Abstract
A general expression for the pressure distribution on the inclined flat rectangular bottom of a ship penetrating the water surface is derived by matched asymptotic expasion on the bases of the shallow draft and gravity free assumptions which are essentially equal to those made by Wagner in the 2-D theory. The flow field is divided into two regions, the outer region where the linearity assumption holds and the 3-D flat plate formulation is utilized to have the outer solution and the edge region where the impact phenomena occur and the solution is constructed by using its flow similarity to the 2-D planing plate case of which solution is known analytically. Both solutions are matched asymptotically to make them determinate and the composite solution valid in the entire region is derived. The calculated results are compared to the experiment which was conducted to measure the pressure distribution over the inclined box-shaped hypothetical ship. Some of the assumptions made in the present formulation such as uniform tranverse distribution and no pileups of the perturbed water are found to be satisfactory by comparison with the experiment. Agreements in the peak impact pressure are very good if considerations are made to the fact that the measured peak pressure has averaged value over the pressure gauge membrane.
