Foil planforms

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IOM skippers will have noticed the small fillets or leading edge root extensions on some keel fins and rudders, the interesting "knee" or "elbow" shape of some fins, and the rounded "pear" shape of some rudders. In the case of fillets, the root chord of the foil is increased. In the case of the "elbow" or "pear" planforms, the root chord of the foil is reduced. The following pictures show the fillets on my Ikon fin, and a roughly equivalent "elbow" fin. (These two fin and bulb arrangements are called "T" keels, because of the central placement of their bulb.)

Fin with fillets Elbow fin

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:

When a hull heels it generates an asymmetric underwater form. This asymmetry generates a small amount of lift, it may not be efficient, but it's there. Lift over a 3D foil, due to end effects and bleed from the high to the low pressure side, generates a spanwise crossflow. The hull will generate such a crossflow. This hull crossflow increases the inflow angle to the root of the keel, in addition to the leeway of the hull through the water. This increased angle of attack at the root means that the lift generated by the foil (for a particular chord length) will be greater close to the hull. The fillets on your Ikon's foils increase the chord length in this area and so increase the lift by an amount out of proportion to the change in chord length alone.

Unfortunately this is NOT A GOOD THING as this causes a spike in the spanwise lift distribution close to the hull and pulls the lift distribution away from the minimum drag optimum of an ellipse to a higher drag distribution.

From this drag-driven analysis of a foil's planform it would make sense to do the opposite and REDUCE the chord at the root to try and approximate more closely to the minimum drag, optimum elliptical lift distribution.

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.

Prognathous bulb

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:

I thought of this [prognathous bulb idea] some time ago, and played around some. The problem is that if the fin is torsionally soft enough to be twisted by the bulb, in waves of just the right frequency, the critical frequency [of the fin plus bulb] may be excited. When that happens, the boat nearly stops. It almost looks like it will self destruct. The benefits to be gained I think are quite marginal, and no sailor would want to have a boat such that in certain conditions it is essentially dead in the water. I think you would always be open to the problem where just the right (wrong) conditions would simply put you out of the hunt.

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...

2005-12-18


2011 Lester Gilbert