Computer programs for predicting motions of a ship or barge in waves usually include a viscous roll damping component, representing the effect of vortex shedding at bilge keels and other sharp edges. The viscous roll damping term is usually calculated by means of an empirical formula, and the predicted motions tend to vary according to the procedure chosen. Comparisons with model test data suggest that the theoretical discrete vortex method can predict the roll damping of rectangular barges with sharp corners and bilge keels quite well, but there seems to be no entirely satisfactory method for rounded sections. This paper investigates the form of the viscous roll damping term, and possible ways in which sway and heave motions of the vessel and wave particle motions might affect the roll response. Numerical examples suggest that the roll and sway equations may be decoupled if the motions are defined relative to a certain "roll centre". Sway, heave and particle velocities may also affect the roll response through relative velocity terms implicit in the vortex damping formula. These relative velocity terms were found to have little effect on the roll response, however, justifying the use of a vortex damping term which depends on roll velocity only. Comparisons with motions measured during model tests in regular and irregular waves confirmed the general conclusions of the numerical study, and supported the practice of determining the roll damping from forced-roll or free-decay model tests or simulations in still water. The sample calculations were performed using both time-domain simulations and frequency-domain methods, the latter with equivalent linearisation of the quadratic damping term. Frequency domain methods are more economic, and satisfactorily predicted roll motions in regular waves and the exceedance distribution of response in irregular waves.

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