Learning to fly in the U.S. Army

Support of an Airplane by Its Wings.—An airplane is supported just as definitely as though on top of a post, and by the same law, namely reaction. If you try to sweep the air downward with a wing held at a slight angle, the air just before it consents to be pushed downward, delivers a momentary reaction which is upward. If you have a bag of air in your hand it exerts no push upward of course; but the minute you give it a quick push downward it resists, due to its inertia, thus delivering an upward “reaction” against your hand.

Whenever you move anything, it reacts an amount just equal to the force that is moving it; if you move a bullet out of a gun, just before starting the bullet reacts and you have “kick.” If you should shoot a thousand guns downward, the reaction would be considerable, and for the instant might be sufficient to support heavy weight.

The airplane is a device for pushing downward millions of little bullets, made out of air and exceedingly small and light. The wing of an airplane sweeps through these bullets, or molecules, of air like a horizontal plow, wedges the particles downward in vast numbers and in a continual stream, making up in amount what is lacking in weight, so that as long as the airplane rushes along, there are many thousands of cubic feet of air forced down beneath its wings, delivering up a reaction that results in complete support for the machine. This reaction is just as definite and secure as though the machine were supported from the ground on wheels, but it disappears entirely when the airplane is at rest. Part of the whir of a training machine as it glides back to earth is made by the air driven downward from the wings; the same phenomenon may be noticed when a bat flies close to your ears at night, and if you were a few feet below the airplane as it flew, you would feel the rush of air driven downward from its wings (see Fig. 16).

The net result of all the reactive pushes from this air is lift. It may amount to several pounds for every square foot of the wing surface.

This is all that need be said about why the air supports an airplane; all you have to remember is that as long as you have the forward sweeping movement, you will have the lift.

The forward movement is absolutely essential, however, and to maintain it requires a lot of horsepower and gasoline. For it is by means of the engine and propeller that this forward movement is maintained. The engine is a device for creating forward movement—the propeller drives the machine ahead in exactly the same way as is the case in a torpedo, or steamboat.

Lift.—Assuming that we have all the forward motion needed, let us now investigate the lift that results. Experimenters such as the Wrights and others have found out how to get this lift most conveniently. Lift depends upon the four following factors:

1. Relation of Area of Wings to Support.—Consider a small wing; suppose it to be held by hand outside a train window in a given attitude, its area being 1 sq. ft. It tends to lift a certain amount, say 5 lb. Now increase its size to 2 sq. ft. and it will lift with 10-lb. force, tending to get away from your grasp. Rule: When only the area of a wing is changed, its lift varies with the area. If, as above mentioned, you can get 5 lb. of lift from each square foot of wing surface, you can by the same sign get 10-lb. of lift from 2 sq. ft. And if you have 500 sq. ft. of surface you can get 2500 lb. of lift.

Regarding area of wing surface, the pilot does not have to worry in a flight since he can do nothing to change it anyway. All he needs to know is that in different airplanes small wing area accompanies high speed and small weight-carrying capacity, as in the case of the Fokker and Sopwith speed scouts (see Fig. 17). Conversely, large wing areas are used for heavy load carrying and slow speed (see Fig. 18). Speed and weight-carrying capacity thus appear to be antagonistic and can not both be attained with efficiency, but only at the expense of enormous power. The incompatibility between high speed and weight carrying keeps the designer busy in efforts toward a reconciliation.

2. Density.—The second factor affecting the lift is the character of the air itself. I refer to the density of the air. The heavier each particle of air becomes, the more reaction it can furnish to the wing that drives it downward; so on days when the barometer is high the wing will lift more than on other days. Now the air is heaviest, or most dense, right near the ground; because in supporting the 50 miles or so of air above it, it becomes compressed and has more weight per cubic foot. Therefore, the wing gets more lift at a low altitude than at a high. Some airplanes will fly when low down but won’t fly at all high up. In Mexico, for instance, when the punitive expedition started out they were already at an altitude of several thousand feet above sea level. The airplanes had been built for use at places like New York and England, close to sea level, and when our army officers tried to fly with them in Mexico, they would not fly properly, and the factory had to redesign them.

Regarding density, the pilot should know that for a low density he should theoretically get a high speed. As density decreases, high up in the air, the speed tends to increase, and moreover he gets more speed for the same amount of gasoline. Unfortunately, at an altitude the motor power falls off, so that nowadays the speed is not faster high up than low down; but when the motor builders succeed in designing their motors to give the same horsepower at 20,000 ft. as they do on the ground, airplanes will be able to reach terrific speed by doing their work above the clouds.

It is found desirable to give large wings to airplanes which are going to fly at high altitudes, so as to offset the lack of density by an increase in area, thus leaving the angle range—that is, the speed range—as large as possible. The army airplanes in Mexico mentioned above were simply given a new set of larger wings to offset the lower air density in Mexico, and thereafter flew better.

3. Angle of Incidence.—The angle of incidence is defined as the angle between the wing-chord and the line of flight. The line of flight is the direction of motion of the airplane, and is distinct from the axis of the airplane which corresponds with the line of flight only for a single angle of incidence. If the line of flight is horizontal, the airplane may be flying tail-high, tail-level, or tail-low; that is, its axis may have varying positions for a given line of flight. This is true, if the line of flight is inclined, as in climbing. It is a mistake to confuse the line of flight with the axis of the machine.

The angle of incidence of the wings of the U. S. training machine may have any value from 15° down. When the angle is smaller the lift of the wings is smaller. Consider the model wing held out of a train window; if its front edge is tilted up to an angle of 15° with the line of motion it will lift say 1 lb.; if reduced to a 10° angle, it will lift less, say ⅔ lb. A model of the training-machine wing could be tilted down to an angle several degrees less than zero before its lift disappeared, because it is a curved, not a flat wing; this angle would be the “neutral-lift” angle; notice then that O° is not a neutral-lift angle, and therefore may be used in flight.

If the model wing were tilted up to an angle greater than 15°, the lift would not increase any more, but would be found to decrease. For this wing, 15° is called the critical, or “Stalling” angle, beyond which it is unwise to go.

4. Velocity.—If the model wing which is imagined to be held out of the car window, is held now in a fixed position at a given angle of incidence, any change of the train’s speed will result in a change of lift; should the speed rise from 30 miles per hour to double this value, the lift would increase enormously, fourfold in fact.

Lift varies as the square of the speed. Thus any increase or decrease of speed results in a great increase or decrease of lift.

Interdependence of Angle of Incidence and Velocity.—The four factors above mentioned all contribute to the lift; if in an airplane wing each factor be given a definite value, the resulting lift is determined according to the formula:

L = KrAV²

Two only of these quantities change materially in flight, the angle and the velocity; the lift itself remains substantially the same under most normal circumstances. The angle always changes simultaneously with the velocity, increasing when the velocity decreases. Thus the drop of lift due to velocity decrease is balanced by gain of lift due to angle increase, and the lift remains unchanged when speed changes.

Speed change then requires that the pilot alter the angle of incidence simultaneously with the throttle; so there are two things to do, unlike the case of the automobile where only the throttle is altered.

Minimum Speed.—When, in slowing up an airplane, the angle of incidence reaches the 15° limit, no further decrease of speed is allowable; therefore, the critical angle determines the minimum limit of speed. If for any reason the machine exceeds the 15° limit, it must speed up to gain support; that is, the pilot has to increase angle and speed simultaneously instead of oppositely.

Efficiency of Airplane Wings.—I said at the beginning of this chapter that the airplane was a device for pushing down an enormous quantity of air. A certain amount of force has to be furnished in order to keep the airplane moving, and this force is furnished by the engine and propeller. The propeller by giving a certain amount of push in a horizontal direction to the airplane wing enables this wing to extract from the air ten or twenty times this amount of push in a vertical direction; that is, the airplane wing will give you 10 lb. or more of lifting in exchange for 1 lb. of push.

The propeller push is necessary to overcome the drift or resistance of the wings to forward motion. It appears then that the airplane wing as it moves through the air has two forces on it, one acting straight up and called “lift,” the other acting straight back and called “drift” (see Fig. 19). The lift is several times greater than the drift, and the situation is quite analogous to that of a kite, which rises upward in the air due to its lift but at the same time drifts backward with the wind due to its drift. In the case of the kite the string takes up an angle which just balances the joint effect of the lift and drift.

The efficiency of an airplane wing is indicated by the ratio of lift to drift, and for a given lift, the efficiency is best, therefore, for small drift. If the lift is 1900 lb. and the wing drift 190 lb.,

Wing efficiency = Lift or weight/Wing drift = ¹⁹⁰⁰/₁₉₀ = 10

Factors Determining Best Efficiency.—It goes without saying that an airplane wing should attain the best efficiency it can, and there are several ways of doing this.

The first relates to the question of angle of incidence; we have already discussed the effect of angle on lift, but when we come to discuss its effect on efficiency we find that there is only one angle at which we can get the best efficiency. This is a small angle, about 3° to 6°; at this angle the lift is nowhere near as much as it would be at 10° or 15°, but the drift is so small compared to the lift that it is found desirable in airplanes to employ these small angles for normal flight. As the angle increases above this value of maximum efficiency, the efficiency drops off, and when you get up to the stalling angle, the efficiency becomes very low indeed (see Fig. 20).

The second way to get good efficiency is to choose the shape of the wings properly. For instance, early experimenters tried to get results with flat wings, and failed completely, for the flat wing proved to be very inefficient. When it was observed that birds had curved wings, this principle was applied to early experiments and then for the first time man was able to obtain support in a flying machine. The fundamental principle of efficiency in wings is that they must be curved, or cambered, as it is sometimes called. This is because as the wing rushes onward it wants to sweep the air downward smoothly and without shock, as can be done only when the wing is curved (see air flow, Fig. 21).

The question of wing curvature is exceedingly important then; we find that the curvature of its upper surface is particularly so. We notice that airplane wings all have a certain thickness in order to enclose the spars and ribs; it is not necessarily a disadvantage for them to be thick, due to the fact that the upper curve of the wing does most of the lifting anyway, and the lower side is relatively unimportant. You can make the lower surface almost flat, without much hurting the effect of the wing, so long as the upper surface remains properly curved. However, the upper surface must be accurately shaped, and is so important that in some machines we find cloth is not relied on to maintain this delicate shape, but thin wood veneer is used (I refer to the front upper part of the wing). In general, then, wings are thick toward the front and taper down to a thin trailing edge.

You may wonder how it was found that the upper surface of the wing was the most important; and I will say that this was one of the interesting discoveries of the early history of aerodynamics. People at first thought that a wing sweeping through the air derived its support entirely from the air which struck the bottom of the wing, and they assumed that if the bottom of the wing were properly shaped, the top did not matter; that is, all the pressure in the air was delivered up against the bottom surface. But a French experimenter conceived the idea of inserting little pressure gages at various points around the wing. He found, it is true, that there was considerable pressure exerted in the air against the bottom of the wing; but he found a more surprising fact when he measured the condition above the wing. When he applied his gage to the upper surface of the wing, it read backward, that is, showed a vacuum, and a very pronounced one. He found that there was a vacuum sucking the top part of the wing upward twice as hard as the pressure underneath was pushing; so that two-thirds of the total lift on this wing was due to vacuum above it (see Fig. 22).

In the diagram the shaded area on top of the wing represents vacuum above, that below the wing represents pressure beneath.

Aspect Ratio.—The third factor in wing efficiency has to do with the plan shape. It was early found that square wings were not much good, and that if you made them wide in span like those of a bird, the efficiency was best (see Fig. 23). Aspect ratio is the term which gives the relation of the span to the fore and aft dimension of the wing, and this relation is usually equal to six or so. The reason why large aspect ratios are advantageous is as follows:

The tips of all wings are inefficient, because they allow the air to slip sideways around the ends, and there is all the trouble of disturbing this air without extracting any considerable lift from it. In a wide-span wing these inefficient wing tips are only a small percentage of the total area, but in a small-span wing they may be an important consideration (see Fig. 24).

Wing Arrangements.—All the foregoing remarks in this chapter have applied only to a single wing. They apply in general to double or triple wings (biplanes and triplanes), but the matter of arranging multiple wings affects the efficiency.

The monoplane with its single layer of wings is the most efficient type of flying machine. We find if we arrange wings into the biplane shape that the presence of the upper wing interferes with the vacuum formed above the lower wing, and the efficiency decreases (see Fig. 22). The same is true of the triplane and the quadruplane arrangement. If all we wanted in airplanes was efficiency, we would use monoplanes, but the biplane is pretty popular now in spite of its low efficiency; this is because it can be much more strongly trussed than the monoplane, and also because of the fact that sufficient area may be secured with less span of wings.

It may be said that the low efficiency of the biplane can be somewhat relieved by spacing the upper and lower wings at a considerable distance apart; but if they are spaced at a distance much greater than the chord, it requires extra long struts and wires, and the resistance and weight of these will offset the advantage of wider spacing; so that practically biplane-wing efficiency may be taken as 85 per cent. of monoplane efficiency.

It remains to mention the tandem arrangement, used in all airplanes, where the tail is a tandem surface in conjunction with the wings. A surface located in the position of an airplane tail is at a disadvantage and shows low efficiency for flight purposes. This is because the main wings deflect the air downward and when the tail comes along it meets air which has a more or less downward trend, instead of encountering fresh, undisturbed air (see Fig. 16).

Resistance of an Airplane to Motion.—Earlier in this chapter the support of an airplane was explained and it was seen that the weight was exactly equalled by the lift or support; it was also explained that the production of this lift required considerable force in moving the wings rapidly through the air. It is not only the wings, however, which require force to overcome the resistance to motion. In order to have any wings at all it is unfortunately necessary to supply also struts, wires, etc., for bracing these wings, also a motor and seat for the passenger, which are usually included inside a fuselage, also wheels for landing and various control surfaces. None of these accessories to the wings contribute material lift, but they involve a large amount of resistance which is therefore a dead loss. Note carefully that there are two distinct sorts of resistance: (1) that of the wings, which is the necessary price paid for securing lift; (2) that of all the rest of the machine, in return for which nothing beneficial is received, and which therefore has sometimes been called “parasite” or “deadhead” resistance.

In a typical training machine the total resistance to be overcome if forward motion is maintained is as follows: (See Fig. 26.)

At 72 miles per hour:

At a speed of 57 miles per hour:

At a speed of 43 miles per hour:

It is seen that the above resistance values total to the highest figure at the lowest speed, and that the lowest value of resistance occurs at an intermediate speed; the resistance decreases as the speed decreases from 73 to 57 miles per hour; but a further decrease in speed finds the resistance running up rapidly so that at minimum speed the resistance is very great again. This is due to the fact that at high speeds the deadhead resistance exceeds that of the wings but at slow speeds although the deadhead resistance is very small, the wings being turned up to a large angle within the air, have a resistance which is at its maximum. This seems clear enough when we remember that the lift of the wings remains the same as the angle decreases (and speed goes up) but that the efficiency of the wings increases so that the wing resistance is a smaller fraction of the lift at high speed than at low speed.

Cause of Resistance.—Wing resistance, which is affected, as mentioned previously, by the wing curvature, can not be decreased unless new and improved sorts of wings are invented. As to deadhead resistance, it may be decreased in future by methods of construction which eliminate unessential parts. In a high-speed airplane in this country an attempt was made to eliminate the wires altogether and most of the struts (because the wiring is one of the largest single items of deadhead resistance); so far the attempt has failed for structural reasons. In the monoplane type of airplane of course the struts are eliminated, which is an advantage from the standpoint of resistance.

As long as struts, wires, etc., are used at all, the minimum resistance can be secured by giving them a proper “stream-line” shape. The stream-line shape is one in which the thickest part is in front and tapers off to a point in the rear, like a fish. If, for instance, we take round rods instead of the struts of the training machine above mentioned and having the same thickness, the resistance might be 80 lb. instead of 20 lb.; and if we take a rod whose shape is elliptical with its axes in a ratio of 1 to 5 the resistance might be 40 lb. instead of 20 lb.; and if we took the stream-line struts out of the training machine and put them back sharp edge foremost, the resistance would be increased. The advantage of the stream-line shape is that it provides smooth lines of flow for the air which has been thrust aside at the front to flow back again without eddies to the rear. This is not possible in the case of the round strut, behind which will be found a whirl of eddies resulting in a vacuum that tends to suck it backward. By fastening a stream-line tail behind the round rod the eddies are greatly reduced, as is the vacuum. The wires of the airplane are subject to the same law and if the training machine above mentioned had stream-line wires instead of round wires we might expect them to have less than 70 lb. resistance. The fuselage should always be given as nearly a stream-line shape as the presence of the motor and tanks will permit; and it must all be inclosed smoothly in “doped” fabric in order that the air-flow phenomena may operate. As for the wheels, they must of necessity be round, but by enclosing them with fabric the air flow past them is more easy and the resistance may be halved.

Total Resistance.—The necessity has been explained of discriminating between wing and deadhead resistance; if we are talking about wings we may ignore everything except the wing resistance (commonly called “wing drift”), but if we are talking about the whole airplane, we then must refer to the total resistance, which includes all the others and is overcome by the propeller thrust. “Skin-friction” resistance has not been mentioned nor need it be more than to say that any surface moving through air attributes part of its resistance to the actual friction of the air against it, and therefore should be as smooth as possible.

Motor Power Required for Flying.—The reason resistance interests us is that motor power is required to propel the airplane against it; more and more power as the resistance and speed increase. Obviously, the power required is least when the resistance is small, i.e., when the speed is intermediate between minimum and maximum. It takes more power to fly at minimum speed than at this intermediate speed. Of course it also takes more power to fly at maximum speed, where again the resistance is high.

Maximum Speed.—Ordinarily, for moderate speeds, airplanes have a margin of power at which the throttle need not be opened wide; should speed be increased the resistance and horsepower required will increase steadily until the throttle is wide open and motor “full out;” this establishes the maximum speed of an airplane; there is no margin of power, no climb is possible. The only way to increase speed is to use the force of gravity in addition to the motor force. It may be interesting to know what is the maximum possible speed in the case of a vertical dive with the motor shut off; it will be about double the maximum horizontal speed as may be readily seen from the fact that the thrust in the direction of motion is now no longer horizontal and equal to the resistance but is vertical and equal to the weight of the machine; that is, the thrust may be increased fivefold, and the speed resulting will be increased correspondingly, if the motor be running in such a vertical dive the velocity may be slightly increased though at this speed of motion the propeller would not have much efficiency.

There is danger in such high speeds; the stresses in the machine are increased several times merely by the increased resistance, and if the angle of incidence should be suddenly brought up to a large value at this high speed the stress would again be increased so that the total stress increase theoretically might be as high as fourteen times the normal value, thus exceeding the factor of safety. It is for such reasons that the maximum strength is desirable in airplanes; holes must not be carelessly drilled in the beams but should be located if anywhere midway between the top and bottom edges, where the stress will be least; initial stresses, due to tightness of the wires, should not be too great.

Climbing Ability.—Climbing ability refers to the number of feet of rise per minute or per 10 min. In order to climb, extra horsepower is required beyond that necessary for more horizontal flight. The machine can, for instance, fly at 56 miles per hour at which speed it requires 43 hp. If now the throttle is opened up so as to increase the horsepower by 22, making a total of 65 hp., the machine will climb at the rate of 380 ft. per minute, maintaining approximately the same flight speed. If instead of 65 hp., it were 54 hp. the speed of climb would be about one-half of the 380, or 190 ft. per minute; the flight speed again remaining approximately as before; that is, any margin of horsepower beyond the particular value of horsepower required may be used for climbing without material change of the flight speed. It is necessary here to state that lift does not increase during climb; and while for the instant that a climb commences there may be, due to acceleration, more lift on the wings than balances the weight, this does not remain true after a steady rate of climb is reached. To illustrate, in a wagon drawn uphill by horses the wheels which support the wagon do not exert any more support than on the level, and the entire force to make the wagon ascend is supplied through extra hard pulling by the horses. Thus in a climbing airplane the propeller furnishes all the climbing force and lift is no greater than in horizontal flight. In fact, the actual lift force may be even less, as the weight of the airplane is partly supported by the propeller thrust which is now inclined upward slightly.

To secure maximum climbing ability, we must determine at what velocity the margin of motor power is the greatest. In the above-mentioned machine we know that the horsepower required for support is least for a speed of near 55 miles per hour, and it is near speed where therefore the excess margin of power is greatest and at which climbing is best done. An airplane designed chiefly for climbing must have low values of motor power necessary for support, namely, must have small resistance, therefore small size, therefore small weight.

Gliding Angle.—Gliding angle denotes the angle at which the airplane will glide downward with the motor shut off and is spoken of as 1 in 5, 1 in 6, etc., according as it brings the airplane 1 mile down for each 5, 6, etc., miles of travel in the line of flight. The gliding angle of a machine may be found by dividing the total resistance into the weight:

Gliding angle = Weight/Total resistance.

In the above-mentioned airplane it is one in 6.6 when the resistance is 288 lb., that is, when the speed is 57 miles per hour. At any other speed the resistance increases and hence the gliding angle decreases. Hence the importance of putting the airplane into its proper speed in order to secure the best gliding angle.

The Propeller.—The propeller or “screw,” by screwing its way forward through the air, is able to propel the airplane at the desired velocity. Regarding principles of propeller action the matter can be hastily summarized in the following brief lines. The propeller blades may be regarded as little wings moving in a circular path about the shaft; and they have a lift and drift as do the regular wings. The lift is analogous to the thrust; to secure this thrust with least torque (drift) the blades are set at their most efficient angle of incidence, and while the blade appears to have a steep angle near the hub, it actually meets the air in flight at the same angle of incidence from hub to tip.

Propeller Pitch.—Pitch is best defined by analogy to an ordinary wood-screw; if the screw is turned one revolution it advances into the wood by an amount equal to its pitch. If the air were solid, a propeller would do the same, and the distance might be 8 ft., say. Actually the air yields, and slips backward, and the propeller advances only 6 ft. Its “slip” is then 8 minus 6, equals 2 ft., or 25 per cent. Such a propeller has an 8-ft. pitch, and a 25 per cent. slip.

This “slip stream” blows backward in a flight so that the tail of an airplane has air slipping past it faster than do the wings. Hence the air forces at the tail are greater than might be expected. The rudder and elevators therefore give a quicker action when the propeller is rotating than when, as in the case of a glide, it is not.

Washout.—Due to torque of the motor, the airplane tends to rotate in the opposite direction to the propeller. This tendency may be neutralized by giving one wing tip a smaller angle of incidence, called “washout,” so that the machine normally tends to neutralize the torque-effect.

PRINCIPLES OF AIRPLANE EQUILIBRIUM

Introductory.—Under this head will be discussed: (a) features of airplane design which tend to maintain equilibrium irrespective of the pilot; (b) matters of voluntary controlling operations by the pilot. As regards (a) the tendency of the airplane toward inherent stability acts to oppose any deviation from its course whether the pilot so desires or not. The more stable is a machine, the less delicately is it controlled, and the present consensus of opinion among pilots is that a 50-50 compromise between stability and controllability is the best thing.

In questions of airplane equilibrium the starting point is the center of gravity; obviously, if the center of gravity were back at the tail or up at the nose there would be no balance; the proper place for it is the same spot where all the other forces such as thrust, lift and resistance act; there it is easy to balance them all up. But it is not always easy to bring the line of thrust and the line of total resistance into coincidence, because the line of thrust is the line of the propeller shaft and when this is high up as in the case of some pushers it may be several inches above the line of resistance. And as the thrust is above the resistance there is a tendency to nose the machine down; to balance which the designer deliberately locates the center of gravity sufficiently far behind the center of lift so that there is an equal tendency to tip the nose upward; and all four forces mentioned completely balance each other. But things may happen to change the amount or position of these forces during flight, and if this does happen the first thing to do is to restore the balance by bringing in a small new force somewhere. In an actual airplane this small restoring force is supplied at each critical moment first, by the tail, etc., of the airplane and second, by voluntary actions of the pilot. The center of gravity of any airplane may be determined easily by putting a roller under it and seeing where it will balance, or by getting the amount of weight supported at the wheels and tail, according to the method of moments.

Longitudinal Stability.—Longitudinal stability has to do with the tendency of an airplane to maintain its proper pitching angle. It was said above that the four forces of lift, resistance, thrust and weight always exactly balanced due to their size and their position. Now the first consideration about longitudinal stability is that while the centers of gravity and other forces remain in a fixed position, the center of lift changes its position whenever the angle of incidence (that is the speed) is changed. The phenomenon of shift of center of pressure applies only to the wings and to the lift (the position of center of resistance remains practically fixed at all angles).

Note the effect on center of pressure position of a change of wing angle (see Fig. 20). The wing used on the U. S. training machine has a center of lift which is about in the middle of the wing when flying at a small angle of maximum speed; but if the angle is increased to the stalling angle of 15°, the center of pressure moves from midway of the wing to a point which is about one-third the chord distance of the wing from the front edge. The lift may travel about ½ foot, and it is equal in amount to the weight of the machine (that is, nearly a ton), and the mere effect of changing the angle from its minimum to its maximum value therefore tends to disturb the longitudinal equilibrium with a force which may be represented as 1 ton acting on a lever arm of ½ ft. Suppose that the airplane is balancing at an angle of 2° so that the center of gravity coincides with the center of lift for this angle; now if a gust of wind causes the angle to increase for an instant to 2¼°, the center of lift will move forward and tend to push the front edge of the wing up, thus increasing the angle further to 2½°. Then the center of lift, of course, moves further forward to accommodate the increase of angle, and in a fraction of a second the wing would rear up unless it were firmly attached to the airplane body and held in its proper position by the tail. Similarly if for any reason the proper angle of 2° were decreased, the same upset would follow, only this time tending to dive the wing violently to earth. This tendency is neutralized in an airplane by the “Penaud Tail Principle.”

There are certain shapes of wings in which the center of pressure travels in the reverse direction; a flat plate, for example; or a wing having its rear edge turned up so that the general wing shape is like a thin letter “S.” Such wings as these would not tend to lose their proper angle, because when the angle is changed for any reason the center or pressure in these wings moves in just the manner necessary to restore them to their proper position; but these wings are inefficient and are not in present use on airplanes.