Fig. 29.—Diagrams illustrating theory and application of longitudinal dihedral angle.
Fig. 29.—Diagrams illustrating theory and application of longitudinal dihedral angle.
Fig. 29.—Diagrams illustrating theory and application of longitudinal dihedral angle.
The Penaud Tail Principle.—Rule.—The horizontal tail must have a smaller angle of incidence than the wings. The upsetting force above mentionedmust be met by a strong opposite righting force, and this latter is furnished by the horizontal tail surface. In the angle of equilibrium of 2° 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 2¼° and the lift moves forward tending to rear it up, the wing being rigidly fastened to the body pushesthe tail downward so that the tail now begins to have a small lift force upon it due to its angle of ¼°; and this newly created force, though small, acts at such a long lever arm that it exceeds the rearing force of the wing and will quickly restore the airplane to 2°. This action depends upon the principle of the Penaud Tail 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 we have rear surfaces which actually are lifting surfaces in normal flight, the requisite being that the wings themselves shall in such cases be at an even greater angle than the tail. No mention has been made of the elevator control, because its action is additional to the above-mentioned stability. The elevator is able to alter the lift on the tail; such alteration requires, of course, immediate change of angle of the wings so that equilibrium shall again follow; and this equilibrium will be maintained until the lift at the tail is again altered by some movement of the elevator control. Thus the elevator may be considered as a device for adjusting the angle of incidence of the wings.
The air through which the wings have passed receives downward motion, and therefore a tail which is poised at zero angle with the line of flight may actually receive air at an angle of -2° or -3°. In the above case we would expect an actual downward force on the tail, unless this tail is given a slight arch on its top surface (for it is known thatarched 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 properlyproportioning 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 at just the right height (i.e., level with the center of gravity) the side forces will not rotate the machine at all and will simply oppose the skidding without upsetting equilibrium.
Fig. 30.—Diagram showing effect on lateral stability of dihedral angle and non-skid fins.(a) Machine flying level. (b) Machine tips and side-slips: excess pressure is created on windward wing and fins, (c) Machine has side-slipped and rotated back to level.
Fig. 30.—Diagram showing effect on lateral stability of dihedral angle and non-skid fins.(a) Machine flying level. (b) Machine tips and side-slips: excess pressure is created on windward wing and fins, (c) Machine has side-slipped and rotated back to level.
Fig. 30.—Diagram showing effect on lateral stability of dihedral angle and non-skid fins.
(a) Machine flying level. (b) Machine tips and side-slips: excess pressure is created on windward wing and fins, (c) Machine has side-slipped and rotated back to level.
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 ismake 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 in, 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.
Fig. 31.—Deperdussin control.System used in U. S. training airplanes.
Fig. 31.—Deperdussin control.System used in U. S. training airplanes.
Fig. 31.—Deperdussin control.
System used in U. S. training airplanes.
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 maintain directional stability the “vertical stabilizer” is used, which acts in a manner analogous to the feather on 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.
Directional Control.—The rudder gives directional control in exactly the same way that it does on a boat; it should be said, however, that the rudder is sometimes used without any intention of changing the direction, that is, it is used simultaneously with the ailerons as a means of neutralizing their swerving tendency. The ailerons, of course, at the same time that they restore lateral balance create a disadvantageous tendency to swerve the machine away from its directional course; that is what the rudder must neutralize. Moreover, the rudder is frequently used against side winds to maintain rectilinear motion.
Banking.—Banking combines the lateral and directional control, which should be operated simultaneously so as to tilt the machine and at the same time maintain the radius of turn. The wings are tilted in a bank because in going around a curve of a certain radius the weight of the machine creates a centrifugal force in a horizontal direction and if the curved path is to be maintained this centrifugal force must be neutralized; and this is done by inclining the force of lift inward until it has a horizontal component equal to the centrifugal force. That is why the angle of bank must be rigidly observed, or else the inward component of the lift will change. Now as soon as the wings bank up, the lift force is no longer all vertical and therefore may not be enough to support the weight of the machine. To offset this have plenty of motor power for speed in a bank; and do not try to climb while banking.
It is better to bank too little than too much; too little results in skidding which may be easily cured; too much results in side slipping inward and if the tail surface is too great in this latter case, a spiral dive may result—so look out for over banking.
It is better for the beginner in banking to move his ailerons first and then move the rudder; for if he moves the rudder first there will be skidding outward, forward speed will drop and a stall may result. On high angles of banking, over 45°, it should be noted that the elevators are now more nearly vertical than horizontal and operate as a rudder; similarly the rudder’s function is reversed, and to turn down the rudder will be used.
Damping in an Airplane.—Above have been mentioned the restoring forces which tend toward airplane equilibrium. Now these restoring forces tend to push the machine back to equilibrium and even beyond in exactly the same way that gravity causes a pendulum to swing about its point of equilibrium. This can sometimes be noticed in the case of an automobile when travelling at high speed along country roads where a sort of slow oscillation from side to side may be noticed due to the forceful maintenance of equilibrium of the body in its forward motion. This oscillation in an airplane would be serious unless there were means of damping it out and these means are: first, the wings; second, the tail surfaces; third, the weight and inertia of the machine itself. Regarding inertia it should be said that a machine with weight distributed farfrom the center of gravity, such as the double-motor airplane has a large tendency to resist the rolling motions associated with lateral stability. But from the same sign airplanes with large moment of inertia are difficult to deviate from any given attitude, and therefore have the name of being “logy.” The proper proportioning of an airplane’s parts to secure first, the restoring forces; second, the proper damping force; third, the proper amount of moment of inertia, is a very delicate matter and beyond the scope of the present chapter.