A Study of the Roll Motion by Means of a Free Decay Test

In this study, a method for the extraction of damping by tracing free roll decay is presented. For this purpose, in calm waters, a bulk carrier model is given a large initial roll angle and then released. Consequently, the roll motion is recorded. Restoring coefficients and virtual moments of inertia for the model are determined by means of an inclining test and recording the damped period, respectively. The linear damping coefficient is evaluated by using the damping ratio. Four different forms of combinations of restoring moment and damping coefficient are assumed in order to determine the nonlinear form of the roll motion. These equations are numerically solved for various damping coefficients and results are compared with the experimental data. By virtue of this comparison, the damping coefficients are determined for each case. It may be concluded that the use of the nonlinear restoring moment, which is an odd polynomial of the fifth order, and the cubic form for the nonlinear damping moment best fits the roll behavior for the ship model. The amount of energy dissipated by the damping moments is also calculated in the time domain. The energy method also confirms that the nonlinear form of restoring force in conjunction with the cubic form of the damping force is the best solution of the roll motion for small to large angles.