Model experiments and direct stability assessments on pure loss of stability in stern quartering waves

The criteria for direct stability assessment of pure loss of stability are currently under development at IMO as part of second-generation intact stability criteria. For providing an accurate and practical mathematical model, a four-stage approach has been adopted herein. Firstly, a surge-sway-heave-roll-pitch-yaw coupled mathematical model (6-DOF) is newly established, with unified expressions based on an MMG standard method and existing mathematical models of broaching and parametric rolling. The heave and pitch motions are obtained by a strip method with the speed variation considered. They determine the instantaneous relative position of the ship to waves. Then, the corresponding nonlinear Froude-Krylov roll restoring variation is calculated by integrating the wave pressure up to the wave surface. Secondly, model tests are carried out in stern quartering waves to validate the predictions. Thereafter, the effect of some crucial terms on the prediction is studied. Terms such as the higher-order manoeuvring coefficients, the rudder force, the diffraction forces are investigated. Finally, the types of roll motions observed during pure loss of stability are identified. The results show that pure loss of stability is not "pure" but the proposed coupled 6-DOF model can be utilized for the direct assessment of the vulnerability at this failure mode.