Steve Holland tells me he is a student of yacht design at Southampton, and has reminded me that we need to consider the cross-flow beneath a heeled hull. These are the points he makes:
There may be another good reason to reduce the root chord of the foils of a beamier hull, and that is to lessen the ventilation effects on keel and rudder when these hulls heel. Because of the hull beam and the resulting increased stiffness, skippers of the "skiff"-type hulls carry their suits into higher wind ranges than narrow-beam hulls. It is not unusual to be able to see the keel fin and rudder root out of the water of a well-heeled skiff, and to be able to see the resulting turbulence this causes. Narrowing the root chord of these foils is meant to reduce this turbulence, reduce the drag, and reposition the lost foil area further down, well below the water surface to where it can do useful work.
Perhaps it is worth considering more carefully the required change in aerofoil cross section of the fin from root to tip. Given the hull cross-flow, it is clear that the fin, ideally, needs to twist somewhat to accommodate the higher angle of attack at the root. A rotating fin is not permitted by class rules, but an equivalent change would be to have a significantly thicker section profile at the root with maximum thickness further forward. This more rounded entry would accommodate the higher angle of attack better. The disadvantage, of course, is that the thicker section adds to drag on the run.
Alternatively, we can have an "L" shape keel, shown in the first of the diagrams here. When the boat heels, the bulb will tend to twist the fin in such a way that the root is effectively twisted off, or washed out.
While the fin, ideally, needs to twist off because of the higher angle of attack at the root, then needs to twist back in its mid-span to meet the "normal" leeway angle of attack, it also needs to twist off again at the tip because of the upwash induced there, just like the twist needed in the sails because of their induced upwash. So if we accommodate the higher angle of attack at the root with a thicker chord and maximum thickness further forward, perhaps we can accommodate the need for tip twist by carefully regulating the torsional stiffness of the lower third of the fin and locating the bulb CG well forward of the fin's leading edge. This gives us a "reverse L" shaped keel with a prognathous bulb, shown in the second diagram. As the hull heels, the weight of the bulb will twist the fin and induce wash-out, producing the sort of twist we need to reduce tip drag and premature stall.
In either case, arranging the keel as an "L" or "reverse L" shape places the fin, and hence the sail plan, either much further forward, or much further aft than current designs. If we have a "reverse L", presumably the boat is a little less nimble in the tack, though has better directional stability, with the converse applying with a regular "L" shape.
Larry Robinson offers a caution:
Finally, the page on balance points out that the more symmetric the heeled waterplane is, the less the lift produced by the hull. This was thought to provide a better-balanced boat as the wind gusts or lulls. It may also be the case that a more symmetric heeled waterplane produces less lift-induced drag, as well as producing less cross-flow under the hull, allowing the fin and rudder to work better.
We also know that some hull designs produce more asymmetric heeled waterplanes than other designs. Such designs thus produce more cross-flow and lift around the hull, and (we're guessing here, of course) might benefit if their keel was more like the "L" type. Where the hull design provides a more symmetric heeled waterplane, then it will generate relatively less cross-flow and lift, and would be better with the usual "T" keel or maybe a slightly prognathous "reverse L" keel. Hmmm...
©2011 Lester Gilbert