An analytical procedure for time domain simulation of roll motion of the warped planing hulls

Abstract

Prediction of the roll motion is considered as an important problem in planing hull motion, since safety of the craft highly depends on it at high speeds. Accordingly, the main aim of the present study is to analyze this motion in time domain and estimate its amplitude at various frequencies. In many of the earlier works performed for predicting the motion of planing hulls, the 2d + t theory has been used. However, in all of these studies, water entry phenomenon was modeled without considering the asymmetric condition. In order to overcome this problem, a mathematical model is hereby proposed for prediction of the roll motion which is derived by applying an analytical model of the water entry in which asymmetric condition is taken into account. The suggested method may be used for the warped planing boats. Validity of the model is examined by comparing the obtained results against different experimental results. Another objective of the present study is to examine the effects of deadrise angle, longitudinal center of the gravity and the hullform on the amplitude of motion and hull response. The response is investigated at different conditions: (1) sinusoidal exciting moment, (2) a fixed existing moment and (3) an initial roll angle without any exciting moment. The proposed model is also used to evaluate the horizontal forces and moments acting on the hull during the roll motion.