[Tartan34C]

John,
My thought with the ice skater was to show that with the same amount of energy having a different distribution of weight changed the speed of rotation. As the skater brings in their arms the polar moment of inertia is reduced so either less energy is needed to spin at the same speed or the same energy will spin you at a higher speed. I think you have it right and this is how "conservation of angular momentum" works. The polar moment of inertia is a description of how mass is arranged around a point of rotation. To put a number to it involves, as one part of the equation, breaking the body into infinitely small pieces and multiplying the distance squared of each piece to the axis of rotation. A real limitation from my lack of education is that I know how to use this in a cookbook way of design but I don’t understand the math behind it so my explanation may be lacking clarity. I think the bottom line is that two otherwise identical boats with only the draft and ballast being different the shoal draft boat needs less energy to capsize. Now having said that there are several papers published that say shoal draft boats are less likely to capsize in a storm. The reasoning behind that has to do with the beam of a shoal draft boat and the way a wave moves. In this discussion we are only considering identical boats with different keels and not the design from scratch of a shoal draft boat with all the changes made to accommodate what is really an entirely different design so I am ignoring those studies for the moment.

The rolling resistance of different keels is not a factor in practical design so I never really thought about it. But I see some papers were published by SNAME and RINA on the subject of active and passive anti-rolling methods for ships. It looks like the conclusion of the studies of passive systems are that the greatest contribution of drag or resistance when rotating a fin is from the eddies at the end of the fin and not from the surface area of the fin. So less surface area and longer ends is more effective at reducing roll. I take that to mean if you take two keels that are identical and mount one on end and one on edge the one on edge is better at reducing roll because it has a longer edge making eddies. A practical application of this is the long shallow bilge keels on ships. Of course keeping the bilge keels within the box formed by a ships draft and beam keeps them from getting damaged by grounding on laying alongside a wharf so that’s another advantage of long shallow keels on ships instead of using keels that have a short root and extend a long way from the body of the ship.
All the best,
Robert Gainer