100-Year Analysis of Roll Decay for Surface-Ship Models

Abstract A history is described on roll decay analysis for experiments with surface-ship scale models at the Naval Warfare Center Carderock Division (NSWCCD), a naval hydrodynamic facility known as David Taylor Model Basin (DTMB). The earliest roll decay analysis for a model test is from a report in 1923 that compares roll decay analysis for bilge keels off and on. A time history plot provides a measurement of roll period. The roll damping is indicated graphically by a curve fit of the peaks. With modern methods, the damping coefficient is computed with a curve fit of exponential damping. An early example of the estimate of roll damping is by log decrement of the ratio of successive roll peak pairs in 1976. More recently, both damping coefficient and period are computed from a curve fit of exponentially decaying cosine function, which is the solution of a second-order ordinary differential equation with constant coefficients. The largest uncertainty in damping coefficient is by log decrement, and lowest by the exponential cosine with the exponential fit of peaks in between. For the log decrement method, roll period must be computed independently. The roll period is calculated from the time between zero crossings in the time series, the time between peaks, or the peak in the power spectrum of the roll angle.