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Airfoil Lifting Force Misconception
Widespread in K-6 Textbooks

William Beaty 1996
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New: common lift miscons, Cambridge U., also Yale, also Vtsium and XKCD comic

Beat around in the underbrush of aerodynamics and you'll encounter an interesting question:
Amazingly enough, this question is still argued in many places, from K-6 grade classrooms all the way up to major pilot schools, and even in the engineering departments of major aircraft companies. This is unexpected, since we would assume that aircraft physics was completely explored early this century. Obviously the answers must be spelled out in detail in numerous old dusty aerodynamics texts. However, this is not quite the case. Those old texts contain the details of the math, but it's the *interpretation* of the math that causes the controversy. There is an ongoing Religious War over both the way we should understand the functioning of wings, and over the way we should explain them in children's textbooks. It's even erupted into the news, see news links below. The two sides of the controversy are as follows:

  • The physics explanation, NEWTONIAN or ATTACK ANGLE: wings are forced upwards because they are tilted and they deflect air. The air behind the wing is flowing downwards, while the air far ahead of the wing is not. A wing's trailing edge must be sharp, and it must be aimed diagonally downward if it's to create lift. Both the upper and lower surfaces of the wing act to deflect the air. The upper surface deflects air downwards because the airflow "sticks" to the wing surface and follows the tilted wing (this phenomena is called "Coanda effect" or "Flow Attachment.") Air's inertia is critical: after the wing has passed by, air must remain flowing downwards ...and the lifting force does not arise in extremely viscous fluids. Airplanes fly because of Newton's 3rd law (action/reaction forces,) the law of Conservation of Momentum, and the Coanda effect.
  • The popular explanation, PATH-LENGTH or AIRFOIL-SHAPE: wings do not deflect air: the air far behind the wing is flowing the same as the air far ahead. Instead, wings are essentially "sucked upwards" because the airfoil shape has a longer surface on top. Airfoils are curved on top and flat below, and therefore the air follows a longer path above than below. Hunks of air which get divided at the leading edge of a wing must join each other again at the trailing edge. Since the upper surface of the wing is longer, it causes the upper air to flow faster than the lower, which (by Bernoulli's principle) creates lower pressure above. Because lift is caused by the shape of the wing, wings can create lift at zero attack angle. They can create lift simply from path-length difference which leads to pressure difference, and no air needs to be deflected. After a wing has passed by, the air does not remain moving downwards. (This explanation is seriously flawed.)
This webpage is biased towards the ATTACK ANGLE view. See just about any K-6 science book for the PATH LENGTH argument. (Note that the controversy extends far beyond grade school, and even some pilot training manuals still contain the discredited "path length" explanation.)

Also there are three other explanations of lift: the circulation-based explanation, the flow-turning or streamline-curvature explanation, and the 3D vortex-shedding explanation. These three appear in advanced textbooks, where they form the basis of the mathematics used by aircraft designers. They rely on Bernoulli's equation. The misleading "popular" or "airfoil-shape" explanation commonly appears in children's science books, magazine articles, and in pilot's textbooks. On the other hand, the public rarely if ever encounters explanations based upon circulation, upon vortex shedding, or upon Newton's Laws.

Thin green laser-scanned dye cloud, when 777 model flys through it, it suddenly moves down and develops an opposite-rotating vortex pair.

A possible solution to the controversy:

Billb's balloon analogy to aircraft: vortex shedding
Note well: Newton and Bernoulli do not contradict each other. Explanations which are based on Newton's and on Bernoulli's principles are completely compatible. Air-deflection and Newton's Laws explain 100% of the lifting force. Air velocity and Bernoulli's equation also explains 100% of the lift. There is no 60% of one and 40% of the other. One of them looks at pressure forces, the other looks at F=mA accelerated mass. For the most part they're just two different ways of simplifying a single complicated subject. Much of the controversy arises because one side or the other insists that only *their* view is correct. They insist that only a *single* explanation is possible, and the opposing view is therefore wrong. In other words... which is the One True Way to crack an egg? This is a war between the Big-endians and Little-endians from "Gulliver's Travels." They simply refuse to acknowledge that there are several valid yet independent approaches to solving the problem. They insist that their version must be the Single Right Answer, the "One True Path," and anyone who disagrees is a dangerous heretic infidel who must be attacked and silenced.

Social psychology aside, there are also several serious mistakes usually associated with the "popular" explanation described above. Those who believe the "popular" explanation are wrongly insisting that any parcels of air divided by the wing's leading edge must meet again at the trailing edge. This is incorrect. Actually it doesn't even occur: experiments easily show that the air above a wing far outraces the air below, and parcels never meet again. (In fact, if a wing is adjusted so the parcels really do merge, this is always the zero-lift configuration!) The same people also believe that wings fly only because of pressure, and that wings don't need to deflect the oncoming air downwards. Also incorrect. These and several other mistakes commonly appear in elementary science texts, as well as in popular articles about aircraft physics. These mistakes change the popular "airfoil-shape" explanation into a system of misconceptions. I explore these below.

Also, those who firmly adhere to the popular explanation have been successful in convincing many authors that there can only be a single best method for explaining aerodynamic lift, and that the "Airfoil-shape" method is far better than the "Attack-angle" method. I strongly disagree with this, and believe that the correct versions of both explanations should be in constant use. Since the Newton method gives a better intuitive grasp of the issues, that method is more appropriate for elementary explanations aimed at the public and for introductory material for science students and pilots. On the other hand, the "Airfoil Shape" or circulation-based explanation is less intuitive, yet it dovetails very well with lifting force calculations, so it is very useful in mathematical modeling, for physics students, for aircraft design, fluid flow simulation software, etc.

The Truth shall set you free... But first it will piss you off!



1. Your personal theory is wrong, and nobody should listen to you.

Answer: Ha, if it was just me saying it, you'd be wise to be suspicious. On the other hand, Science is based on the questioning of authority. Sometimes the combined voices of famous and important unquestionable authorities are nothing when compared to a single quiet voice who says "and yet it moves." But fortunately where airfoils are concerned, we're way past that part. I'm no Galileo, and it's not just me saying all this stuff.

The latest version of this controversy was started in 1990 by the aerodynamicist Dr. Klaus Weltner with his paper in American Journal of Physics which calls airfoil explanations into question. There were earlier incidents, such as the popular pilot's training book "Stick and Rudder." I first posted my own amateur articles here in 1995 when the web became available. Since then Gale Craig published How Airplanes Really Fly , Jan-Olov Newborg started a campaign to correct many sources, the late Jef Raskin published his article in Quantum, Dr. John Denker of Bell Labs put it in his online pilot's textbook, the NASA Glenn Research Center included the controversy in their public education program, and aerodynamicists Anderson and Eberhardt published a textbook based on those ideas: Understanding Flight. The controversy recently made it into the New York Times as well as several magazines and aerodynamics websites (see links below.) So... if you want to be suspicious, be suspicious of anyone who tries to pretend that no problems exists, or that this controversy is really just some individual's little pet theory.

2. How could so many scientists, engineers, and authors be so wrong?

- First and foremost, the airfoil lifting-force is an example of propulsion, where the airfoil injects energy and momentum into the air. This is forbidden in the Bernoulli world, so Bernoulli's equations cannot explain propellers, jet engines, helicopters, sails, or airplane wings. Bernoulli only works if we transform the airplane into a venturi by making the wingspan infinitely wide. (Imagine an infinitely-wide helicopter prop, or bird wing!) An infinite wing injects zero energy and momentum into the air, instead it's an example of ground-effect flight. It only produces forces between two surfaces.

- Second, the airfoil math is correct, so wing-designs work regardless of the designers' belief system. Airfoils work fine for ground-effect WIG craft or for normal wings. Incorrect beliefs about wing-functions have little impact, as long as engineers don't use the beliefs to alter the fluid simulations.

- Errors can infect grade-school textbooks and spread widely to many books. All aerodynamics people once were kids, so they can pick up a misconception which they never question, and which persists into their adult careers as aircraft experts. Even more advanced textbooks can give explanations which contain errors at much higher level, e.g. the 2D-centric explanations which imply that infinite wings are normal and acceptable, while finite 3D wings are a bizarre special case. That's backwards. It's the 3D wing which is actually real, while the infinitely-wide wings of the 2D world are the unphysical odditiy, and an example of ground-effect flight.

- Henri Coanda's old experimental work on boundary-layer attachment was marginalized, even ridiculed, rather than merged with the rest of aerodynamics or included in college textbooks. Air is nonlinear, with no simple math solutions which simply explain either flow-attachment or turbulence. As a result, a big piece of aerodynamics concepts is missing. After he dies, Nobelist W. Lamb supposedly was hoping to "ask God" how turbulence works. He could have instead asked God an equivalent unsolved question: how do wings really work? Wings work by creating vorticity from nothing, which is also the signature of turbulence. The lifting force is inescapably a product of turbulence, of nonlinear vortex-shedding, so many experts turn away.

- Cambered wings at high Reynolds number have a positive effective attack angle even when the geometrical attack angle is zero. This confuses everyone, even some experts. They see only the zero geometrical angle and believe that the cambered wing cannot deflect air. They don't realize that the down-tilted trailing edge of a cambered wing has far more effect upon an air parcel than does the rest of the entire un-tilted wing. In other words, the sloping rear half of an un-tilted cambered wing is strongly interacting with air because of air's inertia. A cambered wing flings air downwards as if the wing were tilted. A cambered wing can have a large AOA and a zero AOA ...both at the same time. Very confusing to the uninitiated.

- A two-dimensional diagram (also called the 'infinite wing diagram,') is misleading. It depicts ground-effect flight where altitude above a surface is always much less than one wingspan. Any explanation based on this type of diagram does not apply to the vortex-shedding flight of 3-dimensional aircraft when they're far above the ground. These Two-dimensional diagrams are not just simplified, they're genuinely wrong, since typically they neglect to show the floor and ceiling of the 2D wind tunnel which receives the weight of the wing as an instantaneous contact-force. In 2D diagrams the floor and ceiling are an essential part of the system, and their effects do not diminish as they are removed to infinite distance. In other words, two-dimensional airfoil diagrams depict an odd type of "venturi flight" situation, where the wing is trapped in "ground-effect mode," while genuine aircraft fly far from the ground and have no instantaneous weight applied to the Earth's surface. (Then, the ground is illegally erased from the 2D diagram!) To explain lift in high-flying aircraft, we absolutely require a 3D diagram with its vortex downwash wake. Real wings fly because of vortex-shedding, and they're lifted upwards as they fling a mass-bearing vortex-pair downwards. Yet introductory textbooks always use the misleading two-dimensional diagrams which depict only the regime of ground-effect flight: "venturi-flight" of infinitely-wide wings.

- The presence of multiple possible explanations can trigger religious wars, "Swiftian Battles" between adherents to one side and the other. Sometimes one side wins; swaying the audience and stomping out the other explanation... even though parts of both explanations are valid, and even though both explanations are required for complete understanding. We cannot really grasp wing operation unless we know several different ways to explain them. In the same way, toolkits need both hammers AND screwdrivers... and anyone who searches for a "One True Tool," while angrily emptying out the rest of their toolbox, is severely limiting their own expertise.

"I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic."
    - physicist H. Lamb, 1932 address to the British AAS
3. Why are you prejudiced against the Bernoulli-based theory? Bernoulli's equation is perfectly correct.
Huh? Read my stuff again. Please tell me where I attack Bernoulli. Instead I only attack the "popular theory," also called the Equal Transit-Time explanation. By the way, the correct version of the Bernoulli explanation is called Circulation Theory. Another version is called Flow-turning Theory. Anyone who claims to support the Bernoulli side of the controversy, yet isn't familiar with Circulation as explained in intro texts, is laboring in ignorance. Go see John Denker's page for plenty of info and illustrations about circulation-based explanation. On the other hand, yes, Bernoulli can't be used, since real wings function by injecting energy and momentum into the air. Bernoulli doesn't cover that. Instead we need Euler's equations, of which Bernoulli is a subset. We also need fluid simulation, since most instances of Euler (e.g. vortex-shedding) will have only numeric (computer) solutions.

Bill B.'s "Newtonian" Articles & Misc.Controversy

The "Airfoil Mistake" in the news


Discussions, message threads

Relevant forums


Other websites


"Newtonian" Lifting Force References

Cliff Swartz, "Numbers Count", editorial in THE PHYSICS TEACHER, p536, Vol34, Dec 1996

Gale Craig, NEWTONIAN AERODYNAMICS FUNDAMENTALS, 1995, Regenerative Press, Anderson Indiana 46011, ISBN: 0964680602

Prof. Klaus Weltner, AERODYNAMIC LIFTING FORCE, The Physics Teacher (magazine), Feb 1990, pp78-82

K. Weltner, BERNOULLI'S LAW AND AERODYNAMIC LIFTING FORCE, The Physics Teacher, Feb 1990, pp84-86

K. Weltner, A COMPARISON OF EXPLANATIONS OF THE AERODYNAMIC LIFTING FORCE, Am. J. of Physics, 55 (1) Jan. 1987 pp50-54

Langewiesche, Wolfgang, STICK AND RUDDER, 1975 Tab Books, ISBN: 0070362408

N.H. Fletcher, MECHANICS OF FLIGHT, Physics Education, Wiley, NY 11975, pp385-389



Here is the typical "Airfoil shape" or "Popular" explanation of airfoil lift which commonly appears in childrens' science books:

As air approaches a wing, it is divided into two parts, the part which flows above the wing, and the part which flows below. In order to create a lifting force, the upper surface of the wing must be longer and more curved than the lower surface. Because the air flowing above and below the wing must recombine at the trailing edge of the wing, and because the path along the upper surface is longer, the air on the upper surface must flow faster than the air below if both parts are to reach the trailing edge at the same time. The "Bernoulli Principle" says that the total energy contained in each part of the air is constant, and when air gains kinetic energy (speed) it must lose potential energy (pressure,) and so high-speed air has a lower pressure than low-speed air. Therefore, because the air flows faster on the top of the wing than below, the pressure above is lower than the pressure below the wing, and the wing driven upwards by the higher pressure below. In modern wings the low pressure above the wing creates most of the lifting force, so it isn't far from wrong to say that the wing is essentially 'sucked' upwards. (Note however that "suction" doesn't exist, because air molecules can only push upon a surface, and they never can pull.)

MY NOTES:      (1996)

Uh oh, wind tunnel photographs of lift-generating wings reveal a serious problem with the above description! They show that the divided parcels do not recombine at the trailing edge. Whenever an airfoil is adjusted to give lift, then the parcels of air above the wing move far faster than those below, and the lower parcels lag far behind. After the wing has passed by, the parcels remain forever divided. This has nothing to do with the wing's path lengths. This even applies to thin flat wings such as a "flying barn door." The wind tunnel experiments show that the "wing-shape" argument regarding difference in path-length is simply wrong.

Also, real-world aircraft demonstrate another fallacy. In order to create lift, must a wing have greater path length on the upper surface than on the lower? No. Thin cambered (curved) wings such as those on hang gliders and on rubberband-powered balsa gliders, have equal path length above and below, yet they generate lift. Still the air does flow faster above these wings than below. However, since there is no difference in path length, we cannot refer to path length to explain the difference in air speed above and below the thin wing. The typical "airfoil shape" explanation cannot tell us why a paper airplane can fly, because it does not tell us why the air above the paper wing moves faster.

It is also a fallacy that in order to create lift, a wing *must* be more curved on top. In fact, wings which are designed for high speed and aerobatics are symmetrical streamlined shapes, with equal curvature above and below. Some exotic airfoil shapes are even flat on top and more curved on the bottom! (NASA's "supercritical" wing designs, for example.)

If the typical "popular" or "airfoil-shape" explanation is correct, then how can symmetrical wings and thin cambered wings work at all? How can rubberband balsa gliders work? Those who support the "path length" explanation will sometimes suggest that some other method must be used to explain these particular wings. But if so, why then do so many books put forth only the above "popular" explanation as the single explanation of aerodynamic lift? Why do they avoid detailing or even mentioning any other important explanations of lifting force?

The cloth aircraft of old had single-layer wings having identical path length above and below. If the "Wing-shape" or "popular" explanation is correct and path-length is very important, how can the Wrights' flyer have worked at all? Conversely, we do find that thin airfoils such as the Wrights' have faster flow on the upper surface than the lower surface. Since the path lengths are identical, how can we explain this?

The above "path length" viewpoint would predict that the addition of a lump to the top of a wing should always increase the lift (since it increases the upper surface path length.) In fact, the addition of a lump does not increase lift. This suggests that there is a problem with the "airfoil shape" explanation of lift.

Forces on sailboat sails are explained using the typical "pathlength/wingshape" explanation above. But sailboat sails are thin cloth membranes with identical path-lengths on either side. Why should air on either side of a sail have different velocities if the path length is the same?

Children have experience with rubberband-powered balsa wood aircraft having wings composed of a single flat layer of very thin wood. Paper airplanes usually have flat thin wings. These aircraft cannot fly? How can the "path length" version explain their successful operation?

Regardless of the angle of attack, if a wing does not deflect air downwards, it creates no lift at all. To say otherwise would go against the law of Conservation of Momentum. Yet those who believe in the "airfoil-shape" explanation commonly state that wings operate only by pressure, and Newton's laws are unimportant. This is a direct violation of basic physics principles. Bernoulli's equation incorporates basic physics, and anyone who depart from Newton must automatically depart from Bernoulli as well. Besides buoyancy and helium balloons, the only way to remain aloft is to take some matter and accelerate it downwards. The downward force applied to the matter is equal to the upward force applied by the matter against the craft. Rockets work like this, as do ship propellers, jet engines, helicopters, ...and wings!

Some people argue that the "path length" explanation must be right, since some wings generate lift even at zero angle of attack. However, Attack-angle is determined geometrically, by drawing a line between the tip of the leading and trailing edge. This geometrically-determined attack angle can be misleading:

[GIF: add an off-center bump, then tilt the wing to

Small bumps on the leading edge of a blunt-nosed wing have a large effect on where the line is drawn. These bumps strongly affect the determination of "attack angle, yet these bumps may have little if any effect on the lifting forces being generated. Also, once the "zero AOA" geometry has convinced us to tilt the trailing edge downwards, inertial effects will cause the airfoils to deflect air downwards from its trailing edge more than it deflects air upwards at its leading edge. The downward tilt of the trailing edge generates significant lift even when the wing as a whole is lift even angle of attack. This type of wing may APPEAR at zero attack angle. The inertia of air causes the air to flow straight from the trailing edge of the airfoil. Because of inertia, the trailing edge of a cambered airfoil itself behaves as a tilted plane, and therefore the airfoil effectively has a positive angle which causes air to be deflected. Other cambered wings are similar; they still have a positive "effective" attack angle even when their geometrical attack angle is zero. The trailing edge, not the airfoil itself, determines lift.

Some people argue that flat wings, symmetrical aerobatic wings, Supercritical wings, and thin cloth wings do not employ the Bernoulli Effect, and these wings must instead be explained by Newton and attack angle. But as mentioned above, if jet fighters and the Wright Flyer use Attack Angle rather than Bernoulli Effect, why do the books teach only Bernoulli Effect? At the very least, these books are ignoring an entire class of aircraft by never mentioning Attack Angle. However, even these thin wings and symmetrical wings exhibit the full-blown Bernoulli principle! There is a large difference in speed between the upper and lower air streams along flat wings. If a flat sheet of plywood is tilted into the air stream, the air flows faster above the sheet than below, the divided parcels never rejoin, and lift is generated by the pressure difference. But the flat sheet also deflects the air, and just as much lift is generated by deflection of air. In fact, 100% of aerodynamic lift can be explained by pressure forces and the Bernoulli principle. And 100% of lift can be explained by F=mA and Newton's third law. They are two different ways of explaining a single event. However, any appeals to differences in path length are simply wrong, and any book which uses that explanation is acting to spread science misconceptions.

An alternate explanation of lift: "ATTACK ANGLE"

As air flows over a wing, the flow adheres to the surfaces of the wing. 
This is called flow-attachment, also the "Coanda effect."  Because the 
wing is tilted, the air is deflected downwards as it moves over the wing's 
surfaces.  Air which flows below the wing is pushed downwards by the wing 
surface, and because the wing pushes down on the air, the air must push 
upwards on the wing, creating a lifting force.  Air which flows over the 
upper surface of the wing is adhering to the surface also.  The wing 
"pulls downwards" on the air as it flows over the tilted wing and off the 
trailing edge, and so the air pulls upwards on the wing, creating more 
lifting force.  (Actually the air follows the wing because of reduced 
pressure, the "pull" is not really an attraction.)  The lifting force is 
created by Newton's Third Law and by conservation of momentum, as the 
flowing air which has mass is deflected downward as the wing moves 
forward.  Because of Coanda Effect, the upper surface of the wing actually 
deflects more air than does the lower surface.

   My notes on "attack angle":

	If you understand the "attack angle" explanation, then the causes
	of other aircraft phenomena such as wingtip vortex will suddenly
	become clear.  The air at the trailing edge of the wing is 
	streaming downwards into the surrounding still air.  The edge 
	of this mass of air curls up as the air moves downwards, creating 
	the "wingtip vortex."  A similar effect can be seen when a drop
	of dye falls into clear water: the edge of the mass of dye curls
	up as the dye forces itself downwards into the water, resulting
	in a ring vortex which moves downwards.

	There is one major error associated with the "attack angle"
	explanation.  This is the idea that only the LOWER surface of
	the wing can generate a lifting force.  Some people imagine that
	air bounces off the bottom of the tilted wing, and they come to
	the mistaken belief that this is the main source of the lifting
	force.  Even Newton himself apparantly made this mistake, and so
	overestimated the necessary size of man-lifting craft. In reality,
	air is deflected by both the upper and the lower surfaces of the
	wing, with the major part being deflected by the upper surface.

	Because a large, heavy aircraft must deflect an enormous amount of 
	air downwards, people standing under a low-flying aircraft are,
	after a short delay, subjected to a huge downblast of air.  They 
	are essentially feeling a portion of the pressure which supports 
	the plane.   Imagine standing below a helicopter that hovers a
	few tens of yards above the ground.  Enormous downwash?  Now
	imagine that helicopter flying along at 150mph, or imagine the
	blades detaching and flying away perpendicular to travel, like 
	wings, and you end up with the usual physics of fixed-wing 
	aircraft.  All aircraft wings are essentially sucking in air from 
	all directions and flinging it downwards.  This fact gets lost 
	when the aircraft moves horizontally much faster than its downwash 
	moves vertically.  Some people even come to believe that wings 
	don't deflect air at all, or leave air moving downwards after the 
	aircraft has passed by.

	The downwash can be useful: when a cropduster flies low over a 
	field, the spray is injected into the airflow coming from the 
	wings.  Rather than trailing straight back behind the craft, the 
	spray is sent downwards by the downwash from the wings.  Also, 
	during takeoff the downwash interacts with the ground and
	causes lift to greatly increase.  Pilots often use this effect to 
	gain a large airspeed just after takeoff.  Because of downwash 
	"ground effect," their engine needs to do much less work in 
	keeping their aircraft aloft, therefore the extra power available 
	can be used to speed up the plane.

	To create adequate lift at extremely low speeds, an airfoil 
	must be operated at a large angle of attack, and this leads to 
	airflow detachment from wing's the upper surface (stall.)  To
	prevent this, the airfoil must be carefully shaped.  A good low-
	speed airfoil is much more curved on the top, since lift can be
	created only if the wing surface carefully deflects air downwards
	by adhesion.  Thus one origin of the misconception involving "more
	curved upper surface."  The surface must be curved to prevent 
	stall, not to create lift but to avoid losing lift. The situation 
	with the lower surface is different, since the lower surface can 
	deflect the air by collision.  Even so, it makes sense to have the 
	lower surface be somewhat concave, so that the air is slowly 
	deflected as it proceeds along, and so the upwards pressure is 
	distributed uniformly over the lower surface.

	Why does flowing air adhere to the upper surface of the wing?  This
	is called flow-attachment, also "the Coanda effect."  Apparently 
	Dr. Bernoulli has a better PR department than Dr. Coanda, (grin!), 
	since everyone has heard of Bernoulli, while Coanda is rarely 
	mentioned in textbooks.

	The only correct part of the "wingshape/pathlength" explanation of
	lift is the description of the Bernoulli effect itself.  But the 
	"Bernoulli Effect" can also be interpreted thus: because the 
	wing is tilted, it creates a pocket of reduced pressure behind its
	upper surface.  Air must rush into this pocket.  And at the tilted
	lower surface, air collides with the surface and creates a region
	of increased pressure.  Any air which approaches the high pressure
	region is slowed down.  Therefore, the pressure is the cause of
	the air velocity, not vice-versa as in the "airfoil-shape"
	explanation above.  Also, it is wrong to imagine that the low
	pressure above the wing is caused by the "Bernoulli effect" while
	the high pressure below the wings is not.  Both pressure
	variations have similar origin, but opposite values.

	The "airfoil shape" explanation could be very useful in 
	calculating the lifting force of an airfoil.  Knowing the fluid 
	velocity at all points on the airfoil surface, the pressure may be 
        calculated via Bernoulli's equation at all points, and if the
        pressure at each point is vector summed, the total lifting force
	upon the wing will be obtained.  The trick then is knowing how to
	obtain the fluid velocities.  Appeals to differences in pathlength
	do not work, so other methods (circulation and Kutta condition)
	must be used.

Parts of the Airfoil Misconception

  1. Wings create lift because they are curved on top and flat on the bottom. Incorrect.
  2. Part of the lifting force is due to Bernoulli effect, and part is due to Newton's 2nd law. Incorrect.
  3. To produce lift, the shape of the wing is critical. YES AND NO.
  4. The Bernoulli effect pertains to the shape of the wing, while Newton's laws pertain to the angle of attack. Incorrect.
  5. Air which is divided by the leading edge must recombine at the trailing edge. Incorrect.
  6. The upper surface of an airfoil must be longer than the lower surface. Incorrect.
  7. The tilt of the wing produces part of the lift. The shape of the wing produces the rest. Incorrect.
  8. A wing is really just the lower half of a venturi tube. Incorrect.
  9. The upper surface of a wing will deflect air, but the lower surface is horizontal, so it has little effect. Incorrect.
  10. Airfoils need not deflect any air; pressure differences alone can produce lift. Incorrect.
  11. Ship propellors, rudders, rowboat oars, and helicopter blades all deflect water or air. But airplane wings are entirely different. NOPE.
  12. The "Coanda effect" only applies to thin liquid jets, not to airfoils and flow attachment. Incorrect.
  13. An airfoil can create lift even at zero attack angle. Misleading.
  14. Cambered airfoils create lift at zero AOA, which proves that the "Newtonian" theory of lift is wrong. Incorrect.
  15. The "Newtonian" theory of lift is wrong because downwash happens far behind the wing where it can have no effect. Incorrect.

1. Wings create lift because they are curved on top and flat on the
   bottom.   INCORRECT.

     Incorrect because only some wings look like that, while other wings are
     symmetrical (they're the same on top and bottom,) while still others 
     are flat on top  ...and curved on the bottom!   And don't forget the 
     hang-gliders and the Wright Brothers' flyer, both of which used thin 
     fabric wings with equal curvature top and bottom.  The lifting force
     does not vanish if an airplane flys upside-down.  Explanations for
     flight involve other things, and not airfoil asymmetry.

2. Part of the lifting force is due to Bernoulli effect, and part is due 
   to Newton.   INCORRECT

     Incorrect because ALL wings, regardless of shape or degree of tilt,
     must create 100% of their lift because of Newton.  To say otherwise 
     would mean that a wing could violate Newton's Laws!  Yet at the same 
     time, ALL wings create 100% of their lift because of the Bernoulli 
     Equation.  This is true because 100% of the lifting force comes from
     pressure differences on the wings' surfaces.

     In fact, we can explain the lifting force by "Newton," by ignoring 
     the pressure differences and instead measuring the dense deflected 
     air and calculating the change in momentum.

     And of course we can explain 100% of the lifting force by "Bernoulli", 
     by looking at air speeds and then calculating the air pressure on 
     every part of the wing surface.  See the NASA site.

3. To produce lift, the shape of the wing is critical.  YES AND NO.

     Incorrect because aerodynamic scientists have found that there are
     two critical features of all airfoils:  the trailing edge of the wing
     must be fairly sharp, and the trailing edge of the wing must be 
     angled downwards.  This is discussed in advanced textbooks in the
     chapters on circulatory flow, in the section on "Kutta Condition."

     Static wings are allowed to have all sorts of crazy airfoil shapes, 
     but if they don't have a downwards-tilted trailing edge which is 
     sharp, they won't lift an airplane.

     Other features of wing-shape are important but not critical.  For
     example, in order to prevent stall, the leading edge of the wing
     must be fairly bulbous and the wing's upper surface must lack
     sharp curves as well as being fairly smooth (no bumpy screws or
     rivets allowed.)  If the wing's leading edge is too sharp, or if
     its upper surface is made wrong, then the flow of air above the wing 
     will break loose or "detach," and it will no longer be guided 
     downwards by the upper surface.  This problem is called a "stall," 
     and during a stall the amount of lifting force contributed by the 
     upper wing surface becomes very small.

4. The Bernoulli effect pertains to the shape of the wing, while 
   Newton's laws pertain to the angle of attack.  INCORRECT.

     Incorrect because Newton's laws pertain to all features of the wing; 
     both to wing shape and attack angle.   Exactly the same thing is true 
     of Bernoulli's equation: angle of attack is critical, but wing shape
     has effects too.  Wings don't violate Newton's laws, and wings in 
     conventional flight (slower than the speed of sound) don't violate 
     Bernoulli's equation.  See #2 above.

5. Air which is divided by the leading edge must recombine at the 
   trailing edge.  INCORRECT.

    Incorrect, since wind tunnel experiments and aerodynamic math will both
    show that the upper and lower air flows do not recombine.  See these 
    wind-tunnel photos which illustrate this lack of recombining.  Also 
    see the NASA Site which debunks this widespread fallacy.

6. In order to generate lift, the upper surface of an airfoil must be more
  strongly curved than the lower surface?  INCORRECT

   Incorrect, since lift can be generated by symmetrical airfoil such as 
   those used on acrobatic aircraft.  Lift can also be generated by
   thin fabric airfoils, by sheets of paper (paper airplanes), by tilted
   pieces of flat plywood, or by "supercritical" airfoils which are more
   curved on the BOTTOM than the top.

9. The upper surface of a wing will deflect air, but the lower surface is 
   horizontal, so it has little effect. INCORRECT.

     Incorrect, but for an interesting reason.

     If a thin flat wing deflects air downwards, diagrams show that the 
     air above the wing and the air below the wing are equally deflected.
     Both the upper and lower surfaces create the lifting force.

     If we then make this wing thicker and streamlined, the total amount 
     of deflected air and the lifting force remain the same...  but the 
     air below the wing APPEARS less deflected, and the air above the wing 
     appears more deflected.  Also, the pressure below the wing APPEARS
     to provide less lift.  This happens because a thick wing must push 
     air out of its way, and as the flowing air splits up and down to make
     a space for the oncoming wing, air below the wing takes a straighter 
     path.  It takes a straighter path because the thickness of the wing
     bends air upwards at the same time as the tilt of the wing bends air
     downwards.  This has no effect on the lifting force, since the air 
     above the wing takes a more curved path, so THE PRESSURE DIFFERENCE
     REMAINS THE SAME AS IT WAS FOR A THIN WING.  The thick wing is 
     making us confused.  The thick wing SEEMS to get more lift from the 
     curved streamlines above the wing than from the straight streamlines 
     below, but this is an illusion.  The thick wing distorts the stream-
     lines.  Examine the streamlines surrounding a thin wing to see the 
     truth.  The lift comes from the DIFFERENCE between the two flows, and 
     changing the thickness of the wing will alter the appearance of the 
     air flows without changing the difference or changing the lifting 

3. Flat thin wings generate lift entirely because of Newton; because they
   are tilted, while thick curved wings generate lift exclusively because 
   of "Bernoulli Effect?"  INCORRECT.

Think a moment: if a wing
  when a flat thin wing is given a positive angle of attack,
    the air above the wing speeds up, and the air below the wing slows
    down.  100 percent of the lifting force can be explained using 
    either the "Bernoulli effect" or the Newton/Coanda principles.
    These two simply are a pair of alternate viewpoints on the same
    situation, and it's wrong to try to break the lifting force 
    into a separate percentage of "Bernoulli" force and an "attack angle" 

- Asymmetrical airfoils produce lift because of their special shape, while 
  symmetrical airfoils produce lift because they are tilted?  INCORRECT.

- A symmetrical airfoil cannot create lift? INCORRECT

- Aircraft cannot fly upside down?  INCORRECT

- The decreased pressure above an airfoil creates much more lifting force
  than the increased pressure below the airfoil.  Since the decreased
  pressure above is supposedly caused by the Bernoulli effect, while the
  increased pressure below is supposedly caused by collision of air with
  the tilted wing, the "Bernoulli effect" supplies the lift.  Therefore 
  the "angle of attack" effects are of less importance and can be ignored 
  in order to simplify the explanation?  INCORRECT.

    Incorrect, because both the increased pressure below the airfoil and
    the decreased pressure above are created entirely by the Bernoulli
    effect.  ALSO, both are caused by the angle of attack and the forces
    resulting from the deflection of massive air.  100% of the lifting
    force can be explained by appeals to the Bernoulli effect.  But also
    100% of the lifting force can be explain by the process of deflection
    of air by the wing.  However, explaining the difference in air speed
    above and below the wing is not straightforward.

- The low pressure above an airfoil produces suction.  The lifting force
  is an upwards suction force. INCORRECT.

    Incorrect.  Air molecules produce pressure upon a surface by colliding
    with that surface.  They do not attract that surface.  In other words,
    SUCTION DOES NOT EXIST.  When you suck air through a straw,
    you are lowering the pressure within the straw.  There is no suction.
    Instead, the outside atmosphere PUSHES the air into the straw.
    So, while it is true that the pressure above the wing is low, it is
    not true that the lifting force is caused by suction.  Instead, the
    lifting force is caused by the pressure-difference.  If the pressure
    above the wing should fall, then the ambient pressure below the wing
    will force the airplane to move upwards.

- The air in front of the leading edge of an airfoil and the air behind
  the trailing edge are moving at zero degrees deflection?  INCORRECT.

    Incorrect, since with a real aircraft, the air moves slightly upwards
    to meet the leading edge of the wing, but then it is projected greatly
    downwards from the trailing edge, creating a "downwash" flow.
    Although the "upwash" equals the "downwash" in a 2-dimensional wind 
    tunnel experiment, this is not true in practice with real airplanes. 
    (2D wind tunnels depict ground-effect flight, not normal flight.)
    With a real airplane flying high above the earth, if the "upwash" and
    the "downwash" flows were equal, yet the lifting force was non-
    zero, then this would totally violate the law of conservation of
    momentum.  Unfortunately for the "airfoil-shape" camp, fundamental
    physics principles must be satisfied, and Newton's laws are not
    selectively violated by airfoils. In order to create an upwards
    lifting force, there must be a net downward acceleration of parcels of
    air.  Planes fly by pushing air downwards, which creates a pressure
    difference across a wing.  Air-deflection and pressure are linked.  
    You cannot have one without the other.

- Airplane propellors, rudders, jet turbine blades, and helicopters all 
  function by deflecting air to create force.  They throw the air one way,
  and the air pushes them the other way.  But airplane wings are 
  different? Wings operate by a separate kind of physics, and are "sucked 
  upwards" by the Bernoulli effect?  INCORRECT.

    Incorrect, because the real world cannot tell the difference between 
    an airplane wing and a helicopter blade.  It does not know that a
    ship's rudder and an airplane wing are different.  Wings, rudders, 
    propellors, oars;  all these devices work by identical principles: 
    they throw massive fluid one way, and are thrown the other way by 
    action/reaction forces.  Bernoulli's equation does have bearing, since 
    the action/reaction forces express themselves as a pressure difference 
    across the surfaces of the object which deflects the fluid.

- An airfoil can generate lift without deflecting air downward? INCORRECT.

    Incorrect. If it did so, it would be staying in the air without
    ejecting mass downwards, and this would violate the Conservation
    of Momentum law.  Yes, balloons remain aloft without ejecting mass,
    but balloons function via bouyancy forces, and an airplane wing
    obviously does not.  Think about it: a helicopter hovers because it
    throws air downwards.  Yet a 'copter blade is simply a moving wing!
    If wings did not fling air downwards, if wings remained aloft only
    through pressure differences, then helicopter blades would do the
    same, and there would be no downblast below a helicopter.

- An airfoil can generate a lifting force without causing a reaction 
  force against the air?  INCORRECT.

    Incorrect.  If it did so, it would violate Newton's Third Law of
    Motion, the law of equal action and reaction forces.

- The majority of textbooks use the popular 'path length' or 'airfoil
  shape' explanation of lift, and it is inconceivable that this many books
  could be wrong.  Therefore, the "path length" explanation is the 
  correct one?  INCORRECT.

    Incorrect, this argument from authority is simply wrong.  It is also
    dangerous, since it convinces us to never question authority and to 
    close our eyes to authors' errors.  If we trust the concensus 
    agreements of others, then we become sheep which follow a leaderless 
    herd.  Beware of this habit!  As the NASA space shuttle managers who 
    closed their eyes to the Challanger booster seal problem found out, 
    the real world is all too real.  Nature ignores politics, and 
    scientific facts are determined by evidence, not by majority votes.

- The 'Coanda effect' only involves narrow jets of air, and has little to
  do with airfoil operation, so its exclusion from explanations of lift is
  understandable and justified?  INCORRECT.

    Incorrect, the Coanda effect involves the adhesion of a flow to a
    surface.  It applies to ANY flowing fluid, not just to narrow jets. 
    If the airflow across a wing did not adhere to the wing, the wing
    would be permanently in the 'stall' regiem of operation.  During
    "stall", it would not deflect air across its upper surface, and it
    would produce a greatly diminished lifting force.

- There are two explanations of airfoil lifting force: angle of attack, and
  pressure differential.  The 'pressure differential' explanation is correct,
  and the 'angle of attack' is misleading and can be ignored?  INCORRECT.

    Incorrect.  Both explanations are useful once the incorrect parts of
    the "path length" explanation have been removed.  They are two
    different "mental models," they are two different ways of looking at
    one complicated situation.  Paraphrasing the physicist R. Feynman:
    "Unless you have several different ways of looking at something, you
    don't really understand it."  A complete understanding requires that
    we easily shift between alternate viewpoints.  Wings really do
    produce lift when velocity differences create a vertically-
    directed pressure differential across their surface area.  But also,
    they really do produce lift by reacting against air and driving it
    downwards.  Unfortunately the airfoil-shape-based explanation has 
    become connected with several incorrect add-on explanations; the
    "path-length" fallacy for example.

- An airfoil can generate lift at zero angle of attack?  MISLEADING

    Not entirely wrong: depending on how we define 'angle of 
    attack', a wing may be at zero angle of attack even though it 
    obviously *acts* tilted and deflects the oncoming air downwards.
    This is a fight between semantics and reality.  If the rear portion of
    a wing is tilted downwards and deflects the air downwards, shouldn't
    it by definition have a positive angle of attack?
    No, not if 'angle of attack' is measured by drawing a line between the
    tips of the leading and trailing edges of the wing crossection.  If
    the leading edge is bulbous, then small details on the leading edge
    can radically change the location of the drawn line without radically
    changing the interaction of the wing with the air.  If such a wing is
    then rotated to force it to take a "zero" angle, that rotation in
    reality tilts the wing to a positive attack angle and generates lift.

- Cambered airfoils produce lift at zero AOA, which proves that the
  "Newton" explanation is wrong?  INCORRECT

    Incorrect.  Air has mass, and this means that it has inertia.  Because
    of inertia, an exhaust port can produce a narrow jet of air, yet an
    intake port cannot pull a narrow jet inwards from a distance.  This
    concept applies to wings.  When a cambered airfoil moves forwards at
    zero AOA (Angle of Attack,) air moves up towards the leading edge, and
    air also flows downwards off of the trailing edge.  The air which
    flows downwards behind the wing keeps moving downwards, and so the
    rear half of the wing controls the angle of the downwash, while the
    leading edge has little effect.  (In aerodynamics, this is called the 
    "Kutta Condition.")  In a cambered wing at zero AOA, the rear half of 
    the wing behaves as an airfoil with positive AOA.  On the whole, the 
    cambered airfoil BEHAVES as if it has a positive AOA, even though the 
    geometrical angle of attack is zero.

- A properly shaped airfoil gives increased lift because the air on the 
  upper surface moves faster than the air on the lower?  MISLEADING

    Not entirely wrong.  This is only half the story.  A properly
    shaped airfoil gives increased lift because the airflow does not
    easily "detach" from the upper surface, so the upper airflow can 
    generate lift even at large angles of attack and at low aircraft 
    speeds.  A sheet of plywood makes a poor wing because the airflow will 
    "detach" from the upper surface of the wood when the sheet is tilted 
    more than a tiny bit. This is called "stall", and it causes the upper 
    surface of the wing to stop contributing a lifting force.  A properly 
    designed wing must spread the net deflection of air widely across its 
    upper leading surface rather than concentrating all the deflection at 
    its leading edge.  Hence, the upper surfaces of most wings are 
    designed with the curvature which avoids immediate flow-detachment and 
    stall.  The shape of wings does not create lift, instead it only
    avoids stall.

- The "Newton" explanation is wrong because downwash occurs BEHIND the 
  wing, where it can have no effects?  Downwash can't generate a lifting
  force?   INCORRECT.

    Wrong, and silly as well!  The above statement caught fire on the
    sci.physics newsgroup.  Think for a moment: the exhaust from a rocket
    or a jet engine occurs BEHIND the engine.  Does this mean that
    action/reaction does not apply to jets and rockets?  Of course not.
    It's true that the exhaust stream doesn't directly push on the inner
    surface of a rocket engine.  The lifting force in rockets is caused
    by acceleration of mass, and within the exhaust plume the mass
    is no longer accelerating.  In rocket engines, the lifting force 
    appears in the same place that the exhaust is given high velocity:
    where gases interact inside the engine.

    And with aircraft, the lifting force appears in the same place that
    the exhaust (the downwash) is given high downwards velocity.  If a 
    wing encounters some unmoving air, and the wing then throws the air 
    downwards, the velocity of the air has been changed, and the wing will 
    experience an upwards reaction force.  At the same time, a downwash- 
    flow is created.  To calculate the lifting force of a rocket engine, 
    we can look exclusively at the exhaust velocity and mass, but this 
    doesn't mean that the rocket exhaust creates lift.  It just means that
    the rocket exhaust is directly proportional to lift (since the exhaust
    velocity and the lifting force have a common origin.)  The same is 
    true with airplane wings and downwash.   To have lift at high 
    altitudes, we MUST have downwash, and if we double the downwash, we 
    double the lifting force.  But downwash doesn't cause lift, instead 
    the wing's interaction with the air both creates a lifting force and 
    gives the air a downwards velocity (by F=MA, don't you know!)

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