out by Lord Rayleigh, whose explanation is substantially as follows:—
When the plane undergoes the edgewise component of its motion, it abandons air which has been set in motion (normally) at its trailing edge, and embraces air that has not been set in motion at its leading edge. This exchange obviously results in an augmentation in its resistance. This reasoning applied to the “step by step” motion evidently continues to apply when the steps become infinitely small and the motion continuous, consequently the pressure will be greater than that due to the normal component alone, as is found experimentally to be the case.
It appears to the author that the augmentation of pressure will be greater than might be supposed from the foregoing reasoning, for the abandoned air, having motion in the same direction as the plane, will impede the flow of air round the following edge and so maintain a greater pressure difference between its two faces; likewise the new air seized by the advancing edge being already in circulation round that edge has a higher velocity relatively to the plane than the normal component of motion, so that the pressure it will develop will be greater than if it had been merely new air coming into the grasp of the plane. We are now evidently touching on the subject of Chap. IV., and dealing with the pressure due to the cyclic disturbance; this aspect of the subject will be resumed later.
§ 150. The Sine-Squared Law Applicable in a Particular Case.—It is evident from the foregoing reasoning that planes of different aspect ratio[1] will have their normal pressure components augmented to different degrees, inasmuch as the relative extent of their leading and trailing edges differ.
If we consider the case of a plane of extreme proportion it is
- ↑ A term used in the present work to denote the lateral dimension of an aeroplane, or other aerofoil, in terms of its fore and aft dimension, denoted by the symbol n.
207
