This is an excerpt from a draft of an earlier article that I wrote for a different purpose but which addresses the basic issues that you are asking about.
The impact of the keel and rudder design on the tendency of a particular boat to capsize has become a bit of a controversial topic. The testing that resulted in the wake of the Fastnet Disaster seemed to come up with what might appear to be contradictory information. I hope to explain some of those contradictions.
To begin with, studies of the contribution of waves on capsize have shown that it requires a breaking wave that is twice the beam of the boat for the wave to be a major contributing factor in causing a capsize. On most ballasted keel sailing cruisers of a reasonably modern design (i.e. mid-20th century onward) a true capsize is not possible without a wave of that description. This would suggest that greater beam would be better in resisting waves, but as the studies showed that as boats became beamier and the beam of the boat was carried further into the ends of the boat at some point the rail of the boat would dip into the water and its suddenly increasing resistance could contribute to a capsize.
Of course greater beam or carrying the beam into the ends of the boat also adds to form stability, and it was shown that boasts with a lot of form stability have an increased tendency to stay perpendicular to face of the wave and so are more likely to be pushed to a greater heel angle by the wave.
Breaking wave studies showed that there was a difference in speed between the water at the surface of the wave and water deeper in the wave. This difference in speed results in what is referred to as surface sheer. In theory the deeper the keel, the greater the difference in surface sheer induced speeds experienced by between the hull at the surface and the bottom of the keel. In theory, since the hull experiences faster moving water than the tip of the keel, the boat is pushed over to a steeper heel angle by the rotational difference between the two speeds. This was thought to be especially true in smaller breaking waves, waves that were just large enough to contribute to a capsize because in really big waves the surface layer is so much deeper that for all practical purposes the entire boat and keel experiences water speeds that are essentially the same.
The current thinking is that any detrimental effect from surface sheer of deep draft is easily offset by having the greater stability that can be achieved by a deeper keel. Another aspect that determined the impact of surface sheer is the aspect ratio of the keel as it pertains to the likelihood of a keel stalling at deep angles of attack.
To explain, when you have a deep draft keel that is short fore and aft, there is a tendency of that keel to stall as the water is moving closer to perpendicular to the keel. When the keel stalls, it generates smaller sideward resistance relative to its area. A shallow draft keel that is longer in length, (such as full keel, or even the Peterson style IOR keel mentioned above) has less of a tendency to stall. Normally a stalled keel would be a negative producing a lot of leeway, but in this case the tendency of modern deep fin keels to stall reduces the impact of surface sheer and so reduces the tendency for surface sheer to rapidly heel the boat. As a result, even if shallower than a modern fin with bulb, a full keel or lower aspect ratio keel could actually have greater tendency towards a surface sheer induced capsize.
Then there is the issue of roll moment of inertia. This is another one of those seemingly contradictory items. In theory, a boat with a higher roll moment of inertia is less prone to capsize due to wave action. Roll moment of inertia is the resistance due to the weight of the boat to accelerating the speed of speed of the boat’s roll for any given roll impact. It is not the same as stability. Roll moment of Inertia is calculated as the amount of weight multiplied by its distance from the instantaneous Roll Axis (the imaginary axis about which the boat rolls at any angle of heel). In other words, a small weight that is a long distance from the roll axis (say at the top of the mast) would have the same impact on Roll Moment of Inertia as a very large weight that was closer to the roll axis (say in the keel). This would suggest that a heavy mast could reduce the chances of a boat capsizing. But this is not really the case.
To explain this it is important to understand the relationship of roll inertia to the motion of the boat on a wave. If you visualize a boat starting down the face of a wave from the crest, the force of gravity tries to pull the boat sideways and the keel tries to resist this sideward motion. The difference between these two forces, creates a rotational force (a moment) trying to heel the boat over. If we compare two boats, with equal rotational forces but one has much greater roll moment of inertia, the boat with a lot of rotational inertia will resist that rotation and so initially will not heel as fast as a boat with minimal roll inertia relative to the forces that are being imparted into the boat. This makes a big difference in short close waves, but in waves big enough to capsize a boat, as the two boats slide down the wave, at some point the heel angle of the two boats becomes very similar, and the boat with the larger roll moment of inertia has stored more kinetic energy, and that stored energy will become significant as the boats reach the trough of the wave.
As the boat reaches the trough, the angle of the wave face flattens out, and so the force of gravity lessens and so does the acceleration of the sideward speed of the boat. That slowing of the boats sideward speeds causes the boat to want to stand back up. A boat with a minimal roll inertia will stand up more quickly than a boat with a high roll moment of inertia. Here the high inertia of the boat causes it to continue to roll further past the point at which the roll moment forces are reversing. This can actually result in the boom dipping into the bottom of the trough, or worse yet, the mast dipping into the back of the next wave either of which are the equivalent of applying the brakes and forcing the boat over further, perhaps exceeding its limit of positive stability.
And here is where the location of the weight becomes critical. In the case of a boat that has a high roll moment of inertia that is the result of weight carried high in the boat (say a heavy mast or teak decks) the position of that weight, will be such that it is helping to lever the boat over further and therefore contributes to a capsize, even though its high roll moment of inertia may actually seem to reduce the likelihood of a capsize. On the other hand, if the high roll moment of inertia was the result of something carried low in the boat, say a heavy bulb on the end of a fin keel, then that weight would be attempting to right the boat and as such would somewhat mitigate the tendency to continue the roll.
To touch on a couple more points contained this discussion, while deep fins with bulbs may require more careful engineering than other forms of keels they do offer some major advantages from a stability, capsize resistance, and motion comfort standpoint relative to full keel or longer shoal keel designs. While some of the longer keel designs are easier to bolt to a boat, bear in mind that a boat is a system and that one of the key findings of the testing was that IOR era boats (which includes boats with the Peterson style keels described above), tended to have too high a vertical center of gravity and too much form stability and hull forms that promoted a rather uncomfortable motion. These boats also had a high roll moment of inertia but one that came with a high vertical center of gravity.
The other question was about the bilge keels used on Westerlys. I would first off disagree completely that Westerlys are seen as seaworthy designs. While they were seen at one time as reasonably good cruising boats, similar to CCA and IOR era boats which were also considered good cruising boats at one time, that time has long past.
As far as bilge keels are concerned, whether they contribute to a capsize or not depends very heavily on their design and execution as well as the design of the boat they are attached to.. As done on the Westerly I would think that they would tend to fall in the category of a low aspect ratio foil with a high roll moment inertia and a high vertical center of gravity, making them somewhere between neutral to perhaps being a liability in terms of contributing to a capsize.
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Curmudgeon at Large- and rhinestone in the rough, sailing my Farr 11.6 on the Chesapeake Bay
Last edited by Jeff_H; 01-03-2010 at 12:23 PM.