A Prediction Method and Model Experiments on Surf-Riding and Broaching in Stern-Quartering Waves

At present, the International Maritime Organization (IMO) has issued interim guidelines for the direct stability assessment of surf-riding and broaching for the second-generation intact stability criteria. Accurately and efficiently predicting surf-riding and broaching remains a key problem to be solved for the direct stability assessment of surf-riding and broaching. Therefore, a six-degree-of-freedom(6DOF) coupled mathematical model is established in this paper. Firstly, the four-degree-of-freedom(4DOF) coupled equations of surge–sway–roll–yaw motions are built based on the traditional MMG maneuvering mathematical model by considering Froude–Krylov forces, diffraction forces and restoring forces, and the heave and pitch are approximately calculated by iteratively solving improved static equilibrium equations in real-time, effectively solving the divergence problem in direct time-domain seakeeping calculations of high-speed ships in stern-quartering waves. Secondly, the hydrodynamic lift forces due to the coexistence of wave particle velocity and ship forward velocity are taken into account in the propeller-thrust and rudder-force models. In addition, the real-time emersion of twin rudders in waves is considered in the rudder-force models. At the same time, the free-running model experiments with a ONR tumblehome vessel are carried out in stern-quartering waves, and the pure loss of stability and broaching motions are observed. Finally, comparative validations between the calculations and the experiments of surf-riding and broaching in stern-quartering waves are carried out, and the effects of the ship speed, the instantaneous wetted surface of the hull, rudder exposure, heave and pitch motions on predicting surf-riding and broaching motions are investigated. The computation results show that the established 6DOF mathematical model has enough accuracy to be used for the direct stability assessment of the surf-riding and broaching failure modes.