The Shallow Water Effect on Linear Derivatives

Abstract

Ship manoeuvring studies require that the derivatives in the equations of motion are known for the particular ship. This is accomplished by calculation or experiment in deep water, but there are problems in shallow water, since the derivatives become functions of water depth, as well as ship geometry. A simple semi-empirical correction has been previously published, but has now been found to be in error. Revised equations are given here for the case of hulls with elliptical body sections and new equations are suggested for hulls with rectangular body sections. These equations can then be used to scale the deep water derivatives to values appropriate to a particular shallow water condition.