Coupled roll and directional stability characteristics of surface ships.

Abstract

The problem of roll, sway and yaw motions of surface ships is considered. A mathematical model is developed which consists of the nonlinear maneuvering equations and incorporates cross coupling between sway force, yaw moment and the roll angle induced during a steady turn. The hydrodynamic derivatives and coefficients of a typical container ship were used as the base-line study model. The coupled system of nonlinear algebraic equations is formulated and solved to predict the steady state roll angle, sway velocity and turning rate as a function of the rudder angle. The results are then compared to that of the decoupled systems currently employed. A local perturbation is implemented in the vicinity of the above steady states to investigate dynamic stability of motion. Sensitivity analysis with respect to important design parameters such as speed loss during turning, approach speed, transverse metacentric height and trim is performed. Results demonstrate the significance of the coupling between roll, sway and yaw and the need to incorporate similar studies in the ship design and analysis process.