Roll dynamics of a Ro-Ro ship

The prediction of ship stability during the early stages of design is very important from the point of safety. Ships experience six modes of rigid body motions in a seaway, which can be split into two groups as translatory and oscillatory motions. Out of the six motions of a ship, the critical motion leading to capsize of a vessel is the rolling. In the present study, particular attention is paid to the performance of a ship in beam sea. The rolling motion of a ship has been described by a nonlinear differential equation taking into account the nonlinearities in both the restoring moment and the damping moment. Solution of differential equation of roll motion is sought using MATLAB. The effect of different representation of restoring moment on roll motion is investigated. It is seen that, the effect of different representation of restoring moment on roll motion depends on the characteristics of the GZ curve. A parametric investigation is undertaken to identify the effect of different parameters viz., wave steepness, encountering frequency etc., on the capsizing conditions of a ship. The rolling response of ship is determined in the frequency domain. The analysis has been carried out by varying both the wave steepness and the wave frequency. The approach has been demonstrated considering a Ro-Ro ship as test vessel.