A study of hydrodynamics of three-dimensional planing surface

The hydrodynamic problem of 3D planing surface is studied by a finite element approach. The planing surface is represented by a number of pressure patches whose strengths are constant at each element. The unknown pressure strength is obtained by using the free surface elevation condition under the planing surface and Kutta condition at the transom stern. Previous studies indicate that, when the constant pressure distribution method is used, the number of buttocks should be less than five or six, otherwise the calculated pressure distribution will start to oscillate and even become divergent. In the present study, after careful examination of the influence coefficients, it is found that the accuracy of the influence coefficients matrix is very important to the convergence of the solution, especially when the number of elements is relatively high. The oscillation of the pressure distribution can be avoided by constant element method if the influence coefficients are sufficiently accurate. The predicted results of the present paper with more number of buttocks are in good agreement with other researchers'. It is concluded that the irregularity of the pressure distribution found in previous studies is most likely caused by the low accuracy in their calculation of the influence coefficients, not by the method itself.