Aeroplane Construction and Operation

by John B. Rathbun

Elements of Stability. When we balance a board on a fulcrum so that it stands in a perfectly horizontal position, the board is said to be "In equilibrium," or is supported at its "Center of gravity." There is only one point at which a body will balance, and this point is at the center of gravity or "C. G." In an aeroplane, the combined mass of the body, motor, wings, fuel, chassis, tail and live load has a center of gravity or a balancing point at which the lift must be applied if the machine is to rest in equilibrium. When the center of lift (or center of pressure) does not pass through the center of gravity of the aeroplane, some other force must be applied to overcome the unbalanced condition. When the machine is unbalanced in a fore and aft direction with the tail low, a force must be applied by the elevator flaps that is opposite and equal to the moment of the unbalanced forces. An aeroplane is stable when it is balanced in such a way that it returns to a state of equilibrium after meeting with a disturbance.

When disturbed, a stable body does not usually return instantly to its position of equilibrium, but reaches it after a series of decreasing oscillations. The heavier the body, and the more compact its form, the longer will it oscillate about its fulcrum before coming to rest. By arranging broad surfaces at the ends of the oscillating body, a portion of the energy will be expended in creating air currents, and the motion will be readily "damped out." If the damping effect is so great that the body does not swing back after once reaching the position of equilibrium, the body is said to be "dead beat," or "dynamically stable." There is a great difference between the static forces that tend to return the body to a position of equilibrium and the dynamic retarding forces that tend to damp out the oscillations. Usually, a body with excessive static stability is far from being stable in a true sense, since such a body tends to oscillate longer, and more violently, than one in which the static restoring forces are not so strongly marked. A body may be statically but not dynamically stable, but a dynamically stable body must of necessity be statically stable.

Static stability in calm air is determined by the location of the center of gravity, the center of lift, the center of propeller thrust, the center of area of the surfaces, and the center of the forward resistance. The forces acting through these centers are: (1) The weight; (2) The lifting force; (3) The propeller thrust; (4) The resistance. The weight and lift are vertical forces equal and opposite in direction. The thrust and resistance are horizontal forces, also equal and opposite in direction. When all of these forces intersect at a common point, they will completely neutralize one another and the body will be in equilibrium.

Dynamic stability is attained by the use of large damping surfaces such as the stabilizer surface, fins, and the elevator. These act to kill the oscillations set up by the static righting couples or forces. Without suitable damping surfaces the machine would soon be out of control in gusty weather since successive wind gusts will act to increase the oscillations of the righting forces until the machine will turn completely over. On the other hand, an aeroplane can be too stable and therefore difficult to steer or control in gusts because of its tendency toward changing its attitude with every gust in order to restore its equilibrium. A machine should only be partially stable, and the majority of pilots are firmly set against any form of mechanical or inherent control. No matter how simple the method, mechanical control always introduces a certain amount of mechanism that may go wrong. The question of stability has already been solved to a sufficient extent.

A disturbance that simply changes the direction of travel is not considered an unstable force since it normally does not tend to endanger the machine. Nearly any machine, equipped with any possible form of control apparatus, tends to change its direction when being righted.

Axes of Stability. An aeroplane has six degrees of freedom or motion. Three are of translation or straight line motion, and three are of rotation about rectangular axes. It can travel forward in a straight line, rise and fall in a vertical plane, or skid sidewise. When it rolls from side to side about the fore and aft axis (X axis) it is laterally unstable. When pitching up and down in a fore and aft direction, and around an axis parallel with the length of the wings (Y axis), the machine is said to be longitudinally unstable. When swinging or "Yawing" from right to left about a vertical axis (Z axis) it is unstable in "Yaw."

Rolling is resisted by the ailerons, pitching by the elevators and stabilizer, and yawing by the vertical directional rudder. Lateral oscillation are damped out by the wing surfaces and by vertical surfaces or "Fins." Longitudinal oscillations are damped mostly by the stabilizer and elevator surfaces. Directional or yawing vibrations are corrected by the damping action of the vertical tail fin, vertical rudder and the sides of the body, the latter also serving to damp out longitudinal vibrations. On an absolutely calm day, the pilot can shut off the motor and glide down without touching the controls if the machine is longitudinally stable. The glide generally starts with a few pitching oscillations, but these gradually are damped out by the tail as soon as the machine picks up its natural gliding angle and speed, and from this point it will continue without oscillating.

The Spiral and Nose Dive. There are two forms of instability that have not yet been fully corrected, and both are highly dangerous. One of these is known as the "spiral dive" or nose spin, and the other as the straight nose dive. The aeroplane in a spiral nose dive rotates rapidly about a vertical axis during the dive. Spiral instability resulting from lateral instability, can be minimized by decreasing the area of the vertical rudder and by the proper placing of fins so that there is not so great an excess of vertical area to the rear of the C. G.

The covered-in body acts as a fin and will be productive of spiral instability if the area is not properly distributed. In the majority of cases the rear of the body is equivalent to a large fin placed to the rear of the C. G. A fin above the G. G. tends to reduce all spiralling.

Stability and Speed. An aeroplane in straight horizontal flight must be driven at such an angle, and such a speed, that the weight is just sustained. To be inherently stable the machine must always tend to increase its speed by diving should the power be cut off in any way. An aeroplane that does not tend to increase its speed in this way, "Stalls" or becomes out of control. Any machine that will automatically pick up its gliding angle after the propeller thrust has ceased is at least partially inherently stable, and if it does not possess this degree of stability, other forms of stability are practically worthless. The machine having the smallest, flattest gliding angle is naturally safest in cases of power failure, and hence the gliding angle is somewhat related to the subject of stability.