Frequency Dependence of Hydrodynamic Coefficients in Roll

A series of tow tank tests were performed to determine whether the added mass moment of inertia in roll and damping roll coefficient for a planing hull are frequency dependent. The model was forced in roll while running at planing speeds. The model was free to heave and pitch, but restrained in sway and yaw. The roll motion, pitch motion, speed and the force required for the roll oscillation where recorded. From these data, the roll stiffness coefficient, the damping roll coefficient, and the added mass moment of inertia in roll were calculated at various oscillation frequencies. The roll damping showed no frequency dependence. The added mass moment of inertia showed no frequency dependence at high frequencies. At low frequencies the added inertia appeared dependent on both frequency and speed. However, analysis shows that the added inertia calculation is highly sensitive to the error in the measured forcing moment amplitude at low frequency. Therefore, to accurately determine the coefficients at low frequencies, there must be tighter error control of the forcing moment measurements or an increased number of test runs.