A unified numerical method for broaching and loss of stability in astern seas

The interim guidelines of second-generation intact stability criteria and their explanatory note were issued by the IMO in 2022. However, due to their complexity, the direct stability assessments of broaching and loss of stability still need to be made easier for users. Therefore, the mathematical models for broaching and loss of stability in astern seas are studied in this paper. Firstly, a time-domain 6 DOF numerical model is adopted, combining seakeeping and maneuvering mathematical models. Secondly, the hydrodynamic forces, heave, and pitch motions are obtained by an enhanced strip method with the upright hull at different speeds in the frequency domain. Then, their time-domain values are transferred from their frequency-domain values with the speed variation considered. Thirdly, the time-domain varied wet hull in waves is captured by the 6 DOF ship motion. Then, the Froude–Krylov and the hydrostatic forces in the surging, swaying, rolling, and yawing directions are simulated considering the wave pressure around the wet hull. Fourthly, the exposure of the twin rudders and the wave-particle velocity are considered for predicting broaching. Finally, the calculated results are compared with the published results. The results show that the time-domain 6 DOF coupled numerical model can be unified for predicting broaching and loss of stability in the astern seas.