Abstract
A concept for analytical representation of the capsize rate, a measure directly related to damage ship survivability, has attracted attention ever since the first attempts were made to explain the behaviour of a damaged ship in waves. Attempts in the late 1990s helped to enhance understanding and facilitate characterisation of phenomena pertaining to capsize probability and time to capsize in given environments and loading conditions, but a consistent verifiable formulation is still lacking. In this respect, pursuing an analytical approach to express the capsize rate offers many advantages, time efficiency being amongst the most important. In an era when stability/survivability calculations are required to be carried out in real time, there is a need for a model accounting for the random nature of capsize whilst achieving accuracy close to that of time-domain simulations with simple hydrostatic calculations. This study is an attempt to establish a new methodology for survivability assessment by means of a multivariable analytical model based on numerical simulations, validated against the results of physical model tests.
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Notes
- 1.
Given that the significant wave height at which the capsizes are observed is a random variable, the confidence interval would simply be a band of wave heights containing most of the area under the p(Hs|capsize) probability density function curve. Instead, the boundaries of the capsize band are expressed with the use of the following equalities: \(\left( {H_{S} } \right)_{low} = \left. {H_{S} } \right|_{{P_{f} (H_{S} ) = \alpha }}\) and \(\left( {H_{S} } \right)_{high} = \left. {H_{S} } \right|_{{P_{f} (H_{S} ) = 1 - \alpha }}\), where α is some (small) number.
- 2.
PROTEUS 3 is a software suite for time-domain seakeeping analysis of intact and damaged ships http://www.brookesbell.com/service/software/design-software/proteus-simulation-sofware.
- 3.
At the time of writing.
- 4.
This follows the classical definition of probability, expressed as the ratio of favourable experiment outcomes over the total number of trials. It would become a probability of capsize (conditional on loading condition and wave parameters) if the number of trials approached infinity.
- 5.
A time series of seakeeping either by means of numerical simulations or physical model tests.
- 6.
Relative to the critical significant wave height.
- 7.
Word large in this context refers rather to computational or experimental effort than actual, numerical size of the data.
- 8.
The reference follows the nomenclature of OriginPro software package http://www.originlab.com/doc/Origin-Help/Boltzmann-FitFunc.
- 9.
The parameter dx is referred to by analogy to dynamic system response to step input. In context of current application is a span parameter (related to slope at inclusion point).
References
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Jasionowski, A., Vassalos, D., Guarin, L., “Time-Based Survival Criteria for Passenger Ro-Ro Vessels”, 6th International Ship Stability Workshop, Webb Institute, 2002.
Jasionowski, A., Vassalos, D., Scott, A., Ship Vulnerability to flooding, 3rd international conference for maritime safety, Berkeley, California, 2007.
Vassalos, D., Turan, O. and Pawlowski, M.: “Dynamic Stability Assessment of Damaged Ships and Proposal of Rational Survival Criteria”, Journal of Marine Technology, Vol. 34, No. 4, pp 241–269, October 1997.
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Tsakalakis, N., Cichowicz, J., Vassalos, D. (2019). The Capsize Band Concept Revisited. In: Belenky, V., Spyrou, K., van Walree, F., Almeida Santos Neves, M., Umeda, N. (eds) Contemporary Ideas on Ship Stability. Fluid Mechanics and Its Applications, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-030-00516-0_26
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DOI: https://doi.org/10.1007/978-3-030-00516-0_26
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