6. Probability of Ship Capsizing due to Pure Loss of Stability in Quartering Seas

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This study presents a theoretical method for calculating probabilities of capsizing due to pure loss of stability for a ship running in short crested waves and fluctuating wind. This method is intended to be used for a risk analysis to develop stability criteria of a ship in quartering seas. It is assumed that the ship motions are consist of stationary part and unstationary part. Then we integrate a probability density function of the stationary motions on the safe domain that is determined by separatorices of the unstationary dynamical system. Reduction of restoring moment due to wave profile is fully taken into account by Grim's effective wave concept. Numerical examples for a coastal trawler indicate that the capsizing probability T' n quartering seas is larger than that in following and beam seas when wind velocity is 10 m/sec. However when wind velocity is 20 m/sec, they also indicate that the capsizing probability in beam seas is larger than that in following and quartering seas. Furthermore, the present method was validated by the Monte Carlo simulations in time domain. Therefore, the present method has a possibility to be effective for developing stability criteria.
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