Trans RINA, Vol 152, Part A2, Intl J Maritime Eng, Apr-Jun 2010


more of the criteria. The minimum wave height in which it capsized could then be scaled to determine the critical wave height or seastate for the ship. The problem with model tests of criteria, rather than specific ships, is that the model equally could represent a ship of a different size, at a different scale. Indeed it could represent a ship of any size. Only at one scale would the test represent a ship that just complies with the minimum criteria. Smaller ships would fail the criteria and larger ships would have stability in excess of the minimum criteria because, although regulatory criteria do not vary with ship size, the GZ values are not non-dimensional. This highlighted the fact that the level of safety provided by the criteria is dependent on the size of the vessel and the seastate in which it operates. Criteria based on the positive range of stability are the exception to this, because range is a non-dimensional parameter, unlike GZ or the area under the GZ curve.


The objective of the study proved difficult to satisfy for a number of reasons: • In order to compare the levels of safety given by the differing criteria it is necessary to compare vessels of the same size, and there is not a simple definition of equivalent size of a multihull compared with a monohull.


It could be length, displacement passenger numbers for example.


• The criteria address specific values of GZ or areas under the curves, and these could be satisfied with different shaped curves. It soon became clear that the critical seastate is highly dependent on the range of positive stability, which is not regulated.


• Some of the criteria do not address the residual stability with passenger crowding moments applied, and to compare them with minimum requirements of residual stability was meaningless.


The outcome of the work was a recommendation for a new criterion, or method of estimating the minimum level of safety of a vessel, given its size and stability. Following extensive analysis of the minimum wave heights to capsize, together with various measures of stability, it was recognised that vulnerability to capsize depended largely on the residual range of stability and, to a lesser extent, on the maximum righting moment. A strong relationship was found between the critical wave height and the following combination of residual stability characteristics:


Range RMmax B


Where range is the range of positive residual stability, RMmax is the maximum residual righting moment, and B is the beam of the vessel. This differs from the parameters used in most conventional stability criteria because it includes displacement in the righting moment term, which is beneficial, and beam, which is not. Although wide beam provides good initial stability, if


0.00 0.02 0.04 0.06 0.08 0.10 0.12


or


two vessels of different beams have similar stability characteristics, the one with the wider beam generally will be more vulnerable to capsize.


Naval architects are very familiar with the concept that the area under the GZ curve represents the energy to resist capsize, and with its use as a measure of safety. It is tempting therefore, to try to relate it, or the product of the range of


stability and GZmax, to relates to


Research Project 509 demonstrated, however, that those parameters are less reliable measures


resistance. The formula does not represent a simple physical characteristic, but


this formula. of capsize the capsize


resistance which is dominated by the range of residual stability, supported to a lesser extent by the maximum righting moment.


The expression is not dimensionless, but effectively has the same dimension as the critical wave height. A purist might prefer to express the range in radians, replace the maximum righting moment with the product of


the


volume of displacement and GZ and incorporate a constant to maintain the correct relationship. The author takes a pragmatic view however, and prefers the use of more familiar engineering quantities for the sake of simplicity.


Intact Monohulls Damaged Monohulls Intact Catamarans Damaged Catamarans Damaged Trimaran


0.0 0.2 0.4 0.6 0.8


Range(RMmax)0.5 LB


Figure 2 Relationship between stability and the minimum wave height to capsize from research Project 509.


Figure 2 presents a summary of the model test capsize data, and demonstrates that the critical wave height appears to be independent of hull shape or damage configuration.


The data have been rendered 1.0 1.2


non-


dimensional using the overall length to normalise both axes. The stability parameters which are frequently regulated, such as GZ values and GZ curve areas, were studied on their own and in various combinations, but none collapsed the data as effectively as that shown here. These results, together with observations of the models’ behaviour, led us to the belief that the vulnerability to capsize is not dependent on the form of the vessel, the number of hulls or the existence or extent of damage. All configurations may be considered as simple floating bodies characterised by their residual stability curves.


A - 86 ©2010: The Royal Institution of Naval Architect


Min. Wave Height to Capsize/L


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