Lateral forces on ships in steady motion parallel to banks or beaches

A mathematical formulation for the motion of a slender ship in shallow water parallel to straight bottom contours is described. From this, a singular integral equation which determines the vorticity on the ship is derived, together with a numerical procedure for solving this integral equation. Particular attention is paid to the trailing edge of the ship, so that the correct solution of the integral equation is found. Numerical results for the cases of a bank or a uniformly sloping beach are provided. The effect of changing the water plane shape of ships is investigated, as well as the effects of changing the local water depth, distance to beach or bank, beach angle and yaw. General conclusions are drawn where possible and illustrate the properties of the bottom geometry.