Very nice posts, Mike.
Stephen and others:
As we know transversal moment of inertia is one of the important factors to seaworthiness and it is also related to seakindliness through the roll period.
Usual formula for whatever moment of inertia is I= mass* radius^2 = m*k^2
In the STIX, could we consider moment of inertia is somehow reflected in the Beam Displacement Factor (FBD) as this factor is partially intended to indicate the resistance to capsize in breaking waves? Maybe, but I think this is not enough. It should be more specifically considered, as Eliasson asked for.
In what I call the the 'Old' ratios and parameters system, moment of inertia is estimated as (imperial units):
I = (disp^1.744 )/35.5
and roll period as:
T = 6.28*( I /(82.43*LWL*(.82*Beam)^3))^.5
Roll period, on its side, is related with roll acceleration for a 10º roll angle at a position located 1.5 ft inwards from the maximum beam:
Roll Acceleration = (6.28/T)^2*radius*(roll angle*3.14/180)/32.2
The Stability Index is
SI = T/Bmax (normal flared sides)
Curves for SI and its effect on crews can be found in Marchaj's book, page 75.
Usually a roll period in seconds in the range of the beam in metres (maybe even slightly bigger) is desirable from the point of view of seakindliness (comfort), but also from the point of view of seaworthiness, as this means the boat has a reasonable transversal inertia to improve behaviour in steep or breaking waves conditions, not tending to follow the wave's slope, but remaining more close to the transverse resting position when moving (mast tendency to tilt towards the wave instead of outwards). Very long rolling periods would be, on the other hand, not only also uncomfortable, but even dangerous. It is also usually considered that T should be between 4 and 8 seconds, depending on the vessel.
On the other hand, a beamy and light boat with it's short rolling period, may enter resonant rolling with shorter transversal componet of waves than a heavier one. As period of encounter is related to waves' speed, this to their length and this to their height, a heavier boat is comparably able to resist bigger seas, once again generally speaking.
So seakindliness (comfort in these threads has to be understood as seakindliness) and seaworthiness are closely related. But seaworthiness is more than seakindliness, because it's also related to watertightness, structural strength, etc, etc.
(By the way: Ted Brewer's Motion Comfort Ratio, MCR = DISP / (.65*BEAM^4/3*(.7*LWL+.3*LOA)) is also related with the inertia (mass) of the boat, but in this case relative to heave motions. A heavier boat will also have more gentle heave motions than a beamier and lighter one. Maybe the name 'comfort' confuses some people, making them think in carpets, sofas, washing machines and the like. Probably 'heave ratio' or the like would have been a more adequate name).
Longitudinal inertia is not analized in the 'old' ratios, neither in STIX (Displacement Length Factor, FDL, is not intended to that end, but related with the general responsiveness of the boat, penalizing it if excessively high. Remember STIX is a Mom&Dad's intended index, not a racing one). And maybe it's a pity, but as the longitudinal gyradius is much bigger than the transversal one, longitudinal movements use to be more comfortable than transversal ones. But resonant pitching has also to be avoided, as it can be also very dangerous (I think, Stephen, your 'bad' experience when sailing that heavy boat you mentioned, was related to this. Probably a rhumb change would have helped, what you'd probably had done if cruising. But as you were racing....)
Of course
Seakindliness and
Seaworthiness are not the only legs in the table. We need a third one to keep it stable:
Seamanship. So behaviour of a boat at sea is always a 'three Ss' matter. We should always talk about the triple S combination, or
SSS as has been suggested by several posters, absolutely. Could we think about an SSS index to be given to boat-crew combinations....?
Altering rhumb and speed of the boat as to avoid resonant rolling or pitching is an skipper's decission, not a boat's (Excepting Murielle's one?
). And this brings an interesting question to me: Is there any autopilot/reefing/trimming system able to decide and execute a change in rhumb and/or speed if things become dangerous? It would be pretty nice for solo or reduced skippering.
More in this line of thoughts...could we get an authomated sailboat with a high SSS Index, not needing any crew....? (Definitive triumph of machines over humankind...
)
Cheers.
