Experimental Study on Extinction Curve Fitting Expressions of Ship Roll Damping

Abstract

Roll damping plays a crucial role in the accurate prediction of ship roll motion. In potential flow theory, viscous roll damping is not inherently accounted for and therefore must be introduced through experimental model test results. Free roll decay tests are commonly conducted to determine roll damping characteristics, including both linear and nonlinear damping (quadratic) components. In experimental practice, roll damping coefficients obtained from roll decay tests are often expressed using different mathematical formulations, such as linear, quadratic, and Bertin’s equations. In this study, free roll decay tests were performed on three ship models, and the resulting roll decay responses were analyzed using the three damping expressions for curve extinctions of measured data. The linear and quadratic roll damping coefficients were extracted for each model and formulation. The results indicate that the selected extinction curve expression and fitting method significantly influence the estimated roll damping coefficients. In addition, the choice of using peak-to-peak or trough-to-trough data in the roll decay analysis was found to affect the obtained damping values. Based on the comparative analysis, it is concluded that averaging the damping coefficients derived from both peak-based and trough-based fitting provides a more representative estimation of roll damping for the tested ship models.