Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/186

§ 122 Fig. 71, a plane of infinite lateral extent moving edgewise, may be taken as an aeroplane at evanescent angle. Fluid infinite.

Fig. 72, the same as Fig. 71, but with more powerful cyclic component, showing form of motion in greater detail.

Fig. 73, combined system due to two superposed planes, separated 1⅛ times their width. Planes and fluid infinite.

Fig. 74, elliptical cylinder of infinite lateral extent, in infinite expanse of fluid.

Fig. 75, an aeroplane of evanescent angle in vicinity of boundary surface.

§ 123. Energy in the Periptery.—A body in motion in a fluid is known to carry with it kinetic energy due to the fluid disturbance in addition to that due to its proper mass (§§ 81, 84). A superposed cyclic motion adds to the energy so carried. A cyclic motion around a cylinder or cylindrical filament, or round about a plane, in an infinite expanse of fluid contains an infinite quantity of energy (§ 85), and the resulting peripteroid motion for these cases will consequently require an infinite quantity of energy for its production. We must consequently regard Figs. 70, 71, 72, 73, 74 in the light of types of motion, rather than an actual form of motion that we could produce if the circumstances of hypothesis were materialised. If, however, we limit the expanse of fluid by a boundary, such as in Fig. 75, the energy of the cyclic motion immediately becomes finite, for the number of squares is limited (§ 86), so that the flow as here depicted is not open to the same objection.

The quantity of energy in the particular case given in Fig. 75 is equal to that of a body of fluid moving with the aeroplane, whose area is approximately one-seventh of that of the square on the aeroplane section.

The quantity of energy contained in peripteroid motion, and its relation to the load supported, is a matter that awaits more complete investigation.