Theoretical study on the effect of parametric rolling on added resistance in regular head seas |
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| Authors: | Jiang Lu Naoya Umeda Kun Ma |
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| Institution: | (1) Department of Naval Architecture and Ocean Engineering, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian, 116024, Liaoning, China;(2) Department of Naval Architecture and Ocean Engineering, Osaka University, 2-1 Yamadaoka, Suita Osaka, 565-0871, Japan;(3) Ship CAD Engineering Centre, Dalian University of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian, 116024, Liaoning, China |
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| 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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