Dynamic motions of planing vessels in head seas

The dynamic response of planing vessels in regular head seas is investigated numerically. Nonlinear time domain simulations were performed using a 2D + t theory (two-dimensional plus time dependent theory). A prismatic hull form was assumed. We employed a two-dimensional (2D) boundary element method to solve the initial boundary value problems in 2D cross planes, in which nonlinear free-surface conditions and exact body boundary conditions were satisfied. At each time step, the total force and moment on the hull could be obtained by using the sectional forces calculated in those 2D planes. Heave and pitch motions were then acquired by solving the equations for those motions. The calculated heave and pitch responses were compared with the experiments by Fridsma (A systematic study of the rough-water performance of planing boats. Davidson Laboratory Report R-1275, 1969) for two different Froude numbers. Three-dimensional (3D) corrections at the transom stern were applied to show the influence of the 3D effect at the stern on the numerical results. Ship motions were affected by the 3D corrections, especially near the resonance frequency, while the phase angles were slightly affected and the acceleration peaks at the bow near the resonance frequency were sensitive to the 3D corrections. Other error sources in the theoretical results are also mentioned.