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.

§ 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.

§ 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.

§ 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.

§ 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.

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.

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]

§ 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.

§ 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.

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.

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.