Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/121

Rh are distributed along an axis (or axis plane for two-dimensional motion in a three-dimensional space), and it is an established proposition that any solid whatever, in motion in a fluid, may be imitated by an appropriate distribution of sources and sinks situated on its surface, and it follows that within certain limitations as to abruptness of contour, an equivalent exists for every stream line solid of revolution in point sources and sinks distributed along an axis, and for every cylinder of stream line section in line sources and sinks located on an axial plane. The distribution of sources and sinks that will produce any particular form is only known in a few special cases, such as those of the elliptical cylinder and ellipsoid, in which the number is infinite. Any finite distribution can be investigated by the graphic method by repeated compounding of system on system; a comprehensive way of investigating cases of infinite distribution is at present lacking. It may be noted that in all cases the investigation commences with the source and sink system, the form of the corresponding solid being obtained as a resultant; the reverse process can only be effected by recognising the solid as belonging to some particular system, and consequently only certain solutions are possible.

It is evident that if we take any pair of Rankine's “oogenous neoids” and trim fore and aft to form water lines (Fig. 43), we can regard the process as equivalent to a number of sources in the region a a a, and sinks in the region b b b, in order to generate and absorb the stream flux that otherwise runs to