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.
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
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,
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 units),
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.