Controlling the parametric roll of a container ship model by changing the forward velocity

Abstract

Parametric roll on ships is a resonance phenomenon whose onset causes heavy roll oscillations leading to dangerous situations for the ship, the cargo and the crew. It affects both small vessels with marginal stability and large container ships if four conditions are met simultaneously: the wave length and ship length are approximately equal, the frequency of encounter wave is twice the roll natural frequency, the ship’s roll damping is low enough and the wave height exceeds a limit value characteristic to each vessel. A good start to capture the basic features of the parametric roll is to cancel the couplings between roll and the other motions of the ship and to analyse the influence of parameters on the ship stability and the appearance of large roll amplitudes by using one-degree-of-freedom model. By doing this, one realizes that, besides increasing the damping, the roll motion can be stabilized by changing the wave encounter frequency in such a way that the resonance condition is no longer fulfilled. Two parameters mainly affect the encounter frequency: the ship forward velocity and the heading angle. In the paper, we have numerically investigated the effect of increasing or decreasing the forward speed on the roll amplitudes. We followed two strategies. In the first, we allowed the speed to change with a constant acceleration (positive or negative) so that the encounter frequency has left the dangerous region of the resonance. In the second strategy, we changed the forward speed up and down around a value that generates large roll amplitudes, by using different periodic profiles such as sinusoidal, saw tooth or trapezoidal. We noticed that both control techniques generally managed to significantly reduce the roll amplitudes (with a few exceptions). At the same time, we found that very important in how the amplitudes diminish are parameters like the moment of time when the control is activated, the speed rate of change or the period and amplitude of the speed change around the average value (in the second strategy). The data used in the paper have been obtained from experiments with a container ship model in a towing tank followed by expansion to a full scale ship.