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
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
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.
LIMIT AREA FROM EQU TO t OR RA0 > m
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
LIMIT AREA FROM EQU TO 15 OR RA0 > 0.01
If there was already an energy requirement in the criterion, this would add to
it and not replace it.
UPDATE: June, 2018
In some cases, the loll might be such that the vessel has a range of equilibrium,
instead of a clearly defined angle. This leads to inconsistent evaluation of any
limits that depend on the angle of equilibrium and can cause irregularities in the
limit margins shown in the MAXVCG report.
One solution is to apply a limit that forces a decernable first intercept. There
are two parts to this solution, the first is a GM limit, such as
LIMIT GM AT EQU > 0.1 m
The second part is to force the GM to be calculated from the slope of the righting
arm curve. This is accomplished with the /GM parameter which can be applied to the
RAH, SOLVE MAXVCG, and MAXVCG commands. The /GM:MODU option uses the widest range
of angles for the slope calculation and is preferrable for this purpose
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Creative Systems, Inc.