On wave resistance

Abstract

The case here considered is that of a solid whose dimensions are small compared with its depth below the free surface, travelling horizontally under water. The particular case of a circular cylinder advancing at right angles to its length was easily solved from considerations of group-velocity. The more difficult problem of the sphere was worked out by Havelock by direct calculation of the pressures exerted on its surface. In a subsequent paper this rather arduous process was avoided by a calculation of the travelling pressures, applied to the free surface, which would produce the same wave system. The work done by these must be equivalent to that which, in the actual case, is expended on the sphere to maintain its motion. The same principle was further employed by him to find the wave-resistance of other solids of revolution, in particular that of a spheroid. There would appear to be room for an investigation on a more general plan in which no restriction is made as to the form of the solid, which affects only the values to be attributed to certain constants (familiar in another connection) in the final results. For example, it is not necessary even to assume that the solid is moving in one of the directions of free “permanent translation” of which it is capable, and some attention is paid to cases where this condition is departed from. As a further variation from previous methods a small viscous force is introduced, and the work done against resistance is equated to the dissipation of energy.