Soft Wing Sail

[markdrela]

Thin airfoils are capable of the highest CL and CL/CD values, but only within a narrow CL range (or alpha range). Below is the calculated drag polar for an airfoil very similar to the Liebeck airfoil that Tom showed. The airfoil has attached flow only in the range alpha = 11-15, or CL = 2.65 - 3.05 , in which the L/D is phenomenal. Above alpha = 15 degrees, the entire surface aft of 45% chord separates suddenly, and below 11 degrees most of the bottom surface separates suddenly, and the drag skyrockets in both cases. So such a thin airfoil is pretty much out of the question on an airplane, even before structural consideration are brought in.

But a soft sail allows the possibility of changing the camber of a thin airfoil, which can greatly extend the low-drag range if done appropriately. So a thin airfoil which always has the appropriate camber shape dialed in at any given operating point will in general be superior to a thick airfoil.

Obviously, structural requirements can change the picture entirely. If the airfoil must have a very large bending stiffness, as in the case of a wing or cantilever sail, then the thin airfoil is not an option, and thick airfoils must be used.

[markdrela]

Below is a Cp(x) plot for this airfoil at the max-L/D point. It's not exactly the Liebeck airfoil, but a reversed-engineered version. The second page also shows the corresponding surface pressure vectors.

The near-zero thickness allows most of the bottom surface to be at nearly stagnation pressure, which substantially adds to the CL. A 15% thick airfoil would not carry this high pressure on the bottom, and as a result its max CL would be roughly 2.3 rather than 3.0.

[Erwan]

Hi Everybody,
Wing sail is an option for A-cat as long as the rules do not prohibit it yet.
A soft reversible asymetric section is probably a better option than a symetric rigid one.
Tom & Mark arguments about thin section advantages are very convincing.

[Erwan]

Sorry I posted the former msg by error before I finished writting.
My interest in Liebeck wing section is old, because A -Cat rig has little power downwind.

Unfortunatly I never found the Liebeck wing section coordinates (X,Y) to run on XFOIL (Thank you Mark), in order to see how it works at low reynolds (300 000).

If anybody can tell me where to find such data. Thank you in advance

I guess that for low reynolds theorically I have to investigate "Laminar Rooftop" wing section ?

But if we consider freestream 30 feet above the water is a bit turbulent beyond 6/7 knts, is it a better option to investigate "Turbulent Rooftop",
despite low speed & low reynolds conditions ?

Thanks and best regards

EK

[BarendGrobler]

Hey Ilan!
I was interested in the Dyna-rig and thats really why I read this thread. I see a South African flag on the boat on your website, was the boat tested here? whats the link?
Cheers
Barend

[Ilan Gonen]

Barend
No. The boat is registered there.
The work on building the wing and initial tests was done in Slovenia. We are now in Turkey.
Ilan

[tspeer]

Originally Posted by Erwan

Hi Everybody,
Wing sail is an option for A-cat as long as the rules do not prohibit it yet.
A soft reversible asymetric section is probably a better option than a symetric rigid one.
Tom & Mark arguments about thin section advantages are very convincing.

The main point I'm trying to make is that the notion that because aircraft wings are very efficient and have thick sections, while sails have thin sections and generally lower lift/drag ratios, and therefore a thick sectioned sail will aerodynamically superior to a sail rig with a thin section simply because it is thick, is a mistaken idea. Airplanes have thick sections because they are structurally stronger and because they have to operate efficiently at low lift coefficients in cruise. This is generally not the case for most sailing craft, except for very high-speed craft like landyachts and iceboats.

A sail rig can operate at comparatively high lift coefficients even in high winds because it has the luxury of being able to reduce area. This makes the narrower operating range of the thin section acceptable.

There may well be a place for a thick section in a sail rig, but it needs to come from the design requirements, not from thickness for thickness-sake. A good example is a wingmast, which has a thick leading edge to minimize the windward separation bubble. But the thickness doesn't need to extend for the entire chord.

The Omer wingsail is an interesting design, and the indications are that it is more efficient than a conventional rig. The thick section may provide more leading edge thrust than a thin section like a staysail. But it also has many other drag-reducing features, like a cantilevered mast that eliminates the windage of stays, and a larger span with improved planform and twist for lower induced drag. These factors can easily overwhelm any difference in profile drag due to the choice of section. One would have to do a detailed accounting of the sources of drag to determine what contribution the section shape made.

One other word of caution regarding high-lift sections. The flat-rooftop-concave-pressure-recovery design approach of the Liebeck and Drela high-lift sections is basically a high-Reynolds number philosophy. At low Reynolds number, it is prone to developing a large separation bubble at the start of the pressure recovery, and performance may suffer - both in terms of maxium lift and profile drag.

For low Reynolds number, a more convex shape to the pressure distribution that controls the position and size of the laminar separation bubble, plus a modest adverse pressure gradient to the rooftop for some laminar pressure recovery, may be a more successful strategy. Once the lee side and leading edge are designed, the windward contour might be blended to match the lee contour for zero thickness aft of, say, the first third of the chord. This would shape a wingmast or pocket-luff sail in a way that might be difficult to achieve by manipulating the windward pressure distribution in an inverse design method.

[markdrela]

Originally Posted by tspeer

For low Reynolds number, a more convex shape to the pressure distribution that controls the position and size of the laminar separation bubble, plus a modest adverse pressure gradient to the rooftop for some laminar pressure recovery, may be a more successful strategy.

Correct. The max-lift airfoil I showed, which is designed for Re=5M, actually starts to fall apart below about Re=2M, due to the formation of a massive separation bubble. At 300K it would be fully separated at all angles of attack, and behave more or less as a bluff body.

In the mid-80's Liebeck actually realized that his max-lift airfoils had such separation bubble problems, and started designing airfoils with Cp distributions which more gradually blended the laminar rooftop into the steep pressure recovery, to allow a shallow and relatively innocuous separation bubble to form. One example is the LNV109A airfoil.

The attached plots compare the Re=5M max-lift airfoil I showed earlier, with a significantly modified version which is intended for Re=300K. As you can see they are quite different.

[tspeer]

Originally Posted by markdrela

...The attached plots compare the Re=5M max-lift airfoil I showed earlier, with a significantly modified version which is intended for Re=300K. As you can see they are quite different.

A Cl of 2+ at Re=300K is nothing to sneeze at! Pretty cool.

[tspeer]

Originally Posted by markdrela

...In the mid-80's Liebeck actually realized that his max-lift airfoils had such separation bubble problems, and started designing airfoils with Cp distributions which more gradually blended the laminar rooftop into the steep pressure recovery, to allow a shallow and relatively innocuous separation bubble to form. One example is the LNV109A airfoil...

Liebeck looked at the lee side pressure distributions and optimized the rooftop+Stratford distribution that resulted in the maximum lift. But I've always been curious about the role of the bottom surface presssure distribution and aft loading.

Liebeck's high-lift airfoils had very little aft loading, but sections by Wortmann typically had a moderate amount of aft loading and some sections by Eppler had a huge amount of aft loading. I realize that the boundary layer code in Eppler couldn't handle separation like the inverse BL code in XFOIL does, so one could get carried away with an unrealistic amount of aft loading. But it seemed to me that Liebeck could have accepted more pitching moment in return for some aft loading that would have resulted in a longer rooftop.

Liebeck's lower surface pressure distribution was a flat segment followed by a linear favorable pressure gradient to the trailing edge. The favorable pressure gradient essentially cut a corner off the area between the two curves, reducing the maximum lift. But what set the level of the "floor", and could aft loading have been used to reduce the amount of favorable pressure gradient? After all, if the rooftop+Stratford distribution maximized the contribution of the upper surface, the contribution of the lower surface would be maximized if it could be held near stagnation for as much of the chord as possible.

I took the LNV109A, kept the upper surface contour, and reshaped the lower surface so that it was close to the upper surface for approximately half the chord or more. Then I used XFOIL's inverse method, MDES, to smooth out the wiggles and reshape the pressure peak on the lower surface. I also tried adding some aft loading. The MDES redesigns invariably added some thickness back in, so I alternated between carving at the geometry and using the inverse code.

As I tried to get more out of the bottom, the camber started to become extreme, and it became impossible to get a converged boundary layer solution, even at large angles of attack. The reason should have been obvious from the start. If one could attain the ideal of stagnation pressure all along the bottom, the flow there would be stopped completely. It would be essentially indistinghishable from the inside of a massive separation bubble - provided that the flow reattached by the trailing edge. If if didn't reattach, then the lower surface would be stalled and the whole section ineffective.

So the favorable pressure gradient on the windward side of the Liebeck sections is essential to keeping the flow attached on the bottom. If the thickness is zero, then there's an intimate connection between the allowable pressure gradients on both sides. I had thought that one could design the lee side pressure gradient and let the windward pressures fall out from the zero thickness. But that's not necessarily the case. Adding thickness by building up from the lee-side contour will reduce lift, but not just any lee-side contour will do.

This may also help explain something that all sailors know - a cupped leech is bad. I've often wondered if a cupped leech could be beneficial by providing aft loading. But in addition to the possibility of separated flow on the leeward side of the leech, it may also have the effect of promoting separation and drag on the windward side. Something more to investigate!

[markdrela]

Originally Posted by tspeer

Liebeck looked at the lee side pressure distributions and optimized the rooftop+Stratford distribution that resulted in the maximum lift. But I've always been curious about the role of the bottom surface presssure distribution and aft loading.

My gut feeling is that the Stratford recovery all the way to the TE is not optimal for max lift. With a "cupped" TE, you can gain a lot of bottom loading at the expense of just a bit of top separation, for a net lift gain. Aftrer adding the aft camber to the Re=300K airfoil I showed, the CLmax increased and the polar improved substantially. The polar plot also shows the S1223 airfoil, which has a substantial aft camber, and is also better than the Stratford-type airfoil. The UIUC data shows a measured CLmax = 2.12 at Re=300K (with an imperfect hand-built model), so I think the benefit of the aft camber on CLmax is real.

[tspeer]

Wow - that's quite an improvement.

I may have been trying for too much aft loading.

All of these sections have a hollow shape to their aft contours. I wonder if it would be beneficial in a mainsail to apply the leech tension well inboard of the leech itself, so as to allow the battens to curve to leeward aft of there. Basically an unsupported roach, especially at the foot.

[markdrela]

Originally Posted by tspeer

Wow - that's quite an improvement.
I may have been trying for too much aft loading.

Possibly. I tried adding more aft camber on the 5s airfoil, but it didn't get any better.

All of these sections have a hollow shape to their aft contours. I wonder if it would be beneficial in a mainsail to apply the leech tension well inboard of the leech itself, so as to allow the battens to curve to leeward aft of there. Basically an unsupported roach, especially at the foot.

Actually, the 5s upper surface has only the slightest concavity. Coordinates attached. In any case, duplicating this sufficiently accurately on a soft sail with battens doesn't seem easy. One possibility might be to use lots of part-chord battens, from 90% to 100% chord, say, to enforce the aft camber.

[Retired Geek]

Just playing around with variations on Marks last foil in XFLR5, while its possible to get more CL or L/D its damn hard, if not impossible to get both at the same time.

[Erwan]

Tom, Mark, GK,

I was away for a few days, but I kept an eye on these topics. First of all , thank you for taking time to write long, insightfull and very pedagogic messages that I are very usefull for me. Special thanks for you Tom, with your spreadsheet and documents you have paved my road for a rational analysis, instead of an intuitive borderline esoteric guessing as illustrated by my split tip analysis.