent. Four +times at least the resistance in the case of aerial locomotion has to +be overcome to that obtained from ordinary locomotion on land. The +above refer, of course, to full-sized machines; for a model the +resistance is probably nearer 14 or 15 per cent. + +§ 3. This resistance is made up of-- + + 1. Aerodynamic resistance. + 2. Head resistance. + 3. Skin-friction (surface resistance). + +The first results from the necessity of air supporting the model +during flight. + +The second is the resistance offered by the framework, wires, edges of +aerofoils, etc. + +The third, skin-friction or surface resistance, is very small at low +velocities, but increases as the square of the velocity. To reduce the +resistance which it sets up, all surfaces used should be as smooth as +possible. To reduce the second, contours of ichthyoid, or fish-like, +form should be used, so that the resultant stream-line flow of the +medium shall keep in touch with the surface of the body. + +§ 4. As long ago as 1894 a series of experiments were made by the +writer[6] to solve the following problem: given a certain length and +breadth, to find the shape which will offer the least resistance. The +experiments were made with a whirling table 40 ft. in diameter, which +could be rotated so that the extremity of the arm rotated up to a +speed of 45 miles an hour. The method of experimenting was as follows: +The bodies (diam. 4 in.) were balanced against one another at the +extremity of the arm, being so balanced that their motions forward and +backward were parallel. Provision was made for accurately balancing +the parallel scales on which the bodies were suspended without +altering the resistance offered by the apparatus to the air. Two +experiments at least (to avoid error) were made in each case, the +bodies being reversed in the second experiment, the top one being put +at the bottom, and _vice versa_. The conclusions arrived at were:-- + +For minimum (head) resistance a body should have-- + +1. Its greatest diameter two-fifths of its entire length from its +head. + +2. Its breadth and its depth in the proportion of four to three. + +3. Its length at least from five to nine times its greatest breadth +(nine being better than five). + +4. A very tapering form of stern, the actual stern only being of just +sufficient size to allow of the propeller shaft passing through. In +the case of twin propellers some slight modification of the stern +would be necessary. + +5. Every portion of the body in contact with the fluid to be made as +smooth as possible. + +6. A body of such shape gives at most only _one-twentieth_ the +resistance offered by a flat disk of similar maximum sectional area. + +_Results since fully confirmed._ + +[Illustration: FIG. 1.--SHAPE OF LEAST RESISTANCE.] + +The design in Fig. 2 is interesting, not only because of its probable +origin, but because of the shape of the body and arrangement of the +propellers; no rudder is shown, and the long steel vertical mast +extending both upwards and downwards through the centre would render +it suitable only for landing on water. + +§ 5. In the case of a rubber-driven model, there is no containing body +part, so to speak, a long thin stick, or tubular construction if +preferred, being all that is necessary. + +The long skein of elastic, vibrating as well as untwisting as it +travels with the machine through the air, offers some appreciable +resistance, and several experimenters have _enclosed_ it in a light +tube made of _very thin_ veneer wood rolled and glued, or paper even +may be used; such tubes can be made very light, and possess +considerable rigidity, especially longitudinally. If the model be a +biplane, then all the upright struts between the two aerofoils should +be given a shape, a vertical section of which is shown in Fig. 3. + +§ 6. In considering this question of resistance, the substance of +which the aerofoil surface is made plays a very important part, as +well as whether that surface be plane or curved. For some reason not +altogether easy to determine, fabric-covered planes offer +_considerably_ more resistance than wooden or metal ones. That they +should offer _more_ resistance is what common sense would lead one to +expect, but hardly to the extent met with in actual practice. + +[Illustration: FIG. 2.--DESIGN FOR AN AEROPLANE MODEL (POWER DRIVEN). + +This design is attributed to Professor Langley.] + +_Built up fabric-covered aeroplanes[7] gain in lightness, but lose in +resistance._ In the case of curved surfaces this difference is +considerably more; one reason, undoubtedly, is that in a built up +model surface there is nearly always a tendency to make this curvature +excessive, and much more than it should be. Having called attention to +this under the head of resistance, we will leave it now to recur to it +later when considering the aerofoil proper. + +[Illustration: FIG. 3.--HORIZONTAL SECTION OF VERTICAL STRUT +(ENLARGED.)] + +§ 7. Allusion has been made in this chapter to skin friction, but no +value given for its coefficient.[8] Lanchester's value for planes from +½ to 1½ sq. ft. in area, moving about 20 to 30 ft. per second, is + + 0·009 to 0·015. + +Professor Zahm (Washington) gives 0·0026 lb. per sq. ft. at 25 ft. per +second, and at 37 ft. per second, 0·005, and the formula + + _f_ = 0·00000778_l_^{·93}_v_^{1·85} + +_f_ being the average friction in lb. per sq. in., _l_ the length in +feet, and _v_ the velocity in ft. per second. He also experimented +with various kinds of surfaces, some rough, some smooth, etc. + +His conclusion is:--"All even surfaces have approximately the same +coefficient of skin friction. Uneven surfaces have a greater +coefficient." All formulæ on skin friction must at present be accepted +with reserve. + +§ 8. The following three experiments, however, clearly prove its +_existence_, and _that it has considerable effect_:-- + +1. A light, hollow celluloid ball, supported on a stream of air +projected upwards from a jet, rotates in one direction or the other as +the jet is inclined to the left or to the right. (F.W. Lanchester.) + +2. When a golf ball (which is rough) is hit so as to have considerable +underspin, its range is increased from 135 to 180 yards, due entirely +to the greater frictional resistance to the air on that side on which +the whirl and the progressive motion combine. (Prof. Tait.) + +3. By means of a (weak) bow a golf ball can be made to move point +blank to a mark 30 yards off, provided the string be so adjusted as to +give a good underspin; adjust the string to the centre of the ball, +instead of catching it below, and the drop will be about 8 ft. (Prof. +Tait.) + +FOOTNOTES: + +[6] _Vide_ "Invention," Feb. 15, 22, and 29, 1896. + +[7] Really aerofoils, since we are considering only the supporting +surface. + +[8] I.e., to express it as a decimal fraction of the resistance, +encountered by the same plane when moving "face" instead of "edge" on. + + + + +CHAPTER III. + +THE QUESTION OF BALANCE. + + +§ 1. It is perfectly obvious for successful flight that any model +flying machine (in the absence of a pilot) must possess a high degree +of automatic stability. The model must be so constructed as to be +naturally stable, _in the medium through which it is proposed to drive +it_. The last remark is of the greatest importance, as we shall see. + +§ 2. In connexion with this same question of automatic stability, the +question must be considered from the theoretical as well as from the +practical side, and the labours and researches of such men as +Professors Brian and Chatley, F.W. Lanchester, Captain Ferber, +Mouillard and others must receive due weight. Their work cannot yet be +fully assessed, but already results have been arrived at far more +important than are generally supposed. + +The following are a few of the results arrived at from theoretical +considerations; they cannot be too widely known. + +(A) Surfaces concave on the under side are not stable unless some form +of balancing device (such as a tail, etc.) is used. + +(B) If an aeroplane is in equilibrium and moving uniformly, it is +necessary for stability that it shall tend towards a condition of +equilibrium. + +(C) In the case of "oscillations" it is absolutely necessary for +stability that these oscillations shall decrease in amplitude, in +other words, be damped out. + +(D) In aeroplanes in which the dihedral angle is excessive or the +centre of gravity very low down, a dangerous pitching motion is quite +likely to be set up. [Analogy in shipbuilding--an increase in the +metacentre height while increasing the stability in a statical sense +causes the ship to do the same.] + +(E) The propeller shaft should pass through the centre of gravity of +the machine. + +(F) The front planes should be at a greater angle of inclination than +the rear ones. + +(G) The longitudinal stability of an aeroplane grows much less when +the aeroplane commences to rise, a monoplane becoming unstable when +the angle of ascent is greater than the inclination of the main +aerofoil to the horizon. + +(H) Head resistance increases stability. + +(I) Three planes are more stable than two. [Elevator--main +aerofoil--horizontal rudder behind.] + +(J) When an aeroplane is gliding (downwards) stability is greater than +in horizontal flight. + +(K) A large moment of inertia is inimical (opposed) to stability. + +(M) Aeroplanes (naturally) stable up to a certain velocity (speed) may +become unstable when moving beyond that speed. [Possible explanation. +The motion of the air over the edges of the aerofoil becomes +turbulent, and the form of the stream lines suddenly changes. +Aeroplane also probably becomes deformed.] + +(N) In a balanced glider for stability a separate surface at a +negative angle to the line of flight is essential. [Compare F.] + +(O) A keel surface should be situated well above and behind the centre +of gravity. + +(P) An aeroplane is a conservative system, and stability is greatest +when the kinetic energy is a maximum. [Illustration, the pendulum.] + +§ 3. Referring to A. Models with a plane or flat surface are not +unstable, and will fly well without a tail; such a machine is called a +simple monoplane. + +[Illustration: FIG. 4.--ONE OF MR. BURGE WEBB'S SIMPLE MONOPLANES. + +Showing balance weight A (movable), and also his winding-up gear--a +very handy device.] + + +§ 4. Referring to D. Many model builders make this mistake, i.e., the +mistake of getting as low a centre of gravity as possible under the +quite erroneous idea that they are thereby increasing the stability of +the machine. Theoretically the _centre of gravity should be the centre +of head resistance, as also the centre of pressure_. + +In practice some prefer to put the centre of gravity in models +_slightly_ above the centre of head resistance, the reason being that, +generally speaking, wind gusts have a "lifting" action on the machine. +It must be carefully borne in mind, however, that if the centre of +wind pressure on the aerofoil surface and the centre of gravity do not +coincide, no matter at what point propulsive action be applied, it can +be proved by quite elementary mechanics that such an arrangement, +known as "acentric," produces a couple tending to upset the machine. + +This action is the probable cause of many failures. + +[Illustration: FIG. 5.--THE STRINGFELLOW MODEL MONOPLANE OF 1848.] + +§ 5. Referring to E. If the propulsive action does not pass through +the centre of gravity the system again becomes "acentric." Even +supposing condition D fulfilled, and we arrive at the following most +important result, viz., that for stability:-- + +THE CENTRES OF GRAVITY, OF PRESSURE, OF HEAD RESISTANCE, SHOULD BE +COINCIDENT, AND THE PROPULSIVE ACTION OF THE PROPELLER PASS THROUGH +THIS SAME POINT. + +[Illustration: FIG. 6.--THE STRINGFELLOW MODEL TRIPLANE OF 1868.] + +§ 6. Referring to F and N--the problem of longitudinal stability. +There is one absolutely essential feature not mentioned in F or N, and +that is for automatic longitudinal stability _the two surfaces, the +aerofoil proper and the balancer_ (elevator or tail, or both), _must +be separated by some considerable distance, a distance not less than +four times the width of the main aerofoil_.[9] More is better. + +[Illustration: FIG. 7. _PÉNAUD 1871_] + +§ 7. With one exception (Pénaud) early experimenters with model +aeroplanes had not grasped this all-important fact, and their models +would not fly, only make a series of jumps, because they failed to +balance longitudinally. In Stringfellow's and Tatin's models the main +aerofoil and balancer (tail) are practically contiguous. + +Pénaud in his rubber-motored models appears to have fully realised +this (_vide_ Fig. 7), and also the necessity for using long strands of +rubber. Some of his models flew 150 ft., and showed considerable +stability. + +[Illustration: FIG. 8.--TATIN'S AEROPLANE (1879). + +Surface 0·7 sq. metres, total weight 1·75 kilogrammes, velocity of +sustentation 8 metres a second. Motor, compressed air (for description +see § 23, ch. iv). Revolved round and round a track tethered to a post +at the centre. In one of its jumps it cleared the head of a +spectator.] + +With three surfaces one would set the elevator at a slight plus angle, +main aerofoil horizontal (neither positive nor negative), and the tail +at a corresponding negative angle to the positive one of the elevator. + +Referring to O.[10] One would naturally be inclined to put a keel +surface--or, in other words, vertical fins--beneath the centre of +gravity, but D shows us this may have the opposite effect to what we +might expect. + +In full-sized machines, those in which the distance between the main +aerofoil and balancers is considerable (like the Farman) show +considerable automatic longitudinal stability, and those in which it +is short (like the Wright) are purposely made so with the idea of +doing away with it, and rendering the machine quicker and more +sensitive to personal control. In the case of the Stringfellow and +Tatin models we have the extreme case--practically the bird entirely +volitional and personal--which is the opposite in every way to what we +desire on a model under no personal or volitional control at all. + +[Illustration: FIG. 9.--CLARK'S MODEL FLYER. + +Main aerofoil set at a slight negative angle. Dihedral angles on both +aerofoils.] + +The theoretical conditions stated in F and N are fully borne out in +practice. + +And since a curved aerofoil even when set at a _slight_ negative +angle has still considerable powers of sustentation, it is possible to +give the main aerofoil a slight negative angle and the elevator a +slight positive one. This fact is of the greatest importance, since it +enables us to counteract the effect of the travel of the "centre of +pressure."[11] + +[Illustration: FIG. 10.--LARGE MODEL MONOPLANE. + +Designed and constructed by the author, with vertical fin (no dihedral +angle). With a larger and more efficient propeller than the one here +shown some excellent flights were obtained. Constructed of bamboo and +nainsook. Stayed with steel wire.] + +§ 8. Referring to I. This, again, is of primary importance in +longitudinal stability. The Farman machine has three such +planes--elevator, main aerofoil, tail the Wright originally had _not_, +but is now being fitted with a tail, and experiments on the +Short-Wright biplane have quite proved its stabilising efficiency. + +The three plane (triple monoplane) in the case of models has been +tried, but possesses no advantage so far over the double monoplane +type. The writer has made many experiments with vertical fins, and has +found the machine very stable, even when the fin or vertical keel is +placed some distance above the centre of gravity. + +§ 9. The question of transverse (side to side) stability at once +brings us to the question of the dihedral angle, practically similar +in its action to a flat plane with vertical fins. + +[Illustration: FIG. 11.--SIR GEORGE CAYLEY'S FLYING MACHINE. + +Eight feathers, two corks, a thin rod, a piece of whalebone, and a +piece of thread.] + +§ 10. The setting up of the front surface at an angle to the rear, or +the setting of these at corresponding compensatory angles already +dealt with, is nothing more nor less than the principle of the +dihedral angle for longitudinal stability. + +[Illustration: FIG. 12.--VARIOUS FORMS OF DIHEDRALS.] + +As early as the commencement of last century Sir George Cayley (a +man more than a hundred years ahead of his times) was the first to +point out that two planes at a dihedral angle constitute a basis of +stability. For, on the machine heeling over, the side which is +required to rise gains resistance by its new position, and that which +is required to sink loses it. + +§ 11. The dihedral angle principle may take many forms. + +As in Fig. 12 _a_ is a monoplane, the rest biplanes. The angles and +curves are somewhat exaggerated. It is quite a mistake to make the +angle excessive, the "lift" being thereby diminished. A few degrees +should suffice. + +Whilst it is evident enough that transverse stability is promoted by +making the sustaining surface trough-shaped, it is not so evident what +form of cross section is the most efficient for sustentation and +equilibrium combined. + +[Illustration: FIG. 13.] + +It is evident that the righting moment of a unit of surface of an +aeroplane is greater at the outer edge than elsewhere, owing to the +greater lever arm. + +§ 12. The "upturned tip" dihedral certainly appears to have the +advantage. + +_The outer edges of the aerofoil then should be turned upward for the +purpose of transverse stability, while the inner surface should remain +flat or concave for greater support._ + +§ 13. The exact most favourable outline of transverse section for +stability, steadiness and buoyancy has not yet been found; but the +writer has found the section given in Fig. 13, a very efficient one. + +FOOTNOTES: + +[9] If the width be not uniform the mean width should be taken. + +[10] This refers, of course, to transverse stability. + +[11] See ch. vi. + + + + +CHAPTER IV. + +THE MOTIVE POWER. + + +SECTION I.--RUBBER MOTORS. + +§ 1. Some forty years have elapsed since Pénaud first used elastic +(rubber) for model aeroplanes, and during that time no better +substitute (in spite of innumerable experiments) has been found. Nor +for the smaller and lighter class of models is there any likelihood of +rubber being displaced. Such being the case, a brief account of some +experiments on this substance as a motive power for the same may not +be without interest. The word _elastic_ (in science) denotes: _the +tendency which a body has when distorted to return to its original +shape_. Glass and ivory (within certain limits) are two of the most +elastic bodies known. But the limits within which most bodies can be +distorted (twisted or stretched, or both) without either fracture or a +LARGE _permanent_ alteration of shape is very small. Not so rubber--it +far surpasses in this respect even steel springs. + +§ 2. Let us take a piece of elastic (rubber) cord, and stretch it with +known weights and observe carefully what happens. We shall find that, +first of all: _the extension is proportional to the weight +suspended_--but soon we have an _increasing_ increase of extension. In +one experiment made by the writer, when the weights were removed the +rubber cord remained 1/8 of an inch longer, and at the end of an hour +recovered itself to the extent of 1/16, remaining finally permanently +1/16 of an inch longer. Length of elastic cord used in this experiment +8-1/8 inches, 3/16 of an inch thick. Suspended weights, 1 oz. up to 64 +oz. Extension from ¼ inch up to 24-5/8 inches. Graph drawn in Fig. +14, No. B abscissæ extension in eighths of an inch, ordinates weights +in ounces. So long as the graph is a straight line it shows the +extension is proportional to the suspended weight; afterwards in +excess. + +[Illustration: FIG. 14.--WEIGHT AND EXTENSION. + +B, rubber 3/16 in. thick; C, 2/16 in. thick; D, 1/16 in. thick. A, +theoretical line if extension were proportional to weight.] + +In this experiment we have been able to stretch (distort) a piece of +rubber to more than three times its original length, and afterwards it +finally returns to almost its original length: not only so, a piece of +rubber cord can be stretched to eight or nine times its original +length without fracture. Herein lies its supreme advantage over steel +or other springs. Weight for weight more energy can be got or more +work be done by stretched (or twisted, or, to speak more correctly, by +stretched-twisted) rubber cord than from any form of steel spring.[12] +It is true it is stretched--twisted--far beyond what is called the +"elastic limit," and its efficiency falls off, but with care not +nearly so quickly as is commonly supposed, but in spite of this and +other drawbacks its advantages far more than counterbalance these. + +§ 3. Experimenting with cords of varying thickness we find that: _the +extension is inversely proportional to the thickness_. If we leave a +weight hanging on a piece of rubber cord (stretched, of course, beyond +its "elastic limit") we find that: _the cord continues to elongate as +long as the weight is left on_. For example: a 1 lb. weight hung on a +piece of rubber cord, 8-1/8 inches long and 1/8 of an inch thick, +stretched it--at first--6¼ inches; after two minutes this had +increased to 6-5/8 (3/8 of an inch more). One hour later 1/8 of an +inch more, and sixteen hours later 1/8 of an inch more, i.e. a sixteen +hours' hang produced an additional extension of ¾ of an inch. On a +thinner cord (half the thickness) same weight produced _an additional +extension_ (_after_ 14 _hours_) _of _10-3/8 _in_. + +N.B.--An elastic cord or spring balance should never have a weight +left permanently on it--or be subjected to a distorting force for a +longer time than necessary, or it will take a "permanent set," and not +return to even approximately its original length or form. + +In a rubber cord the extension is _directly proportional to the +length_ as well as _inversely proportional to the thickness and to the +weight suspended_--true only within the limits of elasticity. + +[Illustration: FIG. 15.--EXTENSION AND INCREASE IN VOLUME.] + +§ 4. =When a Rubber Cord is stretched there is an Increase of +Volume.=--On stretching a piece of rubber cord to _twice_ its +original (natural) length, we should perhaps expect to find that the +string would only be _half_ as thick, as would be the case if the +volume remained the same. Performing the experiment, and measuring the +cord as accurately as possible with a micrometer, measuring to the +one-thousandth of an inch, we at once perceive that this is not the +case, being about _two-thirds_ of its former volume. + +§ 5. In the case of rubber cord used for a motive power on model +aeroplanes, the rubber is _both_ twisted and stretched, but chiefly +the latter. + +Thirty-six strands of rubber, weight about 56 grammes, at 150 turns +give a torque of 4 oz. on a 5-in. arm, but an end thrust, or end pull, +of about 3½ lb. (Ball bearings, or some such device, can be used to +obviate this end thrust when desirable.) A series of experiments +undertaken by the writer on the torque produced by twisted rubber +strands, varying in number, length, etc., and afterwards carefully +plotted out in graph form, have led to some very interesting and +instructive results. Ball bearings were used, and the torque, measured +in eighths of an ounce, was taken (in each case) from an arm 5 in. in +length. + +The following are the principal results arrived at. For graphs, see +Fig. 16. + +§ 6. A. Increasing the number of (rubber) strands by _one-half_ +(length and thickness of rubber remaining constant) increases the +torque (unwinding tendency) _twofold_, i.e., doubles the motive power. + +B. _Doubling_ the number of strands increases the torque _more than +three times_--about 3-1/3 times, 3 times up to 100 turns, 3½ times +from 100 to 250 turns. + +C. _Trebling_ the number of strands increases the torque at least +_seven times_. + +The increased _size_ of the coils, and thereby _increased_ extension, +explains this result. As we increase the number of strands, the +_number_ of twists or turns that can be given it becomes less. + +D. _Doubling_ the number of strands (length, etc., remaining +constant) _diminishes_ the number of turns by _one-third to +one-half_. (In few strands one-third, in 30 and over one-half.) + +[Illustration: FIG. 16.--TORQUE GRAPHS OF RUBBER MOTORS. + + Abscissæ = Turns. Ordinates = Torque measured in 1/16 of an oz. + Length of arm, 5 in. + + A. 38 strands of new rubber, 2 ft. 6 in. long; 58 grammes weight. + B. 36 strands, 2 ft. 6 in. long; end thrust at 150 turns, 3½ lb. + C. 32 strands, 2 ft. 6 in. long. + D. 24 " " " + E. 18 " " " weight 28 grammes. + F. 12 " 1 ft. 3 in. long + G. 12 " 2 ft. 6 in. long.] + +E. If we halve the length of the rubber strands, keeping the _number_ +of strands the same, the torque is but slightly increased for the +first 100 turns; at 240 turns it is double. But the greater number of +turns--in ratio of about 2:1--that can be given the longer strand much +more than compensates for this. + +F. No arrangement of the strands, _per se_, gets more energy (more +motive power) out of them than any other, but there are special +reasons for making the strands-- + +G. As long and as few in number as possible. + +1. More turns can be given it. + +2. It gives a far more even torque. Twelve strands 2 ft. 6 in. long +give practically a line of small constant angle. Thirty-six strands +same length a much steeper angle, with considerable variations. + +A very good result, which the writer has verified in practice, paying +due regard to _both_ propeller and motor, is to make-- + +H. _The length of the rubber strands twice[13] in feet the number of +the strands in inches_,[14] e.g., if the number of strands is 12 their +length should be 2 ft., if 18, 3 ft., and so on. + +§ 7. Experiments with 32 to 38 strands 2 ft. 6 in. long give a torque +curve almost precisely similar to that obtained from experiments made +with flat spiral steel springs, similar to those used in watches and +clocks; and, as we know, the torque given by such springs is very +uneven, and has to be equalised by use of a fusee, or some such +device. In the case of such springs it must not be forgotten that the +turning moment (unwinding tendency) is NOT proportional to the amount +of winding up, this being true only in the "balance" springs of +watches, etc., where _both_ ends of the spring are rigidly fastened. + +In the case of SPRING MOTORS.[15] + +I. The turning moment (unwinding tendency) is proportional to the +difference between the angle of winding and yielding, proportional to +the moment of inertia of its section, i.e., to the breadth and the +cube of its thickness, also proportional to the modulus of elasticity +of the substance used, and inversely proportional to the length of the +strip. + +§ 8. Referring back to A, B, C, there are one or two practical +deductions which should be carefully noted. + +Supposing we have a model with one propeller and 36 strands of +elastic. If we decide to fit it with twin screws, then, other reasons +apart, we shall require two sets of strands of more than 18 in number +each to have the same motive power (27 if the same torque be +required).[16] This is an important point, and one not to be lost +sight of when thinking of using two propellers. + +Experiments on-- + +§9. =The Number of Revolutions= (turns) =that can be given to Rubber +Motors= led to interesting results, e.g., the number of turns to +produce a double knot in the cord from end to end were, in the case of +rubber, one yard long:-- + + No. of Strands. No. of Turns. No. of Strands. No. of Turns. + 4 440 16 200 + 8 310 28 170 + 12 250 + +It will be at once noticed that the greater the number of rubber +strands used in a given length, the fewer turns will it stand in +proportion. For instance, 8 strands double knot at 310, and 4 at 440 +(and not at 620), 16 at 200, and 8 at 310 (and not 400), and so on. +The reason, of course, is the more the strands the greater the +distance they have to travel round themselves. + +§ 10. =The Maximum Number of Turns.=--As to the maximum number of +permissible turns, rubber has rupture stress of 330 lb. per sq. in., +_but a very high permissible stress_, as much as 80 per cent. The +resilience (power of recovery after distortion) in tension of rubber +is in considerable excess of any other substance, silk being the only +other substance which at all approaches it in this respect, the ratio +being about 11 : 9. The resilience of steel spiral spring is very +slight in comparison. + +A rubber motor in which the double knot is not exceeded by more than +100 turns (rubber one yard in length) should last a good time. When +trying for a record flight, using new elastic, as many as even 500 or +600 or even more turns have been given in the case of 32-36 strands a +yard in length; but such a severe strain soon spoils the rubber. + +§ 11. =On the Use of "Lubricants."=--One of the drawbacks to rubber is +that if it be excessively strained it soon begins to break up. One of +the chief causes of this is that the strands stick together--they +should always be carefully separated, if necessary, after a +flight--and an undue strain is thereby cast on certain parts. Apart +also from this the various strands are not subject to the same +tension. It has been suggested that if some means could be devised to +prevent this, and allow the strands to slip over one another, a +considerable increase of power might result. It must, however, be +carefully borne in mind that anything of an oily or greasy nature has +an injurious effect on the rubber, and must be avoided at all costs. +Benzol, petroleum, ether, volatile oils, turpentine, chloroform, +naphtha, vaseline, soap, and all kinds of oil must be carefully +avoided, as they soften the rubber, and reduce it more or less to the +consistence of a sticky mass. The only oil which is said to have no +action on rubber, or practically none, is castor oil; all the same, I +do not advise its use as a lubricant. + +There are three only which we need consider:-- + + 1. Soda and water. + 2. French chalk. + 3. Pure redistilled glycerine. + +The first is perfectly satisfactory when freshly applied, but soon +dries up and evaporates. + +The second falls off; and unless the chalk be of the softest kind, +free from all grit and hard particles, it will soon do more harm than +good. + +The third, glycerine, is for ordinary purposes by far the best, and +has a beneficial rather than a deleterious effect on the rubber; but +it must be _pure_. The redistilled kind, free from all traces of +arsenic, grease, etc., is the only kind permissible. It does not +evaporate, and a few drops, comparatively speaking, will lubricate +fifty or sixty yards of rubber. + +Being of a sticky or tacky nature it naturally gathers up dust and +particles of dirt in course of time. To prevent these grinding into +the rubber, wash it from time to time in warm soda, and warm and apply +fresh glycerine when required. + +Glycerine, unlike vaseline (a product of petroleum), is not a grease; +it is formed from fats by a process known as _saponification_, or +treatment of the oil with caustic alkali, which decomposes the +compound, forming an alkaline stearate (soap), and liberating the +glycerine which remains in solution when the soap is separated by +throwing in common salt. In order to obtain pure glycerine, the fat +can be decomposed by lead oxide, the glycerine remaining in solution, +and the lead soap or plaster being precipitated. + +By using glycerine as a lubricant the number of turns that can be +given a rubber motor is greatly increased, and the coils slip over one +another freely and easily, and prevent the throwing of undue strain on +some particular portion, and absolutely prevent the strands from +sticking together. + +§ 12. =The Action of Copper upon Rubber.=--Copper, whether in the form +of the metal, the oxides, or the soluble salts, has a marked injurious +action upon rubber. + +In the case of metallic copper this action has been attributed to +oxidation induced by the dissolved oxygen in the copper. In working +drawings for model aeroplanes I have noticed designs in which the +hooks on which the rubber strands were to be stretched were made of +_copper_. In no case should the strands be placed upon bare metal. I +always cover mine with a piece of valve tubing, which can easily be +renewed from time to time. + +§ 12A. =The Action of Water, etc., on Rubber.=--Rubber is quite +insoluble in water; but it must not be forgotten that it will absorb +about 25 per cent. into its pores after soaking for some time. + +Ether, chloroform, carbon-tetrachloride, turpentine, carbon +bi-sulphide, petroleum spirit, benzene and its homologues found in +coal-tar naphtha, dissolve rubber readily. Alcohol is absorbed by +rubber, but is not a solvent of it. + +§ 12B. =How to Preserve Rubber.=--In the first place, in order that it +shall be _possible_ to preserve and keep rubber in the best condition +of efficiency, it is absolutely essential that the rubber shall be, +when obtained, fresh and of the best kind. Only the best Para rubber +should be bought; to obtain it fresh it should be got in as large +quantities as possible direct from a manufacturer or reliable rubber +shop. The composition of the best Para rubber is as follows:--Carbon, +87·46 per cent.; hydrogen, 12·00 per cent.; oxygen and ash, 0·54 per +cent. + +In order to increase its elasticity the pure rubber has to be +vulcanised before being made into the sheet some sixty or eighty yards +in length, from which the rubber threads are cut; after vulcanization +the substance consists of rubber plus about 3 per cent. of sulphur. +Now, unfortunately, the presence of the sulphur makes the rubber more +prone to atmospheric oxidation. Vulcanized rubber, compared to pure +rubber, has then but a limited life. It is to this process of +oxidation that the more or less rapid deterioration of rubber is due. + +To preserve rubber it should be kept from the sun's rays, or, indeed, +any actinic rays, in a cool, airy place, and subjected to as even a +temperature as possible. Great extremes of temperature have a very +injurious effect on rubber, and it should be washed from time to time +in warm soda water. It should be subjected to no tension or +compression. + +Deteriorated rubber is absolutely useless for model aeroplanes. + +§ 13. =To Test Rubber.=--Good elastic thread composed of pure Para +rubber and sulphur should, if properly made, stretch to seven times +its length, and then return to its original length. It should also +possess a stretching limit at least ten times its original length. + +As already stated, the threads or strands are cut from sheets; these +threads can now be cut fifty to the inch. For rubber motors a very +great deal so far as length of life depends on the accuracy and skill +with which the strands are cut. When examined under a microscope (not +too powerful) the strands having the least ragged edge, i.e., the best +cut, are to be preferred. + +§ 14. =The Section--Strip or Ribbon versus Square.=--In section the +square and not the ribbon or strip should be used. The edge of the +strip I have always found more ragged under the microscope than the +square. I have also found it less efficient. Theoretically no doubt a +round section would be best, but none such (in small sizes) is on the +market. Models have been fitted with a tubular section, but such +should on no account be used. + +§ 15. =Size of the Section.=--One-sixteenth or one-twelfth is the best +size for ordinary models; personally, I prefer the thinner. If more +than a certain number of strands are required to provide the necessary +power, a larger size should be used. It is not easy to say _what_ this +number is, but fifty may probably be taken as an outside limit. +Remember the size increases by area section; twice the _sectional_ +height and breadth means four times the rubber. + +§ 16. =Geared Rubber Motors.=--It is quite a mistake to suppose that +any advantage can be obtained by using a four to one gearing, say; all +that you do obtain is one-fourth of the power minus the increased +friction, minus the added weight. This presumes, of course, you make +no alteration in your rubber strands. + +Gearing such as this means _short_ rubber strands, and such are not to +be desired; in any case, there is the difficulty of increased friction +and added weight to overcome. It is true by splitting up your rubber +motor into two sets of strands instead of one you can obtain more +turns, but, as we have seen, you must increase the number of strands +to get the same thrust, and you have this to counteract any advantage +you gain as well as added weight and friction. + +§ 17. The writer has tried endless experiments with all kinds of +geared rubber motors, and the only one worth a moment's consideration +is the following, viz., one in which two gear wheels--same size, +weight, and number of teeth--are made use of, the propeller being +attached to the axle of one of them, and the same number of strands +are used on each axle. The success or non-success of this motor +depends entirely on the method used in its construction. At first +sight it may appear that no great skill is required in the +construction of such a simple piece of apparatus. No greater mistake +could be made. It is absolutely necessary that _the friction and +weight be reduced to a minimum_, and the strength be a maximum. The +torque of the rubber strands on so short an arm is very great. + +Ordinary light brass cogwheels will not stand the strain. + +A. The cogwheels should be of steel[17] and accurately cut of diameter +sufficient to separate the two strands the requisite distance, _but no +more_. + +B. The weight must be a minimum. This is best attained by using solid +wheels, and lightening by drilling and turning. + +C. The friction must be a minimum. Use the lightest ball bearings +obtainable (these weigh only 0·3 gramme), adjust the wheels so that +they run with the greatest freedom, but see that the teeth overlap +sufficiently to stand the strain and slight variations in direction +without fear of slipping. Shallow teeth are useless. + +D. Use vaseline on the cogs to make them run as easily as possible. + +[Illustration: FIG. 17.--GEARED RUBBER MOTOR. + +Designed and constructed by the writer. For description of the model, +etc., see Appendix.] + +E. The material of the containing framework must be of maximum +strength and minimum lightness. Construct it of minimum size, box +shaped, use the thinnest tin (really tinned sheet-iron) procurable, +and lighten by drilling holes, not too large, all over it. Do not use +aluminium or magnalium. Steel, could it be procured thin enough, would +be better still. + +F. Use steel pianoforte wire for the spindles, and hooks for the +rubber strands, using as thin wire as will stand the strain. + +Unless these directions are carefully carried out no advantage will be +gained--the writer speaks from experience. The requisite number of +rubber strands to give the best result must be determined by +experiment. + +§ 18. One advantage in using such a motor as this is that the two +equal strands untwisting in opposite directions have a decided +steadying effect on the model, similar almost to the case in which two +propellers are used. + +The "best" model flights that the writer has achieved have been +obtained with a motor of this description.[18] + +In the case of twin screws two such gearings can be used, and the +rubber split up into four strands. The containing framework in this +case can be simply light pieces of tubing let into the wooden +framework, or very light iron pieces fastened thereto. + +Do not attempt to split up the rubber into more than two strands to +each propeller. + + +SECTION II.--OTHER FORMS OF MOTORS. + +§ 18A. =Spring Motors.=--This question has already been dealt with +more or less whilst dealing with rubber motors, and the superiority of +the latter over the former pointed out. Rubber has a much greater +superiority over steel or other springs, because in stretch-twisted +rubber far more energy can be stored up weight for weight. One pound +weight of elastic can be made to store up some 320 ft.-lb. of energy, +and steel only some 65 lb. And in addition to this there is the +question of gearing, involving extra weight and friction; that is, if +flat steel springs similar to those used in clockwork mechanism be +made use of, as is generally the case. The only instance in which such +springs are of use is for the purpose of studying the effects of +different distributions of weight on the model, and its effect on the +balance of the machine; but effects such as this can be brought about +without a change of motor. + +§ 18B. A more efficient form of spring motor, doing away with gearing +troubles, is to use a long spiral spring (as long as the rubber +strands) made of medium-sized piano wire, similar in principle to +those used in some roller-blinds, but longer and of thinner steel. + +The writer has experimented with such, as well as scores of other +forms of spring motors, but none can compare with rubber. + +The long spiral form of steel spring is, however, much the best. + +§ 18C. =Compressed Air Motors.=--This is a very fascinating form of +motor, on paper, and appears at first sight the ideal form. It is so +easy to write: "Its weight is negligible, and it can be provided free +of cost; all that is necessary is to work a bicycle pump for as many +minutes as the motor is desired to run. This stored-up energy can be +contained in a mere tube, of aluminium or magnalium, forming the +central rib of the machine, and the engine mechanism necessary for +conveying this stored-up energy to the revolving propeller need weigh +only a few ounces." Another writer recommends "a pressure of 300 lb." + +§ 18D. A pneumatic drill generally works at about 80 lb. pressure, +and when developing 1 horse-power, uses about 55 cubic ft. of free air +per minute. Now if we apply this to a model aeroplane of average size, +taking a reservoir 3 ft. long by 1½ in. internal diameter, made of +magnalium, say--steel would, of course, be much better--the weight of +which would certainly not be less than 4 oz., we find that at 80 lb. +pressure such a motor would use + + 55/Horse Power (H.P.) + +cub. ft. per minute. + +Now 80 lb. is about 5½ atmospheres, and the cubical contents of the +above motor some 63 cub. in. The time during which such a model would +fly depends on the H.P. necessary for flight; but a fair allowance +gives a flight of from 10 to 30 sec. I take 80 lb. pressure as a fair +practical limit. + +§ 18E. The pressure in a motor-car tyre runs from 40 to 80 lb., +usually about 70 lb. Now 260 strokes are required with an ordinary +inflator to obtain so low a pressure as 70 lb., and it is no easy job, +as those who have done it know. + +§ 19. Prior to 1893 Mr. Hargraves (of cellular kite fame) studied the +question of compressed-air motors for model flying machines. His motor +was described as a marvel of simplicity and lightness, its cylinder +was made like a common tin can, the cylinder covers cut from sheet tin +and pressed to shape, the piston and junk rings of ebonite. + +One of his receivers was 23-3/8 in. long, and 5·5 in. diameter, of +aluminium plate 0·2 in. thick, 3/8 in. by 1/8 in. riveting strips were +insufficient to make tight joints; it weighed 26 oz., and at 80 lb. +water pressure one of the ends blew out, the fracture occurring at the +bend of the flange, and not along the line of rivets. The receiver +which was successful being apparently a tin-iron one; steel tubing was +not to be had at that date in Sydney. With a receiver of this +character, and the engine referred to above, a flight of 343 ft. was +obtained, this flight being the best. (The models constructed by him +were not on the aeroplane, but ornithoptere, or wing-flapping +principle.) The time of flight was 23 _seconds_, with 54½ double +vibrations of the engines. The efficiency of this motor was estimated +to be 29 per cent. + +§ 20. By using compressed air, and heating it in its passage to the +cylinder, far greater efficiency can be obtained. Steel cylinders can +be obtained containing air under the enormous pressure of 120 +atmospheres.[19] This is practically liquid air. A 20-ft. cylinder +weighs empty 23 lb. The smaller the cylinder the less the +proportionate pressure that it will stand; and supposing a small steel +cylinder, produced of suitable form and weight, and capable of +withstanding with safety a pressure of from 300 to 600 lb. per sq. +in., or from 20 to 40 atmospheres. The most economical way of working +would be to admit the air from the reservoir directly to the motor +cylinders; but this would mean a very great range in the initial +working pressure, entailing not-to-be-thought-of weight in the form of +multi-cylinder compound engines, variable expansion gear, etc. + +§ 21. This means relinquishing the advantages of the high initial +pressure, and the passing of the air through a reducing valve, whereby +a constant pressure, say, of 90 to 150, according to circumstances, +could be maintained. By a variation in the ratio of expansion the air +could be worked down to, say, 30 lb. + +The initial loss entailed by the use of a reducing valve may be in a +great measure restored by heating the air before using it in the motor +cylinders; by heating it to a temperature of only 320°F., by means of +a suitable burner, the volume of air is increased by one half, the +consumption being reduced in the same proportion; the consumption of +air used in this way being 24 lb. per indicated horse-power per hour. +But this means extra weight in the form of fuel and burners, and what +we gain in one way we lose in another. It is, of course, desirable +that the motor should work at as low a pressure as possible, since as +the store of air is used up the pressure in the reservoir falls, until +it reaches a limit below which it cannot usefully be employed. The air +then remaining is dead and useless, adding only to the weight of the +aeroplane. + +§ 22. From calculations made by the writer the _entire_ weight of a +compressed-air model motor plant would be at least _one-third_ the +weight of the aeroplane, and on a small scale probably one-half, and +cannot therefore hold comparison with the _steam engine_ discussed in +the next paragraph. In concluding these remarks on compressed-air +motors, I do not wish to dissuade anyone from trying this form of +motor; but they must not embark on experiments with the idea that +anything useful or anything superior to results obtained with +infinitely less expense by means of rubber can be brought to pass with +a bicycle pump, a bit of magnalium tube, and 60 lb. pressure. + +§ 22A. In Tatin's air-compressed motor the reservoir weighed 700 +grammes, and had a capacity of 8 litres. It was tested to withstand a +pressure of 20 atmospheres, but was worked only up to seven. The +little engine attached thereto weighed 300 grammes, and developed a +motive power of 2 kilogram-metres per second (_see_ ch. iii.). + +§ 23. =Steam-Driven Motors.=--Several successful steam-engined model +aeroplanes have been constructed, the most famous being those of +Professor Langley. + +Having constructed over 30 modifications of rubber-driven models, and +experimented with compressed air, carbonic-acid gas, electricity, and +other methods of obtaining energy, he finally settled upon the steam +engine (the petrol motor was not available at that time, 1893). After +many months' work it was found that the weight could not be reduced +below 40 lb., whilst the engine would only develop ½ H.P., and +finally the model was condemned. A second apparatus to be worked by +compressed air was tried, but the power proved insufficient. Then came +another with a carbonic-acid gas engine. Then others with various +applications of electricity and gas, etc., but the steam engine was +found most suitable; yet it seemed to become more and more doubtful +whether it could ever be made sufficiently light, and whether the +desired end could be attained at all. The chief obstacle proved not to +be with the engines, which were made surprisingly light after +sufficient experiment. _The great difficulty was to make a boiler of +almost no weight which would give steam enough._ + +§ 24. At last a satisfactory boiler and engine were produced. + +The engine was of 1 to 1½ H.P., total weight (including moving +parts) 26 oz. The cylinders, two in number, had each a diameter of +1¼ in., and piston stroke 2 in. + +The boiler, with its firegrate, weighed a little over 5 lb. It +consisted of a continuous helix of copper tubing, 3/8 in. external +diameter, the diameter of the coil being 3 in. altogether. Through the +centre of this was driven the blast from an "Ælopile," a modification +of the naphtha blow-torch used by plumbers, the flame of which is +about 2000° F.[20] The pressure of steam issuing into the engines +varied from 100 to 150 lb. per sq. in.; 4 lb. weight of water and +about 10 oz. of naphtha could be carried. The boiler evaporated 1 lb. +of water per minute. + +The twin propellers, 39 in. in diam., pitch 1¼, revolved from 800 +to 1000 a minute. The entire aeroplane was 15 ft. in length, the +aerofoils from tip to tip about 14 ft., and the total weight slightly +less than 30 lb., of which _one-fourth was contained in the +machinery_. Its flight was a little over half a mile in length, and of +1½ minutes' duration. Another model flew for about three-quarters +of a mile, at a rate of about 30 miles an hour. + +It will be noted that engine, generator, etc., work out at about 7 lb. +per H.P. Considerable advance has been made in the construction of +light and powerful model steam engines since Langley's time, chiefly +in connexion with model hydroplanes, and a pressure of from 500 to 600 +lb. per sq. in. has been employed; the steam turbine has been brought +to a high state of perfection, and it is now possible to make a model +De Laval turbine of considerable power weighing almost next to +nothing,[21] the real trouble, in fact the only one, being the steam +generator. An economization of weight means a waste of steam, of which +models can easily spend their only weight in five minutes. + +§ 25. One way to economize without increased weight in the shape of a +condenser is to use spirit (methylated spirit, for instance) for both +fuel and boiler, and cause the exhaust from the engines to be ejected +on to the burning spirit, where it itself serves as fuel. By using +spirit, or some very volatile hydrocarbon, instead of water, we have a +further advantage from the fact that such vaporize at a much lower +temperature than water. + +§ 26. When experimenting with an engine of the turbine type we must +use a propeller of small diameter and pitch, owing to the very high +velocity at which such engines run. + +Anyone, however, who is not an expert on such matters would do well to +leave such motors alone, as the very highest technical skill, combined +with many preliminary disappointments and trials, are sure to be +encountered before success is attained. + +§ 27. And the smaller the model the more difficult the problem--halve +your aeroplane, and your difficulties increase anything from fourfold +to tenfold. + +The boiler would in any case be of the flash type of either copper or +steel tubing (the former for safety), with a magnalium container for +the spirit, and a working pressure of from 150 to 200 lb. per sq. in. +Anything less than this would not be worth consideration. + +§ 28. Some ten months after Professor Langley's successful model +flights (1896), experiments were made in France at Carquenez, near +Toulon. The total weight of the model aeroplane in this case was 70 +lb.; the engine power a little more than 1 H.P. Twin screws were +used--_one in front and one behind_. The maximum velocity obtained was +40 miles per hour; but the length of run only 154 yards, and duration +of flight only a few seconds. This result compares very poorly with +Langley's distance (of best flight), nearly one mile, duration 1 min. +45 sec. The maximum velocity was greater--30 to 40 miles per hour. The +total breadth of this large model was rather more than 6 metres, and +the surface a little more than 8 sq. metres. + +§ 29. =Petrol Motors.=--Here it would appear at first thought is the +true solution of the problem of the model aeroplane motor. Such a +motor has solved the problem of aerial locomotion, as the steam engine +solved that of terrestrial and marine travel, both full sized and +model; and if in the case of full sized machines, then why not models. + +[Illustration: FIG. 18.--MR. STANGER'S MODEL IN FULL FLIGHT.] + +[Illustration: FIG. 19.--MR. STANGER'S PETROL-DRIVEN MODEL AEROPLANE. + +(_Illustrations by permission from electros supplied by the "Aero."_)] + +§ 30. The exact size of the smallest _working_ model steam engine that +has been made I do not know,[22] but it is or could be surprisingly +small; not so the petrol motor--not one, that is, that would _work_. +The number of petrol motor-driven model aeroplanes that have actually +flown is very small. Personally I only know of one, viz., Mr. D. +Stanger's, exhibited at the aero exhibition at the Agricultural Hall +in 1908. + +[Illustration: FIG. 20.--MR. STANGER'S MODEL PETROL ENGINE.] + +[Illustration: FIG. 21.--MR. STANGER'S MODEL PETROL ENGINE.] + + In Fig. 21 the motor is in position on the aeroplane. Note + small carburettor. In Fig. 20 an idea of the size of engine may + be gathered by comparing it with the ordinary sparking-plug + seen by the side, whilst to the left of this is one of the + special plugs used on this motor. (_Illustrations by permission + from electros supplied by the "Aero."_) + +§ 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. + +[Illustration: FIG. 22.--ONE-CYLINDER PETROL MOTOR. + +(_Electro from Messrs. A.W. Gamage's Aviation Catalogue._)] + +The propeller, 29 in. in diam. and 36 in. in pitch, gives a static +thrust of about 7 lb. The machine has a spread of 8 ft. 2 in., and is +6 ft. 10 in. in length. Total weight 21 lb. Rises from the ground when +a speed of about 16 miles an hour is attained. A clockwork +arrangement automatically stops the engine. The engine air-cooled. The +cylinder of steel, cast-iron heads, aluminium crank-case, double float +feed carburetter, ignition by single coil and distributor. The +aeroplane being 7 ft. 6 in. long, and having a span 8 ft. + +§ 32. =One-cylinder Petrol Motors.=--So far as the writer is aware no +success has as yet attended the use of a single-cylinder petrol motor +on a model aeroplane. Undoubtedly the vibration is excessive; but this +should not be an insuperable difficulty. It is true it is heavier in +proportion than a two-cylinder one, and not so efficient; and so far +has not proved successful. The question of vibration on a model +aeroplane is one of considerable importance. A badly balanced +propeller even will seriously interfere with and often greatly curtail +the length of flight. + +§ 33. =Electric Motors.=--No attempt should on any account be made to +use electric motors for model aeroplanes. They are altogether too +heavy, apart even from the accumulator or source of electric energy, +for the power derivable from them. To take an extreme case, and +supposing we use a 2-oz. electric motor capable of driving a propeller +giving a static thrust of 3 oz.,[23] on weighing one of the smallest +size accumulators without case, etc., I find its weight is 4½ oz. +One would, of course, be of no use; at least three would be required, +and they would require practically short circuiting to give sufficient +amperage (running them down, that is, in some 10 to 15 seconds). Total +weight, 1 lb. nearly. Now from a _pound_ weight of rubber one could +obtain a thrust of _pounds_, not ounces. For scale models not intended +for actual flight, of course, electric motors have their uses. + +FOOTNOTES: + +[12] Also there is no necessity for gearing. + +[13] In his latest models the writer uses strands even three times and +not twice as long, viz. fourteen strands 43 in. long. + +[14] This refers to 1/16 in. square sectioned rubber. + +[15] Of uniform breadth and thickness. + +[16] In practice I find not quite so high a proportion as this is +always necessary. + +[17] Steel pinion wire is very suitable. + +[18] See Appendix. + +[19] As high a pressure as 250 atmospheres has been used. + +[20] There was a special pump keeping the water circulating rapidly +through the boiler, the intense heat converting some of it into steam +as it flowed. The making of this boiler alone consumed months of work; +the entire machine taking a year to construct, with the best +mechanical help available. + +[21] Model Steam Turbines. "Model Engineer" Series, No. 13, price +6_d._ + +[22] See Introduction, note to § 1. + +[23] The voltage, etc., is not stated. + + + + +CHAPTER V. + +PROPELLERS OR SCREWS. + + +§ 1. The design and construction of propellers, more especially the +former, is without doubt one of the most difficult parts of model +aeroplaning. + +With elastic or spring driven models the problem is more complicated +than for models driven by petrol or some vaporized form of liquid +fuel; and less reliable information is to hand. The problem of +_weight_, unfortunately, is of primary importance. + +We will deal with these points in due course; to begin with let us +take:-- + + +THE POSITION OF THE PROPELLER. + +In model aeroplanes the propeller is usually situated either in front +or in the rear of the model; in the former case it is called a TRACTOR +SCREW, i.e., it pulls instead of pushes. + +As to the merits of the two systems with respect to the tractor, there +is, we know, in the case of models moving through water a distinct +advantage in placing the propeller behind, and using a pushing or +propulsive action, on account of the frictional "wake" created behind +the boat, and which causes the water to flow after the vessel, but at +a lesser velocity. + +In placing the propeller behind, we place it in such a position as to +act upon and make use of this phenomenon, the effect of the propeller +being to bring this following wake to rest. Theoretically a boat, +model or otherwise, can be propelled with less horse-power than it can +be towed. But with respect to aeroplanes, apart altogether from the +difference of medium, there is _at present_ a very considerable +difference of _form_, an aeroplane, model or otherwise, bearing at +present but little resemblance to the hull of a boat. + +Undoubtedly there is a frictional wake in the case of aeroplanes, +possibly quite as much in proportion as in the case of a boat, +allowing for difference of medium. Admitting, then, that this wake +does exist, it follows that a propulsive screw is better than a +tractor. In a matter of this kind constructional considerations, or +"ease of launching," and "ability to land without damage," must be +given due weight. + +In the case of model aeroplanes constructional details incline the +balance neither one way nor the other; but "ease in launching" and +"ability to land without damage" weigh the balance down most decidedly +in favour of a driving or propulsive screw. + +In the case of full-sized monoplanes constructional details had most +to do with the use of tractors; but monoplanes are now being built +with propulsive screws.[24] + +In the case of models, not models of full-sized machines, but actual +model flyers, the writer considers propulsive screws much the +best.[25] + +In no case should the propeller be placed in the centre of the model, +or in such a position as to _shorten the strands of the elastic +motor_, if good flights are desired. + +In the case of petrol or similar driven models the position of the +propeller can be safely copied from actual well-recognised and +successful full-sized machines. + +§ 2. =The Number of Blades.=--Theoretically the number of blades does +not enter into consideration. The mass of air dealt with by the +propeller is represented by a cylinder of indefinite length, whose +diameter is the same as that of the screw, and the rate at which this +cylinder is projected to the rear depends theoretically upon the pitch +and revolutions (per minute, say) of the propeller and not the number +of blades. Theoretically one blade (helix incomplete) would be +sufficient, but such a screw would not "balance," and balance is of +primary importance; the minimum number of blades which can be used is +therefore _two_. + +In marine models three blades are considered best, as giving a better +balance. + +In the case of their aerial prototypes the question of _weight_ has +again to be considered, and two blades is practically the invariable +custom.[26] Here, again, constructional considerations again come to +the fore, and in the case of wooden propellers one of two blades is of +far more easy construction than one of three. + +By increasing the number of blades the "thrust" is, of course, more +evenly distributed over a larger area, but the weight is considerably +increased, and in models a greater advantage is gained by keeping down +the weight than might follow from the use of more blades. + +§ 3. =Fan versus Propeller.=--It must always be most carefully borne +in mind that a fan (ventilating) and a propeller are not the same +thing. Because many blades are found in practice to be efficient in +the case of the former, it is quite wrong to assume that the same +conclusion holds in the case of the latter. + +By increasing the number of blades the skin friction due to the +resistance that has to be overcome in rotating the propeller through +the air is added to. + +Moreover a fan is stationary, whilst a propeller is constantly +_advancing_ as well as _rotating_ through the air. + +The action of a fan blower is to move a small quantity of air at a +high velocity; whereas the action of a propeller is, or should be, to +move _a large quantity of air at a small velocity_, for the function +of a screw is to create thrust. Operating on a yielding fluid medium +this thrust will evidently be in proportion to the mass of fluid +moved, and also to the velocity at which it is put in motion. + +But the power consumed in putting this mass of fluid in motion is +proportional to the mass and to the _square_ of the velocity at which +it moves. From this it follows, as stated above, that in order to +obtain a given thrust with the least loss of power, the mass of fluid +acted on should be as large as possible, and the velocity imparted to +it as little as possible. + +A fan requires to be so designed as to create a thrust when stationary +(static thrust), and a propeller whilst moving through the air +(dynamic thrust). + +§ 4. =The Function of a Propeller= is to produce dynamic thrust; and +the great advantage of the use of a propeller as a thrusting or +propulsive agent is that its surface is always active. It has no +_dead_ points, and its motion is continuous and not reciprocating, and +it requires no special machinery or moving parts in its construction +and operation. + +§ 5. =The Pitch= of a propeller or screw is the linear distance a +screw moves, backwards or forwards, in one complete revolution. This +distance is purely a theoretical one. When, for instance, a screw is +said to have a pitch of 1 ft., or 12 in., it means that the model +would advance 1 ft. through the air for each revolution of the screw, +provided that the propeller blade were mounted in _solid_ guides, like +a nut on a bolt with one thread per foot. In a yielding fluid such as +water or air it does not practically advance this distance, and hence +occurs what is known as-- + +§ 6. =Slip=, which may be defined as the distance which ought to be +traversed, but which is lost through imperfections in the propelling +mechanism; or it may be considered as power which should have been +used in driving the model forward. In the case of a locomotive running +on dry rails nothing is lost in slip, there being none. In the case of +a steamer moored and her engines set going, or of an aeroplane held +back prior to starting, all the power is used in slip, i.e. in putting +the fluid in motion, and none is used in propulsion. + +Supposing the propeller on our model has a pitch of 1 ft., and we give +the elastic motor 100 turns, theoretically the model should travel 100 +ft. in calm air before the propeller is run down; no propeller yet +designed will do this. Supposing the actual length 77 ft., 23 per +cent. has been lost in "slip." For this to be actually correct the +propeller must stop at the precise instant when the machine comes to +ground. + +Taking "slip" into account, then-- + +_The speed of the model in feet per minute = pitch (in feet) × +revolutions per minute -- slip (feet per minute)._ + +This slip wants to be made small--just how small is not yet known. + +If made too small then the propeller will not be so efficient, or, at +any rate, such is the conclusion come to in marine propulsion, where +it is found for the most economical results to be obtained that the +slip should be from 10 to 20 per cent. + +In the case of aerial propellers a slip of 25 per cent. is quite good, +40 per cent. bad; and there are certain reasons for assuming that +possibly about 15 per cent. may be the best. + +§ 7. It is true that slip represents energy lost; but some slip is +essential, because without slip there could be no "thrust," this same +thrust being derived from the reaction of the volume of air driven +backwards. + +The thrust is equal to-- + +_Weight of mass of air acted on per second × slip velocity in feet per +second._ + +In the case of an aeroplane advancing through the air it might be +thought that the thrust would be less. Sir Hiram Maxim found, however, +as the result of his experiments that the thrust with a propeller +travelling through the air at a velocity of 40 miles an hour was the +same as when stationary, the r.p.m. remaining constant throughout. The +explanation is that when travelling the propeller is continually +advancing on to "undisturbed" air, the "slip" velocity is reduced, but +the undisturbed air is equivalent to acting upon a greater mass of +air. + +§ 8. =Pitch Coefficient or Pitch Ratio.=--If we divide the pitch of a +screw by its diameter we obtain what is known as pitch coefficient or +ratio. + +The mean value of eighteen pitch coefficients of well-known full-sized +machines works out at 0·62, which, as it so happens, is exactly the +same as the case of the Farman machine propeller considered alone, +this ratio varying from 0·4 to 1·2; in the case of the Wright's +machine it is (probably) 1. The efficiency of their propeller is +admitted on all hands. Their propeller is, of course, a slow-speed +propeller, 450 r.p.m. The one on the Blériot monoplane (Blériot XI.) +pitch ratio 0·4, r.p.m. 1350. + +In marine propulsion the pitch ratio is generally 1·3 for a slow-speed +propeller, decreasing to 0·9 for a high-speed one. In the case of +rubber-driven model aeroplanes the pitch ratio is often carried much +higher, even to over 3. + +Mr. T.W.K. Clarke recommends a pitch angle of 45°, or less, at the +tips, and a pitch ratio of 3-1/7 (with an angle of 45°). Within limits +the higher the pitch ratio the better the efficiency. The higher the +pitch ratio the slower may be the rate of revolution. Now in a rubber +motor we do not want the rubber to untwist (run out) too quickly; with +too fine a pitch the propeller "races," or does something remarkably +like it. It certainly revolves with an abnormally high percentage of +slip. And for efficiency it is certainly desirable to push this ratio +to its limit; but there is also the question of the + +§ 9. =Diameter.=--"The diameter (says Mr. T.W.K. Clarke) should be +equal to one-quarter the span of the machine." + +If we increase the diameter we shall decrease the pitch ratio. From +experiments which the writer has made he prefers a lower pitch ratio +and increased diameter, viz. a pitch ratio of 1·5, and a diameter of +one-third to even one-half the span, or even more.[27] Certainly not +less than one-third. Some model makers indulge in a large pitch ratio, +angle, diameter, and blade area as well, but such a course is not to +be recommended. + +§ 10. =Theoretical Pitch.=--Theoretically the pitch (from boss to +tip) should at all points be the same; the boss or centre of the blade +at right angles to the plane of rotation, and the angle decreasing as +one approaches the tips. This is obvious when one considers that the +whole blade has to move forward the same amount. In the diagrams Figs. +23 and 24 the tip A of the propeller travels a distance = 2 {pi} R every +revolution. At a point D on the blade, distant _r_ from the centre, +the distance is 2 {pi} _r_. In both instances the two points must advance +a distance equal to the pitch, i.e. the distance represented by P O. + +[Illustration: FIG. 23.] + +[Illustration: FIG. 24. + +A O = 2 {pi} R; D O = 2 {pi} _r_.] + +A will move along A P, B along B P, and so on. The angles at the +points A, B, C ... (Fig. 24), showing the angles at which the +corresponding parts of the blade at A, B, C ... in Fig. 23 must be set +in order that a uniform pitch may be obtained. + +§ 11. If the pitch be not uniform then there will be some portions of +the blade which will drag through the air instead of affording useful +thrust, and others which will be doing more than they ought, putting +air in motion which had better be left quiet. This uniform total pitch +for all parts of the propeller is (as already stated) a decreasing +rate of pitch from the centre to the edge. With a total pitch of 5 +ft., and a radius of 4 ft., and an angle at the circumference of 6°, +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. + +§ 12. =To Ascertain the Pitch of a Propeller.=--Take any point on one +of the blades, and carefully measure the inclination of the blade at +that point to the plane of rotation. + +If the angle so formed be about 19° (19·45),[28] i.e., 1 in 3, and the +point 5 in. from the centre, then every revolution this point will +travel a distance + + 2 {pi} _r_ = 2 × 22/7 × 5 = 31·34. + +Now since the inclination is 1 in 3,[29] the propeller will travel +forward theoretically one-third of this distance, or + + 31·43/3 = 10·48 = 10½ in. approx. + +Similarly any other case may be dealt with. If the propeller have a +uniform _constant angle_ instead of a uniform pitch, then the pitch +may be calculated at a point about one-third the length of the blade +from the tip. + +§ 13. =Hollow-Faced Blades.=[30]--It must always be carefully borne +in mind that a propeller is nothing more nor less than a particular +form of aeroplane specially designed to travel a helical path. It +should, therefore, be hollow faced and partake of the "stream line" +form, a condition not fulfilled if the face of the blade be flat--such +a surface cutting into the air with considerable shock, and by no +means creating as little undesirable motion in the surrounding medium +as possible. + +It must not be forgotten that a curved face blade has of necessity an +increasing pitch from the cutting to the trailing edge (considering, +of course, any particular section). In such a case the pitch is the +_mean effective pitch_. + +§ 14. =Blade Area.=--We have already referred to the fact that the +function of a propeller is to produce dynamic thrust--to drive the +aeroplane forward by driving the air backwards. At the same time it is +most desirable for efficiency that the air should be set in motion as +little as possible, this being so much power wasted; to obtain the +greatest reaction or thrust the greatest possible volume of air should +be accelerated to the smallest velocity. + +In marine engineering in slow-speed propellers (where cavitation[31] +does not come in) narrow blades are usually used. In high-speed marine +propellers (where cavitation is liable to occur) the projected area of +the blades is sometimes as much as 0·6 of the total disk area. In the +case of aerial propellers, where cavitation does not occur, or not +unless the velocity be a very high one (1500 or more a minute), narrow +blades are the best. Experiments in marine propulsion also show that +the thrust depends more on the disk area than on the width of the +blades. All the facts tend to show that for efficiency the blades of +the propeller should be narrow, in order that the air may not be acted +on for too long a time, and so put too much in motion, and the blades +be so separated that one blade does not disturb the molecules of air +upon which the next following one must act. Both in the case of marine +and aerial propellers multiplicity of blades (i.e. increased blade +area) tends to inefficiency of action, apart altogether from the +question of weight and constructional difficulties. The question of +increasing pitch in the case of hollow-faced blades, considered in the +last paragraph, has a very important bearing on the point we are +considering. To make a wide blade under such circumstances would be to +soon obtain an excessive angle. + +In the case of a flat blade the same result holds, because the air has +by the contact of its molecules with the "initial minimum width" been +already accelerated up to its final velocity, and further area is not +only wasted, but inimical to good flights, being our old bugbear +"weight in excess." + +Requisite strength and stiffness, of course, set a limit on the final +narrowness of the blades, apart from other considerations. + +§ 15. The velocity with which the propeller is rotated has also an +important bearing on this point; but a higher speed than 900 r.p.m. +does not appear desirable, and even 700 or less is generally +preferable.[32] In case of twin-screw propellers, with an angle at the +tips of 40° to 45°, as low a velocity of 500 or even less would be +still better.[33] + +§ 16. =Shrouding.=--No improvement whatever is obtained by the use of +any kind of shrouding or ring round the propeller tips, or by +corrugating the surface of the propeller, or by using cylindrical or +cone-shaped propeller chamber or any kind of air guide either before +or after the propeller; allow it to revolve in as free an air-feed as +possible, the air does not fly off under centrifugal force, but is +powerfully sucked inwards in a well-designed propeller. + +[Illustration: FIG. 25. + +A TUBE OF AIR.] + +[Illustration: FIG. 26. + +A CYLINDER OF AIR.] + +§ 17. =General Design.=--The propeller should be so constructed as to +act upon a tube and not a "cylinder" of air. Many flying toys +(especially the French ones) are constructed with propellers of the +cylinder type. Ease of manufacture and the contention that those +portions of the blades adjacent to the boss do little work, and a +slight saving in weight, are arguments that can be urged in their +favour. But all the central cut away part offers resistance in the +line of travel, instead of exerting its proportionate propulsive +power, and their efficiency is affected by such a practice. + +§ 18. A good =Shape= for the blades[34] is rectangular with rounded +corners; the radius of the circle for rounding off the corners may be +taken as about one-quarter of the width of the blade. The shape is not +_truly rectangular, for the width of this rectangular at (near) the +boss should be one-half the width at the tip_. + +The thickness should diminish uniformly from the boss to the tip. (In +models the thickness should be as little as is consistent with +strength to keep down the weight). _The pitch uniform and large._ + +[Illustration: FIG. 27.--O T = 1/3 O P.] + +§ 19. =The Blades, two in number=, and hollow faced--the maximum +concavity being one-third the distance from the entering to the +trailing edge; the ratio of A T to O P (the width) being 0·048 or 1 : +21, these latter considerations being founded on the analogy between a +propeller and the aerofoil surface. (If the thickness be varied from +the entering to the trailing edge the greatest thickness should be +towards the former.) The convex surface of the propeller must be taken +into account, in fact, it is no less important than the concave, and +the entire surface must be given a true "stream line" form. + +[Illustration: FIG. 28.] + +[Illustration: FIG. 29.] + +If the entering and trailing edge be not both straight, but one be +curved as in Fig. 28, then the straight edge must be made the +_trailing_ edge. And if both be curved as in Fig. 29, then the +_concave_ edge must be the trailing edge. + +§ 19. =Propeller Design.=--To design a propeller, proceed as follows. +Suppose the diameter 14 in. and the pitch three times the diameter, +i.e. 52 in. (See Fig. 30.) + +Take one-quarter scale, say. Draw a centre line A B of convenient +length, set of half the pitch 52 in. -- ¼ scale = 5¼ in. = C - D. +Draw lines through C and D at right angles to C D. + +With a radius equal to half the diameter (i.e. in this case 1¾ in.) +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. + +Divide one of the sides E G into the same number of equal parts +(twelve) as shown. Through these points draw lines parallel to F E or +H G. + +And through the twelve points of division on the semicircle draw lines +parallel to F H or E G as shown. The line drawn through the successive +intersections of these lines is the path of the tip of the blade +through half a revolution, viz. the line H S O T E. + +S O T X gives the angle at the tip of the blades = 44°. + +Let the shape of the blade be rectangular with rounded corners, and +let the breadth at the tip be twice that at the boss. + +Then the area (neglecting the rounded off corners) is 10½ sq. in. + +[Illustration: FIG. 30.--PROPELLER DESIGN. + +One quarter scale. Diameter 14 in. Pitch 52 in. Angle at tip 44°.] + +The area being that of a rectangle 7 in. × 1 in. = 7 sq. in. plus area +of two triangles, base ½ in., height 7 in. Now area of triangle = +half base × height. Therefore area of both triangles = ½ in. × 7 +in. = 3½ sq. in. Now the area of the disc swept out by the +propeller is + + {pi}/4 × (diam.)² ({pi} = 22/7) + +[Illustration: FIG. 31.--PROPELLER DESIGN. + +Scale one-eighth for A B and B C; but sections of blade are +full-sized.] + +And if _d_ A _r_ = the "disc area ratio" we have + + (_d_ A _r_) × {pi}/4 × (14)² = area of blade = 10½, + +whence _d_ A _r_ = 0·07 about. + +[Illustration: FIG. 32.] + +[Illustration: FIG. 33.] + +In Fig. 31 set off A B equal to the pitch of the propeller (42 in.), +one-eighth scale. Set off B C at right angles to A B and equal to + + {pi} × diameter = 22/7 × 14 = 44 in. to scale 5½ in. + +Divide B C into a convenient number of equal parts in the figure; five +only are taken, D, E, F, G, H; join A D, A E, A F, A G, A H and +produce them; mark off distances P O, S R, Y T ... equal to the width +of the blade at these points (H P = H O; G S = G R ...) and sketch in +the sections of blade as desired. In the figure the greatest concavity +of the blade is supposed to be one-third the distances P O, S R ... +from PS.... The concavity is somewhat exaggerated. The angles A H B, A +G B, A F B ... represent the pitch angle at the points H, G, F ... of +the blade. + +Similarly any other design may be dealt with; in a propeller of 14 in. +diameter the diameter of the "boss" should not be more than 10/16 in. + +§ 20. =Experiments with Propellers.=--The propeller design shown in +Figs. 32 and 33, due to Mr. G. de Havilland,[35] is one very suitable +for experimental purposes. A single tube passing through a T-shaped +boss forms the arms. On the back of the metal blade are riveted four +metallic clips; these clips being tightened round the arm by +countersunk screws in the face of the blade. + +The tube and clips, etc., are all contained with the back covering of +the blade, as shown in Fig. 35, if desired, the blade then practically +resembling a wooden propeller. The construction, it will be noticed, +allows of the blade being set at any angle, constant or otherwise; +also the pitch can be constant or variable as desired, and any "shape" +of propeller can be fitted. + +The advantage of being able to _twist_ the blade (within limits) on +the axis is one not to be underestimated in experimental work. + +[Illustration: FIG. 34.--THE AUTHOR'S PROPELLER TESTING APPARATUS.] + +With a view to ascertain some practical and reliable data with respect +to the _dynamic_, or actual thrust given when moving through free air +at the velocity of actual travel, the author experimented with the +apparatus illustrated in Figs. 34 and 35, which is so simple and +obvious as to require scarcely any explanation. + +The wires were of steel, length not quite 150 ft., fitted with wire +strainers for equalising tension, and absolutely free from "kinks." +As shown most plainly in Fig. 35, there were two parallel wires +sufficiently far apart for the action of one propeller not to affect +the other. Calling these two wires A and B, and two propellers _x_ and +_y_, then _x_ is first tried on A and _y_ on B. Results carefully +noted. + +[Illustration: FIG. 35.--PROPELLER TESTING. + +Showing distance separating the two wires.] + +Then _x_ is tried on B and _y_ on A, and the results again carefully +noted. If the results confirm one another, the power used in both +cases being the same, well and good; if not, adjustments, etc., are +made in the apparatus until satisfactory results are obtained. This +was done when the propellers "raced" one against the other. At other +times one wire only was made use of, and the time and distance +traversed was noted in each case. Propellers were driven through +smoke, and with silk threads tied to a light framework slightly larger +than their disc area circumference. Results of great interest were +arrived at. These results have been assumed in much that has been said +in the foregoing paragraphs. + +[Illustration: FIG. 36.--ONE GROUP OF PROPELLERS TESTED BY THE AUTHOR.] + +Briefly put, these results showed:-- + +1. The inefficiency of a propeller of the fan blower or of the static +thrust type. + +2. The advantage of using propellers having hollow-faced blades and +large diameter. + +3. That diameter was more useful than blade area, i.e. given a certain +quantity (weight) of wood, make a long thin blade and not a shorter +one of more blade area--blade area, i.e., as proportionate to its +corresponding disc area. + +4. That the propeller surface should be of true stream-line form. + +5. That it should act on a cylinder and not tubes of air. + +6. That a correctly designed and proportioned propeller was just as +efficacious in a small size of 9 in. to 28 in. as a full-sized +propeller on a full-sized machine. + +[Illustration: FIG. 37.--AN EFFICIENT PROPELLER, BUT RATHER HEAVY. + +Ball bearings, old and new. Note difference in sizes and weights. +Propeller, 14 in. diam.; weight 36 grammes.] + +A propeller of the static-thrust type was, of course, "first off," +sometimes 10 ft. or 12 ft. ahead, or even more; but the correctly +designed propeller gradually gathered up speed and acceleration, just +as the other fell off and lost it, and finally the "dynamic" finished +along its corresponding wire far ahead of the "static," sometimes +twice as far, sometimes six times. "Freak" propellers were simply not +in it. + +[Illustration: FIG. 38.--"VENNA" PROPELLER. + +A 20 per cent. more efficient propeller than that shown in Fig. 41; 14 +per cent. lighter; 6 per cent. better in dynamic thrust--14 in. diam.; +weight 31 grammes.] + +Metal propellers of constant angle, as well as wooden ones of uniform +(constant) pitch, were tested; the former gave good results, but not +so good as the latter. + +The best angle of pitch (at the tip) was found to be from 20° to 30°. + +In all cases when the slip was as low as 25 per cent., or even +somewhat less, nearly 20 per cent., a distinct "back current" of air +was given out by the screw. This "slip stream," as it is caused, is +absolutely necessary for efficiency. + +§ 21. =Fabric-covered= screws did not give very efficient results; the +only point in their use on model aeroplanes is their extreme +lightness. Two such propellers of 6 in. diameter can be made to weigh +less than 1/5 oz. the pair; but wooden propellers (built-up principle) +have been made 5 in. diameter and 1/12 oz. in weight. + +§ 22. Further experiments were made with twin screws mounted on model +aeroplanes. In one case two propellers, both turning in the _same_ +direction, were mounted (without any compensatory adjustment for +torque) on a model, total weight 1½ lb. Diameter of each propeller +14 in.; angle of blade at tip 25°. The result was several good +flights--the model (_see_ Fig. 49c) was slightly unsteady across the +wind, that was all. + +In another experiment two propellers of same diameter, pitch, etc., +but of shape similar to those shown in Figs. 28 and 29, were tried as +twin propellers on the same machine. The rubber motors were of equal +weight and strength. + +The model described circled to the right or left according to the +position of the curved-shaped propeller, whether on the left or right +hand, thereby showing its superiority in dynamic thrust. Various +alterations were made, but always with the same result. These +experiments have since been confirmed, and there seems no doubt that +the double-curved shaped blade _is_ superior. (See Fig. 39.) + +§ 23. =The Fleming-Williams Propeller.=--A chapter on propellers would +scarcely be complete without a reference to the propeller used on a +machine claiming a record of over a quarter of a mile. This form of +propeller, shown in the group in Fig. 36 (top right hand), was found +by the writer to be extremely deficient in dynamic thrust, giving the +worst result of any shown there. + +[Illustration: FIG. 39.--CURVED DOUBLE PROPELLER. + +The most efficient type yet tested by the writer, when the blade is +made hollow-faced. When given to the writer to test it was flat-faced +on one side.] + +[Illustration: FIG. 40.--THE FLEMING-WILLIAMS MODEL.] + +It possesses large blade area, large pitch angle--more than 45° at the +tip--and large diameter. These do not combine to propeller efficiency +or to efficient dynamic thrust; but they do, of course, combine to +give the propeller a very slow rotational velocity. Provided they give +_sufficient_ thrust to cause the model to move through the air at a +velocity capable of sustaining it, a long flight may result, not +really owing to true efficiency on the part of the propellers,[36] but +owing to the check placed on their revolutions per minute by their +abnormal pitch angle, etc. The amount of rubber used is very great for +a 10 oz. model, namely, 34 strands of 1/16 in. square rubber to each +propeller, i.e. 68 strands in all. + +[Illustration: FIG. 41.--THE SAME IN FLIGHT. + +(_Reproduced by permission from "The Aero."_)] + +On the score of efficiency, when it is desired to make a limited +number of turns give the longest flight (which is the problem one +always has to face when using a rubber motor) it is better to make use +of an abnormal diameter, say, more than half the span, and using a tip +pitch angle of 25°, than to make use of an abnormal tip pitch 45° and +more, and large blade area. In a large pitch angle so much energy is +wasted, not in dynamic thrust, but in transverse upsetting torque. On +no propeller out of dozens and dozens that I have tested have I ever +found a tip-pitch of more than 35° give a good dynamic thrust; and for +length of flight velocity due to dynamic thrust must be given due +weight, as well as the duration of running down of the rubber motor. + +§ 24. Of built up or carved out and twisted wooden propellers, the +former give the better result; the latter have an advantage, however, +in sometimes weighing less. + +FOOTNOTES: + +[24] _Note._--Since the above was written some really remarkable +flights have been obtained with a 1 oz. model having two screws, one +in front and the other behind. Equally good flights have also been +obtained with the two propellers behind, one revolving in the +immediate rear of the other. Flying, of course, with the wind, +_weight_ is of paramount importance in these little models, and in +both these cases the "single stick" can be made use of. _See also_ ch. +iv., § 28. + +[25] _See also_ ch. viii., § 5. + +[26] Save in case of some models with fabric-covered propellers. Some +dirigibles are now being fitted with four-bladed wooden screws. + +[27] Vide Appendix. + +[28] Vide Equivalent Inclinations--Table of. + +[29] One in 3 or 0·333 is the _sine_ of the angle; similarly if the +angle were 30° the sine would be 0·5 or ½, and the theoretical +distance travelled one-half. + +[30] _Flat-Faced Blades._--If the blade be not hollow-faced--and we +consider the screw as an inclined plane and apply the Duchemin formula +to it--the velocity remaining the same, the angle of maximum thrust is +35¼°. Experiments made with such screws confirm this. + +[31] Cavitation is when the high speed of the screw causes it to carry +round a certain amount of the medium with it, so that the blades +strike no undisturbed, or "solid," air at all, with a proportionate +decrease in thrust. + +[32] In the Wright machine r.p.m. = 450; in Blériot XI. r.p.m. = 1350. + +[33] Such propellers, however, require a considerable amount of +rubber. + +[34] But _see also_ § 22. + +[35] "Flight," March 10, 1910. (Illustration reproduced by +permission.) + +[36] According to the author's views on the subject. + + + + +CHAPTER VI. + +THE QUESTION OF SUSTENTATION THE CENTRE OF PRESSURE. + + +§ 1. Passing on now to the study of an aeroplane actually in the air, +there are two forces acting on it, the upward lift due to the air +(i.e. to the movement of the aeroplane supposed to be continually +advancing on to fresh, undisturbed _virgin_ air), and the force due to +the weight acting vertically downwards. We can consider the resultant +of all the upward sustaining forces as acting at a single point--that +point is called the "Centre of Pressure." + +Suppose A B a vertical section of a flat aerofoil, inclined at a small +angle _a_ to the horizon C, the point of application of the resultant +upward 'lift,' D the point through which the weight acts vertically +downwards. Omitting for the moment the action of propulsion, if these +two forces balance there will be equilibrium; but to do this they must +pass through the same point, but as the angle of inclination varies, +so does the centre of pressure, and some means must be employed +whereby if C and D coincide at a certain angle the aeroplane will come +back to the correct angle of balance if the latter be altered. + +In a model the means must be automatic. Automatic stability depends +for its action upon the movement of the centre of pressure when the +angle of incidence varies. When the angle of incidence increases the +centre of pressure moves backwards towards the rear of the aerofoil, +and vice versa. + +Let us take the case when steady flight is in progress and C and D are +coincident, suppose the velocity of the wind suddenly to +increase--increased lifting effect is at once the result, and the fore +part of the machine rises, i.e. the angle of incidence increases and +the centre of pressure moves back to some point in the rear of C D. +The weight is now clearly trying to pull the nose of the aeroplane +down, and the "lift" tending to raise the tail. The result being an +alteration of the angle of incidence, or angle of attack as it is +called, until it resumes its original position of equilibrium. A drop +in the wind causes exactly an opposite effect. + +[Illustration: FIG. 42.] + +§ 2. The danger lies in "oscillations" being set up in the line of +flight due to changes in the position of the centre of pressure. Hence +the device of an elevator or horizontal tail for the purpose of +damping out such oscillations. + +§ 3. But the aerofoil surface is not flat, owing to the increased +"lift" given by arched surfaces, and a much more complicated set of +phenomena then takes place, the centre of pressure moving forward +until a certain critical angle of incidence is reached, and after +this a reversal takes place, the centre of pressure then actually +moving backwards. + +The problem then consists in ascertaining the most efficient aerocurve +to give the greatest "lift" with the least "drift," and, having found +it, to investigate again experimentally the movements of the centre of +pressure at varying angles, and especially to determine at what angle +(about) this "reversal" takes place. + +[Illustration: FIG. 43.] + +§ 4. Natural automatic stability (the only one possible so far as +models are concerned) necessitates permanent or a permanently +recurring coincidence (to coin a phrase) of the centre of gravity and +the centre of pressure: the former is, of course, totally unaffected +by the vagaries of the latter, any shifting of which produces a couple +tending to destroy equilibrium. + +§ 5. As to the best form of camber (for full sized machine) possibly +more is known on this point than on any other in the whole of +aeronautics. + +In Figs. 44 and 45 are given two very efficient forms of cambered +surfaces for models. + +[Illustration: FIG. 44.--AN EFFICIENT FORM OF CAMBER. + + B D Maximum Altitude. A C Chord. + Ratio of B D: A C :: 1:17. A D 1/3 of A C.] + +[Illustration: FIG. 45.--ANOTHER EFFICIENT FORM. + +Ratio of B D to A C 1 to 17. AD rather more than ¼ of A C.] + +The next question, after having decided the question of aerocurve, or +curvature of the planes, is at what angle to set the cambered surface +to the line of flight. This brings us to the question of the-- + +§ 6. =Dipping Front Edge.=--The leading or front edge is not +tangential to the line of flight, but to a relative upward wind. It is +what is known as the "cyclic up-current," which exists in the +neighbourhood of the entering edge. Now, as we have stated before, it +is of paramount importance that the aerofoil should receive the air +with as little shock as possible, and since this up-current does +really exist to do this, it must travel through the air with a dipping +front edge. The "relative wind" (the only one with which we are +concerned) _is_ thereby met tangentially, and as it moves onward +through the air the cambered surface (or aerocurve) gradually +transforms this upward trend into a downward wake, and since by +Newton's law, "Action and reaction are equal and opposite," we have +an equal and opposite upward reaction. + +We now know that the top (or convex side) of the cambered surface is +practically almost as important as the underneath or concave side in +bringing this result about. + +The exact amount of "dipping edge," and the exact angle at which the +chord of the aerocurve, or cambered surface, should be set to the line +of flight--whether at a positive angle, at no angle, or at a negative +angle--is one best determined by experiment on the model in question. + +[Illustration: FIG. 46.] + +But _if at any angle, that angle either way should be a very small +one_. If you wish to be very scientific you can give the underside of +the front edge a negative angle of 5° to 7° for about one-eighth of +the total length of the section, after that a positive angle, +gradually increasing until you finally finish up at the trailing edge +with one of 4°. Also, the form of cambered surface should be a +paraboloid--not arc or arc of circles. The writer does not recommend +such an angle, but prefers an attitude similar to that adopted in the +Wright machine, as in Fig. 47. + +§ 7. Apart from the attitude of the aerocurve: _the greatest depth of +the camber should be at one-third of the length of the section from +the front edge, and the total depth measured from the top surface to +the chord at this point should not be more than one-seventeenth of the +length of section_. + +§ 8. It is the greatest mistake in model aeroplanes to make the camber +otherwise than very slight (in the case of surfaced aerofoils the +resistance is much increased), and aerofoils with anything but a _very +slight_ arch are liable to be very unstable, for the aerocurve has +always a decided tendency to "follow its own curve." + +[Illustration: FIG. 47.--ATTITUDE OF WRIGHT MACHINE.] + +The nature of the aerocurve, its area, the angle of inclination of its +chord to the line of flight, its altitude, etc., are not the only +important matters one must consider in the case of the aerofoil, we +must also consider-- + +§ 9. Its =Aspect Ratio=, i.e. the ratio of the span (length) of the +aerofoil to the chord--usually expressed by span/chord. In the Farman +machine this ratio is 5·4; Blériot, 4·3; Short, 6 to 7·5; Roe +triplane, 7·5; a Clark flyer, 9·6. + +Now the higher the aspect ratio the greater should be the efficiency. +Air escaping by the sides represents loss, and the length of the sides +should be kept short. A broader aerofoil means a steeper angle of +inclination, less stability, unnecessary waste of power, and is +totally unsuited for a model--to say nothing of a full-sized machine. + +In models this aspect ratio may with advantage be given a higher value +than in full-sized machines, where it is well known a practical safe +constructional limit is reached long before theory suggests the +limit. The difficulty consists in constructing models having a very +high aspect ratio, and yet possessing sufficient strength and +lightness for successful flight. It is in such a case as this where +the skill and ingenuity of the designer and builder come in. + +It is this very question of aspect ratio which has given us the +monoplane, the biplane, and the triplane. A biplane has a higher +aspect ratio than a monoplane, and a triplane (see above) a higher +ratio still. + +It will be noticed the Clark model given has a considerably higher +aspect ratio, viz. 9·6. And even this can be exceeded. + +_An aspect ratio of_ 10:1 _or even_ 12:1 _should be used if +possible._[37] + +§ 10. =Constant or Varying Camber.=--Some model makers vary the camber +of their aerofoils, making them almost flat in some parts, with +considerable camber in others; the tendency in some cases being to +flatten the central portions of the aerofoil, and with increasing +camber towards the tips. In others the opposite is done. The writer +has made a number of experiments on this subject, but cannot say he +has arrived at any very decisive results, save that the camber should +in all cases be (as stated before) very slight, and so far as his +experiments do show anything, they incline towards the further +flattening of the camber in the end portions of the aerofoil. It must +not be forgotten that a flat-surfaced aerofoil, constructed as it is +of more or less elastic materials, assumes a natural camber, more or +less, when driven horizontally through the air. Reference has been +made to a reversal of the-- + +§ 11. =Centre of Pressure on Arched Surfaces.=--Wilbur Wright in his +explanation of this reversal says: "This phenomenon is due to the fact +that at small angles the wind strikes the forward part of the aerofoil +surface on the upper side instead of the lower, and thus this part +altogether ceases to lift, instead of being the most effective part of +all." The whole question hangs on the value of the critical angle at +which this reversal takes place; some experiments made by Mr. M.B. +Sellers in 1906 (published in "Flight," May 14, 1910) place this angle +between 16° and 20°. This angle is much above that used in model +aeroplanes, as well as in actual full-sized machines. But the +equilibrium of the model might be upset, not by a change of attitude +on its part, but on that of the wind, or both combined. By giving (as +already advised) the aerofoil a high aspect ratio we limit the travel +of the centre of pressure, for a high aspect ratio means, as we have +seen, a short chord; and this is an additional reason for making the +aspect ratio as high as practically possible. The question is, is the +critical angle really as high as Mr. Seller's experiments would show. +Further experiments are much needed. + +FOOTNOTES: + +[37] Nevertheless some models with a very low aspect ratio make good +flyers, owing to their extreme lightness. + + + + +CHAPTER VII. + +MATERIALS FOR AEROPLANE CONSTRUCTION. + + +§ 1. The choice of materials for model aeroplane construction is more +or less limited, if the best results are to be obtained. The lightness +absolutely essential to success necessitates--in addition to skilful +building and best disposition of the materials--materials of no undue +weight relative to their strength, of great elasticity, and especially +of great resilience (capacity to absorb shock without injury). + +§ 2. =Bamboo.=--Bamboo has per pound weight a greater resilience than +any other suitable substance (silk and rubber are obviously useless as +parts of the _framework_ of an aeroplane). On full-sized machines the +difficulty of making sufficiently strong connections and a liability +to split, in the larger sizes, are sufficient reasons for its not +being made more use of; but it makes an almost ideal material for +model construction. The best part to use (split out from the +centrepiece) is the strip of tough wood immediately below the hard +glazed surface. For struts, spars, and ribs it can be used in this +manner, and for the long strut supporting the rubber motor an entire +tube piece should be used of the requisite strength required; for an +ordinary rubber motor (one yard long), 30 to 50 strands, this should +be a piece 3/8 in. in diameter, and weight about 5/8 oz. per ft. +_Bamboo may be bent_ by either the "dry" heat from a spirit lamp or +stove, or it may be steamed, the latter for preference, as there is +no danger of "scorching" the fibres on the inside of the bend. When +bent (as in the case of other woods) it should be bound on to a +"former" having a somewhat greater curvature than the curve required, +because when cool and dry it will be sure to "go back" slightly. It +must be left on the former till quite dry. When bending the "tube" +entire, and not split portions thereof, it should be immersed in very +hot, or even boiling, water for some time before steaming. The really +successful bending of the tube _en bloc_ requires considerable +patience and care. + +Bamboo is inclined to split at the ends, and some care is required in +making "joints." The ribs can be attached to the spars by lashing them +to thin T strips of light metal, such as aluminium. Thin thread, or +silk, is preferable to very thin wire for lashing purpose, as the +latter "gives" too much, and cuts into the fibres of the wood as well. + +§ 3. =Ash=, =Spruce=, =Whitewood= are woods that are also much used by +model makers. Many prefer the last named owing to its uniform freedom +from knots and ease with which it can be worked. It is stated 15 per +cent. additional strength can be imparted by using hot size and +allowing it to soak into the wood at an increase only of 3·7 per cent. +of weight. It is less than half the weight of bamboo, but has a +transverse rupture of only 7,900 lb. per sq. in. compared to 22,500 in +the case of bamboo tubing (thickness one-eighth diameter) and a +resilience per lb. weight of slightly more than one half. Some model +makers advocate the use of =poplar= owing to its extreme lightness +(about the same as whitewood), but its strength is less in the ratio +of about 4:3; its resilience is very slightly more. It must be +remembered that wood of the same kind can differ much as to its +strength, etc., owing to what part of the tree it may have been cut +from, the manner in which it may have been seasoned, etc. For model +aeroplanes all wood used should have been at least a year in +seasoning, and should be so treated when in the structure that it +cannot absorb moisture. + +If we take the resilience of ash as 1, then (according to Haswell) +relative resilience of beech is 0·86, and spruce 0·64. + +The strongest of woods has a weight when well seasoned of about 40 lb. +per cub. ft. and a tenacity of about 10,000 lb. per sq. in. + +[Illustration: FIG. 47A.--"AEROPLANE ALMA." + +A very effective French Toy Monoplane.] + +§ 4. =Steel.=--Ash has a transverse rupture of 14,300 lb. per sq. in., +steel tubing (thickness = 1/30 its diameter) 100,000 lb. per sq. in. +Ash weighs per cub. ft. 47 lb., steel 490. Steel being more than ten +times as heavy as ash--but a transverse rupture stress seven times as +high. + +Bamboo in tube form, thickness one-third of diameter, has a +transverse rupture of 22,500 lb. per sq. in., and a weight of 55 lb. +per cub. ft. + +Steel then is nine times as heavy as bamboo--and has a transverse +rupture stress 4·4 times as great. In comparing these three substances +it must be carefully borne in mind that lightness and strength are not +the only things that have to be provided for in model aeroplane +building; there is the question of _resistance_--we must offer as +small a cross-section to moving through the air as possible. + +Now while ash or bamboo and certain other timbers may carry a higher +load per unit of weight than steel, they will present about three to +three and a half times the cross-section, and this produces a serious +obstacle, while otherwise meeting certain requirements that are most +desirable. Steel tubing of sufficiently small bore is not, so far as +the writer knows, yet on the market in England. In France very thin +steel tubes are made of round, oval, hexagon, etc., shape, and of +accurate thickness throughout, the price being about 18s. a lb. + +Although suitable steel tubing is not yet procurable under ordinary +circumstances, umbrella steel is. + +§ 5. =Umbrella Section Steel= is a section 5/32 in. by 1/8 in. deep, 6 +ft. long weighing 2·1 oz., and a section 3/32 in. across the base by +1/8 in. deep, 6 ft. long weighing 1·95 oz. + +It is often stated that umbrella ribs are too heavy--but this entirely +depends on the length you make use of, in lengths of 25 in. for small +aerofoils made from such lengths it is so; but in lengths of 48 in. +(two such lengths joined together) the writer has used it with great +success; often making use of it now in his larger models; the +particular size used by him weighs 13½ grammes, to a length of 25 +in. He has never had one of these aerofoils break or become +kinked--thin piano wire is used to stay them and also for spars when +employed--the front and ends of the aerofoil are of umbrella steel, +the trailing edge of steel wire, comparatively thin, kept taut by +steel wire stays. + +§ 6. =Steel Wire.=--Tensile strength about 300,000 lb. per sq. in. For +the aerofoil framework of small models and for all purposes of +staying, or where a very strong and light tension is required, this +substance is invaluable. Also for framework of light fabric covered +propellers as well as for skids and shock absorber--also for hooks to +hold the rubber motor strands, etc. No model is complete without it in +some form or another. + +§ 7. =Silk.=--This again is a _sine qua non_. Silk is the strongest of +all organic substances for certain parts of aeroplane construction. It +has, in its best form, a specific gravity of 1·3, and is three times +as strong as linen, and twice as strong in the thread as hemp. Its +finest fibres have a section of from 0·0010 to 0·0015 in diameter. It +will sustain about 35,000 lb. per sq. in. of its cross section; and +its suspended fibre should carry about 150,000 ft. of its own +material. This is six times the same figure for aluminium, and equals +about 75,000 lb. steel tenacity, and 50 more than is obtained with +steel in the form of watch springs or wire. For aerofoil surface no +substance can compare with it. But it must be used in the form of an +"oiled" or specially treated silk. Several such are on the market. +Hart's "fabric" and "radium" silk are perhaps the best known. Silk +weighs 62 lb. per cub. ft., steel has, we have seen, 490 lb., thus +paying due regard to this and to its very high tensile strength it is +superior to even steel wire stays. + +§ 8. =Aluminium and Magnalium.=--Two substances about which a great +deal has been heard in connection with model aeroplaning; but the +writer does not recommend their use save in the case of fittings for +scale models, not actual flyers, unless especially light ones meant +to fly with the wind. Neither can compare with steel. Steel, it is +true, is three times as heavy as aluminium, but it has four or five +times its strength; and whereas aluminium and magnalium may with +safety be given a permissible breaking strength of 60 per cent. and 80 +per cent. respectively, steel can easily be given 80 per cent. Being +also less in section, resistance to air travel is again less as in the +case of wood. In fact, steel scores all round. Weight of magnalium : +weight of aluminium :: 8:9. + +§ 9. =Alloys.=--During recent years scores, hundreds, possibly +thousands of different alloys have been tried and experimented on, but +steel still easily holds its own. It is no use a substance being +lighter than another volume for volume, it must be _lighter and +stronger weight for weight_, to be superior for aeronautical purpose, +and if the difference be but slight, question of _bulk_ may decide it +as offering _less resistance_. + +§ 10. =Sheet Ebonite.=--This substance is sometimes useful for +experiments with small propellers, for it can be bent and moulded in +hot water, and when cold sets and keeps its shape. _Vulcanized fibre_ +can be used for same purpose. _Sheet celluloid_ can be used in the +same way, but in time it becomes brittle and shrinks. _Mica_ should be +avoided. _Jointless cane_ in various sizes is a very useful +material--the main aerofoil can be built of it, and it is useful for +skids, and might be made more use of than it is.[38] _Three ply wood_, +from 1/50 in. in thickness, is now on the market. Four or five ply +wood can also be obtained. To those desiring to build models having +wooden aerofoils such woods offer the advantage of great strength and +extreme lightness. + +Referring to Table V. (Timber) at the end of the book, apparently the +most suitable wood is Lombardy poplar; but its light weight means +increased bulk, i.e. additional air resistance. Honduras mahogany is +really a better all-round wood, and beech is not far behind. + +Resilience is an important factor. Ash heads the list; but mahogany's +factor is also good, and in other respects superior. + +Lombardy poplar ought to be a very good wood for propellers, owing to +its lightness and the ease with which it can be worked. + +_Hollow reeds_, and even _porcupine quills_, have been pressed into +the service of the model maker, and owing to their great strength and +extreme lightness, more especially the latter, are not without their +uses. + +FOOTNOTES: + +[38] The chief advantage of cane--its want of stiffness, or facility +in bending--is for some parts of the machine its chief disadvantage, +where stiffness with resilience is most required. + + + + +CHAPTER VIII. + +HINTS ON THE BUILDING OF MODEL AEROPLANES. + + +§ 1. The chief difficulty in the designing and building of model +aeroplanes is to successfully combat the conflicting interests +contained therein. Weight gives stability, but requires extra +supporting surface or a higher speed, i.e. more power, i.e. more +weight. Inefficiency in one part has a terrible manner of repeating +itself; for instance, suppose the aerofoil surface inefficient--badly +designed--this means more resistance; more resistance means more +power, i.e. weight, i.e. more surface, and so on _ad infinitum_. + +It is because of circumstances like the above that it is so difficult +to _design_ really good and efficient flying models; the actual +building of them is not so difficult, but few tools are required, none +that are expensive or difficult to use. + +In the making of any particular model there are special points that +require special attention; but there are certain general rules and +features which if not adhered to and carefully carried out, or as +carefully avoided, will cause endless trouble and failure. + +§ 2. In constructing a model aeroplane, or, indeed, any piece of +aerial apparatus, it is very important not to interrupt the continuity +of any rib, tube, spar, etc., by drilling holes or making too thinned +down holding places; if such be done, additional strength by binding +(with thread, not wire), or by slipping a small piece of slightly +larger tube over the other, must be imparted to the apparatus. + +§ 3. Begin by making a simple monoplane, and afterwards as you gain +skill and experience proceed to construct more elaborate and +scientific models. + +§ 4. Learn to solder--if you do not know how to--it is absolutely +essential. + +§ 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 this aerofoil and not the balancing elevator, or tail, +that _first_ encounters the upsetting gust, and the effect of such a +gust acting first on the larger surface is often more than the +balancer can rectify in time to avert disaster. The proper place for +the propeller is behind, in the wake of the machine. If the screw be +in front the backwash from it strikes the machine and has a decidedly +retarding action. It is often contended that it drives the air at an +increased velocity under (and over) the main aerofoil, and so gives a +greater lifting effect. But for proper lifting effect which it can +turn without effort into air columns of proper stream line form what +the aerofoil requires is undisturbed air--not propeller backwash. + +The rear of the model is the proper place for the propeller, in the +centre of greatest air disturbance; in such a position it will recover +a portion of the energy lost in imparting a forward movement to the +air, caused by the resistance, the model generally running in such +air--the slip of the screw is reduced to a corresponding degree--may +even vanish altogether, and what is known as negative slip occur. + +§ 6. Wooden or metal aerofoils are more efficient than fabric covered +ones. But they are only satisfactory in the smaller sizes, owing, for +one thing, to the smash with which they come to the ground. This being +due to the high speed necessary to sustain their weight. For +larger-sized models fabric covered aerofoils should be used. + +§ 7. As to the shape of such, only three need be considered--the (_a_) +rectangular, (_b_) the elongated ellipse, (_c_) the chamfered rear +edge. + +[Illustration: FIG. 48.--(_a_), (_b_), (_c_).] + +§ 8. The stretching of the fabric on the aerofoil framework requires +considerable care, especially when using silk. It is quite possible, +even in models of 3 ft. to 4 ft. spread, to do without "ribs," and +still obtain a fairly correct aerocurve, if the material be stretched +on in a certain way. It consists in getting a correct longitudinal and +transverse tension. We will illustrate it by a simple case. Take a +piece of thickish steel pianoforte wire, say, 18 in. long, bend it +round into a circle, allowing ½ in. to 1 in. to overlap, tin and +solder, bind this with soft very thin iron wire, and again solder +(always use as little solder as possible). Now stitch on to this a +piece of nainsook or silk, deforming the circle as you do so until it +has the accompanying elliptical shape. The result is one of double +curvature; the transverse curve (dihedral angle) can be regulated by +cross threads or wires going from A to B and C to D. + +[Illustration: FIG. 49.] + +[Illustration: FIG. 49A.--MR. T.W.K. CLARKE'S 1 OZ. MODEL.] + +The longitudinal curve on the camber can be regulated by the original +tension given to it, and by the manner of its fixing to the main +framework. Suitable wire projections or loops should be bound to it by +wire, and these fastened to the main framework by binding with _thin_ +rubber cord, a very useful method of fastening, since it acts as an +excellent shock absorber, and "gives" when required, and yet +possesses quite sufficient practical rigidity. + +§ 9. Flexible joints are an advantage in a biplane; these can be made +by fixing wire hooks and eyes to the ends of the "struts," and holding +them in position by binding with silk or thread. Rigidity is obtained +by use of steel wire stays or thin silk cord. + +[Illustration: FIG. 49B.--MR. T.W.K. CLARKE'S 1 OZ. MODEL. + +Showing the position of C. of G., or point of support.] + +§ 10. Owing to the extra weight and difficulties of construction on so +small a scale it is not desirable to use "double surface" aerofoils +except on large size power-driven models. + +§ 11. It is a good plan not to have the rod or tube carrying the +rubber motor connected with the outrigger carrying the elevator, +because the torque of the rubber tends to twist the carrying +framework, and interferes with the proper and correct action of the +elevator. If it be so connected the rod must be stayed with piano +wire, both longitudinally (to overcome the pull which we know is very +great), and also laterally, to overcome the torque. + +[Illustration: FIG. 49C.--A LARGE MODEL AEROPLANE. + +Shown without rubber or propellers. Designed and constructed by the +writer. As a test it was fitted with two 14 in. propellers revolving +in the _same_ direction, and made some excellent flights under these +conditions, rolling slightly across the wind, but otherwise keeping +quite steady. Total weight, 1½ lb.; length, 6 ft.; span of main +aerofoil, 5 ft. Constructed of bamboo, cane, and steel wire. Front +skids steel wire. Back skids cane. Aerofoil covering nainsook.] + + +§ 12. Some builders place the rubber motor above the rod, or bow frame +carrying the aerofoils, etc., the idea being that the pull of the +rubber distorts the frame in such a manner as to "lift" the elevator, +and so cause the machine to rise rapidly in the air. This it does; but +the model naturally drops badly at the finish and spoils the effect. +It is not a principle that should be copied. + +[Illustration: FIG. 49D.--A VERY LIGHT WEIGHT MODEL. + +Constructed by the author. Provided with twin propellers of a modified +Fleming-Williams type. This machine flew well when provided with an +abnormal amount of rubber, owing to the poor dynamic thrust given by +the propellers.] + +§ 13. In the Clarke models with the small front plane, the centre of +pressure is slightly in front of the main plane. + +The balancing point of most models is generally slightly in front, or +just within the front edge of the main aerofoil. The best plan is to +adjust the rod carrying the rubber motor and propeller until the best +balance is obtained, then hang up the machine to ascertain the centre +of gravity, and you will have (approximately) the centre of pressure. + +[Illustration: FIG. 49E.--USEFUL FITTINGS FOR MODELS. + +1. Rubber tyred wheels. 2. Ball-bearing steel axle shafts. 3. Brass wire +strainers with steel screws; breaking strain 200 lb. 4. Magnalium +tubing. 5. Steel eyebolt. 6. Aluminium "T" joint. 7. Aluminium "L" +piece. 8. Brass brazed fittings. 9. Ball-bearing thrust. 10. Flat +aluminium "L" piece. (_The above illustrations taken (by permission) +from Messrs. Gamage's catalogue on Model Aviation._)] + +§ 14. The elevator (or tail) should be of the non-lifting type--in +other words, the entire weight should be carried by the main aerofoil +or aerofoils; the elevator being used simply as a balancer.[39] If the +machine be so constructed that part of the weight be carried by the +elevator, then either it must be large (in proportion) or set up at a +large angle to carry it. Both mean considerably more resistance--which +is to be avoided. In practice this means the propeller being some +little distance in rear of the main supporting surface. + +[Illustration: FIG. 49F.--USEFUL FITTINGS FOR MODELS. + +11. Aluminium ball thrust and racket. 12. Ball-bearing propeller, +thrust, and stay. + +(_The above illustrations taken (by permission) from Messrs. Gamage's +catalogue on Model Aviation._)] + +§ 15. In actual flying models "skids" should be used and not "wheels"; +the latter to be of any real use must be of large diameter, and the +weight is prohibitive. Skids can be constructed of cane, imitation +whalebone, steel watch or clock-spring, steel pianoforte wire. Steel +mainsprings are better than imitation whalebone, but steel pianoforte +wire best of all. For larger sized models bamboo is also suitable, as +also ash or strong cane. + +§ 16. Apart from or in conjunction with skids we have what are termed +"shock absorbers" to lessen the shock on landing--the same substances +can be used--steel wire in the form of a loop is very effectual; +whalebone and steel springs have a knack of snapping. These shock +absorbers should be so attached as to "give all ways" for a part side +and part front landing as well as a direct front landing. For this +purpose they should be lashed to the main frame by thin indiarubber +cord. + +§ 17. In the case of a biplane model the "gap" must not be less than +the "chord"--preferably greater. + +In a double monoplane (of the Langley type) there is considerable +"interference," i.e. the rear plane is moving in air already acted on +by the front one, and therefore moving in a downward direction. This +means decreased efficiency. It can be overcome, more or less, by +varying the dihedral angle at which the two planes are set; but cannot +be got rid of altogether, or by placing them far apart. In biplanes +not possessing a dihedral angle--the propeller can be placed +_slightly_ to one side--in order to neutralise the torque of the +propeller--the best portion should be found by experiment--unless the +pitch be very large; with a well designed propeller this is not by any +means essential. If the propeller revolve clockwise, place it towards +the right hand of the machine, and vice versa. + +§ 18. In designing a model to fly the longest possible distance the +monoplane type should be chosen, and when desiring to build one that +shall remain the longest time in the air the biplane or triplane type +should be adopted.[40] For the longest possible flight twin propellers +revolving in opposite directions[41] are essential. To take a concrete +case--one of the writer's models weighed complete with a single +propeller 8½ oz. It was then altered and fitted with two propellers +(same diameter and weight); this complete with double rubber weighed +10¼ oz. The advantage double the power. Weight increased only 20 +per cent., resistance about 10 per cent., total 30 per cent. Gain 70 +per cent. Or if the method of gearing advocated (see Geared Motors) be +adopted then we shall have four bunches of rubber instead of two, and +can thereby obtain so many more turns.[42] The length of the strands +should be such as to render possible at least a thousand turns. + +The propellers should be of large diameter and pitch (not less than +35° at the tips), of curved shape, as advocated in § 22 ch. v.; the +aerofoil surface of as high an aspect ratio as possible, and but +slight camber if any; this is a very difficult question, the question +of camber, and the writer feels bound to admit he has obtained as long +flights with surfaces practically flat, but which do, of course, +camber slightly in a suitable wind, as with stiffer cambered surfaces. + +Wind cambered surfaces are, however, totally unsuitable in gusty +weather, when the wind has frequently a downward trend, which has the +effect of cambering the surface the wrong way about, and placing the +machine flat on the ground. Oiled or specially prepared silk of the +lightest kind should be used for surfacing the aerofoils. Some form of +keel, or fin, is essential to assist in keeping the machine in a +straight course, combined with a rudder and universally jointed +elevator. + +The manner of winding up the propellers has already been referred to +(_see_ chap. iii., § 9). A winder is essential. + +Another form of aerofoil is one of wood (as in Clarke's flyers) or +metal, such a machine relying more on the swiftness of its flight than +on its duration. In this the gearing would possibly not be so +advantageous--but experiment alone could decide. + +The weight of the machine would require to be an absolute minimum, and +everything not absolutely essential omitted. + +It is quite possible to build a twin-screw model on one central stick +alone; but the isosceles triangular form of framework, with two +propellers at the base corners, and the rubber motors running along +the two sides and terminating at the vertex, is preferred by most +model makers. It entails, of course, extra weight. A light form of +skid, made of steel pianoforte wire, should be used. As to the weight +and size of the model, the now famous "one-ouncers" have made some +long flights of over 300 yards[43]; but the machine claiming the +record, half a mile,[44] weighs about 10 oz. And apart from this +latter consideration altogether the writer is inclined to think that +from 5 oz. to 10 oz. is likely to prove the most suitable. It is not +too large to experiment with without difficulty, nor is it so small as +to require the skill of a jeweller almost to build the necessary +mechanism. The propeller speed has already been discussed (_see_ ch. +v., § 15). The model will, of course, be flown with the wind. The +_total_ length of the model should be at least twice the span of the +main aerofoil. + +FOOTNOTES: + +[39] This is a good plan--not a rule. Good flying models can, of +course, be made in which this does not hold. + +[40] This is in theory only: in practice the monoplane holds both +records. + +[41] The best position for the propellers appears to be one in front +and one behind, when extreme lightness is the chief thing desired. + +[42] Because the number of strands of rubber in each bunch will be +much less. + +[43] Mr. Burge Webb claims a record of 500 yards for one of his. + +[44] Flying, of course, with the wind. _Note._--In the "Model +Engineer" of July 7, 1910, will be found an interesting account (with +illustrations) of Mr. W.G. Aston's 1 oz. model, which has remained in +the air for over a minute. + + + + +CHAPTER IX. + +THE STEERING OF THE MODEL. + + +§ 1. Of all the various sections of model aeroplaning that which is +the least satisfactory is the above. + +The torque of the propeller naturally exerts a twisting or tilting +effect upon the model as a whole, the effect of which is to cause it +to fly in (roughly speaking) a circular course, the direction +depending on whether the pitch of the screw be a right or left handed +one. There are various devices by which the torque may be +(approximately) got rid of. + +§ 2. In the case of a monoplane, by not placing the rod carrying the +rubber motor in the exact centre of the main aerofoil, but slightly to +one side, the exact position to be determined by experiment. + +In a biplane the same result is obtained by keeping the rod in the +centre, but placing the bracket carrying the bearing in which the +propeller shaft runs at right angles horizontally to the rod to obtain +the same effect. + +§ 3. The most obvious solution of the problem is to use _two_ equal +propellers (as in the Wright biplane) of equal and opposite pitch, +driven by two rubber motors of equal strength. + +Theoretically this idea is perfect. In practice it is not so. It is +quite possible, of course, to use two rubber motors of an equal number +of strands (equality should be first tested by _weighing_). It should +be possible to obtain two propellers of equal and opposite pitch, +etc., and it is also possible to give the rubber motors the same +number of turns. In practice one is always wound up before the other. +This is the first mistake. They should be wound up _at the same time_, +using a double winder made for the purpose. + +The fact that this is _not_ done is quite sufficient to give an +unequal torsion. The friction in both cases must also be exactly +equal. Both propellers must be released at exactly the same instant. + +Supposing _all_ these conditions fulfilled (in practice they never +are), supposing also the propellers connected by gearing (prohibitive +on account of the weight), and the air quite calm (which it never is), +then the machine should and undoubtedly would _fly straight_. + +For steering purposes by winding up one propeller _many more times_ +than the other, the aeroplane can generally speaking be steered to the +right or left; but from what I have both seen and tried twin-screw +model aeroplanes are _not_ the success they are often made out to be, +and they are much more troublesome to deal with, in spite of what some +say to the contrary. + +The solution of the problem of steering by the use of two propellers +is only partially satisfactory and reliable, in fact, it is no +solution at all.[45] The torque of the propeller and consequent +tilting of the aeroplane is not the only cause at work diverting the +machine from its course. + +§ 4. As it progresses through the air it is constantly meeting air +currents of varying velocity and direction, all tending to make the +model deviate more or less from its course; the best way, in fact, the +only way, to successfully overcome such is by means of _speed_, by +giving the aeroplane a high velocity, not of ten or twelve to fifteen +miles an hour, as is usual in built up fabric-covered aerofoils, but a +velocity of twenty to thirty miles an hour, attainable only in models +(petrol or steam driven) or by means of wooden or metal aerofoils. + +§ 5. Amongst devices used for horizontal steering are vertical "FINS." +These should be placed in the rear above the centre of gravity. They +should not be large, and can be made of fabric tightly stretched over +a wire frame, or of a piece of sheet magnalium or aluminium, turning +on a pivot at the front edge, adjustment being made by simply twisting +the fin round to the desired angle. As to the size, think of rudder +and the size of a boat, but allow for the difference of medium. The +frame carrying the pivot and fin should be made to slide along the rod +or backbone of the model in order to find the most efficient position. + +§ 6. Steering may also be attempted by means of little balancing tips, +or ailerons, fixed to or near the main aerofoil, and pivoted (either +centrally or otherwise) in such a manner that they can be rotated one +in one direction (tilted) and the other in the other (dipped), so as +to raise one side and depress the other. + +§ 7. The model can also be steered by giving it a cant to one side by +weighting the tip of the aerofoil on that side on which it is desired +it should turn, but this method is both clumsy and "weighty." + +§ 8. Another way is by means of the elevator; and this method, since +it entails no additional surfaces entailing extra resistance and +weight, is perhaps the most satisfactory of all. + +It is necessary that the elevator be mounted on some kind of universal +joint, in order that it may not only be "tipped" or "dipped," but also +canted sideways for horizontal steering. + +§ 9. A vertical fin in the rear, or something in the nature of a +"keel," i.e. a vertical fin running down the backbone of the machine, +greatly assists this movement. + +If the model be of the tractor screw and tail (Blériot) type, then the +above remarks _re_ elevator apply _mutatis mutandis_ to the tail. + +§ 10. It is of the most vital importance that the propeller torque +should be, as far as possible, correctly balanced. This can be tested +by balancing the model transversely on a knife edge, winding up the +propeller, and allowing it to run down, and adjusting matters until +the torque and compensatory apparatus balance. As the torque varies +the mean should be used. + +In the case of twin propellers, suspend the model by its centre of +gravity, wind up the propellers, and when running down if the model is +drawn forward without rotation the thrust is equal; if not adjustment +must be made till it does. The easiest way to do this _may_ be by +placing one propeller, the one giving the greater thrust, slightly +nearer the centre. + +In the case of two propellers rotating in opposite directions (by +suitable gearing) on the common centre of two axes, one of the axes +being, of course, hollow, and turning on the other--the rear propeller +working in air already driven back by the other will require a coarser +pitch or larger diameter to be equally efficient. + +FOOTNOTE: + +[45] These remarks apply to rubber driven motors. In the case of +two-power driven propellers in which the power was automatically +adjusted, say, by a gyroscope as in the case of a torpedo--and the +_speed_ of each propeller varied accordingly--the machine could, of +course, be easily steered by such means; but the model to carry such +power and appliances would certainly weigh from 40 lb. to 60 lb. + + + + +CHAPTER X. + +THE LAUNCHING OF THE MODEL. + + +§ 1. Generally speaking, the model should be launched into the air +_against the wind_. + +§ 2. It should (theoretically) be launched into the air with a +velocity equal to that with which it flies. If it launch with a +velocity in excess of that it becomes at once unstable and has to +"settle down" before assuming its normal line of flight. If the +velocity be insufficient, it may be unable to "pick up" its requisite +velocity in time to prevent its falling to the ground. Models with +wooden aerofoils and a high aspect ratio designed for swift flying, +such as the well-known Clarke flyers, require to be practically +"hurled" into the air. + +Other fabric-covered models capable of sustentation at a velocity of 8 +to 10 miles an hour, may just be "released." + +§ 3. Light "featherweight" models designed for long flights when +travelling with the wind should be launched with it. They will not +advance into it--if there be anything of a breeze--but, if well +designed, just "hover," finally sinking to earth on an even keel. Many +ingenious pieces of apparatus have been designed to mechanically +launch the model into the air. Fig. 50 is an illustration of a very +simple but effective one. + +§ 4. For large size power-driven models, unless provided with a +chassis and wheels to enable them to run along and rise from the +ground under their own power, the launching is a problem of +considerable difficulty. + +§ 5. In the case of rubber-driven models desired to run along and rise +from the ground under their own power, this rising must be +accomplished quickly and in a short space. A model requiring a 50 ft. +run is useless, as the motor would be practically run out by that +time. Ten or twelve feet is the limit; now, in order to rise quickly +the machine must be light and carry considerable surface, or, in other +words, its velocity of sustentation must be a low one. + +[Illustration: FIG. 50.--MR. POYNTER'S LAUNCHING APPARATUS. + +(_Reproduced by permission from the "Model Engineer."_)] + +§ 6. It will not do to tip up the elevator to a large angle to make it +rise quickly, because when once off the ground the angle of the +elevator is wrong for actual flight and the model will probably turn a +somersault and land on its back. I have often seen this happen. If the +elevator be set at an increased angle to get it to rise quickly, then +what is required is a little mechanical device which sets the elevator +at its proper flight angle when it leaves the ground. Such a device +does not present any great mechanical difficulties; and I leave it to +the mechanical ingenuity of my readers to devise a simple little +device which shall maintain the elevator at a comparatively large +angle while the model is on the ground, but allowing of this angle +being reduced when free flight is commenced. + +§ 7. The propeller most suitable to "get the machine off the ground" +is one giving considerable statical thrust. A small propeller of fine +pitch quickly starts a machine, but is not, of course, so efficient +when the model is in actual flight. A rubber motor is not at all well +adapted for the purpose just discussed. + +§ 8. Professor Kress uses a polished plank (down which the models slip +on cane skids) to launch his models. + +§ 9. When launching a twin-screw model the model should be held by +each propeller, or to speak more correctly, the two brackets holding +the bearings in which the propeller shafts run should be held one in +each hand in such a way, of course, as to prevent the propellers from +revolving. Hold the machine vertically downwards, or, if too large for +this, allow the nose to rest slightly on the ground; raise (or swing) +the machine up into the air until a little more than horizontal +position is attained, and boldly push the machine into the air (moving +forward if necessary) and release both brackets and screws +simultaneously.[46] + +§ 10. In launching a model some prefer to allow the propellers to +revolve for a few moments (a second, say) _before_ actually launching, +contending that this gives a steadier initial flight. This is +undoubtedly the case, see note on page 111. + +§ 11. In any case, unless trying for a height prize, do not point the +nose of the machine right up into the air with the idea that you will +thereby obtain a better flight. + +Launch it horizontally, or at a very small angle of inclination. When +requiring a model to run along a field or a lawn and rise therefrom +this is much facilitated by using a little strip of smooth oilcloth on +which it can run. Remember that swift flying wooden and metal models +require a high initial velocity, particularly if of large size and +weight. If thrown steadily and at the proper angle they can scarcely +be overthrown. + +FOOTNOTE: + +[46] Another and better way--supposing the model constructed with a +central rod, or some suitable holdfast (this should be situated at the +centre of gravity of the machine) by which it can be held in one +hand--is to hold the machine with both hands above the head, the right +hand grasping it ready to launch it, and the left holding the two +propellers. Release the propellers and allow them a brief interval +(about half a second) to start. Then launch boldly into the air. The +writer has easily launched 1½ lb. models by this means, even in a +high wind. Never launch a model by one hand only. + + + + +CHAPTER XI. + +HELICOPTER MODELS. + + +§ 1. There is no difficulty whatever about making successful model +helicopters, whatever there may be about full-sized machines. + +§ 2. The earliest flying models were helicopters. As early as 1796 Sir +George Cayley constructed a perfectly successful helicopter model (see +ch. iii.); it should be noticed the screws were superimposed and +rotated in opposite directions. + +§ 3. In 1842 a Mr. Phillips constructed a successful power-driven +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 +rushed on the principle of Hero's engines (Barker's Mill Principle +probably). By the escape of steam from the arms the fans were caused +to revolve with immense energy, so much so that the model rose to an +immense altitude and flew across two fields before it alighted. The +motive power employed was obtained from the combustion of charcoal, +nitre and gypsum, as used in the original fire annihilator; the +products of combustion mixing with water in the boiler and forming +gas-charged steam, which was delivered at high pressure from the +extremities of the eight arms.[47] This model and its flight (fully +authenticated) is full of interest and should not be lost sight of, as +in all probability being the first model actuated by steam which +actually flew. + +The helicopter is but a particular phase of the aeroplane. + +§ 4. The simplest form of helicopter is that in which the torque of +the propeller is resisted by a vertical loose fabric plane, so +designed as itself to form a propeller, rotating in the opposite +direction. These little toys can be bought at any good toy shop from +about 6_d._ to 1_s._ Supposing we desire to construct a helicopter of +a more ambitious and scientific character, possessing a vertically +rotating propeller or propellers for horizontal propulsion, as well as +horizontally rotating propellers for lifting purposes. + +[Illustration: FIG. 51.--INCORRECT WAY OF ARRANGING SCREWS.] + +§ 5. There is one essential point that must be carefully attended to, +and that is, _that the horizontal propulsive thrust must be in the +same plane as the vertical lift_, or the only effect will be to cause +our model to turn somersaults. I speak from experience. + +When the horizontally revolving propellers are driven in a horizontal +direction their "lifting" powers will be materially increased, as they +will (like an ordinary aeroplane) be advancing on to fresh undisturbed +air. + +§ 6. I have not for ordinary purposes advocated very light weight wire +framework fabric-covered screws, but in a case like this where the +thrust from the propeller has to be more than the total weight of the +machine, these might possibly be used with advantage. + +§ 7. Instead of using two long vertical rods as well as one long +horizontal one for the rubber strands, we might dispense with the two +vertical ones altogether and use light gearing to turn the torque +action through a right angle for the lifting screws, and use three +separate horizontal rubber strands for the three propellers on a +suitable light horizontal framework. Such should result in a +considerable saving of weight. + +[Illustration: FIG. 52.--CORRECT MANNER. A, B, C = Screws.] + +§ 8. The model would require something in the nature of a vertical fin +or keel to give the sense of direction. Four propellers, two for +"lift" and two for "drift," would undoubtedly be a better +arrangement. + +FOOTNOTE: + +[47] Report on First Exhibition of Aeronautical Society of Great +Britain, held at Crystal Palace, June 1868. + + + + +CHAPTER XII. + +EXPERIMENTAL RECORDS. + + +A model flying machine being a scientific invention and not a toy, +every devotee to the science should make it his or her business to +keep, as far as they are able, accurate and scientific records. For by +such means as this, and the making known of the same, can a _science_ +of model aeroplaning be finally evolved. The following experimental +entry forms, left purposely blank to be filled in by the reader, are +intended as suggestions only, and can, of course, be varied at the +reader's discretion. When you _have_ obtained carefully established +data, do not keep them to yourself, send them along to one of the +aeronautical journals. Do not think them valueless; if carefully +arranged they cannot be that, and may be very valuable. + + +EXPERIMENTAL DATA. + + FORM I. + + Column Headings: + + A: Model + B: Weight + C: Area of Supporting Surface + D: Aspect Ratio + E: Average Length of Flight in Feet + F: Maximum Flight + G: Time of Flight, A. average + H: M. maximum + I: Kind and Direction of Wind + J: Camber + K: Angle of Inclination of Main Aerofoil to Line of Flight + + -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+----- + A | B | C | D | E | F | G | H | I | J | K + -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+----- + | | | | | | A | M | | | + 1 | | | | | | | | | | + 2 | | | | | | | | | | + 3 | | | | | | | | | | + 4 | | | | | | | | | | + 5 | | | | | | | | | | + 6 | | | | | | | | | | + 7 | | | | | | | | | | + 8 | | | | | | | | | | + 9 | | | | | | | | | | + 10 | | | | | | | | | | + 11 | | | | | | | | | | + 12 | | | | | | | | | | + | | | | | | | | | | + -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+----- + + FORM I.--_continued_. + + Column Headings: + + A: Model + B: Weight of (Rubber) Motor + C: Kind of Rubber, Flat, Square or Round + D: Lenght in Inches and Number of Strands + E: Number of Turns + F: Condition at End of Flight + G: Number of Propellers (No.) and Diameter (Diam.) + H: Number of Blades + I: Disc Area (DiscA.) and Pitch (Pitch) + J: Percentage of Slip + K: Thrust + L: Torque in Inche-Ounces + + ----+----+----+-----+----+----+-----+----+-----+----+----+----+ + A | B | C | D | E | F | G | H | I | J | K | L | + ----+----+----+-----+----+----+-----+----+-----+----+----+----+ + | | | | | | | | | | | | | | | + 1 | | | | | | | | | | | | | | | + 2 | | | | | | | | | | | | | | | + 3 | | | | | | | | | | | | | | | + 4 | | | | | | | | | | | | | | | + 5 | | | | | | | | | | | | | | | + 6 | | | | | | | | | | | | | | | + 7 | | | | | | | | | | | | | | | + 8 | | | | | | | | | | | | | | | + 9 | | | | | | | | | | | | | | | + 10 | | | | | | | | | | | | | | | + 11 | | | | | | | | | | | | | | | + 12 | | | | | | | | | | | | | | | + | | | | | | | | | | | | | | | + ----+----+----+-----+----+----+-----+----+-----+----+----+----+ + + + + +CHAPTER XIII. + +MODEL FLYING COMPETITIONS. + + +§ 1. From time to time flying competitions are arranged for model +aeroplanes. Sometimes these competitions are entirely open, but more +generally they are arranged by local clubs with both closed and open +events. + +No two programmes are probably exactly alike, but the following may be +taken as fairly representative:-- + +1. Longest flight measured in a straight line (sometimes both with and +against the wind).[48] + +2. Stability (both longitudinal and transverse). + +3. Longest glide when launched from a given height without power, but +with motor and propeller attached. + +4. Steering. + +5. Greatest height. + +6. The best all-round model, including, in addition to the above, +excellence in building. + +Generally so many "points" or marks are given for each test, and the +model whose aggregate of points makes the largest total wins the +prize; or more than one prize may be offered-- + +One for the longest flight. + +One for the swiftest flight over a measured distance. + +One for the greatest height. + +One for stability and steering. + +And one for the best all-round model. + +The models are divided into classes:-- + +§ 2. _Aero Models Association's Classification, etc._ + + A. Models of 1 sq. ft. surface and under. + B. " 2 sq. ft. " " + C. " 4 sq. ft. " " + D. " 8 sq. ft. " " + E. " over 8 sq. ft. + +All surfaces, whether vertical, horizontal, or otherwise, to be +calculated together for the above classification. + +All round efficiency--marks or points as percentages:-- + + Distance 40 per cent. + Stability 35 " + Directional control 15 " + Gliding angle 10 "[49] + +Two prizes:-- + +One for length of flight. + +One for all-round efficiency (marked as above). + +Every competitor to be allowed three trials in each competition, the +best only to count. + +All flights to be measured in a straight line from the starting to the +landing point. + +Repairs may be made during the competition at the direction of the +judges.[50] + +There are one or two other points where flights are _not_ made with +and against the wind. The competitors are usually requested to start +their models from within a given circle of (say) six feet diameter, +and fly them _in any direction_ they please. + +"Gliding angle" means that the model is allowed to fall from a height +(say) of 20 ft. + +[Illustration: FIG. 53.--MODEL DESIGNED AND CONSTRUCTED BY THE AUTHOR +FOR "GREATEST HEIGHT." + +A very lightly built model with a very low aspect ratio, and screw +giving a very powerful dynamic thrust, and carrying rather a large +amount of rubber. Climbs in left-handed spirals.] + +"Directional control," that the model is launched in some specified +direction, and must pass as near as possible over some indicated +point. + +The models are practically always launched by hand. + +§ 3. Those who desire to win prizes at such competitions would do well +to keep the following points well in mind. + +1. The distance is always measured in a straight line. It is +absolutely essential that your model should be capable of flying +(approximately) straight. To see, as I have done, model after model +fly quite 150 to 200 yards and finish within 50 yards of the +starting-point (credited flight 50 yards) is useless, and a severe +strain on one's temper and patience. + +[Illustration: FIG. 54.--THE GAMAGE CHALLENGE CUP. + +Open Competition for longest flight. Crystal Palace, July 27. Won by +Mr. E.W. Twining.] + +[Illustration: FIG. 55.--MEDAL WON BY THE AUTHOR IN THE SAME +COMPETITION.] + +2. Always enter more than one model, there nearly always is an +entrance fee; never mind the extra shilling or so. Go in to win. + +3. It is not necessary that these models should be replicas of one +another. On some days a light fabric-covered model might stand the +best chance; on another day, a swift flying wooden or metal aerofoil. + +Against the wind the latter have an immense advantage; also if the day +be a "gusty" one.[51] + +4. Always make it a point of arriving early on the ground, so that you +can make some trial flights beforehand. Every ground has its local +peculiarities of air currents, etc. + +5. Always be ready in time, or you may be disqualified. If you are +flying a twin-screw model use a special winder, so that both +propellers are wound up at the same time, and take a competent friend +with you as assistant. + +6. For all-round efficiency nothing but a good all-round model, which +can be absolutely relied on to make a dozen (approximately) equivalent +flights, is any good. + +7. In an open distance competition, unless you have a model which you +can rely on to make a _minimum_ flight of 200 yards, do not enter +unless you know for certain that none of the "crack" flyers will be +present. + +8. Do not neglect the smallest detail likely to lead to success; be +prepared with spare parts, extra rubber, one or two handy tools, wire, +thread, etc. Before a lecture, that prince of experimentalists, +Faraday, was always careful to see that the stoppers of all the +bottles were loose, so that there should be no delay or mishap. + +9. If the rating of the model be by "weight" (1 oz., 2 oz., 4 oz., +etc.) and not area, use a model weighing from 10 oz. to a pound. + +10. If there is a greatest height prize, a helicopter model should win +it.[52] (The writer has attained an altitude of between three and four +hundred feet with such.) The altitude was arrived at by observation, +not guesswork. + +11. It is most important that your model should be able to "land" +without damage, and, as far as possible, on an even keel; do not omit +some form of "skid" or "shock-absorber" with the idea of saving +weight, more especially if your model be a biplane, or the number of +flights may be restricted to the number "one." + +12. Since the best "gliding" angle and "flying" angle are not the +same, being, say, 7° in the former case and 1°-3°, say, in the latter, +an adjustable angle might in some cases be advantageous. + +13. Never turn up at a competition with a model only just finished and +practically untested which you have flown only on the morning of the +competition, using old rubber and winding to 500 turns; result, a +flight of 250 yards, say. Arrived on the competition ground you put on +new rubber and wind to 750 turns, and expect a flight of a quarter of +a mile at least; result 70 yards, _measured in a straight line_ from +the starting-point. + +14. Directional control is the most difficult problem to overcome with +any degree of success under all adverse conditions, and 15 per cent., +in the writer's opinion, is far too low a percentage; by directional I +include flying in a straight line; personally I would mark for +all-round efficiency: (A) distance and stability, 50 per cent.; (B) +directional control, 30 per cent.; (C) duration of flight, 20 per +cent. In A the competitor would launch his model _in any direction_; +in B as directed by the judges. No separate flights required for C. + +FOOTNOTES: + +[48] The better way, undoubtedly, is to allow the competitor to choose +his direction, the starting "circle" only to be fixed. + +[49] Or 10 per cent. for duration of flight. + +[50] In another competition, held under the rules and regulations of +the Kite and Model Aeroplane Association for the best all-round model, +open to the world, for machines not under 2 sq. ft. of surface, the +tests (50 marks for each) were:--A. Longest flight in a straight line. +B. Circular flight to the right. C. Circular flight to the left. D. +Stability and landing after a flight. E. Excellence in building of the +model. + +[51] On the assumption that the model will fly straight. + +[52] If permitted to enter; if not see Fig. 53. + + + + +CHAPTER XIV. + +USEFUL NOTES, TABLES, FORMULÆ, ETC. + + +§ 1. COMPARATIVE VELOCITIES. + + Miles per hr. Feet per sec. Metres per sec. + 10 = 14·7 = 4·470 + 15 = 22 = 6·705 + 20 = 29·4 = 8·940 + 25 = 36·7 = 11·176 + 30 = 44 = 13·411 + 35 = 51·3 = 15·646 + +§ 2. A metre = 39·37079 inches. + + _In order to convert_:-- + Metres into inches multiply by 39·37 + " feet " 3·28 + " yards " 1·09 + " miles " 0·0006214 + Miles per hour into ft. per min. multiply by 88·0 + " min. " sec. " 88·0 + " hr. into kilometres per hr. " 1·6093 + " " metres per sec. " 0·44702 + Pounds into grammes multiply by 453·593 + " kilogrammes " 0·4536 + +§ 8. Total surface of a cylinder = circumference of base × height + 2 +area of base. + +Area of a circle = square of diameter × 0·7854. + +Area of a circle = square of rad. × 3·14159. + +Area of an ellipse = product of axes × 0·7854. + +Circumference of a circle = diameter × 3·14159. + +Solidity of a cylinder = height × area of base. + +Area of a circular ring = sum of diameters × difference of diameters × +0·7854. + +For the area of a sector of a circle the rule is:--As 360 : number of +degrees in the angle of the sector :: area of the sector : area of +circle. + +To find the area of a segment less than a semicircle:--Find the area +of the sector which has the same arc, and subtract the area of the +triangle formed by the radii and the chord. + +The areas of corresponding figures are as the squares of corresponding +lengths. + + § 4. 1 mile = 1·609 kilometres. + 1 kilometre = 1093 yards. + 1 oz. = 28·35 grammes. + 1 lb. = 453·59 " + 1 lb. = 0·453 kilogrammes. + 28 lb. = 12·7 " + 112 lb. = 50·8 " + 2240 lb. = 1016 " + 1 kilogram = 2·2046 lb. + 1 gram = 0·0022 lb. + 1 sq. in. = 645 sq. millimetres. + 1 sq. ft. = 0·0929 sq. metres. + 1 sq. yard = 0·836 " + 1 sq. metre = 10·764 sq. ft. + +§ 5. One atmosphere = 14·7 lb. per sq. in. = 2116 lb. per sq. ft. = +760 millimetres of mercury. + +A column of water 2·3 ft. high corresponds to a pressure of 1 lb. per +sq. in. + +1 H.P. = 33,000 ft.-lb. per min. = 746 watts. + +Volts × amperes = watts. + +{pi} = 3·1416. _g_ = 32·182 ft. per sec. at London. + +§ 6. TABLE OF EQUIVALENT INCLINATIONS. + + Rise. Angle in Degs. + 1 in 30 1·91 + 1 " 25 2·29 + 1 " 20 2·87 + 1 " 18 3·18 + 1 " 16 3·58 + 1 " 14 4·09 + 1 " 12 4·78 + 1 " 10 5·73 + 1 " 9 6·38 + 1 " 8 7·18 + 1 " 7 8·22 + 1 " 6 9·6 + 1 " 5 11·53 + 1 " 4 14·48 + 1 " 3 19·45 + 1 " 2 30·00 + 1 " {square root}2 45·00 + +§ 7. TABLE OF SKIN FRICTION. + +Per sq. ft. for various speeds and surface lengths. + + -----------------+-------------+-------------+-------------+------------ + Velocity of Wind | 1 ft. Plane | 2 ft. Plane | 4 ft. Plane | 8 ft. Plane + -----------------+-------------+-------------+-------------+------------ + 10 | ·00112 | ·00105 | ·00101 | ·000967 + 15 | ·00237 | ·00226 | ·00215 | ·00205 + 20 | ·00402 | ·00384 | ·00365 | ·00349 + 25 | ·00606 | ·00579 | ·00551 | ·00527 + 30 | ·00850 | ·00810 | ·00772 | ·00736 + 35 | ·01130 | ·0108 | ·0103 | ·0098 + -----------------+-------------+-------------+-------------+------------ + +This table is based on Dr. Zahm's experiments and the equation + + _f_ = 0·00000778_l_^{-0·07}_v_^{1·85} + +Where _f_ = skin friction per sq. ft.; _l_ = length of surface; _v_ = +velocity in feet per second. + +In a biplane model the head resistance is probably from twelve to +fourteen times the skin friction; in a racing monoplane from six to +eight times. + +§ 8. TABLE I.--(METALS). + + --------------+------------+-----------------+------------- + Material | Specific | Elasticity E[A] | Tenacity + | Gravity | | per sq. in. + --------------+------------+-----------------+------------- + Magnesium | 1·74 | | {22,000- + | | | {32,000 + Magnalium[B] | 2·4-2·57 | 10·2 | + Aluminium- } | | | + Copper[C]} | 2·82 | | 54,773 + Aluminium | 2·6 | 11·1 | 26,535 + Iron | 7·7 (about)| 29 | 54,000 + Steel | 7·8 (about)| 32 | 100,000 + Brass | 7·8-8·4 | 15 | 17,500 + Copper | 8·8 | 36 | 33,000 + Mild Steel | 7·8 | 30 | 60,000 + | | | + --------------+------------+-----------------+------------- + [A] E in millions of lb. per sq. in. + [B] Magnalium is an alloy of magnesium and aluminium. + [C] Aluminium 94 per cent., copper 6 per cent. (the best + percentage), a 6 per cent. alloy thereby doubles the + tenacity of pure aluminium with but 5 per cent. + increase of density. + --------------+------------+-----------------+------------- + +§ 9. TABLE II.--WIND PRESSURES. + + _p_ = _kv²_. + +_k_ coefficient (mean value taken) ·003 (miles per hour) = 0·0016 ft. +per second. _p_ = pressure in lb. per sq. ft. _v_ = velocity of wind. + + Miles per hr. Ft. per sec. Lb. per sq. ft. + 10 14·7 0·300 + 12 17·6 0·432 + 14 20·5 0·588 + 16 23·5 0·768 + 18 26·4 0·972 + 20 29·35 1·200 + 25 36·7 1·875 + 30 43·9 2·700 + 35 51·3 3·675 + +§ 10. Representing normal pressure on a plane surface by 1; pressure +on a rod (round section) is 0·6; on a symmetrical elliptic cross +section (axes 2:1) is 0·2 (approx.). Similar shape, but axes 6:1, and +edges sharpened (_see_ ch. ii., § 5), is only 0·05, or 1/20, and for +the body of minimum resistance (_see_ ch. ii., § 4) about 1/24. + +§ 11. TABLE III.--LIFT AND DRIFT. + +On a well shaped aerocurve or correctly designed cambered surface. +Aspect ratio 4·5. + + Inclination. Ratio Lift to Drift. + 0° 19:1 + 2·87° 15:1 + 3·58° 16:1 + 4·09° 14:1 + 4·78° 12:1 + 5·73° 9·6:1 + 7·18° 7·9:1 + +Wind velocity 40 miles per hour. (The above deduced from some +experiments of Sir Hiram Maxim.) + +At a velocity of 30 miles an hour a good aerocurve should lift 21 oz. +to 24 oz. per sq. ft. + + +§ 12. TABLE IV.--LIFT AND DRIFT. + +On a plane aerofoil. + + N = P(2 sin {alpha}/1 + sin² {alpha}) + + Inclination. Ratio Lift to Drift. + 1° 58·3:1 + 2° 29·2:1 + 3° 19·3:1 + 4° 14·3:1 + 5° 11·4:1 + 6° 9·5:1 + 7° 8·0:1 + 8° 7·0:1 + 9° 6·3:1 + 10° 5·7:1 + + P = 2_kd_ AV² sin {alpha}. + +A useful formula for a single plane surface. P = pressure supporting +the plane in pounds per square foot, _k_ a constant = 0·003 in miles +per hour, _d_ = the density of the air. + +A = the area of the plane, V relative velocity of translation through +the air, and {alpha} the angle of flight. + +Transposing we have + + AV² = P/(2_kd_ sin {alpha}) + +If P and {alpha} are constants; then AV² = a constant or area is +inversely as velocity squared. Increase of velocity meaning diminished +supporting surface (_and so far as supporting surface goes_), diminished +resistance and skin friction. It must be remembered, however, that while +the work of sustentation diminishes with the speed, the work of +penetration varies as the cube of the speed. + + +§ 13. TABLE V.--TIMBER. + + Column Headings: + + A. Material + B. Specific Gravity + C. Weight per Cub. Ft. in Lb. + D. Strength per Sq. In. in Lb. + E. Ultimate Breaking Load (Lb.) span 1' x 1" x 1" + F. Relative Resilience in Bending + G. Modulus of Elasticity in millions of Lb. per Sq. In. for Bending + H. Relative Value. Bending Strength compared with Weight + + ---------------+-----+-------+-------------+-------+-----+-----+---- + A |B | C | D |E |F |G | H + ---------------+-----+-------+-------------+-------+-----+-----+---- + Ash | ·79 | 43-52 |14,000-17,000| 622 |4·69 |1·55 |13·0 + Bamboo | | 25[A]| 6300[53] | |3·07 |3·20 | + Beech | ·69 | 43 |10,000-12,000| 850 | |1·65 |19·8 + Birch | ·71 | 45 | 15,000 | 550 | |3·28 |12·2 + Box |1·28 | 80 |20,000-23,000| 815 | | |10·2 + Cork | ·24 | 15 | | | | | + Fir (Norway | | | | | | | + Spruce) | ·51 | 32 | 9,000-11,000| 450 |3·01 |1·70 |14·0 + American | | | | | | | + Hickory | | 49 | 11,000 | 800 |3·47 |2·40 |16·3 + Honduras | | | | | | | + Mahogany | ·56 | 35 | 20,000 | 750 |3·40 |1·60 |21·4 + Maple | ·68 | 44 | 10,600 | 750 | | |17·0 + American White | | | | | | | + Pine | ·42 | 25 | 11,800 | 450 |2·37 |1·39 |18·0 + Lombardy Poplar| | 24 | 7,000 | 550 |2·89 | 0·77|22·9 + American Yellow| | | | | | | + Poplar | | 44 | 10,000 | |3·63 |1·40 | + Satinwood | ·96 | 60 | |1,033 | | |17·2 + Spruce | ·50 | 31 | 12,400 | 450 | | |14·5 + Tubular Ash, | | | | | | | + _t_ = 1/8 _d_ | | 47 | | |3·50 |1·55 | + ---------------+-----+-------+-------------+-------+-----+-----+---- + + _t_ = thickness: _d_ = diameter. + + [A] Given elsewhere as 55 and 22,500 (_t_ = 1/3_d_), evidently + regarded as solid. + +§ 14.--=Formula connecting the Weight Lifted in Pounds per Square Foot +and the Velocity.=--The empirical formula + + W = (V²C)/_g_ + + Where W = weight lifted in lb. per sq. ft. + V = velocity in ft. per sec. + C = a constant = 0·025. + _g_ = 32·2, or 32 approx. + +may be used for a thoroughly efficient model. This gives +(approximately) + + 1 lb. per sq. ft. lift at 25 miles an hour. + 21 oz. " " 30 " + 6 oz. " " 15 " + 4 oz. " " 12 " + 2·7 oz. " " 10 " + +Remember the results work out in feet per second. To convert +(approximately) into miles per hour multiply by 2/3. + +§ 15. =Formula connecting Models of Similar Design, but Different +Weights.= + + D {proportional to} {square root}W. + +or in models of _similar design_ the distances flown are proportional +to the square roots of the weights. (Derived from data obtained from +Clarke's flyers.) + +For models from 1 oz. to 24-30 oz. the formula appears to hold very +well. For heavier models it appears to give the heavier model rather +too great a distance. + +Since this was deduced a 1 oz. Clarke model of somewhat similar design +but longer rubber motor has flown 750 ft. at least; it is true the +design is not, strictly speaking, similar, but not too much reliance +must be placed on the above. The record for a 1 oz. model to date is +over 300 yards (with the wind, of course), say 750 ft. in calm air. + +§ 16. =Power and Speed.=--The following formula, given by Mr. L. Blin +Desbleds, between these is-- + + W/W{0} = (3_v{0}_)/(4_v_) + ¼(_v_/_v{0}_)³. + + Where _v{0}_ = speed of minimum power + W{0} = work done at speed _v{0}_. + W = work done at speed _v_. + +Making _v_ = 2_v{0}_, i.e. doubling the speed of minimum power, and +substituting, we have finally + + W = (2-3/8)W{0} + +i.e. the speed of an aeroplane can be doubled by using a power 2-3/8 +times as great as the original one. The "speed of minimum power" being +the speed at which the aeroplane must travel for the minimum +expenditure of power. + +§ 17. The thrust of the propeller has evidently to balance the + + Aerodynamic resistance = R + The head resistance (including skin friction) = S + +Now according to Renard's theorem, the power absorbed by R + S is a +minimum when + + S = R/3. + +Having built a model, then, in which the total resistance + + = (4/3)R. + +This is the thrust which the propeller should be designed to give. Now +supposing the propeller's efficiency to be 80 per cent., then P--the +minimum propulsion power + + = (4/3)R × 100/80 × 100/75 × _v_. + +Where 25 per cent. is the slip of the screw, _v_ the velocity of the +aeroplane. + +§ 18. =To determine experimentally the Static Thrust of a +Propeller.=--Useful for models intended to raise themselves from the +ground under their own power, and for helicopters. + +The easiest way to do this is as follows: Mount the propeller on the +shaft of an electric motor, of sufficient power to give the propeller +1000 to 1500 revolutions per minute; a suitable accumulator or other +source of electric energy will be required, a speedometer or speed +counter, also a voltmeter and ammeter. + +Place the motor in a pair of scales or on a suitable spring balance +(the former is preferable), the axis of the motor vertical, with the +propeller attached. Rotate the propeller so that the air current is +driven _upwards_. When the correct speed (as indicated by the speed +counter) has been attained, notice the difference in the readings if a +spring balance be used, or, if a pair of scales, place weights in the +scale pan until the downward thrust of the propeller is exactly +balanced. This gives you the thrust in ounces or pounds. + +Note carefully the voltage and amperage, supposing it is 8 volts and +10 amperes = 80 watts. + +Remove the propeller and note the volts and amperes consumed to run +the motor alone, i.e. to excite itself, and overcome friction and air +resistance; suppose this to be 8 volts and 2 amperes = 16; the +increased load when the propeller is on is therefore + + 80 - 16 = 64 watts. + +All this increased power is not, however, expended on the propeller. + +The lost power in the motor increases as C²R. + +R = resistance of armature and C = current. If we deduct 10 per cent. +for this then the propeller is actually driven by 56 watts. + +Now 746 watts = 1 h.p. + + {therefore} 56/746 = 1/13 h.p. approx. + +at the observed number of revolutions per minute. + +§ 19. N.B.--The h.p. required to drive a propeller varies as the cube +of the revolutions. + +_Proof._--Double the speed of the screw, then it strikes the air twice +as hard; it also strikes twice as much air, and the motor has to go +twice as fast to do it. + +§ 20. To compare one model with another the formula + + Weight × velocity (in ft. per sec.)/horse-power + +is sometimes useful. + +§ 21. =A Horse-power= is 33,000 lb. raised one foot in one minute, or +550 lb. one foot in one second. + +A clockwork spring raised 1 lb. through 4½ ft. in 3 seconds. What +is its h.p.? + + 1 lb. through 4½ ft. in 3 seconds + is 1 lb. " 90 ft. " 1 minute. + + {therefore} Work done is 90 ft.-lb. + = 90/33000 = 0·002727 h.p. + +The weight of the spring was 6¾ oz. (this is taken from an actual +experiment), i.e. this motor develops power at the rate of 0·002727 +h.p. for 3½ seconds only. + +§ 22. =To Ascertain the H.P. of a Rubber Motor.= Supposing a propeller +wound up to 250 turns to run down in 15 seconds, i.e. at a mean speed +of 1200 revolutions per minute or 20 per second. Suppose the mean +thrust to be 2 oz., and let the pitch of the propeller be 1 foot. Then +the number of foot-pounds of energy developed + + = (2 oz. × 1200 revols. × 1 ft. (pitch)) / 16 oz. + += 150 ft.-lb. per minute. + +But the rubber motor runs down in 15 seconds. + + {therefore} Energy really developed is + + = (150 × 15) / 60 = 37·5 ft.-lb. + +The motor develops power at rate of 150/33000 = 0·004545 h.p., but for +15 seconds only. + +§ 23. =Foot-pounds of Energy in a Given Weight of Rubber= +(experimental determination of). + + Length of rubber 36 yds. + Weight " 2-7/16 oz. + Number of turns = 200. + + 12 oz. were raised 19 ft. in 5 seconds. + i.e. ¾ lb. was raised 19 × 12 ft. in 1 minute. + i.e. 1 lb. was raised 19 × 3 × 3 ft. in 1 minute. + = 171 ft. in 1 minute. + +i.e. 171 ft.-lb. of energy per minute. But actual time was 5 seconds. + +{therefore} Actual energy developed by 2-7/16 oz. of rubber of 36 +yards, i.e. 36 strands 1 yard each at 200 turns is + + = 171/12 ft.-lb. + + = 14¼ ft.-lb. + +This allows nothing for friction or turning the axle on which the cord +was wound. Ball bearings were used; but the rubber was not new and +twenty turns were still unwound at the end of the experiment. Now +allowing for friction, etc. being the same as on an actual model, we +can take ¾ of a ft.-lb. for the unwound amount and estimate the +total energy as 15 ft.-lb. as a minimum. The energy actually developed +being at the rate of 0·0055 h.p., or 1/200 of a h.p. if supposed +uniform. + +§ 24. The actual energy derivable from 1 lb. weight of rubber is +stated to be 300 ft.-lb. On this basis 2-7/16 oz. should be capable of +giving 45·7 ft.-lb. of energy, i.e. three times the amount given +above. Now the motor-rubber not lubricated was only given 200 +turns--lubricated 400 could have been given it, 600 probably before +rupture--and the energy then derivable would certainly have been +approximating to 45 ft.-lb., i.e. 36·25. Now on the basis of 300 +ft.-lb. per lb. a weight of ½ oz. (the amount of rubber carried in +"one-ouncers") gives 9 ft.-lb. of energy. Now assuming the gliding +angle (including weight of propellers) to be 1 in 8; a perfectly +efficient model should be capable of flying eight times as great a +distance in a horizontal direction as the energy in the rubber motor +would lift it vertically. Now 9 ft.-lb. of energy will lift 1 oz. 154 +ft. Therefore theoretically it will drive it a distance (in yards) of + + (8 × 154)/3 = 410·6 yards. + +Now the greatest distance that a 1 oz. model has flown in perfectly +calm air (which never exists) is not known. Flying with the wind 500 +yards is claimed. Admitting this what allowance shall we make for the +wind; supposing we deduct half this, viz. 250 yards. Then, on this +assumption, the efficiency of this "one ouncer" works out (in +perfectly still air) at 61 per cent. + +The gliding angle assumption of 1 in 8 is rather a high one, possibly +too high; all the writer desires to show is the method of working out. + +Mr. T.W.K. Clarke informs me that in his one-ouncers the gliding +angle is about 1 in 5. + +§ 25. =To Test Different Motors or Different Powers of the Same Kind +of Motor.=--Test them on the same machine, and do not use different +motors or different powers on different machines. + +§ 26. =Efficiency of a Model.=--The efficiency of a model depends on +the weight carried per h.p. + +§ 27. =Efficiency of Design.=--The efficiency of some particular +design depends on the amount of supporting surface necessary at a +given speed. + +§ 28. =Naphtha Engines=, that is, engines made on the principle of the +steam engine, but which use a light spirit of petrol or similar agent +in their generator instead of water with the same amount of heat, will +develop twice as much energy as in the case of the ordinary steam +engine. + +§ 29.=Petrol Motors.= + + Horse-power. No. of Cylinders. Weight. + ¼ Single 4½ lb. + ½ to ¾ " 6½ " + 1½ Double 9 " + +§ 30. =The Horse-power of Model Petrol Motors.=--Formula for rating of +the above. + + (R.P.M. = revolutions per minute.) + + H.P. = ((Bore)² × stroke × no. of cylinders × R.P.M.)/12,000 + +If the right-hand side of the equation gives a less h.p. than that +stated for some particular motor, then it follows that the h.p. of the +motor has been over-estimated. + +[Illustration: FIG. 56.] + +§ 30A. =Relation between Static Thrust of Propeller and Total Weight +of Model.=--The thrust should be approx. = ¼ of the weight. + +§ 31. =How to find the Height of an Inaccessible Object by Means of +Three Observations taken on the Ground (supposed flat) in the same +Straight Line.=--Let A, C, B be the angular elevations of the object +D, as seen from these points, taken in the same straight line. Let the +distances B C, C A and A B be _a_, _b_, _c_ respectively. And let +required height P D = _h_; then by trigonometry we have (see Fig. 56) + + _h²_ = _abc_/(_a_ cot²A - _c_ cot²C + _b_ cot²B). + +§ 32. =Formula= for calculating the I.H.P. (indicated horse-power) of +a single-cylinder double-acting steam-engine. + +Indicated h.p. means the h.p. actually exerted by the steam in the +cylinder without taking into account engine friction. Brake h.p. or +effective h.p. is the actual h.p. delivered by the crank shaft of the +engine. + + I.H.P. = (2 × S × R × A × P)/33,000. + + Where S = stroke in feet. + R = revolutions per minute. + A = area of piston in inches. + P = mean pressure in lb. exerted per sq. in. on the piston. + +The only difficulty is the mean effective pressure; this can be found +approximately by the following rule and accompanying table. + + +TABLE VI. + + ---------+----------+---------+----------+---------+--------- + Cut-off | Constant | Cut-off | Constant | Cut-off | Constant + ---------+----------+---------+----------+---------+--------- + 1/6 | ·566 | 3/8 | ·771 | 2/3 | ·917 + 1/5 | ·603 | ·4 | ·789 | ·7 | ·926 + 1/4 | ·659 | 1/2 | ·847 | 3/4 | ·937 + ·3 | ·708 | ·6 | ·895 | ·8 | ·944 + 1/3 | ·743 | 5/8 | ·904 | 7/8 | ·951 + ---------+----------+---------+----------+---------+--------- + +Rule.--"Add 14·7 to gauge pressure of boiler, this giving 'absolute +steam pressure,' multiply this sum by the number opposite the fraction +representing the point of cut-off in the cylinder in accompanying +table. Subtract 17 from the product and multiply the remainder by 0·9. +The result will be very nearly the M.E.P." (R.M. de Vignier.) + + +FOOTNOTE: + +[53] Given elsewhere as 55 and 22,500 (_t_ = 1/3 _d_), evidently +regarded as solid. + + + + +APPENDIX A. + +SOME MODELS WHICH HAVE WON MEDALS AT OPEN COMPETITIONS. + + +[Illustration: FIG. 57.--THE G.P.B. SMITH MODEL.] + +The model shown in Fig. 57 has won more competition medals than any +other. It is a thoroughly well designed[54] and well constructed +model. Originally a very slow flyer, the design has been simplified, +and although by no means a fast flyer, its speed has been much +accelerated. Originally a one-propeller machine, it has latterly been +fitted with twin propellers, with the idea of obtaining more +directional control; but in the writer's opinion, speaking from +personal observation, with but little, if any, success. The steering +of the model is effected by canting the elevator. Originally the +machine had ailerons for the purpose, but these were removed owing, I +understand, to their retarding the speed of the machine. + +In every competition in which this machine has been entered it has +always gained very high marks for stability. + +[Illustration: FIG. 58.--THE GORDON-JONES DIHEDRAL BIPLANE.] + +Up to the time of writing it has not been provided with anything in +the nature of fins or rudder. + +Fig. 58 is a biplane very much after the type of the model just +alluded to, but the one straight and one curved aerofoil surfaces are +here replaced by two parallel aerofoils set on a dihedral angle. The +large size of the propeller should be noted; with this the writer is +in complete agreement. He has not unfortunately seen this model in +actual flight. + +The scientifically designed and beautifully made models illustrated in +Fig. 59 are so well known that any remarks on them appear +superfluous. Their efficiency, so far as their supporting area goes, +is of the highest, as much as 21 oz. per square foot having been +carried. + +[Illustration: FIG. 59.--MESSRS. T.W.K. CLARKE AND CO.'S MODEL +FLYERS.] + +For illustrations, etc., of the Fleming-Williams model, _see_ ch. v., +§ 23. + +(Fig. 60.) This is another well-constructed and efficient model, the +shape and character of the aerofoil surfaces much resembling those of +the French toy monoplane AL-MA (see § 4, ch. vii.), but they are +supported and held in position by quite a different method, a neat +little device enabling the front plane to become partly detached on +collision with any obstacle. The model is provided with a keel (below +the centre of gravity), and rudder for steering; in fact, this machine +especially claims certainty of directional control. The writer has +seen a number of flights by this model, but it experiences, like other +models, the greatest difficulty in keeping straight if the conditions +be adverse. + +The model which will do this is, in his opinion, yet to be evolved. +The small size of the propellers is, of course, in total disagreement +with the author's ideas. All the same, the model is in many respects +an excellent one, and has flown over 300 yards at the time of writing. + +[Illustration: FIG. 60.--THE DING SAYERS MONOPLANE.] + +More than a year ago the author made a number of models with +triangular-shaped aerofoils, using umbrella ribs for the leading edge +and steel piano wire for the trailing, but has latterly used aerofoils +of the elongated ellipse shape. + +Fig. 61 is an illustration of one of the author's latest models which +won a Bronze Medal at the Long Distance Open Competition, held at the +Crystal Palace on July 27, 1910, the largest and most keenly contested +competition held up to that date. + +The best and straightest flight against the wind was made by this +model. + +On the morning of the competition a flight of about 320 yards +(measured in a straight line) was made on Mitcham Common, the model +being launched against the wind so as to gain altitude, and then +flying away with the breeze behind the writer. Duration of flight 50 +seconds. The following are the chief particulars of the +model:--Weight, 7½ oz. Area of supporting surface, 1-1/3 sq. ft. +Total length, 4 ft. Span of main aerofoil, 25 in. Aspect ratio, 4 : 1. +Diameter of propeller, 14 in. Two strand geared rubber motor, carrying +altogether 28 strands of 1/16 square rubber cord 43 in. long. The +propeller was originally a Venna, but with the weight reduced by +one-third, and considerable alteration made in its central contours. +The front skid of steel pianoforte wire, the rear of jointless cane +wire tipped; the rear skid was a necessity in order to protect the +delicate gearing mechanism, the weight of which was reduced to a +minimum. + +[Illustration: FIG. 61.--THE AUTHOR'S "GRASSHOPPER" MODEL.] + +The very large diameter of the propeller should be noted, being 56 +per cent. of the span. The fin, high above the centre of gravity, was +so placed for transverse stability and direction. At the rear of the +fin was a rudder. The small amount of rubber carried (for a long +distance machine) should also be noted, especially when allowing for +friction in gearing, etc. + +The central rod was a penny bamboo cane, the large aerofoil of +jointless cane and Hart's fabric, and the front aerofoil of steel wire +surfaced with the same material. + + +LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, GREAT WINDMILL +STREET, W., AND DUKE STREET, STAMFORD STREET, S.E. + +FOOTNOTE: + +[54] The design is patented. + + + + + _October, 1910_ + +A SHORT LIST OF + +SCIENTIFIC BOOKS + +PUBLISHED AND SOLD BY + +E. & F.N. SPON, Limited, + +57 Haymarket, London, S.W. + +SOLE ENGLISH AGENTS for the Books of-- + + MYRON C. CLARK, NEW YORK + THE BUSINESS CODE COMPANY, CHICAGO + SPON & CHAMBERLAIN, NEW YORK + + + PAGE + AERONAUTICS 2 + AGRICULTURE 2 + ARCHITECTURE 3 + ARTILLERY 5 + BRIDGES AND ROOFS 5 + BUILDING 3 + CEMENT AND CONCRETE 7 + CIVIL ENGINEERING 8 + DICTIONARIES 11 + DOMESTIC ECONOMY 12 + DRAWING 13 + ELECTRICAL ENGINEERING 14 + FOREIGN EXCHANGE 19 + GAS AND OIL ENGINES 20 + GAS LIGHTING 20 + HISTORICAL; BIOGRAPHICAL 21 + HOROLOGY 22 + HYDRAULICS 22 + INDUSTRIAL CHEMISTRY 24 + IRRIGATION 27 + LOGARITHM TABLES 28 + MANUFACTURES 24 + MARINE ENGINEERING 28 + MATERIALS 30 + MATHEMATICS 31 + MECHANICAL ENGINEERING 33 + METALLURGY 36 + METRIC TABLES 38 + MINERALOGY AND MINING 38 + MUNICIPAL ENGINEERING 45 + NAVAL ARCHITECTURE 28 + ORGANISATION 40 + PHYSICS 41 + PRICE BOOKS 42 + RAILWAY ENGINEERING 43 + SANITATION 45 + STRUCTURAL DESIGN 45 + TELEGRAPH CODES 47 + WARMING; VENTILATION 47 + WATER SUPPLY 48 + WORKSHOP PRACTICE 49 + USEFUL TABLES 52 + MISCELLANEOUS 53 + + + _Full particulars post free on application. + All books are bound in cloth unless otherwise stated._ + + _NOTE: The Prices in this Catalogue apply to books sold in + the United Kingdom only._ + + + AERONAUTICS + + =The Atmosphere=: its characteristics and dynamics. By F.J.B. + CORDEIRO. With 35 illus. 129 pp. medium 8vo. (_New York, 1910_) + + _net_ 10 6 + + =Theory and Practice of Model Aeroplaning.= By V.E. JOHNSON. 61 + illus. 150 pp. crown 8vo. (_1910_) + + _net_ 3 6 + + =How to Build a 20-ft. Biplane Glider.= By A.P. MORGAN. 31 + illus. 60 pp. crown 8vo, limp. (S. & C. SERIES, NO. 14.) (_New + York, 1909_) + + _net_ 1 6 + + =Flight-Velocity.= By A. SAMUELSON. 4 plates, 42 pp. 8vo, + sewed. (_1906_) + + _net_ 2 0 + + =Resistance of Air and the Question of Flying.= By A. + SAMUELSON. 23 illus. 36 pp. 8vo, sewed. (_1905_) + + _net_ 2 0 + + + AGRICULTURE. + + =Hemp.= A Practical Treatise on the Culture for Seed and Fibre. + By S.S. BOYCE. 13 illus. 112 pp. crown 8vo. (_New York, 1900_) + + _net_ 2 0 + + =The Fertilisation of Tea.= By G.A. COWIE. With 17 illus. 68 + pp. crown 8vo, sewed. (_1908_) + + _net_ 2 6 + + =Farm Drainage.= By H.F. FRENCH. 100 illus. 284 pp. crown 8vo. + (_New York, 1904_) + + _net_ 4 6 + + =Talks on Manures.= By J. HARRIS. New edition, 366 pp. crown + 8vo. (_New York, 1893_) + + _net_ 6 6 + + =Coffee=, its Culture and Commerce in all Countries. By C.G.W. + LOCK. 11 plates, 274 pp. crown 8vo. (_1888_) + + 12 6 + + =Sugar, a Handbook for Planters and Refiners.= By the late J.A. + R. NEWLANDS and B.E.R. NEWLANDS. 236 illus. 876 pp. demy 8vo. + (_London, 1909_) + + _net_ 1 5 0 + + =Hops=, their Cultivation, Commerce and Uses. By P.L. SIMMONDS. + 143 pp. crown 8vo. (_1877_) + + 4 6 + + =The Future of Cocoa-Planting=. By H. HAMEL SMITH. With + illustrations, 95 pp. crown 8vo, sewed. (_1908_) + + _net_ 1 0 + + =Estate Fences=, their Choice, Construction and Cost. By A. + VERNON. Re-issue, 150 illus. 420 pp. 8vo. (_1909_) + + _net_ 8 6 + + + ARCHITECTURE AND BUILDING. + + =The Hydropathic Establishment and its Baths.= By R.O. ALLSOP. + 8 plates, 107 pp. demy 8vo. (_1891_) + + 5 0 + + =The Turkish Bath=, its Design and Construction. By R.O. + ALLSOP. 27 illus. 152 pp. demy 8vo. (_1890_) + + 6 0 + + =Public Abattoirs=, their Planning, Design and Equipment. By + R.S. AYLING. 33 plates, 100 pp. demy 4to. (_1908_) + + _net_ 8 6 + + =The Builder's Clerk.= By T. BALES. Second edition, 92 pp. + fcap. 8vo. (_1904_) + + 1 6 + + =Glossary of Technical Terms= used in Architecture and the + Building Trades. By G.J. BURNS. 136 pp. crown 8vo. (_1895_) + + 3 6 + + =Chimney Design and Theory.= By W.W. CHRISTIE. Second edition, + 54 illus. 200 pp. crown 8vo. (_New York, 1902_) + + _net_ 12 6 + + =Approximate Estimates.= By T.E. COLEMAN. Third edition, 481 + pp. oblong 32mo, leather. (_1907_) + + _net_ 5 0 + + =Stable Sanitation and Construction.= By T.E. COLEMAN. 183 + illus. 226 pp. crown 8vo. (_1897_) + + _net_ 6 0 + + =Architectural Examples= in Brick, Stone, Wood and Iron. By W. + FULLERTON. Third edition, 245 plates, 254 pp. demy 4to. + (_1908_) + + _net_ 15 0 + + =Bricklaying System.= By F.B. GILBRETH. Fully illustrated, 321 + pp. 8vo. (_New York, 1909_) + + _net_ 12 6 + + =Field System.= By F.B. GILBRETH. 194 pp. 12mo leather. (_New + York, 1908_) + + _net_ 12 6 + + =The Building Trades Pocket Book.= Compiled by R. HALL. 12mo. + With interchangeable diary + + _net_ 1 6 + + Ditto ditto, in leather + + _net_ 2 6 + + =The Clerk of Works' Vade Mecum.= By G.G. HOSKINS. Seventh + edition, 52 pp. fcap. 8vo. (_1901_) + + 1 6 + + =A Handbook of Formulæ, Tables, and Memoranda=, for + Architectural Surveyors and others engaged in Building. By J.T. + HURST. Fifteenth edition, 512 pp. royal 32mo, roan. (_1905_) + + _net_ 5 0 + + =Quantity Surveying=, for the Use of Surveyors, Architects, + Engineers and Builders. By J. LEANING. Fifth edition, 936 pp. + demy 8vo. (_1904_) + + _net_ 1 5 0 + + =Obstruction to Light.= A Graphic Method of determining + Problems of Ancient Lights. By H.B. MOLESWORTH. 9 folding + plates, 4to. (_1902_) + + _net_ 6 0 + + =Suburban Houses.= A series of practical plans. By J.H. + PEARSON. 46 plates and 12 pp. text, crown 4to. (_1905_) + + _net_ 7 6 + + =Solid Bitumens=, their Physical and Chemical Properties and + Chemical Analysis. By S.F. PECKHAM. 23 illus. 324 pp. 8vo. + (_New York, 1909_) + + _net_ 1 1 0 + + =Roman Architecture, Sculpture and Ornament.= By G.B. PIRANESI. + 200 plates, reproduced in facsimile from the original. 2 vols. + Imperial folio, in wrappers. (_1900_) + + _net_ 2 2 0 + + =The Seven Periods of English Architecture=, defined and + illustrated. By E. SHARPE. Third edition, 20 steel plates, + royal 8vo. (_1888_) + + 12 6 + + =Our Factories, Workshops and Warehouses=, their Sanitary and + Fire-Resisting Arrangements. By B.H. THWAITE. 183 illus. 282 + pp. crown 8vo. (_1882_) + + 9 0 + + =Elementary Principles of Carpentry.= By T. TREDGOLD and J.T. + HURST. Eleventh edition, 48 plates, 517 pp. crown 8vo. (_1904_) + + 12 6 + + =Practical Stair Building and Handrailing.= By W.H. WOOD. 32 + plates, 91 pp. crown 4to. (_1894_) + + 10 6 + + =Spons' Architects' and Builders' Pocket Price-Book=, + Memoranda, Tables and Prices. Edited by CLYDE YOUNG. Revised by + STANFORD M. BROOKS. Illustrated, 552 pp. 16mo, leather cloth + (size 6½ in. by 3¾ in. by ½ in. thick). Issued annually + + _net_ 3 0 + + =Heating Engineers' Quantities.= By W.L. WHITE and G.M. WHITE. + 4 plates, 33 pp. folio. (_1910_) + + _net_ 10 6 + + + ARTILLERY. + + =Guns and Gun Making Material.= By G. EDE. Crown 8vo. (_1889_) + + 6 0 + + =Treatise on Application of Wire to Construction of Ordnance.= + By J.A. LONGRIDGE. 180 pp. 8vo. (_1884_) + + 1 5 0 + + =The Progress of Artillery: Naval Guns.= By J.A. LONGRIDGE. + 8vo, sewed. (_1896_) + + 2 0 + + =The Field Gun of the Future.= By J.A. LONGRIDGE. 8vo, sewed. + (_1892_) + + 2 6 + + + BRIDGES, ARCHES, ROOFS, AND STRUCTURAL DESIGN. + + =Strains in Ironwork.= By HENRY ADAMS. Fourth edition, 8 plates, 65 + pp. crown 8vo. (_1904_) + + 5 0 + + =The Practical Designing of Structural Ironwork.= By HENRY ADAMS. 13 + plates, 194 pp. 8vo. (_1894_) + + 8 6 + + =Designing Ironwork.= By HENRY ADAMS. Second series. 8vo, sewed. + + Part I. A Steel Box Girder. (_1894_) + + _net_ 0 9 + + " II. Built-up Steel Stanchions. (_1901_) + + _net_ 1 3 + + " III. Cisterns and Tanks. (_1902_) + + _net_ 1 0 + + " IV. A Fireproof Floor. (_1903_) + + _net_ 1 0 + + =A Practical Treatise on Segmental and Elliptical Oblique or Skew + Arches.= By G.J. BELL. Second edition, 17 plates, 125 pp. royal 8vo. + (_1906_) + + _net_ 1 1 0 + + =Economics of Construction in relation to Framed Structures.= By R.H. + Bow. Third thousand, 16 plates, 88 pp. 8vo. (1873) + + 5 0 + + =Theory of Voussoir Arches.= By Prof. W. CAIN. Third edition, 201 pp. + 18mo, boards. (_New York, 1905_) + + _net_ 2 0 + + =New Formulæ for the Loads and Deflections= of Solid Beams and + Girders. By W. DONALDSON. Second edition, 8vo. (_1872_) + + 4 6 + + =Plate Girder Railway Bridges.= By M. FITZMAURICE. 4 plates, 104 pp. + 8vo. (_1895_) + + 6 0 + + =Pocket Book of Calculations in Stresses.= By E.M. GEORGE. 66 illus. + 140 pp. royal 32mo, half roan. (_1895_) + + 3 6 + + =Strains on Braced Iron Arches= and Arched Iron Bridges. By A.S. + HEAFORD. 39 pp. 8vo. (_1883_) + + 6 0 + + =Tables for Roof Framing.= By G.D. INSKIP. Second edition, 451 pp. + 8vo, leather. (_New York, 1905_) + + _net_ 12 6 + + =Stresses in Girder and Roof Frames,= for both dead and live loads, + by simple Multiplication, etc. By F.R. JOHNSON. 28 plates, 215 pp. + crown 8vo. (_1894_) + + 6 0 + + =A Graphical Method for Swing Bridges.= By B.F. LA RUE. 4 plates, 104 + pp. 18mo, boards. (_New York, 1892_) + + _net_ 2 0 + + =Notes on Cylinder Bridge Piers= and the Well System of Foundations. + By J. NEWMAN. 144 pp. 8vo. (_1893_) + + 6 0 + + =A New Method of Graphic Statics= applied in the Construction of + Wrought Iron Girders. By E. OLANDER. 16 plates, small folio. (_1887_) + + 10 6 + + =Reference Book for Statical Calculations.= By F. RUFF. With diagrams, + 140 pp. crown 8vo. (_1906_) + + _net_ 5 0 + + =The Strength and Proportion of Riveted Joints.= By B.B. STONEY. 87 + pp. 8vo. (_1885_) + + 5 0 + + =The Anatomy of Bridgework.= By W.H. THORPE. 103 illus. 190 pp. crown + 8vo. (_1906_) + + _net_ 6 0 + + + CEMENT AND CONCRETE. + + =Portland Cement:= its Manufacture, Testing and Use. By D.B. BUTLER. + Second edition, 97 illus. 396 pp. demy 8vo. (_1905_) + + _net_ 16 0 + + =Theory of Steel-Concrete Arches= and of Vaulted Structures. By W. + CAIN. Fourth edition, 27 illus. 212 pp. 18mo, boards. (_New York, + 1906_) + + _net_ 2 0 + + =Cement Users' and Buyers' Guide.= By CALCARE. 115 pp. 32mo, cloth. + (_1901_) + + _net_ 1 6 + + =Diagrams for Designing Reinforced Concrete Structures.= By G.F. + DODGE. 31 illus. 104 pp. oblong folio. (_New York, 1910_) + + _net_ 17 0 + + =Cements, Mortars, and Concretes;= their Physical properties. By M.S. + FALK. 78 illus. 176 pp. 8vo. (_New York, 1904_) + + _net_ 10 6 + + =Concrete Construction, Methods and Cost.= By H.P. GILLETTE and C.S. + HILL. 310 illus. 690 pp. 8vo. (_New York, 1908_) + + _net_ 1 1 0 + + =Engineers' Pocket-Book of Reinforced Concrete.= By E.L. HEIDENREICH. + 164 illus. 364 pp. crown 8vo, leather, gilt edges. (_New York, 1909_) + + _net_ 12 6 + + =Concrete Inspection.= By C.S. HILL. Illustrated, 179 pp. 12mo. (_New + York, 1909_) + + _net_ 4 6 + + =Reinforced Concrete.= By E. MCCULLOCH. 28 illus. 128 pp. crown 8vo. + (_New York, 1908_) + + _net_ 6 6 + + =Concrete and Reinforced Concrete.= By H.A. REID. 715 illus. 884 pp. + royal 8vo. (_New York, 1907_) + + _net_ 21 0 + + =Theory and Design of Reinforced Concrete Arches.= By A. REUTERDAHL. + 41 illus. 126 pp. 8vo. (_New York, 1908_) + + _net_ 8 6 + + =Practical Cement Testing.= By W.P. TAYLOR. With 142 illus. 329 pp. + demy 8vo. (New York, 1906) + + _net_ 12 6 + + =Concrete Bridges and Culverts.= By H.G. TYRRELL. 66 illus. 251 pp. + crown 8vo, leather + + _net_ 12 6 + + + CIVIL ENGINEERING. + + CANALS, SURVEYING. + + (_See also_ IRRIGATION _and_ WATER SUPPLY.) + + =Practical Hints to Young Engineers Employed on Indian Railways.= By + A.W.C. ADDIS. With 14 illus. 154 pp. 12mo. (_1910_) + + _net_ 3 6 + + =Levelling,= Barometric, Trigonometric and Spirit. By I.O. BAKER. + Second edition, 15 illus. 145 pp. 18mo, boards. (_New York, 1903_) .. + + _net_ 2 0 + + =Notes on Instruments= best suited for Engineering Field Work in India + and the Colonies. By W.G. BLIGH. 65 illus. 218 pp. 8vo. (_1899_) + + 7 6 + + =The Sextant and other Reflecting Mathematical Instruments.= By + F.R. BRAINARD. 33 illus. 120 pp. 18mo, boards. (_New York, 1891_) + + _net_ 2 0 + + =Practical Designing of Retaining Walls.= By Prof. W. CAIN. Fifth + edition, 14 illus. 172 pp. 18mo, boards. (_New York, 1908_) + + _net_ 2 0 + + =The Maintenance of Macadamised Roads.= By T. CODRINGTON. Second + edition, 186 pp. 8vo. (_1892_) + + 7 6 + + =Retaining Walls in Theory and Practice.= By T.E. COLEMAN. 104 illus. + 160 pp. crown 8vo. (_1909_) + + _net_ 5 0 + + =The Barometrical Determination of Heights.= By F.J.B. CORDEIRO. + Crown 8vo, limp leather. (_New York, 1898_) + + _net_ 4 6 + + =On Curved Masonry Dams.= By W.B. COVENTRY. 8vo, sewed. (_1894_) + + 2 0 + + =A Practical Method of Determining the Profile of a Masonry Dam.= By + W.B. COVENTRY. 8vo, sewed. (_1894_) + + 2 6 + + =The Stresses on Masonry Dams= (oblique sections). By W.B. COVENTRY. + 8vo, sewed. (_1894_) + + 2 0 + + =Tables for facilitating the Calculation of Earthworks.= By D. + CUNNINGHAM. 120 pp. royal 8vo + 10 6 + + =Handbook of Cost Data for Contractors and Engineers.= By H.P. + GILLETTE. 1854 pp. crown 8vo, leather, gilt edges. (_New York, 1910_) + + _net_ 1 1 0 + + =Rock Excavation, Methods and Cost.= By H.P. GILLETTE. 56 illus. 376 + pp. crown 8vo. (_New York, 1904_) + + _net_ 12 6 + + =High Masonry Dams.= By E.S. GOULD. With illus. 88 pp. 18mo, boards. + (_New York, 1897_) + + _net_ 2 0 + + =Grace's Tables for Curves,= with hints to young engineers. 8 figures, + 43 pp. oblong 8vo. (_1908_) + + _net_ 5 0 + + =Grace's Earthwork Tables.= 36 double-page tables, 4to. (_1907_) + + _net_ 12 6 + + =Railway Tunnelling= in Heavy Ground. By C. GRIPPER. 3 plates, 66 pp. + royal 8vo. (_1879_) + + 7 6 + + =Levelling and its General Application.= By T. HOLLOWAY. Second + edition, 53 illus. 147 pp. 8vo. (_1895_) + + 5 0 + + =Waterways and Water Transport= in different Countries. By J.S. JEANS. + 55 illus. 520 pp. 8vo. (_1890_) + + _net_ 9 0 + + =Table of Barometrical Heights to 20,000 Feet.= By W.H. MACKESY, with + some practical suggestions by Sir Guildford Molesworth. 1 plate, 24 + pp. royal 32mo. (_1882_) + + 3 0 + + =Aid Book to Engineering Enterprise.= By E. MATHESON. Third edition, + illustrated, 916 pp. medium 8vo, buckram. (_1898_) + + 1 4 0 + + =A Treatise on Surveying.= By R.E. MIDDLETON and O. CHADWICK. Second + edition, royal 8vo. + + Part I. 11 plates, 296 pp. (_1904_) + + 10 6 + + " II. Fully illustrated, 334 pp. (_1906_) + + 10 6 + + =A Pocket Book of Useful Formulæ and Memoranda,= for Civil and + Mechanical Engineers. By Sir G.L. MOLESWORTH and H.B. MOLESWORTH. With + an Electrical Supplement by W.H. MOLESWORTH. Twenty-sixth edition, 760 + illus. 901 pp. royal 32mo, French morocco, gilt edges. (_1908_) + + _net_ 5 0 + + =The Pocket Books of Sir G.L. Molesworth and J.T. Hurst,= printed on + India paper and bound in one vol. Royal 32mo, russia, gilt edges. + + _net_ 10 6 + + =Metallic Structures: Corrosion and Fouling and their Prevention.= By + J. NEWMAN. Illustrated, 385 pp. crown 8vo. (_1896_) + + 9 0 + + =Scamping Tricks and Odd Knowledge= occasionally practised upon Public + Works. By J. NEWMAN. New impression, 129 pp. crown 8vo. (_1908_) + + _net_ 2 0 + + =Earthwork Slips and Subsidences= on Public Works. By J. NEWMAN. + 240 pp. crown 8vo. (_1890_) + + 7 6 + + =Co-ordinate Geometry= as applied to Land Surveying. By W. PILKINGTON. + 5 illus. 44 pp. 12mo. (_1909_) + + _net_ 1 6 + + =Diagrams for the Graphic Calculation of Earthwork Quantities.= By + A.H. ROBERTS. Ten cards, fcap. in cloth case + + _net_ 10 6 + + =Pioneering.= By F. SHELFORD, illustrated. 88 pp. crown 8vo. (_1909_) + + _net_ 3 0 + + =Topographical Surveying.= By G.J. SPECHT. Second edition, 2 plates + and 28 illus. 210 pp. 18mo, boards. (_New York, 1898_) + + _net_ 2 0 + + =Spons' Dictionary of Engineering,= Civil, Mechanical, Military and + Naval. 10,000 illus. 4300 pp. super royal 8vo. (_1874, Supplement + issued in 1881_). Complete with Supplement, in 11 divisions + + _net_ 3 10 0 + + Ditto ditto in 4 vols. + + _net_ 3 3 0 + + =Surveying and Levelling Instruments.= By W.F. STANLEY. Third edition, + 372 illus. 562 pp. crown 8vo. (_1901_) + + 7 6 + + =Surveyor's Handbook.= By T.U. TAYLOR. 116 illus. 310 pp. crown 8vo, + leather, gilt edges. (_New York, 1908_) + + _net_ 8 6 + + =Logarithmic Land Measurement.= By J. WALLACE. 32 pp. royal 8vo. + (_1910_) + + _net_ 5 0 + + =Hints on Levelling Operations.= By W.H. WELLS. Second edition, 8vo, + sewed. (_1890_) + + _net_ 1 0 + + =The Drainage of Fens and Low Lands= by Gravitation and Steam Power. + By W.H. WHEELER. 8 plates, 175 pp. 8vo. (_1888_) + + 12 6 + + =Stadia Surveying,= the theory of Stadia Measurements. By A. WINSLOW. + Fifth edition, 148 pp. 18mo, boards. (_New York, 1902_) + + _net_ 2 0 + + =Handbook on Tacheometrical Surveying.= By C. XYDIS. 55 illus. 3 + plates, 63 pp. 8vo. (_1909_) + + _net_ 6 0 + + + DICTIONARIES. + + =Technological Dictionary in the English, Spanish, German and French + Languages.= By D. CARLOS HUELIN Y ARSSU. Crown 8vo. + + Vol. I. ENGLISH-SPANISH-GERMAN-FRENCH. + 609 pp. (_1906_) + + _net_ 10 6 + + Vol. II. GERMAN-ENGLISH-FRENCH-SPANISH. + 720 pp. (_1908_) + + _net_ 10 6 + + Vol. III. FRENCH-GERMAN-SPANISH-ENGLISH. + In preparation. + + Vol. IV. SPANISH-FRENCH-ENGLISH-GERMAN. + 750 pp. (_1910_) + + _net_ 10 6 + + =English-French and French-English Dictionary of the Motor-Car, Cycle + and Boat.= By F. LUCAS. 171 pp. crown 8vo. (_1905_) + + _net_ 5 0 + + =Spanish-English Dictionary of Mining Terms.= By F. LUCAS. 78 pp. 8vo. + (_1905_) + + _net_ 5 0 + + =English-Russian and Russian-English Engineering Dictionary.= By L. + MEYCLIAR. 100 pp. 16mo. (_1909_) + + _net_ 2 6 + + =Reed's Polyglot Guide to the Marine Engine,= in English, French, + German and Norsk. Second edition, oblong 8vo. (_1900_). + + _net_ 6 0 + + + DOMESTIC ECONOMY. + + =Food Adulteration and its Detection.= By J.P. BATTERSHALL. 12 plates, + 328 pp. demy 8vo. (_New York, 1887_) + + 15 0 + + =How to Check Electricity Bills.= By S.W. BORDEN. 41 illus. 54 pp. + crown 8vo. (_New York, 1907_) + + _net_ 2 0 + + =Practical Hints on Taking a House.= By H.P. BOULNOIS. 71 pp. 18mo. + (_1885_) + + 1 6 + + =The Cooking Range,= its Failings and Remedies. By F. DYE. 52 pp. + fcap. 8vo, sewed. (_1888_) + + 0 6 + + =The Kitchen Boiler and Water Pipes.= By H. GRIMSHAW. 8vo, sewed. + (_1887_) + + _net_ 1 0 + + =Cookery and Domestic Management,= including economic and middle class + Practical Cookery. By K. MELLISH. 56 coloured plates and 441 illus. + 987 pp. super-royal 8vo. (_1901_) + + _net_ 16 0 + + =Spons' Household Manual.= 250 illus. 1043 pp. demy 8vo. (_1902_) + + 7 6 + + Ditto ditto half-bound French morocco + + 9 0 + + =Handbook of Sanitary Information= for Householders. By R.S. TRACY. 33 + illus. 114 pp. 18mo. (_New York, 1900_) + + 2 6 + + + DRAWING. + + =The Ornamental Penman's,= Engraver's and Sign Writer's Pocket Book of + Alphabets. By B. ALEXANDER. Oblong 12mo, sewed + + 0 6 + + =The Draughtsman's Handbook= of Plan and Map Drawing. By G.G. ANDRE. + 87 illus. and 34 plain and coloured plates, 162 pp. crown 4to. + (_1891_) + + 9 0 + + =Slide Valve Diagrams:= a French Method for their Construction. By L. + BANKSON. 18mo, boards. (_New York, 1892_) . . . + + _net_ 2 0 + + =A System of Easy Lettering.= By J.H. CROMWELL. With Supplement by G. + MARTIN. Sixth thousand, oblong 8vo. (_New York, 1900_) + + _net_ 2 0 + + =Plane Geometrical Drawing.= BY R.C. FAWDRY. Illustrated, 185 pp. + crown 8vo. (_1901_) + + _net_ 3 0 + + =Twelve Plates on Projection Drawing.= By O. GUETH. Oblong 4to. (_New + York, 1903_) + + _net_ 3 0 + + =Hints on Architectural Draughtsmanship.= By G.W.T. HALLATT. Fourth + edition, 80 pp. 18mo. (_1906_) + + _net_ 1 6 + + =A First Course of Mechanical Drawing= (Tracing). By G. HALLIDAY. + Oblong 4to, sewed + + 2 0 + + =Drawings for Medium-sized Repetition Work.= By R.D. SPINNEY. With 47 + illus. 130 pp. 8vo. (_1909_) + + _net_ 3 6 + + =Mathematical Drawing Instruments.= By W.F. STANLEY. Seventh edition, + 265 illus. 370 pp. crown 8vo. (_1900_) + + 5 0 + + + ELECTRICAL ENGINEERING. + + =Practical Electric Bell Fitting.= By F.C. ALLSOP. Tenth edition, 186 + illus. including 8 folding plates, 185 pp. crown 8vo. (_1903_) + + 3 6 + + =Telephones:= their Construction and Fitting. By F.C. ALLSOP. Eighth + edition, 184 illus. 222 pp. crown 8vo. (_1909_) + + 3 6 + + =Thermo-electric Reactions= and Currents between Metals in Fused + Salts. By T. ANDREWS. 8vo, sewed. (_1896_) + + 1 0 + + =Auto-Transformer Design.= By A.H. AVERY. 25 illus. 60 pp. 8vo. + (_1909_) + + _net_ 3 6 + + =Principles of Electric Power= (Continuous Current) for Mechanical + Engineers. By A.H. BATE. 63 illus. 204 pp. crown 8vo. (_1905_) + (FINSBURY TECHNICAL MANUAL) + + _net_ 4 6 + + =Practical Construction of Electric Tramways.= By WILLIAM R. BOWKER. + 93 illus. 119 pp. 8vo. (_1903_) + + _net_ 6 0 + + =Design and Construction of Induction Coils.= By A.F. COLLINS. 155 + illus. 272 pp. demy 8vo. (_New York, 1909_) + + _net_ 12 6 + + =Switchboard Measuring Instruments= for Continuous and Polyphase + Currents. By J.C. CONNAN. 117 illus. 150 pp. 8vo, cloth. (_1908_) + + _net_ 5 0 + + =Electric Cables, their Construction and Cost.= By D. COYLE and F.J. + O. HOWE. With many diagrams and 216 tables, 467 pp. crown 8vo, + leather. (_1909_) + + _net_ 15 0 + + =Management of Electrical Machinery.= By F.B. CROCKER and S.S. + WHEELER. Eighth edition, 131 illus. 223 pp. crown 8vo. (_New York, + 1909_) + + _net_ 4 6 + + =Electric Lighting:= A Practical Exposition of the Art. By F.B. + CROCKER. Royal 8vo. (_New York._) + + Vol. I. =The Generating Plant.= Sixth edition, 213 illus. 470 + pp. (_1904_) + + _net_ 12 6 + + Vol. II. =Distributing Systems and Lamps.= Second edition, 391 + illus. 505 pp. (_1905_) + + _net_ 12 6 + + =The Care and Management of Ignition Accumulators.= By H.H.U. CROSS. + 12 illus. 74 pp. crown 8vo, limp. (S. & C. SERIES, NO. 19.) (_1910_) + + _net_ 1 6 + + =Elementary Telegraphy and Telephony.= By ARTHUR CROTCH. 238 illus. + 223 pp. 8vo. (_1903._) (FINSBURY TECHNICAL MANUAL) + + _net_ 4 6 + + =Electricity and Magnetism in Telephone Maintenance.= By G.W. + CUMMINGS. 45 illus. 137 pp. 8vo. (_New York, 1908_) . .. + + _net_ 6 6 + + =Grouping of Electric Cells.= By W.F. DUNTON. 4 illus. 50 pp. fcap. + 8vo. (1906) + + _net_ 1 6 + + MAGNETS AND ELECTRIC CURRENTS. By Prof. J.A. FLEMING. Second edition, + 136 illus. 417 pp. crown 8vo (_1902_) + + _net_ 5 0 + + =Notes on Design of Small Dynamo.= By GEORGE HALLIDAY. Second edition, + 8 plates, 8vo. (_1895_) 2 6 =Practical Alternating Currents and Power + Transmission.= By N. HARRISON. 172 illus. 375 pp. + crown 8vo. (_New York, 1906_) + + 10 6 + + =Making Wireless Outfits.= By N. HARRISON. 27 illus. 61 pp. crown 8vo, + limp. (S. & C. SERIES, NO. 11.) (_New York, 1909_) + + _net_ 1 6 + + =Wireless Telephone Construction.= By N. HARRISON. 43 illus. 73 pp. + crown 8vo, limp. (S. & C. Series, No. 12.) (_New York, 1909_) + + _net_ 1 6 + + =The Phoenix Fire Office Rules= for Electric Light and Electrical + Power Installations. By M. HEAPHY. Thirty-seventh edition, 8vo, sewed. + (_1908_) + + 0 6 + + =Testing Telegraph Cables.= By Colonel V. HOSKIOER. Third edition, + crown 8vo. (_1889_) + + 4 6 + + =Long Distance Electric Power Transmission.= By R.W. HUTCHINSON. 136 + illus. 345 pp. crown 8vo. (_New York, 1907_) + + _net_ 12 6 + + =Theory and Practice of Electric Wiring.= By W.S. IBBETSON. 119 illus. + 366 pp. crown 8vo. (_1909_) + + _net_ 5 0 + + =Practical Electrical Engineering for Elementary Students.= By W.S. + IBBETSON. With 61 illus. 155 pp. crown 8vo. (_1910_) + + _net_ 3 0 + + =General Rules recommended for Wiring= for the Supply of Electrical + Energy. Issued by THE INSTITUTION OF ELECTRICAL ENGINEERS. 8vo, sewed. + (_Revised, April 1907_) + + _net_ 0 6 + + =Form of Model General Conditions= recommended by THE INSTITUTION OF + ELECTRICAL ENGINEERS for use in connection with Electrical Contracts. + 8vo, sewed. (_1906_) + + _net_ 1 0 + + =A Handbook of Electrical Testing.= By H.R. KEMPE. Seventh edition, + 285 illus. 706 pp. demy 8vo. (_1908_) + + _net_ 18 0 + + =Application of Electricity to Railway Working.= By W.E. LANGDON. + 142 illus. and 5 plates, 347 pp. 8vo. (_1897_) + + 10 6 + + =How to Become a Competent Motorman.= By V.B. LIVERMORE and J. + WILLIAMS. 45 illus. 252 pp. 12mo. (_New York, 1903_) + + _net_ 4 6 + + =Electromagnets,= their design and construction. By A.N. MANSFIELD. 36 + illus. 155 pp. 18mo, boards. (_New York, 1901_) + + _net_ 2 0 + + =Telephone Construction, Methods and Cost.= By C. MAYER. With + Appendices on the cost of materials and labour by J.C. SLIPPY. 103 + illus. 284 pp. crown 8vo. (_New York, 1908_) + + _net_ 12 6 + + =Induction Coils.= By N.H. SCHNEIDER. Second edition, 79 illus. 285 + pp. crown 8vo. (_New York, 1901_) + + _net_ 4 6 + + =Electric Gas Lighting.= By N.H. SCHNEIDER. 57 illus. 101 pp. 12mo. + (S. & C. SERIES, NO. 8.) (_New York, 1901_) + + _net_ 2 0 + + =How to Install Electric Bells, Annunciators and Alarms.= By N.H. + SCHNEIDER. 59 illus. 63 pp. crown 8vo, limp. (S. & C. SERIES, NO. 2.) + (_New York, 1905_) + + _net_ 1 6 + + =Modern Primary Batteries,= their construction, use and maintenance. + By N.H. SCHNEIDER. 54 illus. 94 pp. crown 8vo, limp. (S. & C. SERIES, + NO. 1.) (_New York, 1905_) + + _net_ 1 6 + + =Practical Engineers' Handbook on the Care and Management of Electric + Power Plants.= By N.H. SCHNEIDER. 203 illus. 274 pp. crown 8vo. (_New + York, 1906_) + + _net_ 5 0 + + =Electrical Circuits and Diagrams,= illustrated and explained. By N.H. + SCHNEIDER. 8vo, limp. (S. & C. SERIES, NOS. 3 AND 4.) (_New York_) + + Part 1. 217 illus. 72 pp. (_1905_) + + _net_ 1 6 + + Part 2. 73 pp. (_1909_) + + _net_ 1 6 + + =Electrical Instruments and Testing.= By N.H. SCHNEIDER. Third + edition. 133 illus. 239 pp. crown 8vo. (_New York, 1907_) + + _net_ 4 6 + + =Experimenting with Induction Coils.= By N.H. SCHNEIDER. 26 illus. 73 + pp. crown 8vo, limp. (S. & C. SERIES, NO. 5.) (_New York, 1906_) + + _net_ 1 6 + + =Study of Electricity for Beginners.= By N.H. SCHNEIDER. 54 illus. 88 + pp. crown 8vo, limp. (S. & C. SERIES, NO. 6.) (_New York, 1905_) + + _net_ 1 6 + + =Practical Electrics:= a Universal Handybook on Every Day Electrical + Matters. Seventh edition, 126 illus. 135 pp. 8vo. (S. & C. SERIES, NO. + 13.) (_New York, 1902_) + + _net_ 1 6 + + =The Voltaic Accumulator:= an elementary treatise. By E. REYNIER. + Translated from the French by J.A. BERLY. 62 illus. 202 pp. 8vo + + 9 0 + + =Dry Batteries:= how to Make and Use them. By a DRY BATTERY EXPERT. + With additional notes by N.H. SCHNEIDER. 30 illus. 59 pp. crown 8vo, + sewed. (S. & C. SERIES, NO. 7.) (_New York, 1905_) + + _net_ 1 6 + + =The Diseases of Electrical Machinery.= By E. SCHULZ. Edited, with a + Preface, by Prof. S.P. THOMPSON. 42 illus. 84 pp. crown 8vo + + _net_ 2 0 + + =Electric Toy-Making.= By T.O. SLOANE. Fifteenth edition, 70 illus. + 183 pp. crown 8vo. (_New York, 1903_) + + _net_ 4 6 + + =Electricity Simplified.= By T.O. SLOANE. Tenth edition, 29 illus. 158 + pp. crown 8vo. (_New York, 1901_) + + _net_ 4 6 + + =How to become a Successful Electrician.= By T.O. SLOANE. Third + edition, illustrated, crown 8vo. (_New York, 1899_) + + _net_ 4 6 + + =Electricity:= its Theory, Sources and Applications. By J.T. SPRAGUE. + Third edition, 109 illus. 658 pp. crown 8vo. (_1892_) + + _net_ 7 6 + + =Telegraphic Connections.= By C. THOM and W.H. JONES. 20 plates, 59 + pp. oblong 8vo. (_New York, 1892_) + + _net_ 3 6 + + =Röntgen Rays= and Phenomena of the Anode and Cathode. By E.P. + THOMPSON and W.A. ANTHONY. 105 illus. 204 pp. 8vo. (_New York, 1896_) + + _net_ 4 6 + + =Dynamo Electric Machinery.= By Prof. S.P. THOMPSON. Seventh edition, + demy 8vo. (FINSBURY TECHNICAL MANUAL.) + + Vol. I. =Continuous-Current Machinery.= With 4 coloured and 30 + folding plates, 573 illus. 984 pp. (_1904_) + + _net_ 1 10 0 + + Vol. II. =Alternating Current Machinery.= 15 coloured and 24 + folding plates, 546 illus. 900 pp. (_1905_) + + _net_ 1 10 0 + + =Design of Dynamos= (Continuous Currents). By Prof. S.P. THOMPSON. 4 + coloured and 8 folding plates, 243 pp. demy 8vo. (_1903_) + + _net_ 12 0 + + =Schedule for Dynamo Design,= issued with the above. 6_d_. each, 4_s_. + per doz., or 18_s_. per 100 _net_ + + =Curves of Magnetic Data for Various Materials.= A reprint on + transparent paper for office use of Plate L from Dynamo Electric + Machinery, and measuring 25 in. by 16 in. + + _net_ 0 7 + + =The Electromagnet.= By C.R. UNDERHILL. 67 illus. 159 pp. crown 8vo. + (_New York, 1903_) + + _net_ 6 6 + + =Practical Guide to the Testing of Insulated Wires and Cables.= By + H.L. WEBB. Fifth edition, 38 illus. 118 pp. crown 8vo. (_New York, + 1902_) + + _net_ 4 6 + + + FOREIGN EXCHANGE. + + =English Prices with Russian Equivalents= (at Fourteen Rates of + Exchange). English prices per lb., with equivalents in roubles and + kopecks per pood. By A. ADIASSEWICH. 182 pp. fcap. 32mo, roan. + (_1908_) + + _net_ 1 0 + + =English Prices with German Equivalents= (at Seven Rates of Exchange). + English prices per lb., with equivalents in marks per kilogramme. By + St. KOCZOROWSKI. 95 pp. fcap. 32mo, roan. (_1909_) + + _net_ 1 0 + + =English Prices with Spanish Equivalents.= At Seven Rates of Exchange. + English prices per lb., with equivalents in pesetas per kilogramme. By + S. LAMBERT. 95 pp. 32mo, roan. (_1910_) + + _net_ 1 0 + + =English Prices with French Equivalents= (at Seven Rates of Exchange). + English prices per lb. to francs per kilogramme. By H.P. MCCARTNEY. 97 + pp. 32mo, roan. (_1907_) + + _net_ 1 0 + + =Principles of Foreign Exchange.= By E. MATHESON. Fourth edition, 54 + pp. 8vo, sewed. (_1905_) + + _net_ 0 3 + + + GAS AND OIL ENGINES. + + =The Theory of the Gas Engine.= By D. CLERK. Edited by F.E. IDELL. + Third edition, 19 illus. 180 pp. 18mo, boards. (_New York, 1903_) + + _net_ 2 0 + + =The Design and Construction of Oil Engines.= By A.H. GOLDINGHAM. + Third edition, 112 illus. 260 pp. crown 8vo. (_New York, 1910_) + + _net_ 10 6 + + =Gas Engine in Principle and Practice.= By A.H. GOLDINGHAM. 107 illus. + 195 pp. 8vo, cloth. (_New York, 1907_) + + _net_ 6 6 + + =Practical Hand-Book on the Care and Management of Gas Engines.= By + G. LIECKFELD. Third edition, square 16mo. (_New York, 1896_) + + 3 6 + + =Elements of Gas Engine Design.= By S.A. MOSS. 197 pp. 18mo, boards. + (_New York, 1907_) + + _net_ 2 0 + + =Gas and Petroleum Engines.= A Manual for Students and Engineers. + (FINSBURY TECHNICAL MANUAL.) By Prof. W. ROBINSON. _Third edition in + preparation_ + + + GAS LIGHTING. + + =Gas Analyst's Manual= (incorporating Hartley's "Gas Analyst's Manual" + and "Gas Measurement"). By J. ABADY. 102 illustrations, 576 pp. demy + 8vo. (_1902_) + + _net_ 18 0 + + =Gas Works:= their Arrangement, Construction, Plant and Machinery. By + F. COLYER. 31 folding plates, 134 pp. 8vo. (_1884_) + + _net_ 8 6 + + =Transactions of the Institution of Gas Engineers.= Edited by WALTER + T. DUNN, _Secretary_. Published annually. 8vo + + _net_ 10 6 + + =Lighting by Acetylene.= By F. DYE. 75 illus. 200 pp. crown 8vo. + (_1902_) + + _net_ 6 0 + + =A Comparison of the English and French Methods of Ascertaining the + Illuminating Power of Coal Gas.= By A.J. VAN EIJNDHOVEN. Illustrated, + crown 8vo. (_1897_) + + 4 0 + + =Gas Lighting and Gas Fitting.= By W.P. GERHARD. Second edition, 190 + pp. 18mo, boards. (_New York, 1894_) + + _net_ 2 0 + + =A Treatise on the Comparative Commercial Values of Gas Coals and + Cannels.= By D.A. GRAHAM. 3 plates, 100 pp. 8vo. (_1882_) + + 4 6 + + =The Gas Engineer's Laboratory Handbook.= By J. HORNBY. Third edition, + revised, 70 illus. 330 pp. crown 8vo. (_1910_) + + _net_ 6 0 + + + HISTORICAL AND BIOGRAPHICAL. + + =Extracts from the Private Letters of the late Sir William Fothergill + Cooke,= 1836-9, relating to the Invention and Development of the + Electric Telegraph; also a Memoir by LATIMER CLARK. Edited by F.H. + WEBB. Sec. Inst.E.E. 8vo. (_1895_) + + 3 0 + + =A Chronology of Inland Navigation= in Great Britain. By H.R. DE + SALIS. Crown 8vo. (1897) + + 4 6 + + =A History of Electric Telegraphy= to the year 1837. By J.J. FAHIE. 35 + illus. 542 pp. crown 8vo. (_1889_) + + 2 0 + + =History and Development of Steam Locomotion on Common Roads.= By W. + FLETCHER. 109 illus. 288 pp. 8vo + + 5 0 + + =Life as an Engineer:= its Lights, Shades, and Prospects. By J.W.C. + HALDANE. 23 plates, 338 pp. crown 8vo. (_1905_) + + _net_ 5 0 + + =Philipp Reis,= Inventor of the Telephone: a Biographical Sketch. By + Prof. S.P. THOMPSON. 8vo, cloth. (_1883_) + + 7 6 + + =The Development of the Mercurial Air Pump.= By Prof. S.P. THOMPSON. + Illustrated, royal 8vo, sewed. (_1888_) + + 1 6 + + + HOROLOGY. + + =Watch and Clock Maker's Handbook,= Dictionary and Guide. By F.J. + BRITTEN. Tenth edition, 450 illus. 492 pp. crown 8vo. (_1902_) + + _net_ 5 0 + + =The Springing and Adjusting of Watches.= By F.J. BRITTEN. 75 illus. + 152 pp. crown 8vo. (_1898_) + + _net_ 3 0 + + =Prize Essay on the Balance Spring= and its Isochronal Adjustments. By + M. IMMISCH. 7 illus. 50 pp. crown 8vo. (_1872_) + + 2 6 + + + HYDRAULICS AND HYDRAULIC MACHINERY. + + (_See also_ WATER SUPPLY.) + + =Pumps:= Historically, Theoretically and Practically Considered. By + P.R. BJÖRLING. Second edition, 156 illus. 234 pp. crown 8vo. (_1895_) + + 7 6 + + =Pump Details.= By P.R. BJÖRLING. 278 illus. 211 pp. crown 8vo. + (_1892_) + + 7 6 + + =Pumps and Pump Motors:= A Manual for the use of Hydraulic Engineers. + By P.R. BJÖRLING. Two vols. 261 plates, 369 pp. royal 4to. (_1895_). + + _net_ 1 10 0 + + =Practical Handbook on Pump Construction.= By P.R. BJÖRLING. Second + edition, 9 plates, 90 pp. crown 8vo. (_1904_) + + 5 0 + + =Water or Hydraulic Motors.= By P.R. BJÖRLING. 206 illus. 287 pp. + crown 8vo. (_1903_) + + 9 0 + + =Hydraulic Machinery,= with an Introduction to Hydraulics. By R.G. + BLAINE. Second edition with 307 illus. 468 pp. 8vo. (FINSBURY + TECHNICAL MANUAL). (_1905_) + + _net_ 14 0 + + =Practical Hydraulics.= By T. BOX. Fifteenth edition, 8 plates, 88 pp. + crown 8vo. (_1909_) + + _net_ 5 0 + + =Hydraulic, Steam, and Hand Power Lifting and Pressing Machinery.= By + F. COLYER. Second edition, 88 plates, 211 pp. imperial 8vo. (_1892_) + + _net_ 10 6 + + =Pumps and Pumping Machinery.= By F. COLYER. + + Vol. I. Second edition, 53 plates, 212 pp. 8vo (_1892_) + + _net_ 10 6 + + Vol. II. Second edition, 48 plates, 169 pp. 8vo. (_1900_) + + _net_ 10 6 + + =Construction of Horizontal and Vertical Water-wheels.= By W. CULLEN. + Second edition, small 4to. (_1871_) + + 5 0 + + =Donaldson's Poncelet Turbine= and Water Pressure Engine and Pump. + By W. DONALDSON. 4to. (_1883_) + + 5 0 + + =Principles of Construction and Efficiency of Water-wheels.= By W. + DONALDSON. 13 illus. 94 pp. 8vo. (_1876_) + + 5 0 + + =Practical Hydrostatics and Hydrostatic Formulæ.= By E.S. GOULD. 27 + illus. 114 pp. 18mo, boards. (_New York, 1903_) + + _net_ 2 0 + + =Hydraulic and other Tables= for purposes of Sewerage and Water + Supply. By T. HENNELL. Third edition, 70 pp. crown 8vo. (_1908_) + + _net_ 4 6 + + =Hydraulic Tables= for finding the Mean Velocity and Discharge in Open + Channels. By T. HIGHAM. Second edition, 90 pp. super-royal 8vo. + (_1898_) + + 7 6 + + =Tables for Calculating the Discharge of Water= in Pipes for Water and + Power Supplies. Indexed at side for ready reference. By A.E. SILK. 63 + pp. crown 8vo. (_1899_) + + 5 0 + + =Simple Hydraulic Formulæ.= By T.W. STONE. 9 plates, 98 pp. crown 8vo. + (_1881_) + + 4 0 + + + INDUSTRIAL CHEMISTRY AND MANUFACTURES. + + =Perfumes and their Preparation.= By G.W. ASKINSON. Translated from + the Third German Edition by I. FUEST. Third edition, 32 illus. 312 pp. + 8vo. (_New York, 1907_) + + _net_ 12 6 + + =Brewing Calculations,= Gauging and Tabulation. By C.H. BATER. 340 pp. + 64mo, roan, gilt edges. (_1897_) + + _net_ 1 6 + + =A Pocket Book for Chemists,= Chemical Manufacturers, Metallurgists, + Dyers, Distillers, etc. By T. BAYLEY. Seventh edition, 550 pp. royal + 32mo, roan, gilt edges. (_1905_) + + _net_ 5 0 + + =Practical Receipts= for the Manufacturer, the Mechanic, and for + Home use. By Dr. H.R. BERKELEY and W.M. WALKER. 250 pp. demy 8vo. + (_1902_) + + _net_ 7 6 + + =A Treatise on the Manufacture of Soap and Candles,= Lubricants and + Glycerine. By W.L. CARPENTER and H. LEASK. Second edition, 104 illus. + 456 pp. crown 8vo. (_1895_) + + 12 6 + + =A Text Book of Paper Making.= By C.F. CROSS and E.J. BEVAN. Third + edition, 97 illus. 411 pp. crown 8vo. (_1907_) + + _net_ 12 6 + + =C.B.S. Standard Units and Standard Paper Tests.= By C.F. CROSS, E.J. + BEVAN, C. BEADLE and R.W. SINDALL. 25 pp. crown 4to. (_1903_) + + _net_ 2 6 + + =Soda Fountain Requisites.= A Practical Receipt Book for Druggists, + Chemists, etc. By G.H. DUBELLE. Third edition, 157 pp. crown 8vo. + (_New York, 1905_) + + _net_ 4 6 + + =The Chemistry of Fire= and Fire Prevention. By H. and H. INGLE. 45 + illus. 290 pp. crown 8vo. (_1900_) + + 9 0 + + =Ice-Making Machines.= By M. Ledoux and others. Sixth edition. 190 pp. + 18mo, boards. (_New York, 1906_) + + _net_ 2 0 + + =Brewing with Raw Grain.= By T.W. Lovibond. 75 pp. crown 8vo. (1883) + + 5 0 + + =Sugar, a Handbook for Planters and Refiners.= By the late J.A.R. + NEWLANDS and B.E.R. NEWLANDS. 236 illus. 876 pp. demy 8vo. (_London, + 1909_) + + _net_ 1 5 0 + + =Principles of Leather Manufacture.= By Prof. H.R. PROCTER. 101 illus. + 520 pp. medium 8vo. (_1908_) + + _net_ 18 0 + + =Leather Industries Laboratory Handbook= of Analytical and + Experimental methods. By H.R. PROCTER. Second edition, 4 plates, 46 + illus. 450 pp. demy 8vo. (_1908_) + + _net_ 18 0 + + =Theoretical and Practical Ammonia Refrigeration.= By I.I. REDWOOD. + Sixth thousand, 15 illus. 146 pp. square 16mo. (_New York, 1909_) + + _net_ 4 6 + + =Breweries and Maltings.= By G. SCAMMELL and F. COLYER. Second + edition, 20 plates, 178 pp. 8vo. (_1880_) + + _net_ 6 0 + + =Factory Glazes for Ceramic Engineers.= By H. RUM-BELLOW. Folio. + Series A, Leadless Sanitary Glazes. (_1908_) + + _net_ 2 2 0 + + =Text Book of Physical Chemistry.= By C.L. SPEYERS. 224 pp. demy 8vo. + (_New York, 1898_) + + 9 0 + + =Spons' Encyclopædia of the Industrial Arts,= Manufactures and + Commercial Products. 1500 illus. 2100 pp. super-royal 8vo. (_1882_) In + 2 Vols. cloth + + _net_ 2 2 0 + + =Pigments, Paints and Painting.= By G. TERRY. 49 illus. 392 pp. crown + 8vo. (_1893_) + + 7 6 + + =Tables for the Quantitative Estimation of the Sugars.= By E. WEIN and + W. FREW. Crown 8vo. (_1896_) + + 6 0 + + =Workshop Receipts.= For the use of Manufacturers, Mechanics and + Scientific Amateurs. New and thoroughly revised edition, crown 8vo. + (_1909_) each + + _each net_ 3 0 + + Vol. I. ACETYLENE LIGHTING _to_ DRYING. 223 illus. 532 pp. + + Vol. II. DYEING _to_ JAPANNING. 259 illus. 540 pp. + + Vol. III. JOINTING PIPES _to_ PUMPS. 256 illus. 528 pp. + + Vol. IV. RAINWATER SEPARATORS _to_ WINES. 250 illus. 520 pp. + + =Practical Handbook on the Distillation of Alcohol from Farm + Products.= By F.B. WRIGHT. Second edition, 60 illus. 271 pp. crown + 8vo. (_New York, 1907_) ... ... + + _net_ 4 6 + + =The Manufacture of Chocolate= and other Cacao Preparations. By P. + ZIPPERER. Second edition, 87 illus. 280 pp. royal 8vo. (_1902_) + + _net_ 16 0 + + + IRRIGATION. + + =The Irrigation Works of India.= By R.B. BUCKLEY. Second edition, with + coloured maps and plans. 336 pp. 4to, cloth. (_1905_) + + _net_ 2 2 0 + + =Facts, Figures, and Formulæ for Irrigation Engineers.= By R.B. + BUCKLEY. With illus. 239 pp. large 8vo. (_1908_) + + _net_ 10 6 + + =Irrigated India.= By Hon. ALFRED DEAKIN. With Map, 322 pp. 8vo. + (_1893_) + + 8 6 + + =Indian Storage Reservoirs,= with Earthen Dams. By W.L. STRANGE. 14 + plates and 53 illus. 379 pp. demy 8vo. (_1904_) + + _net_ 1 1 0 + + =Irrigation Farming.= By L.M. WILCOX. Revised edition, 113 illus. 494 + pp. crown 8vo. (_New York_) + + _net_ 8 6 + + =Egyptian Irrigation.= By Sir W. WILLCOCKS. Second edition out of + Print. _A few copies of the First Edition (_1889_) are still + to be had. Price 15s. net._ + + =The Nile Reservoir Dam at Assuan,= and After. By Sir + _W. WILLCOCKS._ Second edition, 13 plates, super-royal 8vo. + (_1903_) + + _net_ 6 0 + + =The Assuan Reservoir and Lake Moeris.= By Sir W. WILLCOCKS. With text + in English, French and Arabic. 5 plates, 116 pp. super-royal 8vo. + (_1904_) + + _net_ 5 0 + + =The Nile in 1904.= By Sir W. Willcocks. 30 plates, 200 pp. + super-royal 8vo. (_1904_) + + _net_ 9 0 + + + LOGARITHM TABLES. + + =Aldum's Pocket Folding Mathematical Tables.= Four-figure logarithms, + and Anti-logarithms, Natural Sines, Tangents, Cotangents, Cosines, + Chords and Radians for all angles from 1 to 90 degrees. On folding + card. _Net_ 4_d._ 20 copies, _net_ 6_s._ + + =Tables of Seven-figure Logarithms= of the Natural Numbers from 1 to + 108,000. By C. BABBAGE. Stereotype edition, 8vo + + 7 6 + + =Short Logarithmic= and other Tables. By W.C. UNWIN. Fourth edition, + small 4to + + 3 0 + + =Logarithmic Land Measurement.= By J. WALLACE. 32 pp. royal 8vo. + (_1910_) + + _net_ 5 0 + + =A.B.C. Five-figure Logarithms with Tables, for Chemists.= By C.J. + WOODWARD. Crown 8vo + + _net_ 2 6 + + =A.B.C. Five-figure Logarithms= for general use, with lateral index + for ready reference. By C.J. WOODWARD. Second edition, with cut + lateral Index, 116 pp. 12mo, limp leather + + _net_ 3 0 + + + MARINE ENGINEERING AND NAVAL ARCHITECTURE. + + =Marine Propellers.= By S.W. BARNABY. Fifth edition, 5 plates, 56 + illus. 185 pp. demy 8vo. (_1908_) + + _net_ 10 6 + + =Marine Engineer's Record Book:= Engines. By B.C. BARTLEY. 8vo, roan + + _net_ 5 0 + + =The Engineer's and Draughtsman's Data Book= for Workshop and Office + Use. Third edition, crown 8vo, roan + + 3 0 + + =Yachting Hints,= Tables and Memoranda. By A.C. FRANKLIN. Waistcoat + pocket size, 103 pp. 64mo, roan, gilt edges + + _net_ 1 0 + + =Steamship Coefficients, Speeds and Powers.= By C.F.A. FYFE. 31 + plates, 280 pp. fcap. 8vo, leather. (_1907_) + + _net_ 10 6 + + =Steamships and Their Machinery,= from first to last. By J.W.C. + HALDANE. 120 illus. 532 pp. 8vo. (_1893_) + + 15 0 + + =Tables for Constructing Ships' Lines.= By A. HOGG. Second edition, + 8vo + + 7 0 + + =Submarine Boats.= By G.W. HOVGAARD. 2 plates, 98 pp. crown 8vo. + (_1887_) + + 5 0 + + =Tabulated Weights= of Angle, Tee, Bulb, Round, Square, and Flat Iron + and Steel for the use of Naval Architects, Ship-builders, etc. By C.H. + JORDAN. Sixth edition, 640 pp. royal 32mo, French morocco, gilt edges. + (_1909_) + + _net_ 7 6 + + =Particulars of Dry Docks,= Wet Docks, Wharves, etc. on the River + Thames. Compiled by C.H. JORDAN. Second edition, 7 coloured charts, + 103 pp. oblong 8vo. (_1904_) + + _net_ 2 6 + + =Marine Transport of Petroleum.= By H. LITTLE. 66 illus. 263 pp. crown + 8vo. (_1890_) + + 10 6 + + =Questions and Answers for Marine Engineers,= with a Practical + Treatise on Breakdowns at Sea. By T. LUCAS. 12 folding plates, 515 pp. + gilt edges, crown 8vo. (_New York, 1902_) + + _net_ 8 0 + + =Reed's Examination Papers for Extra First Class Engineers=. Fourth + edition, 14 plates and 188 illus. 550 pp. 8vo. (_1902_) + + _net_ 18 0 + + =Reed's Engineers' Handbook to the Board of Trade Examinations= for + certificates of Competency as First and Second Class Engineers. + Nineteenth edition, 37 plates, 358 illus. 696 pp. 8vo + + _net_ 14 0 + + =Reed's Marine Boilers.= Second edition, crown 8vo + + _net_ 4 6 + + =Reed's Useful Hints to Sea-going Engineers.= Fourth edition, 8 + plates, 50 illus. 312 pp. crown 8vo. (_1903_) + + _net_ 3 6 + + + MATERIALS. + + =Practical Treatise on the Strength of Materials.= By T. BOX. Fourth + edition, 27 plates, 536 pp. 8vo. (_1902_) + + _net_ 12 6 + + =Treatise on the Origin, Progress, Prevention and Cure of Dry Rot in + Timber.= By T.A. BRITTON. 10 plates, 519 pp. crown 8vo. (_1875_) + + 7 6 + + =Twenty Years' Practical Experience of Natural Asphalt= and Mineral + Bitumen. By W.H. DELANO. 33 illus. 73 pp. crown 8vo, parchment. + (_1893_) + + 2 0 + + =Stone:= how to get it and how to use it. By Major-Gen. C.E. LUARD, + R.E. 8vo, sewed. (_1890_) + + 2 0 + + =Testing of Pipes= and Pipe-joints in the Open Trenches. By M.M. + PATERSON. 8vo, sewed (_1879_) + + 2 0 + + =Solid Bitumens.= By S.F. PECKHAM. 23 illus. 324 pp. 8vo. (_New York, + 1909_) + + _net_ 1 1 0 + + =Lubricants, Oils and Greases.= By I.I. REDWOOD. 3 plates, 8vo. + (_1898_) + + _net_ 6 6 + + =Practical Treatise on Mineral Oils= and their By-Products. By I.I. + REDWOOD. 67 illus. 336 pp. demy 8vo. (_1897_) + + 15 0 + + =Silico-Calcareous Sandstones,= or Building Stones from Quartz, Sand + and Lime. By E. STOFFLER. 5 plates, 8vo, sewed. (_1901_) + + _net_ 4 0 + + =Proceedings of the Fifth Congress, International Association for + Testing Materials.= English edition. 189 illus. 549 pp. demy 8vo. + (_1910_). + + Paper + + _net_ 15 0 + + Cloth + + _net_ 18 0 + + + MATHEMATICS. + + =Imaginary Quantities.= By M. ARGAND. Translated by PROF. HARDY. 18mo, + boards. (_New York_) + + _net_ 2 0 + + =Text Book of Practical Solid Geometry.= By E.H. DE V. ATKINSON. + Revised by MAJOR B.R. WARD, R.E. Second edition, 17 plates, 8vo. + (_1901_) + + 7 6 + + =Quick and Easy Methods of Calculating,= and the Theory and Use of the + Slide Rule. By R.G. BLAINE. Third edition, 6 illus. 152 pp. 16mo, + leather cloth. (_1907_) + + 2 6 + + =Symbolic Algebra,= or the Algebra of Algebraic Numbers. By W. CAIN. + 18mo, boards. (_New York_) + + _net_ 2 0 + + =Nautical Astronomy.= By J.H. COLVIN. 127 pp. crown, 8vo. (_1901_) + + _net_ 2 6 + + =Chemical Problems.= By J.C. FOYE. Fourth edition, 141 pp. 18mo, + boards. (_New York, 1898_) + + _net_ 2 0 + + =Primer of the Calculus.= By E.S. GOULD. Second edition, 24 illus. 122 + pp. 18mo, boards. (_New York, 1899_) + + _net_ 2 0 + + =Elementary Treatise on the Calculus= for Engineering Students. By J. + GRAHAM. Third edition, 276 pp. crown 8vo. (_1905_). (FINSBURY + TECHNICAL MANUAL) + + 7 6 + + =Manual of the Slide Rule.= By F.A. HALSEY. Second edition, 31 illus. + 84 pp. 18mo, boards. (_New York, 1901_) + + _net_ 2 0 + + =Reform in Chemical and Physical Calculations.= By C.J.T. HANSSEN. + 4to. (_1897_) + + _net_ 6 6 + + =Algebra Self-Taught.= By P. HIGGS. Third edition, 104 pp. crown 8vo. + (_1903_) + + 2 6 + + =Galvanic Circuit investigated Mathematically.= By G.S. OHM. + Translated by WILLIAM FRANCIS. 269 pp. 18mo, boards. (_New York, + 1891_) + + _net_ 2 0 + + =Elementary Practical Mathematics.= By M.T. ORMSBY. 420 pp. demy 8vo. + (_1900_) + + _net_ 7 6 + + =Elements of Graphic Statics.= By K. VON OTT. Translated by G.S. + CLARKE. 93 illus. 128 pp. crown 8vo. (_1901_) + + 5 0 + + =Figure of the Earth.= By F.C. ROBERTS. 18mo, boards. (_New York_) + + _net_ 2 0 + + =Arithmetic of Electricity.= By T. O'C. SLOANE. Thirteenth edition, + crown 8vo. (_New York, 1901_) + + _net_ 4 6 + + =Graphic Method for Solving certain Questions in Arithmetic or + Algebra.= By G.L. VOSE. Second edition with 28 illus. 62 pp. 18mo, + boards. (_New York, 1902_) + + _net_ 2 0 + + =Problems in Electricity.= A Graduated Collection comprising all + branches of Electrical Science. By R. WEBER. Translated from the + French by E.A. O'KEEFE. 34 illus. 366 pp. crown 8vo. (_1902_). + + _net_ 7 6 + + + MECHANICAL ENGINEERING. + + STEAM ENGINES AND BOILERS, ETC. + + =Handbook for Mechanical Engineers.= By HY. ADAMS. Fourth edition, 426 + pp. crown 8vo. (_1897_) + + _net_ 4 6 + + =Appleby's Handbooks of Machinery.= Many illustrations, 8vo. Sections + 2, 3, 4 and 6 + + _each_ 3 6 + + Section 5 + + 5 0 + + Section 1.--Prime Movers. _Out of Print._ + Section 2.--Hoisting Machinery, Winding Engines, etc. + Section 3.--_Out of print._ + Section 4.--Machine Tools and Accessories. + Section 5.--Contractors' Plant and Railway Materials. + Section 6.--Mining, Colonial and Manufacturing Machinery. + + =Engineers' Sketch Book of Mechanical Movements.= By T.W. BARBER. + Fifth edition, 3000 illus. 355 pp. 8vo. (_1906_) + + _net_ 10 6 + + =The Repair and Maintenance of Machinery.= By T.W. BARBER. 417 illus. + 476 pp. 8vo. (_1895_) + + 10 6 + + =Slide Valve and its Functions=, with special reference to Modern + Practice in the United States. By J. BEGTRUP. 90 diagrams, 146 pp. + medium 8vo. (_New York, 1902_) + + _net_ 8 0 + + =Practical Treatise on Mill Gearing.= By T. BOX. Fifth edition, 11 + plates, 128 pp. crown 8vo. (_1892_) + + 7 6 + + =Safety Valves.= By R.H. BUELL. Third edition, 20 illus. 100 pp. 18mo, + boards. (_New York, 1898_) + + _net_ 2 0 + + =Machine Design.= By Prof. W.L. CATHCART. Part I. FASTENINGS. 123 + illus. 291 pp. demy 8vo. (_New York, 1903_) + + _net_ 12 6 + + =Chimney Design and Theory.= By W.W. CHRISTIE. Second edition, 54 + illus. 192 pp. crown 8vo. (_New York, 1902_) + + _net_ 12 6 + + =Furnace Draft:= its Production by Mechanical Methods. By W.W. + CHRISTIE. 5 illus. 80 pp. 18mo, boards. (_New York, 1906_) + + _net_ 2 0 + + =Working and Management of Steam Boilers and Engines.= By F. COLYER. + Second edition, 108 pp. crown 8vo. (_1902_) + + 3 6 + + =The Stokers' Catechism.= By W.J. CONNOR. 63 pp. limp cloth. (_1906_) + + _net_ 1 0 + + =Treatise on the use of Belting for the Transmission of Power.= By + J.H. COOPER. Fifth edition, 94 illus. 399 pp. demy 8vo. (_New York, + 1901_) + + _net_ 12 6 + + =The Steam Engine considered as a Thermodynamic Machine.= By J.H. + COTTERILL. Third edition, 39 diagrams, 444 pp. 8vo. (_1896_) + + 15 0 + + =Fireman's Guide=, a Handbook on the Care of Boilers. By K.P. + DAHLSTROM. Ninth edition fcap. 8vo. (_New York, 1902_) + + _net_ 1 6 + + =Heat for Engineers.= By C.R. DARLING. 110 illus. 430 pp. 8vo. + (_1908._) (FINSBURY TECHNICAL MANUAL.) + + _net_ 12 6 + + =Diseases of a Gasolene Automobile=, and How to Cure Them. By A.L. + DYKE and G.P. DORRIS. 127 illus. 201 pp. crown 8vo. (_New York, 1903_) + + _net_ 6 6 + + =Belt Driving.= By G. HALLIDAY. 3 folding plates, 100 pp. 8vo. + (_1894_) + + 3 6 + + =Worm and Spiral Gearing.= By F.A. HALSEY. 13 plates, 85 pp. 18mo, + boards. (_New York, 1903_) + + _net_ 2 0 + + =Commercial Efficiency of Steam Boilers.= By A. HANSSEN. Large 8vo, + sewed. (1898) + + 0 6 + + =Corliss Engine.= By J.T. HENTHORN. Third edition, 23 illus. 95 pp. + square 16mo. (S. & C. SERIES, No. 20.) (_New York, 1910_) + + _net_ 1 6 + + =Liquid Fuel= for Mechanical and Industrial Purposes. By E.A. + BRAYLEY HODGETTS. 106 illus. 129 pp. 8vo. (_1890_) + + 5 0 + + =Elementary Text-Book on Steam Engines and Boilers.= By J.H. + KINEALY. Fourth edition, 106 illus. 259 pp. 8vo. (_New York, + 1903_) + + _net_ 8 6 + + =Centrifugal Fans.= By J.H. KINEALY. 33 illus. 206 pp. fcap. + 8vo, leather. (_New York, 1905_) + + _net_ 12 6 + + =Mechanical Draft.= By J.H. KINEALY. 27 original tables and 13 + plates, 142 pp. crown 8vo. (_New York, 1906_) + + _net_ 8 6 + + =The A.B.C. of the Steam Engine=, with a description of the + Automatic Governor. By J.P. LISK. 6 plates, 12mo. (S. & C. + SERIES, No. 17.) (_New York, 1910_) + + _net_ 1 6 + + =Valve Setting Record Book.= By P.A. LOW. 8vo, boards. + + 1 6 + + =The Lay-out of Corliss Valve Gears.= By S.A. MOSS. Second + edition, 3 plates, 108 pp. 18mo, boards. (_New York, 1906_) + + _net_ 2 0 + + =Steam Boilers=, their Management and Working. By J. PEATTIE. + Fifth edition, 35 illus. 230 pp. crown 8vo. (_1906_) + + _net_ 4 6 + + =Treatise on the Richards Steam Engine Indicator.= By C.T. + PORTER. Sixth edition, 3 plates and 73 diagrams, 285 pp. 8vo. + (_1902_) + + 9 0 + + =Practical Treatise on the Steam Engine.= By A. RIGG. Second + edition, 103 plates, 378 pp. demy 4to. (_1894_) + + 1 5 0 + + =Power and its Transmission.= A Practical Handbook for the + Factory and Works Manager. By T.A. SMITH. 76 pp. fcap. 8vo. + (_1910_) + + _net_ 2 0 + + =Drawings for Medium Sized Repetition Work.= By R.D. SPINNEY. + With 47 illus. 130 pp. 8vo. (_1909_) + + _net_ 3 6 + + =Slide Valve Simply Explained.= By W.J. TENNANT. Revised by + J.H. KINEALY. 41 illus. 83 pp. crown 8vo. (_New York, 1899_) + + _net_ 4 6 + + =Shaft Governors.= By W. TRINKS and C. HOOSUM. 27 illus. 97 pp. + 18mo, boards. (_New York, 1905_) + + _net_ 2 0 + + =Slide and Piston Valve Geared Steam Engines.= By W.H. UHLAND. + 47 plates and 314 illus. 155 pp. Two vols. folio, half morocco. + (_1882_) + + 1 16 0 + + =How to run Engines and Boilers.= By E.P. WATSON. Fifth + edition, 31 illus. 160 pp. crown 8vo. (_New York, 1904_) + + 3 6 + + =Position Diagram of Cylinder with Meyer Cut-off.= By W.H. + WEIGHTMAN. On card. (_New York_) + + _net_ 1 0 + + =Practical Method of Designing Slide Valve Gearing.= By E.J. + WELCH. 69 diagrams, 283 pp. Crown 8vo. (_1890_) + + 6 0 + + =Elements of Mechanics.= By T.W. WRIGHT. Eighth edition, + illustrated, 382 pp. 8vo. (_New York, 1909_) + + _net_ 10 6 + + + METALLURGY. + + IRON AND STEEL MANUFACTURE. + + =Life of Railway Axles.= By T. ANDREWS. 8vo, sewed. (_1895_) + + 1 0 + + =Microscopic Internal Flaws in Steel Rails and Propeller + Shafts.= By T. ANDREWS. 8vo, sewed. (_1896_) + + 1 0 + + =Microscopic Internal Flaws, Inducing Fracture in Steel.= By T. + ANDREWS. 8vo, sewed. (_1896_) + + 2 0 + + =Relations between the Effects of Stresses= slowly applied and + of Stresses suddenly applied in the case of Iron and Steel: + Comparative Tests with Notched and Plain Bars. By P. BREUIL. 23 + plates and 60 illus. 151 pp. 8vo. (_1904_) + + _net_ 8 0 + + =Brassfounders' Alloys.= By J.F. BUCHANAN. Illustrated, 129 pp. + crown 8vo. (_1905_) + + _net_ 4 6 + + =Foundry Nomenclature.= The Moulder's Pocket Dictionary and + concise guide to Foundry Practice. By JOHN F. BUCHANAN. + Illustrated, 225 pp. crown 8vo. (_1903_) + + _net_ 5 0 + + =American Standard Specifications for Steel.= By A.L. COLBY. + Second edition, revised, 103 pp. crown 8vo. (_New York, 1902_) + + _net_ 5 0 + + =Galvanised Iron=: its Manufacture and Uses. By J. DAVIES. 139 + pp. 8vo. (_1899_) + + _net_ 5 0 + + =Management of Steel.= By G. EDE. Seventh edition, 216 pp. + crown 8vo. (_1903_) + + 5 0 + + =Galvanising and Tinning=, with a special Chapter on Tinning + Grey Iron Castings. By W.T. FLANDERS. 8vo. (_New York_) + + _net_ 8 6 + + =Cupola Furnace.= A practical treatise on the Construction and + Management of Foundry Cupolas. By E. KIRK. Third edition, 78 + illus. 450 pp. demy 8vo. (_New York, 1910_) + + _net_ 15 0 + + =Practical Notes on Pipe Founding.= By J.W. MACFARLANE. 15 + plates, 148 pp. 8vo + + 12 6 + + =Atlas of Designs concerning Blast Furnace Practice.= By M.A. + PAVLOFF. 127 plates, 14 in. by 10½ in. oblong, sewed. + (_1902_) + + _net_ 1 1 0 + + =Album of Drawings relating to the Manufacture of Open Hearth + Steel.= By M.A. PAVLOFF. + + Part I. Open Hearth Furnaces. 52 plates, 14 in. by 10½ in. + oblong folio in portfolio. (_1904_) + + _net_ 12 0 + + =Metallography Applied to Siderurgic Products.= By H. SAVOIA. + Translated by R.G. CORBET. With 94 illus. 180 pp. crown 8vo. + (_1910_) + + _net_ 4 6 + + =Modern Foundry Practice.= Including revised subject matter and + tables from SPRETSON'S "Casting and Founding." By J. SHARP. + Second edition, 272 illus. 759 pp. 8vo. (_1905_) + + _net_ 1 1 0 + + =Roll Turning for Sections in Steel and Iron.= By A. SPENCER. + Second edition, 78 plates, 4to. (_1894_) + + 1 10 0 + + + METRIC TABLES. + + =French Measure and English Equivalents.= By J. BROOK. Second + edition, 80 pp. fcap. 32mo, roan. (_1906_) + + _net_ 1 0 + + =A Dictionary of Metric and other useful Measures.= By L. + CLARK. 113 pp. 8vo. (_1891_) + + 6 0 + + =English Weights, with their Equivalents in kilogrammes per + cent.= By F.W.A. LOGAN. 96 pp. fcap. 32mo, roan. (_1906_) + + _net_ 1 0 + + =Metric Weights with English Equivalents.= By H.P. MCCARTNEY. + 84 pp. fcap. 32mo. (_1907_) + + _net_ 1 0 + + =Metric Tables.= By Sir G.L. MOLESWORTH. Fourth edition, 95 pp. + royal 32mo. (_1909_) + + _net_ 2 0 + + =Tables for Setting out Curves= from 200 metres to 4000 metres + by tangential angles. By H. WILLIAMSON. 4 illus. 60 pp. 18mo. + (_1908_) + + _net_ 2 0 + + + MINERALOGY AND MINING. + + =Rock Blasting.= By G.G. ANDRE. 12 plates and 56 illus. in + text, 202 pp. 8vo. (_1878_) + + 5 0 + + =Winding Plants for Great Depth.= By H.C. BEHR. In two parts. + 8vo, sewed. (_1902_) + + _net_ 2 2 0 + + =Practical Treatise on Hydraulic Mining in California.= By A.J. + BOWIE, Jun. Tenth edition, 73 illus. 313 pp. royal 8vo. (_New + York, 1905_) + + _net_ 1 1 0 + + =Manual of Assaying Gold, Silver, Copper and Lead Ores.= By + W.L. BROWN. Twelfth edition, 132 illus. 589 pp. crown 8vo. + (_New York, 1907_) + + _net_ 10 6 + + =Fire Assaying.= By E.W. BUSKETT. 69 illus. 105 pp. crown 8vo. + (_New York, 1907_) + + _net_ 4 6 + + =Tin=: Describing the Chief Methods of Mining, Dressing, etc. + By A.G. CHARLETON. 15 plates, 83 pp. crown 8vo. (_1884_) + + 12 6 + + =Gold Mining and Milling= in Western Australia, with Notes upon + Telluride Treatment, Costs and Mining Practice in other Fields. + By A.G. CHARLETON. 82 illus. and numerous plans and tables, 648 + pp. super-royal 8vo. (_1903_) + + _net_ 1 5 0 + + =Miners' Geology and Prospectors' Guide.= By G.A. CORDER. 29 + plates, 224 pp. crown 8vo. (_1907_) + + _net_ 5 0 + + =Blasting of Rock in Mines, Quarries, Tunnels, etc.= By A.W. + and Z.W. DAW. Second edition, 90 illus. 316 pp. demy 8vo. + (_1909_) + + _net_ 15 0 + + =Handbook of Mineralogy=; determination and description of + Minerals found in the United States. By J.C. FOYE. 18mo, + boards. (_New York, 1886_) + + _net_ 2 0 + + =Conversations on Mines.= By W. HOPTON. Ninth edition, 33 + illus. 356 pp. crown 8vo. (_1891_) + + 4 6 + + =Our Coal Resources= at the End of the Nineteenth Century. By + Prof. E. HULL. 157 pp. demy 8vo. (_1897_) + + 6 0 + + =Hydraulic Gold Miners' Manual.= By T.S.G. KIRKPATRICK. Second + edition, 12 illus. 46 pp. crown 8vo. (_1897_) + + 4 0 + + =Economic Mining.= By C.G.W. LOCK. 175 illus. 680 pp. 8vo. + (_1895_) + + _net_ 10 6 + + =Gold Milling=: Principles and Practice. By C.G.W. LOCK. 200 + illus. 850 pp. demy 8vo. (_1901_) + + _net_ 1 1 0 + + =Mining and Ore-Dressing Machinery.= By C.G.W. LOCK. 639 + illus. 466 pp. super-royal 4to. (_1890_) + + 1 5 0 + + =Miners' Pocket Book.= By C.G.W. LOCK. Fifth edition, 233 + illus. 624 pp. fcap. 8vo, roan, gilt edges. (_1908_) + + _net_ 10 6 + + =Tests for Ores, Minerals and Metals of Commercial Value.= By + R.L. MCMECHEN. 152 pp. 12mo. (_New York, 1907_) + + _net_ 5 6 + + =Practical Handbook for the Working Miner and Prospector=, and + the Mining Investor. By J.A. MILLER. 34 illus. 234 pp. crown + 8vo. (_1897_) + + 7 6 + + =Theory and Practice of Centrifugal Ventilating Machines.= By + D. MURGUE. 7 illus. 81 pp. 8vo. (_1883_) + + 5 0 + + =Examples of Coal Mining Plant.= By J. POVEY-HARPER. Second + edition, 40 plates, 26 in. by 20 in. (_1895_) + + _net_ 4 4 0 + + =Examples of Coal Mining Plant, Second Series.= By J. + POVEY-HARPER. 10 plates, 26 in. by 20 in. (_1902_) + + _net_ 1 12 6 + + + ORGANISATION. + + ACCOUNTS, CONTRACTS AND MANAGEMENT. + + =Organisation of Gold Mining Business=, with Specimens of the + Departmental Report Books and the Account Books. By NICOL + BROWN. Second edition, 220 pp. fcap. folio. (_1903_) + + _net_ 1 5 0 + + =Manual of Engineering Specifications= and Contracts. By L.M. + HAUPT. Eighth edition, 338 pp. 8vo. (_New York, 1900_) + + _net_ 12 6 + + =Depreciation of Factories=, Municipal, and Industrial + Undertakings, and their Valuation. By E. MATHESON. Fourth + edition, 230 pp. 8vo, cloth. (_1910_) + + _net_ 10 6 + + =Aid Book to Engineering Enterprise.= By E. MATHESON. Third + edition, 916 pp. 8vo, buckram. (_1898_) + + 1 4 0 + + =Office Management.= A handbook for Architects and Civil + Engineers. By W. KAYE PARRY. New impression, 187 pp. medium + 8vo. (_1908_) + + _net_ 5 0 + + =Commercial Organisation of Engineering Factories.= By H. + SPENCER. 92 illus. 221 pp. 8vo. (_1907_) + + _net_ 10 6 + + + PHYSICS. + + COLOUR, HEAT AND EXPERIMENTAL SCIENCE. + + =The Entropy Diagram= and its Applications. By M.J. BOULVIN. 38 + illus. 82 pp. demy 8vo. (_1898_) + + 5 0 + + =Physical Problems and their Solution.= By A. BOURGOUGNON. 224 + pp. 18mo, boards. (_New York, 1897_) + + _net_ 2 0 + + =Heat for Engineers.= By C.R. DARLING. 110 illus. 430 pp. 8vo. + (_1908_) (FINSBURY TECHNICAL MANUAL) + + _net_ 12 6 + + =The Colourist.= A method of determining colour harmony. By + J.A.H. HATT. 2 coloured plates, 80 pp. 8vo. (_New York, 1908_) + + _net_ 6 6 + + =Engineering Thermodynamics.= By C.F. HIRSCHFELD. 22 illus. 157 + pp. 18mo, boards. (_New York, 1907_) + + _net_ 2 0 + + =Experimental Science=: Elementary, Practical and Experimental + Physics. By G.M. HOPKINS. Twenty-third edition, 920 illus. 1100 + pp. large 8vo. (_New York, 1902_) + + _net_ 1 1 0 + + =Reform in Chemical and Physical Calculations.= By C.J.T. + HANSSEN. Demy 4to. (_1897_) + + _net_ 6 6 + + =Introduction to the Study of Colour Phenomena.= By J.W. + LOVIBOND. 10 hand coloured plates, 48 pp. 8vo. (_1905_) + + _net_ 5 0 + + =Practical Laws and Data on the Condensation of Steam in Bare + Pipes=; to which is added a Translation of PECLET'S Theory and + Experiments on the Transmission of Heat through Insulating + Materials. By C.P. PAULDING. 184 illus. 102 pp. demy 8vo. (_New + York, 1904_) + + _net_ 8 6 + + =The Energy Chart.= Practical application to reciprocating + steam-engines. By Captain H.R. SANKEY. 157 illus. 170 pp. 8vo. + (_1907_) + + _net_ 7 6 + + + PRICE BOOKS. + + =Approximate Estimates.= By T.E. COLEMAN. Third edition, 481 + pp. oblong 32mo, leather. (_1907_) + + _net_ 5 0 + + =Railway Stores Price Book.= By W.O. KEMPTHORNE. 500 pp. demy + 8vo. (_1909_) + + _net_ 10 6 + + =Spons' Engineers' Price Book.= A Synopsis of Current Prices + and Rates for Engineering Materials and Products. Edited by + T.G. MARLOW. 650 pp. folio. (_1904_) + + _net_ 7 6 + + =Spons' Architects' and Builders' Pocket Price Book=, + Memoranda, Tables and Prices. Edited by CLYDE YOUNG. Revised by + STANFORD M. BROOKS. Illustrated, 552 pp. 16mo, leather cloth + (size 6½ in. by 3¾ in. by ½ in. thick). Issued annually + + _net_ 3 0 + + + RAILWAY ENGINEERING. + + =Practical Hints to Young Engineers Employed on Indian + Railways.= By A.W.C. ADDIS. With 14 illus. 154 pp. 12mo. + (_1910_) + + _net_ 3 6 + + =Railroad Curves and Earthwork.= By C.F. ALLEN. Third edition, + 4 plates, 198 pp. 12mo, leather, gilt edges. (_New York, 1903_) + + _net_ 8 6 + + =Field and Office Tables=, specially applicable to Railroads. + By C.F. ALLEN. 293 pp. 16mo, leather. (_New York, 1903_) + + _net_ 8 6 + + _The two above combined in one vol. limp leather_ + + _net_ 12 6 + + =Up-to-date Air Brake Catechism.= By R.H. BLACKALL. + Twenty-third edit. 5 coloured plates, 96 illus. 305 pp. crown + 8vo. (_New York, 1908_) + + _net_ 8 6 + + =Simple and Automatic Vacuum Brakes.= By C. BRIGGS, G.N.R. 11 + plates, 8vo. (_1892_) + + 4 0 + + =Notes on Permanent-way Material=, Plate-laying, and Points and + Crossings. By W.H. COLE. Fifth edition, 32 plates, 176 pp. + crown 8vo. (_1905_) + + _net_ 7 6 + + =Statistical Tables of the Working of Railways= in various + countries up to the year 1904. By J.D. DIACOMIDIS. Second + edition, 84 pp. small folio, sewed. (_1906_) + + _net_ 16 0 + + =Locomotive Breakdowns=, Emergencies and their Remedies. By + GEO. L. FOWLER, M.E. and W.W. WOOD. Fifth edition, 92 illus. + 266 pp. 12mo. (_New York, 1908_) + + _net_ 4 6 + + =Permanent-Way Diagrams.= By F.H. FRERE. Mounted on linen in + cloth covers. (_1908_) + + _net_ 3 0 + + =Formulæ for Railway Crossings and Switches.= By J. GLOVER. 9 + illus. 28 pp. royal 32mo. (_1896_) + + 2 6 + + =Data relating to Railway Curves and Super elevations=, shown + graphically. By J.H. HAISTE. On folding card for pocket use + + _net_ 0 6 + + =Setting out of Tube Railways.= By G.M. HALDEN. 9 plates, 46 + illus. 68 pp. crown 4to. (_1907_) + + _net_ 10 6 + + =Railway Engineering, Mechanical and Electrical.= By J.W.C. + HALDANE, 141 illus. 563 pp. 8vo. (_1897_) + + 15 0 + + =Tables for setting-out Railway Curves.= By C.P. HOGG. A series + of cards in neat cloth case + + 4 6 + + =The Construction of the Modern Locomotive.= By G. HUGHES. 300 + illus. 261 pp. 8vo. (_1894_) + + 9 0 + + =Practical Hints for Light Railways= at Home and Abroad. By + F.R. JOHNSON. 6 plates, 31 pp. crown 8vo. (_1896_) + + 2 6 + + =Handbook on Railway Stores Management.= By W.O. KEMPTHORNE. + 268 pp. demy 8vo. (_1907_) + + _net_ 10 6 + + =Railway Stores Price Book.= By W.O. KEMPTHORNE. 487 pp. demy + 8vo. (_1909_) + + _net_ 10 6 + + =Tables for setting out Curves= for Railways, Roads, Canals, + etc. By A. KENNEDY and R.W. HACKWOOD. 32mo + + _net_ 2 0 + + =Railroad Location Surveys and Estimates.= By F. LAVIS. 68 + illus. 270 pp. 8vo. (_New York, 1906_) + + _net_ 12 6 + + =Tables for Computing the Contents of Earthwork= in the + Cuttings and Embankments of Railways. By W. MACGREGOR. Royal + 8vo + + 6 0 + + =Bridge and Tunnel Centres.= By J.B. MCMASTERS. Illustrated, + 106 pp. 18mo, boards. (_New York, 1893_) + + _net_ 2 0 + + =Pioneering.= By F. SHELFORD. Illustrated, 88 pp. crown 8vo. + (_1909_) + + _net_ 3 0 + + =Handbook on Railway Surveying= for Students and Junior + Engineers. By B. STEWART. 55 illus. 98 pp. crown 8vo. (_1909_) + + _net_ 2 6 + + =Spiral Tables.= By J.G. SULLIVAN. 47 pp. 12mo, leather. (_New + York, 1908_) + + _net_ 6 6 + + =Modern British Locomotives.= By A.T. TAYLOR. 100 diagrams of + principal dimensions, 118 pp. oblong 8vo. (_1907_) + + _net_ 4 6 + + =Locomotive Slide Valve Setting.= By C.E. TULLY. Illustrated, + 18mo + + _net_ 1 0 + + =The Walschaert Locomotive Valve Gear.= By W.W. WOOD. 4 plates + and set of movable cardboard working models of the valves, 193 + pp. crown 8vo. (_New York, 1907_) + + _net_ 6 6 + + =The Westinghouse E.T. Air-Brake Instruction Pocket Book.= By + W.W. WOOD. 48 illus. including many coloured plates, 242 pp. + crown 8vo. (_New York, 1909_) + + _net_ 8 6 + + + SANITATION, PUBLIC HEALTH AND MUNICIPAL ENGINEERING. + + =Sewers and Drains for Populous Districts.= By J.W. ADAMS. + Ninth edition, 81 illus. 236 pp. 8vo. (_New York, 1902_) + + _net_ 10 6 + + =Public Abattoirs=, their Planning, Design and Equipment. By + R.S. AYLING. 33 plates, 100 pp. demy 4to. (_1908_) + + _net_ 8 6 + + =Sewage Purification.= By E. BAILEY-DENTON. 8 plates, 44 pp. + 8vo. (_1896_) + + 5 0 + + =Water Supply and Sewerage of Country Mansions= and Estates. By + E. BAILEY-DENTON. 76 pp. crown 8vo. (_1901_) + + _net_ 2 6 + + =Sewerage and Sewage Purification.= By M.N. BAKER. Second + edition, 144 pp. 18mo, boards. (_New York, 1905_) + + _net_ 2 0 + + =Sewage Irrigation by Farmers.= By R.W.P. BIRCH. 8vo, sewed. + (_1878_) + + 2 6 + + =Sanitary House Drainage=, its Principles and Practice. By T.E. + COLEMAN. 98 illus. 206 pp. crown 8vo. (_1896_) + + 6 0 + + =Stable Sanitation and Construction.= By T.E. COLEMAN. 183 + illus. 226 pp. crown 8vo. (_1897_) + + 6 0 + + =Public Institutions=, their Engineering, Sanitary and other + Appliances. By F. COLYER. 231 pp. 8vo. (_1889_) + + _net_ 2 0 + + =Discharge of Pipes and Culverts.= By P.M. CROSTHWAITE. Large + folding sheet in case. + + _net_ 2 6 + + =A Complete and Practical Treatise on Plumbing and Sanitation: + Hot Water Supply, Warming and Ventilation=, Steam Cooking, Gas, + Electric Light, Bells, etc., with a complete Schedule of Prices + of Plumber's Work. By G.B. DAVIS and F. DYE. 2 vols. 637 illus. + and 21 folding plates, 830 pp. 4to, cloth. (_1899_) + + _net_ 1 10 0 + + =Standard Practical Plumbing.= By P.J. DAVIES. + + Vol. I. Fourth edition, 768 illus. 355 pp. royal 8vo. (_1905_) + + _net_ 7 6 + + Vol. II. Second edition, 953 illus. 805 pp. (_1905_) + + _net_ 10 6 + + Vol. III. 313 illus. 204 pp. (_1905_) + + _net_ 5 0 + + =Conservancy, or Dry Sanitation versus Water Carriage.= By J. + DONKIN. 7 plates, 33 pp. 8vo, sewed. (_1906_) + + _net_ 1 0 + + =Sewage Disposal Works=, their Design and Construction. By W.C. + EASDALE. With 160 illus. 264 pp. demy 8vo. (_1910_) + + _net_ 10 6 + + =House Drainage and Sanitary Plumbing.= By W.P. GERHARD. Tenth + edition, 6 illus. 231 pp. 18mo, boards. (_New York, 1902_) + + _net_ 2 0 + + =Engineering Work in Towns and Cities.= By E. MCCULLOCH. 44 + illus. 502 pp. crown 8vo. (_New York, 1908_) + + _net_ 12 6 + + =The Treatment of Septic Sewage.= By G.W. RAFTER. 137 pp. 18mo, + boards. (_New York, 1904_) + + _net_ 2 0 + + =Reports and Investigations on Sewer Air= and Sewer + Ventilation. By R.H. REEVES. 8vo, sewed. (_1894_) + + 1 0 + + =The Law and Practice of Paving= Private Street Works. By W. + SPINKS. Fourth edition, 256 pp. 8vo. (_1904_) + + _net_ 12 6 + + + STRUCTURAL DESIGN. + + (_See_ BRIDGES AND ROOFS.) + + + TELEGRAPH CODES. + + =New Business Code.= 320 pp. narrow 8vo. (Size 4¾ in. by + 7¾ in. and ½ in. thick, and weight 10 oz.) (_New York, + 1909_) + + _net_ 1 10 0 + + =Miners' and Smelters' Code= (formerly issued as the =Master + Telegraph Code=). 448 pp. 8vo, limp leather, weight 14 oz. + (_New York, 1899_) + + _net_ 2 10 0 + + =Billionaire Phrase Code=, containing over two million + sentences coded in single words. 56 pp. 8vo, leather. (_New + York, 1908_) + + _net_ 6 6 + + + WARMING AND VENTILATION. + + =Hot Water Supply.= By F. DYE. Fifth edition, 48 illus. 86 pp. + crown 8vo. (_1902_) + + _net_ 3 0 + + =A Practical Treatise upon Steam Heating.= By F. DYE. 129 + illus. 246 pp. demy 8vo. (_1901_) + + _net_ 10 0 + + =Practical Treatise on Warming Buildings by Hot Water.= By F. + DYE. 192 illus. 319 pp. 8vo. cloth. (_1905_) + + _net_ 8 6 + + =Charts for Low Pressure Steam Heating.= By J.H. KINEALY. Small + folio. (_New York_) + + 4 6 + + =Formulæ and Tables for Heating.= By J.H. KINEALY. 18 illus. 53 + pp. 8vo. (_New York, 1899_) + + 3 6 + + =Mechanics of Ventilation.= By G.W. RAFTER. Second edition, + 18mo, boards. (_New York, 1896_) + + _net_ 2 0 + + =Principles of Heating.= By W.G. SNOW. 62 illus. 161 pp. 8vo. + (_New York, 1907_) + + _net_ 8 6 + + =Furnace Heating.= By W.G. SNOW. Fourth edition, 52 illus. 216 + pp. 8vo. (_New York, 1909_) + + _net_ 6 6 + + =Ventilation of Buildings.= By W.G. SNOW and T. NOLAN. 83 pp. + 18mo, boards. (_New York, 1906_) + + _net_ 2 0 + + =Heating Engineers' Quantities.= By W.L. WHITE and G.M. WHITE. + 4 plates, 33 pp. folio. (_1910_) + + _net_ 10 6 + + + WATER SUPPLY. + + (_See also_ HYDRAULICS.) + + =Potable Water and Methods of Testing Impurities.= By M.N. + BAKER. 97 pp. 18mo, boards. (_New York, 1905_) + + _net_ 2 0 + + =Manual of Hydrology.= By N. BEARDMORE. New impression, 18 + plates, 384 pp. 8vo. (_1906_) + + _net_ 10 6 + + =Boiler Waters=, Scale, Corrosion and Fouling. By W.W. + CHRISTIE. 77 illus. 235 pp. 8vo, cloth. (_New York, 1907_) + + _net_ 12 6 + + =Water Softening and Purification.= By H. COLLET. Second + edition, 6 illus. 170 pp. crown 8vo. (_1908_) + + _net_ 5 0 + + =Treatise on Water Supply=, Drainage and Sanitary Appliances of + Residences. By F. COLYER. 100 pp. crown 8vo. (_1899_) + + _net_ 1 6 + + =Report on the Investigations into the Purification of the Ohio + River Water= at Louisville, Kentucky. By G.W. FULLER. 8 plates, + 4to, cloth. (_New York, 1898_) + + _net_ 2 2 0 + + =Purification of Public Water Supplies.= By J.W. HILL. 314 pp. + 8vo. (_New York, 1898_) + + 10 6 + + =Well Boring for Water, Brine and Oil.= By C. ISLER. _New + edition in the Press._ + + =Method of Measuring Liquids Flowing through Pipes by means of + Meters of Small Calibre.= By Prof. G. LANGE. 1 plate, 16 pp. + 8vo, sewed + + _net_ 0 6 + + =On Artificial Underground Water.= By G. RICHERT. 16 illus. 33 + pp. 8vo, sewed. (_1900_) + + _net_ 1 6 + + =Notes on Water Supply= in new Countries. By F.W. STONE. 18 + plates, 42 pp. crown 8vo. (_1888_) + + 5 0 + + =The Principles of Waterworks Engineering.= By J.H.T. TUDSBERY + and A.W. BRIGHTMORE. Third edition, 13 folding plates, 130 + illus. 447 pp. demy 8vo. (_1905_) + + _net_ 1 1 0 + + + WORKSHOP PRACTICE. + + =A Handbook for Apprenticed Machinists.= By O.J. BEALE. Second + edition, 89 illus., 141 pp. 16mo. (_New York, 1901_) + + _net_ 2 6 + + =Bicycle Repairing.= By S.D.V. BURR. Sixth edition, 200 illus. + 208 pp. 8vo. (_New York, 1903_) + + _net_ 4 6 + + =Practice of Hand Turning.= By F. CAMPIN. Third edition, 99 + illus. 307 pp. crown 8vo. (_1883_) + + 3 6 + + =Calculation of Change Wheels for Screw Cutting on Lathes.= By + D. DE VRIES. 46 illus. 83 pp. 8vo. (_1908_) + + _net_ 3 0 + + =Milling Machines and Milling Practice.= By D. DE VRIES. With + 536 illus. 464 pp. medium 8vo. (_1910_) + + _net_ 14 0 + + =French-Polishers' Manual.= By a French-Polisher. 31 pp. royal + 32mo, sewed. (_1902_) + + _net_ 0 6 + + =Art of Copper Smithing.= By J. FULLER. Third edition, 475 + illus. 325 pp. royal 8vo. (_New York, 1901_) + + _net_ 12 6 + + =Saw Filing and Management of Saws.= By R. GRIMSHAW. New + edition, 81 illus. 16mo. (_New York, 1906_) + + _net_ 3 6 + + =Paint and Colour Mixing.= By A.S. JENNINGS. Fourth edition. 14 + coloured plates, 190 pp. 8vo. (_1910_) + + _net_ 5 0 + + =The Mechanician=: a Treatise on the Construction and + Manipulation of Tools. By C. KNIGHT. Fifth edition, 96 plates, + 397 pp. 4to. (_1897_) + + 18 0 + + =Turner's and Fitter's Pocket Book.= By J. LA NICCA. 18mo, + sewed + + 0 6 + + =Tables for Engineers and Mechanics=, giving the values of the + different trains of wheels required to produce Screws of any + pitch. By LORD LINDSAY. Second edition, royal 8vo, oblong + + 2 0 + + =Screw-cutting Tables.= By W.A. MARTIN. Seventh edition, royal + 8vo, oblong + + 1 0 + + =Metal Plate Work=, its Patterns and their Geometry, for the + use of Tin, Iron and Zinc Plate Workers. By C.T. MILLIS. Fourth + edition, 280 diagrams, 470 pp. crown 8vo. (_1906_) + + 9 0 + + =Engineers' and General Smiths' Work.= The smith and forgeman's + handbook of practical smithing and forging. By T. MOORE. 401 + illus. 248 pp. crown 8vo. (_1906_) + + _net_ 5 0 + + =Modern Machine Shop Construction=, equipment and management. + By O.E. PERRIGO. 208 illus. 343 pp. crown 4to. (_New York, + 1906_) + + _net_ 21 0 + + =Turner's Handbook on Screw-cutting=, Coning, etc. By W. PRICE. + Fcap. 8vo + + 1 0 + + =Introduction to Eccentric Spiral Turning.= By H.C. ROBINSON. + 12 plates, 23 illus. 48 pp. 8vo. (_1906_) + + _net_ 4 6 + + =Manual of Instruction in Hard Soldering.= By H. ROWELL. Sixth + edition, 7 illus. 66 pp. crown 8vo. (_New York, 1910_) + + _net_ 3 0 + + =Pocket Book on Boilermaking, Shipbuilding=, and the Steel and + Iron Trades in General. By M.J. SEXTON. Sixth edition, 85 + illus. 319 pp. royal 32mo, roan, gilt edges. (_1909_) + + _net_ 5 0 + + =Power and its Transmission.= A Practical Handbook for the + Factory and Works Manager. By T.A. SMITH. 76 pp. fcap. 8vo. + (_1910_) + + _net_ 2 0 + + =Spons' Mechanics' Own Book=: A Manual for Handicraftsmen and + Amateurs. Sixth edition, 1430 illus. 720 pp. demy 8vo. (_1903_) + + 6 0 + + Ditto ditto half morocco + + 7 6 + + =Spons' Workshop Receipts for Manufacturers, Mechanics and + Scientific Amateurs.= New and thoroughly revised edition, crown + 8vo. (_1909_) + + _each net_ 3 0 + + Vol. I. ACETYLENE LIGHTING _to_ DRYING. 223 illus. 532 pp. + + Vol. II. DYEING _to_ JAPANNING. 259 illus. 540 pp. + + Vol. III. JOINTING PIPES _to_ PUMPS. 256 illus. 528 pp. + + Vol. IV. RAINWATER SEPARATORS _to_ WINES. 250 illus. 520 pp. + + =Gauges at a Glance.= By T. TAYLOR. Second edition, post 8vo, oblong, + with tape converter. (_1900_) + + _net_ 5 0 + + =Simple Soldering=, both Hard and Soft. By E. THATCHER. 52 + illus. 76 pp. crown 8vo, limp. (S. & C. SERIES, NO. 18.) (_New + York, 1910_) + + _net_ 1 6 + + =The Modern Machinist.= By J.T. USHER. Fifth edition. 257 + illus. 322 pp. 8vo. (_New York, 1904_) + + _net_ 10 6 + + =Practical Wood Carving.= By C.J. WOODSEND. 108 illus. 86 pp. + 8vo. (_New York, 1897_) + + _net_ 4 6 + + =American Tool Making= and Interchangeable Manufacturing. By + J.W. WOODWORTH. 600 illus. 544 pp. demy 8vo. (_New York, 1905_) + + _net_ 17 0 + + + USEFUL TABLES. + + =Weights and Measurements of Sheet Lead.= By J. ALEXANDER. + 32mo, roan + + _net_ 1 6 + + =Tables of Parabolic Curves= for the use of Railway Engineers + and others. By G.T. ALLEN. Fcap. 16mo + + 4 0 + + =Barlow's Tables of Squares=, Cubes, Square Roots, Cube Roots + and Reciprocals. Crown 8vo + + 6 0 + + =Tables of Squares.= By E.E. BUCHANAN. Ninth edition, 12mo + + _net_ 4 6 + + =Land Area Tables.= By W. CODD. Square 16mo, on a sheet mounted + on linen and bound in cloth + + 3 6 + + =Tables for Setting out Curves= from 101 to 5000 feet radius. + By H.A. CUTLER and F.J. EDGE. Royal 32mo + + _net_ 2 6 + + =Transition Curves.= By W.G. FOX. 18mo, boards. (_New York_) + + _net_ 2 0 + + =Tables of some of the Principal Speeds= occurring in + Mechanical Engineering, expressed in Metres per second. By P. + KEERAYEFF. 18mo, sewed + + 0 6 + + =Calculating Scale.= A Substitute for the Slide Rule. By W. + KNOWLES. Crown 8vo, leather + + _net_ 1 0 + + =Planimeter Areas.= Multipliers for various scales. By H.B. + MOLESWORTH. Folding sheet in cloth case. + + _net_ 1 0 + + =Tables of Seamless Copper Tubes.= By I. O'TOOLE. 69 pp. oblong + fcap. 8vo. (_1908_) + + _net_ 3 6 + + =Rownson's Iron Merchants' Tables= and Memoranda, Weights and + Measures. 86 pp. 32mo, leather + + 3 6 + + =Spons' Tables and Memoranda for Engineers.= By J.T. HURST, + C.E. Twelfth edition, 278 pp. 64mo, roan, gilt edges. (_1907_) + + _net_ 1 0 + + Ditto ditto in celluloid case + + _net_ 1 6 + + =Optical Tables and Data=, for the use of Opticians. By Prof. + S.P. THOMPSON. Second edition, 130 pp. oblong 8vo. (_1907_) + + _net_ 6 0 + + =Traverse Table=, showing Latitudes and Departure for each + Quarter degree of the Quadrant, and for distances from 1 to + 100, etc.; 18mo, boards. + + _net_ 2 0 + + =Fifty-four Hours' Wages Calculator.= By H.N. WHITELAW. Second + edition, 8vo. + + _net_ 2 6 + + =Wheel Gearing.= Tables of Pitch Line Diameters, etc. By A. + WILDGOOSE and A.J. ORR. 175 pp. fcap. 32mo. (_1903_) + + _net_ 2 0 + + +MISCELLANEOUS. + + =Time Chart.= The time of day at any place in the World at a + glance. By Dr. F.J.B. CORDEIRO. On card. + + _net_ 1 0 + + =The Atmosphere=: Its Characteristics and Dynamics. By F.J.B. + CORDEIRO. With 35 illus. 129 pp. medium 8vo. (_New York, 1910_) + + _net_ 10 6 + + =Model Steam Engine Design.= By R.M. DE VIGNIER. 34 illus. 94 + pp. crown 8vo, limp. (_New York, 1907_) + + _net_ 1 6 + + =Popular Engineering.= By F. DYE. 704 illus. 477 pp. crown 4to. + (_1895_) + + _net_ 5 0 + + =The Phonograph=, and how to construct it. By W. GILLETT. 6 + folding plates, 87 pp. crown 8vo. (_1892_) + + 5 0 + + =Particulars of Dry Docks=, Wet Docks, Wharves, etc. on the + River Thames. By C.N. JORDAN. Second edition, 7 coloured + charts, 103 pp. oblong 8vo. (_1904_) + + _net_ 2 6 + + =Spons' Engineer's Diary and Year Book=, issued annually. 4to. + + 3 6 + + =New Theories in Astronomy.= By W. STIRLING. 335 pp. demy 8vo. + (_1906_) + + _net_ 8 6 + + =The American Hardware Store.= A Manual of approved methods of + arranging and displaying hardware. By R.R. WILLIAMS. 500 illus. + 448 pp. royal 8vo. (_New York, 1896_) + + _net_ 7 6 + + =Practical Wood Carving.= By C.J. WOODSEND. 108 illus. 86 pp. + 8vo. 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SPON, Ltd., 57 Haymarket, London, S.W. + + +LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED. + + + + + JUST OUT THE LATEST + +The + +Aeroplane Portfolio + +By D. ROSS KENNEDY + + +Containing nine sheets of scale drawings of the following celebrated +Aeroplanes. + + Biplane type;--Wright, Farman, Voisin, Cody, Herring-Curtis. + + Monoplanes;--Rep, Antoinette, Santos Dumont, and Blériot. + +Each of these machines are here shown in End View, Plan and Elevation. + +Including booklet which contains a description of each machine. + +This timely set of drawings should prove of value to everyone +interested in this important new industry. + +The complete set mailed to any part of the world postpaid on receipt +of + + _net_ 55c. + + SPON & CHAMBERLAIN + PUBLISHERS OF TECHNICAL BOOKS + 123-5 Liberty Street,--New York + + + + +[Illustration] + +The Percy Pierce Flyer + +A FAMOUS PRIZE WINNER + + A + Large Scale Drawing + of this famous model, + with all measurements and details + +showing a front elevation, a side elevation and a top plan, with full +descriptive matter. Anybody can make an =EXACT DUPLICATE= of this +Prize Winner for himself at small cost. + +DO IT NOW + +Complete set of materials in the rough with drawing and instructions, +Postpaid, $1.15 + +The drawing and instructions 15c postpaid + + + + + Make Your Own + GLIDER + +How to make a 20 ft. Biplane Gliding Machine + +That will carry an ordinary man + + +PracticaI handbook on the construction of a Biplane Gliding Machine +enabling an intelligent reader to make his first step in the field of +aviation with a comprehensive understanding of some of the principals +involved. By Alfred Powell Morgan. Contents of Chapters: 1. The +Framework, Assembling and finishing the wood. 2. Covering the planes, +Laying out the fabric and fastening it. 3. Trussing, Fastening the tie +rods and trueing the glider. 4. Gliding flight. The principals +involved. Instructions and precautions. 5. Remarks. Fully illustrated +with detail drawings. By Mail. In paper, postpaid, 25c. + +In handsome cloth binding, postpaid, 55c. + + =Flying Machines, Past, Present and Future.= A popular account + of flying machines, dirigible balloons and aeroplanes. + Describing many different kinds of machines, and their chief + feature. By A.W. Marshall and Henry Greenly. 138 pages 23 + illustrations and many plates, 12 mo. boards. By mail 55c. + + =Model Flying Machines.= Their design and construction by W.G. + Aston. A first rate little book showing numerous methods of + propelling models, making propellors, construction of different + kinds of models, etc., etc. 130 pages, 94 illustrations. 12 mo. + boards, by mail 55c. + +=Model Aeroplanes.= How to Build and Fly Them, by E.W. Twining. A set +of 5 full-size scale drawings for three different models with +descriptive illustrated book explaining how to make and fly them. + + Postpaid : : : : 55c + +=No. 2 Model.= Complete set of parts in the rough to make up this +model. (Without drawings), + + Postpaid : : 65c + +[Illustration: No. 3 Model] + +=No. 3 Model.= Complete set of parts in the rough (without drawings). +This makes up into a beautiful little model. + + Postpaid : : : : $1.15 + + +=Model Gliders, Birds, Butterflies and Aeroplanes.= + +How to make and fly them, by E.W. Twining. Consisting of one large +sheet of 12 butterflies and two birds printed in bright colors. One +small cardboard Model Glider with descriptive illustrated book showing +how to make and fly them. + + Postpaid : : : : 55c + + + + + * * * * * + + + Transcriber's Notes + + Obvious punctuation and spelling errors and inconsistent hyphenation + have been corrected. + + Italic text is denoted by _underscores_ and bold text by =equal signs=. + + The OE ligature has been replaced by the separate characters. + + The fractions ¼, ½ and ¾ are represented using the Latin-1 characters, + but other fractions use the / and - symbols, e.g. 3/8 or 2-5/8. + + The exponents 2 and 3 are represented using ² and ³ respectively, but + other exponents are indicated by the caret character, for example, + v^{1·85} + + Subscripts are simply enclosed in braces, e.g. W{0}. + + Other symbols that cannot be represented have been replaced by words + in braces: {alpha}, {pi}, {therefore}, {square root} and + {proportional to}. + + The skin friction formulæ given on pages 11 and 128 have been corrected + by comparison with other sources. Respectively, the formulæ were + originally printed as + _f_ = 0·00000778_l_^{9·3}_v_^{1·85} + and + _f_ = 0·00000778_l_ - ^{00·7}_v_^{1·85} + + In ambiguous cases, the text has been left as it appears in the + original book. + + + + + +End of the Project Gutenberg EBook of The Theory and Practice of Model +Aeroplaning, by V. E. Johnson + +*** END OF THE PROJECT GUTENBERG EBOOK 41135 *** |