DESIGN

Throwing a new curve at keels Eric Sponberg assesses current keel design and

comes up with a logically different idea

So-called elliptical keels have be­come de rigueur on many top compet­itive racing sailboats because, i n

' theory, they develop high l i f t for par­t icular ly low drag, These quasi-elliptical keels may be doing exactly the opposite, however. Here's an arm¬

', chair view of keel design to correct a few wrongs and point it in a new di¬

V rection.-, ; . i Although it works under water, in a more or less vertical plane, a keel

• works just as an airfoil does in the hor¬izontal. As such it produces two forces, lift and drag (Fig. 1). L i f t allows the boat to go to windward, but drag slows the boat down. A n airfoil that irdduceè the least drag for the most ift is shaped like an ellipse.

f ;v'C. A. Marchaj, i n his book Aero/ . Hydrodynamics of Sailing, explains that an elliptically shaped foi l has a distribution of l i f t along its span that,

. when plotted oh a graph, makes a , curve similar to half an ellipse. Be-

';• cause of this kind of l i f t distribution, '̂ stich a foil also has a uniform amount ofdownwash along the trailing edge.

Downwash is a result of Newton's

root chord short and narrow

Figure 2: Shapo comparison be­tween the Peterson keel and a typical quasi-elliptical keel r

downwash at Xi the foil

second law of motion, which says that for every action there is an equal and opposite reaction. That is, as the foil

lifts up (to windward), some­thing must go down (to lee­ward)—namely, the water flow coming off the trailing edge. The direction of this water flow is mostly straight off the trailing edge, but the flow bends slightly away from the foil , opposite to the d i rec t ion of l i f t . Down-wash—this bending ofthe flow away f rom the f o i l —is least when it is un i form along the span, as happens on an ellipti­cal foi l .

Coincident w i t h u n i f o r m downwash, the tip vortices (the whir l of flow off tho tips) are smallest when the foil is ellipti­cal. Both downwash and lip vor­tices uro thu physical result of induced drag, that part of tho total keel drag that unavoidably

Figure 1: Lift and drag develop from the keel's angle of incidence • v , to the water flow (a). An elliptical airfoil (b) has a constant lift co­efficient, an elliptical lift distribu­tion, and uniform downwash along the trailing edge

comes w i t h the generation of l i f t . ' Some energy is required to create in­duced drag, so obviously, i f you can minimize it, you have more energy' loft for lift . As Marchaj summarizes, " A n u n t w i s t e d f o i l of e l l i p t i c a l p l a n f o r m . . . can be regarded as an ideal planform. Aerodynamically, the merit of a foi l can therefore be mea­sured by the closeness wi th which the . load distribution curves over the foi l span approximates to the semj^elliptic form." Our keels, thoroforo, should bo. elliptical. Right? Right. '.

The present generation of quasi-elliptical keels is the next stop be­yond the "Peterson keel," which Doug . Peterson first used on Ganbare i n

SAIL DECEMBER 1988 31 •

1974 (Fig. 2). Peterson's keel was a sig­nificant advance in keel design at the time, but by the 1980s designers felt it could be improved—that is, made at least somewhat elliptical. The surgery involved shortening and narrowing the root chord, curving the trailing edge like part of an ellipse, and mak­ing the keel fatter i n the middle than at the ends. That's fine, but does the re­sult have an elliptical l i f t distribution, uniform downwash, and a small t ip vortex? No one really knows because, to my knowledge, no comprehensive analytical study has ever been done on eUiptical or quasi-elliptical keels to

Flow around hull and keel root produces a large wave trough

properly test their effectiveness. There is a rationale behind these

changes. First, the shortened chord at the keel root is intended to reduce in­terference drag. Interference drag is the result of f low interference between the hull and the keel. It is a real phe­nomenon and can make the drag on the keel double the amount predicted by ideal fluid-flow theory Its effect is seen i n the photograph above. The wave trough at the middle of the hull is due, in part, to the presence of the

keel and its proximity to the free su face ofthe water. On the opposite sic of the boat there is a much less pn nounced trough. These troughs ar respectively, the low-pressure an high-pressure effects of hull/keel flo ' interference. Some designers reasó that the shorter the root chord of tf keel, the less the pressure differenc on the two sides of the keel and, then fore, the less the interference drag, am not sure that follows, as w i l l be ex­plained shortly '

Second, the elliptical trailing edg makes the planform more elliptica which we need to have. Hardly anyor plays wi th the leading edge, choosir almost always to leave i t straigh There may be merit i n letting it'''cur\ somewhat, however, as i n the new di sign described later. For now, the trai ing edge is fair game, apparently, so we make it elhptical, we w i l l have a ell iptical , or quasi-elliptical, plar form. Right? Well, maybe.' "

Third, the keel is fatter i n the middl simply because the longer section there are naturally thicker than tb shorter ones at the ends, i f they are a the same general airfoil shape. M o i lead ballast in the thick middle sec tions lowers the keel's center of graA

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is faired generously into the hull

Figure 3: The profile of the Sponberg keel shows how each section Is centered along an arc running from root to tip. The thickness of root and tip pro­motes flow parallel to the chords of the sections. Perspective view shows a fence and an endplate

ity. This lowers the boat's center of gravity, which improves stability No argument there, but i n total, what do we have?

Marchaj explains that, as the root chord of a keel is reduced even to a point (never mind how to attach it to the hul l l , the f low more easily stalls and separates, and this can spread spanwise down the keel. Stall ing means the production of l i f t stops al­together, and separating means the f low detaches from the foi l surface. Stall and separation occur because the hul l is an ineffective endplate— the h u l l does not protect the f low around the root of the keel from the f low around itself or from the waves at the free surface of the water As a re­sult, says Marchaj, there is "a conse­quent considerable increase in drag and decrease i n l i f t . " Although the root of the keel cannot be reduced to a t ip for obvious structural reasons, tending toward that direction makes drag more and l i f t less, the exact oppo­site of what it was expected to do.

The elhptical keel also completely ignores another f l o w effect called cross flow. Cross flow is the tendency of the boundary layer on the keel sur­face to f l o w toward the t i p . The

boundary layer is a thin f i l m of water that attaches itself to the foi l by fric­t ion and the water's own viscosity. Cross f low encourages premature sep­aration and stall wi th a corresponding decrease in l i f t and increase in drag.

Does the elliptical keel reduce or eliminate this cross flow? I think not. Image yourself as a water molecule about to get hit by the elliptical keel at its mid-depth, where it is thickest. The surface curvature w i l l tend to make you cross-flow either toward the root or toward the tip. Once you start cross-f l o w i n g , l i f t decreases and drag increases.

So what is to be done? We want an eUiptical planform for an elliptic hft distribution because it produces the least amount of induced drag (uni­form downwash and small-tip vor­tex). We also want no cross flow—that is, the flow should be exactly parallel to the chord of the keel.

To achieve this we begin witir an el­liptical planform, wi th whatever area is required and whatever span our de­sign draft allows. We need a suitable section shape, and the latest aerody­namic research is pointing to the so-called low-speed airfoils, the LS(1) series ft'om NASA. These airfoils are designed to be highly efficient for low-speed f lu id flow.

Nothing in keel design says we have to keep our chosen section the same ratio of thickness to length all along the keel span. In fact, consider your­self a water molecule riding up over the sm'face of a Peterson keel. Lower

down the span, the rate of leading-edge curvature is less, so it is an easier climb, and that's where you go. Sup­pose we make it a harder climb by making the lower sections relatively thicker? Then, i f we skew the keel along an arc, so that the sections at mid-span are farther aft than those at the root and tip, you are going to stay right where you are and not slip side­ways. Just to make sure you stay there, we'll put an end cap on the t ip and a fence in the middle.

Finally what should we do about the keel root, where the f low around the h u l l interferes w i t h the f l o w around the keel? How about gently merging the hul l and-keel flows to­gether by shaping a nice transition between the two? We may not get a whole lot more l i f t by putting a gener­ous fairing in the hul /keel joint, but at least we won't be increasing drag. Happily, a generously faired jo in t greatly improves the structural capa­bilities of the design. We have room for keel bolts, wh ich can be m.ade smaller and spread wider apart.

Once cross-flowing starts, drag increases and iift decreases. So what is to be done?

Figure 3 shows a new keel design incorporating all these ideas. It has an elliptical planform so l i f t distribution is elliptical, downwash is min imum and uni form, and the t ip vortex is m i n i m a l . I t is skewed on an aft-curving arc to promote f low over the center of the span; parallel to the chords of the keel, thereby eliminat­ing cross flow. The f low is assisted by the fence. The keel is faired gener­ously into the hull to blend hul l and keel flows together and reduce inter­ference drag. Finally an endplate pre­vents loss of flow off the t ip .

Some testing in the towing tank and at f u l l scale w i l l no doubt fine-tune this design. Proper play between leading-edge curvature, skew, and thickness distribution may make the fence unnecessary for example. I n the meantime, are there any takers for the "Sponberg keel"? " ^ ^ ^

Newport, Rhode Island, naval archi­tect Eric Sponberg recently has been designing freestanding rigs, hulls, and new keel shapes.

3 4 DECEMBER 1988 SAIL