The MaxVCG run in the attached files shows an odd behaviour with the limit margin not converging to zero. The only limit used is:
LIMIT ABSOLUTE ANGLE AT EQUIL < 10.
I have tried to formulate the LIM differently:
LIMIT ANGLE from EQUIL to ABS 10 < 0
LIMIT INCL < 10
And this improves the run for HMMT= 160, but not for HMMT=50. It seems that HMMT smaller than about 70t.m poses problem.
Everytime you review a MAXVCG result, it's important to verify that at least one of the limit margins is zero. See An explanation of the Margin % in Maxvcg output.
In this case we see right away the limit margins are positive. In a RAH result, positive limit margins are a good thing, but as we will see, in a MAXVCG result, positive limit margins sometimes indicate a dangerous condition.
The first thing to check anytime you see positive limit margins is whether it is possible for the vessel to capsize at a lower VCG than would result in a zero limit margin. These cases are more likely when only one limit is present and especially if the limit(s) doesn't address stability directly.
What do I mean by not addressing stability directly? Well, it's important to remember that MAXVCG seeks the VCG which passes the criteria by the smallest positive margin; a margin of zero is ideal. So an adequate MAXVCG criteria must guarantee acceptable stability characteristics when the limit margin is zero. Does this single limit guarantee stability? As we will see, stability can be compromised before the stability limit is reached.
Returning to the case at hand, what forces are present that would cause the equilibrium angle to exceed 10 degrees? Off-center TCG values increase the equilibrium angles as the VCG is raised, but the
MAXVCG process assumes TCG=0. Similarly, heeling moments increase the equilibrium heel angle as the VCG is increased. When the heeling moment is small, it is possible that the GM drops below 0 at a VCG which doesn't exceed the heel limit.
Lets examine how to verify that the VCG is limited by capsize? Luckily, it can be done with a simple run file which investigates a displacement and trim that fails to achieve zero limit margin. See related article: How the Maxvcg iteration process works. We'll choose the 1500 LT displacement case to investigate. We first run an identical Maxvcg test at 1500 LT as a base case, then use a macro to slowly iterate the VCG toward our maximum VCG value, to see how the vessel responds with a slightly lower and higher VCG. In our test you'll notice that just after the achieved MAXVCG, limit margins are undefined and not plotted, then the equlibrium heel drops off a cliff toward 180 degree, therefore capsize.
This case illustrates a significant danger of using MAXVCG with an inadequate criteria. The criteria needs to ensure that the vessel has acceptable stability characteristics even when the stability margins are zero. To accomplish this, the limits must specify the desired characteristics of the righting arm curve. On the face of it, an equilibrium angle of less than 10 degrees doesn't actually indicate anything about the stability margin. After all, a vessel with an equilibrium of 11 degrees can easily be safer than one with an equilibrium of 9 degrees!
Area limits tend to be very reliable indicators of adequate stability. Combined with a minimum range of stability limit, there are usually no problems getting to zero limit margin while maintaining desirable stability characteristics.
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