Predictions of porpoising inception for planing vessels

The inception of porpoising is theoretically predicted for planing vessels. Two different approaches are presented. First, a linear stability analysis is applied to find the porpoising limits while the hydrodynamic coefficients, i.e. added mass and damping coefficients, are determined by either a simplified method or a numerical method. Another approach is to seek the porpoising limits by performing nonlinear time domain simulations. Either the simplified method or the numerical method is used in the simulations. In the numerical method, a 2D+t theory together with a boundary element method is employed. The trim angle limits for porpoising are determined by changing the longitudinal position of the centre of gravity (COG) of the vessel and keeping the forward speed constant. The predicted porpoising limits are compared with Day and Haag’s (Planing boat porpoising, Thesis, Webb Institute of Naval Architecture, 1952) experimental results. The influences of parameters such as the load coefficient, the vertical position of COG and the radius of gyration of the ship are investigated by varying those parameters in the linear stability analysis. In the nonlinear time-domain simulations, by trying different longitudinal position of COG, one can find the critical trim angle when the porpoising commences. The obtained trim limits agree generally with those predicted by the linear stability analysis. Bounded oscillations for the unstable cases near the critical trim angle can be seen in the time-domain simulations due to the nonlinear effects.