Ship roll control and power absorption using a U-tube anti-roll tank

The work reported in this paper is concerned with ship roll control using a U-tube anti-roll tank (ART). Special attention is paid to the determination of the wave-generated input power and how this power is distributed between a portion absorbed by the tank fluid motion and another portion dissipated by the ship roll. It is analytically determined in the paper how the natural frequency and the damping ratio of a U-tube ART should be tuned to maximise the power absorbed by the tank assuming a perfectly flat spectrum of the moment representing the excitation of the ship by waves. It is found that such tuning also minimises the average kinetic energy of the ship roll. This is because the power input of the wave excitation moment into the ship-plus-tank system does not depend on how the ART is tuned. However, if a more realistic situation is considered, where the roll excitation moment is calculated using a standard wave spectrum, then the power input will mildly vary with the tuning of the tank damping ratio. Nevertheless, the maximisation of the power absorbed approximately corresponds to the minimisation of the mean kinetic energy of the ship roll.