The Science of Aeronautics

THE SCIENCE OF AERONAUTICS The year 1909 opened a new era in the history of aeronautics. Towards the end of 1908, the `Frights had made their _flights. The value of the aeroplane as a weapon became obvious ; how valuable, it was left for the World War to show. Little was known of the forces affecting aircraft in motion; of the laws regulating the flow of air in their neighbourhood; the conditions required for balance and safety; the relation between the form and dimensions of the supporting planes and the weight carried; or the mechanism necessary for the control of the machine in flight.

The internal combustion engine had made flight possible, but the way to combine efficiency and lightness was but vaguely understood. The propeller brought problems of its own; naval architects had made a study of the action of the screw in a ship; to what extent did the conclusions they had reached apply to an airscrew? It was clear that there was much to learn and many directions in which research and experiment, conducted under proper supervision, could help.

Experiments in aerodynamics had been made by Langley in 1891. Zahm at a later date (19o2–o3) had measured the air velocity, pressure and friction on surfaces of various forms. Stanton, at the national physical laboratory, had experimented on the resistance of surfaces in a current of air and the pressure of the wind on plates. Lanchester, in his Aerodynamics, had de scribed similar measurements. Lord Rayleigh, in various papers of great importance dating from 1876, had discussed questions of the resistance of fluids and, in 1899, contributed to the Man chester Memoirs a paper on the mechanical principles of flight ; but no organized attack on the questions raised by the flight of a body heavier than air had been made.

Abroad, the airship had attracted more interest. In 1906 the society for the study of airships was formed in Germany, divided into branches dealing respectively with meteorology, dynamics, construction and engineering. Their first report, March 1907, describes in full detail programmes of the work proposed in these various branches ; specially interesting is the account it gives of the method of testing resistance to the motion of an airship by means of a model in a wind tunnel and other proposals by Prof. Prandtl for testing model airships by means of towing by automobile.

Advisory Committees for Aeronautics.

Early in 1909, R. B. (later Lord) Haldane suggested that a section devoted to research in aeronautics might be established at the national physical laboratory. In May of that year the prime minister, H. H. Asquith, announced that this had been done and that, for the superintendence of the investigations and to advise on scien tific problems arising in connection with the work, he had appointed a special committee—the advisory committee for aeronautics.

Meanwhile, work of a similar character was in progress else where : at Gottingen, under Prandtl ; at Koutchino in Russia, where Riabouchinsky was director ; at a somewhat later date in America under the national advisory committee for aeronautics; and in Italy by Crocco; while papers on stability had been pub lished by B. F. Lanchester and Soreau.

Aerodynamics.

In studying the forces to which aircraft are subject in flight, mathematics alone are of but little help; the dynamics of the air are too complex for a complete theory, and recourse must be had to experiment.

In the case of a body heavier than air an upward force, or lift, must be provided which, when the motion is horizontal, will just balance the weight. As the aircraft moves forward various actions produce a resistance to its motion, and unless a force is provided to balance that resistance, the drag on the machine, it will come to rest ; the mechanism must provide a propelling force which for uniform speed must just balance the drag.

Now we have seen already that when a flat surface inclined at a small angle to the direction of motion is moved forward through the air it experiences a resistance—drag—opposing the motion and a force—the lift—at right angles to that motion.

To carry a given weight how large must this surface be, at what speed must it move and at what angle to the direction of motion should it be placed? What will be the resistance to its motion and what horse power must be supplied? What is the best form of surface for the purpose both in section and in plan? How must matters be arranged so as to secure controllability and reasonable safety to the flyer? Such were some of the questions to be answered.

Since 1909, many, perhaps all, of these and similar questions have been answered in part by observation and experiment on full scale machines, in part by the use of suitable models in a wind tunnel.

The Wind Tunnel.

W. Froude had shown that by towing the model of a ship in a tank and measuring the force required to tow it, the resistance to the motion of the ship at sea and the horse power required to propel it could be calculated.

In tank experiments the model is towed through water, but the problem is one of relative motion. If it were possible to obtain a steady stream of water free from eddies and turbulence, the model might be stationary and the water stream past it. This was the method adopted by those investigating the pressure of moving air on surfaces exposed to its action. Arrangements were devised to produce a steady flow of air through a closed channel and measure its speed. The model was placed in this stream and attached to a balance specially designed to measure the forces acting on it.

Imagine the air stream in the tunnel to be horizontal, and take as an example a narrow rectangular plate placed with its longer edge horizontal and at right angles to the direction of the wind and its plane inclined at a definite angle to the same. This angle is known as the angle of attack. The balance is such that the hori zontal force or drag, the vertical force or lift at right angles to the wind direction, and the couple tending to turn the model about an axis parallel to its length can all be measured. The last observation enables the position of the centre of pressure, or point in which the resultant of the wind forces intersects the model, to be determined.

In fig. 3, ACB represents a section of the model by a vertical plane through the wind direction. C is the centre of pressure through which acts the resultant force; the balance measures its components, the lift, the drag, and also the couple tending to rotate the model about an axis perpendicular to the paper through some point depending on the attachment to the balance.

Details of the various forms of wind tunnel in use and of the balances and their method of attachment to the model will be found in the article on AERODYNAMICS, to which reference should be made.

It is found that, so long as the angle of attack remains the same, the lift, the drag and the r Duple are approximately pro portional to the product of the density of the air, the square of the speed and the area of the surface on which it acts; so we may write where M represents the couple ; the coefficients Kr), are constant so long as a the angle of attack is not varied ; p is the air density, S the area of the plane and V the air speed.

The three coefficients depend on the angle of attack; by making observations at various inclinations of the surface to the wind we can draw a curve for each of the quantities L, D, M and thus read off their values at any angle of attack.

Scale Effect.

But this is for the model. How can we step from it to the actual machine? Froude had shown that for a ship there was a definite relation depending on the size and speed of model and ship. Lord Rayleigh investigated the condition, which must hold in order that the motion of the air round the model should be .similar to that near the machine. He found that, assuming the medium in which the motion takes place to be identically the same in both cases, the condition was expressed by the statement that v/ should be the same for model and machine, v being the speed and 1 some length determining the scale in each case. Now, clearly this condition cannot be satis fied; for both the speed and size of the model are necessarily less than those of the machine itself. Experiment, however, has shown that in many cases it is not necessary to fufil the strict condition; we may apply the equations already given to the machine using the value of the coefficients, .etc., found from the model experiments. With the need for higher accuracy the in vestigation of scale effect has become of great importance, and reference should be made to the article AERODYNAMICS.

Lift and Drag.

The curves for lift and drag depend on the form of the aerofoil under test. For a given incidence the value of KL , the lift coefficient, will be much less for a plane surface than for a wing of good form. Fig. 4 gives the curves for a wing, while in fig. 5 are shown some wing sections. In addition to the lift and drag curves, the ratio of lift to the drag is also plotted and it will be noted that this has a minimum value for a low angle of incidence and increases somewhat rapidly with the incidence. The lift, it is true, increases up to a certain value as the angle of attack is increased; but the drag increases more rap idly. Thus, while a much greater lift is obtained by increasing the angle of the planes to the hor izontal the thrust given by the airscrew necessary to do this in creases in a much more rapid ratio.

Stalling.

The curves for different shaped wings are different and, while we may note that increasing the camber of the upper surface within limits increases the lift, reference for the detailed effect of the shape of the section on the properties of the wing must be made to the article AERODYNAMICS. All curves of the lift have one property in common. As the angle of attack increases still further the lift suddenly falls ; the aeroplane can no longer fly; its power to carry its load has gone and it must fall; it is said to be stalled. If the engine power be sufficient to maintain the speed, then by increasing the angle of attack at which the machine is flown the weight carried can be increased, or alter natively, if the load remain the same while the angle is in creased, the speed can be reduced until at last a limit is reached, the stalling angle is exceeded and the machine, becoming uncon trollable, nose dives and spins to the ground.

A very large proportion of the accidents which occur arise from this; it may be an engine failure or a lapse on the part of the pilot causing him to attempt a turn when going at too slow a speed ; the machine is stalled at too low an altitude and falls; bef ore control can be regained it strikes the ground and is wrecked.

Wind Tunnel Results.

For a full discussion of the equa tions giving the lift and drag and the consequences to be deduced from them reference must be made to AERODYNAMICS. A few of the more obvious consequences may be mentioned here.

Besides its wings, an aeroplane has a tail and elevator, a body fitted with a fin and rudder, an engine and airscrew, with tanks for petrol and oil; all of these contribute to the drag and some to a small extent to the lift, but neglecting these, let us see what conclusions we can draw directly from the equations.

When an aeroplane is flying horizontally at uniform speed the total lift will just balance the weight W. The lift is mostly carried by the wings ; so neglecting for the present the effect of the tail and body we have the result that the weight carried is fottnd by multiplying together the lift coefficient, the density of the air, the area of the wing and the square of the speed.

The loading, the average weight carried by each unit of area of the wings, will be given by dividing this quantity by the area of the wings.

Again, the conditions which must be satisfied if the machine is to climb well can he worked out, and we see how experiments in the wind tunnel can be utilized to predict the performance of the machine.

Conditions for Stalling.

Before passing on to consider other problems, it will be useful to look a little further into the question of stalling. Observations in the wind tunnel made by the aid of smoke or in a water channel show that for a wing of good shape, flying at a small or moderate angle of incidence, the motion of the air is approximately stream line; it flows smoothly past the wing, there is very little eddying or turbulence. As the incidence is increased the eddies formed behind the wing increase also and for a time the lift and drag increase until a condition of affairs is reached in which there is little or no semblance of stream line motion; the wake behind the wing is a mass of turbulent eddies; the drag is very large while the lift falls and is quite un certain as to its value.

The changes outlined are illustrated by the figures 6 and 7. The figures show too why the drag increases as the incidence becomes larger. It is known that in a frictionless fluid, and air is nearly frictionless, there would be no resistance to the motion of a smooth stream-lined body, a body that is, round which the air would flow in stream lines without eddies; that in any actual case there is some small resistance is due to the slight friction between the body and the air ; but when the motion becomes turbulent, energy is necessary to support the turbulence and some of the power required to propel the body is used in supplying this energy; the drag on the body is increased and more power is needed to maintain the speed.

turning to this section of our subject it is necessary to consider what is meant by stability.

A pendulum, such as a ball hung by a string, or a rod balanced vertically on a finger, when at rest, are both in equilibrium.

So long as they are undisturbed the rod and the string both remain vertical, but the effect of a slight disturbance differs in the two cases; if the pendulum be disturbed it oscillates about its equilibrium position for a short time, finally coming to rest as before ; the rod when disturbed falls to the ground unless by skilful movements of the finger it is possible to restore the bal ance. The pendulum exemplifies a case of stable equilibrium, the rod of unstable ; similar considerations apply to a body in a state of steady motion, an aeroplane (say) moving horizontally with constant speed. Imagine that by some means—a sudden downward gust for example—the motion is slightly disturbed and the nose takes a downward direction. Suppose too that the pilot does nothing to counteract this, then two things may happen, the nose may rise again—of its own accord as it were—and after a few oscillations up and down the machine may recover its hori zontal path. Like the pendulum it is stable, it can be flown with out touching the controls, unless of course the initial disturbance is too violent. When the engine has once been adjusted to give the power necessary to maintain horizontal flight at the specified speed the machine will continue to fly thus of itself. On the other hand, the initial disturbance may increase, the nose may continue to drop, the machine like the rod on the finger is unstable and action is required on the pilot's part in order to recover the steady horizontal flight. It is not possible here to discuss the conditions necessary for stabil ity; it must suffice to state that they require the knowledge of a number of quantities known as stability derivatives which can be determined by suitable experi ments in an air tunnel.

As to the relative advantages of stability and instability much might be written ; stability brings with it consequences which for some purposes are disadvantageous. The machine has, as it were, a will of its own, once set to a certain course it tries to keep to it ; it is less easy to manoeuvre, to be deflected by the pilot from its course and forced into the sudden changes of motion and aspect needed, say, for military purposes.

For a fighting machine too great stability is a disadvantage ; on the other hand, for a civil machine designed to go from one aerodrome to another at a given speed, stability is a marked advantage ; it adds to the safety of the aircraft and it diminishes greatly the strain on the pilot.

Modern Theories.

So far, we have been discussing the ele ments of aerodynamics and the manner in which wind tunnel experiments may be used to determine the characteristics of a machine.

Reference must be made to the article on AERODYNAMICS for a description of the various forms of wind tunnel now in use, and an account of how, following up some very early work by Lanchester the lift and drag of an aeroplane wing have been de rived in the first instance by Prandtl and his school at Giittingen, from the fundamental equations giving the circulation set up in the air around the wing and the vortices shed from its tips and trailing edge. Much work on the same lines has been done under research committees working in England and America. Fig. 8 (p. 247) shows the most modern wind tunnel adopted in Great Britain.