Polynomial model and extinction curve analysis of ship viscous roll damping by way of decay data

The accurate prediction of ship roll motions requires reliable estimation of viscous roll damping, which remains a challenging task due to the non-linear and amplitude-dependent nature of roll dynamics. In this study, the viscous roll damping of ships is investigated through model tests and computational fluid dynamics simulations. A large container ship, dominated by linear damping, and an offshore supply vessel, characterised by non-linear damping, are selected as representative case studies. Free roll decay motions under different initial roll angles are analysed, and linear and non-linear viscous roll damping coefficients are identified using polynomial extinction curve fitting within the framework of polynomial damping models. Equivalent linear roll damping coefficients corresponding to different damping models are subsequently determined by means of the energy method. The comparative analysis reveals the influence of alternative polynomial damping models and extinction curve analysis methods on viscous roll damping estimation. Based on these findings, a recommended methodology for calculating viscous roll damping from free roll decay data is proposed, providing improved accuracy and applicability for ship motion prediction.