Steady performance prediction of a heeled planing boat in calm water using asymmetric 2D+T model

Abstract

This article presents a simple mathematical model for predicting the running attitude of warped planing boats fixed in a heel angle and free to trim and sinkage. The proposed model is based on asymmetric 2D+T theory utilizing a pressure equation which is previously introduced in the literature to compute the hydrodynamic force acting on a heeled planing hull. Integration of pressure distribution on the asymmetric wedge sections enables the suggested model to compute trim angle, center of gravity rise, resistance, and heeling moment acting on the heeled planing boat in calm water. The hydrostatic force in addition to two drag forces acting on the pressure area and spray area are also taken into account. Finally, a computational algorithm is introduced to find the running attitude of the heeled planing boats. The validity of the proposed model is examined by comparing the obtained running attitudes for two planing hulls series with zero heel angle and computed lift force and heeling moment of a heeled planing boat against available experimental data. Based on the comparisons, favorable accuracy is observed for both symmetrical and asymmetrical conditions. Moreover, it is shown that existence of a heel angle can lead to a decrease in trim angle and resistance, while it intensifies the center of gravity rise of planing boats. It is also observed that as the beam Froude number increases, the heeling moment of the heeled boat reduces.