History of Aviation - Chapter 3.2
It was seen that the weight was exactly equaled 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:
Wings 160 lb.
Deadhead Wiring 70
Struts 20 195
Total 355 lb.
At a speed of 57 miles per hour:
Wings 158 lb.
Deadhead resistance 130
Total 288 lb.
At a speed of 43 miles per hour:
Wings 350 lb.
Deadhead resistance 125
Total 475 lb.
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 dead-bead 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 enclosed 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 vertical dive with the motor shut off; it will be about double the maximum horizontal speed as may -readily seen from the fact that the thrust in the
reaction of motion is now no longer horizontal an equal to the resistance but is vertical and equal t the weight of the machine; that is, the thrust may b increased fivefold, and the speed resulting will b 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 mm. 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, main taming approximately the same flight speed If instead of 65 hp., it were 54hp. 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
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 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 pas it faster than do the wings. Hence the air force 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 the best thing.
In questions of airplane equilibrium the point is the center of gravity; obviously, if center of gravity were back at the tail or up at nose there would be no balance; the proper for it is the same spot where all the other f such as thrust, lift and resistance act; there it easy to balance them all up. But it is not as easy to bring the line of thrust and the line of resistance into coincidence, because the line 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 150, 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 balancing at an angle of 2degrees so that the center gravity coincides with the center of lift for this angle; now if a gust of wind causes the angle increase for an instant to 2 ¼ degrees, the center of will move forward and tend to push the front ed of the wing up, thus increasing the angle further 2.½degrees. Then the center of lift, of course, move further forward to accommodate the increase angle, and in a fraction of a second the wind 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 2degrees 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.
The Penaud Tail Principle.-Rule.--The horizontal tail must have a smaller angle of incidence than the wings. The upsetting force above men-
tioned must be- met by a strong opposite righting force, and this latter is furnished by the horizontal tail surface. In the angle of equilibrium of 2degrees above mentioned, the flat horizontal stabilizer will perhaps have no force acting on it at all because it is edgewise to the air and its angle of incidence is zero. When the angle of the wing increases to 2 1/4 and the lift moves forward tending to rear it up, the wing being rigidly fastened to the body pushes the tail downward so that the tail now beg have a small lift force upon it due to its angle of ¼ degree-and this newly created force, though small, ac such a long lever arm that it exceeds the real force of the wing and will quickly restore the plane to 2 degrees. This action depends upon the principle of the Penaud Tall or longitudinal "Dihedral which requires that the front wings of an airplane make a larger angle with the wind than the rear surface. This principle holds good even when have rear surfaces which actually are lifting s faces in normal flight, the requisite being that t wings themselves shall in such cases be at an ever greater angle than the tail. No mention has b made of the elevator control, because its action additional to the above-mentioned stability. The elevator is able to alter the lift on the tail; such alteration requires, of course, immediate change angle of the wings so that equilibrium shall again follow; and thus equilibrium will be maintained until the lift at the tail is again altered by some movement of the elevator control. Thus the elevator may considered as a device for adjusting the angle o incidence of the wings.
The air through which the wings have passes receives downward motion, and therefore a tai which is poised at zero angle with the line of flight may actually receive air at an angle of -2 degrees or - 3degrees In the above case we would expect an actual down ward force on the tail, unless this tail is given a slight arch on its top surface (for it is known that) arched surfaces have an angle of zero lift which is negative angle).
Longitudinal Control.-Steering up or down is done by the elevator, which as explained above is merely a device for adjusting the angle of incidence of the wings. The elevator controls like all the other controls of an airplane depend for their quick efficient action upon generous speed; they can not be expected to give good response when the machine is near its stalling speed. The elevators like the rudder are located directly in the blast of the propeller and in case the speed of motion should become very slow, the elevators may be made to exert considerable controlling force if the motor is opened up to blow a strong blast against them. This is good. to bear in mind when taxying on the ground because if the motor is shut off at the slow speed of motion the elevator and rudder will lose their efficacy. The propeller blast, due to a 25 per cent. slip, adds 25 per cent. of apparent speed to those parts which are in its way, and therefore the tail forces are affected as the square of this increase, that is, the forces may be 50 per cent. greater with the propeller on than off.
Lateral Stability.-This depends upon the keel surface or total side area of an airplane. The keel surface includes all the struts, wires, wheels, wings, as well as body, against which a side wind can blow. Skidding and side-slipping have the same effect as a side wind, and the resulting forces acting against the side of the machine should be made useful instead of harmful. This is done by properly proportioning the keel or side surface. If keel surface is low, the side force will rotate the airplane about its axis so that the windward wing sinks; if high, so that it rises. But if the keel surface is just the right height (i.e., level with the center gravity) the side forces will not rotate the machine at all and will simply oppose the skidding without upsetting equilibrium.
Lateral Dihedral.-Now when an airplane appears to have its keel-surface center too low, the easiest way to raise it level with the center of gravity is to give the wings a dihedral angle, that is
make them point upward and outward from the body. Thus their projection, as seen in a side view, is increased, and the effect is to add some keel surface above the center of gravity, thus raising the center of total keel surface.
A further advantage of the lateral dihedral is that any list of the airplane sideways is automatically corrected (see Fig. 30). The low wing supports better than the high wing, because a side slip sets iii, hence will restore the airplane to level position.
Non-Skid-Fins. Where for the above-mentioned purposes an excessive dihedral would be needed, resort may be had to non-skid-fins erected vertically edgewise to the line of flight above or beneath the topwing. These are used in marine machines to balance the abnormally large keel surface of the boat or pontoon below.
Lateral Control. By means of ailerons, lateral control is maintained voluntarily by the pilot; the aileron on the low tip is given a greater angle of incidence while on the high tip a less angle of incidence thus restoring the proper level of the machine. Notice that the efficacy of the ailerons depends upon speed of motion of the airplane, irrespective of propeller slip because the propeller slip does not reach the ailerons. Therefore, at stalling speeds the ailerons may not be expected to work at their best, and when lateral balance is upset at slow speeds it is necessary to dive the machine before enough lateral control can be secured to restore the balance.
Directional Stability.-Directional stability has to do with the tendency of an airplane to swerve to
- the right or left of its proper course. To rnaintai4 directional stability the "vertical stabilizer'~ is used~ which acts in a manner analogous to the feather of an arrow. Thus in case of a side slip the tail will swing and force the airplane nose around into the direction of the side slip so that the airplane tends to meet the relative side wind "nose-on" as it should. The vertical stabilizer should not be too
large, however, as then any side pressure due to deviation from a rectilinear course will cause the machine to swerve violently; the wing which is outermost in the turn will have preponderance of lift due to its higher speed; that is, the airplane will get into a turn where there is too much bank and a spiral dive may result.
Page 77 and 78 on directional control was torn from this book and are missing. Thus ends chapter 3