Effects of vertical motions on roll of planing hulls

Roll motion of a planing hull can be easily triggered at high speeds, causing a significantchange in hydrodynamic pressure pattern, which can threaten the stability of the vessel.Modeling and investigating roll motion of a planing vessel may require a strong couplingbetween motions in vertical and transverse planes. In the present paper, we have used amathematical model to analyze the roll of a planing hull by coupling surge, heave, pitch,and roll motions using 2D+T theory to study the effects of roll-induced vertical motionson roll coefficients and response. Mathematically computed forces and moments as wellas roll dynamic response of the vessel are seen to be in fair quantitative agreement withexperimentally measured values of previously published data. Using the 2D+T method,it has been shown that to model the roll of a planing hull at high speeds, we need to considerthe effects of heave, pitch, and surge motions. Through our mathematical modeling, it isfound that freedom in vertical motions increases time-dependent roll damping and addedmass coefficients, especially at early planing speeds. The results of dynamic response simulationssuggest that freedom in the vertical plane can decrease the roll response