A six-DOF theoretical model for steady turning maneuver of a planing hull

Abstract

The current paper presents simulations for steady turning of a planing craft by developing a new mathematical model. To solve the problem, it is assumed that the craft is free in six-degrees of freedom and all motions are strongly coupled. Maneuvering forces and moments acting on the vessel are computed using 2D + T theory. Virtual added mass terms of two-dimensional (2D) sections are integrated over the entire length of the craft. The final equation for the motion of the vessel in six-degrees of freedom is obtained which is then solved in the time domain. Final three-dimensional (3D) forces and moments contain strongly coupled added mass, damping, steady maneuvering, and restoring hydrostatic forces and moments. Simulations are compared against experimental data and it is shown that the developed method has reasonable accuracy in prediction of turning motion of two planing vessels. Effects of beam Froude Number and rudder angle on steady turning motion of a planing hull have also been studied. It is found that when the vessel is free in six-degrees of freedom, the turning radius and yaw rate of the vessel are smaller while the steady surge speed is not affected significantly.