Trans RINA, Vol 152, Part A4, Intl J Maritime Eng, Oct-Dec 2010
starboard. During this period, differences in roll angles at the same time of up to about 4º occur. The equilibrium heel angles generally agree with that predicted using hydrostatic software.
It is noticeable that runs P1_R14, P1_R15 and P1_R28 have similar extreme port roll angles, and exhibit a similar behaviour, whereas runs P1_R12 and P1_R16 have a similar extreme port roll angle which is different to the other three runs.
Of interest is that the maximum roll angle in the initial phase is greater than the final equilibrium roll angle. As the initial roll angle will be dominated by the roll damping, and the way in which the water floods into the model immediately following damage, both could have a very important influence on the likelihood of survival. For example, if the initial heel angle exceeds the angle of vanishing stability in the damaged condition, the model will capsize.
5.1(b) Pitch Motions
The pitch motions for the five runs are plotted as functions of time in Figure 8. Note that the roll angle for each run has also been included in this figure (right axis), to assist with the interpretation of
the pitch
motions. There is very little difference in pitch for the first 10 seconds after damage initiation, with a small difference occurring after
that, before
reaches a similar pitch angle for each of the runs. 5.1(c) Water levels in compartments
The water levels at the wave probes for each of these runs are plotted as functions of time in Figures 9 – 13, along with the roll angles for each of these runs. Note that as the water level did not reach the wave probe in the 1st deck on the port side in the centre compartment (1Centre-S23) in any of these runs, the results from this probe are not included.
As can be seen, there are differences in the water levels for each of these runs, although the final equilibrium values are similar.
In general, the first few seconds
after the damage initiation showed very similar results, with any deviations occurring after about 8 seconds following the damage event, corresponding to where the roll angles also differed between runs.
The water level in the only bottom tank where the level was measured (0Fwd-S06 – Figure 9) shows initially similar results for the different runs, however the time for the final equilibrium to be reached is different. This may be due to the way that the air exited the tank, with clear vortexes forming in some cases. The reason that this tank did not fill completely is that some air was entrapped, preventing the water from rising further at the inboard (upper) edge of the tank where the wave probe was located.
the model
The water level in the centre tank on the starboard side close to the damage on the 2nd deck also showed little difference initially between the five runs (2Centre-S12 – Figure 10).
The later differences correspond to
differences in roll angle. This probe is fully submerged upon reaching the equilibrium position in all five runs.
The water levels at the wave probes on the 2nd deck at the port side both showed what appeared to be two different phenomena, with runs P1_R12 and P1_R16 exhibiting one behaviour, and runs P1_R14, P1_R15 and P1_R28 another behaviour, as seen in Figures 11 and 12. For water to reach either of these wave probes it had to pass right across the model, and through openings in both the port and starboard longitudinal bulkheads (see Figure 5b).
The two different patterns of behaviour in the water level for these two compartments exhibited by runs P1_R12 and P1_R16 compared to the behaviour exhibited by runs P1_R14, P1_R15 & P1_R28 also corresponded to the difference in roll angle behaviour noted above.
Finally, the water level on the aft bulkhead in the aft compartment on the starboard side (1Aft-S17) did not rise until well after the damage was initiated, and the model was heeling to starboard, close to its equilibrium position (Figure 13). For each of the runs the time that the water level reached the wave probe was slightly different, however the rate of rise of the water level was similar, as was the equilibrium value.
5.2 EFFECT OF KG
A number of runs were conducted with different vertical centre of gravity (KG) positions as given in Table 2. The roll radius of gyration was only measured for the single case of KG = 173mm (where kxx = 140mm), however, it is believed that this value would have
varied by less than 8% for the configurations.
The results are plotted as functions of time in Figures 14 – 18. For clarity, the results from only two of the five runs with a KG value of 173 mm are included. These approximate to the two extreme values for that condition.
5.2(a) Roll angle
As can be seen in Figure 14, the runs with the higher centre of gravity positions result in a greater initial heel angle, a greater intermediate heel angle to port, and a greater equilibrium heel angle. For the lowest KG value tested, the model does not heel to port during the run, although the starboard heel angle is reduced after the initial value, before increasing to the equilibrium value. This demonstrates the importance of changes in
other KG
©2010: The Royal Institution of Naval Architects
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