Airfoil Lifting Force Misconception
William Beaty 1996
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Beat around in the underbrush of aerodynamics and you'll encounter an
HOW DO AIRPLANE WINGS *REALLY* WORK?!
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:
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.
A possible solution to the controversy:
Billb's balloon analogy to aircraft: vortex sheddingNote 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.
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
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.
FREQUENTLY ASKED QUESTIONS1. 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.
2. How could so many scientists, engineers, and authors be so wrong?
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 & Controversy
The "Airfoil Mistake" in the news
Discussions, message threads
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
HOW AIRPLANES FLY
THE TWO COMPETING EXPLANATIONS FOUND IN K-6 BOOKS: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.
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":