On the Parametric Resonance of Tumblehome Hullforms in a Longitudinal Seaway

Abstract

This work presents a numerical study of the influence of topside shape on parametric roll in longitudinal seas. The ONR 3 Topsides hulls are used to compare the single degree-of-freedom rolling response of a destroyer-sized vessel with flared (model 5613), tumblehome (model 5613-1), and wallsided (model 5613-2) shapes above the waterline. Through this relative comparison, the key aspects of parametric resonance of a tumblehome hullform are highlighted, namely the reduction in head seas forward speed required to encounter parametric roll. A variant on the Mathieu equation is used to simulate roll motions.