Theoretical Investigations on Slamming of Cone-Shaped Bodies

Abstract

A general expression for the pressure distribution on a cone penetrating the water surface is derived from the similar procedure developed by Wagner for a wedge. The effect of trapped air between the falling body and the water is ignored for this investigation. The pressure distributions, velocity potentials, stream functions, and piled-up water phenomenon are summarized and compared with those for the wedge. Wagner provided a theoretical analysis on the slamming of a wedge [1,2,3].3 His approach was to approximate the wedge as an equivalent flat plate provided that the wedge had a small deadrise angle. By means of the velocity potential technique and the Bernoulli equation, he derived equations for determining the pressure distributions on the impact surface of the wedge. A cone piercing the water surface has been studied experimentally by Watanabe [4] and theoretically by Shiffman and Spencer [5]. However, their work provided only the total force acting on the impact surface of a cone. The purpose of the present work is therefore to determine theoretically the slamming pressure distribution of a cone. The similar approaches developed by Wagner for his wedge equations are used for this investigation.