Development and Optimization of Mathematical Model of High Speed Planing Dynamics

A nonlinear mathematical model capable of prediction load and motions of high speed planing craft in the longitudinal plane has been developed. The development of the model is based on the mathematical model presented by Zarnick (1978). Following the principle of 2D strip theory and wedge water entry problem, a high speed planing hull is divided into a number of transverse sections. Sectional forces are evaluated, and then, integrating along the ship length, total force and moment are obtained which leads to corresponding instantaneous acceleration. By integration using a time marching scheme, velocity and displacement are obtained. Solution of the motions of a planing craft based upon strip theory and wedge water impact is well known and offers fast computational times useful for simulation and design. However it is necessary to understand the balance between rapid computation and accuracy of this approach. Thus, The influence of the controlling parameters, such as number of sections and time step, in the accuracy, stability and computational times of the simulation in calm water and regular waves is investigated. The optimum model is finally validated against the original model of Zarnick (1978) and the experiments of Fridsma (1969)