manner the forces and moments acting on the model under varying conditions may be determined. All the countries in the world have such windtunnels, and many manufacturers of aircraft have their own. Thus a designer of a new shape of airplane wing will have a model made as exactly as possible, and will then in the wind-tunnel test its lift and drag under different angles of attack, determine the motion of its center of pressure, etc. All of these data are extremely useful. Again many experiments may be performed in wind-tunnels upon such problems as:

(a) The effect of the presence of the fuselage of an airplane upon the action of the propeller;

(b) The effect of giving different shapes to the trailing edge of a wing upon the distribution of force over wing;

(c) The relative aerodynamic advantages of biplane or monoplane construction for certain types of airplanes.

μ

No one can overestimate the usefulness of all the information which has been obtained from observation upon models; but the method suffers from one fundamental weakness. It is not possible to deduce exact conclusions as to the aerodynamic properties of a full-scale aircraft from the knowledge of those properties for models of the aircraft. There are forces of two distinct types acting upon an aircraft when it moves through the air; one of these depends upon the inertia of the air, that is, upon the density of the air and its velocity relative to the aircraft; the other upon the viscosity of the air. When a model of an aircraft is placed in an air-stream, no change is made in the nature of the air, but since the dimensions of the model differ from those of the full-size aircraft, the relative importance of the two types of forces is changed. It has been known for many years, from certain quite elementary considerations, that the aerodynamic properties of aircraft and model agree only for one special condition. If V is the relative velocity between the air and the solid body, p is the density of the air, u is its coefficient of viscosity and L is a linear dimension of the solid body (e.g., the diameter of a cylinder or strut, the length of the chord or span of an airplane wing, the length of an airship, etc.), then the aerodynamic properties are the PVL same if the fraction is the same for the aircraft in flight and the model in the wind-tunnel. This fraction is called the Reynolds number, and obviously is of fundamental importance. In the use of a model, therefore, in an ordinary wind-tunnel, while V may approach that of the actual flight of the aircraft, and while p and u are the same, L is much smaller, being perhaps one-twentieth for an airplane and one-three-hundredth for an airship. So it is apparent why the method itself is defective. In spite of this fact, and for reasons which need not be elaborated here, the method does yield important and useful results, and it has given, in the main, the store of data from which the designer of aircraft has drawn. It is seen at once that the method can be improved; can, in fact, be made theoretically ideal, if the density of the air used in the wind-tunnel is compressed as much as the linear dimension of the aircraft is diminished, for under these circumstances, the product of pL does not change, and it is known that μ, the viscosity, is not affected greatly. The difficulty of securing these ideal conditions is a purely engineering one; it is to place the entire wind-tunnel in the interior of a tank in which the air may be compressed as much as is desired. A wind-tunnel of this type has been made by the National Advisory Committee for Aeronautics of this country and is in operation at its laboratories at Langley Field, Virginia. With the results now being obtained in this laboratory, the aeronautic engineer may make his designs with absolute confidence.

Another method which has been perfected within recent years has been one consisting of making observations upon actual aircraft while in flight or in making maneuvers. (In this way, correction factors have been

obtained which could be applied to data determined in wind-tunnel experiments upon models.) This method requires the operation of a large number of recording instruments for the accurate registration of velocities, accelerations, pressures, etc. By means of these, the actual motions of aircraft under varying conditions, of the distribution of pressure over all parts of their surfaces, of the motions of the control surfaces (rudder, ailerons, elevators), of the forces required of the pilot to secure results, etc., have all been determined to a high degree of accuracy. This information is especially important in helping the designer to make a proper distribution of his loads so as to give the proper strength to the structure and yet not to increase the weight, and also to know exactly what are the essential conditions for safety in flight, for controllability, i.e., ease of altering the state of flight, and for maneuverability, i.e., rapidity of alteration of the condition of flight. The larger part of the improvements made in recent years in the design of both airships and airplanes is due directly to the information obtained by this experimentation with full-size aircraft.

Still another method is available today, which unfortunately has not yet been used extensively in this country but which was used by Germany with the utmost success in the war. This consists of the application of the theory of hydrodynamics to aeronautical problems. This subject has been perfected by the work of mathematicians and physicists, and forms one of the most beautiful illustrations of applied mathematics. The general theory is available to everyone in Horace Lamb's admirable treatise on hydrodynamics, which is a perfect storehouse of information. The difficulty in the past has been to apply it. Air, as a fluid, is compressible-as distinct from an ideal liquid; and it shows viscosity when one layer moves over another or when a solid body moves through it. These facts make it impossible, at present, to apply the equations of hydrodynamics to such a fluid; the mathematical operations are too difficult, except in a few comparatively unimportant cases. Careful consideration, however, shows that for many practical problems, of interest to aeronautical engineers, it is allowable to treat the air as of constant density and to neglect its viscosity. This last comes practically into account only in the immediate neighborhood of the surface of the aircraft and the compressibility of the air becomes an essential feature only when velocities of 1000 feet a second or 12 miles a minute are considered. In other words, for a large class of problems, air may be treated as an "ideal liquid." Attention was first drawn to this fact by W. Kutta and by L. Prandtl. But, granting it, great difficulties still remain. There is no general method, that is practicable, for treating mathematically the motion in a liquid of a solid body of any arbitrary shape. Actual aircraft, either airships or airplanes, have irregular shapes, fixed appendages and movable parts; so they cannot be discussed directly. The plan has been, therefore, to simplify the problem by selecting for mathematical treatment certain ideal shapes and by making, when necessary, certain physical assumptions. The general problem has been simplified enormously by the recognition of the fact that in the actual flight of aircraft there are many conditions under which the air particles in any plane remain in that plane during flow, thus, being an illustration of uniplanar flow (two-dimensional). The importance of this fact lies in the knowledge of a general method of the mathematical treatment of such motions. Thus when an airship is moving under pitch (or yaw), the portion of the air flow created by the pitch (i.e., the transverse flow) near the center of the ship is practically uniplanar, since there the airship has a cylindrical shape.

The flow about airships has been discussed in two quite distinct ways. Since the lines of flow of the fluid are along the surface of the airship, one mode of attacking the problem theoretically is to deduce such a distribution of sources and sinks along an axis as will give lines of flow which, when combined with a uniform flow-due to the motion of the airship-will give

lines of flow lying in a surface identical with that of the airship. The whole character of the flow everywhere may then be deduced from the strength and distribution of the sources and sinks. This would then enable one to calculate the distribution of pressure over the surface of the airship. This method has been used with great success by G. Furhmann, who tried various distributions of sources and sinks, thus obtaining by trial various surfaces of flow which agreed as accurately as need be with the surfaces of actual airship types. The resulting pressures obtained by calculation were found to agree most closely with pressures actually observed, except at points near the stern where, of course, agreement was not expected, since it is at those points that the effect of viscosity in the surface layer of air makes itself felt most.

M. Munk has solved the same problem in the case of an ellipsoid of revolution by an ingenious deduction from a general formula of Lamb's concerning the flow past an ellipsoid. Munk's formula for the pressure applies also to an airship flying with an angle of yaw (or pitch).

Another interesting and important problem concerning airships has also been solved by Munk, using general mechanical principles. This is the determination of the unstable moment acting upon the airship when flying with an angle of yaw in either a straight or circling path. And, taking into account the fact of the uniplanar flow in central transverse planes if there is transverse motion of the airship, Munk has established the distribution of transverse forces acting on the ship when in straight or circling flight, with a small angle of yaw. Knowing the unstable moment and the centrifugal force, in the case of circling flight, the properties of the fins, the stationary fixed surfaces attached to the airship near its stern, may be discussed. In short, Munk's formulas are absolutely essential for the designer of airships and furnish information which could otherwise be obtained only by most elaborate observations.

The theory of airplane wings is divided naturally into two parts, that concerned with the effect of the cross-section of the wing, its profile, and that which takes into account the effect of the tips of the wing. The former really treats the wing as if it had a span of infinite length, and the flow is, then, strictly uniplanar. The problem of the flow in this case was first successfully attacked by W. Kutta and by N. Joukowski. Kutta was the first to show that in order to have a transverse force act on the wing, that is, in order to have a lift, it was essential that part of the flow about the wing should be a circulatory flow around it, and he deduced the formula, bearing his name, giving the connection between the amount of the circulation of this flow and the lift. His method then was to deduce the combination of two flows about a circle-the problem being a uniplanar one, one a uniform flow in a certain direction, the other a circulatory flow in circles around the original circle; then by means of a conformal transformation to transform the original circle into some other closed curve and the original lines of flow into lines of flow around this new section; finally so to choose the relation between the velocity of the uniform flow and the circulation in the original problem that in the new one the total resultant flow divides exactly at the "trailing edge" of the section. Following this process Joukowski was able to obtain certain closed curves which resembled greatly some well-known wing profiles, and thus to deduce the nature of the flow about them, the distribution of pressure over the wing, etc. This process of Kutta can be applied to only a limited number of cases; and evidently it cannot be used to deduce the flow about a wing whose section is given arbitrarily.

Munk has developed a much more general method for the discussion of the infinite wing, and has deduced general formulas for the lift, the pitching moment and the position of the center of pressure, for a thin wing of any cross-section. He first shows that, as far as lift and pitching moment are concerned, the flow about the thin wing may be considered—to a good ap

proximation the same as the flow about a curved line (the flow being two-dimensional) which is the medial line between the upper and lower surfaces of the wing, having the direction at any point of the element of the wing. He next shows how Kutta's theorem concerning the lift, combined with his method of treating the flow at the trailing edge, leads to a theorem connecting the lift with the distribution of transverse velocity component along the chord of the wing. This last evidently depends upon the slope of the wing curve at each point. So ultimately Munk obtains his formulas for lift and moment expressed in terms of the geometry of the wing curve. If the co-ordinates of this curve are known, as they are in practice, the values of the lift and moment may be deduced at once. These formulas of Munk may be used to discuss the general properties of any type of wing, without the need of awaiting tests in a wind-tunnel.

In order to describe the effect of the ends of a wing, Prandtl, calling attention to the fact that there must be a circulation around the wing in order to secure lift, compared the wing to a portion of a vortex filament whose two end-portions run off perpendicularly backward from the two wing tips. The velocity of flow due to this vortex would account in a general way for the change of the angle of attack, i.e., the "induced" angle of attack, for the induced drag and for the effect of one wing upon another in a biplane or multiplane. Further, assuming that the strength of the vortex varied along the span, so that the density of lift along the span varies and that vortex filaments run backward off the wing at all points, a still better approximation to reality was secured. By making a proper hypothesis as to the distribution of the lift along the span, definite formulas could be deduced. When these formulas were compared with the results obtained in wind-tunnels, very interesting conclusions could be drawn as to the connection between induced drag and the drag due to viscosity. Prandtl also indicated the solution of the problem which arises, when, instead of having given the distribution of lift, the distribution of induced downwash along the span is specified; and A. Betz solved a special case of the general problem of determining the distribution of lift for a wing of given plan form and a given angle of attack. When Prandtl applied his concept to biplanes, he was able to deduce most interesting theorems, all of importance to designers.

Munk's treatment of the same problems as just discussed, dealing with the finite wing, is much simpler than Prandtl's, involving, as it does, only the ideas of energy and momentum. His general thought is again to discuss uniplanar motion, this time in a transverse layer perpendicular to the line of flight, through which the wing passes. In this case, the front view of a monoplane can be considered a straight line having a length equal to the span, and the uniplanar flow is about this line in a vertical plane. Munk deduces the induced angle of attack and the induced drag, when the span is given, and, also, what is most important, the effect of induction, that is, of the flow itself, in modifying the effective angle of attack, both so far as concerns the lift and as affecting the rolling moment. In short, Munk's method gives exactly the formulas needed by the aeronautical engineer.

Similarly, when applied to biplanes, with or without stagger, Munk's mode of approach is distinctly physical, rather than mathematical, and leads directly to the solution of the problems concerning lift, induced drag, moments and position of center of pressure.

As a consequence of this theoretical work of Prandtl, Betz and Munk, the science of aeronautics has at its disposal certain formulas which enable one to calculate the principal properties of an airplane wing of given profile and dimensions and also of any combination of wings. Furthermore, these formulas make it possible to discuss the effect of modifications in the wings, as, for instance, of changing the ailerons. It is true the formulas are based upon simplifying assumptions; but the results obtained from them are of the same order of accuracy as those obtained from tests in wind-tunnels.

ON THE COMING-OF-AGE OF AVIATION.

On this day twenty-one years ago, that is to say on December 17, 1903, Mr. Orville Wright made the first sustained flight on a power-driven aeroplane. It is true that the flight only lasted for twelve seconds and that the machine was launched into the air by a catapult apparatus. But those twelve seconds were enough for the effect of the catapult to be absorbed and to show that the apparatus was actually sustaining itself by its own power.

From twelve seconds to twelve minutes and thence to twelve hours of sustained flight was a natural progression, and further extension of the period which an aeroplane can be sustained in the air is only a matter of the machine's capacity for carrying fuel.

Claims have been made that the first aeroplane actually to fly was the Avion, a steam-driven twin-screw, tractor monoplane designed and built by Mr. Clément Ader in France. It seems quite probable that the Avion, whose name incidentally has been adopted as the official French word for an aeroplane, did actually hop off the ground under its own power in 1893. And so it may be fairly regarded as one of the great precursors of the modern aeroplane, but certainly it did not maintain itself in flight as did the first Wright.

How the Wright biplane was produced under difficult circumstances by the Wright brothers, Orville and Wilbur, as the result of experiments with gliders from the tops of sandhills on the coast of North Carolina, and how they built their own first 12 horsepower engine in their own cycle shop at Dayton, Ohio, can be read in any history of aviation.

Unhappily Wilbur Wright, who was the moving spirit of the partnership, died of typhoid fever on May 20, 1912. Long before his death the Wright aeroplanes as designed by him and his brother had ceased to contribute towards the progress of aviation. It will always be to the credit of the Wright Brothers in History that they made the first aeroplane which flew under its own power. But like so many pioneers their work arrived at a dead end. The very characteristic of obstinate determination which makes pioneers succeed in a task which superior people had proved to be impossible prevents their minds from expanding and grasping new ideas.

THE NEW PIONEERS.

After the first success of the Wright Brothers came a fresh group of workers for Aviation who really contributed to progress. In the United States Glenn Curtiss developed aircraft which had a performance much superior to those of the Wright Brothers and to him definitely may be assigned the credit for having designed and built the first aircraft which ever flew off and onto water. There is much interest in considering that Mr. Orville Wright, the first man in the World to fly, is still alive and taking a useful philosophic interest in aviation, and that Glenn Curtiss, who really made American aviation in its early days, is still very actively employed in business though still interested in aviation, and that the firm which he founded can fairly claim to lead the World at the moment in its own particular type of aeroplane.

In Europe the pioneers were Ellehammer the Dane and Santos-Dumont the Brazilian who almost at the same time in the autumn of 1906 made long hops.

THE GREAT YEARS.

The great years in the development of aviation were 1907, 1908 and 1909. In 1907 Mr. A. V. Roe built and flew for short distances a triplane from which has been developed the famous Avro biplanes of today. M. Blériot