Abstract
Parametric roll is an amplification of the roll motion due to the periodic variation of the restoring moment in waves. This phenomenon is mostly observed in head and following seas and is the cause of several accidents occurred on container vessels during recent decades. One of the second generation intact stability criteria, currently under finalization and validation by the IMO, requires computing the maximum roll angle with regard to parametric roll. Both proposed methods are relatively complex to implement and require tools that naval architects are not accustomed to. In this paper, we propose an easier alternative method providing the amplitude of parametric roll for any loading condition at any speed, based on energy considerations and assuming a linear GZ. The implementation of this easy method in the corresponding second generation intact stability criterion provides almost the same value of KGmax than the on-degree-of-freedom time simulation proposed by the future regulation.
Highlights
Parametric roll is an amplification of the roll motion of ships due to the periodic variation of the restoring moment in waves
The steady-state roll amplitude in resonance condition is easy to calculate with an energy analysis assuming a linear GZ
The obtained value is the amplitude of parametric roll which may occur in the worst conditions, when the wave encounter frequency is twice the ship’s natural roll frequency
Summary
Parametric roll is an amplification of the roll motion of ships due to the periodic variation of the restoring moment in waves. The new regulation proposes 2 methods: an analytical solution based on a polynomial fit of the GZ curve at the 5th order which directly yields the maximum roll angle, or a numerical solving of the differential equation of parametric roll, equivalent to a one-degree-of-freedom simulation of the behaviour of the ship during rolling. Both methods are relatively complex to implement and require tools that naval architects are not accustomed to. A simplified method which provides the amplitude of steady-state parametric roll is proposed assuming a linear GZ
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