Book of William Question
By: Doc Green

Why does the air passing over a wing speed up?

If we can understand this, we can then apply Bernoulli's law and understand how a wing produces lift.

My primary source of information is John S. Denker's on-line book, Chapter 3. Here's the link:

1. Air has to travel farther over the top.

A widely-published explanation is that the air passing over the top of a wing has farther to travel than the air flowing under the bottom of the wing. Therefore, in order for the air to meet up properly at the trailing edge, the air flowing over the top must flow faster.

This is not correct. True, air flowing over the top must travel farther. However, the explanation is based on the assumption that the two streams of air do indeed meet up "properly" at the trailing edge. This does not happen. In fact, the air traveling over the top, in most cases, will get to the trailing edge BEFORE the air flowing under the wing! And the race is not even close.

By what percentage is the path over the top greater than the distance under the bottom? Measuring one of Denker's airfoils, I came up with 7.5%. It is definitely less than 10%. Based on this, the increase in speed required for the air to "meet up properly" would be greater by about the same percentage. However, to quote Denker, "The maximum velocity produced by this wing at this angle of attack is about twice the free-stream velocity."

In Denker's diagrams, he is simulating a wind tunnel with smoke injected into the flow. That is, the wing is stationary with the air and smoke flowing past it. I prefer to view the same diagrams as having the air and smoke stationary and letting the wing fly through it. So, imagine the wing to be flying from right to left and passing through bands of smoke. The two views are actually equivalent but I'm more comfortable having the airplane doing the flying.

This diagram (Denker's Fig. 3-3) shows by what margin the air flowing over the top gets ahead. As best I can tell, air flowing over the top completes the path in about 30 milliseconds (ms). The air flowing under the bottom takes 40 ms. If we take the chord of the wing to be 6 feet, this gives a speed for . . .

    Air flowing over the top: 6 ft / 0.030 s = 200 ft/s = 136 mph

    Air flowing under the wing: 6 ft 0.040 s = 150 ft/s = 102 mph
Denker's Fig. 3-3

From measurements taken from the diagram, it appears that the front edge of the blue smoke passing over the top is about 2 feet 5 inches beyond the trailing edge by the time the blue smoke at the bottom gets to the trailing edge. And, this displacement is permanent. The air does not rearrange itself back to its original state after the wing is long gone. So much for the traditional wisdom that "the air meets up properly!"

2. Zero slip, Boundary layer, and Maximum Speed

This section gives a little background information. Skip it if you already know what a boundary layer is, and so forth.

Here's a link to the appropriate section in Denker's book. However, few diagrams are present.

A basic principle in the flow of fluids (whether air or a liquid) over a surface is that the part of the fluid that is in actual contact with the surface does not move relative to the surface. It just sits there. This is known as the condition of "zero slip."

What this means for air flowing over a wing is that there is a very thin layer of air near the wing that doesn't move at all. However, just a tiny fraction of an inch from the surface, the air will be moving, but still not as fast as it will be just a bit farther out. This layer in which the speed varies from zero up to the speed that the air has that is well away from the surface is called the "boundary layer." In many instances, the boundary layer will be no thicker than the thickness of a dime.

Nevertheless, the effect is there and it contributes to the fact that the wing tends to drag the air along with it, to some extent. In the diagrams, the columns of smoke that tend to lean to the left show where the air is being dragged along with the wing.

In the diagram at right (Denker's Fig. 3-5), you can see the effect of the boundary layer at the tips of the blue arrows.

Look at the columns of smoke and find where the air and smoke pass over the wing most rapidly. Is it near the wing, like "right next to it?" No. It's actually up above the wing. It's approximately along the line of the ugly red arrow.

Denker's Fig. 3-5

Here's another tidbit. The streamlines will curve away from a region of high pressure and curve toward a region of low pressure. By noting the curvature, you can tell where the regions of high and low pressure are.

Look at the first streamline above the wing. Ahead of the leading edge, it is curving upward. Above the leading edge, it is curving downward. Back near the trailing edge, it is curving upward again, but rather gently. What this shows is that there is a region of high pressure just in front of the leading edge, there is a region of low pressure just above the center of the wing, but the pressure above the wing increases somewhat near the trailing edge because the streamline begins to curve upward again.

The diagram at right (Denker's Fig. 3-7) shows the pressure distribution around a wing at an angle of attack of 10 degrees.

Denker's Fig. 3-7

3. Doc's theory as to why the air speeds up

First, imagine a wing stationary in the air. The air will be distributed evenly all around it and the pressure all around it will be the same.

Now suddenly jerk it to the left an inch or so. The air to the left of the wing will be compressed by the sudden movement. However, what will develop to the right of the wing? There will be an empty space! Well, how empty it will be depends upon how hard and how quickly we jerk the wing. In any event, the pressure will be lower to the right of the wing.

We must realize that air has mass, and it takes time for it to move. The empty space cannot refill with air in "an instant." It will take some time for the air to move in. Not much, but a little.


(By the way. Air is a lot heavier than most people think. A big, empty refrigerator holds almost 2 pounds of air, and you will need to be a pretty strong person to lift the air in a room ... assuming you can get a handle on it.)

If the wing is initially stationary before we jerk it, and then after being jerked to the left, it just sits there and waits for the air to refill the empty space, the air will tend to flow straight in toward the top surface of the wing, more or less at right angles to the wing. And that will be about all there is to it. It may bounce around a little as it settles down, but no significant movement down the wing toward the trailing edge will occur.

Moving wing

But if the wing is moving through the air with considerable speed to the left, the situation is somewhat different. We can imagine the movement of the wing to consist of a very large number of small jerks, but in this case, a pronounced high pressure region will develop up near the leading edge. So what will we have? An empty space (low pressure) distributed along the top of the wing, air trying to refill it (nature abhors a vacuum), and a high-pressure region up to the left, near the leading edge. So what will happen?

The Punch Line:

The high pressure near the leading edge will force the air in that region to flow toward the empty space at the top of the wing. The motion of the air will be very nearly parallel to the surface of the wing. And because the air is being forced to flow by the high pressure, it will pick up speed. The result is that the air flowing over the top of the wing will travel much faster than the air flowing under the wing.

Question: Why doesn't the high pressure in front of the wing cause the air flowing under the bottom to speed up as well?

There is no empty space or low pressure area created under the bottom of the wing (at least to the extent that it is created on the top).

Question: Why doesn't the air just take the shortest route and flow into the empty space by traveling at right angles to the wing?

Well, to an extent, it does. But remember, the high pressure region in front of the leading edge will have a pressure just a bit higher than the pressure above the wing back toward the trailing edge. The actual path taken by the air will consist of the parallel and perpendicular components added together.

The component parallel to the wing will predominate, but its effect becomes less as we proceed toward the trailing edge. In fact, the pressure is somewhat higher back near the trailing edge in part because of the diminished effect of the high pressure at the front, together with the inflow of air at greater angles to the wings surface.

Question: In Denker's diagrams, there's no big puddle of high-pressure air up above the leading edge. Why not?

As the angle of attack increases, the stagnation point at the leading edge moves downward toward the bottom of the wing, even to a point that is aft of the very front of the leading edge. Nevertheless, the effect of the high pressure is the same. In fact, from the stagnation point, air will flow forward a short distance as it rounds the end of the wing cord and finally starts its journey to the rear.

High angle of attack

As the angle of attack becomes greater, it becomes more difficult for the air to "turn the corner" on top of the wing up near the leading edge. This diminishes the flow of air parallel to the wing, and in fact, the stream of air having the highest speed may become separated a considerable distance from the wing.

In this case, back near the trailing edge, the air immediately above the wing will be moving very slowly, relatively speaking, and in some cases, streamline flow can develop near the trailing edge that is "backwards" to the main flow. This is air trying to enter the empty space from the rear. This phenomenon is called "boundary layer separation," and it can occur before the wing stalls, but at this point a stall is not far away.


If the angle of attack is increased just a bit more, the air flow in the portion of the wing toward the rear of the span will break up and become highly turbulent. When this happens, the air becomes a chaotic swirling mass, going every which way without any organized flow. The pressure toward the rear of the wing increases significantly, the lift decreases, and the wing stalls.

4. Another view

Here's a post from Ed on the FlyChallenger list that I believe offers the same explanation as what I have given above, in different words, of course:

Message 56157 Wing lift physics - having fun trying to figure it out
From: Ed Burkhead

I think that if I did a vector analysis of the forces on a bunch of molecules from still air in front of the wing to a little way behind the wing, I'd find something like this:

First, the rounded front of the wing pushes some air up and some air down - perhaps this is about equal but it may not make much difference.

The air forced downward, stays in a relatively high-pressure area because the wing is at a positive angle of attack (even a symmetrical wing). The wing has to exert a pressure on the air to push it down out of the way and the air gives an equal and opposite pressure back up against the wing.

Now for the top of the wing:

First, the wing has to push the air upward and the air will push back downward against the wing. This is NOT what we want since it doesn't lift the plane. It may be balanced against the downward push against the lower air and these may cancel out.

As soon as the wing STARTS curving downward, we start to change over into another mode. Once the air is moving upward (from that initial push), the net result is that the surface of the wing is being pulled away from the motion of the air so we start to get a low pressure area above the wing. As the wing progresses through the air, the shape of the wing is such that the low pressure area is MAINTAINED, even though the air pressure way above the wing is TRYING to force the air back down to near the wing. The wing surface, due to the wing's forward motion and the shape of the wing, keeps retreating from the air.

The net result:

Below the wing, the air is pushed downward a bit and left fairly much undisturbed. The air above the wing is pulled downward by the suction in that low pressure area. The wing is sucked UP into the low pressure area (lift) and the air is sucked DOWN into the low pressure area imparting downward motion to the air. Overall, the net result is that air is thrown downward - sufficiently so to balance and account for the force upward on the wings.

You don't get anything for nothing in physics. To have a net force upward on the wing, there has to be an equal and opposite downward force exerted on SOMETHING, in this case the air. To have an upward force of 1,000 lb., there has to be a downward force on the affected air of exactly the same amount. (Newton's third law is firm on this.) The plane is held up against gravity. The air is flung downward.

Three photographs of downwash in the clouds:

Interesting discussion about downwash in the case of canard surfaces:

Here's another interesting aerodynamic discussion:

5. An Explanation, elegant in its simplicity

In another post, M. G. gives support to Andrew Forber's statement:

#56209 From: M. Gottschalch

Andrew Forber wrote:

> Hey, remember, the air isn't moving horizontally (much). The *wing* is moving. It's just bumping some of the molecules upwards and then sucking them back downwards again.

M. G.:

I'll go along with the first part, the wing is bumping the air molecules up to the top of the hill (that's why the prop has to push so hard) but then they slide down the slope on the back of the wing and they get faster! Then as the angle of attack gets higher, they slide faster 'till they get so fast that they create a vacuum and slow the plane down so much that it stalls.

See it all makes sense. Sort of. Maybe.


6. Symmetrical Airfoils

Once we realize that the additional distance from front to back across the top of the wing plays little if any role in the production of lift, it is easier to understand how a symmetrical airfoil can produce lift, or even a flat surface for that matter.

The key ideas are those of the "empty space" produced on top of the wing and the high-pressure region near the leading edge. Given these ideas, the principles are the same.

Even an ordinary airfoil will produce lift when inverted:

7. The Distant View of Lift Production

If an effort to understand and explain how a wing produces lift, some will cite Bernoulli's theorem and mention that air flows faster over the top of the wing, and others will say that the wing produces a downwash and it's the reaction force to the downwash that produces the lift. So, which of these are correct?

The short answer is, "Both, assuming the principles are applied properly." The difference is that one (Bernoulli) requires a close-in, almost microscopic analysis of the air flow next to the wing. The other allows you to step back away from the wing and consider the amount of air that is "flung downward" by the wing. (Be sure to check out the photos in the links in Ed's message!)

You can't have lift without the downwash, and you can't produce the downwash without the principle of Bernoulli coming into play. But, for purposes of calculation or explanation, one is, for the most part, equivalent to the other.

Here's a similar situation. It is possible to calculate the pressure exerted on the inside of a container of gas (a balloon) by calculating how many molecules are hitting the sides of the container per second and how fast they are going when they hit it. And you will get the right answer. But it is far easier to calculate the pressure using the concepts of volume, temperature, and the total mass of the gas. You can use either approach, but one is far easier than the other.

8. Book of William, Original Questions

Rat wrote:

~~~~~(SHHHHH! For Bill's Nameless Students ONLY!--> Next time ask him how vortex generators work or if an aircraft is lifted into the air from the bottom of the wing or sucked into the air from the top ;)~~~~

OK. I'll have a go at these. Last one first, because it's easy. Is an aircraft lifted into the air from the bottom of the wing or sucked into the air from the top?

Suction . . .

A suction is not a real, physical thing. What it is that most of us refer to as a suction is a difference in pressure between two regions. I'll admit this is more a matter of language than anything else, but ... if I may continue ...

What causes the air/fuel mixture to flow at high speed through the intake manifold on your car or plane? Is it the "suction" produced in the cylinders?

What the piston in the cylinder does on the intake stroke is to create a low pressure region in the cylinder and in the intake manifold. Outside the carb, the atmospheric pressure is considerably higher. The result is that the air (and fuel) is forced by the higher pressure to flow toward the low pressure. It's the concept of "pressure differential."

The difference in pressure is not as great at high altitudes where the atmospheric pressure is less, and it becomes more difficult to get adequate flow of air/fuel into the cylinders. This is were superchargers come into the picture. They increase the pressure feeding the carbs (or whatever) and thereby increase the pressure differential.

Back to the question ...

The low pressure above the wing is not absolutely zero. There is considerable pressure, and force, pushing down on top of the wing. But the high pressure below the wing produces a greater upward force. The upward force on the bottom is greater than the downward force on the top and the result is the lift that carries the wing into the air. It's the high pressure below the wing working in conjunction with the low pressure above it that produces the lift.

Now, I know what you're thinking. If the air above the fabric is actually pushing downward on the fabric, why does it tend to come loose unless it is securely attached to the ribs?

Gee, this is getting complicated! This has to do with the air pressure on the inside of the wing, between the lower and upper fabric. The pressure inside the wing, underneath the top fabric, is greater than the pressure immediately above the fabric where Bernoulli is doing his thing. This difference in pressure produces the force that tends to blow the top fabric off.

How does a Vortex Generator (VG) work?

Remember the mention of "boundary layer separation" toward the end of Section 3? That refers to the situation where the fast-moving air becomes well-separated from the surface of the wing, and much slower air fills the region between the wing and the fast-moving air. The result is that the slower air next to the wing will be at a higher pressure, and this will reduce the lift of the wing.

Now, a VG is a little rudder of a thing placed on the top surface of the wing not too far back from the leading edge. What it does is deflect a thin stream of air sideways at that point. This produces a funnel-shaped vortex, a swirlie, that rotates about a line drawn from front to back above the wing.

The swirlie is funnel-shaped with the little end near the VG and the big end closer to the trailing edge, and it lies more or less parallel to the fuselage. What it does, toward the rear of the wing, is catch a part of the separated boundary layer (fast air) and flip it over so that fast air once again flows near the top surface of the wing. This reduces the pressure above the rear part of the wing and increases the lift accordingly.

The effect of VGs is significant only at high angles of attack where the boundary layer separation is pronounced. At higher speeds (less angle of attack), the boundary layer is already close to the wing so the vortex generators have little effect. They are said to reduce the stall speed of a Challenger by 5 - 8 mph, but not everyone is of the opinion that they should have them. : )

9. Conclusion

Well, that's about it. Don't know if it's right or not, but it's the best I can do. At any rate, it's interesting to think about on a snowy day when you can't fly, and if some or all of the above is "not exactly the way it is," I hope no harm comes of it. I've never been to aerodynamics school a day in my life!

Seems like I ought to put in a disclaimer or something, just to be fashionable, but I guess I won't.

Speaking of disclaimers, just today I saw one that was placed on a cape of some sort at WalMart that a young kid might wear while being Superman or someone else who can soar through the air:

-- Wearing cape does not enable user to fly.

Doc Green