On the High-Speed Porpoising Instability of a Prismatic Hull

Abstract

Simple closed-form solutions are obtained for the steady-state and transient forces and moments on a prismatic hull at speeds high enough for hydrostatic forces to be negligible and the chines to be above the undisturbed water surface ("chines dry"). We first show that this solution can be transformed to get the correct results for other hydrodynamic problems, such as the vertical impact of a wedge, a slender foil, or the two-dimensional planing of a flat plate. We then show that the full transient solution is essentially identical with Ribner's [1]2 equations for delta wings, except for terms which depend on the reduction in wetted width with heave. These results are employed to study the stability of such a hull on the assumption that only heave and pitch degrees of freedom are important, following the reasoning of Per̂ing [2]. In contradistinction to all four previous studies [2–5], the effect of skin friction is included and is found to be very powerful. If the center of gravity is above the centroid of the wetted area (which it generally is), then the effect of skin friction is stabilizing.