The paper presents a three-dimensional solution for the exciting forces and moments on a ship in waves. Basically the general formulations are based on the source distribution technique, by which the ship hull surface is regarded as the assembly of many panels. With the simplified free surface condition, the influence of ship speed on the hydrodynamic forces is then considered through its modifications of the pressure calculation, body boundary condition and additional contour integral along the interaction of hull surface and the free surface. Three algorithms for treating the corresponding Green functions are used, i.e. (1) The Hess & Smith algorithm for the part of simple source l/r. (2) The complex plane contour integral of Shen & Farell's algorithm for the Double integral of steady flow. (3) The series expansions of Telste & Noblesse's algorithm for the part of Cauchy principal value integral of unsteady flow. The present study reveals that the effect of steady flow is generally small, but it still cannot be neglected in some cases especially for the ship in oblique waves. It is also found that the suitable selection for the body mesh distribution is important by using the present technique.


The two-dimensional theoretical methods, either the ordinary strip theory or the modified strip theory, have been applied to predict the ship motion in waves for many years. Some authors have offered remarkable contributions in the corresponding respects, e.g. KorvinKroukovsky(1955), Salvesen et. al.(1970) and Kim et al.(1980). Recently, because of the amazing development of the high efficient computer, the three-dimensional theory can then be applied to analyze the corresponding hydrodynamic problems. Two classes of linearized theories conventionally have been solved using entirely different methods:

  • Rankine singularity method and

  • Kelvin-Havelock singularity method.

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