The Effect of Air Compressibility in a First Approximation to the Ship Slamming Problem

It has been suggested that the high pressures exerted on the bottom of a ship's hull during slamming are developed in the air trapped between the hull and the water's surface. To test this hypothesis, the two-dimensional, unsteady problem of the flow of air, where compressibility is accounted for, between a rigid, flat-bottomed block falling towards a rigid plane, is solved using a numerical method. The computed pressures exceeded those found experimentally by Maclean [8],2 and it is concluded that the deformation of the water's free surface must be accounted for in order to obtain agreement with the experiment. To the author's knowledge, the numerical method, a modified version of Sauer's method of Near Characteristics, is applied here for the first time, and a maximum allowable time step, for this problem, is found by digital computer experimentation.