Dynamic motions of planing vessels in head seas

Abstract

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.

KeywordsPlaning vessel–2D+t theory–Boundary element method–Seakeeping–Regular waves