Re: Lif and drag coefficients for sails and foils
Originally posted by poul
Hi all
I have some different ideas for various wing sails combinations, and I would like to know some comparable lift and drag coefficinets for the follwing.
normal sail Cl =1.5 Cd = 0.15 Cl/Cd = 10 ??
This will depend greatly on the specific design of the sections, the Reynolds Number (wind speed compared to the chord length), the planform shape, and the type of rig. For example, a sloop rig will probably have a higher CLmax and may have more drag than a cat rig of the same height. And adding a jib to a well designed wingmast may not improve the performance at all over putting the same area into the mainsail.
Another problem you have is you must compare the different types of sections using data from similar sources. It is unwise to compare wind tunnel test data for one section with computational data for another section, for instance, or even between computational codes. XFOIL will do a better job of predicting maximum lift and drag than the older Eppler code, and even XFOIL may be optimistic with regard to maximum lift compared to test data.
Another huge factor is the maximum lift for a two-dimensional section is very different from a three-dimensional wing sail. So you have to know quite a lot about the whole configuration to make a valid comparison.
I've been able to use XFOIL to compute the characteristics of tear-drop type wingmasts. The maximum lift varies radically depending on how the mast is trimmed. For example, a 10% chord wingmast with the sail shaped so the lee side has the same contour as the Clark Y airfoil is predicted to have 2D maximum lift coefficient of 2.1 with ideal trim at a Reynolds number of 1 million. The exact same mast and sail shape is predicted to have a maximum lift coefficient of 1.2 when the mast is rotated to zero degrees (in line with the boom). Rotating the boom past the point where the lee side contour is smooth results in a significant drop in Clmax.
However, even drastic changes in mast design can have surprisingly little effect. Changing the mast size from 5% chord to 40% chord is predicted to have a change in Clmax of about 0.06 so long as the lee side contour is smooth and of the same shape.
No attempt was made in these wingmast designs to achieve the highest lift possible. One could do better with a specific design or by basing the wingmast and sail shape on the lee side contour of a high lift airfoil. The real question is, "What sail shape is achievable in practice?" With today's molded sails and high modulus materials, it may be possible to come very close to the design shape.
So for a wingmast + sail, the most important thing is to know the shape of the mast and sail, and to trim the mast so the lee side has no sharp kinks. I have never seen the precise mast and sail shape tested in the wind tunnel reported in the literature.
Two dimensional airfoil data may be found in the literature. The classic reference is NACA Report 824 (
http://naca.larc.nasa.gov/reports/1945/naca-report-824/), also published in expanded form as "Theory of Wing Sections" by Abbott & von Doenhoff (Dover Books). There have been few symmetrical sections that have been designed for high lift. There are definite limits to what one can do in this area because all you have to work with is the thickness distribution.
The FX 71-L-150 has a maximum lift coefficient of 1.2 at a Reynolds number of 1 million (Wortman, Franz Xaver, "Stuttgarter Profilkatlog I, Friedr. Vieweg & Sohn, 1981).
However, XFOIL is very capable of designing sections of this type. 2D maximim lift coefficients will probably be in the range of 1.2 - 1.4. Less at lower Reynolds numbers.
The maximum theoretical lift coefficient I've seen for a two-dimensional, single element section is 3.06 at a Reynolds number of 5 million. This is not a practical section as it has almost no thickness, but it gives a useful upper bound. More practical cambered sections have been designed with maximum lift coefficients on the order of 2.2 - 2.6. (Liebeck, R. H., "A Class of Airfoils Designed for High Lift in Incompressible Flow," AIAA Journal of Aircraft, Vol. 10, Oct. 1973, pp. 1 - 16)
For example, the Eppler E423 is predicted (Eppler code) to have a maximum lift coefficient in excess of 2.0 at a Reynolds number of 1 million (Eppler, Richard, "Airfoil Design and Data," Springer-Verlag, 1990).
The higher the design lift coefficient, the thinner the section becomes. Ultimately, the section becomes very close to that of a wingmast & sail.
rigid symetrical foil with flap
This depends on whether you are considering plain flaps (no gap at the hinge line) or slotted flaps formed by two or more symmetrical airfoils in tandem. A 30% chord flap will raise the mzximum lift coefficient of the FX 71-150 to 1.8 at a Reynolds number of 1 million.
I know of no published data besides that on my website for symmetrical sections with slotted flaps designed to be used as rigid wing sails. The methods used to calculate these data are VERY crude andthe maximum lift coefficients are HIGHLY questionable. I was also interesed in fairly low Reynolds numbers. At the higher Reynolds numbers of the data quoted above, the maximum lift coefficients would be substantially greater.
One of the best combinations from landsailing competition has proven to be two NACA 0012 sections, with the forward element 60% of the chord and the flap 40% of the total chord. The hinge line is normally located at about 90% of the forward element chord, and the links extending from the flap leading edge (through slots in the forward element trailing edge) sized so the flap just clears the trailing edge of the forward element. A flap deflection of 20 degrees will typically provide best performance. Higher flap deflections may increase CLmax, but the drag also increases rapidly from, say, 30 degrees to 40 degrees flap deflection.
In general, one can use a thick section for the forward element, but the flap should be a thin section. The thin flap section would normally produce sharp pressure peak at the leading edge that would lead to leading edge stall. However, when used as a flap, this pressure peak can be suppressed by moving the flap closer to the trailing edge of the forward element, making the gap smaller. There is an advantage to having the flap and forward element overlap somewhat when the flap is deflected. However, this adds complexity to the mechanism to keep the two elements from interfering when tacking.
Maximum lift coefficients for multi-element rigid wing sections are probably in the range of 2.5 - 3.0+. One must do considerable tuning and adjustment of the slots and flap deflections to optimize the performance.
As a practical matter, I belive it is possible to design a wingmast & sail that is competitive with a rigid wing under most conditions. The A-class catamarans seem to have settled on soft sails while the C-class cats have settled on rigid wings. From what I've seen, a single slotted flap is probably comparable in maximum lift and a double slotted flap will probably have a higher maximum lift than a wingmast & sail. However, the wingmast may have less drag at high lift and will most likely be lighter than the rigid wing and better able to accommodate a wide range of conditions. In landyachts, the best of the rigid wing rigs and the best of the wingmast rigs are neck-and-neck with each other.
As important as the section design is, once one has a reasonably well performing section the more important thing is to get the distribution of lift correct along the span of the rig. A major factor in Cogito's success in winning the C-class Challenge Trophy ("Little America's Cup") was the ability to twist the wing to optimize the spanload distribution. This reduces the induced drag and also allows the different sections from top to bottom to perform near their best angles of attack. This is more important than the differences between one section and another.
. The mechanical problems in having 360+ degrees rotation is relativily easy to solve, but the structual and weight of the rig problems is more difficult to answer. therefore I have to make a feasibility study to see gains and the loses. Right now I think that a 2 masted catamaran is most likely to succeed, but in a few months when I get more time, I will start to play with X-foil, and I also have acces to ansys-flowtran to check the 3d effects, and hopefully discover a genious concept or maybe just forget the hole thing 
