Computation of Wave Resistance and Ship Wave Pattern by the Slender Body Approximation

Abstract

A new approach to the slender body theory for a ship with forward velocity was presented by Maruo in 1982. This new slender ship theory (NSST) is based on an asymptotic expression of Kelvin-source around its track and quite different from other slender ship theories. The source density on the hull surface is determined by an integral equation of the Volterra type of the second kind instead of that of the Fredholm type of the Neumann-Kelvin problem. In the present paper, NSST is applied to the numerical solution for Wigley model. Distributions of source and pressure on the hull surface are solved by marching integration. Wave resistance is obtained by integrating pressure on the hull surface and the values agree well with measured ones. Then wave pattern of the model is calculated and the result is compared with measurement. On the other hand, since E function in the asymptotic expression of Kelvin-source is the complicated formula, it must take much operation time of an electronic computer to calculate E function precisely. A formula of fast numerical solution to E function is also presented in the paper.