A Numerical Method on Large Roll Motion in Beam Seas Under Intact and Damaged Conditions

The second-generation intact stability criteria, including five stability failure modes, were approved by the International Maritime Organization (IMO) in 2020, and it is an urgent task to develop the numerical method for the significant roll motion under dead conditions. Both intact and damaged stability focus on the large roll motion in beam seas. A unified numerical method is studied to predict the large roll motion in regular and irregular beam seas under intact and damaged conditions. Firstly, a sway–heave–pitch–roll–yaw coupled equation named 5-DOF and a sway-roll-yaw coupled motion with the roll-righting arm in still water named 3-DOF are used to predict the large roll motion in regular beam seas under the intact and damaged conditions. Secondly, the method is extended for the large roll motion in irregular beam seas, where the diffraction force in the roll direction and the sway and yaw motion under intact and damaged conditions are calculated by the subharmonic superposition method. Thirdly, the roll-righting arm in the calm water, roll-damping coefficients, and the roll natural roll period, under the intact and damaged conditions, are obtained by software and a free roll decay experiment, respectively. Finally, the numerical results of a patrol boat under intact and damaged conditions are compared to the experimental results. The results show that the sway-roll-yaw coupled motion with the roll-righting arm in still water named 3-DOF can predict the large roll motion in regular and irregular beam seas under intact and damaged conditions.