Calculation of Hydrodynamic Forces on a Ship in Waves Based upon Thin Ship Theory

Abstract

A computational method for three dimensional hydrodynamic forces on a ship with arbitrary hull form advancing in head sea condition is discussed based upon Hanaoka's thin ship theory. Following the linearization of the problem, it is shown that potential functions of Michell's type can be expressed explicitly and the hydrodynamic forces can be integrated directly from the potentials multiplied by hull form curvature in the vertical direction owing to the thin ship assumption. The finite Fourier series is introduced to express aribtrary hull geometry. Upon substitution of the hull form into the hull form characteristic functions, it is shown that the formula for the forces are expressed in a series with special functions like Bessel, Struve and Weber functions. The computation for the radiation and diffraction forces is done for a container ship and the results show good agreement with a strip theory calculation in lower speed range. Discussion is also given to characteristics of the integrands and integration scheme to show that the present method has advantage over other three dimensional calculation methods in both ease of numerical computaion and the accuracy of the results.