Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/38

§ 16 motion corresponding to the particular streamline chosen. Thus we know that the amplitude of the orbit of any particle, measured at right angles to the direction of flight, is equal to that of the corresponding streamline.

We further know that, in general, the particles have a retrograde motion—that is, their final position is astern of their initial position—also that the maximum retrograde velocity is to be found in the region of maximum amplitude. Beyond this we know that the initial motion of any particle is in the same direction as that of the body, and that this initial motion is greater for particles near the axis of flight than for those far away. Let b, b, b, etc., Fig. 5, represent the final position of a series of particles originally situated in the plane a, a, a; then the orbits of these particles will originate on the plane a, a, a, and terminate on the surface b, b, b, and the motion will be of the character shown.

The form of the surface b, b, b, will be different for different forms of body. It will evidently approach the plane a, a, a, asymptotically, and generally will tend to form a cusp pointing along the axis of flight. The development of this cusp is greatest in cases where the extreme entrance and run are of bluff form, as in the Rankine Oval. Fig. 42, where the point of the cusp is never reached, the surface approaching the axis of flight asymptotically. In reckoning the displacement of the fluid (§ 15), the volume included in the cusped surface forward of the plane a, a, must be considered negative, since here the fluid is displaced in the same direction as the motion of the body.