Investigation of Sway, Roll and Yaw Motions of a Ship with Forward Speed: Numerical modeling for flared up conditions

The paper deals with the numerical modeling of sway, roll and yaw motions of a ship for flared-up conditions with zero or nonzero forward speeds in sinusoidal waterway. To compute hydrodynamic forces, we employ nonlinear roll restoring characteristics and speed dependent strip theory that are obtained from the Frank's close-fit method. The governing equations are solved numerically by using Runge-Kutta-Gill method with adaptive step size adjustment algorithm. In order to investigate the effect of nonlinear restoring in roll, numerical experiments have been carried out for a Panamax Container ship under the action of sinusoidal wave of periodicity 11.2 sec with varying wave height and speed. To emulate the soft spring behaviour, nonlinear restoring moment is represented by an odd order polynomial of roll angle where the corresponding coefficients are obtained by analyzing the results of numerical experiments. This modeling approach provides an important guideline to understand the role of various parameters while flared up conditions occurs, emphasizing the need for its controlling mechanisms.