Talk:Lift (force)/Archive 4

Talk page archive
Archive 3 has been created with a link at above right. It is an exact copy of the talk page as it was before this edit (besides the last two sections which I left here). Archive 4, when needed in the future, should be a new subpage (same as creating an article) titled "Talk:Lift (force)/Archive 4" and the link added to the template on this page's code. For further information on archiving see How to archive a talk page. See also User:5Q5 for the used archiving procedure. Thank you. -- Crowsnest (talk) 16:49, 10 April 2009 (UTC)

Is an airfoil a "body"?
The first paragraph says

"An airfoil is a streamlined body that is capable of generating significantly more lift than drag."

Actually, I like the idea and I never really thought of it that way. Good point.

My beef is with calling an airfoil a "body".

An airfoil is a streamwise (more or less) section of a body, a 3D body. Right? Okay, Okay, we all know that an airfoil is a "2D" body and that's that. It has a "2D" flow around it that exerts "2D" forces on it. No problem for us to read that sentence because we automatically translate. We can call it a "body" and none of us flinches. We can call it a "2D body" and know exactly what is meant by that.

I'd like to say "An airfoil is a two-dimensional streamlined body...". That's fine for us, but it opens up a can of worms to explain all the "2D-ness" to the uninitiated.

The other problem is that wing is also a "streamlined body that is capable of generating significantly more lift than drag". So is a turbine blade, a fin, a helicopter rotor, etc. An airplane (especially a glider) is capable of generating significantly more lift than drag too. :-)

Would the Space Shuttle, with an l/d of ~4(?), qualify as an airfoil? :-)

Any ideas on how to fix? Ignore?

--Gummer85 (talk) 23:22, 5 April 2009 (UTC)


 * Good question. It really depends on what the in-line citations say.  In Wikipedia, Airfoil defines an airfoil in terms of the 2D cross-sectional shape; however, this definition and the whole introduction are not supported by any in-line citation.  (There is an opportunity there for someone to improve the article by providing some in-line citations to show verifiability.)  NACA airfoil also uses the word to mean a 2D cross-sectional shape.  Until a contrary meaning is provided in Wikipedia, useage of the word airfoil should be restricted to 2D situations.  Dolphin51 (talk) 00:04, 6 April 2009 (UTC)


 * According to, p. 113:
 * "Throughout this book the term airfoil, often applied to any kind of wing, will be used exclusively to designate the prismatic wing of rectangular plan form."
 * And on p. 112:
 * "...one of the dimensions of the wing, the thickness t is much smaller than the others."
 * According to Encyclopedia Brittanica an airfoil is a
 * "shaped surface, such as an airplane wing, tail, or propeller blade, that produces lift and drag when moved through the air."
 * And NASA says an airfoil is
 * "A streamlined surface designed in such a way that air flowing around it produces useful motion. The cross section of an airplane wing is an airfoil."
 * So it can either be the wing or a cross-section of it. Both options should be included in the WP definition (at least in the airfoil article). As such, calling it a streamlined body is correct: wings and prismatic wings of rectangular plan form are special kinds of bodies. For instance, in a wind tunnel test, when testing an airfoil shape one tests a cylindrical body with the desired airfoil-shape cross section. -- Crowsnest (talk) 22:23, 9 April 2009 (UTC)

Hmmm... Interesting... Surprising... Well referenced...  Good references...  Hmmm... Um... I don't buy it. :-)

Gosh, "airfoil" has always been a cross section in my world. Maybe Von Mises was trying to be expansive in his meaning for his audience. Or maybe Von Mises had the same problem we do (haphazard usage already in situ and difficult to fix) so he fixed it by saying "for the purposes of this book it can mean either". I would suggest that those words, well, "literally", mean for the purposes of that book. The NASA definition is a little wacky I think. "Useful motion"? Huh? I checked up the link's pathname a bit and saw it was "The Beginner's Guide to Aeronautics" targeted at grades K-12. I don't think it could be held up as an official NASA definition. I also looked in the other Dover paperback (Abbot & Von Doenhoff, "Theory of Wing Sections") and in the index, under "airfoil", it says "see Wing sections". I laughed when I saw that! :-)

There is value standing on a good foundation of reference material, but there is nothing without knowledgeable experts (presumably us) who know the real usage. If we really know that in current usage, when practitioners chose words carefully, that they will always use "airfoil" as a 2D section, then we should stand up and assert that meaning, a 50-year old paperback notwithstanding.

I could be out of touch on the question. I've always made the distinction. In my hard core aero days I don't remember more expansive usages by professional practitioners, but my memory could be bad. Does anybody know any modern practitioner that uses Von Mises's expansive meaning? Is it actually used in that loosey-goosey way among experts these days?

I never thought it was incorrect to say an airfoil a was "streamlined body". It is correct. It's a two dimensional streamlined body. I worried that either "2D" needed to be specified, or that if it was specified as 2D, it wouldn't be "high colloquial", but jargon. That is, saying "2D" would be more correct, but it would require explaining the implications of "2D-ness" which could be an off-topic "can-of-worms".

Yes, perhaps mentioning both usages in the airfoil article could be good. Though I think the section aspect should be emphasized.

--Gummer85 (talk) 07:03, 10 April 2009 (UTC)


 * I fully agree. If both wing and wing cross section are used, both should be mentioned in WP, with the emphasis on the wing section (as pointed out by you being the more common phrase). But that is primarily a point for the Airfoil article.
 * Just my opinion: Further it is important to realise two-dimensionality is primarily a mathematical artefact (or concept if you like). An airfoil, as a real thing, always has to be a 3D body. Which can of course be either a wing, or more specific (and common) the "prismatic wing of rectangular plan form". Also the part "foil" in airfoil points towards three-dimensionality. -- Crowsnest (talk) 08:11, 10 April 2009 (UTC)


 * My understanding of the usage of airfoil is the same as that of Crowsnest. It's used sometimes to refer to a real object, and at other times to refer to a section of that real object--a conceptual entity--as he proves in the above refs.  I also agree (without references, though, just my conception) that "foil" entymologically refers to the shape of the real object described, and only to the math abstraction by extension.  Unlike Gummer, until now I have thought of it as referring to the real object.


 * If so, it sounds as though the derivative form has displaced the original in at least Gummer's mind--perhaps in the professional community as a whole. Early in the history of aerodynamics, there was of course an inevitable preoccupation with the 2D models of flight, and even today pedagogues introduce the subject to students via 2D sections.


 * So, I agree with C-nest that Wikipedia should support both common usages. Furthermore, I see no problem with using it exclusively in the first sense (a real object) in the intro to the article--better not to add a tangent on word usage here, as it adds little to reader's understanding.


 * Mark.camp (talk) 14:41, 10 April 2009 (UTC)

'''Misusage .NE. Usage'''

I'm starting to think this discussion belongs in the airfoil article, but I don't know how to move it over there.

I've been thinking about this the last few days, and at this point I've got to be firmly on "the side" of 2D section only for what a "airfoil" is. I just never hear it used in any other way except by mistake. (Although mistakes do abound.)

Von Mises may be the exception, but even he suggested it was 3D only as a prism, possibly implying that usage as "a wing" is misuse. It is necessary of course, to make a 2D section "3D" to test it in a wind tunnel. But then, it must span the tunnel. The test articles might naturally be referred to as "airfoil A", or "airfoil B", etc. because the only thing that differs between them is their cross section. Or if the test articles are prisms finite in span (don't span the tunnel), and nothing changes between them but the cross section, then naturally again, the test articles could be called "airfoils". But, as soon as more than the cross section changes (like planform, twist, etc.) they couldn't be called different "airfoils" (now they're different "wings"). That's my sense of how Von Mises might have allowed for an "airfoil" to be "3D" in some uses.

OR maybe it's one of those "British usage" things. They're always makin' up strange and different words for things, right? :-) It could very well be something like that.  And, that's something I know little about.  Is "airfoil" used that "3d way" by other knowledgeable groups?  It could also be a "time thing" perhaps.  Did a 2D-only use become prevalent over time and dominant sometime before 1970?  Could be, but I have no knowledge there either.

I don't think I'm being a pedagogue here. But, I do think that "misusage" doesn't count as "usage". We should be careful not to roll over so easily just because someone not-fully-knowledgeable misuses the word. Heck, by that policy, we would feel compelled to equate angle of attack with pitch angle. The lay-press gets that one wrong all the time, but it doesn't count as valid usage.

If all it takes is inline citations over on airfoil saying "2D", then I'll find 'em. I'll find bunches of 'em. And, I'll put 'em in there! :-)

--Gummer85 (talk) 06:26, 13 April 2009 (UTC)


 * This definition is given by "The American Heritage® Dictionary of the English Language, Fourth Edition copyright ©2000 by Houghton Mifflin Company. Updated in 2003. Published by Houghton Mifflin Company. All rights reserved.":


 * "A part or surface, such as a wing, propeller blade, or rudder, whose shape and orientation control stability, direction, lift, thrust, or propulsion.


 * Similarly, this definition of an airfoil as a real object is given in "The American Heritage® Science Dictionary Copyright © 2005 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved":




 * Do you consider these two citations sufficient to demonstrate that the 3D sense is common usage?


 * Mark.camp (talk) 13:33, 13 April 2009 (UTC)


 * I consider The American Heritage Science Dictionary is sufficient to support the notion that an airfoil can be a 3-D shape. For technical articles such as Lift (force) and Airfoil, where the topic has acquired its own nomenclature with specialist meanings, English language dictionaries are not ideal because the popular meaning of words is often significantly different to the technical meaning.  Dolphin51 (talk) 03:09, 14 April 2009 (UTC)

Upside-down flight?
After watching the video here, I started wondering, how exactly does a wing-shaped object create lift--even when the aeroplane it is attached to is flying upside-down? Apparently they don't stall, so it would be reasonable to conclude that lift is still being generated somehow... It all makes sense when you're flying the right way up, but when you reverse it, things get whacky. — Kortaggio   Proclamations   Declarations  01:32, 7 April 2009 (UTC)


 * Lift is generated when a wing is moving relative to the air, and there is a non-zero angle of attack between the wing and the vector representing motion between wing and air. Where the ground is at the time is irrelevant.  Dolphin51 (talk) 01:44, 7 April 2009 (UTC)


 * Oh, I guess that's what all the 2D stuff is all about... — Kortaggio   Proclamations   Declarations  01:49, 7 April 2009 (UTC)


 * Ah, that makes a lot of sense, thanks! Just a thought--should this be included in the article? 99.229.30.80 (talk) 01:48, 7 April 2009 (UTC)


 * The second paragraph already contains the following explanations:
 * While common meanings of the word "lift" suggest that lift opposes gravity, lift can be in any direction. When an aircraft is flying straight and level (cruise) all of the lift opposes gravity. However, when an aircraft is climbing, descending, or banking in a turn, for example, the lift is tilted with respect to the vertical and the lift is greater than, or less than, the weight of the aircraft. Lift may also be entirely downwards in some aerobatic manoeuvres, or on the wing on a racing car. In this last case, the term downforce is often used.  Dolphin51 (talk) 01:53, 7 April 2009 (UTC)

Pressure versus speed over cambered surface?
Near the leading edge of a wing, the upwash flow experiences a component of centripetal acceleration as it flows over the cambered surface. For the centripetal component of acceleration, there is no change in speed, but it seems that the amount of centripetal acceleration would still correspond to pressure differential, so it's a pressure differential unrelated to any change in speed, just direction. I'm wondering how significant this non-speed related component of pressure differential is in terms of contribution to lift. Jeffareid (talk) 17:39, 12 April 2009 (UTC)


 * You are correct. The centripetal acceleration is everywhere proportional to the centripetal pressure gradient.  This is required by the fluid dynamics form of Newton's second law and conservation of mass, for case of incompressible flow.


 * How significant to lift is this gradient, near a point on the upper surface near the leading edge?


 * Very!


 * In fact, this gradient is responsible for most of the lift of the wing, especially as one moves aft, and the direction of the force is more and more vertical.


 * To see this, suppose this component of the pressure gradient were zero, starting at that point on the upper surface near the leading edge where the surface is at a 45 degree angle to vertical, and staying at zero all the way to infinity as one moves straight way from the wing along the surface normal.


 * Then the static pressure on the upper surface of the wing at this point would be the same as at infinity = ambient pressure. Now recall that the negative relative pressure on the top of the wing is responsible for the majority of the lift.


 * So, if it were not for the component of pressure gradient normal to the flow in this region, there would be much less lift.


 * Mark.camp (talk) 20:07, 12 April 2009 (UTC)

Curvature of the airflow about the wing, is entirely responsible for generating the net lift on the wing section.

There is no net downwash or upwash, and likewise there is no net curvature of the airflow. The descending bubble of air caused by the trailing vortices is inconsequential to the generation and explanation of lift.

There is however a slender column of air which acts on the wing at any given time. This column of air is contained between the four outermost radial lines of force which connect the two stagnation points and stretch in both upward and downward directions perpendicular to the local flow.

In this slender column of air thus defined, the flow curvature causes radial presure changes which manifest as postive and negative gage pressures on the wing which result in lift. The pocket of air which has the greatest effect on the total lift is located nearest the highest air speed and highest curvature leading edge region of the wing.

People get confused about Bernoullis Equation. The fact is there is another equation, not for streamlines, but for equipotential (zero flow) lines which produce the same exact equation as the Bernoullis Equation. Integrating the radial pressure gradient along the equipotential line from any point on the the wing to the free-stream flow in the far field (which has no residual curvature), gives the same pressure change over the wing as Bernoullis Equation. So the Equation itself is right, but it is the wrong explanation for lift. —Preceding unsigned comment added by 58.110.56.34 (talk) 17:22, 15 September 2009 (UTC)

Is this statement correct?
"One can just as well argue that the downwash behind the airfoil is an effect of the lift force:

It seems not. Downwash is down. Lift is up. So, how could lift cause downwash? It seems that downwash is, instead, caused by the downward force which is the "equal and opposite force" of lift required by Newton's law.

Mark.camp (talk) 01:09, 26 April 2009 (UTC)


 * Mark's point is valid. However, there is a further complication.


 * It is true that in the region behind the airfoil, between the two wingtip vortices, there is downwash. But outside each of the wingtip vortices, and also ahead of the airfoil, there is upwash.  (Migratory birds often fly in a V formation to take advantage of the upwash from the bird ahead.)  What should we say is the cause of this upwash?  Is it lift, or the "equal and opposite force" required by Newton's Third Law?


 * We can avoid this paradox by using the circulation theory of lift, and say both the upwash and the downwash are a consequence of the vortex system around the airfoil. The lift, and the "equal of opposite force" on the air, are related in magnitude to the strength of the vortex system.  This relationship is given by the Kutta-Joukowski theorem.  Dolphin51 (talk) 02:23, 27 April 2009 (UTC)


 * I'm not sure the sentence I quoted from the current article is correct. I don't know enough to suggest a correction, but if it isn't correct, someone should re-write or delete it.


 * Dolphin51, you bring up a good point about the dangers of speaking of differential volumes entering downwash, upwash, wingtip vortex, etc., in isolation, and trying to draw some conclusion about the overall causal relationship to the lift on the wing, or its complement (the downward force of the wing on the air). Lift is a net effect, and one must consider the history of a large body of air, over a long time interval, to explain it.


 * Perhaps text could be added to clarify the point.


 * But even if that isn't done, my concern about the above statement remains.


 * Mark.camp (talk) 12:21, 27 April 2009 (UTC)


 * The statement is based on the ref. from J.D. Anderson, at the end of the paragraph, p357:


 * "However, this explanation really involves the effect of lift, and not the cause. In reality the air pressure on the surface is pushing on the surface, hence creating lift in the upward direction. As a result of the equal-and-opposite principle, the airfoil, surface pushes on the air, imparting a downward force on the airflow, which deflects the air downwards. Hence, the net rate of change of downward momentum created in the airflow because of the presence of the wing can be thought of as an effect due to the surface pressure distribution; the pressure distribution by itself is the fundamental cause of lift."


 * Forces never come alone, but according to Newton's 3rd law always in pairs. So lift on the wing means downward force on the air. By Newton's 2nd law, this implies a downward momentum change to the air, giving downwash. If there is a paradox, it is created by thinking in terms of isolated forces without the reaction force, and thinking in terms of cause and effect. Newton's 3rd law talks about the simultaneous occurrence of action and reaction forces, and Newton's 2nd law is the simultaneous balance of force and momentum change rate. So the reaction force to lift force, on the air, accelerates the air, at the same moment in time and no cause-and-effect relation. The downwash is the integrated effect of this acceleration, and the downwash lags the acceleration and comes later in time.
 * Do you wonder why the downward exhaust gases from a rocket engine are accompanied by a forward force on the rocket?
 * Further this section in the article talks about the downwash behind the wing. Talking about wing-tip vortices, creating upwash, and birds seems off-topic to me, with respect to this subject: the relation between Newton's laws and lift. -- Crowsnest (talk) 14:52, 27 April 2009 (UTC)


 * On this page, we are all in violent agreement about Newton's Laws, and Anderson is right there with us, that old conservative.


 * But my comment was about the sentence as it was worded. I don't think it is expressing the thought that was intended, is it?


 * Mark.camp (talk) 17:19, 27 April 2009 (UTC)


 * I do not see the problem. It is not the whole sentence, there is a colon ":" and after that an explanation in the rest of the sentence and the next one. -- Crowsnest (talk) 22:06, 27 April 2009 (UTC)


 * OK. -- Mark.camp (talk) 01:08, 28 April 2009 (UTC)

(unindent) You have a problem with it, so other people may have a problem with it as well. Dolphin51 agrees with you. So, any suggestions for improvement? -- Crowsnest (talk) 08:01, 28 April 2009 (UTC)


 * Below, I try just removing the phrase whose wording was bothering me. The new paragraph retains the main idea.  But this lazy way out loses some of the logical force of the original.  The deleted phrase exposed the central fallacy of the explanation being refuted (arbitrarily picking deflection as the cause, and its complement as the effect, when Newton's Laws contain no such asymmetry.)


 * But I still cannot think of a concise way to re-word the phrase.


 * "One may be tempted to think that lift can be explained along this line of reasoning, saying that lift on the airfoil is caused by the downward deflection of the airflow. However, this is a misinterpretation of Newton's laws. According to Newton's third law the upward lift is accompanied by a downward force on the air. This latter force is pushing the air down, which results in a downward deflection of the velocity vectors behind the airfoil.[7]
 * "One may be tempted to think that lift can be explained along this line of reasoning, saying that lift on the airfoil is caused by the downward deflection of the airflow. However, this is a misinterpretation of Newton's laws. According to Newton's third law the upward lift is accompanied by a downward force on the air. This latter force is pushing the air down, which results in a downward deflection of the velocity vectors behind the airfoil.[7]


 * Mark.camp (talk) 11:43, 28 April 2009 (UTC)


 * I have looked closely at the sentence in question, and the sentences preceding it. The sentence in question is not making a statement of fact; it is contrasting two slightly incorrect statements.  These sentences could be It is misleading to say lift is caused by downwash.  One can just as well argue that downwash is caused by lift.


 * One of my criticisms of Understanding Flight by Anderson and Eberhardt is that this book states But the lowering of the pressure above the wing is the result of the production of the downwash. My response to that was "Anderson and Eberhardt attempt to explain the lift on a wing as a sequence of events, one causing a second, and the second causing a third. The acceleration of air around a wing, the lowering of air pressure, and the production of downwash all occur simultaneously. One does not cause the other."  See Talk:Bernoulli's principle/Archive 2.


 * So, on balance I see no problem with keeping the sentence in question. It is merely attempting to dismiss the suggestion that downwash causes lift by highlighting that we could say, just as inaccurately, that lift causes downwash. Dolphin51 (talk) 11:48, 28 April 2009 (UTC)


 * Why not simply state that downwash is coexistant with lift (no cause and effect, just coexistance)? The Newton 3rd law pair of forces is a downwards force exerted by the wing onto the air, coexistant with an upwards force exerted by the air onto wing. Newtons 2nd law could show a relationship between the net force between wing and air, and the air's reaction to this force via accelerations, except that due to the distribution of these forces, the actual result is the integral sum of all the affected components. On a side note, I have an issue with the term "circulation", because some readers could imply that there is no net downwash in the vicinity of a wing. The air will continue to have a downards component of velocity, until it reaches the surface of the earth and transfer momentum; it's how the air transfers the downforce from the wing onto the surface of the earth, coexistant with an upwards and opposing force from the surface of the earth. Jeffareid (talk) 12:14, 28 April 2009 (UTC)

Bernoulli's principle
I read awhile ago that it is not Bernoulli's principle that creats life but the fact that the wing is angled up to push the air down. Similar to the way a house fan works. The site is now at http://www.avweb.com/news/airman/183261-1.html I got it by searching Google for "lift doesn't suck". —Preceding unsigned comment added by 66.67.7.123 (talk) 12:03, 28 April 2009 (UTC)


 * I find the Darwin drift figure and animation, showing the downwash, very illustrative: and . -- Crowsnest (talk) 21:58, 28 April 2009 (UTC)


 * Regarding Bernoulli: see Lift (force). The Bernoulli equation is primarily an integration of Newton's second law of motion along a streamline, for inviscid flow. In many cases they are both applicable to calculate the lift on an airfoil.
 * Note that also at zero angle of attack — so not angled up — cambered airfoils produce lift. See the article, Lift (force). -- Crowsnest (talk) 22:14, 28 April 2009 (UTC)
 * That's because of the defintion of angle of attack, leading edge versus trailing edge. The average of the mean camber line angle, makes more sense and it is non-zero. Also cambered airfoils at zero "angle of attack" generate downwash. I prefer "effective angle of attack" were zero lift means zero effective angle of attack, which makes it easier to compare airfoils. Jeffareid (talk) 00:24, 29 April 2009 (UTC)


 * My main point is that also for cambered airfoils with a more-or-less straight lower surface, parallel to the flight direction, there is no pushing-down of air and still there is lift. -- Crowsnest (talk) 07:52, 29 April 2009 (UTC)


 * Also the title of that web page "lift doesn't suck" is a bit misleading, since a person might think it meant that low pressure doesn't occur above the wing. However, this is covered in the content of the web page, which seems pretty good at first glance Jeffareid (talk) 00:23, 29 April 2009 (UTC)


 * Two articles on this subject that are more authoritative and more objective than the Avweb article can be found at the following sites:


 * Bernoulli or Newton: Who’s Right About Lift? by David Ison


 * Bernoulli and Newton by NASA’s Glenn Research Center


 * Dolphin51 (talk) 04:12, 29 April 2009 (UTC)


 * Side comment about Crowsnest's entry:


 * "My main point is that also for cambered airfoils with a more-or-less straight lower surface, parallel to the flight direction, there is no pushing-down of air and still there is lift. -- Crowsnest (talk) 07:52, 29 April 2009 (UTC)


 * I think that
 * a. A mass of air, initially at rest, does acquire downward motion of its center of mass by such a flat bottomed cambered airfoil passing through it.
 * b. It is possible to show that this downward motion can be attributed to the net force exerted on that body by the airfoil over time.
 * If so, then we could say that, at least in some sense, the wing does push down on the air even in this case. True?


 * Mark.camp (talk) 10:59, 29 April 2009 (UTC)


 * Sure, I fully agree. There is downwash behind this cambered airfoil with its lower surface parallel to the onflow. In this case the lower surface of airfoil is not pushing the air down. It is primarily the low pressure at the upper surface that creates the lift in this case, and in most cases. So it pulls the air down (but pushing or pulling is subject to debate, in the end it is the pressure differences on a volume of air that determine the resulting net force on it; so the low pressure at the upper airfoil surface has to be considered in conjunction with the higher pressure further above). -- Crowsnest (talk) 11:16, 29 April 2009 (UTC)


 * We would all agree that, to speak precisely, the lower surface of any object pushes the air down (whether there is relative motion or not), and the upper surface of any object pushes the air up.  It is also convenient and perfectly fine to use the artificial convention of relative pressure, and speak of "suction", pretending for convenience that there are tensile forces in the air.  If we speak clearly, and specify whether we are using actual or relative pressures, there is never any debate about pushing or pulling.  But I agree that we often fail to speak clearly, and unproductive debate results.


 * But I don't think that the 'pushes' of a given part of an airfoil are relevant here. When we say that the wing "pushes" the air down, we aren't saying that some part of the wing, like the bottom,  pushes some part of the air down.  It would be meaningless.


 * We are saying that the wing as a whole pushes down on the whole body of the air.


 * Mark.camp (talk) 17:15, 29 April 2009 (UTC)


 * It actually is meaningless to say the airfoil pushes the whole body of air down. And it gives the impression that all the air is pushed down. The wing only affects a limited amount of air, not all the air. The wing, flying through air at rest, only affects the air in its direct neighbourhood, giving it a downward momentum change rate. After the passage of the wing, this momentum change rate is spread over a larger and larger volume of air, resulting in the air -- in the region where the wing passed -- coming to rest again (but at a lower position), see the animation and figure in the website above.
 * It is perfectly valid to consider the flow above and below the dividing streamline as separate, i.e. the force on the upper and lower surface separately. If an impermeable rigid boundary is placed at the dividing streamline, nothing changes, and you can just consider the pull from the upper surface separately. The main effect being the low pressure at the upper surface, there is nothing wrong with saying that the wing pulls the air down. It is this pulled-down air that, behind the trailing edge, pushes the flow coming from underneath the wing down. -- Crowsnest (talk) 21:55, 30 April 2009 (UTC)

(Reset indent) You wrote


 * "The wing, flying through air at rest, only affects the air in its direct neighbourhood, giving it a downward momentum change rate.

Is it possible, in principle at least, to measure this downward momentum change?

Mark.camp (talk) 15:21, 1 May 2009 (UTC)

Crowsnest wrote (11:16, 29 April 2009 UTC):

"The wing, flying through air at rest, only affects the air in its direct neighbourhood, giving it a downward momentum change rate.

I had never encountered this concept before, that there is a finite neighborhood of disturbed air, beyond which the change in momentum and pressure is zero, in the case of steady state. So I looked up fluid flow and complex potential in one of my old college engineering math textbooks, and again I find no mention of this discrete boundary. On the contrary, the disturbance seems in all cases to go to zero only as distance from the wing approaches infinity, as I have implied. For example, the component of speed due to circulation falls away as 1/r for the flow around a circle.

Crowsnest, can you comment?

Mark.camp (talk) 12:05, 4 May 2009 (UTC)


 * Hi Mark. There is not a finite neighbourhood of disturbed air.  There is certainly no distinct boundary with disturbed air on one side, and undisturbed air on the other.  The extent of disturbance by a line vortex diminishes in proportion to the distance (or perhaps the square of the distance) from the line vortex.  See Biot-Savart law.


 * With two vortices trailing from every wing, and the two vortices rotating in opposite directions, the rate at which disturbance diminishes with distance from the wing is even greater. Consequently there is substantial disturbance close to the path taken by the wing (see Wake turbulence), but that disturbance becomes immeasurably small at a finite distance from the trailing vortices.  I think that is what Crowsnest meant when he wrote that the downward momentum change is only discernible within a finite neighbourhood of the path taken by the wing.


 * It is a bit like magnetism. If you and I are standing at opposite sides of a long room, and I am holding a magnet, theoretically my magnet influences the magnetic field around you.  However, in practical terms, the influence on the magnetic field around you is immeasurably small, but there is no distinct boundary that marks the outer edge of my magnet's field of influence.  Dolphin51 (talk) 12:27, 4 May 2009 (UTC)


 * Yes, I suspect that this is what Crowsnest was trying to say, but I will wait to see. I think he misread my statement, which was merely an effort to say exactly what he did about the momentum being dispersed.  As a result, rather than noting that there is a less precise, more pragmatic way to say it, he contradicted my more precise statement.


 * But regardless, I think that it is a misconception to equate downward momentum change rate of an arbitrary specified air mass with the wing or with an arbitrary region of the wing, if that air mass is so small that part of its boundary is with disturbed air.  I don't know of a physical law relating dP/dt of, say, an arbitrary region called "the downwash region" or "the upwash region" with the entire wing, or with an arbitrary region of the wing, such as "the lower surface".


 * Mark.camp (talk) 15:16, 4 May 2009 (UTC)
 * I misinterpreted Mark's statement, and my answer was imprecise. Effects of the passage of the wing remain where it has passed. -- Crowsnest (talk) 10:06, 5 May 2009 (UTC)

The relationship between lift and vertical momentum of the air
I will take a stab at stating a simplified version of this relationship explicitly, because the article mentions momentum.

If someone can point me to a reference that has the real mccoy, so much the better.

Consider a large cubic mass of air with airfoil or aircraft at its center

Simplifying assumptions:

-infinite body of air (no earth for the downwash to run into)

-no friction (but the Kutta condition holds by proclamation)

-steady flow

-constant density

-molecular nature ignored, so air mass is assumed to have well-defined border.

Find the instantaneous rate of change of downward momentum of this body at some time t. This is proportional to the instantaneous Lift, but for an error equal to the vertical force on the body of air from outside of it.

Lift = dP/dt + error

The value of dP/dt and the error depends on the size of the cube. In the limit of larger body of air, the net force from outside goes to zero (??), thus the error goes to zero.

The limiting value of downward momentum is constant, and is proportional (in SI units, equal) to the lift. Mark.camp (talk) 20:40, 30 April 2009 (UTC)


 * The whole description depends strongly on the frame of reference used. In a frame of reference moving with the body, the flow is steady, so the density and velocity fields are time-independent, and the momentum of the air in any fixed volume is a constant: dP/dt = 0. There, the lift force is balanced by the momentum flux through the surface of the volume of air, see e.g. Reynolds transport theorem. See Landau & Lifshitz pp. 68–69 and pp. 153–155; or Batchelor p. 387. -- Crowsnest (talk) 12:38, 5 May 2009 (UTC)


 * Thanks. I neglected to specify the frame of reference.  To the above must be added


 * The frame of reference is that of still air. The airfoil is moving in this frame of reference.


 * If you would, please add the technical term for this frame (Lagrangian or Euler)? I can never remember which is which.


 * Mark.camp (talk) 19:03, 5 May 2009 (UTC)
 * That is the Lagrangian reference frame, following a certain amount of air always consisting of the same air parcels. -- Crowsnest (talk) 23:00, 5 May 2009 (UTC)


 * Thank you. My attempt now has this change:


 * "Simplifying and other assumptions:
 * --The frame of reference is that of still air. The airfoil is moving in this frame of reference (called the Lagrangian reference frame).
 * --infinite body of air (no earth for ...."


 * Note: my purpose here is to establish offline agreement about the underlying precise, hard facts re the ubiquitous "momentum explanation (?)". It remains to be determined if any new article text is really required, and if so, to draft usable text.


 * PS: I now have a mnemonic. "Grange" means "farm".  So the "Lagrangean" is the frame of a Depression-era farmer pausing in his field to look up and see a barnstorming biplane buzzing by, so low that he feels on his face the cooling effect of negative time derivative of the vertical component momentum.


 * The Euler is the frame of the pilot, wiping his goggles free of the spattered Eul from the radial engine.


 * Mark.camp (talk) 23:55, 5 May 2009 (UTC)
 * The Lagrangian frame is not the reference frame of the still air. At some initial time t=0 you mark a certain amount of air (paint it pink, if you like). And then you follow this amount of air, always consisting of the same air, and see what happens with its (vertical) momentum when the lifting body passes through it. -- Crowsnest (talk) 07:28, 6 May 2009 (UTC)
 * In the Lagrangian description, you follow an air parcel and describe its kinematics and dynamics. In the Eulerian description an infinitesimal volume at a fixed location is studied, in the frame of reference you choose to use. Because fluid (with its momentum) is entering and leaving the volume, you have also to consider the momentum fluxes through the boundary of the volume to keep track of the momentum balance. To be precise, Batchelor (p. 71) does not talk about Lagrangian and Eulerian frames of reference (as is often done, and I did above), but about a Lagrangian and Eulerian specification of the flow field. Since both can be applied in different frames of reference, e.g. the one moving with the airfoil and one fixed to the still air far ahead of the wing.
 * With respect to your specification of the momentum balance of an integral volume of air, you have to choose both the frame of reference and for what kind of volume you want to make the balance. If you choose the frame of reference moving with the body, as well as a fixed (stationary) volume in this frame with the body in it, both the flow and the volume are steady, and the time derivative of the momentum will be zero (&part;P/&part;t=0). The lift force is balanced by the flux of vertical momentum through the boundaries of the volume.
 * If you choose a volume which always consists of the same air parcels, so in a Lagrangian fashion moving with the flow, the lift is reflected in the change rate of vertical momentum &part;P/&part;t, in both the frame of reference fixed to the body and the one fixed to the still air far ahead. The momentum fluxes through its boundaries are zero (in inviscid theory).
 * If you take a frame of reference fixed to the still air far ahead, and take a fixed volume in space, there will be both a temporal rate of change in the volume as well as momentum fluxes through the boundaries. If this volume is taken larger and larger, at the moment the lifting body is somewhere near its centre, the momentum fluxes through the boundaries become smaller and smaller. So the momentum balance approaches &part;P/&part;t in the limit. -- Crowsnest (talk) 09:16, 6 May 2009 (UTC)


 * Yes, this was what I was trying, not very well, to say in the above.


 * Then I have a question.


 * From what you say, does it follow that it would be inaccurate (at least if we continue to choose Lagrangian specification of the flow field, and the frame of reference of still air far before the wing) to describe the relevant body of air (the body whose rate of momentum change is proportional to lift) as the region "behind the wing" (the "downwash" region)?  Would it be correct instead to identify it as a much more inclusive region, which even includes air in front of the wing?  (And the larger the body considered, the more accurate the statement, since taking the limit is necessary to eliminate what I called the "error" due to external momentum fluxes)


 * I have assumed so, and have therefore made an edit in one place where this (presumed) error occurs. I re-identified the body as "the air", from the region of "downwash" and the region "behind the wing".


 * If my conclusion is incorrect, please revert the change. (Perhaps the original text is correct if one chooses Eulerian flow field specification?  I admit I did not consider this possibility)


 * Mark.camp (talk) 11:38, 28 May 2009 (UTC)

A comment
I feel that this article is much less understandable now than the article that was here about a year ago. Was there a reason to change the concept of this article and stop relying on NASA's explanation? —Preceding unsigned comment added by 128.139.226.34 (talk) 20:05, 24 May 2009 (UTC)


 * Some older versions: 8 June 2007, 3 January 2008 and 21 May 2008. Can you indicate some points which make (the one closest to what you remember as a much better one) more understandable to you than the present version? -- Crowsnest (talk) 20:29, 24 May 2009 (UTC)


 * The 3 January 2008 version might be better in some aspects. What disturbs me most is that one popular explanation (the chapter "Lift in an established flow") is shown as the correct one while the second ("deflection of air") is shown as false. As far as I know both of them have shortcoming and contain assumptions but also provide some elementary explanation. I think that they have to be shown together as alternative experimental (not theoretical) explanations. On the other hand it is known that the ETT assumption is usually wrong and this point isn't stressed enough. —Preceding unsigned comment added by 128.139.226.34 (talk) 10:11, 25 May 2009 (UTC)


 * "Deflection of air" could be paraphrased as:


 * A. "According to accepted scientific principles, if body X deflects body Y down, then X experiences lift.


 * B. "The wing deflects a body of air down."


 * C. "Therefore, the wing experiences lift."


 * It's correct, given suitable precise definitions of its terms, but leads immediately to the more difficult question: "why does the wing deflect the air down?" To know the second answer is necessary to a complete understanding of lift.


 * Mark.camp (talk) 21:33, 25 May 2009 (UTC)


 * Agree completely. The critique that I'd make of the current article is that it jumps headlong into answering question 2 before answering question 1. Wings deflect air downward.  Newton's law says that this implies an upward force. Presenting this simple  and correct (if incomplete) explanation of the phenomenon early in the article would clear up a lot of confusion.  Once we've stated "air goes down plane goes up" we can then delve into why and how the air is deflected, along with methods of computing the lift (Navier-Stokes, Circulation, Bernoulli, etc.)


 * The article as it stands now is rather incomprehensable to someone who is not already familiar with the material. Given the persistence of the incorrect popular explanation, we owe it to the readers to de-bunk it clearly early in the article and present an easy to understand and physically correct explanation before filling the blackboard with equations and jargon.  Yes, the "deflection of air" explanation is incomplete (one might say shallow) and the article would be poor if it stopped there.  But it's a very good place to start.
 * - Mr swordfish (talk) 19:30, 24 June 2009 (UTC)


 * The direction in which a wing deflects the air depends on the orientation of the wing and the vector representing the relative velocity of the wing and the atmosphere. (This orientation  is indicated by the angle of attack.)  The wing of an airplane usually deflects the air down so that lift is upwards, but the horizontal stabilizer usually deflects the air up so that lift is downwards.  When an airplane is performing a loop and is upside-down at the top of the loop, the air is deflected up so that lift is downwards. Dolphin51 (talk) 23:23, 25 May 2009 (UTC)


 * Of course, and this point about the semantics is already made in the article. It wasn't the subject of my post, however.
 * Mark.camp (talk) 11:52, 26 May 2009 (UTC)


 * @128.139.226.34: Many thanks for your comments. It is very valuable to get information on how the page appears to readers, and on comparisons with previous versions. Most striking to me, in your comments, is that you interpret "deflection of air" as presented in the present version as being false; while that certainly is not the intention. Downward deflection of the air flow and lift are direct consequences of each other through Newton's 2nd and 3rd law. But Newtons 2nd and 3rd law are not sufficient to explain why the air flow is deflected downward (see Mark.camp above).
 * The attempts to provide information on the subtleties involved, as well as those presented with respect to ETT, seem to provide confusion and disturb the clarity of presentation in the article, as you experience it. Your distinction, for the downward flow deflection, between experimental evidence and theoretical explanation can certainly be of help for a clearer depiction in the article. -- Crowsnest (talk) 16:53, 26 May 2009 (UTC)


 * @Crowsnest: I have to agree with 128.139.226.34 here. When you say that the "deflection of air" explanation is a "misinterpretation of Newton's Law", that would lead most people to think that this explanation is false. However, NASA's explanation of how wings work, Lift flow from turning, is basically the same idea:  Air is deflected down, so the wing is pushed up.  Why not simply re-iterate this explanation here and leave out the strong language?


 * Whether the lift force causes the deflection or the deflection causes the lift force is one for the philosophers. Either interpretation is as valid as the other, and to call one a "misinterpretion" is unnecessarily harsh and misleading in itself.  Mr swordfish (talk) 15:12, 24 June 2009 (UTC)


 * No, that is not for philosophers, it is at the core of understanding fluid dynamics. For instance, take the momentum equations of an inviscid fluid: the Euler equations state Newton's 2nd law for a continuum description of a fluid. It gives a balance between pressure gradients (forces) and momentum changes. It is nonsense to state that the pressure gradients cause the momentum changes, or vice versa. When the pressure changes, momentum changes as well; and the other way round. The equations describe a simultaneous interaction, a balance between pressure gradients and momentum changes, which can not be solved by these momentum equations alone: besides, one needs mass conservation, and an equation of state. The latter describing the relation between pressure and other flow quantities, e.g. pressure and density.
 * And when integrated over an adequate control volume, the result is the lift force and downward flow deflection. So, it is a misinterpretation to really assume (i.e. other than a linguistic way of writing) that one is the cause and the other is the effect. -- Crowsnest (talk) 22:14, 24 June 2009 (UTC)


 * Ok. You have a philisophical approach to physics that seems to boil down to the claim that there are no causes and effects, only equations expressing relationships.  I disagree with that philosophy.  So do most other people.  You're certainly entitled to it, but it *is* more properly the domain of philosophy than physics.


 * Agree that one has to be careful when interpreting equations (which are just math after all) to imply cause and effect. Nonetheless, there is such a thing, as MarkCamp's sled example below shows fairly clearly.


 * Mr swordfish (talk) 15:03, 26 June 2009 (UTC)

I want to add support to Mr swordfish's idea that lift being produced by "downward" deflection is fundamental and that it should always be said first. I think it should be said first and emphasized. Everything else is not an explanation of lift, but an explanation of how the flow gets deflected and/or how the deflection manifests itself as a force on the wing. And luckily, lift being produced by deflection of flow is the easiest for lay people to grasp as well! If they read that first and then understand nothing else, they will still come away knowing 90% of what they need to know. --Gummer85 (talk) 00:43, 25 June 2009 (UTC)


 * Which side do you agree with in the following argument? The facts are that the child's sled, initially at rest, was pushed by the father.  It accelerated. The debate is over how to explain the phenomenon.


 * A: It is clear that the force exerted by the father on the sled caused the sled to accelerate.


 * B: No, it is nonsense to state that the force exerted by the dad caused the increase in velocity of the sled, or vice versa. When the force of the Dad changes, the velocity of the Kid changes as well; and the other way round. The equations describe a simultaneous interaction, a balance between the force exerted by Pop and the velocity changes of Junior plus Sled.


 * If you agree with A, then you must (respectfully and with regret) disagree with Crowsnest.


 * If you agree with Crowsnest, then you must disagree with A. (And with me, but like the Dread Pirate Robert, I am a Person of No Consequence).


 * Mark.camp (talk) 01:53, 25 June 2009 (UTC)


 * Comment. There is the huge risk of this turning again into the ever re-appearing: "what is the (fundamental) cause of lift" discussion. Which, how nice it may be, is not the point, since this is about writing an encyclopedic article, well sourced, etc. If there are conflicting views (and there are) in reliable sources, the significant ones should be represented in the article. And in a balanced way. So the discussion should not be on whether A or B is the most fundamental one, but how to represent them in the article. -- Crowsnest (talk) 06:18, 25 June 2009 (UTC)


 * Gosh Crowsnest, I have to disagree with you there. The article really is awful.  It's suffers from "too many cooks" syndrome and many other maladies.  Mr swordfish is just the only one brave enough to declare that the Emperor has no clothes.  The article is moribund because too many people watch it and don't let anyone change it without a rigmarole.  It is indeed, like Mr swordfish said: "...rather incomprehensable to someone who is not already familiar with the material."  I think this line of discussion was going somewhere and you seem to be saying "we've all been through this before so let's stop".  I gotta disagree there.  It's our responsibility as knowledgeable editors to apply that knowledge in determining what is fundamental, what is important to say first, how to organize, etc.  These things are OKAY to discuss, and they were being discussed.  To tell you the truth, I had long ago given up on changing even a word in this article.  It's just that untouchable.  I don't have the stomach for it.  I was hoping to encourage someone else to attack it with a big picture, a good framework, and the guts to be correct.  To do that requires discussion.


 * Mr swordfish was right about deflection being fundamental. Among the reliable sources out there there will be no disagreement on the correctness of deflection.  As to how it gets placed and framed in an article requires an editor's knowledge and courage to place it in a way that helps a lay reader understand.  It's an editor's call as to what's fundamental.  It's our responsibility.  It is my opinion that the elevation of deflection to prominence is critical to a rescue of this article.  It certainly needs to be removed from among the "discredited list" where it sits now**.


 * --Gummer85 (talk) 07:43, 25 June 2009 (UTC)
 * **Deflection is currently only discussed in a tone that implies that deflection is wrong. I know it's not really saying that.  It's saying that deflection in and of itself (without a mechanism to induce a pressure distribution) is incomplete***.  But lay readers can't make that discernment.  To a lay reader, the current text makes it look like like deflection is a discredited idea.  Gummer85 (talk) 08:06, 25 June 2009 (UTC)
 * ***So deflection by itself is incomplete, so what? Complete it by describing the mechanisms of deflection, don't throw out deflection.  Deflection is central.  I say the current focus on only mechanisms is incomplete (and needlessly pedantic) without emphasis on the essential deflection.  Gummer85 (talk) 19:49, 25 June 2009 (UTC)

It appears that I'm not alone in my opinion that this article is ripe for a re-write. Looking back a year or so, it appears to have de-evolved. For instance, the first paragraph under "Physical Explanation" is
 * Lift is generated when an object turns a fluid away from its direction of flow. When the object and fluid move relative to each other in a way that turns the fluid flow, the pair of the force required to do this is an equal and opposite force on the wing. The component of this force that is perpendicular to the direction of flow is known as lift.

This is far clearer than what's there now. Mr swordfish (talk) 15:03, 26 June 2009 (UTC)
 * I would even say that the text you quote is overly general. The weasel words emplaced to 1) allow for any perpendicular deflection, and 2) explain the equivalence of relative flow, interfere with the main idea the text wants to explain.  The text tries to say too much.  It can be useful to constrain the explanation to simply "downwash" because a lay reader (and us experts most of the time) think of lift in that way.  The fact that it can turn flow sideways and still be lift can be explained separately.  Same goes for the equivalence of relative wind.  The text is good only because it shows our "essential deflection" as fundamental, which I suppose does make it immensely better than explanations that ignore or diminish deflection.


 * --Gummer85 (talk) 17:22, 26 June 2009 (UTC)
 * That's a fair criticism. I included that quotation only to demonstrate that that picking a version more or less at random from about a year ago produces a better article than what we have today. Your use of the word rescue above is apt.
 * --Mr swordfish (talk) 13:27, 27 June 2009 (UTC)

Ah. Yeah. I guess I couldn't help analyzing the text. :-) I've found there is a constant influx of well-intentioned "chaos" making its way into popular Wikipedia articles.  It's caused by the fact that anyone can edit (which has positive effects too of course).  It makes for the "one step backwards" part of "two steps forward, one step back".  It requires constant diligence by knowledgeable editors to keep things right.  I'm not so sure that any article can be very good for any decent period of time (particularly the big articles) because knowledgeable editors' time and energy really is a finite resource.  This (lift) subject is the Big One in aeronautics, right?.  Everyone pays attention to it and everyone thinks they know better.  Everyone discerns some minute way that some text isn't perfectly correct.  Pretty soon the article reads like lawyerese and it's filled with equations.  Too many impassioned cooks make for a tough Mexican Standoff. And we're all impassioned! :-) This article is a tough nut.  I talk a lot about how it could be better, but I don't dare take it on.  I'd make my own "Gummerpedia" first and only allow proven knowledgeable  editors to edit it.  Anyone could comment, but only the proven could actually edit. That's what I'd do by golly.  :-)

--Gummer85 (talk) 02:51, 28 June 2009 (UTC)

More Concern
I found myself here from looking at the article on wings after looking for something on bird flight. I am concerned with the lack of detail on scale phenomena and such things as the importance of feathers to birds. There is a lot that needs to be improved yet about the overall site.Julzes (talk) 17:51, 26 May 2009 (UTC)
 * Any ideas? A separate article? A section here? Probably there is an established collection of scientific publications on this, I expect simple-mindedly; for establishing notability and verifiability. Go ahead, if you like to. -- Crowsnest (talk) 22:03, 26 May 2009 (UTC)


 * IMHO, a section on lift in bird or animal flight, within this same article, would be consistent with its present title, which is not restricted to lift in man-made objects. If we can lasso an expert to write a paragraph or two, it would fill out the article nicely: there are so many fascinating differences between animal flight and that of man-made craft and devices.


 * Mark.camp (talk) 16:56, 27 May 2009 (UTC)


 * And don't forget insect flight. -- Crowsnest (talk) 17:01, 27 May 2009 (UTC)


 * For sure. By "bird or animal flight", I meant "at least bird flight (the concern of this Talk section), and better yet, about animals in general (insects, insect-like animals, bats, etc.) if they have interesting variations concerning lift.  (And only Lift, since this is not an article about flight.)


 * Mark.camp (talk) 19:29, 27 May 2009 (UTC)

Behind the wing
Article contains this text:
 * "John D. Anderson explains the relationship between lift and downwash as follows: "The wing deflects the airflow such that the mean velocity vector behind the wing is canted slightly downward. Hence, the wing imparts a downward component of momentum to the air; that is, the wing exerts a force on the air, pushing the flow downward. From Newton's third law, the equal and opposite reaction produces a lift."

(Emphasis mine).

Thus, Anderson is inferring that the Newtonian connection is between the wing reaction force and the momentum [1] of the region behind the wing. (or body of air which is behind the wing at a certain point of time, if you choose Lagrangian flow field specification).

I have two questions.

1. Is it correct to select this region or body, assuming that one more clearly defines its boundaries (if one chooses Eulerian specification) or boundaries at a specified point in time (if Lagrangian--boundaries change with time in this case)?

2. If so, what are those boundaries (Eulerian) or those boundaries/point in time (Lagrangian)? For example, could we specify a Eulerian region which makes his statement correct, perhaps by taking the limit of the volume, as the right boundary is moved to the right?

[1] Anderson is, properly, making the simplification of assuming constant density, so velocity is a good proxy for momentum, and this point is irrelevant to my questions.

Mark.camp (talk) 16:54, 6 June 2009 (UTC)

Article Re-organization
Based on the comments in "A comment" above, I propose re-organizing the "Description of lift on an airfoil" section ordering the topics as follows: The simple explanation based on flow turning and deflection, citing NASA site & Babinsky.  The "popular" explanation together with a debunking of "equal transit time fallacy". The main body as it exists now. Other alternative explanations. 

This will present the more easily understandable explanations first, and will help with readability. Comments?

Mr swordfish (talk) 16:02, 2 July 2009 (UTC)


 * Hi Mr S. Proposals to re-organize and improve articles are always welcome.  I have a couple of suggestions.


 * Firstly, the ideal way to re-organize and improve an article is to create a personal Sandbox, use your Sandbox to develop your changes, use the Talk page to announce the existence of the improved version on your Sandbox, invite comments, and then paste your version into the main article. This has a couple of major advantages – you can work in peace without your changes being reverted or disturbed by other users, and other users can give you comments before you actually paste into the main article.  Information about starting a User sub-page (a personal Sandbox) is available at WP:USERSUBPAGE.  I have a personal Sandbox which can be seen by first visiting my User page.


 * Secondly, many users have described the equal transit time theory as a fallacy. This is a judgemental use of the word fallacy.  It is not Wikipedia’s role to arbitrate on competing ideas.  The role of Wikipedia is to present the equal transit time theory and criticisms of that theory, all with suitable references and in-line citations; to also present more accurate models of lift such as the Circulation theory of lift and the Kutta condition with suitable references and in-line citations.  In Lift (force) there is a place for presenting factual information about equal transit time, but it must be called a theory, not a fallacy.  Our personal points of view are irrelevant in Wikipedia.  Wikipedia aims for a neutral point of view. Dolphin51 (talk) 04:43, 3 July 2009 (UTC)


 * Please define what you mean by "judgmental". It seems that the exercise of good judgment in writing and editing articles is essential, doesn't it?  (I don't mean of course deciding which of competing expert opinions is correct, where the best experts currently disagree, or where matters of opinion or taste are involved.  We cannot presume to do that.)
 * Mark.camp (talk) 02:09, 6 July 2009 (UTC)


 * The American Heritage Dictionary of the English Language (4th ed) defines it as “inclined to make judgments, especially moral or personal ones”.  Wikipedia has a  policy of always presenting a neutral point of view.  A judgmental point of view is the exact opposite.


 * In the case of the equal transit time theory, there are citable sources which present this theory in all seriousness. There are other citable sources that dismiss the equal transit time theory as incorrect.  This situation is very common.  In situations like this, Wikipedia can acknowledge the existence of both theories, describe the popular views of them both, report both factually, and support all statements by suitable references and in-line citations.  Greater coverage and emphasis should be given to the more numerous and better-accepted of the two approaches.  Wikipedia’s coverage of competing ideas must present a neutral point of view.


 * For example, in a Wikipedia article about a politician it is Wikipedia’s mission to present the facts about the politician, and the spectrum of published ideas about his legacy, all supported by suitable references and in-line citations. It is not the role of Wikipedia to make an independent judgment of whether that politician was good or bad, and present that judgment in the article.  Even in the case of an article about a politician widely acknowledged to be an evil dictator, Wikipedia presents the facts, accompanied by the various views to be found in citable sources.  Wikipedia does not present the judgment of one or more Wikipedia users, or use emotional language to hint at a judgment.


 * It is mostly in the choice of words. To refer to the equal transit time theory as a fallacy would be an unreasonable judgment.  A more appropriate way of capturing the essential information would be to write that the equal transit time theory is considered by several authors to be a fallacy, and support that statement by suitable references and in-line citations, pointing to several authors who actually use the word fallacy in connection with the equal transit time theory. Dolphin51 (talk) 02:54, 6 July 2009 (UTC)


 * Let's be careful here - there's a theory of lift that is based on equal transit times. Calling that a theory is correct.  However, as the article points out, it's based on an incorrect assumption - that the air must rejoin when it reaches the trailing edge. This assumption is widely known as the "Equal Transit Time Fallacy", or if we want to use neutral language, the "Equal Transit Time Assertion"


 * At the risk of going off into the weeds of semantics here, my view is that calling the Equal Transit Time Assertion a "theory" is misleading in itself. There is no empirical evidence for it, neither is there any physical model that predicts it.  Wherever I've seen it, it's merely asserted without any supporting argument or evidence.  It is readily shown to be false by experimental evidence and by most physical models. In what sense is it a theory?


 * Anyway, my plan for the re-org does not include changing that section very much (if at all); the main impact of the re-org would be to place it earlier in the article, before the reader's eyes have glazed over from all the jargon and equations. If there are issues with the current verbiage, we can address that as a separate issue.


 * Mr swordfish (talk) 15:49, 6 July 2009 (UTC)


 * To call a scientific theory of lift a fallacy is not judgmental, by the dictionary definition cited above. Scientific theories on mundane and impersonal subjects like aerodynamics are objective (objectively true or objectively false), rather than "personal or moral".  So no statement that a scientific theory of lift is fallacious can properly be excluded on the basis of judgementalism.  I think you are confusing judgementalism with violations of the NPOV policy, which is a different thing altogether.  If there were a bona fide scientific controversy over ETA, then NPOV policy would forbid it being called a fallacy--that would be a non-neutral, though non-judgemental, point of view.   But because there is no controversy over it among aerodynamicists, I think it may be helpful to make the reader aware that it is not valid.


 * Mark.camp (talk) 19:25, 6 July 2009 (UTC)


 * Mark Camp wrote I think it may be helpful to make the reader aware that it is not valid. We are all in passionate agreement on this point!  Above, I wrote A more appropriate way of capturing the essential information would be to write that "the equal transit time theory is considered by several authors to be a fallacy", and support that statement by suitable references and in-line citations, pointing to several authors who actually use the word fallacy in connection with the equal transit time theory.


 * I'm sure we are all in agreement that calling it the Equal Transit Time theory, or assertion, or model or idea would be reasonable. Some want to call it a fallacy, perhaps without bothering to cite some published source that calls it a fallacy.  How would you feel if I edited the article and called it the Equal Transit Time Stupidity?  Again I'm sure we would all agree that would be unreasonably judgmental, especially as I am unable to cite any source that calls it Stupidity.  Dolphin51 (talk) 23:36, 6 July 2009 (UTC)


 * OK. I won't use the word "fallacy".  It seems that, at least in your mind, "fallacy" has a pejorative sense, (like the word "stupid"). To you it also suggests an ad hominem attack.  You're correct that to call an argument "stupid" would be an ad hominem argument ("judgmental").  But for the record, "fallacy" in standard English is neither pejorative nor subjective. It means basically "false" or logically flawed, in a purely objective sense, and implies nothing about the author or holder of the theory or argument.


 * Rest assured that I would never use insulting or judgmental wording in an article.

Mark.camp (talk) 22:18, 14 July 2009 (UTC)


 * Mr swordfish's re-organization of this article has used the word fallacy but he has used it skillfully. The article now states that others have described ETT as a fallacy, and Mr swordfish has cited three sources to support use of that word.  The article does not suggest that one or more Wikipedia users have used the word fallacy on the grounds that, as a result of their original research, they believe ETT to be fallacious.  There is a significant difference.  Well done Mr swordfish.  Dolphin51 (talk) 23:05, 14 July 2009 (UTC)


 * Per Dolphin51's recommendation, I have created a draft in my sandbox http://en.wikipedia.org/wiki/User:Mr_swordfish/Lift . Comments?  I'll leave it up for a few days before applying the changes to the live article.


 * Althoug the diff tool doesn't show it all that clearly most of the changes are minimal, with the exception of the description of Newton/deflection/turning/ theory which has been reworked for clarity and simplicity.  Some headings have been re-named and re-ordered.  The two "simple" explanations have been moved to the top in the interest of readability.


 * Mr swordfish (talk) 21:44, 7 July 2009 (UTC)


 * Mr swordfish's re-work is an improvement. I have replied at User talk:Mr swordfish/Lift.  Dolphin51 (talk) 22:58, 7 July 2009 (UTC)


 * Thanks, Dolphin51


 * What is an appropriate length of time to allow comments on the draft before replacing the current article? 3 days? 7 days?  More? Less?  Mr swordfish (talk) 18:05, 8 July 2009 (UTC)


 * I find the draft to be an improvement, so I might be biased, but I think 3 days would be sufficient for all those who are monitoring Talk:Lift (force) on their Watchlists. 3 days should be the minimum.  If a fierce debate develops it would be appropriate to allow the debate to run its course and that may take a bit longer.  Dolphin51 (talk) 22:46, 8 July 2009 (UTC)


 * Three days have now passed since I posted the draft, and over a week has gone by since I proposed the changes. Seeing no "fierce debate" I'm publishing the changes.  Please discuss here before major revisions.  Thanks.  Mr swordfish (talk) 21:57, 10 July 2009 (UTC)

Lift vector : Nomination for deletion
On 16 June 2009 a new article titled Lift vector was created. It appears to me to be technically incorrect on at least one point, and where it is correct it duplicates information already provided at Lift (force). I have nominated Lift vector for deletion. If you are interested, please visit WP:Articles for deletion/Lift vector and contribute to the debate.

The point I consider to be technically incorrect is the suggestion that changing the angle of attack will increase or decrease the lift vector. This is only correct if the airspeed of the aircraft remains unchanged and the aircraft's longitudinal static stability is neutral so that the maneuver load factor is not restored towards its original value. I would consider it more accurate if the article took the approach that the lift vector changes whenever the aircraft weight or maneuver load factor changes. Dolphin51 (talk) 05:40, 30 July 2009 (UTC)


 * An article on Lift Vector seems redundant when we already have an article on Lift Force. A force *is* a vector, so "lift vector" is just a slightly less precise wording of "lift force".  I'd vote for a redirection to Lift(force).  Mr swordfish (talk) 14:21, 30 July 2009 (UTC)

Add a Reference to Abbott and von Doenhoff, "Theory of Wing Sections"
Any list of references on airfoil lift would be incomplete without mention of the book still generally regarded as a requirement for all students and teachers of aviation theory - Ira H. Abbott and Albert E. von Doenhoff, "Theory of Wing Sections", LOC # 60-1601, 1959, Dover Publications, New York. Its very popularity over the years now despite its early publication date and theorizing make it indispensable for a complete picture on what has been and continues to be said. I would hesitate to discuss any facet of lift force creation with anyone who has incomplete ideas on flow irrotationality and flow continuity as discussed in Chapter 2 of this book, which defines better than anywhere else to my knowledge the stream function, "psi", and the cross stream function, "phi". Yes, lift is generated by deflection of the air mass flow downwards (remembering that air density is 2 pounds per cubic yard at sea level and can assume large values in large volumes) but using only the math of averaging results in the appearance of a constant with an unknown value in the derived formula. The more complete theories, you see, eliminate this constant. Meanwhile, the references of those such as Eberhardt and Anderson are valid and bring much needed updates to this work. Aircraft, now up to 500 tons of weight, do not fly as if on a magic carpet but observe conservation of momentum by means of their wing downwash to the earth below, which thereby sees their full weight despite their flight paths being high above. To calculate the lift force with precision, however, one had best understand the airflow on a streamline by streamline basis, for which this famous book provides an introduction. Need I also say that the modern technology of wind energy also derives much of its theorizing from these same sources. Some help in reviewing this subject and this reference may also be found in the "Wind Theory" section of http://www.integener.com. 67.150.5.71 (talk) 14:39, 15 August 2009 (UTC)


 * I agree. Abbott and Doenhoff's famous book is already a reference on Lift coefficient, Drag coefficient and Pitching moment.  Dolphin51 (talk) 22:55, 17 August 2009 (UTC)

Upon rereading this post (my own) on 26 November 2009, it would only be added that flow theory is complex and more thorough, as stated, but is known to be just kinematical in nature, that is, the fluid mass is not considered and the flow descriptions are valid for any inviscid fluid simply because it is a fluid. Sometimes kinematics and its detail just adds confusion to the issue and many now have come to see it as unnecessary and avoid it altogether, doing so by taking flow averages instead, which leads to overall conclusions just as correct. Being grateful for the help and copied (stolen?) quotes taken from this Wikipedia material, the favor is returned here by contributing a thought or two. Thanks and the "Wind Theory" section of http://www.integener.com remains available and even further expanded since the last post. 66.81.105.235 (talk) 14:35, 26 November 2009 (UTC)

Outline of an explanation of lift
As a non-expert, I have learned much about the cause of lift from this talk page and from related talk pages, though I am still not very knowledgeable. If I had to try a theoretical outline of a simplistic explanation of lift at the present early stage of my learning, it would be something like this.

An aerofoil has a rather sharp trailing edge. For physical reasons related to friction and explained elsewhere, the trailing stagnation point will be tend to be forced to this location, over a range of AoA's. We switch at this point to the simplifying assumptions of the "complex potential" model. If we apply Newton's third law, the continuity condition, and the condition of impermeability (flow must be tangent vector or zero vector at the surface of the foil) we can show that throughout that range, the ordinate of this aft stagnation point, with respect to the rest of the wing, acts as a "control" over the sense and magnitude of the circulation, with there being some neutral AoA that yields zero circulation. Also we can show that the sense and magnitude of lift is determined by the sense and magnitude of the circulation. Therefore, controlling the AoA of such a wing controls the lift.

Once the cause of lift is understood, it would be very helpful to give an accounting of the relationship of lift to momentum in a wing creating lift, even though this account by itself doesn't provide a satisfactory explanation of lift, since it assumes the momentum transfer, rather than accounting for it. In logical terms, if we assume that Newtons' third law is accepted, then attempting to explain lift by assuming transfer of vertical momentum is a form of formal fallacy called "begging the question".

It would also be important to point out how the very strange position of the leading edge stagnation point in a streamline diagram or photo, is explained by the above (rather than being assumed, which tends to happen in many supposed explanations).

Mark.camp (talk) 22:06, 17 August 2009 (UTC)


 * Some important information about the trailing edge stagnation point can be found at Starting vortex and Kutta condition. Dolphin51 (talk) 22:58, 17 August 2009 (UTC)


 * Thanks, D51. The Kutta link is especially good.
 * Mark.camp (talk) 16:37, 18 August 2009 (UTC)

A more rigorous physical description
On 25 October 2009 User:GanjaManja made the following comment on Lift (force): ''This rigorous explanation is well written, but does not appear to actually combine the various effects to provide a reason that lift is produced - could someone with a good intuition for this please provide a conclusive description? Thanks''

See diff. Comments and replies to GanjaManja should be made here on the Talk page. I will delete the hidden comments from the article. Dolphin51 (talk) 21:50, 25 October 2009 (UTC)

Add a Pressure Difference section?
A few days ago someone added the following to the article as a caption to the Equal-Transit-time diagram:


 * "Aeroplanes get their lift by differences between air pressure above and below the wing, as air flows over it. The theory here states that if the wing is designed with more curvature on top than below, the air will flow faster on the top of the wing, causing air pressure to be lower than the bottom, pulling the aeroplane up."

I removed it because the assertion that wings derive lift through pressure differences is out of context in this section. However, it is possible to describe the lift in terms of pressure differences - everyone agrees that there are differences in air pressure on the top and bottom of a wing generating lift, the hard part is explaining *why* the pressure differences arise. Should we add an elementary section on this theory?Mr swordfish (talk) 15:48, 7 January 2010 (UTC)


 * You have written that the hard part is explaining why the pressure differences arise. I disagree.  The difficulty is explaining why the speed of the air over one side of an airfoil is faster than over the other side whenever the airfoil is generating lift.  (To explain that phenomenon it helps to make use of the Kutta condition and the Kutta-Joukowski theorem.)  Once this difficulty has been overcome and the explanation has established that the airspeed is faster over one side than the other it is very easy to explain why this difference is accompanied by a difference in air pressure - Bernoulli's principle!


 * Over the years there have been numerous attempts to eliminate Bernoulli's principle from explanations of lift generated by airfoils, usually because editors mistakenly believe Bernoulli's principle is the same thing as the Equal Transit Time model. Dolphin51 (talk) 21:46, 7 January 2010 (UTC)


 * Does the speed difference cause the pressure difference or is it the other way around? Bernoulli's law merely correlates the two, the formula alone doesn't  say anything about cause and effect.  However, wherever I have seen the literature weigh in on cause vs effect, the author interprets the physics to be: pressure differences cause the change in velocity, not the other way around.


 * For instance: Klaus & Ingelman-Sundberg:
 * "The faster flow at the upper side of the wing is the consequence of low pressure and not its cause." and
 * "The conventional explanation of aerodynamical lift based on Bernoulli’s law and velocity differences mixes up cause and effect. The faster flow at the upper side of the wing is the consequence of low pressure and not its cause."


 * Bauman:
 * Bernoulli’s equation tell us that a pressure difference causes a change in speed, and pressure differences are caused by curvature of flow...


 * Babinsky:
 * if the pressure drops in the x-direction (dp/dx < 0) the pressure at the rear is higher than at the front and the particle experiences a positive) net force. According to Newton’s second law, this force causes an acceleration and the particle’s velocity increases as it moves along the streamline.


 * So, I'd be cautious about explaining the pressure differences as a consequence of the speed differential since this stands the physics on it's head. Nonetheless, there are pressure differences, and it's possible to explain lift as a direct consequence of these pressure differences.  The article might be improved by adding a section on pressure differences. I might take a shot at it in coming weeks


 * Agree that Bernoulli is not the same thing as Equal Transit Time, and the article is careful to make that distinction when discussing ETT.Mr swordfish (talk) 19:13, 8 January 2010 (UTC)


 * Thanks for your research, and your quotations. That is impressive.


 * Bernoulli's principle merely states that a change in pressure and a change in fluid speed occur simultaneously. Bernoulli correctly avoided attempting to identify one as the cause and the other as the effect.  The cause of the changes in pressure and speed around an airfoil is the shape of the airfoil and its orientation to the flow.


 * In physics there are many examples of this simultaneous coexistence of two parameters. For example, when we throw a ball into the air its kinetic energy decreases and its potential energy increases.  It would be foolish to contemplate whether the change in kinetic energy causes the increase in potential energy, or the other way round.  When one increases, the other must decrease because the sum of the two, the mechanical energy, remains constant.  Identically, in a fluid flow, the potential energy (static pressure) plus the kinetic energy (dynamic pressure) remains constant (called total pressure or stagnation pressure).


 * So when amateurs talk about the change in pressure causing the change in fluid speed around an airfoil, or the other way round, they are not making good sense.


 * It is reasonable to observe a force accelerating an object and say the force causes the acceleration, rather than the other way round. That is partially explained by saying there is no law about force plus acceleration is a constant.  Dolphin51 (talk) 07:27, 9 January 2010 (UTC)


 * It might not make good sense when "amateurs" talk about cause and effect, but the citations I provided are not from amateurs - they're phd physicists published in peer-reviewed physics journals. They say pressure difference causes the change in speed and not the other way around.


 * While I can't fault someone for taking an agnostic approach and limiting their commentary to saying merely that speed and pressure are just two parameters that co-exist with a certain relationship, the peer-reviewed literature goes farther and speaks directly to cause and effect: the pressure change causes the speed change and not the other way around. As (amateur) wiki-editors, it's our job to present the results of independent research, the gold standard being peer-reviewed academic literature. It's not my amateur opinion that counts here, it's the three citations above.  If you'd like a fourth, there's Brusca:


 * A common student reaction to the concept of the Bernoulli effect is to ask: 'How can an increase in velocity cause a decrease in pressure?' I point out to them they are confusing cause and effect: it is the pressure drop which causes the increase in velocity... http://www.iop.org/EJ/article/0031-9120/21/1/307/pev21i1p14.pdf?request-id=b46b9e2f-6e78-4727-a740-640ce840150b


 * But I've gotten a bit off topic here. I'd like to re-focus on ways to improve this article. What do you think about adding a section under "other theories" dealing with pressure?  I'm a bit conflicted since it's not really another theory - the other descriptions include treatments of the pressure differences.  Yet, I come back to Try0yrt's verbiage that I removed - "Aeroplanes get their lift by differences between air pressure above and below the wing, as air flows over it." - this is a correct statement that's easily understood by laymen, it just needs some context.  Mr swordfish (talk) 20:40, 11 January 2010 (UTC)


 * I agree that this article must contain an explanation based on the notion of the difference in pressure on the two surfaces of an airfoil. In one of John D Anderson's books (Introduction to Flight?) he makes an excellent philosophical assessment of lift, looking for the most fundamental explanation of the phenomenon.  He concludes that the most fundamental explanation is that there is a difference in pressure across the airfoil.


 * Part of the theme of the current article is that there is more than one legitimate explanation of lift. All of them are reasonable, and each person is at liberty to choose the one that appeals most.  The greatest error occurs when someone concludes that his explanation is correct and therefore all other explanations must be incorrect.  Here are some popular examples of different explanations:


 * pressure difference across the airfoil (and this causes a difference in airspeed in accordance with Bernoulli's principle)
 * airspeed difference across the airfoil (and this causes a difference in pressure in accordance with Bernoulli's principle)
 * greater vorticity in the flow adjacent to the upper surface of the airfoil than adjacent to the lower surface (and this causes a difference in airspeed across the airfoil, and this leads to a difference in pressure in accordance with Bernoulli's principle)
 * momentum of the airflow approaching the airfoil is inclined slightly upwards in response to the bound vortex, and momentum of the airflow leaving the airfoil is inclined slightly downwards. The rate of change of momentum shows the presence of a force exerted on the fluid by the airfoil.  The equal-and-opposite force exerted on the airfoil by the fluid is called lift.


 * And so on. If some people prefer the notion that difference in pressure causes the difference in airspeed that is their prerogative.  However, they should not be so dogmatic as to say that the alternative view (difference in airspeed causes difference in pressure) is incorrect.


 * I like the description you have attributed to Babinsky. If Bauman is saying that Bernoulli's principle tells us that pressure differences are caused by curvature of flow, I would challenge Bauman.  I don't believe Bernoulli had anything to say about pressure differences being caused by curvature of flow.  I am not impressed by the quotation attributed to Klaus & Ingelman-Sundberg.  Economics concerns itself with cause and effect but physics does not - in physics many things can be said to coexist; they occur simultaneously.  With the explanation attributed to K & I-S the student runs the risk of imagining that pressure difference leads airspeed difference.  The student might imagine that because pressure difference causes airspeed difference, the difference in pressure must arise first and the airspeed difference follows a fraction of a second later.  (I wonder if K & I-S would say that the decay in kinetic energy of a ball causes the increase in potential energy, or the increase in potential energy causes the decay in kinetic energy.  I hope they would take the view that the principle of conservation of energy cannot be explained in terms of cause and effect.)  Dolphin51 (talk) 02:15, 12 January 2010 (UTC)

Flow over cambered surface - change in pressure without change in local flow speed?
Using a wing as a frame of reference, the local flow that follows the cambered surface includes a component of acceleration perpendicular to the local flow. The flow further away from the wing is apparently directed at the wing, but the local flow is mostly parallel to the cambered surface.

For this local flow, the component of acceleration perpendicular to the cambered surface would seem to correspond to a component of pressure gradient that doesn't correspond to a change in speed, but only in a change the direction of the flow, which would be a non Bernoulli like interaction for the local flow. I assume the flow further away from the wing that is directed towards the wing surface would be Beroulli like, so the only issue is the local flow near the wing surface.

I have yet to find a good article that deals with this issue.

Jeffareid (talk) 09:22, 22 February 2010 (UTC)


 * I agree with what you have written, up to the point where you say which would be a non-Bernoulli-like interaction for the local flow. Where there are accelerations that cause changes in speed, the speed and static pressure conform to Bernoulli's equation.  (Where there are centripetal accelerations - causing change in direction but not speed - the speed does not change and static pressure remains constant, in accordance with Bernoulli's equation.)  Bernoulli's Principle (when applied to a wing) addresses speeds and static pressures - it doesn't address accelerations.  The only non-Bernoulli situation in the flow around a cambered surface is where viscous forces exist.  This is mostly in the boundary layer close to the surface of the wing.  (Similarly, when considering a wing immersed in transonic, sonic or supersonic flow, there are compressibility effects that cannot be accounted for by Bernoulli's equation.)  Dolphin51 (talk) 11:49, 22 February 2010 (UTC)


 * I was thinking the situation was similar to a vortice, which has a very low pressure core, but speed is minimal at the core.


 * Bernoulli ... doesn't address accelerations. One derivation of Bernoulli equation starts with Newtons 2nd law, F = m a, (the wiki version starts off with m dv/dt = F). So why doesn't Bernoulli address accelerations in the case of a wing? Jeffareid (talk) 23:47, 22 February 2010 (UTC)


 * There is a relationship between acceleration, mass and force. It is Newton's second law of motion.  When changes in altitude can be ignored, Bernoulli's principle states that at all points along a streamline (or in a regional of irrotational flow) the sum of static pressure and dynamic pressure is constant.  (The sum is called total pressure or stagnation pressure, and is constant throughout a region of irrotational flow.)  Bernoulli's principle does not talk about accelerations.  If Bernoulli had talked about accelerations he would only have been re-inventing Newton's second law of motion.  It is true that Bernoulli's principle can be derived using Newton's second law of motion (and Euler's equation) but that is not the same as saying Bernoulli's equation addresses accelerations.


 * At the core of a free vortex the pressure is very low but the speed is infinitely large. In the core of a real vortex the pressure is low, the linear speed is zero and the core rotates like a solid.  (The Rankine vortex is a model of a real vortex.  However, where the core is rotating like a solid body the flow is not irrotational so Bernoulli's principle is not applicable. Dolphin51 (talk) 07:11, 23 February 2010 (UTC)


 * ... but isn't part of the real world flow around a real wing rotational (using the air as a frame of reference)? I read that circulation of flow around a wing is part of the process of producing lift at many web sites (although most don't mention that this uses the air as a frame of reference, air doesn't flow forwards across the lower surface of a wing relative to the wing). You'd also have turbulent flow in the boundary layer about 1/3rd back of the leading edge on most wings, which would interact with the adjacent flow just outside the boundary layer. Jeffareid (talk) 20:02, 23 February 2010 (UTC)


 * When a wing is generating lift there is circulation around any closed path that encloses the wing. (This is the Kutta-Joukowski theorem.)  However, this doesn't mean the flow enclosed by that path is rotational everywhere.  Flow is irrotational wherever vorticity is zero, not wherever circulation is zero.


 * A boundary layer is a region of intense vorticity so the boundary layer is rotational flow. When a body is generating no lift the vorticity in the boundary layer on the top surface is equal and opposite to the vorticity on the bottom surface so the circulation around the body is zero.  But when an airfoil is generating lift the flow over the top surface is much faster than the flow over the bottom surface; there is more vorticity in the boundary layer on the top surface than the vorticity on the bottom surface; and a non-zero circulation exists around every closed path that encloses the wing.


 * The flow in the boundary layer is rotational and represents a significant amount of vorticity. Outside the boundary layer vorticity is zero, the flow is irrotational and Bernoulli's principle holds true. Dolphin51 (talk) 23:32, 23 February 2010 (UTC)