Damage Stability Criterion Augmentation to Prevent Loll

In some flooding conditions, some vessels can develop extreme ranges of "loll" where the righting arm curve hovers just above the axis. Then, depending on the VCG, it may go to zero or it may go near to zero before rising up to larger values.

In some of these cases it is very difficult or impossible to find a max VCG where all of the margins are zero or positive and at least one is zero. This is because at a certain value of VCG there is a transition from one hump to two humps. At this point, small changes in the VCG cause the second intercept to jump between two very different angles; i.e. for any LIMIT where RA0 or MAX is a terminating angle, the margin value as a function of VCG is discontinuous. At a slightly higher VCG, the LIMIT margin may be negative. At a slightly lower VCG the margin may be positive and quite large.

Some existing damage stability criteria will accept the case where the VCG is just below this point, since the second intercept is technically quite large, the equilibrium angle is small, the GM may be acceptable, and even the area under the curve to RA0 is large. However, there is so little energy under the first part of the curve that the vessel will loll over a range of heel angles which might be quite large, even 60 degrees or more to port and a like angle to starboard! I'm sure none of us would want to be aboard a vessel in such a condition.

Therefore we need to be on guard for such conditions. Typically the MAXVCG results will be abnormal, showing all positive margins. Any time this occurs the righting arm curves should be investigated.

It is clear that initial stability and substantial energy early in the RA curve should be required. A SOLAS passenger damage criterion guards against this condition by requiring that the energy before 22 degrees (from upright) be greater than 0.015 meter-radians (2.82 foot-degrees). Something like this should be in every damage criterion. In its absence, and if such a limit is unacceptably severe, one could use a lesser energy value and a relative angle. For example,
where t is some angle, taken to be relative to equilibrium, and m is some minimum area. The angle chosen for t should be the maximum angle of loll that is acceptable, probably no larger than 15 degrees. However it should be large enough to accommodate enough energy to substantially resist rolling over a hump of that range. In order to supply that energy, the value of m should not be greatly less than the SOLAS passenger requirement. Perhaps no less than 0.01 meter-radians. Using these values, the GHS command would be (in metric units),
If there was already an energy requirement in the criterion, this would add to it and not replace it.

If you would like to see another bulletin created regarding a specific topic, please email Creative Systems, Inc. at

Copyright (C) 2011 Creative Systems, Inc.