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Mr.BA
Topic Author
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### Lift On An Airfoil

Hi everyone,

Excuse me as this is not the typical kind of question to be asked in this particular forum.

I'm currently in high school we're just into bernoulli's equation and one of the applications is the airfoil. Our textbooks states that the fundamental source of lift is the difference in velocity of airflow over and under the wing hence the difference in pressures which will in return create lift. I've got no problems with this for now.

However it also states that as the airfoil flies through the air, for the velocity of air over the airfoil to be faster than the underside, the air that is separated at the leading edge must converge at the trailing edge. How true is this? If it is, can anyone offer an explanation beyond just the shape of the airfoil on why this will happen? I've done a bit of research on the internet and some sites states that this is not true, that wind tunnel tests have shown otherwise.

Also, just wondering if anyone have figures of how much air can a B747 wing divert downwards per second travelling at Mach.86? If the overwing diverts air downwards, in other words, pulling the air from the top to fill the space or iar that has been just diverted downwards - how does this create lift?

Appreciate any inputs or help!

Thanks,

Mr.BA
Boeing747 万岁!

lehpron
Posts: 6846
Joined: Tue Jul 10, 2001 3:42 am

### RE: Lift On An Airfoil

 Quoting Mr.BA (Thread starter):However it also states that as the airfoil flies through the air, for the velocity of air over the airfoil to be faster than the underside, the air that is separated at the leading edge must converge at the trailing edge. How true is this?

I used to think that but it is not really true. As air goes over the top it drops in presssure and speeds up, but as air goes under the foil the pressure increases and it slows. If a fluid particle were separated in front of the wing, the bottom would lag the top.

 Quoting Mr.BA (Thread starter):I've done a bit of research on the internet and some sites states that this is not true, that wind tunnel tests have shown otherwise.

Exactly.

 Quoting Mr.BA (Thread starter):Also, just wondering if anyone have figures of how much air can a B747 wing divert downwards per second travelling at Mach.86? If the overwing diverts air downwards, in other words, pulling the air from the top to fill the space or air that has been just diverted downwards - how does this create lift?

You are describing downwash, but it does not lift an air plane. FYI, in front of the wing there is an upwash, does it pull the plane down? No.

The basic lift equation is:

L = 1/2 (rho) A V2 CL

letters & symbols mean:

(lift force or weight of the plane) = 0.5 x (density of air refered to by greek letter rho, which looks like an upside-down and flipped over #9) x (wing reference area) x (velocity^2) x (coefficient of lift)

That latter piece of the equation is unique to every wing shape in the world even non-wing surfaces, like sheets of cardboard. In order to stay at the same altitude, a plane must speed up to maintain the lift, you can try this on a flight sim program. A low speed renders an up angle and as you speed up, the plane rotates down to almost flat. Why? All wings have a built-in angle of attack when attached to the plane, this angle is designed for cruise. This still does what you described above, the change in pressure, to lift the plane. But because the plane moves faster, we don't need so much angle.

In terms of a possible why does air pressure drop on top of the wing? Path of least resistance. Look, low pressure sucks, no pun intended. If you were air floating in the sky and an airplane passed by with its wing coming right at you, you would get caught up in the upwash and get sent right over the top. You got sucked by the low pressure already on top of the wing, created by the motion of the plane. If you were low enough, you might get pushed down by the underside and more so by the downwash.

The meaning of life is curiosity; we were put on this planet to explore opportunities.

FredT
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Joined: Thu Feb 07, 2002 9:51 pm

### RE: Lift On An Airfoil

No, the air does not meet up again at the trailing edge. The air going above the wing typically gets there first. In most cases, the air going below the air also accelerates, creating a pressure lower than that of the surrounding atmosphere, but not as low as on top of the wing. Hence, you get lift.

Bernoulli's theorem holds true, but it has to be applied right. The equal transit time and half venturi theories are examples of applying it wrong.

What creates lift is the wing pushing air down. The downwash is indeed directly related to lift. There's more downwash than upwash (even if it all equals out in the end).

The reason for the pressure drop? One way of getting your head around it: The air is following a curved surface. All things moving want to go straight ahead. In order to make them follow a curved path, you have to have a force pulling them towards the inside of the turn.
The air trying to go straight ahead while the wing surface curves away creates a low pressure near the wing. This low pressure generates lift and also pulls the air in, making it follow the curvature of the wing surface. Eventually the (centripetal) force generated by the low pressure equals the force required to make the airflow bend just enough to follow the wing. It's not the complete explanation, but it goes a long way towards understanding.

Cheers,
Fred
I thought I was doing good trying to avoid those airport hotels... and look at me now.

Mr.BA
Topic Author
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### RE: Lift On An Airfoil

Thanks guys for the explanations. I guess I can conclude that the understanding we were made to accept that air separated at the leading edge converges at the trailing edge is flawed. But it's ironic that if we don't include this in our answers we won't get all the marks!

 Quoting FredT (Reply 2):The air trying to go straight ahead while the wing surface curves away creates a low pressure near the wing. This low pressure generates lift and also pulls the air in, making it follow the curvature of the wing surface. Eventually the (centripetal) force generated by the low pressure equals the force required to make the airflow bend just enough to follow the wing. It's not the complete explanation, but it goes a long way towards understanding.

Do you mind going in further about how exactly lift is generated when air is being made to follow the curvature of the wing? Excuse me if I am missing something here.. thanks!
Boeing747 万岁!

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Joined: Thu Nov 08, 2001 1:04 am

### RE: Lift On An Airfoil

 Quoting Mr.BA (Reply 3):Do you mind going in further about how exactly lift is generated when air is being made to follow the curvature of the wing? Excuse me if I am missing something here.. thanks!

There are 3 Laws of Newton...

1) A Body will remain with constant velocity when the sum of all external forces acting on the body are zero.

2) Force = Accelleration x Mass

3) If Body A acts upon Body B, then Body B will act an exactly equal and opposite force on Body A

Now, as the air flows over the wing, the wing will apply a force on the airflow to make it follow the curvature... correct?

This is rule #1 Because the sum of the external forces does not equal zero, then the air will change velocity...

I now refer to rule #3... The wing (Body A) acts a force upon the airflow (Body B) downwards... Which means Body B (the airflow) acts in an exactly opposite direction (Up) on body A (the wing). It also does this with exactly the same amount of force... (which lifts the aircraft).

Now, if you could weigh the down coming airflow from an aircraft in flight, it would be the same mass of the aircraft...
Whoever said "laughter is the best medicine" never had Gonorrhea

Goldenshield
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### RE: Lift On An Airfoil

 Quoting Lehpron (Reply 1):(density of air refered to by greek letter rho, which looks like an upside-down and flipped over #9)

According to all of my character fonts, it's represented by the letter 'P.'
Two all beef patties, special sauce, lettuce, cheese, pickles, onions on a sesame seed bun.

corey07850
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Joined: Wed Feb 04, 2004 4:33 am

### RE: Lift On An Airfoil

 Quoting Mr.BA (Reply 3): Do you mind going in further about how exactly lift is generated when air is being made to follow the curvature of the wing? Excuse me if I am missing something here.. thanks!

This is called the coanda effect... Have you ever gone to pour a cup of coffee from the pot only to have the coffee dribble down the side of the pot rather than simply pouring out?? This is the coanda effect in action. Fluids tend to follow curved surfaces.

Google up Coanda Effect and you should get a ton of research about it

 Quoting Goldenshield (Reply 5):According to all of my character fonts, it's represented by the letter 'P.'

Correct, rho is a funky looking "p", which is similar to what a 9 looks like mirrored sideways (not flipped over though)

OldAeroGuy
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### RE: Lift On An Airfoil

 Quoting FredT (Reply 2):Bernoulli's theorem holds true, but it has to be applied right. The equal transit time and half venturi theories are examples of applying it wrong.

While the equal transit time is not strictly true, there cannot be much difference between upper and lower surface transit time. Partially separated upper surface flow would be one example where there is a difference. However, you do get a loss of performance due to the separation. The lift curve (CL vs Alpha) begins to bend over and CL/CD decreases.

 Quoting FredT (Reply 2):The air trying to go straight ahead while the wing surface curves away creates a low pressure near the wing. This low pressure generates lift and also pulls the air in, making it follow the curvature of the wing surface.

This is a bit backwards. What creates the low pressure is increased velocity of the local airflow. This is classic Bernoulli. Why does the velocity increase?

The reason is that the distance between the airfoil section leading edge stagnation point (point on the leading edge of the airfoil where there is zero surface velocity) and the wing trailing edge is greater on the upper surface than the lower surface.

Let's say that two air molecules are at the stagnation point. If one travels over the upper surface and the other travel along the lower surface, they must arrive at the trailing edge at about the same time. Since the upper surface is a longer distance, the upper molecule must travel faster than the lower molecule. There will be a significant area on the upper surface where the air is traveling faster than the velocity of the airplane. On the lower surface, there is a significant area where the air is traveling slower than velocity of the airplane. The faster velocity creates a pressure less than atmospheric static pressure. The lower velocity creates a pressure greater than atmospheric static pressure. Both effects are explained by Bernoulli. The difference in upper and lower surface pressures produces lift.

Thinking about how lift symmetrical airfoils generate lift can help explain the different surface distance effect. When a symmetric airfoil is at zero angle of attack, the stagnation point is directly on the airfoil leading edge. The distance from the stagnation point to the trailing edge is the same on both upper and lower surfaces. Therefore the pressure distribution is the same on both surfaces and no lift is produced.

To produce lift, the airfoil angle of attack relative to the airflow must be increased. When this happens, the stagnation point moves to the lower surface. Now the distance from stagnation point to the trailing edge on the upper surface is increased and the distance on the lower surface from stagnation point to trailing edge is decreased. Upper surface velocities must increase and lower surface velocities must decrease if upper surface and lower surface molecules are to meet at the trailing edge at about the same time. This produces the differential pressure distributions noted earlier and lift is the result.
Airplane design is easy, the difficulty is getting them to fly - Barnes Wallis

2H4
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### RE: Lift On An Airfoil

 Quoting OldAeroGuy (Reply 7):Let's say that two air molecules are at the stagnation point. If one travels over the upper surface and the other travel along the lower surface, they must arrive at the trailing edge at about the same time.

Question for you, AeroGuy....I once had an aero instructor who explained that mass air flow accounts for this as much or more than Bernoulli's explanation.

I've tried searching for mass air flow...as it relates to aviation...and can only find mass air flow sensors for cars.

What was my instructor getting at? What exactly is the mass air flow theory, and how does mass air flow relate to what is being discussed?

2H4

Intentionally Left Blank

WingedMigrator
Posts: 1771
Joined: Wed Oct 26, 2005 9:45 am

### RE: Lift On An Airfoil

 Quoting OldAeroGuy (Reply 7):Upper surface velocities must increase and lower surface velocities must decrease if upper surface and lower surface molecules are to meet at the trailing edge at about the same time.

Looks like this thread has come full circle...

This meeting at the trailing edge at about the same time is what the original poster seemed to be (rightly) uncomfortable with. Why would they meet at the same time, or "about" the same time? Just what value of "about" is enough to produce lift?

In my opinion, this explanation of lift is based on a faulty assumption (that upper and lower particles must meet at the trailing edge at or "about" the same time) and over-reaching interpretation of Bernouilli's "principle".

I couldn't say it better than Wikipedia:

 Quoting Wikipedia: It is important to note that the only cause of the change in fluid velocity is the difference in pressures either side of it. It is very common for the Bernoulli effect to be quoted as if it states that a change in velocity causes a change in pressure. The Bernoulli principle does not make this statement and it is not the case.

That's why I've never been a fan of the Bernouilli explanation of things... it's too easy to attribute more to this effect than was really meant by the mathematician who came up with it.

I find that the best explanation is often the simplest: airplanes fly by simple conservation of momentum, because they push air down. It's neither romantic nor mysterious.

Sorry if I'm re-hasing age old debates

FredT
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### RE: Lift On An Airfoil

 Quoting OldAeroGuy (Reply 7):While the equal transit time is not strictly true, there cannot be much difference between upper and lower surface transit time.

Yes, there can. Count the pulses. 7 vs. 9.

 Quoting OldAeroGuy (Reply 7):This is a bit backwards. What creates the low pressure is increased velocity of the local airflow. This is classic Bernoulli. Why does the velocity increase?

And what creates the increased velocity? Yes, the pressure gradient (i e the pressure drop in the direction the air flows). There is never a velocity change in a fluid without a pressure gradient, and never a pressure gradient without a velocity change. Chicken and egg, egg and chicken.

The only force acting on an air parcel is the pressure difference between two opposite sides of it. And

acceleration = Force / mass = (pressure behind - pressure in front) / mass

 Quoting OldAeroGuy (Reply 7):The reason is that the distance between the airfoil section leading edge stagnation point (point on the leading edge of the airfoil where there is zero surface velocity) and the wing trailing edge is greater on the upper surface than the lower surface.

No, see above.

 Quoting OldAeroGuy (Reply 7):Let's say that two air molecules are at the stagnation point. If one travels over the upper surface and the other travel along the lower surface, they must arrive at the trailing edge at about the same time

They must not, and they rarely do. See above.

 Quoting OldAeroGuy (Reply 7):On the lower surface, there is a significant area where the air is traveling slower than velocity of the airplane.

Often, especialy at low AoA, the air travels faster than the free-stream velocity over the lower surface as well.

 Quoting 2H4 (Reply 8):Question for you, AeroGuy....I once had an aero instructor who explained that mass air flow accounts for this as much or more than Bernoulli's explanation.

In fact, they go hand in hand. Bernoulli holds true and applies, with some restrictions such as incompressible flow. But what matters for the lift generated is how much air the wing can shove downwards. There is no way around Newton's action/reaction.

Cheers,
Fred
I thought I was doing good trying to avoid those airport hotels... and look at me now.

keta
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### RE: Lift On An Airfoil

 Quoting OldAeroGuy (Reply 7):If one travels over the upper surface and the other travel along the lower surface, they must arrive at the trailing edge at about the same time

That's the same argument as the "equal transit-time", which is false. They don't have to get there "about" the same time. Just see FredT's post.

The wing diverts the air down, and that's why it produces lift. In order to get the air down, there must be circulation, which makes a clockwise flow around the wing. Now there are different velocities below and above, and now you can use Bernoulli to calculate the pressure in each point.

As I see, Bernoulli does not explain why air is diverted down. But you can use it to calculate the lift.

However, I still have a hard time understanding how the air is diverted down. I have heard about the Coanda effect, which states that the air tries to stay attached to the surface. But I have seen airfoils with "horizontal" trailing edges (see here or here) and I don't know how this would apply.

The circulation is the preferred explanation. I have read that initially a small counter-clockwise vortex is formed in the trailing edge, which separates from the foil. Since the circulation is constant, a clockwise flow generates around the wing. But I don't understand how, if you increase the angle of attack, increases the circulation; how is this new circulation connected to the inicial vortex (in a 2d wing), so the total is constant? I don't understand well how a wing produces circulation, but I know that's what produces lift.
Where there's a will, there's a way

FredT
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Joined: Thu Feb 07, 2002 9:51 pm

### RE: Lift On An Airfoil

 Quoting Keta (Reply 11):which makes a clockwise flow around the wing

...when viewed from the left.

 Quoting Keta (Reply 11):However, I still have a hard time understanding how the air is diverted down. I have heard about the Coanda effect, which states that the air tries to stay attached to the surface. But I have seen airfoils with "horizontal" trailing edges (see here or here) and I don't know how this would apply.

Mainly the air is sucked down by the low pressure above the wing. The flat, or even upcurved, trailing edges on some airfoils create a local higher pressure near the trailing edge but there is still low pressure over most of the airfoils top surface. The upcurved trailing edges I have seen that I can think of have been intended to create a neutral moment about the wing, e g for use in flying wings (Horten).

I really should wait for AeroWeanie to reply, this is his home field.
I thought I was doing good trying to avoid those airport hotels... and look at me now.

Oryx
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### RE: Lift On An Airfoil

 Quoting 2H4 (Reply 8):I've tried searching for mass air flow...as it relates to aviation...and can only find mass air flow sensors for cars.

I understand mass air flow as mass of air per second. The basic principle of level flight is that lift = weight i.e. mass of the air accelerated downwards times accelaration = mass of the aircraft times gravity (accelaration).
or L = G
and
m_plane * g = m_air * a

As you are accelarating some amount of air downwards you get a downwards movement of a given mass of air wich you can messure as mass per time.

 Quoting Keta (Reply 11):However, I still have a hard time understanding how the air is diverted down.

The flow in proximity of an impermeable wall (i.e. the wing) must follow the surface of the wall as it can neither flow into the wall nor detach from the wall without leaving a hole i.e. a vacuum which would suck the fluid back to the wall. OK I know this is not scientific language. Even if you have separated flow at a stalled wing the molekules closest to the wall follow its curvature.

keta
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### RE: Lift On An Airfoil

 Quoting FredT (Reply 12):Mainly the air is sucked down by the low pressure above the wing. The flat, or even upcurved, trailing edges on some airfoils create a local higher pressure near the trailing edge but there is still low pressure over most of the airfoils top surface. The upcurved trailing edges I have seen that I can think of have been intended to create a neutral moment about the wing, e g for use in flying wings (Horten)

Thanks FredT. I see that the pressure above is less than below, if it wasn't it wouldn't fly. But I guess the Coanda effect cannot always explain how the air is diverted down.

 Quoting FredT (Reply 12):I really should wait for AeroWeanie to reply, this is his home field.

I want him to arrive here soon, too.

 Quoting Oryx (Reply 13): The flow in proximity of an impermeable wall (i.e. the wing) must follow the surface of the wall as it can neither flow into the wall nor detach from the wall without leaving a hole i.e. a vacuum which would suck the fluid back to the wall. OK I know this is not scientific language. Even if you have separated flow at a stalled wing the molekules closest to the wall follow its curvature.

Yes I understand that, that's basically the Coanda effect, but why is the air going down after the wing? Is it because of inertia? And if it was only because of that, in a foil like the ones showed above, the air would be following a horizontal path in the trailing edge and after, which is not the case.

[Edited 2006-02-06 11:52:58]
Where there's a will, there's a way

Oryx
Posts: 123
Joined: Fri Nov 18, 2005 9:25 pm

### RE: Lift On An Airfoil

 Quoting Keta (Reply 14):Yes I understand that, that's basically the Coanda effect, but why is the air going down after the wing? Is it because of inertia?

Yes mainly. In the absence of any force the flow particles should just keep on moving in a straight line. The problem is that the wing changes the pressure field in a very large area (see the curvature of the flow even on the uppermost line of points). I have got a plot of the pressure field of a wing in post stall regime laying before me, where the lowest pressure is behind the trailing edge, bending the streamlines upwards. So the wing not only change the direction of the particles at the surface but also at quite some distance.

As far as I can see, and judging from the overall flow field the trailing edge of the airfoil in the above picture is pointing downwards. The flow is separating on the suction side of the flap in the sense that there is circulating fluid, but nevertheless even the outer flow is following the wings curvature.

OldAeroGuy
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Joined: Sun Dec 05, 2004 6:50 am

### RE: Lift On An Airfoil

 Quoting FredT (Reply 10):Yes, there can. Count the pulses. 7 vs. 9.

Two questions for you.

1) Why did you chose an illustration that is for a flaps down configuration with a separated wake? Remember, this was an example I mentioned where there can be a difference in the transit times due to the separation. Do you have a similar illustration for a flaps up case with little separation?

2) Where is the stagnation point in your illustration? Try counting the time intervals from there. The stagnation point is not at the section leading edge. Define the stagnation point and then let's try to count the time intervals from the stagnation point to the trailing edge, assuming that flow field cuts you're showing are constant time hacks.

 Quoting FredT (Reply 10):And what creates the increased velocity? Yes, the pressure gradient (i e the pressure drop in the direction the air flows). There is never a velocity change in a fluid without a pressure gradient, and never a pressure gradient without a velocity change. Chicken and egg, egg and chicken.

While I agree with it's a chicken and egg situation, the local surface curvature is what controls the pressure gradient and velocity. And surface curvature defines the transit distance.

 Quoting FredT (Reply 10):Often, especially at low AoA, the air travels faster than the free-stream velocity over the lower surface as well.

No argument here, but lift is reduced accordingly. Recall my example of a symmetric airfoil. At zero angle of attack, there are areas on the lower surface where the local velocity is higher than the freestream, matching the upper surface velocity. Since the upper and lower surface pressure distributions are the same, no lift is produced.

 Quoting Keta (Reply 11):The wing diverts the air down, and that's why it produces lift. In order to get the air down, there must be circulation, which makes a clockwise flow around the wing. Now there are different velocities below and above, and now you can use Bernoulli to calculate the pressure in each point. As I see, Bernoulli does not explain why air is diverted down. But you can use it to calculate the lift.

Correct, you can integrate the upper and lower pressure distributions to calculate the sectional lift. The circulation is created by the difference in velocities between upper and lower surfaces. Think about a rotating cylinder placed in a flow field. The cylinder rotation creates circulation and the circulation creates lift with a resultant downward displacement of the flow field. Again, you can calculate the lift by integrating upper and lower cylinder pressures.

 Quoting Oryx (Reply 13):The flow in proximity of an impermeable wall (i.e. the wing) must follow the surface of the wall as it can neither flow into the wall nor detach from the wall without leaving a hole i.e. a vacuum which would suck the fluid back to the wall.

It's not impossible for the fluid to detach from the surface. This routinely happens when the local static pressure drops below free stream static. Instead of sucking the fluid back to the surface, the flow reverses on the surface as free stream air invades the void. When enough air has separated from the surface a stall results.

The Coanda effect is really present when the initial flow source has more energy than the freestream. Think about the difference between the total pressure of engine exhaust vs freestream total pressure.
Airplane design is easy, the difficulty is getting them to fly - Barnes Wallis

Smalbany
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Joined: Fri Aug 06, 2004 2:29 am

### RE: Lift On An Airfoil

You guys make my head hurt

I took fluid dynamics - but only as much as a Chem E needs. I'll stick to pipe and open channel flow.

Dan

FredT
Posts: 2166
Joined: Thu Feb 07, 2002 9:51 pm

### RE: Lift On An Airfoil

 Quoting OldAeroGuy (Reply 16):1) Why did you chose an illustration that is for a flaps down configuration with a separated wake? Remember, this was an example I mentioned where there can be a difference in the transit times due to the separation. Do you have a similar illustration for a flaps up case with little separation?

I chose that picture as it was a clear illustration of what happens. It is rather obvious from that picture that flaps extended or not extended won't make the lower surface pulses catch up.

From the page, the link to which I included below the image but which appears not to work,

http://amasci.com/wing/airgif2.html ,

here is another image:

 Quoting OldAeroGuy (Reply 16):2) Where is the stagnation point in your illustration?

Right where a streamline would meet the surface of the wing, as always. The image is a bit blurry, but it is not the least hard to find the stagnation point with reasonable accuracy.

 Quoting OldAeroGuy (Reply 16):Try counting the time intervals from there.

Just what I did. 7 vs. 9.

 Quoting OldAeroGuy (Reply 16):The stagnation point is not at the section leading edge.

No, it rarely is. I never said it was, nor do my statements depend on it. Please, no more smoke screens. People are already having a hard time getting their heads around this without them.

 Quoting OldAeroGuy (Reply 16):Define the stagnation point and then let's try to count the time intervals from the stagnation point to the trailing edge, assuming that flow field cuts you're showing are constant time hack

That is what I did. 7 vs 9.

And more smoke screens.

Unless we make an absurd assumption that the acceleration in the test segment is significant enough to have serious compression in the test chamber, with the pulses timed to make the distances between them where the streamlines aren't much disturbed equal, it can be clearly seen that the pulses are evenly distributed over time.

 Quoting OldAeroGuy (Reply 16):While I agree with it's a chicken and egg situation, the local surface curvature is what controls the pressure gradient and velocity.

Yes, as it is the presence of the surfaces in the free stream which provide the entire disturbance to the free stream. With no surfaces there is no aircraft there, nor a wing, nor any reason to worry about aerodynamics in the first place. I don't think anyone is debating whether it is the presence of the aircraft skin which makes the air move in rather more complex patterns than it does when left alone or not.

 Quoting OldAeroGuy (Reply 16):And surface curvature defines the transit distance.

True. However, the transit time required to cover that distance is till not equal between the top and bottom surface.

The equal transit time theory is long dead and buried. We are kicking a dead horse back and forth here.

Cheers,
Fred
I thought I was doing good trying to avoid those airport hotels... and look at me now.

Starlionblue
Posts: 20700
Joined: Fri Feb 27, 2004 9:54 pm

### RE: Lift On An Airfoil

While the other posts were quite technical and well beyond what I could achieve, I find that reading from here and a few pages on gives a good 30000ft view of the whole thing without getting too complex: http://travel.howstuffworks.com/airplane5.htm.

 Quoting Mr.BA (Thread starter):I'm currently in high school we're just into bernoulli's equation and one of the applications is the airfoil. Our textbooks states that the fundamental source of lift is the difference in velocity of airflow over and under the wing hence the difference in pressures which will in return create lift. I've got no problems with this for now.

You should

 Quoting Mr.BA (Thread starter):However it also states that as the airfoil flies through the air, for the velocity of air over the airfoil to be faster than the underside, the air that is separated at the leading edge must converge at the trailing edge. How true is this?

Well you have, all by yourself, figured out a big objection to the hypothesis. Most people (including myself) didn't question that part.
"There are no stupid questions, but there are a lot of inquisitive idiots." - John Ringo

Mr.BA
Topic Author
Posts: 3310
Joined: Sun Sep 24, 2000 12:26 pm

### RE: Lift On An Airfoil

Is there any relation (mathematical) between speed of the airfoil moving through air and the amount of air it can divert down? I'd be interested to know.

Still, it is very amazing that a wing can divert an amount of air equal to its weight for lift when you think of mass of air and the weight of say a B747!

Thanks very much guys for the discussion very interesting and enlightening.
Boeing747 万岁!

chksix
Posts: 336
Joined: Mon Sep 26, 2005 6:16 pm

### RE: Lift On An Airfoil

Go here: http://www.mh-aerotools.de/airfoils/jf_applet.htm and play around with different airfoils or design your own
The conveyor belt plane will fly

Oryx
Posts: 123
Joined: Fri Nov 18, 2005 9:25 pm

### RE: Lift On An Airfoil

 Quoting Mr.BA (Reply 20):Is there any relation (mathematical) between speed of the airfoil moving through air and the amount of air it can divert down? I'd be interested to know.

Not a simple one. The most basic equation are the Navier-Stokes equations (i.e. the balance of momentun) which are non-linear parttial differential equations. There are simplifications (like neglecting viskosity) to these equations which lead to easier to solve formulars like "line of lift theorie".

Nevertheless one problem still remains: The airfoil is altering the flow in a region which extends very far out i.e. 30 chord-lengths while the local influence descreases with the distance. (In most calculations you consider the flow as undisturbed somewhere at the boundaries of your calculation). So the result of your calculations depends on the "size of the box" (the systems boundaries) you consider around your wing.

What you wanted to do is done reguarly for turbomachines i.e. jet engines or wind energy turbines as the area you have to consider is given by the diameter of the installation. How to do this for a wing - I have no idea but would consider something like the Kutta-Joukowsky-Theorem a good point to start with.

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### RE: Lift On An Airfoil

I still say that people focus too much on the pressures over an below the wing more than they should... pressue can NOT lift a wing, a force CAN... The pressure is a by-product of the forces explained in my post above...
Whoever said "laughter is the best medicine" never had Gonorrhea

prebennorholm
Posts: 7156
Joined: Tue Mar 21, 2000 6:25 am

### RE: Lift On An Airfoil

 Quoting Mr.BA (Reply 20):Still, it is very amazing that a wing can divert an amount of air equal to its weight for lift when you think of mass of air and the weight of say a B747!

There doesn't need to be a similarity between the weight of the plane and the weight of the air "treated" by the wing.

Never mind how we define lift to be created by the airfoil, then the end result of that process is acceleration of air molecules downwards. Acceleration is measured in G or units of gravity.

If we accelerate one pound of air downwards by one G, then it creates one pound of lift. Two Gs = two pounds of lift etc. And consequently for instance 40 tonnes of air by 10 Gs = 400 tonnes of lift.

The wing span of a 747 is just over 200 feet. If we imagine a 200 feet cube of air at sea level then the weight of that air is roughly 300 tonnes, so we are dealing with substantial masses of air. Even at landing speed it takes less than one second to pass through such an imaginary cube into the next cube.

The average wing cord on a 747 is something like 30 feet. At landing speed it takes less than 0.15 seconds for the air to flow from leading edge to trailing edge. During those 0.15 seconds the air masses are treated so violently that it will destroy any aircraft flying through that turbulence within the next half minute or so.

These were no high level scientific words. But I hope that it gives some of us some understanding how this magic of flying heavy weights through the air is possible.

Just one more speculation for fun: If we imagine that we fly in an atmosphere of hydrogen at ordinary sea level pressure, then... Since the mass per volume is 25 times less than our nitrogen/oxygen atmosphere, then we would need 25 times larger wings.
Always keep your number of landings equal to your number of take-offs

vikkyvik
Posts: 12621
Joined: Thu Jul 31, 2003 1:58 pm

### RE: Lift On An Airfoil

 Quoting Kaddyuk (Reply 23):I still say that people focus too much on the pressures over an below the wing more than they should... pressue can NOT lift a wing, a force CAN... The pressure is a by-product of the forces explained in my post above...

Um, but a pressure difference on two sides of a surface IS a force....forces don't just appear on their own. If you create a pressure difference, you create a force.

OldAeroGuy, I'm sorry, but I have to disagree with your post. There is nothing that says that air molecules above and below the wing have to rejoin at the trailing edge. For incompressible flow, conservation of volume takes care of that. And for compressible flow, conservation of mass.

Anyone, correct me if I'm wrong, as it's 1:20 AM.

~Vik
I'm watching Jeopardy. The category is worst Madonna songs. "This one from 1987 is terrible".

Oryx
Posts: 123
Joined: Fri Nov 18, 2005 9:25 pm

### RE: Lift On An Airfoil

I just found this very interesting website on the subject. While it's on an italian server it is only in german.

Flow around a cylinder.

[Edited 2006-02-16 11:25:34]

Mr.BA
Topic Author
Posts: 3310
Joined: Sun Sep 24, 2000 12:26 pm

### RE: Lift On An Airfoil

Just one more question guys... what about the flaps? I know the purpose for the flaps but in what principle does it provide the extra lift? The same reasoning by diverting air downwards from the overwing as it is as the normal wing or is it mainly due to the deflection of the air underwing downwards which in turn produce the lift force?

Thanks.
Boeing747 万岁!

Oryx
Posts: 123
Joined: Fri Nov 18, 2005 9:25 pm

### RE: Lift On An Airfoil

The reasen of existance of flaps is twofold: While on the pressure (bootom-) side of a wing the air can be deflected downwards quite rutaly it does not follow the curvature of the upper side of the wing if the curvature is to strong. So in order to increase the deflection angle, which results in greater lift, the chord of the wing is increased. Thus the air can be defelcted further downwards. Additionaly the gaps between the wing and the flap or the differen parts of the flaps (i.e. double slotted flaps) renew the boundary layer on the surface of the airfoil. Thus - as momentum from the outher flow is transfered tho the near wall region - the onset of flow separation is taken to greater angles of attack.

On the problem of the calculation of lift from the pressure field: What the uncomming air "sees" is an impermeable wall forcing the closest molekuls to the wall the follow it tangents. The pressure adapts such thatthe balance of mass is fullfilled for overy point of the flow field. As the pressure is on part of the stress tensor it is part of the lift, but not the entire lift as in viscous flow shear forces on the surface add to the balance. Only in theoretical non viscous flow (Reynoldsnumber = Infinity) is the pressure the only source of lift.

F14D4ever
Posts: 306
Joined: Sat May 07, 2005 3:20 am

### RE: Lift On An Airfoil

 Quoting Oryx (Reply 28):The reason [for the] existance of flaps is twofold ... in order to increase the deflection angle, which results in greater lift, the chord of the wing is increased

But not all flaps increase chord length; they increase camber, which increases circulation. That takes us back to AeroGuy's post, which is the only one to mention circulation, which is central to an understanding of this topic.
"He is risen, as He said."

Mr.BA
Topic Author
Posts: 3310
Joined: Sun Sep 24, 2000 12:26 pm

### RE: Lift On An Airfoil

A bit about the circulation part, does it mean to say that when the airfoil is flying through air there is a clockwise rotation of the air around airfoil, which means to say air below the airfoil is actually moving towards the leading edge? Apologise for getting back on this didn't really catch this. Thanks once again everyone for the clarifications.
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