An Approximate Calculation Method for Maneuvering Hydrodynamic Forces in Shallow Water

Abstract

Assuming that a ship's hull can be replaced by a rectangular flat wing, a simplified method is examined for calculating the hydrodynamic forces and shedding angles of the trailing vortices in shallow water. This method is based on the INOUE's method developed by applying the nonlinear lifting surface theory. The integral equation, which determines the vorticity distribution and the shedding angle, is solved under the condition of finite water depth. In order to obtain better agreement between observed and calculated values, some discussions are made for improvement of the prediction procedure. A comparison is made between the shedding angles evaluated using induced velocities on wing surface and at the location of trailing vortex. And these calculated values are compared with experimental results. Furthermore, it is indicated that to take account of the retained circulation effect is essential for predicting the hydrodynamic forces in shallow water. By adopting the measured values as the shedding angles, calculation of the hydrodynamic forces is made changing values of the retained coefficient which is defined as the ratio of vorticity at the tip to uniform spanwise vorticity. As a result, it is confirmed that there is a tendency for values of the coefficient to increase with decrement of water depth.