Determination of the Unknown Wetted Surface of Planing Plates by a Formulation Based on High Aspect Ratio Approximation

Abstract

This paper attempts to determine the unknown wetted surface of a free-running planing plate. The perturbation method is applied to analyze both the near and far field flow around a restrained planing plate with comparably large breadth, disregarding gravitational effects. The matching process of each height of water surface leads to a non-linear system of integro-differential equations to determine the distributions of both the wetted length and the apparent circulation around the plate. The serious solution of reduced single integral equation, still holding 3-dimensional characteristics but the so-called downwash effects, diverges from the assumed high aspect ratio solution because of the logarithmic non- linearity. The equation gives an insight into static stability in performance and the limitation in height to restrict the plate in exposure above still water. The configuration of wetted surface obtained displays the behaviour of the spray root line crossing the hard chine well, however, it is unfortunately rather wide to coincide with the experimental one. The free-running condition is estimated.