Potential Flow About Elongated Bodies of Revolution

This report presents a method of solving the problem of axial and transverse potential flows around arbitrary elongated bodies of revolution. The solutions of Laplace's equation for the velocity potentials of the axial and transverse flows, the system of coordinates being an elliptic one in a meridian plane, are known to be of the following form.

If a power-series development of λ in μ is assumed as the equation of the meridian profile in elliptic coordinates, the boundary conditions of the two types of flow yield linear equations for the determination of the coefficients An and An1. It is further shown that a knowledge of these coefficients leads directly to the sink-source
and doublet distributions corresponding to the axial and transverse flows, respectively.

The theory is applied to a body of revolution obtained from a symmetrical Joukowsky profile, a shape resembling an airship hull. The pressure distribution and the transverse-force distribution are calculated and serve as examples of the procedure to be followed in the case of an actual airship. A section on the determination of inertia coefficients is also included in which the validity of some earlier work is questioned.