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```
OK, I'm not going to poke this hornet's nest again.

Instead I'm going to kick it down, stamp on it, squirt it with
the hose, give it a good spraying with bug spray, then set it
on fire for good measure.   If I have time, I'll step on any
stragglers which survive.

:)

See below.

```

Why airfoils are so **EFFING HARD** to understand: A little list.

 2002 William J. Beaty

 1. We tilt our airfoils while denying that we've done so. 2. The pressures around 'bluff' airfoil shapes are misleading. They greatly interfere with explanations of lifting force. (we could simply use thin-wing models instead). 3. In grade-school, textbook diagrams do not explain how real airplanes can stay up there. The diagrams only depict "ground-effect flight." 4. Airfoil diagrams in K-6 textbooks violate Newton's laws, they omit the wind tunnel's "floor" and "ceiling," they wrongly imply that the wing applies force to the air, and they don't show the force-pairs which appear between the airfoil and the distant wind tunnel surfaces. 5. "Infinite wing" models are supposedly sensible? ...while a real three-D wing is weird and distorted? No, the opposite is true. 6. Cambered airfoils give lift at zero angle of attack? Maybe not. 7. A vortex-ring or a vortex-pair acts like a massive object which carries a certain amount of momentum as it travels. Yet it carries no mass at all. 8. We "simplify" things by insisting that the working fluid be infinitely viscous and totally inviscid at the same time. 9. Real 3D wings depend on their vortex-wake, and without it they cannot fly (they would never rise more than a wingspan altitude and escape ground-effect-mode flight.)

1. We tilt our airfoils while denying that we've done so.
Let's make an airfoil by starting with a cylinder, and then placing a fairing behind it to form a blunt streamlined airfoil shape:
```          _----_
/      \
|        |   Cylinder
|        |
\_    _/
----

_----____
/         ----____
|                  ----____
|              ____----
\_    ____----
----      Streamlined airfoil-shape
```
Now lets tilt it to a positive attack angle. But let's pick a very special attack angle, one which puts the lower face of our streamlined shape at zero angle.
```          _----__
/       --__
|            --__
|                --__
\_                  --__
------------------------

Tilted streamlined airfoil

```
Do you think you are looking at a streamlined cylinder-foil which has a positive angle of attack?

WELL YOU'RE NOT!!! No no no!

<Grin!>

You're REALLY looking at an airfoil which is flat on the bottom. And it's curved on top. Also, it's not tilted, the angle of attack is actually zero. It's not tilted in relation to the oncoming air, instead it has an asymmetrical shape which causes lift via the Bernoulli Effect!

If you disagree with us, well, you're a tiny minority, and science proceeds by majority vote, don't you know.

Ooops, I forgot one little thing. Let's add a tiny extra bit to the leading edge. That will keep anyone from noticing that the airfoil is tilted at all.

```
BEFORE                           AFTER
_----__                         _----__
/       --__                    /       --__
|            --__               |            --__
|                --__          |                 --__
\_                  --__      |                     --__
------------------------    ----------------------------
airfoil that's "tilted"      airfoil "with curved top"

```
Isn't that amazing? Just that small change in the leading edge has changed the 20 degree attack angle into a zero attack angle.

Yes, I'm being sarcastic.

The way we choose "zero attack angle" is a genuine cause of confusion. Please realize that Nature makes its own choice of angle, since the air that flows away from the trailing edge of the airfoil determines the pressure distribution and the lifting force. For this reason, the average angle of the airfoil's trailing edge is extremely important. The shape and angle of the leading edge is not so important. To determine the angle of the airfoil, just use your hand to cover the leading edge in the diagram. Ignore the leading edge. Then look at the trailing edge and measure the angle of the line drawn between the upper and lower surfaces.

2. The pressures around streamlined airfoil shapes are misleading. (we should use thin-wing models instead).
If we put a cylinder in a wind tunnel, and adjust things for low Reynolds number (with no turbulence or flow-detachment), then we'll discover that the fluid pressure on the cylinder looks like this:
```           low
_----_
/      \
high |        |  high        Cylinder in a horizontal flow
|        |
\_    _/
----
low
```
Pressures are high at the front and rear of the cylinder. And they are low at the top and bottom. With me so far? If we ignore shear effects, the net drag force will be zero. There's zero drag because the acceleration pattern at the front of the cylinder is the exact opposite of the acceleration at the back. It takes high pressure to turn those flows, but the forces on the front and rear of the cylinder are equal and opposite, so the net drag force is zero.

Now let's look at the forces on a streamlined "cylinder" airfoil.

```
low
_----____       medium
/         ----____
high |                  ----____
|              ____----        Pressures during horizontal flow
\_    ____----
----           medium
low

```
The forces still sum to zero, so drag is still zero. And the flows above and below the airfoil still have low pressure, same as with the cylinder.

Now let's tilt the streamlined shape. But let's tilt it in a very special way, so that the lower face becomes horizontal.

```
_----__   very low
/       --__
high |            --__  very low
|                --__            Pressures during horizontal flow
\_                  --__
------------------------
medium       medium

```
By tilting the shape, we eliminate the low pressure on the bottom surface, but at the same time we make the low pressure on the top surface very low indeed.

Now students, repeat after me:

"The top of the airfoil creates the entire lifting force, and the parcels of air passing BELOW the airfoil do not change as pressure as the air goes by!" (wrong!)

"The airfoil is not tilted. Instead it is flat on the bottom and curved on the top!" (no!)

Everyone believes these statements except the stupid kid in the back of the classroom who is always waving his hand yelling out embarassing questions that the teacher can't answer. He's so stupid! Fortunately we know that the majority is always correct in science. We know that we can always trust what's written in a textbook, so we have no reason to think twice about ignoring that kid.

The stupid kid is going to do badly on the next test. He doesn't even draw the correct diagrams in his notebook. Instead he draws this:

```
pressures:

_____     low
-----_____    low
high         -----_____
high

FIG. 1    TILTING AN AIRFOIL WITH RESPECT TO ONCOMING AIR CREATES
EQUAL AND OPPOSITE REGIONS OF PRESSURE.   THE UPPER AND
LOWER SURFACES BOTH PARTICIPATE EQUALLY IN CREATING "LIFT."

```
Then he draws this:
```

pressures:

medium
medium    -----------------------   medium
medium

FIG. 2   THIN FLAT AIRFOIL DEFLECTS NO AIR, PRESSURE DOESN'T CHANGE,
AND THE LIFTING FORCE IS ZERO

```
Is he right? Doesn't a fundamental difference exist between a thin flat airfoil, versus a thick "cylinder" airfoil? (If there's no big difference, then the stupid kid is right and the experts are wrong.)

Also, if a THICK airfoil usually has a low pressure below itself... and if we can get rid of this low pressure by tilting the airfoil... then maybe the bottom of the airfoil *DOES* create lift after all. Maybe the medium pressure below the tilted thick airfoil is really just a misleading "artifact" caused by the thick wing. Maybe it's a confusing effect caused by the combination of thick airfoil and tilted airfoil. Maybe the thick airfoil would always create low pressure below itself, while the tilted angle of the airfoil creates high pressure. At certain angles the two changes cancel out, and this confuses everyone.

Oh no, if the stupid kid is right, everyone will laugh at us, and we can't have that! Change the subject quickly, before anybody notices.

3. 99.99% of grade-school textbook diagrams depict ground-effect flight. They do not explain how airplanes can stay up there.
Here are a couple of excellent (and correct) diagrams. Unfortunately they are almost always interpreted wrong by all the grade-school authors who explain the origin of the lifting force. Unfortunately many other important diagrams are never presented to students.
http://www.av8n.com/how/gif48/3v.gif (from J. Denker's site)
If we concentrate our attention entirely on diagrams like these, we will never have a correct explanation of airplane flight. Of course these diagrams do explain many issues regarding the lifting force. However, these diagrams are two-dimensional. They are "infinite wing" diagrams, and they do not depict the flight of a real aircraft. Instead they depict flight inside a wind tunnel; "ground-effect flight." Or call it "venturi-effect flight" where the floor and ceiling of the wind tunnel are critically important. These diagrams mostly explain what happens when an aircraft is gliding just above the runway. When an aircraft rises upwards and climbs into the sky, the above diagrams no longer work. Other diagrams must be used.

If your wingspan is infinitely long, tell me how high must you fly before you can escape the ground-effect style of flight? Answer: you cannot escape at all. Real airplanes can escape. Real wings can employ a very different flight mode, but two-dimensional airfoils are trapped. If the wingspan is infinite, then the lifting force always comes entirely from venturi effect. Because of venturi effect, the upwards lifting force on the two-dimensional airfoil must have an equal and opposite downwards force on the floor and ceiling of the wind tunnel. This is true even if the "floor" and "ceiling" of a wind tunnel have been removed to immense distance. In a two dimensional world, the force-pair against the wind tunnel surfaces never changes no matter high the wing flys.

Therefore, the two-dimensional or infinite-wing diagrams *ONLY* depict how ground-effect flight works. They cannot show the aircraft wake, and they cannot show any of the momentum which a real wing dumps into the atmosphere as it flys forward. These diagrams do not explain normal airplane flight. Three dimensional diagrams are required. Here's my attempt at drawing a simplified 3-D diagram:

Disk Balloons
/wing/rotbal.html

4. Airfoil diagrams in K-6 textbooks violate Newton's laws, they omit the "floor" and "ceiling," and they don't show the force-pairs between the airfoil and the floor/ceiling.
Into a wind tunnel we place an airfoil having positive angle-of-attack. We want to examine the lifting force. To eliminate the effects of the ends of the airfoil, we extend it so that it touches the walls of the wind tunnel with a sliding contact.

This is the so-called "infinite wing" situation.

If we measure the forces in this system, we find a venturi effect. Yes, the airfoil generates lift, but there's also a reaction force on the floor and ceiling of the wind tunnel. The source of these two forces is obvious: the airfoil generates a pattern of circulation which extends to the floor and ceiling, and these air motions alter the pressure on the floor and ceiling. In this way the weight of the airfoil is communicated to the Earth (the airfoil is lifted upwards, but the whole wind tunnel experiences an equal and opposite reaction force downwards.)

OK, let's try to get rid of these unwanted forces. We build another wind tunnel, but one which is thin but very tall. The floor and ceiling are far away from our tilted airfoil. Now we again measure the forces on the floor and ceiling. THEY ARE THE SAME AS BEFORE! Ah, the explanation is obvious: it's the circulation pattern again. The circulation extends to the floor and ceiling. Now it extends much further than in our earlier wind tunnel, and the pressures on the floor and ceiling are far less... but those pressures are spread over a larger surface, and the net forces are the same as in the other wind tunnel. The width of the pressure pattern on the floor and ceiling is inversely proportional to the pressures involved.

OK, let's pull the floor and ceiling far, far apart. Does this reduce the forces? Nope. In other words, the weight of the airfoil upon the Earth stays constant. We just cannot get rid of the floor and ceiling of the wind tunnel! No matter, we can ARBITRARILY ERASE THEM FROM OUR DIAGRAMS. That will "simplify" things, right?

But won't someone complain? No, because we can be very sneaky. The upwards attraction force-pair between the airfoil and the ceiling was EQUAL to the downwards repulsion force-pair connected to the floor. Essentially there is one force connected to the bottom of the airfoil and another force pulling up from the top. We can pretend that the two force-pairs are actually a single force-pair: one end of the pair is pushing on the bottom of the airfoil, while the other end essentially pulls upwards from above. Two forces, right? They must be a force pair, and we can erase the floor and ceiling! Well, they're really not, since there's now an unbalanced force pushing the wing upwards. The far ends of those two forces still lie on the floor and ceiling. But no matter, we'll just ignore that. "But doesn't this mean that the airfoil has no weight against the earth, and is lifting itself up by it's own bootstraps?" And what if someone asks how a ship rudder can turn the ship, or how a propellor blade can drive a ship or airplane forward, or how a bird can fly around in a weightless space-station environment. Shhh! Don't mention that, and with luck nobody will notice the problem.

5. "Infinite wing" models are supposedly sensible? ...while real three-D wings are weird and distorted? No, the opposite is true.
If an airfoil is infinitely wide, then in order to create a lifting force, the airfoil doesn't need to deflect any air on average.

Why?

Well, suppose an infinite airfoil did deflect some air. Suppose it left a trail of descending air behind itself. As that air moved downwards, then the air below it would have to descend too. And in order to avoid forming a vacuum above, the air above the descending streamline would also have to descend. Let's draw a simple picture.

If this is the streamline which is bent by a tiny airfoil:

```
----------------------_____
-----_____
-----_____
-----_____

```
...then here's what we also need if one streamline bemds:
```
----------------------_____
-----_____
-----_____
----------------------_____                    -----_____
-----_____
-----_____
----------------------_____                    -----_____
-----_____
-----_____
----------------------_____                    -----_____
-----_____
-----_____
----------------------_____                    -----_____
-----_____
-----_____
----------------------_____                    -----_____
-----_____
-----_____
----------------------_____                    -----_____
-----_____
-----_____

```
See the problem? If we're living in a two-dimensional world, then ANY permanent bending of a horizontal streamline means that we have to deflect an infinite amount of mass; we have to bend ALL the streamlines above and below our one bent streamline. This strange effect only happens in "flatland" worlds.

Two-dimensional airfoil diagrams are weird and bizarre. When compared to a 3D wing, two-D airfoils depict an extremely distorted situation. In our 3D world we're allowed to give a streamline a permanent downwards deflection. The air below the streamline simply gets out of the way. There's an extra dimension in 3D, so new things can occur which were impossible in the 2D world.

Here's a typical streamline near a 2D infinite wing (tiny airfoil is in the center). Note the front-to-back symmetry. There is "upwash" in front of the airfoil, and "downwash" behind. On average, no air is deflected downwards. Also, the pattern of circulating air surrounding the airfoil extends outwards to infinity. These are requirments of the 2D world:

```                         _-_
___---   ---___
__________-----               -----_________

```
And here's what a 3D aircraft does to the still air it encounters:
```    ______________________
---___
---___
---___
---___
---___

```
3D airplanes are allowed to deflect the air, and the air remains deflected and moving down. The same effect cannot exist in a 2D airfoil diagram.

6. Cambered airfoils give positive lift at zero angle of attack?
Airfoils can only function if viscosity is low and inertia is important. In that case the trailing edge of the airfoil is far more important than the leading edge when lift is generated. After all, the air which flows off the trailing edge of the airfoil causes circulation, and circulation causes air-deflection and lift.

When a cambered (curved) airfoil is horizontal, the trailing edge of a airfoil is TILTED with respect to the oncoming air. Yet the airfoil as a whole is NOT TILTED; the angle of attack of the cambered airfoil is zero. Isn't this confusing? The air itself only pays attention to the trailing edge. Shouldn't we define "angle of attack" as being the angle of the trailing edge with respect to the oncoming atmosphere? If we defined AOA in that way, then a cambered airfoil would have a large angle of attack. It would have a large AOA even when the leading and trailing edges are on a horizontal line. If we defined AOA in that way, then the lifting force of a cambered airfoil would have a sensible explanation: tilted wings fling air downwards! Unfortunately we define AOA in relation to the line drawn between leading and trailing edges. Massive confusion is the result, because this gives us an "un-tilted" wing which still deflects air and creates lift.

7. A vortex-ring or a vortex-pair acts like a massive object which carries a certain amount of momentum as it travels, yet it carries no mass at all.
When airplane wings form a downwards-moving vortex wake, are they forcing air downwards? If we inspect the flow-lines in a cross section of the vortex pair, we find that they form closed loops. For every parcel of air which moves downwards, another is moving upwards, and zero mass is being transported. Therefore WINGS DON'T FLING ANY AIR DOWNWARDS. If we stopped thinking at that point we'd be "right." We'd make an enormous blunder, and we'd entirely fail to explain how airplanes work. In truth, airplane wings DO fling air downwards. But they do it with a most unusual method.

When a vortex-pair is moving downwards, it encounters some air which is in it's path. This air is parted by the vortices. It travels upwards on either side, and the vortices move downwards into the space which this creates. Finally, the air which was parted by the vortices is rejoined again behind them. But look at something important: the velocity and momentum of that air. The vortices MOVED that air. They accelerated it upwards. They gave it some upwards momentum. But then they decelerated it again, and the air was left with zero velocity. The vortex-pair lost no momentum as it moved downwards by "one step" through the surrounding air.

What does this mean? It means that any downwards momentum stored within the vortex-pair must remain within the vortex-pair as it moves. In other words, the vortex-pair acts like a huge volume of downwards-moving mass, and it carries momentum as it goes. Yet as the vortex-pair moves downwards, it pushes the surrounding air upwards. Won't the total momentum be zero? No, because the vortex pair takes back all the momentum it has given to the surrounding air. It only makes a temporary loan, so that the surrounding air can be moved from the bottom of the vortex pair to the top (and so the vortex pair can move downwards to take its place.)

Forming a downwards-moving vortex-pair is like firing a bullet downwards: your gun will experience a "kick" of reaction force. Because the wings of an airplane form such a vortex, they must experience an upwards kick. Yet they fling no air downwards! They only fling PURE MOMENTUM downwards. The vortex-pair is a traveling pattern of pure downwards momentum which carries zero mass as it moves. Weeeeeeird!

8. We "simplify" things by insisting that the working fluid be infinitely viscous and totally inviscid at the same time.
When looking at cylinders and airfoils in a wind tunnel diagram, we want to use highly viscous air. That way we can avoid the flow-detachment phenomenon. When air flows around a cylinder, if it's very viscous, then it will "close up" behind the cylinder and there will be no drag.

But the shearing of a viscous fluid causes another kind of drag, and this drag messes up the Bernoulli worldview. So we really must use some totally non-viscous air in our explanations.

Also, when analyzing airfoils, if the air is viscous, then the inertia of the air won't be important, and the "Kutta condition" won't work. There will be no circulation and no lifting force. Therefore we must use non-viscous air.

And if the air is viscous, there will be a wide "boundary layer" which we'll have to deal with. It had better be non-viscious air.

But if we use non-viscous air, there's no reason for the air to follow the rear half of a cylinder! And with non-viscous air, there's no reason for the air to follow the upper surface of a tilted airfoil! Non-viscous air causes a permanent "stall" condition.

We're trapped. We need some very nasty thick viscous air like syrup or tar which is... totally non-viscous. If we only had some of it, then airfoils and the lifting force would be very easy to explain.

This is called "irreducible complexity." If we try to simplify the explanation of wings and the lifting force, then we change reality so much that our explanations become wrong. Einstein warns us to make our explanations only as simple as possible, BUT NO SIMPLER. Highly viscous "inviscid air" used in aerodynamics explanations has gone WAY past Einstein's line in the sand. It falls under the classification of "so simplified that it no longer applies to reality at all." If the air is so inviscid that Bernoulli's Equation applies, then we cannot explain how the upper surface of a tilted plate can cause flow-attachment so that it deflects air downwards, and we cannot explain the low pressure above an airfoil.

9. Real airplanes depend on their vortex-wake, and without it they cannot fly (they can never escape ground-effect flight.)
A rocket can hover above the earth by throwing parcels of mass downwards. We can also get a machine gun and build a "flying machine" which can stay aloft because it flings bullets downwards. The rocket and the machine gun can only stay up because they apply a force to some parcels of mass, and they obey conservation of momentum and the F=MA rule. Are things different for airplanes? Yes and no.

When in normal flight, yes, an airplane essentially flings momentum- bearing air downwards. But while in ground-effect flight at very low altitude, instead the wings press downwards upon the ground, and the ground presses upwards on the wings, with the air allowing the exchange of forces, venturi-style. In ground-effect flight there is a Newtonian force-pair between the wings and the Earth. There are two surfaces involved: the Earth below, and the wing above. But in high-altitude flight the Earth is out of the picture, and an airplane remains aloft because it reacts only against the air. If the Earth were gone entirely, the airplane could still drive around in a huge ball of air, just as a fish could still swim around in a huge ball of water floating in a space station.

As with hovering rockets and downwards-pointing machine guns, an airplane in high-altitude level flight must create a stream of downwards-moving "exhaust." This "exhaust" is obvious: it's the downwards-moving wing tip vortices and all the air which surrounds them. Without this "exhaust" the airplane could not fly. This "exhaust" is as important to flight as the exhaust of a hovering rocket. It's as important as the bullets which are shot out by our downwards-pointing, flying machine gun. Yet most textbook diagrams never discuss this exhaust, and if they do, they treat it as an unwanted effect best gotten rid of. But that's like wanting to get rid of the exhaust expelled by a rocket motor. Physics has bad things to say about any such attempt. And anyone who doesn't understand why rockets (and airplanes) must expel an "exhaust," does not really understand how rocket motors or wings actually work.

The "exhaust" below a wing made visible
(See Hyperphysics and other photos.)

```

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