Porpoising and Dynamic Behavior of Planing Vessels in Calm Water

摘要

The inception of porpoising instability can be predicted by a linear stability analysis. However, the hydrodynamic coefficients, i.e. the added mass and damping coefficients as well as restoring force coefficients, in heave and pitch need to be known in advance. In this paper, these coefficients are calculated by using a 2D+t theory and a Boundary Element Method (BEM) with fully nonlinear free surface conditions with gravity and exact body boundary conditions. The calculated hydrodynamic coefficients depend on the oscillation frequency and the Froude number. In order to investigate the influence of different parameters of the planing vessel to the porpoising limits, a simplified method is applied to calculate the hydrodynamic coefficients. These coefficients are utilized in the linear stability analysis to predict the inception of porpoising. It is found that the load coefficient, the pitch radius of dyration and the vertical position of the centre of gravity can influence the theoretical porpoising limits. The theoretical limits deviate from the experimental limits especially for larger load coefficients. However, by using the 2D+t theory and the BEM to calculate the hydrodynamic coefficients, the agreement can be improved. Finally, a nonlinear time-domain simulation is performed to show the bounded oscillations when porpoising happens.