On the Stability of Antisymmetric Motions of a Ship Equipped with Passive Antirolling Tanks

Until now, the effectiveness of passive antirolling devices, such as tanks, has been checked against the build-up of a large amplitude synchronized rolling motion in monochromatic or narrow band sea. Recently, we have shown that this effectiveness extends also in a general stochastic and short crested sea from any direction. Through the use of a perturbation method, we have also proved that it extends to the so called parametric rolling, i.e. to subharmonic rolling that can be excited as a result of the coupling of heave and roll in longitudinal sea from the stern. The effect of the tanks is to increase the threshold for the onset of subharmonic rolling at least in the first region of instability that was investigated in a second order approximate analysis. Numerical simulation confirms this trend. Recent approaches to stability assessment seem to pay an increasing importance to the simultaneous occurrence of instability in the antisymmetric motions sway, yaw and roll, and synchronism with the external excitation. The coupling among these motions could explain phenomena such as capsizing, loss of control in waves and, probably, broaching-to. In this paper, the stability boundaries as regards the antisymmetric motions are computed for a ship considering the eigenvalues of the system of equations describing the coupled sway, yaw, roll, tanks motions. The results indicate that passive tanks properly adjusted to avoid large amplitude rolling in a beam sea, can play an important role also in reducing the range of instability of these motions.