A submerged body's dynamics model in vertical plane is proposed to simulate motions near free surface. First, a mathematical model is proposed to calculate the wave forces acting on a submerged body, which is based on the wave exciting forces and moments acting on a square pillar. Second, the free surface effect acting on a hull is considered. Finally, a mathematical model for control forces is suggested, which considers the free surface effect and wave orbital motions of fluid particles. Through this process, a control system was designed that can maintain a constant depth below the mean sea level and minimize the pitch angle.
A submerged body, operating beneath a free surface, is subjected to the effects of free surface and incident waves. When wave exciting forces and moments are exerted on the submerged body, suction forces will increase to pull the body to the free surface. If the wave suction forces are greater than the control forces, the submerged body will broach the free surface. Therefore, for submerged bodies moving in the region near free surface, to keep the constant depth is very important for safe operation. Richards and Stoten (1981) proposed a mathematical model of wave exciting forces and moments by sea waves which includes irregular wave loads and effect of the submerged depth. Furthermore, they investigated the control of a submerged body with low speeds in shallow water. Dumlu and Istefanopulos (1995) suggested a submarine's dynamics equation considering the effect of auxiliary tank, and designed a controller with stochastic theory. Sadko (1998) presents wave spectrum and mathematical model of wave with respect to submerged depth. In previous studies, the wave forces and moments with respect to submerged depth were considered in dynamics equations. However, they did not consider the free surface effect on the hydrodynamic coefficient in the equations of motion.
