The ‘Doubting Thomases’ are out in out in full force,  ……but more seriously, members of the jury I will try to make a case, which addresses the issues raised by my esteemed colleagues. (I apologize but this is way too long, but that’s what happens when I try to bang something like this out during lunch hour and don’t have time to edit.)
I’ll start with the issues raised by Seabreeze 97. To quote the heart of Seabreeze’s first point, “On the CCA boats, their waterlines lengthen with heeling (easily equaling conventional short-overhang boats' waterlines), so as they roll, their lengthening waterlines would tend to decrease, not increase, harshness..” (I amtempted to ignore the parenthetical “easily equaling conventional short-overhang boats' waterlines” which ignores the fact that the waterlines on short overhang boats also lengthen with heeling and so the long overhang boat never does catch up with the waterline length of the short overhang boat)
To explain why the long overhangs when coupled result in a more harshness rather than less at large roll angles we need to start by looking at the real shape of the stability curve which plots the righting force against heel angle. We all are used to seeing illustrations of stability curves that loosely appear to be smooth sine curves with ideally the portion of the curve representing positive stability being larger than the portion representing inverted stability. In reality, if you plot the actual point righting force against heel angle for any given boat, there will be a series of humps and shelves that relate to the shape of the boat that is in the water at any given point. Most noticeably for example, typically there is a shelf that occurs between the point that the deck edge hits the water, and the point at which the cabin side hits the water (while it varies considerably with the design of the boat, that shelf is typically occurs around 45 to 60 or so degrees of heel).
When we look at a stability curve for the typical slack bilged, with long overhangs, CCA era hull form, these boats develop very little initial stability and build increased stability very slowly until a heel angle where a large proportion of the counter begins to immerse (typically at a heel angle between 25 and 35 degrees). Anyone who has spent much time sailing typical CCA era boats, will say something to the effect that these boats may be tender at first but at some heel angle they harden up and don’t heel much further. That heel angle where the CCA era boats harden up occurs at s the steep portion of their stability curve. Because of the geometry of the hull and overhangs that point of rapidly increasing stability happens pretty suddenly.
This was done on purpose, because in order to get unrated speed at from the overhangs, CCA era boats needed to be sailed at larger heel angles than se sail more modern designs and designer of that era wanted these boats to heel quickly to that point an not much further. In creating this point at which low initial stability quickly increases, the CCA boats initially roll easily but fetch up sharply as they hit this steep increase in stability.
IOR era boats had a similar lurch in their rolling motion but for other reasons. Although IOR boats had shorter overhangs, they typically were purposely tender at small heel angles and carried close to their max beam at a point about a third of the topsides height above the waterline, and had a topside shape that flared out from a substantially narrower waterline beam to that point. When that bulge hit the water, the roll would stop short with a very noticeable lurch.
Both Seabreeze and Plumper question my choice of the example of putting 500 lbs at the top of the mast to illustrate why the Capsize Screen and Motion Comfort Index is being dismissed as misleading. I chose that example because it was so graphic that I assumed it would easily make the point that if a formula is going to screen for capsize or motion comfort it needs to contain at least some of the critical elements that control capsize.
But to further explain my earlier post, I will start with an example which is more likely to occur in real life than someone bolting 500 lbs perhaps a more normal type of example. We have two owners going to the same manufacturer and buying the same model boat. One plans to go offshore, and the other plans to simply do coastal cruising, but do so elegantly. The Offshore cruiser, opts for the lead keel and the carbon fiber mast hoping to keep the vertical center of gravity low and a non-skid fiberglass deck and a barebones painted plywood with simple varnished mahogany trim for ease of maintenance.
The elegant coastal cruiser, decides he doesn’t need the lead keel and carbon fiber mast and so opts for a cast iron keel, and an aluminum spar. He decides that he wants teak decks and he wants the teak interior which includes solid teak cabinet fronts and raised panel doors.
If we compare the examples and assume that the lead keel has the same shape as the iron keel, and we assume that the boat in question is say a 42 footer which had something like 9,000 lbs of ballast with the lead keel, the iron keel of the same shape would only weight roughly 6,200 lbs. And if for the sake of this example, I suggest that we assume that the boats have an equal displacement, with 2,800 lbs saved on the keel being used up as 1200 lbs of increased interior appointment weight, 1,200 lbs on the teak deck, and the remaining 400 lbs in the heavier rig.
If we looked at the plot of the righting force vs. heel for the offshore vs. coastal cruiser, we would see similar shaped curves because the shape of the curve is predominantly controlled by the shape of the boat in the water at various heel angles. But the offshore boat would have a significantly higher maximum right moment (force) and would have much more area under its curve, and would have a much higher (perhaps as much as 10-15 degrees) limit of positive stability. In other words, the offshore version would be much harder to knock down and if knocked down by a wave, more likely to right than turn turtle than the elegant coastal boat.
Which gets us back to the capsize screen formula. If the capsize screen formula is to have any utility, it should be able to give us some clue as to which boat would be more stable and in this, close to a very real life example, the capsize screen formula fails to give any indication that one boat is far more prone to capsize than the other.
Which is where we begin to hit against theory and the application of theory. In looking at studies of model testing and actual heavy weather conditions, the current theories seem to identify primary and secondary factors as follows: The STIX study group that looked at the various race disasters concluded that the single determinant of the likelihood was waterline length, in other words the longer your water line the less likely you were to be capsized.
Beam came next. But here capsize screen (which only looks at only beam and displacement) seems to get it wrong. The capsize screen formula thinks that the narrower the beam the less likely you are to be capsized while the results of the studies of actual experience suggested that within reason that wider beam translated to less likelihood to be capsized basically stating that it took a wave half the waterline length and twice the beam of the boat to capsize it.
The forces involved are so huge that displacement was seen as having little or no bearing. Then there were as series of other lesser and perhaps more controversial factors. Since in large enough waves to capsize a boat, (again because the forces of a breaking wave is so huge, boats of equal beam were seen as being rolled to roughly the same angle. Here is where roll moment of inertia and VCG come into play. A boat with a larger roll moment of inertia will start to roll a little later than a boat with a lesser roll moment but it will also store more kinetic energy and so will tend to roll further at the ends of the roll than a boat with a lesser roll moment of inertia. That over roll takes place at the end of the slide and so is more likely to keep the boat knocked down longer and potentially allow the boat to stick a spar in the water, which will knock it over further and even potentially induce a roll over. In the case of a boat where the high moment of inertia comes from a heavy keel and light spar, the weight of the keel is trying to right the boat and somewhat offsets the tendency to over roll at the bottom of the wave. But in the case where the high moment of inertia comes from weight up carried up high, the tendency to over-roll is increased and the likelihood of a capsize is increased. But not only would the boat with the higher VCG tend to heel to a larger angle, it has a smaller limit of positive stability making it more prone to rolling over than coming back
Which brings us full circle back to Seabreeze 97’s objection to my earlier example, a boat with a 500 lb weight up its mast would have a tendency to roll further in the wave, and would have less of a tendency to right itself.
I agree that the impact on motion comfort of a 500 lb weight up the mast is more complex than that example suggest which is precisely what Seabreeze 97 is pointing out.
But again, the simpliest way to debunk the Comfort index is by comparing comparing two boats. If we start with a CCA era 40 footer with an LWL =30ft, Beam=12 and Displacement= 20,000lbs we come up with a MCI of 33.94. If we compare that to a 44 footer LWL =39ft, Beam=13ft and Displacement= 24,000lbs we come up with a MCI of 29.8. If weight distribution and VCG, cross sectional shapes, etc were similar, the bigger, proportionately slightly narrower, heavier boat would have a significantly more comfortable motion, yet Brewer’s MCI suggests just the opposite. And missing from the formula is such critical motion impacting elements as VCG or even Ballast to displacement ratio, dampening or even draft, and height of mast and so on. Which comes back to my central point being that the MCI produces such inaccurate results as to be worse than useless as a real comparative tool.
Respectfully,
Jeff
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