While it’s generally accepted that the right sails and sail trim will determine how close you can sail to the apparent wind, a sailboat’s progress to windward also depends on the lift and drag generated by the centerboard and rudder. How much difference does proper foil shape make over a simple rounded leading edge and tapered trailing edge, anyway? Foils operating in fluids, whether air or water, are a well-studied topic. C.A. Marchaj, in his book, Sailing Theory and Practice, discusses the theory and gives the results of actual tests of differences in foil planform (side view), cross-section shape, size, and aspect ratio (AR – length to width). Lacking other constraints, an ideal centerboard, daggerboard, or rudder blade should have a reasonably high AR (greater than 2) planform with a streamlined cross-section that has a parabolic leading edge and a thickness of somewhere near 10 percent of the chord width (the distance from leading edge to trailing edge). A thickness of 8 percent produces less drag but stalls sooner; 12 percent has a higher stall angle but produces more drag.
Exactly where the point of maximum thickness should be located is a matter of some debate. Marchaj suggests it should be at 50 percent of the chord width, halfway between the leading edge and trailing edge, but provides no data to back that up. Other sources suggest that the NACA (National Advisory Committee on Aeronautics) symmetric foil sections, originally developed during aircraft research, are actually a good fit for boat foils operating at low speeds in water. A NACA 0010 foil, for example, has a maximum thickness of 10 percent of the width of the foil, located at 30 percent from the leading edge.
Of course, there are many practical reasons why not all keels, centerboards, and rudders have high AR planforms, but the cross section for a foil of any planform should be streamlined. My personal experience of doing it wrong on one boat, and getting it right on another boat, has convinced me that the NACA sections and guidelines above provide good performance.
HORNPIPE, my first sail-and-oar boat, was an 18’ Kurylko Alaska with a standing-lug ketch rig, and sailed well enough to windward in flat water, but lost 10 to 15 degrees of pointing ability as soon as the water got choppy. I knew it wasn’t poor sail trim. Eventually I got looking at the daggerboard and analyzed it. It was only about 2.5 percent of the sail area and its thickness was only about 6 percent of the chord width, neither big enough or thick enough in my view, and in rough water it lost laminar flow and lift. When I designed my 18′ lug-yawl cruiser, FIRE-DRAKE, I gave it a thicker centerboard with a greater fraction of the sail area, about 4 percent. I also gave it a straight quarter chord line (think of the shape of the wing of a Spitfire aircraft) and a moderately high aspect ratio of about 3:1 for the planform area. To get the daggerboard foil shaped accurately and quickly I opted to have it cut on a computer numerical control (CNC) machine. All that was left for me to do was sand, seal and paint, and make an epoxy-lined hole for the pivot pin.
The results have been what I had hoped for. FIRE-DRAKE sails quite well to windward and maintains its performance in rough water. I sailed in the company of a similar boat—with the same length and beam, the same weight, and the same sail plan—along the south half of the Inside Passage, and that boat’s centerboard was shaped by eye. When sailing to windward, FIRE-DRAKE would consistently point higher and walk away in speed. My centerboard even let me continue sailing to windward when my partner gave up and took to the oars.
Although I had the daggerboard shaped with a CNC router, it is possible to shape a high aspect ratio, fully streamlined foil in the home shop. I’ll walk you through my second project, a kick-up rudder blade that I made at home to replace the original one I built for FIRE-DRAKE. I settled on a planform that is one-quarter of an ellipse with an elliptical leading edge and a straight trailing edge. (The shape would move the center of lateral resistance of the boat aft a few inches, and is intended to lighten the weather helm I’d experienced with the original rubber blade.) I drew the new blade with an aspect ratio of 2.5:1, with a length of 30″ (762 mm) and a maximum chord width of 12″ (305 mm), which would increase the lift and reduce the tip vortex drag.
To draw the planform shape of the quarter ellipse you can use an online graphing tool such as Desmos for a full ellipse. If you center the ellipse at zero, you can drag the two axes out until you get the aspect ratio you want. Since the graph has a grid in the background, you can then print out a screen capture of a quarter of the resulting ellipse and scale up the printed image to the actual dimensions required. If you are comfortable with computers, you can download and run Freeship (available for Windows only) which has a “keel and rudder wizard” that accurately generates several different planforms.
Obtaining the cross-section profile of a chord of a given width is best left to a computer. For any of the NACA foils, like the 0010 foil I mentioned above, Competition Composites Inc. (CCI) has a very simple and handy calculator. You need enter only the chord width and the maximum thickness and it will generate a table of X-Y coordinates that you can copy and print out. They’ll be your offsets for drawing a pattern for the foil cross-section. If you intend to sheathe your foil with ’glass and epoxy, for example, you can also enter the skin thickness and it will calculate the coordinates for the plywood core.
Now, here’s the tricky bit. If you have a rectangular foil planform, you only have one chord width and therefore one section profile for the entire length of the foil. However, if you have any other planform (e.g., half-ellipse, quarter-ellipse, trapezoidal, straight-chord-quarter-line, etc.), the thickness, which will be one-tenth of the chord width, changes along the length of the foil because the chord width changes.
I used the CCI calculator to generate profile coordinates for three different points along the length of the rudder blade: at the root, at about two-thirds of the way along and at about 90 percent of the way to the end. I chose those points because the chord width for my quarter ellipse planform doesn’t change much for the first half of its length, but it changes more quickly toward the tip. The idea is to shape the foil to these profiles at these points and then taper the foil evenly between them. You can lay out your foil plan directly on to the ply or you can use something thin, like doorskin, to make and fine-tune a template, which is what I did.
I made a blank for my rudder by gluing layers of marine ply with epoxy to the required 1″ thickness. I have found that the plywood, in spite of its cross-grain plies, has sufficient strength for the size of small-boat foils that I have built (though the cross-grain would weaken a long thin foil). Plywood does not warp and has the added advantage over solid wood in that the plies create a kind of contour map that give you graphic visual feedback as to the evenness of your surface once you start shaping the foil. You can make a foil with solid wood or even foam plus a ’glass-and-epoxy skin, but without the plywood laminates as guides, you would have to make more section profile templates to ensure a smooth and accurate shape.
The next step is to taper the thickness of the laminated foil blank along its full length. Knowing the required thickness at your chosen points, you can draw a pattern for the curve of the taper and half the thickness of the blade stock and measure how much wood you have to remove at each point. I clamped my 4′ aluminum I-beam level to the flat part of the rudder blade above the shaped part, and used a ruler to measure the depth I had to cut to. To remove the wood for this part of the project, I used my #4 Stanley plane. While I have a power hand planer, I didn’t trust myself with it to not take too much off too quickly.
I made three female half-section profile templates, one for each of the three points noted above, by plotting out the generated X-Y coordinates on pieces of doorskin and carefully cutting them out. One thing to note is that the CCI calculator generates a profile that has a trailing edge of zero thickness. Obviously, this is not practical to build in wood, and a knife edge is not that critical anyway. I adjusted the trailing edges so that the finished edge would end up about 1/3″ (4mm) thick.
Next, I used the profile templates to shape the foil at my three chosen points. I shaped the plywood with a Shinto rasp, regular rasps, and coarse sandpaper. It’s a process of taking some wood off, placing the template, and repeating until you get the section of wood shaped to the templates. Once that is done, I could go to work taking down the wood between the sections, using the ply layers as a guide. I used my block plane, Shinto rasp, and sandpaper for this task. I eyeballed a smooth transition around the tip from the leading edge to the trailing edge.
I sealed the surface of the shaped foil with a couple of coats of epoxy to provide a smooth, hard surface to accept a finish coat of marine epoxy enamel.
I’ve finished the rudder blade, installed it, and have taken it out for its first sea trial. The new foil definitely seems more responsive. It doesn’t require as much tiller movement to turn the boat as the old blade did and tacking seemed quicker. The effort to make the rudder blade and daggerboard with proper NACA foils has paid off with improved performance under sail.
Alex Zimmerman is a semi-retired mechanical technologist and former executive. His first boat was an abandoned Chestnut canoe that he fixed up as a teenager and paddled on the waterways of eastern Manitoba and northwestern Ontario. He started his professional career as a maritime engineer in the Canadian Navy, and that triggered his interest in sailing. He didn’t get back into boatbuilding until he moved back to Vancouver Island in the ’90s, where he built a number of sea kayaks that he used to explore the coast. He built his first sail-and-oar boat in the early 2000s and completed his most recent one in 2016. He says he can stop building boats anytime. He is the author of the recently published book, Becoming Coastal.
For further reading on the pros and cons of the variables in foil design, Competition Composites (CCI) has a good discussion. For those of you who want to go into the math, Paul Zander has a good presentation from nearly 20 years ago, and also, for those inclined that way, an updated discussion with a lot more math.
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