On the transition to planing of a boat

Abstract

This paper is concerned with the problem of the transition to planing of a boat. A steady-state nonlinear solution of the problem is obtained using a theory of fluid sheets for two-dimensional motion of an incompressible inviscid fluid contained in the paper of Green & Naghdi (1977), together with appropriate jump conditions demanded by the theory. The motion of the fluid is coupled with the motion of a free-floating body and detailed analysis is undertaken pertaining to such features as the sinkage, the bow-up trim angle and the determination of the propulsion force. In particular, the results show that the governing mechanism of the hump speed phenomenon is the change in the bow-up trim angle of the boat. The differential equations and the relevant boundary conditions of the problem are reduced to a system of essentially algebraic equations whose solutions are obtained numerically.