Objectives  Surf-riding/broaching is one of the five stability failure modes included in the second generation intact stability criteria by IMO. The current regulation is limited by only applying to ships using propellers. To address this issue, this paper carries out some investigations concerning the surf-riding stability failure of ships using water-jets, so that the regulation can be further completed.

  Methods   Based on the mechanical model of the water-jet unit and the one-dimensional surge motion equation of sequential waves, a mathematical surf-riding model is established. The fourth order Runge-Kutta method is used to solve the equation, and a time domain surf-riding simulation for the water-jet propelled ship is achieved. Taking one high-speed wave-piercing tumblehome as a sample ship, the characteristics of the conditions for the occurrence of surf-riding are obtained through systematic time domain simulations.

  Results  The result shows that, within the range of wave conditions required by IMO's second generation intact stability criteria, surf-riding occurs in 80.9% of cases when the Froude number is 0.4; when the Froude number is reduced to 0.3, the percentage drops to 59.4%.

  Conclusions  This study provides the theoretical model and the numerical approach necessary to evaluate the surf-riding/broaching stability of ships propelled by water-jets, which can be used to evaluate the stability safety of this type of ship.