Wing Shape: Why is Bottom Flatter Than Top?

[Fawzi Da]

Hello everyone!

I wanted to ask: Why is it (usually) that the bottom of a wing is flatter than the top? A detailed reason would be appreciated.

Thank you!

 

[JBA]

Lift is created by creating a lower pressure area on the top of the wing than below it; and the method of doing this is by creating a longer curved flow path and a resulting higher air velocity over the top of the wing than on the shorter path flat bottom. The mass flow must be the same from the front to the back of the wing for both the top and bottom surfaces; so, for the longer length of the curved top the air must flow faster than that of the bottom to maintain the equal mass flow over both surfaces. This higher velocity converts more of the static air pressure to velocity pressure and thereby creates a static pressure differential that results in an upward lifting force on the wing.

 

[rootone]

This configuration is the most suitable for generating lift.
Some reasonably detailed information here.
https://en.wikipedia.org/wiki/Airfoil.

Lift comes from a combination of this aerodynamic shape and the wing's angle of attack.
Designs intended for heavy lifting aircraft have quite a thick wing cross section and pay a penalty for this in terms of increased drag,
which means bigger engines are needed, even though these type of planes are not designed for high speed.
Conversely, planes which are intended for high speed rather than weight lifting have quite a thin cross section, with the curvature of the top surface being much less.

 

[boneh3ad]

and the method of doing this is by creating a longer curved flow path and a resulting higher air velocity over the top of the wing than on the shorter path flat bottom. The mass flow must be the same from the front to the back of the wing for both the top and bottom surfaces; so, for the longer length of the curved top the air must flow faster than that of the bottom to maintain the equal mass flow over both surfaces.

You have to be very careful here, as this explanation sounds suspiciously close to both the equal transit time fallacy and the incorrect Venturi explanation for lift. In fact, a longer path does not guarantee faster flow. In reality, the faster flow has to do with the fact that the trailing stagnation point is artificially fixed to a point at the trailing edge rather than being allowed to move freely (usually via a sharp trailing edge). The the conservation laws dictate that the flow is faster over the top.

Hello everyone!

I wanted to ask: Why is it (usually) that the bottom of a wing is flatter than the top? A detailed reason would be appreciated.

Thank you!

Essentially, the flatter bottom tends to result in a better L/D ratio compared to the symmetric case.

 

[JBA]

boneh3ad, Your point regarding the implication of my explanation is well taken. However, in the circulation theory based upon the rotating cylinder concept, the stagnation pressure point on the under side of the wing is shifted forward from the trailing edge. Actually a NASA Glenn Center summary of the Bernoulli and Newton principle applications to lift states that both principles are flawed simplifications of the complex issue of lift.

Just as a side note, even these days one has to be very careful about what appear to be reliable references. In reviewing the subject a bit I ran across one aerospace refernce that made the false statement that all lift is due angle of attack and an unsymetrical tearshaped (standard) airfoil without an angle of attack does not generate any lift. In reality, a standardized airfoil configuration designated as an NACA 4415 actually has a lift coefficient of .25 as opposed to a symmetrical NACA 0006 airfoil coefficient of 0 at a 0 angle of attack.

 

[David Lewis]

Some confusion may stem from which airfoil reference line angle of attack is measured. On a flat bottom airfoil, you have three choices:
1. chord line
2. lower surface (a.k.a. rigger's line)
3. zero lift axis (a.k.a. zero lift line)

 

[Loren]

Lift is created by creating a lower pressure area on the top of the wing than below it; and the method of doing this is by creating a longer curved flow path and a resulting higher air velocity over the top of the wing than on the shorter path flat bottom. The mass flow must be the same from the front to the back of the wing for both the top and bottom surfaces; so, for the longer length of the curved top the air must flow faster than that of the bottom to maintain the equal mass flow over both surfaces. This higher velocity converts more of the static air pressure to velocity pressure and thereby creates a static pressure differential that results in an upward lifting force on the wing.

Yeah, that's what they teach you in school, but it's not actually true. After 100 years of aviation you think they would get this sorted out, but for some reason the myth lives on.

Angle of attack is what gives a wing lift.

You can fly an aircraft upside down with an airfoil. In fact, aerobatic aircraft have wings with curves on both sides.

It's the trailing edge of the wing that directs air downward (Coanda effect). That's what generates lift, not path length. The inertia of the air mass trailing downward is the real cause.

 

[boneh3ad]

It's the trailing edge of the wing that directs air downward (Coanda effect). That's what generates lift, not path length. The inertia of the air mass trailing downward is the real cause.

It is not the Coanda effect. The Coanda effect concerns a jet of fluid clinging to a surface. A wing does not involve such a jet unless it is one of the few designs with engines attached to blow the exhaust jet along the surface.

 

[russ_watters]

Yeah, that's what they teach you in school, but it's not actually true. After 100 years of aviation you think they would get this sorted out, but for some reason the myth lives on.

Angle of attack is what gives a wing lift.

The way you worded that implies you are saying that positive angle of attack is required for lift, which isn't true for most airfoils (or, rather, it is only true for symmetrical and upside-down airfoils).

It's the trailing edge of the wing that directs air downward (Coanda effect). That's what generates lift, not path length. The inertia of the air mass trailing downward is the real cause.

That's at best a vast oversimplification and if you look at the pressure profile over an airfoil, it looks more like the majority of the lift comes in the front half and top of the airfoil, where the displacement of the airflow away from freestream is greatest, velocity is therefore greatest and pressure drop greatest.

 

[Hysteresis]

boneh3ad, Your point regarding the implication of my explanation is well taken. However, in the circulation theory based upon the rotating cylinder concept, the stagnation pressure point on the under side of the wing is shifted forward from the trailing edge. Actually a NASA Glenn Center summary of the Bernoulli and Newton principle applications to lift states that both principles are flawed simplifications of the complex issue of lift.

You also want to be careful here when discussing "Potential Flow Theory" as this has a huge paradox. The integration states that yes lift can be generated, and it is generated. However the paradox states that the flow is "drag free" which defies the laws of physics. Be careful when using this principle

 

[David Lewis]

Russ Watters, Please give me an example of an airfoil that does NOT require a positive angle of attack to generate lift.

 

[rcgldr]

Russ Watters, Please give me an example of an airfoil that does NOT require a positive angle of attack to generate lift.

In order to generate lift, a wing has to have an positive effective angle of attack, where by definition, the effective angle of attack is zero when the wing produces zero lift. Because of the way angle of attack is defined, usually by the chord line, which is a straight line from the leading to the trailing edge, then a cambered airfoil can produce lift with a negative angle of attack, where the trailing edge is slightly higher than the leading edge (you could think of this as a wing where the trailing edge was trimmed off a bit, resulting in a higher trailing edge). It's easier to see why this happens if you look at the mean camber line instead of the chord line. NASA articles:

http://www.grc.nasa.gov/www/k-12/airplane/geom.html

http://www.grc.nasa.gov/www/k-12/airplane/incline.html

Example airfoil where Cl (coefficient of lift) becomes > 0 at alpha (angle of attack) < 0, look at the Cl versus alpha graph, where Cl = 0.5 at alpha = 0. The side view of the airfoil shows it at 0 alpha.

http://airfoiltools.com/airfoil/details?airfoil=naca4412-il

Main page:

http://airfoiltools.com/airfoil/naca4digit

There are several web sites with a list of airfoils. Back to the original question:

Why is it (usually) that the bottom of a wing is flatter than the top?

Because such air foils are more efficient for "usual" wing loadings and air speed. A good example of an exception is the M2-B2, which was a pre-shuttle re-entry prototype, where a high lift to drag ratio was not a key factor:

 

[russ_watters]

In order to generate lift, a wing has to have an positive effective angle of attack, where by definition, the effective angle of attack is zero when the wing produces zero lift. Because of the way angle of attack is defined, usually by the chord line, which is a straight line from the leading to the trailing edge, then a cambered airfoil can produce lift with a negative angle of attack, where the trailing edge is slightly higher than the leading edge (you could think of this as a wing where the trailing edge was trimmed off a bit, resulting in a higher trailing edge). It's easier to see why this happens if you look at the mean camber line instead of the chord line. NASA articles:

Right, and so the geometric angle of attack is nearly always negative when the effective angle of attack is zero.

You can see this in lift vs aoa graphs:

This is important because it also means in the lowest drag condition (near zero geometric aoa) a wing still provides lift.

 

[cjl]

boneh3ad, Your point regarding the implication of my explanation is well taken. However, in the circulation theory based upon the rotating cylinder concept, the stagnation pressure point on the under side of the wing is shifted forward from the trailing edge. Actually a NASA Glenn Center summary of the Bernoulli and Newton principle applications to lift states that both principles are flawed simplifications of the complex issue of lift.

This isn't really true - the circulation around an airfoil will be such that the trailing stagnation point is at the sharp trailing edge. This is caused by the impact of viscosity at the sharp trailing edge. A non-symmetric airfoil is shaped such that when the airfoil is at zero geometric angle of attack, in order for the trailing stagnation point to be at the sharp trailing edge, the circulation around the airfoil must be nonzero. For any airfoil producing lift, the circulation around the airfoil will be nonzero, and it will be such that the rear stagnation point is at the sharp edge (I'm assuming a nonstalled, subsonic airfoil here). I agree fully with boneh3ad's explanation for lift - a sharp or in some cases flat trailing edge fixes the rear stagnation point, which enforces a circulation around the airfoil. Because of this circulation, you end up with a faster flow over the top (and Bernoulli does indeed apply here), and you also end up with a downwash (Newton also applies). The lift of an airfoil is entirely explainable by integrating the pressure over the entire wing surface, and it is also completely explainable by measuring the massflow and downward velocity of the downwash generated by the wing. These are not two separate methods of generating lift - they're two different ways of measuring, visualizing, and explaining the same lift.

 

[JBA]

Right, and so the geometric angle of attack is nearly always negative when the effective angle of attack is zero.

You can see this in lift vs aoa graphs:

This is important because it also means in the lowest drag condition (near zero geometric aoa) a wing still provides lift.

The above graph is meaningless without a wingfoil shape reference similar to the NACA reference I used in my above post. The problem we are having here is that everyone is focused on high performance jet aircraft that when unpowered have the glide slope of a rock.
To see the real effects of wing profiles for lift you need to be looking into the lift performance of wing profiles on small low speed propeller driven aircraft similar to Piper Cubs and Cessna 150's or 170's that are hard to get on the ground with even a 35 mph headwind. Before you ask, yes, I received my single engine flight certificate and have flown these aircraft.

 

[cjl]

The above graph is meaningless without a wingfoil shape reference similar to the NACA reference I used in my above post. The problem we are having here is that everyone is focused on high performance jet aircraft that when unpowered have the glide slope of a rock.
To see the real effects of wing profiles for lift you need to be looking into the lift performance of wing profiles on small low speed propeller driven aircraft similar to Piper Cubs and Cessna 150's or 170's that are hard to get on the ground with even a 35 mph headwind. Before you ask, yes, I received my single engine flight certificate and have flown these aircraft.

Why would the wing profiles on jet aircraft be irrelevant? Modern jetliners have fantastic airfoils, much better than something you find on a Piper Cub.

 

[JBA]

Not for flying at low speeds. I am not saying that the wing profiles for high speed jets are irrelevant. I am saying that the wing profiles of low speed aircraft are also relevant when discussing the lifting characteristics of various wing profiles.

 

[Randy Beikmann]

Here's a very nice video that shows the errors in the traditional lift argument. The air over the top of the wing travels so much faster than that on the bottom that it reaches the rear of the wing well before, despite the longer path:

http://www.telegraph.co.uk/news/sci.../Cambridge-scientist-debunks-flying-myth.html

If you follow up with this professor's explanations, he states that what matters is that air is deflected downward, which of course is required by impulse and momentum relationships.

 

[cjl]

Here's a very nice video that shows the errors in the traditional lift argument. The air over the top of the wing travels so much faster than that on the bottom that it reaches the rear of the wing well before, despite the longer path:

http://www.telegraph.co.uk/news/sci.../Cambridge-scientist-debunks-flying-myth.html

If you follow up with this professor's explanations, he states that what matters is that air is deflected downward, which of course is required by impulse and momentum relationships.

Yes, but of course, by a force balance argument, it is also required that the pressure on top of the wing is lower than the pressure below it. Solving the details of the flowfield though requires an understanding of circulation.

 

[russ_watters]

The above graph is meaningless without a wingfoil shape reference similar to the NACA reference I used in my above post.

Suffice to say it is a typical of cambered airfoils. The question of zero aoa still resulting in lift was my one and only point in posting it. There are no nitty-gritty details needed for the point I was trying to make that would make it useful to analyze the details of the airfoil.

The problem we are having here is that everyone is focused on high performance jet aircraft...

I haven't seen that from anyone.

To see the real effects of wing profiles for lift you need to be looking into the lift performance of wing profiles on small low speed propeller driven aircraft...

No, there is nothing fundamentally different about different airfoils when it comes to the simple issues we are discussinig.

 

[JBA]

So you are saying there is no fundamental difference between symmetrical and unsymmetrical airfoils. NACA test data and curves do not agree with you when it comes to angle of attack vs lift.

 

[russ_watters]

Here's a very nice video that shows the errors in the traditional lift argument. The air over the top of the wing travels so much faster than that on the bottom that it reaches the rear of the wing well before, despite the longer path:

http://www.telegraph.co.uk/news/sci.../Cambridge-scientist-debunks-flying-myth.html

If you follow up with this professor's explanations, he states that what matters is that air is deflected downward, which of course is required by impulse and momentum relationships.

I really dislike such explanations (and they really are all over the place) because they ask and answer different questions, resulting in wrong understanding of the issues. The video is bad and the accompanying news article is worse. Even the IOPscience article contains similar flaws caused by overzealous debunking of questions they ask themselves.

The main problem is that they take a bunch of different explanations and lump them all into the "equal transit time" fallacy basket even if they never mention the equal transit time fallacy. That's what happened regarding the responses to post #2 of this thread: it doesn't contain the equal transit time fallacy, yet people responded to it as if it did.

 

[cjl]

So you are saying there is no fundamental difference between symmetrical and unsymmetrical airfoils. NACA test data and curves do not agree with you when it comes to angle of attack vs lift.

Do you think that jetliners use symmetrical airfoils?

 

[russ_watters]

So you are saying there is no fundamental difference between symmetrical and unsymmetrical airfoils.

I'm really questioning whether you actually read my posts because you seem to have gotten from them the exact opposite of what I said.

In either case, if you want a more detailed picture than what I provided, showing the airfoil section, rcgldr provided one:
http://airfoiltools.com/airfoil/details?airfoil=naca4412-il

The problem is that I can't easily embed the content in the thread like I could the picture of the lift curve I posted.

 

[Randy Beikmann]

How is the video "bad?" Isn't it clear from it that the flow over the top of the wing is way faster than the "equal time" explanation would predict? That's what he's trying to say. And instead of looking at the article (most articles are superficial), I looked up his website. The explanation he gives is much more basic and intuitive than I've seen elsewhere. I think it's best to start simple, then add detail. This is what he seems to do.

 

[russ_watters]

How is the video "bad?" Isn't it clear from it that the flow over the top of the wing is way faster than the "equal time" explanation would predict? That's what he's trying to say.

I gather that what he intended was to cite and then debunk the "equal transit time theory", but what is wrong is that he cited something that wasn't the equal transit time theory, then debunked the equal transit time theory. Here's what he actually said:

It is often said that lift in a wing is generated because the flow moving over the top surface has a longer distance to travel and therefore needs to go faster. This common explanation is actually wrong. This video shows that the air on the top does move faster, but it doesn't reach the end of the wing at the same time as the air along the bottom.

The first sentence says nothing about the air flowing over the top surface reaching the end of the wing at the same time as the air along the bottom surface, yet he responds to his own statement as if that's what it says. One can certainly nitpick simplifications about that first sentence (it is obviously not all there is to say about lift), but it doesn't contain the flaw he says it contains. The same also happens when someone cite's Bernoulli's principle with respect to airfoils: someone invariably (and very wrongly) assumes they are citing the equal transit time fallacy.

I see this mismatch almost every time someone brings up the equal transit time theory and I see the equal transit time theory brought up almost every time as an unsolicited debunking of something nobody said (such as in this very thread). At this point, the equal transit time myth is practically a myth itself.

 

[Randy Beikmann]

In the article in the link, they do say

"According to conventional wisdom the pressure change happens because the air on the curved upper surface of the wing has further to travel than that below the flat underneath surface, meaning it must travel faster to arrive at the other side of the wing at the same time."

His quote might not be complete in itself, but with this context, I think it becomes clear what he is trying to debunk.

 

[JBA]

I'm really questioning whether you actually read my posts because you seem to have gotten from them the exact opposite of what I said.

In either case, if you want a more detailed picture than what I provided, showing the airfoil section, rcgldr provided one:
http://airfoiltools.com/airfoil/details?airfoil=naca4412-il

The problem is that I can't easily embed the content in the thread like I could the picture of the lift curve I posted.

No, there is nothing fundamentally different about different airfoils when it comes to the simple issues we are discussinig.

I took your above statement out of context since it was located at the bottom below my quote and did not include ...between low speed and jet aircraft... (my error)
At the same time, I keep seeing the general statement "that there cannot be any lift at a zero angle of attack" repeated over and over in this tread; and that is not true, as seen the Cl vs α curve in the sample plots of your above reference where Cl = .50 at α = 0

 

[russ_watters]

In the article in the link, they do say

"According to conventional wisdom the pressure change happens because the air on the curved upper surface of the wing has further to travel than that below the flat underneath surface, meaning it must travel faster to arrive at the other side of the wing at the same time."

His quote might not be complete in itself, but with this context, I think it becomes clear what he is trying to debunk.

Yes, that's an interesting discrepancy. It isn't clear to me where it came from, but it matters a lot that he doesn't say it correctly. As you yourself pointed out, the video is supposed to be the more reliable source, not less. The article contains similar additional errors and when you add them all together, you come away having corrected one error and learned 5 new ones.

The sailboat one is another glaring one, cited in the news article and the iopscience article. They claim that the fact that a sail is thin means the air moving over both surfaces travels the same distance. That's utter nonsense. What makes aerodynamics hard to visualize is that most of what a wing does to the air happens away from the surface and only by looking at the entire flow field can you really see what is going on. Thin airfoils act surprisingly like thick airfoils, just less efficient at doing the job. The air essentially "piles up" under the wing, so much of it doesn't actually follow the curvature of the airfoil. The iopscience article says the distances are "more or less" the same, glossing over the fact that no, they really aren't anywhere close to the same.

You can see in the visualizations of the flow field that the streamlines on the bottom near the leading edge slow down, expand and pile-up, whereas the streamlines over the top are compressed and stretched out.

 

[russ_watters]

At the same time, I keep seeing the general statement "that there cannot be any lift at a zero angle of attack" repeated over and over in this tread; and that is not true, as seen the Cl vs α curve in the sample plots of your above reference where Cl = .50 at α = 0

That's why I said that it looks like you didn't read my post: it was specifically, and correctly, addressing that very point.

 

[JBA]

Thank you for that much needed reference input on the issue.

 

[boneh3ad]

How is the video "bad?" Isn't it clear from it that the flow over the top of the wing is way faster than the "equal time" explanation would predict? That's what he's trying to say. And instead of looking at the article (most articles are superficial), I looked up his website. The explanation he gives is much more basic and intuitive than I've seen elsewhere. I think it's best to start simple, then add detail. This is what he seems to do.

The video is bad, but the conclusions you and the article are drawing from it are bad. The video simply debunks "equal transit time", not the idea that the pressure differential can cause lift. In fact, lift is directly related to that pressure differential. The problem is that the reason the air moves faster over the top is actually quite complicated and not something conducive to the quick, simple explanations that most people are willing to read.

I gather that what he intended was to cite and then debunk the "equal transit time theory", but what is wrong is that he cited something that wasn't the equal transit time theory, then debunked the equal transit time theory. Here's what he actually said:

The first sentence says nothing about the air flowing over the top surface reaching the end of the wing at the same time as the air along the bottom surface, yet he responds to his own statement as if that's what it says. One can certainly nitpick simplifications about that first sentence (it is obviously not all there is to say about lift), but it doesn't contain the flaw he says it contains. The same also happens when someone cite's Bernoulli's principle with respect to airfoils: someone invariably (and very wrongly) assumes they are citing the equal transit time fallacy.

Honestly, the sentence in the video is perfectly fine. As I mentioned in my original post in this thread, if you say the longer path is the reason the air moves faster and pressure goes lower, there are really only two ways to interpret that as working, and both of them are incorrect. The most obvious of those two is the equal transit time fallacy, and the one that requires slightly more of a stretch is the Venturi fallacy. Either way, it's wrong. The most common one is what he addresses in the video.

The article posted by Randy citing the video is just bad.

The sailboat one is another glaring one, cited in the news article and the iopscience article. They claim that the fact that a sail is thin means the air moving over both surfaces travels the same distance. That's utter nonsense. What makes aerodynamics hard to visualize is that most of what a wing does to the air happens away from the surface and only by looking at the entire flow field can you really see what is going on. Thin airfoils act surprisingly like thick airfoils, just less efficient at doing the job. The air essentially "piles up" under the wing, so much of it doesn't actually follow the curvature of the airfoil. The iopscience article says the distances are "more or less" the same, glossing over the fact that no, they really aren't anywhere close to the same.

I have to respectfully disagree with you here. The distances will be quite nearly the same as long as the sail doesn't have too extreme of a curve. In reality, barring flow separation or speeds high enough for compressibility to be a factor, most of the flow does follow the surface of a shape and the flow does not "pile up" at all.

You can see in the visualizations of the flow field that the streamlines on the bottom near the leading edge slow down, expand and pile-up, whereas the streamlines over the top are compressed and stretched out.

That's not what is occurring there. That streamline is very close to the stagnation streamline (or likely partially on top of it) so it actually splits and some air goes each way.

 

[Randy Beikmann]

Ummm, where did I say that pressure differential can't cause lift? For that matter, how could you have lift without pressure differential?

 

[boneh3ad]

The article you posted made a claim about that. It said that the pressure difference explanation was wrong because the author didn't understand the articles he read as the basis for his own article. I never said you specifically made that claim.

 

[Randy Beikmann]

You said "The video is bad, but the conclusions you and the article are drawing from it are bad."

So what conclusions I drew from it are "bad?"

 

[russ_watters]

Honestly, the sentence in the video is perfectly fine. As I mentioned in my original post in this thread, if you say the longer path is the reason the air moves faster and pressure goes lower, there are really only two ways to interpret that as working, and both of them are incorrect. The most obvious of those two is the equal transit time fallacy, and the one that requires slightly more of a stretch is the Venturi fallacy. Either way, it's wrong. The most common one is what he addresses in the video.

As you probably remember, I don't agree with your interpretation of the Venturi analogy, but regardless it is a fact that the path that the air over the top surface takes requires it to move faster than the air over the bottom surface in order to satisfy continuity. If one wants to call it an inside-out Venturi, an obstruction, or just a longer path, the fact that the air is displaced requires an increase in speed, otherwise it would have to compress. I'll say it again another way: the only way to get around an obstruction without compressing is to move faster in the vicinity of the obstruction. Rather than nitpicking the limitations of the analogy, one should amplify what it gets right. In either case, my biggest complaint both about the particular chosen analogy and the unsolicited equal transit time debunking is that so much time is spent pointing out things that aren't quite exactly right that people (not just you) never get around to explaining what actually happens.

And one day, I'm going to build an adjustable area Venturi to show that no matter how far apart you move the sides, there never ceases to be a lower pressure at the throat. But even without me building it, I think you know it is true: The A2/A1=V1/V2 ratio may break down as they move apart, but the principle that the curved surface squeezes the air and causes it to accelerate never goes away.

I have to respectfully disagree with you here. The distances will be quite nearly the same as long as the sail doesn't have too extreme of a curve.

That's the same cop-out as in the article: the less the curve and less the angle of attack, the less the lift. Of course. "Nearly" the same gets further and further from being the same the greater the curvature and greater the aoa, thus greater the lift. Or more directly: the difference in the path lengths is directly related to how much lift is generated.

In reality, barring flow separation or speeds high enough for compressibility to be a factor, most of the flow does follow the surface of a shape and the flow does not "pile up" at all.

The piling-up and stretching-out of the streamlines is quite evident in flow visualizations:

The streamlines start-out nearly uniformly distributed, but in the area of the stagnation point (one streamline is just a touch below the stagnation point) they look to me to be about 10x further apart than at the top of the airfoil. If one isn't getting squeezed perpendicular and the other smooshed lengthwise, I'd like to hear what you would call that!

 

[boneh3ad]

As you probably remember, I don't agree with your interpretation of the Venturi analogy, but regardless it is a fact that the path that the air over the top surface takes requires it to move faster than the air over the bottom surface in order to satisfy continuity. If one wants to call it an inside-out Venturi, an obstruction, or just a longer path, the fact that the air is displaced requires an increase in speed, otherwise it would have to compress.

It is not an inside-out Venturi. I cannot stress that enough. Treating it as such results in a number of incorrect conclusions, not the least of which is a completely incorrect calculation of the velocity field. Consider that if it was an inside-out Venturi, it would also require the air to move faster over the bottom and have a lower pressure than it does in the free stream. This is often the case, but not always, and that fact flies in the face of the Venturi analogy. It is simply incorrect. For more on that, see NASA.

It is also a problem to say that the path over the top requires it to move faster than over the bottom. That statement implies that it even makes sense to treat the two surfaces independently in the fluid-dynamic analysis, and it does not. If you change the bottom surface, it will change the flow over the top and vice versa. They are a coupled system. So yes, the air does move faster over the top, but it is due to the whole shape, not just the shape of the top.

I'll say it again another way: the only way to get around an obstruction without compressing is to move faster in the vicinity of the obstruction. Rather than nitpicking the limitations of the analogy, one should amplify what it gets right.

This flies in the face of the entire argument you just made about the video. You sat there and nitpicked the first sentence even though it was essentially correct.

In either case, my biggest complaint both about the particular chosen analogy and the unsolicited equal transit time debunking is that so much time is spent pointing out things that aren't quite exactly right that people (not just you) never get around to explaining what actually happens.

I've explained time and again what actually happens on this site, and in fact, have put together an Insight that addresses this whole issue that is currently going through some iteration. Maybe that will clear it up more permanently. Suffice it to say that it has to do with the trailing edge shape and viscosity. If there was no viscosity, there would be no lift and the stagnation point would end up on top of the airfoil somewhere. Due to viscosity, there is essentially separation enforced at the sharp trailing edge (it works with a flatback airfoil, too), and the rest of the flow field must react to that viscosity-enforced stagnation point location. At that point it's just conservation of mass and momentum. The net result is that you end up with a circulation around the airfoil, or a bound vortex. This is why you sometimes see lift discussed in terms of the circulation around it, called the Kutta-Joukowski theorem.

And one day, I'm going to build an adjustable area Venturi to show that no matter how far apart you move the sides, there never ceases to be a lower pressure at the throat. But even without me building it, I think you know it is true: The A2/A1=V1/V2 ratio may break down as they move apart, but the principle that the curved surface squeezes the air and causes it to accelerate never goes away.

Of course there would always be a slightly lower pressure, though you would rapidly reach the point where that difference is not measurable. Give me the accuracy of your pressure transducer and I can even tell you when that pressure difference is no longer measurable. And yet, with an airfoil, with the "walls" at infinity, there is still a drastic pressure change. It is not the Venturi effect, has little if anything to the Venturi effect, and cannot be predicted by the Venturi effect.

That's the same cop-out as in the article: the less the curve and less the angle of attack, the less the lift. Of course. "Nearly" the same gets further and further from being the same the greater the curvature and greater the aoa, thus greater the lift. Or more directly: the difference in the path lengths is directly related to how much lift is generated.

I don't think you get what I meant there. The reason the path would be longer with a large curve is that at some point you will end up with a large recirculation bubble inside the sail, and the free stream will track around that. In the absence of that, it will follow the sail. The difference in path lengths is not directly related to how much lift is generated. That logic would then lead to the conclusion that any airfoil whose bottom path is longer generates negative lift, and that is not true.

The piling-up and stretching-out of the streamlines is quite evident in flow visualizations:

The streamlines start-out nearly uniformly distributed, but in the area of the stagnation point (one streamline is just a touch below the stagnation point) they look to me to be about 10x further apart than at the top of the airfoil. If one isn't getting squeezed vertically and the other smooshed horizontally, I'd like to hear what you would call that!

Ah, I see what you were saying now. This is exactly the concept of a streamline. Streamlines are defined such that no mass flow can cross them, so if you take any two streamlines in the flow, the region between them can essentially be treated as a quasi-1D control volume called a streamtube. So when you look at the streamline spacing there, they get closer when the velocity increases since the same mass flow passes between them but with a higher velocity. That is a direct application of the Venturi effect.

 

[russ_watters]

Consider that if it was an inside-out Venturi, it would also require the air to move faster over the bottom and have a lower pressure than it does in the free stream. This is often the case, but not always, and that fact flies in the face of the Venturi analogy.

You're trying to harness your own self-contradiction: yes, it is often the case that the air moves faster and results in a pressure drop along the bottom surface. Most obviously, in a symmetrical airfoil at zero aoa, which, not coincidentally, looks very much like an inside-out Venturi! As the two sides present less symmetrical profiles to the air, the pressure profiles necessarily change. That doesn't fly in the face of the analogy, that is the analogy!

For more on that, see NASA.

Terrible site. Their first objection is the flat statement that a wing is not a Venturi. I should point the to the dictionary.com listing for the word "analogy" because they clearly don't get the point. As with what you are objecting to, all of these objections peck around the periphery without actually addressing the point of the analogy. Most of the other details you provide, so I won't go point by point through the site.

It is also a problem to say that the path over the top requires it to move faster than over the bottom. That statement implies that it even makes sense to treat the two surfaces independently in the fluid-dynamic analysis, and it does not. If you change the bottom surface, it will change the flow over the top and vice versa.

That's a self-contradiction. How can saying the air over the top surface moves faster than over the bottom be treating them separately? They are both right there next to each other in the same sentence.

Still, you can have an airfoil that only has a top surface and no bottom surface. Cars are like that, or even more so any object attached to the ground that wind blows over causes a pressure drop above it. That's what causes roofs to lift off houses in wind storms. Wind wake analysis shows the higher velocity and lower pressure (than freestream) over the top of the building: http://www.advantech.vn/vi/tin-tuc/tin-ansys/1951-mo-phong-ansys-cfd-va-wow-giup-giam-thieu-thiet-hai-do-bao.html
Sorry about the translation: look at the last two images.

This flies in the face of the entire argument you just made about the video. You sat there and nitpicked the first sentence even though it was essentially correct.

You have that exactly backwards: You're right that the first sentence is basically correct: the narrator is the one who nitpicked it, not me! I merely pointed out that what he was nitpicking wasn't even in his own premise! Again, that video is just like how here and in a lot of other places, people jump into debunk the equal transit time fallacy when it isn't being invoked. I don't think that's a coincidence: think equal transit time debunkers wrongly believe that for two streamlines to separate and then meet up again, they must meet in the same alignment. That's why whenever they hear someone say the two streamlines separate and meet up, they wrongly conclude that the statement requires them to align and wrongly invoke/debunk the ETT fallacy.

Due to viscosity, there is essentially separation enforced at the sharp trailing edge (it works with a flatback airfoil, too), and the rest of the flow field must react to that viscosity-enforced stagnation point location. At that point it's just conservation of mass and momentum. The net result is that you end up with a circulation around the airfoil, or a bound vortex. This is why you sometimes see lift discussed in terms of the circulation around it, called the Kutta-Joukowski theorem.

That describes why air goes over the top or bottom surface (why the stagnation point moves down as the angle of attack goes up, for example), but does not address the question of why the air going over the top surface moves faster than the air that moves over the bottom surface (or faster than freestream). And don't look now, but if we dip a toe into what happens at the trailing edge, we could blame Kutta-Joukowski for the equal transit time theory. (from the wiki: "fluids moving along the lower and upper surfaces of the airfoil should meet at the sharp trailing edge").

I erred earlier when I said the A2/A1=V1/V2 ratio doesn't hold for a wing. It does, just not as directly/globally as for a Venturi: for any parcel of air, its own cross sectional area and velocity are always inversely proportional as it moves along its streamline.

Of course there would always be a slightly lower pressure, though you would rapidly reach the point where that difference is not measurable. Give me the accuracy of your pressure transducer and I can even tell you when that pressure difference is no longer measurable.

This simply isn't true. The wind wake analysis link shows a substantial pressure drop associated with flow over the top of a building even though there is no "bottom surface" to the wing or "other side" of the Venturi tube.

I don't think you get what I meant there. The reason the path would be longer with a large curve is that at some point you will end up with a large recirculation bubble inside the sail, and the free stream will track around that. In the absence of that, it will follow the sail.

You were arguing to look at a smaller curve, not a larger curve. I don't think you got what *I* said, because I said almost exactly what you just did: I said "piles up" instead of "recirculation bubble" but in either case, we agree that the air does not follow the curve of the sail, which is precisely why the claimed example doesn't work as it claims it does. Reducing the camber/aoa is an attempt to hide that flaw. But it can only reduce the magnitude, it can't make it go away.

The difference in path lengths is not directly related to how much lift is generated. That logic would then lead to the conclusion that any airfoil whose bottom path is longer generates negative lift, and that is not true.

I'd like to see an example that satisfies your counter-claim. I can't prove a negative, but what I can say is that if you flip an airfoil upside-down (at zero aoa in both cases) so its bottom path length is now longer, it does indeed generate negative lift.

And just to head-off a potential misunderstanding: that is the path length of the parcel of air, not the distance between the geometric leading and trailing edge of the airfoil. If you flip an airfoil over, then give it a ridiculous positive angle of attack, the stagnation point moves way down the "bottom" surface, providing a longer path over the "top".

Ah, I see what you were saying now. This is exactly the concept of a streamline. Streamlines are defined such that no mass flow can cross them, so if you take any two streamlines in the flow, the region between them can essentially be treated as a quasi-1D control volume called a streamtube. So when you look at the streamline spacing there, they get closer when the velocity increases since the same mass flow passes between them but with a higher velocity. That is a direct application of the Venturi effect.

Precisely. Perhaps that renders much of the rest of this discussion moot, but since I already typed-out the whole thing over the past hour, I'm still going to hit "post reply"...

 

[russ_watters]

boneh3ad, I think most of the problem here is a mismatch of two peculiarities of each of our presentations:
1. I didn't do well in my aerospace studies (thus switched to mechanical), which makes many of my presentations imprecise ("piles up" instead of "recirculation bubble") even if the issue at hand is correct (we both agreed that the airflow does not follow the "bottom" curve of the sail).
2. You have adopted a level of rigor (again likely because of your education) that doesn't allow for any imprecision and thus causes you to see only all-or-nothing answers.

 

[boneh3ad]

You're trying to harness your own self-contradiction: yes, it is often the case that the air moves faster and results in a pressure drop along the bottom surface. Most obviously, in a symmetrical airfoil at zero aoa, which, not coincidentally, looks very much like an inside-out Venturi! As the two sides present less symmetrical profiles to the air, the pressure profiles necessarily change. That doesn't fly in the face of the analogy, that is the analogy!

That is not correct though. It is 100% coincidental that a symmetric airfoil looks like an inside-out Venturi. The problems with the model only increase if you add angle of attack or if you remove the symmetry. Like I pointed out before, not all lift-generating airfoils have a longer path over the top, and the Venturi model would say these have to generate negative lift. That is not true. The Venturi model also would imply that the pressure on the bottom has to be lower than ambient. That also is not true.

Terrible site. Their first objection is the flat statement that a wing is not a Venturi. I should point the to the dictionary.com listing for the word "analogy" because they clearly don't get the point. As with what you are objecting to, all of these objections peck around the periphery without actually addressing the point of the analogy. Most of the other details you provide, so I won't go point by point through the site.

Then what exactly is the point of the analogy? I thought the point of the analogy is to address why the air must move faster over the top, thus the lower pressure. That same analogy also implies that a longer path must produce a faster flow than a shorter path, which, again, is false. If the point is just to give a simple analogy so that people can see it should go faster without resorting to equal transit time, it still fails because it still does not describe why the flow goes faster. The fundamental mechanism is different and it leads to wrong conclusions if you get people to start thinking along those lines. That isn't why it should go faster over the top.

That's a self-contradiction. How can saying the air over the top surface moves faster than over the bottom be treating them separately? They are both right there next to each other in the same sentence.

In your post, you simply said that the path over the top requires the air to move faster. That implies that the air over the top will move faster simply because of the shape of the top without regard for the shape of the bottom, which is not a true statement. Further, the entire concept of the Venturi analogy implies that you could treat them separately. It basically implies that you can draw line down both stagnation streamlines and say that the flow above and below those are uniquely determined by the airfoil shape above and below those. That also is not the case. That is another place where the Venturi analogy fails.

Still, you can have an airfoil that only has a top surface and no bottom surface. Cars are like that, or even more so any object attached to the ground that wind blows over causes a pressure drop above it. That's what causes roofs to lift off houses in wind storms. Wind wake analysis shows the higher velocity and lower pressure (than freestream) over the top of the building: http://www.advantech.vn/vi/tin-tuc/tin-ansys/1951-mo-phong-ansys-cfd-va-wow-giup-giam-thieu-thiet-hai-do-bao.html
Sorry about the translation: look at the last two images.

This is obvious and I have never contradicted this, Although, a car absolutely does have two sides unless it has no wheels and is skidding on the ground, in which case you are probably in a James Bond car chase. Also, in the case of the house, this still is not due to the Venturi effect. With a car, on the underside there may be some Venturi-like physics going on, but it is substantially more complicated since viscosity causes air to "stick" to both the underside of the car and the pavement, so it is actually more like Couette flow.

Again, that video is just like how here and in a lot of other places, people jump into debunk the equal transit time fallacy when it isn't being invoked. I don't think that's a coincidence: think equal transit time debunkers wrongly believe that for two streamlines to separate and then meet up again, they must meet in the same alignment. That's why whenever they hear someone say the two streamlines separate and meet up, they wrongly conclude that the statement requires them to align and wrongly invoke/debunk the ETT fallacy.

I wholehearted disagree with this. I'd consider myself in the "equal transit time" debunker category, and that is because equal transit time is wrong. Of course streamlines can meet back up, and by definition, they have to be in alignment because no two streamlines can every cross each other due to continuity. That doesn't require equal transit time or anything, it just requires conservation of mass. Now that that is out of the way, my issue with the original post where I cautioned JBA with his response is because his answer invoked the "longer curved path" of the top surface compared to the bottom. The only way this statement can lead to lift is via either the equal transit time fallacy or via the Venturi fallacy, both of which are provably incorrect. That is also why my response there mentioned both of them since he didn't specify exactly why the longer path causes faster flow.

That describes why air goes over the top or bottom surface (why the stagnation point moves down as the angle of attack goes up, for example), but does not address the question of why the air going over the top surface moves faster than the air that moves over the bottom surface (or faster than freestream).

It absolutely does explain why the air moves faster over the top. In fact, what I said there tells you that as angle of attack increases (barring stall), the trailing stagnation point does not move. It stays at the trailing edge. The leading stagnation point does, which changes the profile and changes the lift and drag. If viscosity was absent, the trailing stagnation point would be free to move as well and would move in tandem with the leading edge stagnation point, resulting in no net circulation, no net pressure force, and no lift. Precisely because the leading stagnation point is free to move and the trailing stagnation is fixed, however, changing angle of attack also changes the circulation, which changes the velocity over the top, which changes the lift.

And don't look now, but if we dip a toe into what happens at the trailing edge, we could blame Kutta-Joukowski for the equal transit time theory. (from the wiki: "fluids moving along the lower and upper surfaces of the airfoil should meet at the sharp trailing edge").

First: you should know better than to trust Wikipedia for everything, especially an issue as obviously contentious as lift. Second, the quote you supplied doesn't even support your premise here. It says that the fluids meet back up at the trailing edge, not that the same parcel has to meet up with the one that split from it at the beginning. It is simply a statement of smooth flow, aka no separation/stall and no voids in the medium.

I erred earlier when I said the A2/A1=V1/V2 ratio doesn't hold for a wing. It does, just not as directly/globally as for a Venturi: for any parcel of air, its own cross sectional area and velocity are always inversely proportional as it moves along its streamline.

This simply isn't true. The wind wake analysis link shows a substantial pressure drop associated with flow over the top of a building even though there is no "bottom surface" to the wing or "other side" of the Venturi tube.

It is true, and it is provably true. Take some duct with area $A_1$ at the inlet and velocity $v_1$. It constricts to $A_2$ and $v_2$. Clearly, $A_1 v_1 = A_2 v_2$. Now, assume we keep moving the top wall up by small increments $dA$. This gives $(A_1 + dA)v_1 = (A_2 + dA)v_2$, or $v_2/v_1 = (A_1 + dA)/(A_2 + dA)$. Now, if we take that to its logical conclusion, where we keep adding small bits to the top duct, we end up with:
\lim_{dA\to\infty}\dfrac{v_2}{v_1} = \lim_{dA\to\infty}\dfrac{A_1 + dA}{A_2 + dA} = 1.
In other words, at the limit of continually increasing one dimension of the duct to infinity, $v_1 = v_2$ and hence $p_1 = p_2$. The reason the wind wake analysis still shows a sizable pressure drop is because your Venturi analogy is flawed and cannot explain lift, nor can it explain the flow over a house. Venturi cannot explain anything that does not occur in a tube with defined, rigid walls.

You were arguing to look at a smaller curve, not a larger curve. I don't think you got what *I* said, because I said almost exactly what you just did: I said "piles up" instead of "recirculation bubble" but in either case, we agree that the air does not follow the curve of the sail, which is precisely why the claimed example doesn't work as it claims it does. Reducing the camber/aoa is an attempt to hide that flaw. But it can only reduce the magnitude, it can't make it go away.

Yes, I was arguing for a smaller curve because with a smaller curve, no recirculation occurs, and the flow tracks right along both sides of a sail. In that case, the analogy used in the IOPScience article works just fine. With a larger curve, there is more likelihood that the flow separates and causes recirculation and the air no longer tracks the sail surface.

I'd like to see an example that satisfies your counter-claim. I can't prove a negative, but what I can say is that if you flip an airfoil upside-down (at zero aoa in both cases) so its bottom path length is now longer, it does indeed generate negative lift.

Take, for example, the lifting body cited by rcgldr earlier in this thread, the M2-F2.

Precisely. Perhaps that renders much of the rest of this discussion moot, but since I already typed-out the whole thing over the past hour, I'm still going to hit "post reply"...

Nope, it does not render the rest of this moot. The Venturi principle applies between streamlines, but trying to apply it to the whole wing because you can't just pick some arbitrary horizontal streamline, as I showed earlier. It changes the answer.

boneh3ad, I think most of the problem here is a mismatch of two peculiarities of each of our presentations:
1. I didn't do well in my aerospace studies (thus switched to mechanical), which makes many of my presentations imprecise ("piles up" instead of "recirculation bubble") even if the issue at hand is correct (we both agreed that the airflow does not follow the "bottom" curve of the sail).

We don't agree to that. The airflow does follow the bottom curve of the sale provided the curvature is not to high or the angle of attack is not to high.

2. You have adopted a level of rigor (again likely because of your education) that doesn't allow for any imprecision and thus causes you to see only all-or-nothing answers.

No, I simply call out patently false statements like the Venturi fallacy when I see them. I am here primarily to help share my fascination with fluid mechanics with others who come with questions, and when I do that, I like to make sure they understand what is actually occurring to the best of their ability. The Venturi principle has no bearing on airfoils and how the generate lift. You can tie it into why streamlines diverge or converge, but that is about it. I am all for simplified models and analogies, but not those that lead people away from the truth.

 

[rcgldr]

The upper surface of a wing or the downind surface of a sail curves (or slopes) away from the relative flow. The air has to centripetally accelerate towards the surface as it follows the surface to fill in what would otherwise be a void (if stalled, then vortices or mostly one large vortice could fill in what would otherwise be a void). This acceleration coexists with a pressure gradient, where pressure decreases as distance from the upper surface decreases. The reduced pressure zone also coexists with higher speed of air in the direction of the flow, since air accelerates from higher pressure zones to lower pressure zones. The relative speed of the air (wrt wing) is greatest at the lowest pressure zone.

The thin trailing edge issue mentioned by boneh3ad helps keep the flow from seperating too soon from the upper surface of a wing, but as seen with the blunt trailing edge of the M2-F2 (where the M2-F3 has rocket nozzles), doesn't prevent it from generating lift, but the lift to drag ratio is low compared to a conventional wing.

The bottom surface of a wing or the upwind surface of a sail normally exerts a centripetal force on the air causing it to curve, coexistant with a pressure gradient, one that increases as distance from the surface decreases. The increase in pressure coexists with a reduction of the relative speed of the flow.

The main thing a wing or sail has to do is divert the relative flow. A wing diverts the relative flow downwards, while a sail diverts the relative flow (apparent wind) aft of the sailboat. Newton third law pair for a wing, wing exerts a downwards and somewhat forwards force onto the air, air exerts an upwards and somewhat backwards force onto the wing.

 

[JBA]

All through the discussions in this thread there has been something bothering me that I could not identify until the last couple of days.
Due to the fact that the majority of airfoil testing resulting in flow diagrams are performed in wind tunnels combined with the fact that we are generally taught to think in terms of "fluid flow" tends mask the fact that, in service, the correct airfoil frame of reference is a static stagnation pressure air region being impacted and displaced by moving wing rather than a static wing immersed in a flowing dynamic (kinetic) surrounding fluid. For this reason, I am becoming a bit skeptical of the standard "streamline" flow line diagrams that do not indicate any type of radial or lateral flow in surrounding air around the frontal impact region of the airfoils. It is one thing to view airfoil flow as the deflection of a moving air stream and another to view it as disturbance of a static fluid. This incorrect frame of reference can also result in statements such as the "attachment of the stagnation point to the rear point of the airfoil" given in one earlier post. Another effect of the static fluid reference is that it would appear to allow for a momentary increase and dissipation of stagnation pressure in the region of the airfoil due to the airfoil volume displacement and compression of the surrounding air medium.

 

[boneh3ad]

The two frames of reference are quivalent. For an airfoil moving at velocity $U_{\infty}$, they two frames only differ by an additive factor of $U_{\infty}$. The pressure distribution in either case is equivalent as well. I am not sure what diagrams you are accustomed to viewing, but typical streamline diagrams with an airfoil will show a disturbance to the incoming streamlines for quite a distance away from the actual airfoil. The velocities from which those streamlines are derived can also be converted directly to the other frame of reference by subtracting $U_{\infty}$. In the case of the stationary air frame of reference, you simply get zero velocity in the flow that hasn't be influenced by the airfoil yet, and then behind it you have the velocity vectors pointing down and forward (indicating the momentum imparted to the air by the opposing forces to lift and drag respectively). Either way, this does not invalidate using the frame that follows the wing.

Further, there is nothing wrong with statements about "attachment of the stagnation point to the rear point of the airfoil", as this is exactly what happens. That is the whole point of the sharp trailing edge. That is not an incorrect statement and therefore cannot be used as a reason for why that frame or reference is "incorrect".

Also, I am not 100% sure what you mean by a momentary increase and dissipation of stagnation pressure in the region of the airfoil. At the end of the day, though, when discussing pressure, the frame of stationary air makes things more difficult, even if the eventual answer you get is the same. At issue is the fact that in this frame of reference, the flow can no longer be treated as steady-state like it can when you use the frame of a stationary wing. That means things like Bernoulli's equation no longer apply (without modification) and trying to think in terms of total pressure like is typical is more complicated. In essence, the moving airfoil adds some energy (and therefore total pressure) to the air when it passes. I believe that is essentially what you meant with the "increase and dissipation" of stagnation pressure but I thought I'd clarify.

 

[Chestermiller]

All through the discussions in this thread there has been something bothering me that I could not identify until the last couple of days.
Due to the fact that the majority of airfoil testing resulting in flow diagrams are performed in wind tunnels combined with the fact that we are generally taught to think in terms of "fluid flow" tends mask the fact that, in service, the correct airfoil frame of reference is a static stagnation pressure air region being impacted and displaced by moving wing rather than a static wing immersed in a flowing dynamic (kinetic) surrounding fluid. For this reason, I am becoming a bit skeptical of the standard "streamline" flow line diagrams that do not indicate any type of radial or lateral flow in surrounding air around the frontal impact region of the airfoils. It is one thing to view airfoil flow as the deflection of a moving air stream and another to view it as disturbance of a static fluid. This incorrect frame of reference can also result in statements such as the "attachment of the stagnation point to the rear point of the airfoil" given in one earlier post. Another effect of the static fluid reference is that it would appear to allow for a momentary increase and dissipation of stagnation pressure in the region of the airfoil due to the airfoil volume displacement and compression of the surrounding air medium.

Newton's second law is invariant with respect to the inertial frame of reference of the observer. So it is perfectly acceptable to describe the behavior from the frame of reference of an observer traveling at the same velocity as the wing. This is entirely equivalent to having the wing in a wind tunnel.

Chet

 

[David Lewis]

Russ Watters, Thank you for your thoughtful reply to my question.
Off-topic, but in the NACA 4412 airfoil data posted in this thread, section moment coefficient varies from +.01 to -.09 depending on angle of attack (Re = 50k). My understanding, however, is that moment coefficient shouldn't vary that much (with respect to alpha) when moment is measured about the aerodynamic center.

 

[rcgldr]

... in the NACA 4412 airfoil data posted in this thread, section moment coefficient varies from +.01 to -.09 depending on angle of attack (Re = 50k).

Link to an image from a thread at another forum showing a similar pattern for CM, where it's most negative at 0 Alpha (AOA).:

http://forums.x-plane.org/index.php?showtopic=64286