FOIL Design Parameters and Performance

Since the Australian wing keel surfaced in 1983, public attention has been focused on radical. keel planform (side view) shapes. Recent designs of keels for 12-Meters, International Offshore Rule racers, and even some production cruising boats have featured forward-swept leading edges, elliptical trailing edges, inverted taper, winglets, and in one case, a keel that pivoted like a rudder.

Yet describing a keel as swept forward or aft, as inversely tapered, or as having shoal draft or a. fin shape ignores one very important "shape factor" Even with an excellent planform shape, a keel may perform miserably if it has a poor foil section.

The foil section (Fig. 1) is the keel's cross-sectional shape, the thickness distribution used to generate dynamic lift just as a bird's or an airplane's wing does. Unlike asymmetrical airplane wings, however, sailboat foils, keels or centerboards to work on both tacks and provide lift in two directions; thus, they must be symmetrical. The foil. sections used today are almost universally selected by the designer from examples described in government and aerospace industry technical literature.

The differences among shapes are often so subtle that not even an aerospace technician can distinguish among them simply by looking. I find it especially curious that. during all the speculation. over Australia II's wing keel, the shape of the foil was never discussed. Did Australia's designer, Ben Lexcen, use one of the commonly available NACA (National Advisory Committee for Aeronautics, NASA's predecessor) foils? Many of these foils are shown, and their characteristics charted, in the designer's bible of foil shapes, Theory of Wing Sections (Ira H. Abbott and Albert E. von Doenhoff, Dover Books, New York). Or maybe the wing keel's foil was a more recent NASA shape.

The proper choice of foil section for a keel is critical to a boat's performance. I recently designed a wing keel for a 6-Meter using a new NASA GAW series foil shape. This foil lowered the boat's vertical center of gravity (VCG) enough to allow removal of 900 pounds of ballast without diminishing the righting force at all. The new NASA section keel is 25 percent thinner than an equal- NACA series 63 keel, which is typically used in sailboat design today.

Let's begin to unravel the mystery of foil shapes by first looking at how they are catalogued and described and then inspecting the attributes of each foil series.

Figure 2 shows five families of foil sections developed by NACA. Each foil shape has a number code that describes such characteristics as foil series, maximum thickness in percent of chord, and camber.

For example, 6, the first digit of the foil designation 65-010, simply indicates the foil series; series 0 through 5 preceded it in design history. The 5 designates the position of minimum pressure in tenths of chord aft of the leading edge at zero degrees angle of leeway. In this case, minimum pressure occurs exactly halfway back from the leading edge. The first 0 indicates that the centerline of the foil is not cambered, or curved; this foil is symmetrical, and its upper and lower halves are mirror images of each other. The last number, 10, describes the maximum thickness of the foil as a percentage of its chord, In this example, the foil thickness is 10 percent of its length; the maximum thickness of a 48 inch long foil is 4.8 inches.

The 00 series foil in. Figure 2 is one of the first developed by NACA and is in. wide rise by today's sailboat designers. In this case, the first two digits indicate that it is a symmetrical foil, and the last two specify its maximum thickness it) percent of chord length.

A sailboat's foil and an. aircraft's foils operate in different media and at different speeds. Not all foils usable for one purpose are also efficient for the other. An. important way to relate performance potential in the two media is with Reynolds numbers, which measure the efficiency of the lift, drag, and stall characteristics.

Reynolds numbers are used to compare the behavior of a foil in a fluid such as air at an altitude of 50,000 feet with that in water near the surface. The Reynolds number takes into account the length of die foil and the viscosity, density, and speed of the fluid passing over it. The equation is written R = VL/u, where V is the velocity in feet per second, L is the length of the chord in feet, and u combines the viscosity and density Of the fluid.

For example, if a wing chord is 5 feet long, the velocity is 88 feet per second (60 miles per hour), and the value of R for air is 0.000157, the Reynolds number will be 2.8 million. In contrast, a keel with an average chord length of 5 feet and a R value for water of 0.0000123 will reach a Reynolds number of 2.8 million at just 6.9 feet per second, or 4.7 miles per hour.

When a designer chooses a foil, die foil shape must have been tested at a Reynolds number that is relevant to keel design. This important calculation tells a designer that the foil shape will work as well in water as it did in air. Some foils have been optimized for narrow ranges of Reynolds numbers and might be unsuitable for use as a keel. or rudder foil.

Other factors affect foil performance. For instance, ideally, water flow over the keel would be smooth at all times and would thus yield low drag, but this is rarely the case. The smooth flow over a foil surface that results in low friction drag is referred to as laminar flow. All foils are designed to encourage laminar flow over the foil to the greatest extent possible. There is always friction, however, between the water and the keel's surface. To a greater or lesser degree, depending on the foil's surface roughness, chord length, and speed, this friction causes water moving next to the foil to slow down and "trip" the faster-flowing water a short distance from the foil surface. This tumbling water is called turbulent flow; it results in. a marked increase in friction drag.

The point at which the flow changes from. laminar to turbulent-the critical Reynolds number-occurs when the Reynolds number exceeds approximately 1.5 million for rough surfaces and 5 million for extremely smooth surfaces. Assuming a common bottom paint surface, if a keel operates at values below the critical 1.5 million Reynolds number, the flow will be very smooth everywhere on the keel. By calculating the length of surface at which the Reynolds number equals the critical value of 1.5 million, the designer can determine what portion of the keel will experience turbulent flow and increased drag.

This calculation accounts for only one form of keel drag that is, friction drag. In a previous article ("Keel Parameters and Performance," August 1985), we discussed the production of induced drag, or drag due to lift. Both forms of drag must be accounted for in keel analysis.

Each family of NACA foils has its own ability to generate lift as well as drag. The lift force can be measured in pounds in the wind tunnel or calculated as a non-dimensional coefficient. Aerodynamicists then plot the lift coefficient versus leeway angle as a lift curve (Figure 3a). The slope of the lift curve is fairly straight, so it can be expressed as a simple ratio. For example, if a foil has a lift-curve slope of 0.1 per degree of leeway and is sailed at 5 degrees, multiplying 0.1 by 5 degrees gives a lift coefficient of 0.5. This coefficient is used to determine how much lift force a keel will generate. The larger it is, for a given leeway angle, the more windward performance will improve, both in speed and pointing ability.

Figure 3b plots for each NACA foil type the lift-curve slope versus thickness as percent of chord length. Note that for every NACA series except the 00, the lift-curve slope increases with increasing thickness, But there are practical limits to how thick a foil can be made without incurring large penalties in drag, since friction drag also increases directly with increasing thickness.

The NACA 63 foil series can be seen in Figure 3b to have the highest lift- slope, but other data indicates that, theoretically, it has the highest friction drag of any foil series. The figures below illustrate the theoretical minimum drag with laminar flow of each foil series.

The minimum drag condition occurs for angles of leeway of less than 2 degrees, Beyond 2 degrees, friction drag rises abruptly. Figure 4 shows drag plotted in curves equivalent to the lift-coefficient curve of Figure 3a. As can be seen., drag can also be expressed as a coefficient.

There are at least two major reasons why the minimum friction drag coefficients in the table above may be difficult to achieve in practical sailboat design, The first reason is roughness. In order to achieve minimum drag coefficients, the keel must be at least as smooth as newly polished gelcoat. This is not practical for most boats kept in the water; their bottom paint is relatively rough.

The second reason is leeway angle. Since very few boats sail at less than 3 degrees of leeway, and. since the minimum drag values in the table are not available above 2 degrees of leeway, the minimum. drag condition is unattainable. Although the keel may be at zero degrees of leeway, it is so only when the tiller is locked. at center position and no steering occurs. As soon as the tiller is moved to a position away from dead downwind, the keel develops an angle of leeway generally larger than 2 degrees. Thus, the keel does not operate in the minimum-drag region even for any significant portion of a run.

Any of the NACA foils, used in a roughened state, has a minimum friction drag coefficient of about 0.0085. There is also the matter of the critical Reynolds number. Depending on the boat's speed and the length of the foil's chord, the flow over a large fraction of the foil may be turbulent anyway.

Generally speaking, a very smooth keel surface is perhaps most valuable at low speeds-perhaps 2 to 3 knots-when the Reynolds number is most likely to be below the critical value of 1.5 million. This condition will occur on light-wind days and just after a tack or gybe. A polished keel surface is valuable in raising the critical Reynolds number above 1.5

million and delaying the onset of turbulent flow.
From this discussion, we can conclude that a designer cannot simply consult a table of foil drag coefficients and select the foil with the lowest value. Furthermore, the choice is complicated by variations in foil stall characteristics and the required location of the keel's longitudinal center of gravity (LCG).

The most discernible difference among the NACA foil series is where the position of maximum thickness occurs along the foil; it can occur between 30 and 45 percent aft of the leading edge. NACA researchers found that positioning the maximum thickness farther forward results in a higher lift-curve slope. For example, the maximum thickness of the NACA series 63 is 35 percent aft of the leading edge. It has the highest lift-curve slope of the foils examined here (Fig. 3). The maximum thickness of the 66 series is 45 percent aft of the leading edge; it has the lowest lift-curve slope of the G6-plus series foils.

NACA also found that the farther aft the maximum-thickness point occurs, the lover the theoretical minimum friction drag. This fact is highlighted in the preceding table of drag coefficients; the 66 series foil has the lowest friction drag and the maximum thickness point farthest aft.

A designer's choice of foil type must balance development of lift force per degree of" leeway as expressed in a higher lift-curve slope against the potential for increased theoretical friction drag, which accompanies high lift characteristics.

When the position of maximum thickness was determined for foil shape, a particular leading-edge shape was required. NACA found it necessary to reduce the radius of the leading edge of the foil as the maximum thickness point was moved aft, as illustrated in the boxed table.

The leading-edge shape is semicircular and is designated in terms of its radius as a percent of the chord length, just as are the foil thickness calculations made earlier.

The leading-edge radius and the forward-section shape of a foil play a large role in determining the foil's stall characteristics. Stall is an important selection criterion for a foil because it determines whether a boat will he easy to steer or will have a groove so narrow that not even an expert helmsman can keep it moving.

Stall can be defined as the leeway angle that, if exceeded, will cause a decrease in lift and a large increase in drag. For example, if a foil generates a lift coefficient of 0.8 at 10 degrees of leeway, 0.9 at 11 degrees, and 0.6 at 12 degrees, the foil will be stalled above 11 degrees of leeway.

The angle above which stall occurs is called the stall angle, and the lift coefficient produced at the stall angle is called the maximum lift coefficient.

Figure 5 illustrates the stall angles, maximum-lift coefficients, and drag coefficients for several NACA foils. Before we review them in detail, some further explanation is in order.

Bear in mind that the characteristics of foils in Figure 5 are for ideal
cases in a wind tunnel. A keel can reach stall conditions at angles smaller than those shown in the figure if the designer does a poor job of figure the keel or rudder planform shape. For example, if a keel is highly swept aft, the tip area of the keel is likely to stall at very small angles of leeway-say, -1 or 5 degrees.

In addition, the surface of the foil is assumed to be verb smooth. Roughness will cause stall to occur at lower than ideal angles of leeway.

Even if full keel stall does not occur, the chosen foil may still exhibit poor performance. Figure 4 shows that as the leeway angle is increased, the minimum drag coefficient increases slowly at first and then rises very rapidly because it is gradually approaching the stall angle with accompanying high drag condition.

It is interesting to notice in Figure 4 that long before stall actually occurs, the small-leading-edge-radius 65 series foil is operating with much higher drag than the 00 and 63 series foils with their larger leading-edge radii. This is an important point. Choosing a fine-edged 65 series foil for its minimum drag near zero degrees for downwind speed exacts a price in higher friction drag when the boat sails to windward at leeway angles of 3 to 8 degrees.

Thickness also plays a role in determining the foil stall angle. Notice in Figure 5a that as the maximum thickness is increased above 6 percent, the stall angle for all foil types rises rapidly until about 13 percent is reached. Beyond this point, additional thickness will cause the stall angle to decrease.

The fact that the stall angle increases with increasing thickness implies that the low-drag region, which for a thin, 6 percent foil might occur up to 2 degrees of leeway: will be extended to 3 to 5 degrees as thickness is increased. Again, however, this effect is limited to thicknesses of less than about 13 percent.

Figures 5b and 5c complement Figure 5a by indicating the lift and drag coefficients that were achieved for several NACA foils when each foil reached its stall angle. These drag coefficients, by the way, are 10 times larger than the values achieved near 8 degrees of leeway, the practical limit of efficiency for many boats.

A designer who is creating a keel begins by first determining the proper location of the center of lateral plane (CLP) for the boat's underbody The CLP must be located where it will balance the effects of the sailplan's center of effort and allow steering without excessive weather helm.

Given a satisfactory hull shape, one way to achieve the desired CLP is to adjust the keel's fore-and-aft location. The designer must place the keel's longitudinal center of gravity directly below the center of buoyancy, of the hull, or at a location that balances the trimming effects of such heavy equipment as the engine, tanks, and furniture. He can do this by choosing a moderate sweep angle and selecting a foil with a position of maximum thickness that helps to put the LCG where he wants it. He can also distribute the lead within the keel planform to meet his goals and avoid compromising the lift and drag characteristics of the keel. Of course, to the extent that the hullform allows, he can choose his keel section and planform and simply move it forward or aft along the hull bottom.

The designer must also contend with draft limitations and the volume of lead ballast to be held by the keel. These limitations will govern how much freedom he has in adjusting the thickness of the foil and the chord lengths. To illustrate these say that a keel must hold 6,000 pounds of lead and has 24 inches of salient keel span (height of keel alone). If we ignore keel foil shapes for a moment in order to get a relative size, we can guess at the keel's dimensions. Since lead weighs about 700 pounds per cubic: foot, it would take 6,000 = 700. or 8.6 cubic feet of keel volume. Since the designer has only 2 feet of keel height, it would take a keel 1 foot thick and 4.3 feet long to give the required volume. But these dimensions represent a foil with a maximum thickness of nearly 25 percent!

As the designer makes the keel longer in an effort to achieve a more reasonable thickness, the Reynolds number increases, and the amount of wetted surface with turbulent flow may also increase. In this extreme example, the designer would do well to lengthen the keel only enough to get the maximum thickness down to 13 to 15 percent.

There are alternatives, however. In the case of a wing-keel, shoal-draft design, for example, the designer has additional foil volume in the winglets to hold ballast. He can then reduce the keel's Reynolds number through a shorter chord length to obtain a foil thickness in the desired 13-15 percent range.
In reviewing the different foil shapes, we have found that the position and amount of maximum thick= ness, as well as the leading-edge radius, play important roles in determining the lift and drag characteristics of foils.

The designer's ability to choose the optimum foil for a keel design comes from an understanding of the varying characteristics of the large catalogue of foils available to him. The use of computer programs to sort rapidly through the many options is becoming more and more a necessity to those who have learned the power of a well-designed keel.