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.