The Deal on Keels
Naval architect Chris Cochran of melvin and Morelli breaks it down for us. Enjoy.
So I was talking to another sailor in the yacht club bar, following a Saturday race in Marina Del Rey, CA. He was trying to tell me something about his boat’s keel, comparing it to one on a similar sized boat. This guy, a well respected sailor in the area, seemed to have a misunderstanding of why his keel was better than the other boat’s. He was on the right track, in that it was better, but sort of misguided why. This got me thinking that if he didn’t totally get it, then there are probably more than a few sailors out there that don’t really get it. So for this next piece, I’ll attempt to describe some of the fundamental keel characteristics and their associated benefits and drawbacks.
The ballast configuration is probably a good place to start. Whether the keel has a bulb or not, the fin (or strut) design can be quite different. This is because the horizontal center of gravity of the ballast and the horizontal center of sideforce of the fin have significant impacts on the yacht’s balance. The center of gravity relative to the center of buoyancy has an effect on the fore/aft trim of the boat, while the center of lateral resistance (where the sideforce acts) relative to the center of the sailplan has an effect on the yacht’s helm balance. Bulb keels can be arranged so that the bulb controls the fore/aft trim, and the strut controls the helm balance. Since each appendage performs its own task, they can be designed and optimized independently. Bulb-less fin keels, on the other hand, are much trickier. Since the ballast is contained in the fin, which also determines the balance of the helm, the fin keel inherently does both jobs. This means that the two design problems cannot be uncoupled, and hence compromises must be made in order trim the boat and balance the helm correctly. These compromises are usually in the form of sweep angles, thick cross sections, tapered tips, etc…
[/url]Regardless of the ballast configuration, the fin (or strut) needs to prevent leeway when sailing to windward or close reaching. The foil does this by creating horizontal lift (to windward), counteracting the transverse force generated by the sails (acting to leeward). Unfortunately the foil also creates drag, especially while developing lift. The obvious goal for straight line speed is to have an efficient foil – one that has the highest possible lift/drag ratio while providing enough lift, and possibly containing the right amount of ballast. Satisfying these tasks is not easy, but luckily the resources poured into aero/hydrodynamic research back in the day have provided us yacht designers with a pretty solid database of information on efficient foils. Starting with a good cross-sectional shape and the required planform area/keel volume, we can use this information to optimize the keel’s characteristics, such as aspect ratio, sweep angle, taper ratio and tip shape, within the yachts performance, structural and hydrostatic constraints.
The section shape is one of the more important characteristics. That is the foil shape at a cross section through the keel, like if you were to cut the bottom of the keel off and look down into it. There are an infinite number of (symmetric) sections out there, and their differences can range from huge to insignificant. Many designers use the popular NACA 6-series for keels, while others design their own shapes using CFD programs. Experimental data for the NACA sections are readily available in an inexpensive little blue bible called the “Theory of Wing Sections”, which is why most people prefer them as opposed to idealistic results from numerical predictions. The NACA 6-series is used for keels because it has a cool little attribute called a drag bucket. In a particular range of low leeway angles, the drag coefficient (a non-dimensional representation of drag, relative to the water density, boat speed and profile area) of the keel remains relatively constant and low. By contrast, foil sections without drag buckets have increased drag coefficients with increasing leeway angles. The downside to the NACA 6-series is that as soon as the foil starts operating outside of the drag bucket, the drag coefficient increases sharply, more so than a non-bucket foil. So in short: if you stay in the bucket, the drag is low, if you go outside the bucket, the drag is high.
The thickness/chord ratio is another important attribute. It shouldn’t be a huge surprise that thin foils have less drag than fat ones. Makes sense right? In reality, that’s only slightly true. For the NACA 6-series the maximum thickness, and its location relative to the leading edge, governs the size of the drag bucket. Thicker foils have a wider bucket range, yet slightly higher drag while in the bucket, compared to thinner foils. Although not as important to straight-line performance, the thickness also has an affect on the keel’s stall angle. Generally speaking, thinner foils will stall sooner (at lower angles of attack, or lower lift coefficients) than thicker foils. This is important when considering certain lift-dependent maneuvers like starts, tacks, mark-roundings, pinching, etc…
The sectional shape and thickness/chord ratios have the greatest effect on the 2-dimensional properties of the foil - the “ideal” performance of the keel without any 3-dimensional tip losses from induced drag (see Yacht Design 101: What a Drag for an explanation on induced drag). The performance of a 3-dimensional foil is very different than a 2D one. In fact, its efficiency is dependent on many things, namely the keel’s span, planform area, aspect ratio, sweep angle and taper ratio.
The mean chord length (mean fore/aft length) and the span (keel draft) are multiplied together to obtain the planform area (profile area). The aspect ratio is the ratio of the span squared to the planform area. The aspect ratio and planform area have a large effect on the lift coefficient (non-dimensional lift, similar to drag coefficient) and induced drag. Keels with low planform area and high aspect ratios can potentially generate as much lift as low aspect ratio keels with more planform area. Higher aspect keels have less induced drag, and hence less total drag, than keels with low aspect ratios. Additionally, foils with high aspect ratios have higher lift coefficients (compared to foils with low aspect ratios), meaning that they don’t require as high a leeway angle to generate the right amount of lift, and hence can comfortably operate inside the drag bucket. But keep in mind, there is a downside to high aspect keels. For one, they generally require a deep keel draft, which is not practical for cruiser/racers. The increased draft also lowers the center of lateral resistance, which causes an increase in the heeling arm (distance from sail center of effort to keel center of lateral resistance) and hence the heeling moment (the opposite of righting moment). This increased heeling moment makes the boat more tender, unless the righting moment is increased correspondingly. Lastly, the reduced planform area leaves the keel more susceptible to stalling during low speed maneuvers, and low-speed pinching.
The sweep angle is the amount of fore/aft rake in the keel, and the taper ratio is the ratio of the root chord to the tip chord. The two are altered together in order to maintain “elliptical loading”, an aerodynamic term referring to the ideal, highly efficient distribution of lift on a true elliptical foil. So what the hell does that mean? Well, an elliptically shaped keel may not be practical for several reasons, so the shape may need to be distorted to correctly balance and trim the boat. Fortunately, the foil can be “tricked” into thinking it is elliptical with the right combination of sweep angle and taper ratio. For instance, if the keel is swept aft 20 degrees, then it should have a 20% taper ratio (tip is 20% as long as the root) in order to maintain elliptical loading. Unfortunately, a 20% taper ratio is not ideal for stability reasons, as it raises the vertical center of gravity of the keel, so a compromise must be made to increase the taper ratio and thus reduce the efficiency. In addition to requiring excess taper ratios, the drawback to large sweep angles is that it slightly increases the drag of the foil, and could also promote early stalling.
There is one additional characteristic worth noting, and this is where the existence of a bulb may actually help the keel’s hydrodynamic performance. If there is an endplate at the end of a foil, its “effective” aspect ratio is increased, and the foil will have added efficiency, without resorting to optimum sweep/taper combinations. It is arguable whether bulbs can be considered true endplates, but experiments have determined that they do make a difference in increasing effective aspect ratio. This is why modern strut/bulb combos have un-swept, un-tapered struts terminating with a bulb in the ‘T’ configuration.
Without going into much more detail, this is about the extent of basic foil and keel theory. Although this was only a brief review, you can start to see how and why all keels are not created equal. The existence of a bulb, the section shape, planform area, the aspect ratio, etc… all have impacts on the efficiency and stall characteristics of the keel. Hopefully after reading this, you will have a better understanding of how and why your keel performs the way it does. Or maybe you’re just more confused. If that’s the case, or if you want to know more about the subject, take a look at the “Theory of Wing Sections”, by Abbot and Von Doenhoff (Dover Publications, 1949), which covers basic foil theory, or “The Aero-Hydrodynamics of Sailing” by C.A. Marchaj (Adlard Coles Nautical, 1979), which applies foil theory to keels, rudders and sails.
02/22/2005
