Surf-riding and broaching in severe following and quartering seas are vital threats for the safety of fast naval and fishing vessels. Excessive roll motions and even capsizing due to lose of stability can occur under surf-riding and broaching. The rudder and its resulting moments are important for the onset of broaching after surf-riding. Thus, the rudder actions under surf-riding condition which lead to ship broaching are identified in this research based on the developed numerical model incorporating the dynamics of rudder and propeller. Numerical simulations on cases with 1, 2 and 3 degree of sudden rudder actions under surf-riding condition are conducted with small and high Froude numbers. It is found that the state of ship motion is not altered by the small rudder disturbance under small Froude number. However, under high Froude number, the state of the vessel is very unstable, and can be easily altered by the small rudder disturbance.


In severe following and quartering waves, high-speed vessels can be accelerated to surf on the wave by the wave surging force. This phenomenon is known as surf-riding. Under the surfing condition, the vessel is in a very unstable dynamic state. Excessive yaw and roll motions can easily occur even with a small disturbance. These excessive motions are referred as broaching and capsizing after surfriding. The rudder is believed to be an important source of disturbance which leads to broaching and even capsizing. It is anticipated that unnecessary rudder actions might induce broaching. Therefore, rudder actions under surf-riding conditions which lead to ship broaching and capsizing are identified in this paper.

Over the last few decades, many efforts have been made on the research of surf-riding and broaching. Grim (1951) conducted the pioneering work on surf-riding based on analytical formula. From then on, researches on surf-riding and broaching are conducted through nonlinear dynamics approaches (Umeda, 1999; Makov, 1969; Spyrou, 1996), numerical simulations (Umeda and Hamamoto, 2000; Umeda and Hashimoto, 2002; Yu, Ma and Gu, 2014) and model experiments(Umeda et al., 1999; Yu et al., 2016; Gu et al., 2018). As an output of these continuous efforts, the draft amendments to Part B of the 2008 IS code to assess broaching are proposed recently in IMO (IMO SDC6/WP.6, 2019). However, as a strongly nonlinear phenomenon, surf-riding and broaching are affected by various factors and detailed investigation needs to be conducted.

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