What Happens When Making a Turn
We are looking downward on an aeroplane ab which has been moving along the straight path cd. At d it begins to describe the circle de, the radius of which is od, around the center o. The outer portion of the plane, at the edge b, must then move faster than the inner edge a. We have seen that the direct air pressure on the plane is proportional to the square of the velocity. The direct pressure P (see sketch on page [22]) will then be greater at the outer than at the inner limb; the lifting force L will also be greater and the outer limb will tend to rise, so that the plane (viewed from the rear) will take the inclined position shown in the lower view: and this inclination will increase as long as the outer limb travels faster than the inner limb; that is, as long as the orbit continues to be curved. Very soon, then, the plane will be completely tipped over.
Necessarily, the two velocities have the ratio om:om´; the respective lifting forces must then be proportional to the squares of these distances. The difference of lifting forces, and the tendency to overturn, will be more important as the distances most greatly differ: which is the case when the distance om is small as compared with mm´. The shorter the radius of curvature, the more dangerous, for a given machine, is a circling flight: and in rounding a curve of given radius the most danger is attached to the machine of greatest spread of wing.
Lateral Stability
This particular difficulty has considerably delayed the development of the aeroplane. It may, however, be overcome by very simple methods—simple, at least as far as their mechanical features are concerned. If the outer limb of the plane is tilted upward, it is because the wind pressure is greater there. The wind pressure is greater because the velocity is greater. We have only to increase the wind pressure at the inner limb, in order to restore equilibrium. This cannot be done by adjusting the velocity, because the velocity is fixed by the curvature of path required: but the total wind pressure depends upon the sail area as well as the velocity; so that by increasing the surface at the inner limb we may equalize the value of L, the lifting force, at the two ends of the plane. This increase of surface must be a temporary affair, to be discontinued when moving along a straight course.
The Aileron
Let us stand in the rear of an aeroplane, the main wing of which is represented by ab. Let the small fan-shaped wings c and d be attached near the ends, and let the control wires, e, f, passing to the operator at g, be employed to close and unclasp the fans. If these fans are given a forward inclination at the top, as indicated in the end view, they will when spread out exert an extra lifting force. A fan will be placed at each end. They will be ordinarily folded up: but when rounding a curve the aviator will open the fan on the inner or more slowly moving limb of the main plane. This represents one of the first forms of the aileron or wing-tip for lateral control.
The more common present form of aileron is that shown in the lower sketch, at s and t. The method of control is the same.