Strip Theory for Underwater Vehicles in Water of Finite Depth

This paper addresses the need to know the unsteady forces and moments on an underwater vehicle in finite depth water, at small enough submergences for it to be influenced by sea waves. The forces are those due to the waves themselves as well as the radiation forces due to unsteady vehicle motions. Knowledge of these forces and the mass distribution of the vehicle allow solution of the equations of motion at a single frequency. Since the theory is linear, any incident wave field can be decomposed into the sum of many individual single frequency sinusoidal waves. The motions due to each frequency component can then be added together to obtain the total predicted vehicle motions. The wave forces are due to the undisturbed sea wave plus those due to the diffracted wave necessary to satisfy boundary conditions on the vehicle. The long used strip theory for ships, with the inviscid flow approximation, is modified for finite depth and inclusion of lift forces on the vehicle fins. The two dimensional solutions for the forces on each strip are found by a different method than is commonly used for strip theory. This form of the theory is easier to deal with and requires much less computing time than a fully three-dimensional approach. Experiments are conducted and their results are compared with the theory. Excellent agreement is found between the theoretical and experimental wave forces, including the diffracted wave. It is shown that inclusion of the forces on the fins not only improves the theoretical wave forces, but also brings the results of theory for the radiation forces and moments due to vehicle motions much closer to the experimental values that the theory without inclusion of fin lift forces.