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


The definition of capsize in the HARDER project was a capsize in each of 5 runs in a particular seastate, so one would expect the data to be statistically sound. The two models which have test points on the safe side of the line were


both tested in the same facility, where the


experimenters reported: “It was also noted that the first wave was decisive for the survival. In many runs the vessel capsized by being hit by the first wave. In these set of runs, the vessel survived the remaining run, if the first wave was successfully passed.” [6] & [7]. This phenomenon was noted during preliminary tests at the Wolfson Unit, and was due to the fact that the models were more vulnerable before the down-wave drift was established. During subsequent


tests the model was


supported until the natural drift was established. Failure to do this in the HARDER tests might have caused some of the results to be a little pessimistic.


The same experimenters also reported that, for these two models, some of the internal ballast was moved to one side to obtain an initial list of 1 – 2.5 degrees to the damage side. Such a shift is significant in terms of the residual GZ and range of stability in the damage case. It appears not to have been accounted for in the analysis, although the details of this are not reported, and so it is possible that these points should be plotted at a lower value on the x-axis; further to the left on the graph.


The models restrained by light lines or soft


tested in the HARDER project were springs


in order to


maintain the desired orientation to beam seas. Whilst minimal restraint is always the aim, it is inevitable that the tethers must apply some forces to the model, or they would not be required. This was the method used initially by the Wolfson Unit in Research Project 509, but it soon became clear that even the slightest restraint could initiate a capsize if the model was close to a critical point, so the models were tested totally unrestrained. If they became misaligned or too close to the tank wall their position was corrected manually, and the tests continued. This was possible because the tests were conducted in regular waves but perhaps would not be practical in tests of long duration in a seastate, as was the case in the HARDER project. It is possible, therefore, that some of the capsizes might have been influenced by the restraint method.


4.2 (b) Model Data from Other Sources


Figure 5 presents the other model test data collected for comparison with the formula. Two of these points are worthy of note. Point A represents a model which capsized twice at this wave height, at different headings and speeds, and with different mechanisms. The Research Project 583 report states that “This vessel had an unusually large range of stability but water was trapped on deck.” This highlights a potential problem with the formula. Because it relates to the residual stability at the time of capsize, account needs to be taken of all heeling moments and factors that reduce the


stability at the time. Water trapped on deck is likely to reduce the GZ substantially and, if taken into account in this case, would move the point to the left on the graph. Such a scenario may not be predictable though, and this suggests that a greater margin of safety might be justified. The alternative view is that this particular vessel was more vulnerable because water could not be cleared efficiently from the deck, and perhaps its water freeing arrangements were inadequate. Point B on the graph was


not a model


0.00 0.05 0.10 0.15 0.20


mathematical model reconstruction incident.


Unsafe zone A B Safe zone 0.0 0.5 1.0 1.5 2.0


Range(RMmax) LB


2.5 0.5


3.0 3.5 4.0


Figure 5 Other model test data collected in Research Project 583.


4.3 SHIP NON-CASUALTIES


As requested by the MCA, the consultants engaged in Research Project 583 also collected reports of vessels operating without incident in heavy seas. Their reasoning is


test, but a non-linear of a real ship


given in their report as: “Examples of ships that


survived waves were important to test out the Wolfson Formula, so as not to preclude any cases where it might predict capsize.” Unfortunately it appears that the basis of the formula was not clearly understood here. It is not a formula that predicts capsize, rather a formula that estimates the minimum possible wave height that could cause capsize. There were many cases during the Wolfson tests when models did not capsize in waves much higher than the critical height, because the waves were not of the critical frequency or because the model was not at the critical heading. In most of these cases, the models showed no signs of vulnerability. For the same reasons, there will be many instances where a ship will survive waves larger than the critical wave height estimated by the formula, and it is understandable that the crew might have no indication that their vessel would be vulnerable should they change their heading or encounter frequency. Additional reasons for survival of ships in larger waves are that a vessel under way is likely to be safer than in the dead ship condition, and its level of safety may be greater than that given by the formula which was designed to be on the conservative side of the envelope of data. The examples they considered are included in Figure 3 as the “Ship survive” data points.


The consultants in Project 583 considered that “The available real ship data and published model results identified in this study


do not provide sufficient


©2010: The Royal Institution of Naval Architects


A - 89


Significant wave height/L


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