The wave resistance of an ellipsoid

Abstract

1. In a recent paper* it was shown how to obtain, to the usual approximation, the wave resistance of a solid of ellipsoidal form submerged at a constant depth below the surface of water and moving horizontally with any orientation of the axes ; and explicit calculations were made for prolate and oblate spheroids moving end-on and broadside-on. The present note is a brief study of an ellipsoid with unequal axes, moving in the direction of the longest axis. It had been intended to examine numerically in some detail the effect of different ratios of the axes upon the resistance-velocity curve ; but the necessary computations would have been lengthy, and the main results of interest may be seen from the form of the expressions obtained for the wave resistance. In the discussion attention is directed specially to cases in which the ratios of the axes are similar to the corresponding ratios for a ship. 2. It is convenient first to evaluate some integrals which occur in the analysis.