We tilt our airfoils while denying that we've done so.
The pressures around 'bluff' airfoil shapes are misleading. They
greatly interfere with explanations of lifting force.
(we could simply use thin-wing models instead).
In grade-school, textbook diagrams do not explain how real airplanes can
stay up there. The diagrams only depict "ground-effect flight."
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
"Infinite wing" models are supposedly sensible? ...while a real
three-D wing is weird and distorted? No, the opposite is true.
Cambered airfoils give lift at zero angle of attack? Maybe not.
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.
We "simplify" things by insisting that the working fluid be
infinitely viscous and totally inviscid at the same time.
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!
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.
/ --__ / --__
| --__ | --__
| --__ | --__
\_ --__ | --__
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
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:
high | | high Cylinder in a horizontal flow
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
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.
high | ----____
| ____---- Pressures during horizontal flow
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
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
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!)
Everyone believes these statements except the stupid kid in the back of
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 airfoil is not tilted. Instead it is flat on the bottom
and curved on the top!" (no!)
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
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:
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
pressure below itself, while the tilted angle of the airfoil creates high
pressure. At certain angles the two changes cancel out, and this confuses
Oh no, if the stupid kid is right, everyone will
laugh at us, and we can't have that! Change the subject quickly, before
3. 99.99% of grade-school textbook diagrams depict ground-effect flight. They do
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
(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
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.
(from M. Colombini's site)
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
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:
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
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.
Well, suppose an infinite airfoil did deflect some air. Suppose it
left a trail of descending air behind itself. As that air moved
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
...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
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
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
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
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
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
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
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
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
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