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If the prediction in relatively small waves of 3m is very good, the prediction in 6m looses quality. The degradation of the comparison in highest waves may have several sources. One of them can simply be related to the prediction of the wave itself. In the simu-lation program, waves are linear and are not limited by breaking effect. When the cumulative distribution of the wave amplitudes is plotted for both sources a similar degradation is also observed. Fig 12: Probability of exceedance of the roll amplitudes. Hs = 3m, Tp =9.64s, 330 deg, 13 kn Fig 13: Probability of exceedance of the roll amplitudes. Hs = 6m, Tp =13.5s, 330 deg, 13 kn However the degradation seems to be smaller for the wave amplitudes than for the roll motion amplitudes which suggest that the prediction of the roll motion is Another way to compare the model tests with FREDYN is to mimic the test procedure with the calculation. The table in Fig 10 shows the wave height that yields a cap-size for a sailing duration of one hour in stern quartering seas (330 deg) at a speed of about 13 knots. Table 2: GM=0.68m, Heading= 330 deg, Vs =13 knots Capsize Conditions FREDYN Tp (s) Wave 1 Wave 2 Model Tests 9.64 6 m 5m > 9m 10.5 6 m 6m 7m 13.5 7 m 8 m 7m The table shows two different waves realizations. These waves are identical from a statistical point of view but their realization (the wave pattern) is different. It is required to obtain an impression of the sensitivity to the wave realization as the wave in the tank and in the cal-culations can only have identical statistical characteris-tics. This table allows several important remarks: There is an obvious discrepancy regarding the shortest waves. FREDYN predicts capsizes in waves as low as 5m significant, while during the model test waves up to 9m were tested during 2 hours of real time without any capsize.
This is a clear indication of a discrepancy be-tween the model tests and the computer simulations. Two reasons have been identified so far and are being investigated: 1) The non-linearity of the waves: during the calcula-tions, the waves might become steeper than in the basin because waves are not limited by breaking effect. 2) Checks on the simulation code revealed that the formulation used to calculate the wave pressure on the ship deck is not correct. Hence in large steep waves, where frequent freeboard exceedances occur, the calcu-lated pressures on deck are expected to be over-estimated. The wave realization is important as it provides differ-ent results. Hence a capsize boundary can only be de-termined if repeated calculations are performed with the same sea state. Calculations and model tests seem to agree better for the longer, less steep waves. Capsize Risk and Designs Comparison Despite the fact that at this stage of the project, an obvi-ous over-prediction of the capsize risk will be obtained with FREDYN it was tempting to use the program to
Hence, four designs cases were investigated numeri-cally. The three first designs correspond to those tested in the basin. A fourth design with a high freeboard (the coaming is totally supressed) and a low GM of 0.68 m was added as well. Table 3 gives for each wave period the lowest wave height for which FREDYN predicts a capsize. The table gives it for each design. According to the existing dis-crepancy with the model tests, the waves with zero up-crossing period below Tz = 8.5 s should not be consid-ered. The prediction for longer periods seems however to be valid. Table 3: Significant wave height yielding to capsize at 13 knots and heading = 330 deg for wave realization no: 1 Tz (s) GM = 0.68 m GM = 0.73 m GM = 1.03 m High FB 6.5 5 m 5 m 5 m 5 m 7.5 6 m 6 m 7 m 6 m 8.5 6 m 6 m 6 m 6 m 9.5 6 m 7 m 8 m 8 m 10.5 7 m 7 m 7 m 8 m 11.5 7 m 7 m 8 m 8 m 12.5 8 m 8 m 8 m Outside range A final risk assessment will be obtained once the prob-ability to encounter each of the wave conditions that yields a capsize will be taken into account. For instance, using the wave statistics of the northern Atlantic Ocean represented below in a wave scatter diagram (Fig. 14). Hs (m)11.5 110.5 1 1 19.5 121118.5 1 2 3 3 2 17.5 1 4 6 5 3 16.5 3 9118 4 15.5 1 9 192013 6 24.5 4 21 37 34 18 7 23.5 1 13 45 64 47 21 6 22.5 4 31 77 80 44 15 4 11.5 1153785118 4 10.5 2 13 22 14 5 1T2 (s) 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5Heading = 30 degModel TestFREDYN Fig 14: GWS North Atlantic scatter diagram all seasons. Capsize boundaries as indicated by model tests and calculated for GM = 0.68 m – 330 deg – 13 knots The occurrences of the conditions where a capsize occurs can be added together providing then the opera-tional probability that the ship capsizes when sailing at a fixed heading and speed in the sea area for which the wave climate statistics were gathered. Table 4 below illustrates this probability for the four design conditions and three different wave realizations.