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.