Abstract
A formula based on Maruo’s theory is presented for the added resistance in regular head seas when parametric rolling occurs. Firstly, the velocity potential of the radiation waves due to parametric rolling, sway and yaw motions should be superposed on the conventional velocity potential. Secondly, the added resistance is averaged within the time duration that is double the encounter period. Thirdly, the stationary-phase method which is used in Maruo’s method is also used to obtain the formula of added resistance in waves with parametric rolling taken into account as well as viscous roll damping. Fourthly, source distribution based on Maruo and Ishii's and Maruo and Iwase’s works is used to calculate the added resistance. Finally, the effect of parametric rolling on added resistance in regular head seas mainly results from viscous roll damping and it becomes larger as the amplitude of parametric rolling becomes larger.
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