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Page 1: basic theory
(There also are two other explanations of lift: the circulation explanation,
and curvature of streamlines explanation. These appear in advanced textbooks,
and they form the basis of the mathematics used by aircraft designers. The
"popular" or "airfoil-shape" explanation commonly appears in children's science
books, magazine articles, and in pilot's textbooks. Explanations based upon
circulation, on curvature of streamlines, or on Newton's Laws appear there only
rarely.) Explanations which are based on Newton's vs. Bernoulli's principles really
aren't as incompatible as many people seem to believe. For the most part they
are simply 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 therefor wrong. Which way to crack an egg?
It's a war between the Big-endians and Little-endians from GULLIVER'S
TRAVELS. However, there are also several serious mistakes usually associated with the
popular explanation described above. People who believe the "popular"
explanation wrongly insist that any divided parcels of air must meet again at
the trailing edge. They wrongly believe that wings don't deflect air downwards.
These and several other mistakes commonly appear in elementary science texts and
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 believe in 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 "Bernoulli" 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.
Pro-Newton Articles & Misc.Controversy
Discussions, message threads
Other websites
Pro-Newton 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 HOW AIRPLANES FLY
THE TWO COMPETING EXPLANATIONS FOUND IN K-6 BOOKS:Here is the typical "Airfoil shape" or "Bernoilli" 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. Therefor, 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: 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 faster than those below, and the lower parcels lag far behind. This even applies to thin flat wings such as a "flying barn door." After the air has passed the wing, the upper and lower parcels of air remain permanently divided. 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 "pro-Bernoulli" 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 "pro-Bernoulli" or "wing-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 "airfoil-shape" viewpoint 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 "pro-Bernoulli" 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 "pro-Bernoulli" 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 "pro-Bernoulli" 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 "Bernoulli/wingshape" explanation of lift. Forces on sailboat sails are explained using the typical "Bernoulli/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 "pro-Bernoulli" 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 bouyancy 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 "pro-Bernoulli" 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: 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, inertial effects will cause a thin, curved airfoil to deflect air downwards from its trailing edge more than it deflects air upwards at its leading edge, and the unequal deflection generates lift even at zero angle of attack. This type of wing may APPEAR to have zero attack angle, but 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 of zero. 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 I said before, 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 difference in speed between the upper and lower air streams. If a flat sheet of plywood is tilted into the air stream, the air flows faster above the sheet than below, 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 the Bernoulli principle. And 100% of lift can be explained by 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 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, therefor 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 "Bernoulli/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 "pro-Bernoulli" explanation is 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- 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. - The air which flows over the top of the curved airfoil must move faster because it has been divided from the air moving below, the two halves of air must recombine at the trailing edge, and the path taken by the upper part of the air is longer? INCORRECT. Incorrect, since in 3-dimensional airflows it is not necessary for the upper and lower air flows to recombine. In real-world situations they actually do not recombine. See these wind-tunnel photos which illustrate this lack of recombining. - 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. Therefor 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. - Flat thin wings generate lift entirely because of their angle of attack, while thick wings with asymmetrical cross section generate lift exclusively because of "Bernoulli Effect?" INCORRECT. Incorrect: 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" force. - The air in front of the leading edge of an airfoil and the air behind the trailing edge is 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. 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. 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 wings are different? Wings 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. All these devices work by identical principles: they throw mass 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 blade. - 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 'pro-Bernoulli' or 'airfoil shape' explanation of lift, and it is inconceivable that this many books could be wrong. Therefore, the "pro-Bernoulli" explanation is the correct one? INCORRECT. Incorrect, this argument from authority is simply wrong. It is also dangerous, since it convinces us to close our eyes to error. If we trust the concensus agreements of others, then we become sheep which follow a leaderless herd. Beware of this habit, for as the NASA managers who closed their eyes to the Challanger booster seal problem found out, the real world is all too real. Scientific facts are not determined by voting! - 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 "pro-Bernoulli" 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 Bernoulli-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 "Bernoull" 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. (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 physical 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 it 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 deflection of air across its upper 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 "Newton" explanation is wrong because downwash occurs BEHIND the wing, where it can have no effects. Downwash cannot generate a lifting force. INCORRECT. Wrong, and silly as well! The above statement caught fire on sci.physics newsgroup. Think for a moment: the exhaust from a rocketa 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 downwash doesn't cause lift in rocket engines. The lifting force is caused by acceleration of mass, and within the downwash, the mass is no longer accelerating. If a wing encounters some unmoving air, and the wing then throws the air downwards, the velocity of the air will be 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. The same is true with airplane wings and downwash. If you are using Lynx, type "c" to email.
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(There also are two other explanations of lift: the circulation explanation,
and curvature of streamlines explanation. These appear in advanced textbooks,
and they form the basis of the mathematics used by aircraft designers. The
"popular" or "airfoil-shape" explanation commonly appears in children's science
books, magazine articles, and in pilot's textbooks. Explanations based upon
circulation, on curvature of streamlines, or on Newton's Laws appear there only
rarely.)
Explanations which are based on Newton's vs. Bernoulli's principles really
aren't as incompatible as many people seem to believe. For the most part they
are simply 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 therefor wrong. Which way to crack an egg?
It's a war between the Big-endians and Little-endians from GULLIVER'S
TRAVELS.
However, there are also several serious mistakes usually associated with the
popular explanation described above. People who believe the "popular"
explanation wrongly insist that any divided parcels of air must meet again at
the trailing edge. They wrongly believe that wings don't deflect air downwards.
These and several other mistakes commonly appear in elementary science texts and
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 believe in 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 "Bernoulli" 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.
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
HOW AIRPLANES FLY
Here is the typical "Airfoil shape" or "Bernoilli" 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. Therefor, 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:
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 faster than those below, and the lower parcels lag
far behind. This even applies to thin flat wings such as a "flying
barn door." After the air has passed the wing, the upper and
lower parcels of air remain permanently divided. 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 "pro-Bernoulli" 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 "pro-Bernoulli" or "wing-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 "airfoil-shape" viewpoint 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
"pro-Bernoulli" 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
"pro-Bernoulli" 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 "pro-Bernoulli" 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 "Bernoulli/wingshape" explanation of
lift.
Forces on sailboat sails are explained using the typical
"Bernoulli/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 "pro-Bernoulli" 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 bouyancy 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 "pro-Bernoulli" 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:
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, inertial effects will cause a thin, curved airfoil to deflect air downwards from its trailing edge more than it deflects air upwards at its leading edge, and the unequal deflection generates lift even at zero angle of attack. This type of wing may APPEAR to have zero attack angle, but 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 of zero. 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 I said before, 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 difference in speed between the upper and lower air streams. If a flat sheet of plywood is tilted into the air stream, the air flows faster above the sheet than below, 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 the Bernoulli principle. And 100% of lift can be explained by 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 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, therefor 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 "Bernoulli/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 "pro-Bernoulli" explanation is 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.
- 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.
- The air which flows over the top of the curved airfoil must move faster
because it has been divided from the air moving below, the two halves of
air must recombine at the trailing edge, and the path taken by the upper
part of the air is longer? INCORRECT.
Incorrect, since in 3-dimensional airflows it is not necessary for the
upper and lower air flows to recombine. In real-world situations they
actually do not recombine. See these wind-tunnel photos which illustrate
this lack of recombining.
- 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. Therefor 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.
- Flat thin wings generate lift entirely because of their angle of attack,
while thick wings with asymmetrical cross section generate lift
exclusively because of "Bernoulli Effect?" INCORRECT.
Incorrect: 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" force.
- The air in front of the leading edge of an airfoil and the air behind
the trailing edge is 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.
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. 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 wings are different? Wings
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. All these devices
work by identical principles: they throw mass 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 blade.
- 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 'pro-Bernoulli' or 'airfoil
shape' explanation of lift, and it is inconceivable that this many books
could be wrong. Therefore, the "pro-Bernoulli" explanation is the
correct one? INCORRECT.
Incorrect, this argument from authority is simply wrong. It is also
dangerous, since it convinces us to close our eyes to error. If we
trust the concensus agreements of others, then we become sheep which
follow a leaderless herd. Beware of this habit, for as the NASA
managers who closed their eyes to the Challanger booster seal problem
found out, the real world is all too real. Scientific facts are not
determined by voting!
- 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 "pro-Bernoulli" 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 Bernoulli-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
"Bernoull" 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. (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 physical 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 it 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 deflection of air across its upper 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 "Newton" explanation is wrong because downwash occurs BEHIND the wing,
where it can have no effects. Downwash cannot generate a lifting force.
INCORRECT.
Wrong, and silly as well! The above statement caught fire on
sci.physics newsgroup. Think for a moment: the exhaust from a rocketa
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 downwash doesn't cause lift in rocket engines.
The lifting force is caused by acceleration of mass, and within the
downwash, the mass is no longer accelerating. If a wing encounters
some unmoving air, and the wing then throws the air downwards, the
velocity of the air will be 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. The same is true with
airplane wings and downwash.