Analysis of Roll Decay for Surface-ship Model Experiments with Uncertainty Estimates

Roll decay of David Taylor Model Basin (DTMB) Model 5720, a 23rd scale free-running model of the research vessel (R/V) Melville, is evaluated with uncertainty estimates. Experimental roll-decay time series was accurately modeled as an exponentially decaying cosine function, which is the solution of a second-order ordinary differential equation for damping coefficient of less than one (N < 1). The curve-fit provides damping coefficient (N), period (T), and offset. Roll period in calm water was dependent on Froude number (Fr) and initial roll angle (a). Roll decay data are from 76 runs for three nominal Froude numbers, Fr = 0, 0.15, and 0.22. The initial roll angle variation was 30 to 250. The natural roll period was 2.139 10.041 s 11.9 %). The decay coefficient data were approximated by a plane in three dimensions with Fr and initial roll amplitudes (a) as the independent variables. Curve-fit results are compared to decay coefficient by log decrement and period from time between zero crossings. Examples demonstrate average values for a single roll decay event from log decrement are the same as values by the curve-fitting method within uncertainty estimates. The uncertainty estimate for the decay coefficient is significantly less by curve-fit method in comparison to log-decrement method. By log decrement, the relative uncertainty increases with decreasing roll amplitude peak; consequently, focus should be on the damping coefficient at the largest peaks, where the uncertainty is the smallest.