Airfoil Lifting Force Misconception
William Beaty 1996
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Beat around in the underbrush of aerodynamics and you'll encounter an
interesting question:
HOW DO AIRPLANE WINGS *REALLY* WORK?Amazingly enough, this question is still argued in many places, from elementary school 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 has erupted into the news, see news links below. The two sides of the controversy are:
Also three other explanations of lift exist: the circulation
explanation, the flow-turning or streamline-curvature explanation, and the
vortex-based 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 or never encounters explanations
based upon circulation, upon curvature of streamlines, or upon Newton's
Laws.
A possible solution to the controversy:
Billb's Airplane Flight AnalogyNote 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. 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 heretic infidel who must be attacked and silenced.
http://amasci.com/wing/rotbal.html
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; experiments easily show that the air above a wing far outraces
the air below, and parcels never meet again. The same people also believe
that wings fly only because of pressure, and that wings don't deflect the
oncoming air downwards. Also incorrect.
These and several
other mistakes commonly appear in elementary science texts, as well as in
popular articles on 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" 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.
Answer: 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 this.The current 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, 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, and this controversy is really just Bill Beaty's little pet theory.
2. How could so many scientists, engineers, and authors be so wrong?
To be added...3. Why are you prejudiced against the Bernoulli-based theory? Bernoulli's equation is perfectly correct.
- Well, the math is correct, so wing designs work regardless of the designers' belief system. Incorrect beliefs have little impact as long as engineers don't use the beliefs to alter the math.
- Errors can infect grade-school textbooks and spread widely to many books. Aero experts were once 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 insist that infinite wings are normal and acceptable, while finite 3D wings are a flawed special case.)
- Henri Coanda's experimental work on boundary-layer attachment has been marginalized rather than merged with the rest of aerodynamics or included in college textbooks. Air is nonlinear, with no simple math solutions that explain turbulence or flow-attachment. As a result, a big piece of aerodynamics concepts is missing. Heisenberg supposedly was hoping to ask god how turbulence works after he dies. He could have instead asked an equivalent unsolved question: how do wings really work?
- Cambered wings at high R have a positive effective attack angle even when the geometrical attack angle is zero. This confuses everyone, even the experts. They see only the zero geometrical angle and believe that the cambered wing is not tilted. They don't realize that the down-tilted trailing edge of a cambered wing has far more effect upon the air flow than the rest of the whole 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 can have a large AOA and a zero AOA, both at the same time.
- A two-dimensional diagram (also called the 'infinite wing diagram,') is misleading. It only depicts ground-effect flight where altitudes are much less than one wingspan. Any explanation based on this type of diagram does not apply to flight at normal altitudes. These Two-dimensional diagrams are not just simplified, they're genuinely wrong, since typically they neglect to show the floor and ceiling of the wind tunnel which receive the weight of the wing as instantaneous reaction forces. 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 a type of venturi situation, while genuine aircraft fly far from the ground and have no instantaneous weight applied to the Earth's surface. To explain lift in high-flying aircraft, a 3D diagram with its vortex downwash wake is absolutely required. Real wings are 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.
- The presence of multiple possible explanations can trigger religious wars, "Swiftian Battles" between adherents to one side and the other, and sometimes one side wins, stomping out the other explanation... even though both explanations are valid, and even though both explanations are essential. We cannot really understand wings unless we know several different ways to explain them. A toolkit needs hammers AND screwdrivers... and anyone who searches for a "One True Tool," while emptying the rest of their mental toolbox, is going to severly limit their own expertise.
Huh? Read my stuff again. Please tell me WHERE I attack Bernoulli. I 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.
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 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 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
subjected to a huge downblast of air. They are essentially feeling
a portion of the pressure which supports the plane.
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 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. 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 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
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