4. Capsizing of a Ship in Quartering Waves

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Model tests on capsizing of a container ship were performed in quartering waves. The encounter angle was varied precisely every 10 degrees by using an autopilot device. Among 763 runs in the irregular and regular waves, 225 capsizings were observed. Most capsizings occurred at the encounter angle 20 to 40 degrees. Below a certain critical advance speed the capsizing never occurred. The direction of capsizing was always to the leeside. Such capsizing may be explained as a simple static one which occurs when the capsizing moment of the wave exceeds statically the decreased restoring moment in quartering waves at the above dangerous range of encounter angle. The reason why the capsizing occurs only in high speed and only to the leeside is also explained in connection with the surf-riding or asymmetric nonlinear surging motion. The capsizing due to the parametric oscillation which had been considered as one of the typical mode of the dynamical capsizing was not observed. Instead, a new mode of dynamical capsizing accompanied with the period bifurcations was observed. Since the period bifurcation may be regarded as a precursor of the chaos in the recently developed nonlinear dynamical systems theory, and the chaos may be regarded as a precursor of the capsizing, the nonlinear phenomena such as the fractal capsizing boundaries in the initial value plane as well as the control parameter plane are examined numerically, though the relation between the capsizing and chaos has not been clarified.
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4. Capsizing of a Ship in Quartering Waves

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