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"

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

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."

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.

Aspect Ratio is ^span/_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.

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.

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.

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.

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.

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.

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 l½ 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 = 0·00000778l ^·93v^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.)

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.

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.

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.

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.

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.

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.

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]

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.

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.

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.

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.

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.

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.

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.)

Fig. 16.—Torque Graphs of Rubber Motors.

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:—

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.

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.