QUESTION:
Why DOES the air go faster over the top 
of a surface inclined w/ a positive angle of 
attack?
In addition, I think I understand "lift is a force
generated by turning a moving fluid" (I can draw a
sensible vector diagram, particularly if I know the
airflow over the top of the wing is faster)
(www.lerc.nasa.gov/www/FMD/airplane/lift1.html), 
but can you explain (in terms a 5th grader could understand)  how this is
related to Bernoulli's law?

ANSWER from Andrew Hahn on April 23, 1998:
This is a great question and it brings out 
one of my pet peeves. In order to make the 
concept simple, some common and quite 
wrong explanations have been offered 
historically.

Wrong explanation #1: An airfoil is flat on 
the bottom and curved on top so air has to 
flow faster over the top to meet the air from
under the airfoil at the trailing edge. Faster 
air has lower pressure and so the airfoil
lifts. There are a lot of problems with this 
like; the air particles don't actually meet at 
the trailing edge, flat plates fly, airplanes 
fly upside down, etc. I could go on, but I 
think you get it.

Wrong explanation #2: Believe it or not, 
my industrial design professor in grad 
school was teaching another wrong 
explanation (to be fair, it is outside of his 
bailiwick). He said that if a curved plate 
were in a channel, then the flow area above 
is restricted while the flow area below
expands and the net effect is lower pressure 
above and higher pressure below. The main 
problem with this is that it doesn't really 
model our airplane because the airflow isn't 
really constrained. This too leads to
inconsistencies. The most obvious is, if you 
place a flat plate at an angle of attack, then 
the flow area above the leading edge increases
 (decreasing speed => increasing pressure) 
while the flow area below the leading edge
decreases (increasing speed => decreasing 
pressure). Since the geometry is symetrical,
there is no net lift but there is a pitching 
moment. In reality, a flat plate at an angle of 
attack has lift but no moment. So, the
result is exactly backwards.

The common problem with these explanations
is that they are modeled on variations of the 
venturi, which is the classic device used to 
demonstrate the Bernoulli principle. 
Unfortunately, airfoils and venturi's change 
the airflow velocity through two totally 
different mechanisims. The venturi changes 
area to speed up or slow down the flow while 
the wing induces circulation.

So, what is circulation? Circulation is a 
component of flow that goes in a circular 
motion, just like a tornado. Early researchers
found that they could represent the complex 
circulatory flow around an airfoil with a
simple vortex (tornado) that runs along the 
span of the wing (We do this sort of thing all 
the time. For example, we represent the 
complex pressure distribution on the surface
of the wing, both top and bottom, with Lift,
Drag and Moment vectors). When this 
horizontal vortex is put in a horizontal flow,
lift is generated. This concept made 
calculation of the lift on a wing possible by 
hand and was a huge breakthrough in
understanding. As an undergrad, I used to 
think that this was just a convenient 
mathematical concoction that gave the right 
answers, but that this didn't really occur. 
How wrong I was. So many effects are 
explained by circulation that it can't be just 
convenient.

What's so special about the wing (airfoil) 
shape that generates this circulatory flow? 
The sharp trailing edge. I'm going to leave out
some of the more obscure arguments and just
relate the most common explanation of what 
happens at the trailing edge. This is a little 
hard to do without pictures, but I'll try to 
explain this as best I can. All fluids have
viscosity, or a resistance to deforming. Some
fluids resist deforming a lot (like molasses) 
while some fluids deform easily (like air). 
Still, air does have some viscosity and this 
makes air very reluctant to turn sharp
corners. So now, take a flat plate (your hand
will do in a pinch) and put it in a horizontal 
flow (out the car window), level (no angle of 
attack). The air hits at the front (leading 
edge) and leaves at the back (trailing edge). 
Now, rotate your wrist so that the leading 
edge goes up and the trailing edge goes down 
(increase angle of attack). You will notice 
that there is a lift and drag force generated. 
This occurs because the air has viscosity. If 
there were no viscosity, the air would hit 
somewhere on the lower side of your hand 
near the leading edge and it would split. Half 
of the flow would travel foreward, turn 
around the leading edge and then flow 
backwards along the top of the plate. Like a 
reflection, the other half of the flow goes 
backwards along the bottom of the plate until 
it gets to the trailing edge. It would then turn
around, and flow forward along the top until 
it met the first half of the flow. Where they 
meet, they would leave your hand. With this 
invicid flow, there is no lift. But remember, 
this doesn't really happen. The difference is 
that the second half of the flow never 
negotiates the turn around the trailing edge 
because it is sharp and the velocity required 
to do this is theoretically infinite. Viscous 
fluids can't do infinite and so the lower half 
just gives up and leaves at the trailing edge. 
It is this difference between what the flow 
wants to do and what it can do that sets up the 
circulatory flow.

This circulatory flow modifies the local air 
velocities over the whole wing, but the 
general effect is to speed up the air over the 
top and retard the air underneath. (This still 
works for thicker airfoils, but the picture
is a little more complicated)

Bernoulli's principle says that faster air has
lower pressure, so the air above the wing 
sees a low pressure. Since air always flows 
from high to low pressure, this starts air 
moving downward. Newton said that 
Force = Mass x Acceleration, so even though 
air has just a little mass, we can generate a
usable force (lift) if we accelerate a lot of 
air downward a little.

Well, that was a mouthful. Let's recap. The 
wing shape forces the air to leave the trailing
edge smoothly which sets up a circulatory 
flow pattern which causes the air velocity to 
increase over the top of the wing which
lowers the pressure which turns the flow 
downward which causes lift. There,
that wasn't so bad was it.