Talk:Lift (force)/Archive 1

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Initial comments

Hi all, I'm a physics grad student and while I'm by no means a lift expert, I have been reading papers on it and I feel like there is a series hole in this article, but don't know enough to fill it. I feel like some one should add a controversy section to the article to make it clear that there are not only misconceptions, but also a large amount of debate amongst people who the lay person would expert to "know". It isn't that I think that anything in the article is really wrong it is just that I feel it is misleading to hide all of the debate inside the discussion section, and that a clear concise overview of why there is a heated, and seemingly ongoing, discussion. Tristan (UCSC) 9/24/06

-- I have been amazed by the diversity & robustness of the debate on this topic. As a practicing aeronautical engineer, my feelings on the topic are that we should recognise that each approach has it's value in the right circumstances. My own experience in the field makes me very very wary of certainties, musts, has to's and dogmas. Does anyone remember the day they learned that light could be a particle and a wave? Both models have their uses. I will be hosting a teenager on work experience at my company soon. Bernouli is ideal for him...he'll learn about observing reality and continuity in a real way. When I talk to my Aerodynamics colleagues, I talk Circulation. When I talk with the future projects office we talk L/D, etc etc. To my mind, each abstraction of reality has it's value and place. cheers, TG

Hi TG, I am also an engineer, and my own experience of physics is that if it isn't clear and solid in an explanation it is usually because the physics is poorly understood. Consider showing your teenager on work experience the formula for, or the physics causing the increase in air velocity over a wing that then causes the pressure reduction according to Bernoulli.... You will find there isn't any reasonable physics to explain this unless you start with the Newtonian version. Then you might consider that there is no physical reason for the air to increase in speed over the wing (except the lower pressure above it) in order for the rest of the Bernoulli version to make any sense. If you cant explain whay the air will go faster over the wing.. then it isnt a valid theory at all. Dave 23-May-06

Dave, Bernoulli theory is a simple statement about energy conservation in fluids, it does not describe mechanisms at all. The mechanism giving rise to the lower pressure/higher speeds over the top of a wing is simple. If a wing has a positive angle of attack a low pressure region has to be created in order to accelerate the air downwards along the back of the wing. If this did not happen a vacuum would be left behind the wing as it passes.Rolo Tamasi 09:06, 8 September 2007 (UTC)

Not true the vacuum would fill from the back of the wing, Its the choice between going through a barn door or a pin hole.PatRobot 02:23, 26 September 2007 (UTC)

It is true! (great style BTW). The air accelerates along all pressure gradients, viz. in all directions possible. As the “notional vacuum” would be along the entire back of the wing the greater element is downwards. However, it is true there is a horizontal component – for the air towards the front of the wing (and for some distance in front of it) this horizontal component above the wing is rearwards and has the effect of accelerating the air from stationary to a maximum rearward velocity component. Towards the rear of the wing the horizontal component is reversed. The associated acceleration here has the effect of slowing the air from this maximum horizontal component to an approximately stationary horizontal component. The horizontal movement is therefore all rearwards and the air is left with little or no horizontal velocity.

The high pressure region below the wing has the reverse effect. It is this mechanism that causes the airspeed relative to the wing to be higher above than below.

The net impact therefore is that the air above the wing is relocated rearwards and given a downwards momentum, which remains after the wing has passed and air below the wing is relocated forward and also retains a downward momentum.

During all of this Newton and Bernoulli rock on together in total harmony Rolo Tamasi 11:33, 26 September 2007 (UTC)

Hi TG, In response to your reference to quantum mechanics (wave / particle duality)...

It is true that both models have uses in the context of how we understand quantum-level events. But it's also true that both models are valid representations of the physical reality. My point is: that particular analogy does not extend to the explaning the phenomena that render the lift force. In this (non-quantum) case there is precisely one explantation for the physics of any given wing-fluid scenario. ( assuming the structures at hand are "bigger than a breadbox" :-) ) There are no two truths in this case, and to propogate such a notion will impede progress, It retains a falsehood in the meme-pool, and casts doubt upon a new truth. Optimally in an educational process, the student should primarily learn the existing conventional truth and (when benificial) be made aware that there are current or recent notewarthy claims that divege from that. ethree@earthlink.net-Aug--06

-- I'm worried here about wading into the debate surrounding the different ways of expressing lift. There are many ways of describing lift, and many of them are right. The Bernoulli/Venturi explanation is not wrong.

Yes the Bernoulli explanation is totally wrong. Apart from the fact that it contradicts the observed ability of a wing to fly inverted, and we know that a paper thin wing works perfectly well which this explanation cannot support, and that it is based on the false assumption that increased velocity causes a reduction in pressure (the opposite being true), it also is based on the initial need for the air to flow faster over the wing in order to "Cause" the pressure reduction and NO ONE ever has an explanation as to why this air would go faster (being longer over the top surface does not somehow magically change into a force)... This change in speed is by definition an acceleration, and by Newtons 3rd law, this requires a net force to cause such. For a gas this "Force" must be in the form of a pressure gradient. Where did the pressure gradient come from??? In order for the gas to accelerate over the wing we MUST already have a pressure gradient along the surface. This pressure gradient is due to the gas being diverted by the passing wing. Several mathematical models fit the observed phenomenon of wing function, but none of them "Explains why it happens" except that the wing accelerates air one way, and the air applies an equal and opposite force in the other direction... lift. Please gentlemen (and ladies if any), apply basic physics to all of your arguments. If the physics does not provide a COMPLETE explanation of the phenomena, then it does not provide anything but heresay or opinion, neither of which helps. Dave 2-1-2006

Sounds like you're attacking the incorrect "popular explanation," not the Bernoulli explanation. The "popular explanation" is also called the "equal transit-time explanation," and says that parcels divided by the leading edge must rejoin at the trailing edge. But if I guessed wrong... then what do you mean by "Bernoulli explanation?" You'd need to define it first before insisting that it's wrong. --Wjbeaty 21:10, 10 January 2006 (UTC)

[Dave's reply] Bernoulli's equation is totally correct within it's stated limitations. It says that the sum of all of the various types of energy in the fluid at one place must be the same as the sum of all the forms of energy at another place in a continuous fluid flow path provided no energy is added or subtracted (and that is all it says). No I am not attacking "the equal transit time falacy". That has been done very effectively elsewhere. I am attacking the explanation of wing lift that says "air goes faster over a wing than under it (for whatever reason), and because of the bernoulli effect the air above the wing therefore has lower pressure than the air below it". Please re-read my explanation above. The only thing that will ever cause air to accelerate is a pressure gradient... Where did that come from to cause the air to accelerate in order to produce the needed pressure gradient to provide lift? Sounds dumb because it is dumb. the pressure gradient above the wing is clearly produced by the acceleration of air downward because the wing is deflecting air downward. (the Newtonian version simply and clearly states this, and it is obviously correct). So the Newtonian explanation shows us why the pressure above a wing is lower, and the pressure under it is higher than the air distant from the wing. This pressure gradient around the wing directly causes the changes in velocity of the air around the wing.Dave 23-Jan-2006

I'm not sure what he meant, but saying Bernoulli is "wrong" is like saying Newton's laws are "wrong". Bernoulli only models a fluid from the assumption the velocity field derives from a potential field. It is enough for lift, drag, etc. Simply the values will be off :) CyrilleDunant 06:58, 11 January 2006 (UTC)

[Dave Reply] I never said or implied that Bernboulli or his equation are wrong. Using Bernoullis equation to explain why wings causes lift is wrong. Please look up a more detailed explanation of Bernoullis equation. Velocity is only one of 5 factors in it, and it doesn't mention anything that I would recognise as a "Potential" field.

When you take the integral of the pressure distribution over the surface of the wing, it adds up to the lift. And the velocity does vary with pressure according to Bernoulli's equation. The only error in that common explanation is that there is no reason for the streamlines to meet at the trailing edge.

No this is not the only error. An extreme error is the assumption that there is somehow an unexplained accleration of the air over the top of the wing. Another extreme error is the assumption that "Bernoulli equation says velocity change causes pressure change". It does not. Dave 2-1-2006

This is not true. Bernoulli does not, in fact, say such a thing. It says that pressure, 'kinetic energy', and potential energy are the result of a potential function phi. Now it might be that depending on the wing shape, you will see an acceleration...CyrilleDunant 06:58, 11 January 2006 (UTC)

[Dave Reply](Cyrille, I get the impression that you didn't read what I wrote..) Bernoulli's eqn says ... p + 1/2 rV^2 + rgh = Constant (p = pressure, r = density, V = velocity, g = gravity, and h = height) This is Bernoullis equation. My statement above is true. The shape of a wing NEVER causes an acceleration. Only a net force (or pressure gradient for a fluid) can cause an acceleration. Of course we will see an acceleration of the air along the upper wing surface (and slowing along the under surface). The shape of the wing didn't cause it. The shape of the wing causes air to deflect following the shape of the wing as the air moves past it. This air deflection (acceleration) requires a pressure increase below, and reduction above the wing. The effective movement of the wing surface relative to the airflow causes the pressure changes that cause the air to follow the wing surface. These pressure changes also cause the changes in air velocity along the surfaces above and below the wing. Shape Never causes accelerations along a surface, only a pressure gradient can do this.

Note the formula... F=ma ... a=F/m Note that shape is not one of the terms in this equation. Dave 23 Jan 2006

The explanation that's currently there, using the Coanda effect to explain downwash and thus lift by Newton's 3rd, is absolutely right, and a very good way of explaining it, but it being right does not make the Bernoulli explanation wrong.

I must agree. But the Bernoulli version being absolutely unsubstantiatable when we attempt to explain the whole theory in terms of real physics does make it wrong. Dave 2-1-2006

Another popular way of talking about lift is through circulation. This is widely used by practioners of aerodynamics but not particularly clear to the layperson. It is also absolutely correct.

Circulation theory is an excellent mathematical expression of what is happening around the wing. It does not explain why wings cause lift at all. Dave 2-1-2006

In fact, the three methods I just described of explaining lift can all be proven to be mathematically equivalent to the others.

Yes they are all mathematically similar (but not equivalent) if we ignore several real factors, and assume various parts of the Bernoulli system that cannot be supported.Dave 2-1-2006

Very interesting. I think the article needs some kind of rewrite or reorganisation that makes all of these points. What I did want to ensure however was that the very common "longer path over the top" explanation was well and truly debunked. Most books aimed at the layman use this explanation and it is definitely wrong. Having eliminated that one, the true explanation is then rather harder to get across to someone without going into some moderately advanced physics, so the Newton's 3rd + Coanda is probably the easiest to understand intuitively.

and is the direct correct answer to the question. If you can actually explain where lift comes from in any other terms that really explain anything I'd be interested to see it. Dave 2-1-2006

You are tilting at windmills my friend. As you see below, in my comment signed almost exactly 2 years ago, I state my belief that all the other "explanations" are resultant phenomena, not causative ones. They might describe what's happening in certain different ways, but they do not explain it. The problem (or benefit, if you prefer) of Bernoulli is that mathematically it's a more useful tool than going from Newtonian first principles, and so that's how it is very often taught, and used in practice. People often either forget or never see that in fact they are already one level removed from the underlying cause. I believe that we have actually done quite well in this article in getting to the heart of the matter without throwing out too much baby with the bathwater. There is probably still room for improvement, but from experience I can tell you that this is a surprisingly emotional topic - people are very unwilling to let go of cherished beliefs, even if they are wrong. We are working on it ;-) Graham 04:11, 7 January 2006 (UTC)

I'm not certain what you mean by Tilting at windmills Graham but your response and interaction are appreciated. I fully agree that the versions other than the "Newtonian" explanation are all explanations of the result, not the cause of lift. Given that we have a wind tunnel model or other real model of a wing so we can test it, I cannot see that the Bernoulli version does anything for us at all. Yes we can measure the velocity and accurately calculate local pressures by using bernoulli. We could more easily measure the wing lift force, drag force and turning moment in order to find centre of lift. We do not need to find various local pressures, and if we did, why not just measure them. Of course we cannot use the Newtonian version to calculate the lift of a yet-non-existant wing without doing some very complex (2D at least) finite element calculations (Which do actually provide reasonable accuracy). We cannot use Bernoulli to do so at all. We never know the velocities above and below a new experimental wing before we test it in a wind tunnel. If we are going to test it to find out the wing performance, we will invariably measure lift, drag and moment directly. So where does Bernoulli become useful?. Yes I agree this is useful and important discussion, and I am always surprised at how easily the Bernoulli version of the CAUSE of lift is accepted, and how reluctant anyone is to accept that it does not explain the cause of lift at all. Could I suggest that the article is about "Why does a wing produce lift" if that is what the article is about then to me the only answer is the Newtonian one. All references to Bernoulli are nothing but misleading and supportive of a theory that has been debunked numerouse times. DAF 10-Jan 2006

You raise a good point. I assume Bernoulli is good for something, but that's because I'm not an aerodynamicist and so I just assume that it must come in somewhere when you are designing aircraft "for real". Perhaps you need it to predict stress on skin rivets or something... Or perhaps, as you say, it's useless, and nothing more than a curiosity deriving from first principles. I have designed model aircraft - I just use the lift equation together with published tables of aerofoil data, as at that scale materials pretty much hang together whatever you do; tried and tested techniques are generally used. So in other words, I see no purpose for Bernoulli either, but I just did make the assumption that it has one, to someone, somewhere. As for tilting at windmills, see Don Quixote. Graham 00:17, 10 January 2006 (UTC)

Thanks Graham. I'm familiar with Don Quixote, and can see several possible meanings hence the ?. I have also designed an ultralight and used published wing data. My father did extensive wind tunnel testing of wing shapes, and collected the test results for lift, drag etc. and they don't involve any use of Bernoulli at all. The B eqn can only be used to find pressure if you know the velocity... so you must have measured the velocity... The easiest most practical way to do this is with a bunch of water tube manometers, which provide pressure directly anyway in order to calculate the air velocity in the first place.

The other effects such as pressure differentials, velocities, etc. are to my mind more easily brought into the picture as resultant phenomena rather than causative ones, though as with many things each person has their own preferences as to how a thing is taught/explained. GRAHAMUK 23:06, 1 Dec 2003 (UTC)

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The pressure difference above and below the wing is less important to create lift than one might think. 90% percent of the lift comes from what is called 'downwash'.

All lift is due to the pressure difference above and below the wing. All of this pressure difference is due to the downward acceleration of the air mass. This is basic physics. DAF

Simply a deflection of the airflow. Air is accelerated downwards. Lots of air! This requires a force and already Newton now that that creates an eqally but opposing force. If one looks at the force that the pressure difference creates for a small Cessna, it is only about 1500 N (approximately 300 pounds).

this is only true if that pressure difference is calculated using the Bernoulli version with equal transit times... both of which are invalid. Dave 2-1-2006

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-- The above is correct. In fact, at some level, ALL of the upward force on the wing must be created by accelerating air downward. You can create all the force on the airmass that you want but your plane is gonna fall out of the sky unless you accelate something. The details of fluid dynamics make the process practical. But the primary phenomenon is newton's third law. I've added a paragraph saying so. I think some work still needs to be done tidying up the terms camber, curve and such. I don't have a detailed enough knowledge of airfoils to get that part right. -- Blimpguy - Fri Jan 24 14:39:31 UTC 2003

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For those who will not read the expanded explanation below, I prepend this brief summary:

• Lift can always be accounted for by pressure measurements
• therefore, it is incorrect to say that lift can not be attributed to pressure
• when calculating pressure, terms such as circulation, Bernoulli Effect and Newton's Law (and I will add Navier-Stokes) develop and are all appropriate accountings of Lift, each with its own assumptions about the real world

To explain: I am a NASA engineer and I am always surprised by the bad science on Lift on the internet. Every physical and mathematical description of lift that exists is a model; an approximation of reality (physics itself--down to the superstring--is but an approximation of reality). Some models make more assumptions than others to apply to specific situations and be easier to work with computationally.

Lift does not exist until it is given a definition by people, and it is defined as a force. Right there, assumptions are made about the nature of air and its consistency. As a force, the most accurate accounting of Lift is a measurement. This is done by measuring pressure.

If you will not believe me, perhaps you will believe Dr John D. Anderson, Jr. (Curator of the National Air and Space Museum) and Dr L. Prandtl (Father of Aerodynamics):

In his book, Fundamentals of Aerodynamics, 2nd Ed., Dr John D. Anderson, Jr. states (p218):

"...the true physical sources of the aerodynamic force on a body are the pressure and shear stress distributions exerted on the surface of the body...lift is 'caused' by the net imbalance of the surface pressure distribution..."

(In the above quote, "shear stress" refers to the "aerodynamic force" known as Drag.)

In his book, Applied Hydro- and Aeromechanics, Dr L. Prandtl states:

(p144) "By decomposing the total force into two components, one in the direction of the flow and another perpendicular to the flow, we are led to the conception of lift...In practical aeronautics, we are interested in bodies (airfoils) where the total resulting force is nearly perpendicular to the direction of the flow, so that in this case the lift is great and the drag small."

On the physical origins of this "total force", Prandtl states (p159) "If a body experiences lift, i.e., a force component perpendicular to the flow of the fluid, we can ascribe this phenomenon only to a certain excess pressure on the bottom side of the body and a certain partial vacuum on the top side."

But generally, measuring pressure is not practical. So math is used to calculate it. Along with these math models come useful relationships like "as velocity increases though a constant area, pressure decreases" that apply only to specific and simplified situations.

I will further explain these calculations:

The best models we have are known as the Conservation Equations. These say things such as "any mass going into a system must equal the amount accumulating within the system minus the amount leaving the system because mass is neither created nor destroyed" etc. No one has ever applied these to aeronautics without assumption because the resulting equations are too hard to work with.

The next best model we have are the Navier-Stokes equations. These are derived from the Conservation Equations with some assumptions, such as "the fluid is Newtonian (true for air)", etc. These have a high degree of accuracy but are still difficult to work with, so more assumptions are generally made at the sacrifice of some accuracy. When the assumptions are made intelligently (i.e. apply well to a given situation), not much accuracy is lost. At this level of generalization, one can see Lift's dependance on air temperature (which would still show up in an accurate pressure measurement).

The next best, then, is the circulation equation of Lift (also derived from the Conservation Equations). Assumptions made to arrive at this point include inviscid flow, etc. These equations are good enough for many high-speed situations in which air compressibility is an important factor.

Newton's Law force = mass * acceleration (again, derived from the Conservation Equations) is the next most accurate. Assumptions made to arrive at this point include incompressible flow (good for low speeds only), etc. In this form, the equations can be visualized by the "airfoil pushing air downward" concept. It should be noted here that when aerodynamicists use the term downwash they are referring to the component of the wingtip vortices that is oriented perpendicularly to the freestream velocity, not "the air that is pushed downward by the airfoil"; a definition that certainly developed from pilots or other laymen and could also have been borrowed from helicopter terminology. An important difference between the two is that to aerodynamicists, downwash does not exist for airfoils, which are two-dimensional constructs, but is defined only for a three-dimensional consideration of the entire wing.

The "Bernoulli Effect" is Newton's Law (above) written for fluid flows. In this form, the equations are usually visualized by the "pressure" concept because of the simple relationship between velocity and pressure. This simple relationship only applies accurately to low-speed flight; Lift can not be calculated this way for any other situation because the calculated pressure would not match the measured (thus true) pressure, but nonetheless, Lift is totally accounted for by the true pressure.

As has been said, it is true that as air seperates above and below the wing, the "parcels" of air that were in contact with each other at the leading edge do not come back in contact with each other at the trailing edge. I suppose if a misconception such as that can persist in the public domain with a mighty tenacity, then the current arguments and misconceptions should come as no surprise.

26 Aug 2004 by Lensim

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Hmm. I'm a little confused. I don't think that the article actually says or suggests that "lift can not be attributed to pressure". If so, then it should definitely be fixed. If not, them I'm not sure where the "bad science" is.

It seems to me that there are differences of opinion about how one wishes to think about the phenomenon of lift rather than right vs. wrong. Specifically, aerodynamicists tend to think in terms of pressure differentials and pilots tend to think in terms of Newton's 3rd. My personal opinion is that a description based on Newton is more effective for the untrained reader. From there it seems reasonable to proceed to the other ways of accounting for lift.

So, with that in mind, the use of the term "downwash" in the article is the pilot's meaning rather the aerodynamicist's meaning. I think a description of the two meanings of the term would be an excellent place to start for a "downwash" article. (I would be particularly careful with NPOV here - pilots are not fond of the engineers' habit of lumping them in with "other laymen".) Blimpguy 15:30, 27 Aug 2004 (UTC)

I am a Pilot, and a Graduate Engineer, and I have designed an aircraft, and would generally be accepted among engineers as being very conversant with Newtonian Physics (everything we are discussing falls into such), and I would call that large flow of air moving down behind a wing "Downwash"(nothing to do with wingtip vortices). I would also insist that ALL lift is due to pressure distribution over the wing (and the fuselarge, but not important), and that ALL lift is the result of accelerating the air as the wing passes, and that the net force applied to the aircraft, is equal and opposite to the force applied to the airmass as a whole. These are just different ways to say the same thing. DAF

Sorry for the confusion. When I said "it is incorrect to say that lift can not be attributed to pressure", I wasn't refering to the article, I was actually refering to your comments from 24 Jan 2003 and those above it. If I misinterpreted them, my apologies.

Touche about pilots/engineers...I will mind that. Perhaps I should have said, "so many people love aircraft and aerodynamics, that everyone wants to spread their knowledge, however accurate or inaccurate it may be." Hmm, come to think of it, I probably should avoid explaining the origin of the misconceptions all together.--Mike L (aka Lensim) 22:08, 27 Aug 2004 (UTC)

Lensim - Ah. Yes, that was sloppy/strident of me. Truth be told, I'm not as careful on talk pages as in articles themselves. But, like you, I have my own pet aeronautics crusade. In my case, it is that Newton's 3rd too often gets "lost in the sauce" when discussing airfoils. I know a fair number of folks (both pilots and engineers by the way) who think that pressure gradiants somehow, in and of themselves, "magically" levitate airplanes. In other words, they have never made the connection between the pressure differentials on the airfoil surfaces and the downward acceleration of the airstream. But, just to be completely clear, do you think the Newton's 3rd part of the story is a "misconception" of some sort? Are there other factual errors in the article that should be addressed? Blimpguy 19:10, 28 Aug 2004 (UTC)

If one wants to associate Lift--a measureable force--with a "downward acceleration of the airstream" they are free to do so. However, this is useful only as a theoretical mind experiment that seems to satisfy some people's curiosity as to how aircraft can fly. Dr's Anderson and Prandtl (refer to the quotes in my 26 August 2004 post) would say that this explanation is not a good physical explanation of Lift and furthermore the only good physical explanation is pressure. All others are theoretical and based on models. Note the following points:

• As a measureable quantity, Lift can be completely accounted for by measuring the pressure changes about the entire aircraft.
• As a measurable quantity, it is impracticle to account for lift by measuring the acceleration of the air mass about the entire aircraft, and no one has ever done so, not even for a helicopter.
• When one does want to imagine Lift as a "downward acceleration of the airstream", it is not practical to imagine a stream of air accelerating off the wing, bearing the aircraft's weight. God forbid this be true, lest we be crushed while watching the 747's land at LaGuardia. And if you've been lucky enough to have the Thunderbirds fly low and fast directly above you as they cut perpendicular to the main flightline at an airshow, you know from experience that you don't feel the aircraft's weight even at low altitude. Rather, when imagining this, imagine the aircraft's weight spread over the infinity of air -- thus the theoretical nature of this visualization. But it is not a misconception to think this way; it is just not physically realizable (just as circulation is theoretical and also not physically realizable). Prandlt himself was fond of imagining "an aircraft's weight as it is transfered to the ground".
• The following is a misconception: "Lift develops from pressure differences AND Newton's thrid law" or "one factor in Lift is Newton's third law" etc. It is one or the other, and when it comes to measuring Lift it is always pressure.

I disagree. Newton’s Laws are absolute (within the valid realm). However they do not describe mechanisms. Pressure is the core of the mechanism. A pressure gradient is the only way that air can be accelerated and pressure is also the only (inviscid) way that a gas can transfer force to a solid (lift).

A wing experiences lift because of the pressure regions and these also must accelerate the air. Newton’s laws are honoured. The air is not like the ground, it does not provide a reaction if a load is put upon it; instead we need to provide something to oppose the lift, which is the acceleration of the air. Thus both Newton and pressure apply.Rolo Tamasi 23:11, 24 September 2007 (UTC)

• I would consider a statement such as "downward acceleration of the air" to be more of an answer to the question "how does an aircraft fly"--more philosophy than science, than an answer to the question "how is Lift derived".

It is a matter of great curiosity to me when a person decides he or she "knows how an aircraft flies". Truly, to the highest level of resolution of reality possible, we do not know. To the highest level of resolution of reality we can currently muster, all aerodynamic forces are due to electromagnetic interactions (as opposed to the other three fundamental interactions: gravity, strong and weak) amongst air molecules and those of the wing; but even this is but a model of reality, and one that is way too hard for engineers to work with. Most engineers are satisfied when they can produce repeatable and useful measurements, and this they do with pressure considerations. Others are free to imagine as they wish...have fun!

--Lensim 01:40, 29 Aug 2004 (UTC)

This same type of argument (electromagnetic interactions.. imprecise models etc..) can be applied to the understanding of absolutely anything. It can also be truly said that we can never know anything to be absolutely true. Both of these arguments are true, and both serve no useful purpose while we are trying to develop an understanding of something at the "Real world" level. In a realistic analysis of aerodynamics, and in particular when we are trying to clarify in this publication "Why does a wing produce lift", Newtonian physics (including all of it's assumptions and simplifications) is absolutely adequate and totaly valid. Dave 23 Jan 2006

I would be careful in saying that circulation is not physically realizable. I'm not sure where you got the idea, really. Consider what the Magnus effect says: that a rotating body in a fluid flow with an axis of rotation perpendicular to the flow will feel a lateral force as a result of its rotation. The key point is that this would work for say, a cylinder--lift would be generated even though a cylindrical tube has no camber and can not have any angle of attack. For the cylinder, the circulation is simply proportional to its rotational speed. In any event, circulation is most definitely "physically realizable," even if our model for it is only an approximation.

--boeman

Lensim- Would you be so kind as to modify your comment and put it in the article for Lift (force) A section on the general causes and pysics behind lift would be nice. Theon 18:23, Aug 27, 2004 (UTC)

Certainly. So as to not step on any toes, I will familiarize myself more with wikipedia etiquete first though.

Where there is an existing page (as in this case) the best approach is usually to improve/fix the existing text rather than replacing/duplicating. Also working on particular bits rather than large-scale rewrites allows others the opportunity to work with you and minimizes the chances of the dreaded revert war. Nonetheless, don't be shy. Help is always appreciated. Regards. Blimpguy 20:24, 28 Aug 2004 (UTC)

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I need some help here. I seem to have two difficulties with this article, regarding the general disdain towards the "Bernoulli principle". First of all, I do vaguely recall having learned in physics class that viscosity *is* crucial to lift. Are you sure I got it wrong? If not, doesn't viscosity account for the inability to explain lift in terms of the Bernoulli principle? Most webpages that rule out Bernoulli's (like Jeff Ruskin's) assume *laminar flow* - which I find a strange assumption. I do recall reading a couple of sources claiming that without viscosity, you get very poor lift. Also, regarding the "coanda effect" and the use of Newton's third law, I think the article is making the same mistake again. I would have accepted these as alternatives to the use of Bernoullii's principle if they were independant explanations. Trouble is, if not for the Bernoulli force and pressure gradients, what, in heaven's name, could possibly deflect the stream of air *from the top of the wing downwards*??? [User:mousomer|mousomer]] 18:24, 9 Nov 2004 (UTC)

In answering: "what, in heaven's name, could possibly deflect the stream of air *from the top of the wing downwards*?", I will ask: what would stop the air moving downwards? My answer is *not a thing*. An object moves through a fluid, and displaces the fluid in the process. The displaced fluid coalesces around the object, remaining attached if the adverse pressure gradient is not too large. If the bottom of the object creates a trailing downward bias in the surrounding fluid, the top fluid will flow down into the space the airfoil created behind and below the trailing edge. 24.131.137.3 01:49, 21 December 2005 (UTC)

More answer.. Viscosity has NOTHING to do with the cause of lift. It does account for some drag on a wing but not a large proportion of the wing drag (I'm guessing 1% to 6%). The Bernoulli version of the cause of lift makes several invalid assumptions listed at the top of this discussion. None of these invalid assumptions has anything to do with viscosity. Some people misunderstand the Coanda effect and incorrectly assume that it needs viscosity to cause it. The Coanda effect very simply demonstrated... we have a flat plate in a fluid but with a gap (not a bubble, but a vacuum) between the top surface and the fluid near it. The fluid is under pressure (just like air is .. 14 psi). The fluid will obviously rush in to fill the gap. So in reality no such gap will exist in the first place. so if we move the plate at some angle through the fluid so that the "Upper" surface effectively moves away from the fluid, the fluid will follow it. if the plate is being used as a wing, then the fluid above the wing will move down to stay in touch with the wing surface as the wing passes. this tendency of a fluid to follow the wing as the wing moves (or curves) away from it is the coanda effect. As air flows over the top of a wing, it could go straight back and not divert downward leaving a "triangle" of air fixed to the top of the wing.. but this air would have moving air above it, dragging the upper part of the "following" air back with the moving air, then the next part of it etc, until all of it had been dragged out of the area above the wing. Again the air flow will end up following the wing surface down. If the curved surface changes direction too rapidly, then the kinetic energy of the moving air will be such that the pressure needed to make the air curve abruptly to follow the wing shape will be more than the pressure needed to suck some air in from behind the wing. This sucked-in air then circulates above the wing forward along the wing surface and backward with the primary airflow (generally it forms a row of rotating air cylinders). This is called turbulence, and the wing is said to have stalled. The obvious result is substantially reduced lift and increased drag. When a wing stalls the Coanda effect is insufficient to maintain nominally laminar flow. Dave 23 Jan 2006

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The Newton's third and Bernoulli explanations are not alternative theories explaining lift. Rather they are different ways of looking at the same phenomenon. Both explanations are valid, but they are useful to different people. Pilots tend to think in terms of the air being shoved downward. Such a view relates in a straightfoward way to the way that an airplane behaves at different speeds and angles of attack. However engineers tend to think in terms of pressure gradiants because they are much easier to model mathamatically.

The "disdain for Bernoulli" is a disagreement over pedagogy, not physics.

No . There is nothing wrong with Bernoulli. And the Bernoulli explanation of lift is invalid.

I don't know enough about fluid dynamics to comment on the other issues you raise.

Blimpguy 19:11, 9 Nov 2004 (UTC)

The newtonian explanation for lift (mind you lets discuss only subsonic flight for the moment) is also incorrect. If yyou run the numbers you find that an airplane will not fly. The BEST way to describe lift is the way that every single aerodynamicist, aero engineer, and fluid dynamics engineer measures, and creates it. Graph the Cp versus %chord length curve. This is done for both the upper and lower surfaces of an airfoil, and the area found by integrating between the curves is the lift. Call it what you must, and explain it via circulation, Bernoulli, or any other system, but in the end, it is simply the difference of the relative pressures above and below the surface. The Bernoulli explanation, it should be noted, is also used in the design and implementation of windtunnels. It is an approximation for the behavior of flow in an incompressible state, and in that range of velocities where we see a more or less incompressible fluid (below about Mach .6) it works very well. 164.107.199.93 15:44, 24 January 2007 (UTC)Jason Mead

Problems with the Boundary Layer discussion

I'm troubled by an error in the paragraph discussing the boundary layer (BL). I'd like to know if any contributors can suggest more accurate language.

The first part of the discussion is limited to definitions, and a concise description of the main differences between laminar and turbulent BL. Unfortunately it goes on to associate the starting vortex with BL separation, and this is incorrect. A starting vortex occurs any time the section lift (circulation) changes. This is required by Helmholtz's laws of vorticity. The state of the BL is not a driving factor in this, and starting vortexes occur - mathematically - in unsteady inviscid flows where there is no BL.

I'm wondering if there's a need to introduce the concept of the starting vortex in a general discussion of aerodynamic lift. It's a pretty advanced concept, and not one I'm used to seeing in overviews for the general public.

What do you think?

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Not advanced at all and can be produced in a bathtub. Please see the entry near the end below entitled, "The Missing Piece of the Puzzle: Air Mass?" AnthonyChessick 16:31, 1 August 2006 (UTC)

I think you'll find that starting vortices can only be produced by viscous effects (ie BL separation). They only occur "mathematically" by way of the Kutta condition which is simply a logical rule to describe viscous flows during inviscid treatment. The state of the BL is irrelevant as separation will always occur at the sharp trailing edge prior to the starting vortex being formed and circulation established. 14:41, 1 April 2006 (UTC)Thilee

Thilee, see the entry near the end below entitled, "The Missing Piece of the Puzzle: Air Mass?" AnthonyChessick 16:31, 1 August 2006 (UTC)

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Maybe we're having a problem with definitions rather than physics. What I, and all the practicing aerodynamicists I know, call a starting vortex is left behind whenever the circulation changes. It is required by the Conservation of Energy, whether the fluid is viscous or not, and it's certainly not produced by boundary layer separation. If you change the circulation of a bound vortex, you must have a mirror image of that change - the starting vortex - or you've spontaneously created energy out of nothing.

What I meant when I described the concept as 'advanced' is that it's superfluous in a general discussion of fluid dynamic lift. Even the overwhelming majority of aeronautical engineers will go through their entire careers without having to analyze the time-varying effects of a starting vortex. The time rate of change of circulation is normally small, and the flow effects induced by a starting vortex decrease with the square of the distance as it moves downstream. That makes it a second-order effect, at best, which is safely neglected in nearly all design and analysis problems. 169.143.0.103 16:55, 18 June 2007 (UTC)

Lift underwater

What about underwater lift? The article is focused on air, not water. I think dynamic lift needs to be merged into this article, but I'm not an expert. Any ideas on how this should be done? KJ 04:30, 2005 Feb 26 (UTC)

Kjoonlee, see the entry near the end below entitled, "The Missing Piece of the Puzzle: Air Mass?" AnthonyChessick 16:31, 1 August 2006 (UTC)

There isn't any difference in the underlying physics bewteen lift in air versus water. Both media are "fluids", and follow the same governing equations. The only difference would be the equations of state, and then only if considering compressible wing theory. Lift is from the same mechanism in both air and water; Fluid is turned downwards, an equal and opposite force pushes the wing upwards. -vmg

about your (great) artical on lift

You said that you wanted to make it easy for anyone to understand you, so let me congratulate you on doing just that.

The problem is that you failed to mention some of the measuring units. I just assumed that since you measured pressure in kg per m2, you where using the metric system but my calculations lead me to suspect otherwise.

I assumed that the wing surfaces where in m2, velocity in km per hour and lift in kilos.

I am not really sure how you can get back in touch with me, so if you could update the lift-page with the correct units I would be one happy wannabenerd!

Thanks a lot, Jesper.

Jesper -- The discussion does not use units of measure because such units are only meaningful/necessary when one is making measurements and/or calculations. When a discussion is entirely abstract, as this one is, units are irrelevant. So, for instance, I can say that the momentum of an object is defined as its mass times its velocity. This is true regardless of whether one chooses to express mass in terms of grams or slugs. So, in fact, there are no "correct" units per se. You should feel free to use your favorite set -- if you are happy with Pascals for pressure, and grams for mass, etc then just think in terms of those. Regards,Blimpguy 00:58, 3 April 2006 (UTC)

The problem is that while you can present a sort of generic formula, you need to use a set of units consistent with each other and that particular formulation for it to work. For example, you could use any coherent system of units such as SI. But then you'd need to have area in square meters, velocity in meters per second, and lift in newtons. Or you could use the absolute fps system with square feet for area, poundals for lift, foot-poundals per square inch for pressure, etc. Or various other sets of units consistent with the formulas given. Anything else, and you need to use the more general form with a constant to account for the necessary uit conversions, or you need to convert to those units before calculating, and convert from them if you want the result in different units. In particular, there is no generally used system of consistent units which would have pascals for pressure and grams for mass. Gene Nygaard 01:16, 3 April 2006 (UTC)

Gene Nygaard, please see the entry near the end below entitled, "The Missing Piece of the Puzzle: Air Mass?" AnthonyChessick 16:31, 1 August 2006 (UTC)

SEVERE Error - D'Alembert's Paradox

This article incorrectly states that D'Alembert's Paradox says that an inviscid flow around an airfoil will generate no force and therefore no lift. This is entirely incorrect. D'Alembert's Paradox states that an inviscid flow causes no *drag* -- it still predicts lift through Bernoulli's Principle. In fact, the calculation of lift using Bernoulli's Principle is usually done making the inviscid assumption. I will be correcting the article to reflect this.-boeman

addition: Upon further reflection, none of the paragraph in question had anything to do with Bernoulli's Principle at all, so I removed it entirely. The paragraph moved its focus from D'Alembert to the Kutta Condition. The Kutta Condition should go in with circulation if it's going to be included. I may add it in there later.

Reinstating the debate, Newton/Bernoulli

This debate has, somewhat like the article itself, become a little disarrayed. It's hard to know where responses should be inserted, since it looks as if other parts are out of order. I'd like to contribute something, but it's hard to know exactly what stage the debate has reached - as far as I can see little or no progress has been made since about August last year (2004). There appear to be a number of worthwhile points made here, by Lensim and others (Lensim, could you sign ALL your entries please - it would help a lot - just append each one with four tildes (~). Even just knowing the dates is a great aid to following the course of a discussion.).

For me, there is no paradox between the Newton vs. Bernoulli explanations - or Acceleration vs. Pressure if you prefer. I agree with Lensim that the acceleration approach is less practical from an engineering perspective, since it's unmeasurable. However, it MUST be happening - planes stay in the air after all - there is a force acting on them opposing gravity, and that force arises from the reaction of the downward acceleration of the air. I think we can, simply from the most basic principle, accept that. In practice the discussion of pressure is probably much more fruitful however, since that is what can be measured, and is what designers and aerodynamicists work with in real life. Since this is also a valid and equally useful way of looking at the problem, we need not settle on "one or the other", but simply incorporate both ideas into the article. Both exist, both are valid. The argument seems to me to be about which came first - which one is cause and which is effect. Maybe it simply doesn't matter, or cannot be determined.

Lensim states that the acceleration approach is not useful for engineers, and that is probably true. It doesn't mean it is not useful to mention in an encyclopedia aimed at mostly non-engineers, who may find the acceleration explanation easier to comprehend. It also doesn't mean that the pressure explanation is incorrect or should be discounted. However, I do take issue with some of Lensim's arguments against the acceleration approach, since they are erroneous. It does not follow at all from the considerations of acceleration that this force is transferred to the ground, or to anyone standing underneath an aircraft flying overhead. The force is transferred wholly to the aircraft - that's what keeps it in the air! There is no net force "left over" that could be felt underneath - the force is doing work levitating the plane. However, this glaring error apart, I generally agree with Lensim's comments. It's not Newton OR Bernoulli, (or Newton AND Bernoulli if you see it that way), but rather both explanations are equally valid and are each other's consequence. Disentangling them is impossible, so perhaps we would be better off moving this argument forward not by trying to decide WHICH is correct, but by deciding how we can incorporate these ideas into the article in a way that is as informative as possible for the readers of wikipedia, without oversimplifying or dumbing down. As Einstein once said, we need an explanation that is a simple as possible, but no simpler.Graham 00:17, 17 May 2005 (UTC)

Not Quite

Graham: "It does not follow at all from the considerations of acceleration that this force is transferred to the ground, or to anyone standing underneath an aircraft flying overhead. The force is transferred wholly to the aircraft - that's what keeps it in the air! There is no net force "left over" that could be felt underneath - the force is doing work levitating the plane. "

The air is most definitely pushed downwards . To put it simply, the air is pushed down and an equal and opposite reaction pushes the aircraft up (or "The lift of a wing is equal to the change in momentum of the air it is diverting down"). See this excellent page which I have linked to from the main article.

Lensim: "When one does want to imagine Lift as a "downward acceleration of the airstream", it is not practical to imagine a stream of air accelerating off the wing, bearing the aircraft's weight. God forbid this be true, lest we be crushed while watching the 747's land at LaGuardia. And if you've been lucky enough to have the Thunderbirds fly low and fast directly above you as they cut perpendicular to the main flightline at an airshow, you know from experience that you don't feel the aircraft's weight even at low altitude. Rather, when imagining this, imagine the aircraft's weight spread over the infinity of air -- thus the theoretical nature of this visualization. But it is not a misconception to think this way; it is just not physically realizable (just as circulation is theoretical and also not physically realizable). Prandlt himself was fond of imagining "an aircraft's weight as it is transfered to the ground"".

When a child encounters a deep patch of mud he wishes to cross, he might run accross it to avoid sinking. We need to apply the same principle to an aircraft before worrying about being crushed. Let's consider a 747, flying level, with a wing area of 500m² and a speed of 80m/s. The weight of the 747 (say 500,000kg) will be spread over 40,000m² (500 × 80) each second. This amounts to a 12.5kg force over every square metre, or a 0.125kg force on the top of your head (10cm by 10cm). Certainly not enough to crush you. In reality, a proportion (or all) of the downwards air momentum, depending on height, will be dissipated by friction and chaotic air movement rather than being transferred to the ground.

Of course, my knowledge is limited so do take this post with a grain of salt. 211.28.152.172 20:24, 24 August 2005 (UTC)

And yet... Newton???

I have given it quite a lot of thought, but I still don't understand the use of Newton's 3rd in this article. The fact that some people misuse Bernoulli does not grant us the right to misuse other physical principles in return.

That there is a downwash of air I do not question. The Coanda effect is easy to demonstate at home. That this downwash explains lift - this I find questionable. You people claim that the only way to account for the fact the airplane stays up in the air is to counter it's weigh by deflecting enough air downwards. Is it so? When I take a large helium baloon, and use it to lift a radar in the air - do I get a constant downwash of air compensating for the radar's weigh? No one in his right mind would suggest Newton's 3rd law as explanation for the lift produced by a hot-air or helium baloon. The lift generated by baloons is entirely due to pressure gradients, which are the correct way to aggregate the momentum transfer between the balloon and the zilions of air molecules surrounding it. I doubt that the blatant use of Newton's law is any better with airplane lift.

And worse: If anyone takes a look at a flow diagram, it can easily be seen that the air above the wing goes much faster than the air below. This yealds a pressure gradient which is unaccountable by a simple use of Newton's. The downwash of air, after all, is from the BACK if the wing. Most of the pressure is on the FRONT. Am I missing some key issue here? mousomer 19:23, 13 November 2005 (UTC)

Invoking a comparison with lighter-than-air craft is certainly leading you down the garden path, since clearly that principle has nothing to do with how heavier-than-air craft stay airborne. What we can say with absolute certainty is that it takes a force to keep an aircraft in the air - it is a force exactly equal to the weight of the aircraft. So where does this force come from? Force is mass x acceleration. So what mass is being accelerated that creates an upward force equal to the aircraft's weight? Well, it MUST LOGICALLY be a mass of air accelerated downward. It is the only thing that CAN give rise to this force, since there is no physical contact with any other supportive medium, and anti-gravity doesn't exist, as far as we know. That's all we need to know; the Coanda effect, air pressure changes, distribution, etc are all corollary effects that arise as a result of this basic principle. For an engineer, it is often less useful to work from first principles rather than use the corollary effects as a more useful predictive tool - and that is what is done, and perhaps why pressure changes are often invoked as a CAUSE rather than an EFFECT. Practically speaking, it doesn't matter what approach you use as long as the answers are right, but since this article is trying to explain lift, rather than explaining how to design a practical wing, we must naturally start with a discussion of Newton. Also, your assertion that downwash comes off the back of the wing is incorrect (perhaps you're mistaking downwash in this context with the more common use of the term which is the downwash understood by pilots - personally I feel that the use of the term here is unhelpful). The acceleration of the air imparts a force over the whole wing surface, not just the back. It also imparts a force on both sides of the wing. It is not to be thought of as a bombardment of the lower surface by oncoming air molecules, creating a deflection upwards, but rather as a gradual 'turning' of the airflow as it crosses the wing. Both upper and lower surfaces contribute to this, and the overall effect is both much more subtle and much more powerful than a naive visualisation of what is happening might lead you to assume. Graham 22:28, 13 November 2005 (UTC)

I ought to add that the force imparted is not equally distributed: the pressure gradients show how the force is distributed. On re-reading what I wrote I thought it might have given the impression that I thought the force was equally distributed - obviously it's not. Graham 22:34, 13 November 2005 (UTC)

I agree with almost everything you wrote. BUT... First of all, what exactly is holding a hot-air balloon in place? What, if not the air around it? "Well, it MUST LOGICALLY be a mass of air accelerated downward." Taken microscopically, of course you're right - both for the air plane and for the balloon. With the balloon, the air molecules which are deflected from the surface of the balloon carry that momentum downwards. But MACROSCOPICALLY? If by "downwash" all we mean is just air molecules bouncing down from the wing - then I have little doubt it's there. But what I understand from the term "downwash of air" is the existance of a measurable stream of air, with enough momentum to counter the weigh of the airplane, and which survives (as a stream, e.g. it does not disperse immidiately) for a considerable amout of distance/time. Is such a thing really there? We know that airstreams are very important with the caonda effect (which is important in jet engines - because the hot jet might bend and burn the back of the plane), and in lifting the concord. I doubt that air stream carries enough momentum with a normal wing. Maybe it does - I do not know, and I would like to know if anybody knows that. It is also important to understand that air IS a medium. It carries aircrafts - when "tended" the right way. mousomer 13:36, 14 November 2005 (UTC)

Mousomer, please, etc., etc., etc. AnthonyChessick 16:31, 1 August 2006 (UTC)

What we have here is a "forest and trees" issue. One has the choice of describing the operation of an airfoil in terms of the integral of pressure differentials or Newton. The editorial choice needs to be made as to which description is most clear to the unititiated. Seems to me that Newton is the big winner here in terms of clarity. I strongly recommend that you take a look at the book "Understanding Flight" as referenced in the article. They present a brilliantly straightforward and clear-eyed treatment of this topic and base their description on Newton alone. Blimpguy 18:12, 14 November 2005 (UTC)

Mousomer, your question about lighter-than-air craft amounts to: "why do things float?" I'm not sure that thinking of this in terms of momentum being transferred to the heavier air molecules is necessarily helpful, if it's happening at all. Much easier to think of it as the lower density material floating like a bubble up through the heavier material. Gravity pulls the heavier material more strongly downwards, which gets underneath the lighter material and buoys it upwards. This is called displacement. This is NOT what is happening when a wing moves through air. The downwash most definitely does exist, with enough momentum to counter the weight of the aircraft. I only wish the term downwash were not used for this, since I believe it's confusing - it gives the impression that there would be air 'blowing' down off the wing like what you might feel from a fan... In reality the air itself is not disturbed that much, because the wing itself moves at a considerable speed through it - there is a momentary disturbance as the wing passes, which might affect the air for a short distance ahead of the wing and a longer distance (maybe 10x its chord?) behind it, but then the air returns to its normal behaviour of just sitting there. (It might be more helpful to consider a helicopter, which really does move the air around a lot - if you've ever stood near one when it's lifting off you'll get a much better intuition for just how much force really is being transferred!) You state: I doubt that air stream carries enough momentum with a normal wing. Apart from being proven that it does, in fact, what else COULD carry enough momentum? There is nothing else there! Matter behaves in ways dictated by the natural laws of the universe. We codify some of those laws and give them names, but the matter itself doesn't "decide" which law it's going to follow - it just does its thing. We might look at it one way and say "ah, that's Newton's third", or another way and say "ah, that's Bernoulli". In this case they are equivalent ways of labelling the same phenomenon. The difficulty for the casual observer is that air is invisible, and lift is a velocity-based phenomenon, making it doubly difficult to "see" what is happening - you need to make the air visible AND keep up with the moving wing in order to get a feel for what's happening. A dry description may not help unless you are especially good at building mental models. I have seen some very nice animations on the web which do make this behaviour very plain, I think they might be linked from the article - highly recommended. I also agree with Blimpguy that some further reading would be worthwhile, though I would also say that if our modest article here isn't as clear or as helpful as it could be, it should be improved - resorting to telling someone to 'go read a better book' is a bit of an admission of failure! Graham 23:14, 14 November 2005 (UTC)

I agree. Pointing to the reference is basically punting. Also, to restate the other side of the argument for a moment, Mousomer does, sort of, have a point. In particular, from Archimedes' original analysis, bouyancy arises because of a difference between the fluid pressure exerted on the top of the body and that exerted on the bottom of the body. If the density inside the body is less than the density of the surrounding fluid, then a net upward force (aerostatic lift - aka bouyancy) is created. Thus, Mousomer correctly points out that there exists at least one form of lift (in particular aerostatic lift) that arises from pressure differences on the body unrelated to downwash. He then goes on to pustulate that aerodynamic lift likewise might possibly arise from pressure differences on the body unrelated to downwash. He's wrong of course. Because, in fact, lift does arise from downwash. But the point, that we haven't "proven" it but merely stated it, is a valid one. It's proabably not reasonable of us to demand that Mousomer describe the next step in the analysis by which the pressure differences lead to lift. We should be able to find a way to make the relationship between downwash and aerodynamic lift irrefutably obvious. I for one will need to mull on it and try to come up with such an explanation. Blimpguy 00:44, 15 November 2005 (UTC)

Interesting... the article over at buoyancy is worth a read, in particular where it discusses relating the forces arising from buoyancy to Newton's first law. The key thing is that both the forces on the object and the medium it is floating in need to be considered. If we think of a wing as a device to create artificial buoyancy, perhaps the analysis might bear fruit - it might in theory be consistent with that approach if everything is taken into account - though to my mind this is much more oblique than the usual way of thinking about lift, and probably not of any benefit - and assuming that it IS consistent with buoyancy, which is not obvious to me. You still have to have the transfer of momentum to the airstream in order to cause the pressure differences, which in turn can be seen as 'faking' buoyancy - but at this point you've already assumed the transfer of momentum - it doesn't seem to me that you can start with buoyancy and work backwards to derive the existence of the downwash - the dynamic effects of the aerofoil and so forth are completely ignored by a purely static analysis. And we know that a wing doesn't create any lift at all if there is no airflow, so it doesn't seem to me that this approach is useful. There, I've talked myself out of it...! Graham 03:19, 15 November 2005 (UTC)

Let me first remark that (at last) I'm immensely enjoying the discussion. I would bet that buoyancy would be an interesting addendum to the article - even if only to explain the difference between it and lift. On my main point, however, I still stand unconvinced: there is a gap between microscopic and macroscopic phenomena. That there is an aggregate of microscopic momenta transfer - this is trivial. Are these momenta actually capable, in real atmospheric conditions, to add up to a considerable stream of air shooting down from the wing? - This is the question. In my eyes, the use of the term "downwash of air" and the use of Newton's 3rd (or Coanda effect) are implicitly suggesting that the answer is in the positive. It might just be so, but I have seen no evidence of that. The reason I like the "pressure gradient" explanation, is that it does not suggest any such thing. Do any of you remember the derivation of Bernoulli's principle? It is derived FROM Newton’s laws, by integrating on layers of air - it is basically a method of passing from microscopic considerations to macroscopic phenomena. As far as engineering goes, it seems to me that real aerodynamics is done using the very complicated Navier-Stocks equation, to which Bernoulli's law is a (somewhat inaccurate) approximation. This article does not have to be as accurate as to give the numerical methods being used in the industry to study the Navier-Stocks equation. Our job here is to produce interesting intermediate-level physical intuitions. As such, the inaccurate use of Bernoulli seems to me to be fine, as long as it is stated to be a crude approximation. I would agree that the use of the Coanda effect or Newton's 3rd would are as acceptable - only you convince me that there is MACROSCOPICAL, measurable, downwash. And the mentioning of the Helicopter issue isn't very convincing. A helicopter's wing to and airplane wing is like a propeller to a fin. mousomer 11:30, 15 November 2005 (UTC)

A propellor/helicopter blade and a wing do not differ in any significant respect - only the way that the relative airflow is created differs. It doesn't matter if a blade is being spun through the air or is attached to a fast-moving aircraft, how lift is produced is the same. To be honest I can't see how I can say anything likely to convince you - I don't understand the distinction you are trying to draw between micro- and macroscopic effects. If, as you seem to accept, there is a large number of small momentum transfers going on, why do you have a problem with the sum of those transfers adding up to a considerable amount (and in fact equal and opposite to the aircraft's weight)? The Navier-Stokes Equations are notoriously difficult to solve, and in fact are unsolvable for any but the most trivial of cases. Bernoulli is more useful because it gives a practical and easy to use tool for predicting lift, more useful than a direct consideration of Newton would do. This doesn't mean Newton should be discounted or relegated to a footnote - what is really happening is that momentum is transferred downwards, and the lift force is simply mass x acceleration of the air in question. If just repeating this as fact doesn't convince (as well it might not!), then why not try re-arranging the classic lift equation to give you the momentum of the air in question. You'll see it works - which is just as well, since the lift equation does correctly predict the lift force obtained by a given wing at a given airspeed (and, a key point to note with the equation is that lift is proportional to the square of velocity - so the force builds up rapidly with airspeed - it's not a linear relationship). The lift equation is based on the assumption that all of the lift is created simply by a downward acceleration of the air mass, so if the word argument doesn't convince you, perhaps the numerical one will! Graham 11:52, 15 November 2005 (UTC)

Mousomer, we didn't make this stuff up. In particular, the chap who teaches fluid dynamics at my local university (a Stanford PhD and whose research focus is also fluid dynamics -- i.e. he's a serious guy who is by no means afraid of complicated math) complains at great length about how students routinely get wrapped up in the mathmatics of lift and loose sight of the basic underlying phenomenon. To paraphrase his words: "Airfoils work by pushing air down. Efficient airfoils are shaped such that the air gets 'whipped over the top' and essentially 'thrown' down. The rest is minutia." Anderson and Eberhardt (Understanding Flight) have an interesting discussion of how all books on flight prior to the 1940's discussed lift in terms of Newton. Somewhere in that timeframe, for reasons unknown, the fashion became to describe lift in terms of Bernoulli. This may have been more interesting for engineers, but it was a very bad thing for pilots. Bernoulli is of no use whatsoever to pilots. In contrast, Newton is critical to developing an intuitive understanding of the relationship between angle of attack and airspeed in producing lift. But in the end, your own struggle to get your head around this basic fact is strong testimony as to why the Bernoulli approach is a bad place to start the story. So Anderson and Eberhardt, amongst others, are trying to get back to the Newtonian basics. I think the article provides an important service by also helping to break the cycle of unnecessary overcomplication. Blimpguy 13:14, 15 November 2005 (UTC)

Request for ID of variables

The section on Bernoulli fails to identify the variables used in the equation. (The other two sections thankfully provide definitions). Some of them a non-specialist can guess at, but the article really should define them. The Bernoulli article gives a different equation, so it does not help. --Blainster 11:26, 4 August 2005 (UTC)

Thank you for making this addition, CyrilleDunant. I am assuming that the frontier of the domain carries units of area, that is, an increment of area. Is that correct? --Blainster 21:55, 4 August 2005 (UTC)

no, no, it is the frontier, the unit is a length (in 2D, of course, in 3D it would be an area :) )! --CyrilleDunant 05:17, 5 August 2005 (UTC)

Newton

Remark; all units in the formula below are assumed to be SI (meter, second, kilogram for mass, Newton for force, Pascal for pressure) My entry to Wikipedia has been reading Jef Raskins vision about lift. Among other sources when trying to understand what was going on was this Wikipedia article. I have made a description on the Dutch Wikipedia lift page. For a newcomer like me (I am an electrical engineer and windsurfer, also interested in wind mills), the end result was that an intuitive explanation of lift of an airfoil is the deflection of air downwards. The pressure differences that result from "bending the air downwards" also result in speed differences and this is exactly what Bernouilli tells us. All the professional calculations are correct of course, but do not give much insight in the reason for lift. Saying that lift is induced by pressure differences does not explain anything, but is just a needed fact for lift as anybody with basic insight in physics will understand. (and these pressure differences are linked speed differences as Bernouilli teaches us).

Force on deflected mass of air

Now, for me it was interesting to make a calculation of the amount of deflected air, needed to explain lift in this way.

Mass m being deflected over an angle $\alpha$ will need a force F to deflect it. Assuming a circular defection path with radius r, we get:

$F={\frac {m.v^{2}}{r}}$ (1)

The mass of air being deflected over an angle $\alpha$ in a layer with height h and width s is:

$m=\rho .h.s.r.\alpha {\frac {}{}}$. (2)

Substituting (2) in (1) gives:

$F=\rho .v^{2}.\alpha .s.h{\frac {}{}}$ (3)

Now we asuume that all air over a certain height h is effectively deflected downward over an angle $\alpha$ and not deflected at all outside this height (this is never true of course, for real calculations we would need the professional calculation methods). Also not all force is transferred to the airfoil, pressure forces "leak around the airfoil".

Now writing the lift formula as :

$F_{L}=C_{L}.\rho .{\frac {V^{2}}{2}}.s.b$ (4),

With s the width of airfoil, and b the airfoil chord.

we can calculate the heigt h under certain asumptions and using "measured data"

I will assume that C_L = 1 is for a deflection angle (this is larger then the angle of attack for a good airfoil) $\alpha$ = 10 º (0,17 radians) we find for h:

$h={\frac {C_{L}.b}{2.\alpha }}=3b$ (5).

This seams a reasonable value for the height (3 times the airfoil chord b)

File:Airfoil airflowl.png

airflow around an airfoil

This is of course a very rough approximation. In reality air defecton and air speed varies with height and once again the professional calculation methods take this into account.

A consequence of the speed differences is that lift is produced for 2/3 at the top side of an airfoil and for 1/3 at the bottom side (that is the average underpressure at the top side is twice the overpressure at the bottom side (from the German wikipedia wing page).

My main concern about the Bernouilli explanation is the popular explanation that is very often used for the speed differences, as I saw this recently once again on a Dutch web page, made by scholars: since the air particles want to be at the end of the wing at the same time they must flow faster at the top side, since they have a longer distance to travel. This is of course complete nonsense.

Explanation illustration:

• Brown = lift,
• P+ overpressure
• P- under pressure
• grey drag
• Blue air speed and direction
• green streamlines

The image may have to be redrawn, since it does not give a practicle situation for a normal flying airplane, the chord is then almost horizontally.

My own description on the Dutch wikipedia page starts with: Suppose you are in a storm holding a piece of plywood in horizontal position. You will hardly feel any force. Now push the downwind side of the plywood low, you will feel an upward force, caused by the reaction of bending the wind downwards. For a good airfoil the flat plate does not work very well, ....etc , and then the remark of a special profile on the top side, because otherwise the wind would not follow the airfoil (go straight through, and cause turbulences), and the Coanda effect as indicator of air to follow the surface being bended downwards and create under pressure and lift as th reaction force. As primary source of lift the reaction forvce of air being bent downwards is given in my own description, followed by the remark that the pressure differences in turn cause speed differences (the underpressure at the top side of the airfoil accelarates the air (pulls in the air), the over pressure at the bottom side slows down the air, and effectively pushes the air upwards to the top side. The resultig stream profile, as shown in the illustration, can be very confusing, since the airflow upward direction "camouflates the net downward bending, but it can be shown that the direction of air leaving the airfoil at the end is determinative for developped force.

Once reading again the article, I stil find the explanation in terms of circulation and rotation difficult to undertsand. The calculations are correct of course, but it does not give an explanation, just a calculation method, and may should be presentes as such; "Calculation of lift ....etc".

Also the notion that Bernouilli gives "another" explanation I think is not true. Pressure differences are linked to speed differences, and that is Bernouilli.

The problem for Wikipedia is that content should reflect "an independent description", and the above may possibly not fulfill this requirement.

Gerben49 11:49, 7 August 2005 (UTC)

Gerben49, please see the entry near the end below entitled, "The Missing Piece of the Puzzle: Air Mass?" AnthonyChessick 16:31, 1 August 2006 (UTC)

Question about history of explanation-debunking

Question: how old is the debunking of the "path-length" explanation? I encountered the topic myself in 1986 when employed as the head of the tech department at Museum of Science in Boston, and I was arguing with exhibit designers regarding a tiny wind tunnel exhibit with a counterweighted airfoil which lifted off from the "ground" when a fan was turned on. The explanation in the display was too obscure (and is now known to be wrong) but we didn't know about the "path-length" error. Then in 1987 the Swiss aerodynamics professor Klaus Weltner published debunking papers in American Journal of Phyics and later in The Physics Teacher. Are these the first papers which hint at the flawed "equal transit-time" explanation? IIRC he didn't specifically point out the error. Years later, around 1997, another aerodynamicist passed me photos which I posted on my website about lifting force misconception: figures 2 and 3 on http://amasci.com/wing/airgif2.html. These were from 1953 and 1992, but they had no earlier wide exposure as far as I know. Myself and Jan-Olov Newborg started pushing these photos and concepts on the physics community in the late 1990s, and they were picked up by NASA GRC, by Anderson/Eberhardt, and eventually made it into the newspapers. Is there any other timetable besides the one I know? Perhaps the problem was widely discussed in the European aero community? If not, then the flawed explanation survived essentially ignored and unquestioned by the professional community until the LATE 1990s!!! If my version is accurate, then this is no ancient well-known debate, instead it's a widespread error recognized by a few lone voices, and which only popped into communal awareness a few years ago, and where the internet, in the form of newsgroup-crusaders on SCI.PHYSICS and REC.AVIATION.PILOTING, caused the debate to pass some sort of global threshold where the technical community finally perceived the problem. --Wjbeaty 08:28, 3 October 2005 (UTC)

My not very informed view is that the path-length theory has never been taken seriously by anyone who actually studied aerodynamics. Its perpetuation is by non-technical people who do not take the trouble to understand lift, yet are trying to explain it to people in a non-technical way. You see this repeated in e.g. children's books, but never in a serious BSc-level or above text book. However I don't have any evidence to support this one way or the other except for a few isolated examples of both. Though in the case of the text book I rely on the classic "Mechanics of Flight" by A.C.Kermode, which dates back to before WW2, and certainly doesn't waste time on the path length approach, instead actively debunking it. That said my edition is the 10th, dating from the 1980s, and its text may not reflect the original edition's. Interestingly, I recently visited the Fleet Air Arm museum at Yeovilton, UK, which features a wind-tunnel with a counterweighted aerofoil section like you describe. They also fall into the lazy and wrong "path length" explanation, which I thought was pretty shameful for a museum of its type. I left a stern rebuke in the vistors book! It's interesting that from time to time physicists have felt the need to publish the debunking papers you mention, though I suspect that this is less because they are stating anything new about lift per se, than reflecting their own frustrations with the everday literature that they might have come across that perpetuates the myth. My reasons for saying this is because surely no-one who worked with the path length theory could go ahead and design a practical aircraft - they would soon find that it's a useless method of predicting wing behaviour, and so would have to go and look up the more reliable physical explanation. Again, this is only speculation - perhaps it is possible to design a useful aircraft without understanding lift, just by relying on the lift equation and published empirical data. However you pose an interesting question, and seem to have tapped into a more reliable source of evidence than I have to hand (I'm generally too lazy to do this sort of hard research!), so you may be right. It would make an interesting thesis to look into the origins of the myth and at what point, if ever, it ceased to be taken as the true explanation. Graham 08:56, 8 October 2005 (UTC)

One point that may have been unclear: the "path length" explanation is a big issue because it has infected pilot training materials, is widely believed to be true by those who teach pilots, and it appears on the pilot licensing exams of various countries including the USA. In other words, if you answer the exam question about lifting force, and DON'T use the "equal transit time" explanation, then you would be marked wrong. I first encountered the topic because of a physicist in Sweden who, with other aerodynamicists there, were fighting to have the pilot licensing exam changed. Years have passed, they succeeded, and I think the USA exam has also been changed. But even so, for the last ten years, if you became a user of rec.aviation.pilot and other formus, and if you dared to question the "equal transit time" explanation of lift... you'd trigger a huge flamewar, as numerous pilots lept to fierce emotional defense of the incorrect material they'd been taught during their training. So, you're probably correct that the error hasn't "infected" the aerodynamics community (but I wouldn't be suprised if it had.) But it certainly has infected other professional communities. It's like a religious war. People who were taught the "equal transit time" explanation, and people whose colleagues were all taught the same wrong explanation, simply cannot face the fact that it's wrong. --Wjbeaty 02:09, 3 December 2005 (UTC)

That's very interesting, and very sad too. The truth is whatever it is, I can't understand people clinging to whatever false belief system they have acquired, once it has been shown to be false - but if it was that easy to ditch the odd beliefs we cherish, I guess religion and war would be ancient history. On the other hand at least here at Wikipedia we have managed to avoid the same trap, and that's something to be proud of! Graham 01:00, 22 December 2005 (UTC)

Two concepts required for understanding

I'd like to introduce two concepts regarding the lifting force controversy which I've never seen mentioned. I discussed them years ago on SCI.PHYSICS when I first realized their importance, but the thread died. When I grasped these for the first time, they cleared up many questions in my mind. I don't quite know how to put these on WP. Perhaps a "lifting force misconceptions" entry would be appropriate?

FIRST CONCEPT: in an airfoil streamline diagram in two dimensions, with a wind-tunnel floor and ceiling present, there's an instantaneous force-pair between the airfoil and the bottom of the wind tunnel, and a second instantaneous force-pair between the airfoil and the ceiling. These are venturi-type forces. They have an interesting property: if we move the floor and ceiling away from the airfoil, the net difference between these force-pairs does not change. In other words, the circulation produced by the airfoil will produce a pressure pattern on the floor and ceiling, and the weight of the airfoil in constant flight will always push the entire wind tunnel downwards. This is basic Newton's-3rd stuff, not complicated at all: reaction forces are not easily escaped. The lifting force in a wind tunnel obeys venturi physics; the forces are double-ended vector phenomena, with equal and opposite force applied to adjacent surfaces. This makes sense, since the pressure pattern created by circulation acting upon the wind tunnel surfaces weakens with increasing distance, yet it expands to a larger pattern with increasing distance, and the two effects cancel out, resulting in a constant downward force equal and opposite to the lift on the airfoil. The net force upon the wind tunnel surfaces is independant of the spacing between floor and ceiling and independant of the vertical position of the airfoil.

The implications are stunning: a two-dimensional airfoil diagram depicts a type of venturi, and the floor/ceiling of the wind tunnel MUST EXIST if we wish to understand the physics. Yet the typical diagram doesn't mention the forces applied to the floor/ceiling, neither does it depict them. Authors wrongly pretend that the floor and ceiling can be erased, and that the 2D airfoil deposits momentum into the air. Unfortunately, if these floor/ceiling surfaces are removed to infinity, the net force applied to them does not decrease. We can't get rid of those surfaces by withdrawing them. Another implication: since the surfaces are always present even if not depicted, and since instantaneous force-pairs are present between wing and floor/ceiling, the two-dimensional airfoil diagram does not depict flight at all. Instead it depicts WIG or "ground effect flight" where a wing has infinite span, or where a wing flys far less than one wingspan above the Earth. This also makes perfect sense: a 2D streamline diagram is an "infinite wing" diagram, and the infinitely-wide wing can never fly high enough to break out of ground-effect flight.

Another note: during ground-effect flight there is no net downwash, instead the upwash ahead of the airfoil and the downwash behind the airfoil are equal, and the lines of circulation are closed, so the airfoil does not really produce a net deflection of air, instead it produces a flow pattern and a pressure pattern which interacts with the distant ground surface: it is a variety of venturi diagram. Let me say that again. The two-dimensional airfoil diagrams used FREAKING EVERYWHERE ...are WRONG. They explain ground-effect flight. They don't explain how airplanes work. An airplane flying at altitude does not rely upon venturi/WIG forces, instead it produces a descending wake: the wing is a "machine" which takes in undisturbed air and leaves it moving downwards; a process which doesn't occur during ground-effect flight.

An airplane normally reacts against the air, not against the surface of the Earth. On the other hand, a two-dimensional airfoil diagram depicts a venturi where the airfoil produces an instantaneous pressure footprint on the floor below the airfoil and on the ceiling surface of the windtunnel, even if those surfaces are infinitely distant. But with a three-dimensional wing, the wing deposits downwards momentum into the oncoming air, and the air forms a descending wake. In a two-dimensional airfoil diagram the wing does not produce a wake and does not leave momentum residing in the air, instead the upstream and downstream flows are mirror-symmetrical, and the airfoil deposits momentum into the wind tunnel surfaces via instantaneous pressure differences (or to be more accurate: pressure differences propagating at the speed of sound.)

This then is probably the main difference between "engineer" viewpoint and "pilot" viewpoint. The "engineer" viewpoint is based on 2D streamline diagrams having infinite wingspan, while the "pilot" viewpoint is based on three-dimensional wings far from the Earth. In a 2D world you can never really fly; you must remain forever trapped in ground-effect mode or "venturi levitation." The explanation of 2D airfoil lift is fundamentally different than the explanation of lift produced by a 3D wing.

Very unsettling, eh? Everything you know is wrong? :)

SECOND CONCEPT: Reaction forces during production of fluid jets are essential to understanding lift. This one is a bit more complicated and subtle, so let's look at an analogy. Suppose you're deep underwater. Suppose you fill a large plastic bag with water and seal it up tight to form a taut balloon. The bag contains several hundred pounds of water. Put your feet against the bag and push off. You both accelerate: you fly in one direction, and the bag flys opposite. Now take another bag from your pocket and quickly repeat the process over and over. Your pocket contains hundreds of these bags. In this way you pull in water from nearly all directions, while also producing a narrow jet of moving water-bags. The "intake" covers nearly 360 degrees solid-angle, while the outflowing jet covers a tiny angle in a particular direction. Your body is driven forward by the difference in momentum between the water in the wide slow intake, versus the momentum of water in the fast narrow jet.

The above explains how ships' propellors work. Propellors act as reaction engines which pull water in from rear, front, and sides, and they expel water as a parallel "beam" surrounded by a hollow cylinder of vorticity. This also is how helicopters fly, and how prop-engine airliners move forward, how jet engines produce thrust. And ...it's also how airplane wings work. A wing takes in air from all directions and then thrusts it in a single downward direction, but this process is somewhat masked by the forward flight. Also, this process doesn't exist at all in 2D streamline diagrams, because in those diagrams wake-downwash and the wingtip trailing vortices cannot exist.

And THAT'S why pilots believe in "Newton reaction flight," while engineers have fallen into the misconception that a two-D streamline diagram somehow contains the explanation of 3D aircraft flight.

Here's another way to put it: physics should be made as simple as possible, but no simpler... and if we try to simplify our explanations of flight by changing a 3D wing streamline diagram into a 2D airfoil diagram, we've stepped over a line into outright error.

PS: Here's my version of the above water-bags explanation applied to wings: http://amasci.com/wing/rotbal.html --Wjbeaty 08:28, 3 October 2005 (UTC)

Does the first concept imply that the equal transit time idea does hold for a real wing flying at altitude? It would seem so, but if not, please explain why. 24.131.137.3 02:54, 21 December 2005 (UTC)

No, equal transit time never works, since regardless of the upper and lower airfoil path lengths, the divided parcels ONLY rejoin each other if upper and lower average velocities are equal and circulation is zero. Pressure difference and lifting force are zero under those conditions. Or in other words, if a wing is creating lift, then the upper parcel must outrace the lower parcel and never rejoin. The larger the lifting force, the more the wing violates the "equal transit time" idea.

The "first concept" above applies to the overall environment of the airfoil, not to the airfoil specifically. The airfoil itself always works the same regardless of whether it's part of a 3D aircraft, or whether it's part of an infinite wing trapped in GE "Ground Effect" mode. The airfoils in realworld wings do the same: they produce lift whether the wing is six inches above the ground or six miles. Yet the overall phenomena can be vastly different: in flight at altitude, the wing applies force only to the air and it leaves a decending wake. But during GE flight the wing applies force to the Earth's surface and there is no wake.--128.95.172.173 00:35, 22 December 2005 (UTC)

Above writer, please see the entry near the end below entitled, "The Missing Piece of the Puzzle: Air Mass?" AnthonyChessick 16:31, 1 August 2006 (UTC)

I wish I could quickly build an open-ended wind tunnel, and a finite span wing, to show this. To avoid the venturi problem Wjbeaty describes, I would point the exit of my open-ended tunnel straight up. Without data, I'm having a difficult time seeing this conclusion. Interestingly, in circa 1988, I took a tour of the Boeing Vertol facility in Philadelphia (as part of an AIAA student group). The large wind tunnel there had an open ceiling and floor (IMS) in the test section. I don't remember if a reason was given. Perhaps the design attempted to reduce the venturi problem, or something else related to vertical flight test articles? --24.131.137.3 02:01, 22 December 2005 (UTC)

There are photos of this experiment online, and diagrams from simulations linked from my Airfoil Misconception page. See the "smoke pulse delay" photos, figures 2 and 3 on my website. Also see the pure math version, fig 3.15 and figs 3.20-3.23 on J. Denker's airfoil page. And for an intuitive approach to explaining entire wings, see down-thrusted disk balloons. Also note: authors usually write as if this "phase delay" stuff is ancient knowledge, but in reality it was only discovered in the 1980s, and the "Old Men" of aerodynamics thought it didn't exist (see Pradtl's diagram, fig. 7 on Physics of flight reviewed by K. Weltner) If even Prandtl made such large errors, and if these errors go back so many decades, it's no wonder that we're confused about airfoil function today. The real problem is that everyone assumes airfoils to be well understood, and this causes people to fight feircely against any suggestion that our understanding needs to be questioned, analyzed, and (vastly!) improved. --Wjbeaty 00:36, 31 December 2005 (UTC)

Do the illustrations on the av8n site model 2-D and 3-D flow? How much span-wise flow occurs over the wing? Does span-wise flow contribute to a relative slowing of chord-wise speed over the top of the wing? If so, how much slowing? --24.131.137.3 02:38, 5 January 2006 (UTC)

suggested merge with Bernoulli

Very bad idea. This pages does a good job of covering multiple ways of accounting for lift. Bernoulli is just one of them.

Likewise, Bernoulli is used in a great variety of fluid flow cases, airfoils are just one of them.

Blimpguy 17:17, 7 October 2005 (UTC)

Well - thats why I only made the suggestion, instead of doing it. But I think the information on this page is actually more informative than the information on the Bernoulli page. Obviously there should be some overlap. But how much? And shouldn't the bernoulli page have everything this one does plus more? --Mikeross 23:02, 7 October 2005 (UTC)

Bernoulli is to lift as Einstein is to mass-energy equivalence. No-one would suggest those two should be merged. Bernoulli is only one way to view lift, bit it isn't itself lift. It also has other applications. I can't see how a merge makes any sense at all. Graham 08:38, 8 October 2005 (UTC)

Lets be clear. No one is suggesting that we merge the two pages. The suggested merge is between the Bernoulli's principle section on the lift page, and the Bernoulli's principle article. The problem is that the article which is entirely dedicated to the Bernoulli's principle is actually missing a lot of information contined in the section on the Lift page. Shouldn't an article devoted to a topic be more informative than a section of a related article? I see two possible solutions:

• Merge all of the information from the section into the article. The section should also reference the article (which it currently does not), so that readers can get more information. Thus, the article would contain all of the information on Bernoulli's principle from the section, plus additional information.
• Merge the content of the article into the section. Then redirect from the article to the Lift page.

I prefer the second solution because it is easier to maintain over the long run, since information is stored in one place (the Lift article). If at a later time, someone contributes a great quantity of information on Bernoulli's priniciple, a separate article could again be created.

--Mikeross 14:28, 10 October 2005 (UTC)

Mikeross, please see the entry near the end below entitled, "The Missing Piece of the Puzzle: Air Mass?" AnthonyChessick 16:31, 1 August 2006 (UTC)

Lift and Sails

This article is fantastic and the debate is fascinating and well-argued. I am a sailing instructor and unfortunately was fed the "longer-path" myth until I heard of the Coanda effect. This is of prime importance to sailors in light-winds where they must make the most of long trailing edges. However, I wonder if you learned aeronautical engineers would like to lend some insight into sails and how they work. Interestingly it is easier to see the falsity of the longer path idea in a sail, where the surface of course has negligible thickness. The air therefore has the same path-length on either side of the canvas. The concept of bending the air, both by deflection and by the Coanda effect are the only plausible explanation. I wonder if this helps lend weight to your argument.

I have always assumed laminar flow is both acquired and desirable across the sail-cloth, but I wonder if anyone knows about turbulent flow and whether this can be beneficial to a sailor. Could we perhaps write a section either under foils or sailing about how a sail works in detail and perhaps add details about more interesting aspects of sail-trim and the non-laminar aspects. I think the myth is often propagated by those who do these sports rather than those that design the craft for the sports.

Interesting point. I'm not really a fluid dynamics guy, so I'll leave it to others to discuss sails per se. However, I have thought that a section on lift in cases other than wings, in particular propellers and sails, would be a good addition. Blimpguy 13:31, 13 October 2005 (UTC)

I think the research done by Arvel Gentry, an aerodynamisit, back in 1971 with respect to thin airfoils (sails are just that) and an updated article from 2006 will do the trick. He has a pdf of his paper here]. The rest of his research can be accessed from [1]. The short answer is that yes, there should be some turbulent flow on the lee side of the sail. This bubble or pocket of air does reattach to the sail and is the best trade off between pointing and speed. Multiple telltales in a line from the luff of the sail back to about a foot or two from the luff will 'show' the size of the bubble and allow the sailor to know how close the sail is to stalling or luffing. HeadSnap (talk) 15:32, 16 January 2008 (UTC)

Laminar/Turbulence

As far as I know turbulence has always to be avoided. It generates extra drag, and at the upper side of a wing (lee side of a sail) will be the onset of the airflow to go straight through, and not bending with the sail surface anymore. For wings techniques are developped that use small holes in the wing through which air is pumped inside, since this prevents the air at the last part of the curvature to become turbulent. The shape of the down wind side of the sail should be optimized (other then for wings) since if the cirvature is not dthere the air would go stright through. At the luff side, the air "has no other choice" the to bend, since it cannot flow through the sail, at the lee side the air flow will leave the sail surface generate turbulenec and extra drag, and generate no lift anymore, if the sail curc. vature has not an optimum curvature. However with saas in siiling and windsurfing, air velocity is relatively low, and there may be other factors that influence the optimum. Reynolds numbers are the indicators.

Gerben49 07:48, 14 November 2005 (UTC)

Not necessarily true. The turbulent flow behaves better than the laminar flow on positive pressure gradients. That is, there is a risk of air "detaching" the upper surface when the pessure increases. For example, what happens in a ball. Turbulent flow stays longer attached to the surface, so avoiding the separation and thus the great drag. You can see small vortex generators in the wings of some aircraft, which disturb the flow. Of course the best would be to have laminar airflow, and that's what is intended to do with laminar wings. Keta 00:39, 17 January 2006 (UTC)

Lift is simple physics

Physics is usually simple or wrong. If I ask "Why does a wing produce lift" and the answer involves "Circulation theory", then I am being told absolutely nothing to answer the question. Similarly but not so clearly, if the answer involves "Bernoulli" then I am also being told nothing that would answer the question any more than saying "Aerodynamics causes lift" would. More importantly it is essential in the whole discussion of aerodynamics and causes of lift to understand that Bernoulli NEVER stated that an increase in velocity causes a decrease in pressure. The Bernoulli equation is an energy balance equation. It does not state what is the cause, or what is the effect. Now going back to simple physics. NOTHING ever changes velocity unless acted upon by a net force... Why would air over a wing go faster? It must have a net force accelerating it. This force is due to the pressure difference above the wing as opposed to that in front of the wing. The air cannot accelerate unless the pressure difference exists to cause it to accelerate. So when any explanation of wing lift starts by saying the air over the wing goes faster, we must ask "WHY would it go faster". There is no answer to this question that fits the Bernoulli explanation. I would think this demands acceptance that the Bernoulli version is rubbish. Yes it fits the measurable wing behaviour provided we dont assume the ludicrouse "equal transit times" assumption. It must fit, because the Bernoulli equation is correct, but the cause and effect relationship necessary to support this theory is always backward. The variation in air speed over or under different parts of a wing are the result of the wing causing lift, not the cause of it.

The simple version... A wing deflects an airflow downward as it passes. This is an inherent acceleration of the air mass, this is inseparable from the need for a change in pressure above and below the wing to cause the acceleration. Arguments about weather it is pressure, or accelerated air causing lift are meaningless.

Why the air below the wing is deflected down is obvious... it cant go through the wing. The air above the wing deflecting downward is the result of the difference in the air pressure above it and the pressure on the wing surface below it accelerating it downward. The reason we dont see the air go straight over the top of the wing leaving a tapered triangle of air moving with the wing between the moving air and the wing top is that such air would be dragged out by the viscosity of the moving air until no such air remains. Dave (B.E.Mech) 2-Jan-2005

Why does the air flow faster over the top? One way to explain this is to compare the usual situation with wing diagrams where the air *DOESN'T* flow faster over the top. For example, on Denker's airfoil page, figure 3.20 shows a tilted wing where the lifting force is zero. The wing is flying in a fluid where viscosity is high and fluid inertia is negligable. Also notice that the fluid approaches the leading edge of the wing in the same fashion that it departs from the trailing edge: it makes a sharp bend around both edges. The pattern of flow is fairly symmetrical, and the average velocity above the wing is the same as the average velocity below... so any parcel which divides at the leading edge will rejoin again after passing the wing. (Also check out his figure 3.17, which better shows the leading/trailing symmetry of this zero-lift state.) There is no average deflection of air, there is no lift, and all the parcels rejoin... yet the wing is tilted to positive AOA! Something is clearly missing. That missing thing is the key to understanding lift.

Now look at the more familiar airfoil diagrams of fig 3.19 and fig 3.22. In these diagrams the inertia of air is dominant. The wing starts "throwing air around" and leaving air moving behind itself. The inertia causes the air to *NOT* make a sharp bend around the trailing edge. Instead the air makes a sharp bend around the leading edge, but then it follows the trailing edge and flows smoothly off. The pattern of flow is no longer symmetrical as it was with the high-viscosity air. And here's the key concept: when the trailing edge starts guiding the air downwards, this could leave a "hole" above the region downward-deflected air, as well as creating a region of high density air below. But rather than the air density changing, instead the velocities change in order to keep the density constant. In other words: air flows faster over the top of the wing in order to fill the "hole" left by the downward-deflected air. And at the same time, air below the wing flows more slowly because it must "get out of the way" of the downward-deflected air.

This HOLE you refer to... I assume you mean low pressure region. If so then you are saying the air rushes in to fill this low pressure region. If so then you are saying there is a low pressure region causing the air to move faster over the top of the wing which causes a low pressure region.... Or are you just restating the Newtonian version of lift? [Dave 23-May-2006]

Doesn't this mean that our simple explanation can ignore most of the wing, while focusing entirely on the angle of the trailing edge? Exactly. Whether the trailing edge is part of a downward-curving camber, or whether it's part of a flat wing that's tilted to positive AOA, in both of these situations the result is the same: the trailing edge deflects the air and the leading edge does not. The rest of the wing experiences the result of this deflection: and the result is a velocity-difference which creates a pressure difference which lifts the wing. It all works out nicely: the wing leaves behind an "exhaust" of downward moving air, and the wing experiences an upward reaction force.. --Wjbeaty 02:40, 7 January 2006 (UTC)

The air flows faster over the top of a wing in normal flight because the pressure above the wing is significantly lower than the surrounding air pressure. If the aircraft flies inverted, the pressure on the bottom of the wing (facing the sky) will be lowest and the air speed over this surface will be fastest. ... and yes the direction of the tail edge of the wing is all about accelerating the air so it will provide a reaction force. The shape of the front of the wing is to penetrate the oncoming air with minimal drag. The curve between the two is chosen to minimise drag (turbulance) for any given lift. It is worth noting that for normal flight and a normal wing section the angle of the leading edge is pointing downward slightly. This can be explained in terms of circulation, but that doesn't tell us much. The pressure under the wing causes air to tend to move forward under the leading edge, and upward in front of the leading edge. The air flow directly in front of the wing is therefore slightly upward relative to the wing, and so the down-facing leading edge penetrates this "new" air directly rather than at some angle relative to the airflow. DAF 10-Jan 2006

Bernoulli is an energy equation.

Bernoulli's equation is a conservation of energy allong streamlines. It alone (as the article explains) gives no insight as to the forces turning the flow. IF there is change in the magnitude of the fluid velocity, the there would be bernoulli contributions to lift, but they would be minor and not anywere on the scale to keep anything aloft. What does give significant enough forces is the conservation of momentum in a turning flow. -vmg

Lift vs Coefficient of Lift

I am looking for a simpler explanation lift and of the term Coefficient of lift. I have been teaching aviation for about 30 years (and while I am living proof that a pilot doesn’t really need to understand this to fly) I would still like a better explanation of the terms. It can even be over simplified "wrong" like most of a pilot’s knowledge of aerodynamic principals seem to be as long as it is useful. Part of my problem is the coefficient of lift is defined with a formula that has a lift in it, and coefficient of lift is used in another formula to define lift. Also neither formula shows the relationship of angle of attack to lift. Can lift be defined with a simple formula that uses variables that a pilot can control?

Back to Coefficient of lift could someone provide an example to illustrate the dimensionless nature of coefficient of lift. I sort of followed the discussion on dimensionless numbers but can’t quite apply it back to coefficient of lift.

--26 April 2006 - TG

Hi there - I'm new to this so I hope I'm editing this in the right way. I think you have an excellent question and whether you realise it or not, your question illustrates some of the points raised elsewhere very well. Equations like the Lift or Drag ones commonly used and mentioned throughout these articles often give the impression of being a law (like Einsteins E=MC²). Somone earlier mentioned that all the various explanations are models of reality and as such they have their uses in the right circumstances, providing the assumptions behind them are understood. This is sound advice indeed. Where confusion creeps in is that equations can be used to express laws(that cannot be violated) or to express observations (8 out of 10 cats prefer tuna).

As the person below rightly states, coefficients are a bit of a cop out. Or more to be a bit more academically correct, they are convenient. They are a convenient way of expressing somthing complex or ill understood, so that 2 or more different things can be compared (eg aircraft, or flight paths, or manoevres). In the case of Lift Coefficient, C_L, or Drag Coefficient, C_D, these have been locked into your aircraft by the designers. Or more precisely the range of them have been locked into the design of your aircraft. So, trying to define what a C_L is in terms of the Lift equation doesent help you that much (a shame, because it's a handy trick that works on many other equations). When you start to get into the detail of how each bit of the aircraft contributes to Lift and Drag (Wing Planform Shape, Sweep, Taper, Anhedral, Aspect Ratio, Paint, Speed,....) you'll soon start to see why C_L and C_D are useful for performance calculations.

I don't know much about training pilots, but maybe a way of bringing it home to them is to do an experiment. At a constant altitude, first fly as slow as possible (just above stall). Measure the angle of aircraft to the horizontal (protractor and plumb line). Then quickly accelerate to maximum speed at that altitude and do the same measurement (hopefully you wont have burned too much fuel so the aircraft weighs roughly the same). You can plot your results on a graph and then get them to predict the C_L for different angles of attack. If you can do this for 2 different types of aircraft (a twin and a single), your students could then start to compare the two sensibly and meaningfully. The aircraft could be physically radically different, but you can compare them sensibly. You can do the experiment with your Leading Edge or Trailing Edge devices deployed too - showing the effect they have on the C_L and Angle of Attack too.

One other way of putting it is "The Pilot chooses a high C_L, in order to keep the aircraft aloft but at a sensible speed for landing. The pilot does this by maintaining a high angle of attack. The pilot may have flaps to assist, which help generate a higher C_L".

If all else fails - an analogy can often help. Two different people can be equally attractive. Their attractiveness coefficient (C_A)is the same. However, if one is the acme of physical perfection but has no personality, the other might be average looking but is funny, wealthy and charismatic. The C_A) might be the same, but it is for totally different reasons!

The best overview of this is Henke Teneke's Simple Science of Flight - where he shows how every animal and aircraft can be compared sensibly, with no more than basic maths skills and a little common sense.

Hope I've helped....

Cheers

Tom Grealy

--12.215.92.251 07:42, 29 January 2006 (UTC)

My view is that physical formulae with "coefficient of ..." terms in them are, in some respects, a cop-out. What they are saying is that the phenomenon is a bit too difficult to unravel, so rather than try we'll just bundle all the "factors" into a number that we can multiply the rest by so that experiment agrees with theory. As long as the "factors" act in a linear fashion, we are OK. This is definitely an oversimplification! But in the case of lift, the coefficient contains essentially two "factors" - the angle of attack and a much less tangible "goodness of the aerofoil" factor. Experiment shows that AoA causes lift to increase almost linearly up to the stall point, but the amount of actual lift produced still varies with the shape of the foil, so rather than try and devise a formula containing AoA (and being an angle, it isn't terribly amenable to being included in a formula containg lots of physical quantities; there is no SI unit for angle for example, and certainly not one that relates to metres, grams and seconds), the multiplier needed to make the experimental results fit the rest of the equation is just wrapped up into a neat little multiplication factor. This works because foil shape is a constant factor - the "goodness" of an aerofoil doesn't depend on airspeed or anything else, it just is as good as it is. The AoA is more or less linear over the region of interest, so we wind up with a number that simply scales the rest. The reason it is dimensionless is because is just a multiplier - you can leave out the coefficient of lift altogether, and dimensionally, the parts of the lift equation remaining still yield a force given an airspeed (squared), an area and a density. Therefore any multiplier has to have no units, otherwise we'd end up with something other than a force! It's also very handy to arrange things this way, because we can look up coefficient of lift for a given aerofoil from a table, or determine it by experiment, and then apply it to any practical design of any size (ignoring scale factors for the moment). I'm not sure if I've made myself very clear here - aerodynamics experts here might find this approach a bit strange, but I'm not a physicist, so I may see things differently. I guess the short answer is that CL represents a "aerofoil goodness factor" which is determined by experiment and the number is chosen to make the physics work. Graham 09:11, 29 January 2006 (UTC)

• Coefficient of lift cannot be used to calculate lift since lift is itself one of its variables, unless co. of lift and all other involved variables are known. The coefficient of lift is used in other calculations (such as finding the coefficient of drag, and stall speed).

A quick illustration why it's dimensionless:

$C_{L}={\frac {L}{q_{\infty }S}}\Rightarrow {\frac {force}{(pressure)(area)}}\Rightarrow {\frac {N}{{N \over m^{2}}m^{2}}}\Rightarrow dimensionless$

L is lift force, q is dynamic pressure (dependant on velocity), S is wing area, N is newtons, and m is meters.

Also, here's a link to a graph illustrating the effect of angle of attack on coefficient of lift.[2] The exact curves are dependant on the type of airfoil, and determined experimentally in wind-tunnels. — TheKMan^talk 18:59, 29 January 2006 (UTC)

plain language restatment of Bernoulli

User 87.112.73.90 added a section that restates the Bernoulli approach to lift in "laymen's terms." I removed the section because it is completely redundant and sort slapped on the end of the article, but I think there is a point to be made here. The text has become very dense and technical, probably more complex than is appropriate for an encyclopedia. I think that less technical explanations would be a good idea somewhere. Should they be interspersed with the more technical descriptions or put into separate section(s)? Blimpguy 20:37, 21 February 2006 (UTC)

The first explanation given in the article, "Reaction due to accelerated air," is not dense and technical. There are no equations in that section. I would also claim that explaining lift thoroughly is just not that simple. The simple, widespread Bernoulli explanation, with its transit time fallacy, is simply wrong. As von Karman said, "When you are talking to technically illiterate people, you must resort to the plausible falsehood, instead of the difficult truth." In the Wikipedia we must present the difficult truth.

Johnny 21:44, 2 March 2006 (UTC)

I find the idea of providing a plausible falshood absolutely repugnant and reprehensible. The Newtonian version tells any layperson why lift is produced in terms he can understand and that are real. How many laypersons understand the Bernoulli principle. It is clear that very few technically minded people actually understand it. Dave 23-May-2006

External links

Three of the six links in the External Links section at the end of the article are to www.av8n.com. Is there any policy on external linking? I think one link to av8n.com should be enough.

Johnny 20:49, 23 February 2006 (UTC)

I removed the link to the http://www.av8n.com/fly/lift.htm, a "Critique of "How Airplanes Fly". It presents a strange, un-vetted argument about lift involving a plank, a trampoline, and balls. This viewpoint is irrelevant to learning about lift, IMHO as a scientist. The lift (force) page is confusing enough to the technically illiterate.

--Johnny 15:21, 6 October 2006 (UTC)

Removal of "common misconceptions"

I reverted the removal of the above section. I believe it is very misguided to remove this because the "equal transit time" explanation is so widespread and frequently authoritatively presented. It is wrong, and it's important to say so. If we don't say so explicitly, we are tacitly giving it credence, since anyone coming to this article with only that in their minds will not go away necessarily disabused of that notion. Yes, it's briefly mentioned in the Bernoulli section, but what's wrong with emphasising it? The statement to the effect that it's not up to us to debunk stuff is not based on any policy that I'm aware of - why not? If something needs debunking, and this definitely does, let's do it. The article does not gain anything from its removal, which is why I put it back. If you want to make your thoughts known on this, please do so, rather than entering into a revert war. Graham 04:47, 6 March 2006 (UTC)

Sure, we shouldn't be spending a lot of time on explaining how lift is not generated (after all, there are millions of ways it's NOT generated!). However, in this case I think the emphasis is justified, because it is so widely put forward as THE explanation. Last year I even came across this in a scientific exhibition of aeronautical principles at the Fleet Air Arm museum at Yeovilton! Even the most well-meaning of texts get this wrong, and in most cases there is nothing one can do about it - even if one is sufficiently motivated to complain it's unlikely to actually achieve anything by it, and in the meantime another generation of kids grows up with the wrong idea firmly embedded in their minds. However, on wikipedia we are not so powerless, and it is possible to do something about it. Indeed, my motivation for writing the section in the first place (which has recognisably survived for about nine months or so) was exactly to give it the emphasis I feel it needs. We may not be Snopes but I feel there is value in debunking where something is very commonly believed yet untrue. I would agree with some tightening of the section if it must be, but not on its removal or working into Bernoulli (which I don't feel is a good idea since it's not Bernoulli that's wrong per se). By keeping it separate there is no chance of a misunderstanding that the equal transit time "explanation" has any credence - if it is not emphasised I believe someone who came to this article with that in mind, read what else was here, would go away not with the idea that ETT was invalid but was another way of stating the truth. I also think that by making it explicit we have a chance over time, as wikipedia becomes a more reliable and credible resource, to start to stop the perpetuation of this myth, and that's important. However, let's see what others think and what, if any, consensus there is. Graham 09:56, 6 March 2006 (UTC)

First off, I'd like to thank moink for her spendid clean-up of this article last week. That said, I'd like to chime in and agree with the notion of keeping the myth-debunking section. This misconception is so strong and so pervasive that it easily merits its own section. Fundementally, I think one of the unique and important values of wikipedia articles is to go beyond a simple cataloging of facts and to address and put into perspective the various differences of belief. Hands-on, real-world contributors can, and should, do this in ways that would be inappropriate for someone who is just acting as a "reporter" and not deeply emersed with the field of work being covered. Engergetically debunking the equal-transit-time myth is a good example of this value. Britannica can be a catalog of fact. Wikipedia is much more and the better for it. Blimpguy 14:27, 6 March 2006 (UTC)

Coanda and some remarks

Surfing the Net I have found a lot of rubbish cocerning the lift force. Net is full od rubbish, sure, but this theme gathers a lot of wholeheartedly devoted and at the same time completely ignorant persons and articles. At this background the wiki article is good enough, but I have some remarks: 1. Explaining, computing, measuring is not the same, right? So there are many methods of computing lift, depending on circumstances and aim, there are many methods od measuring it, there are many didactic methods of teaching about it, but there is only one explanation of physical prosesses involved in it.!

2. The Coanda effect is as enigmatic and mysterious as bouncing up the ball from a playground; both can be qualitatively and quantitatively described using laws of physics: in the Coanda case the conservation and continuity equations and in the second just conservation equation. But at least until now the ball behaviour has been not described as a “Maradona effect”… The same laws govern the fluid flow around the “lift producing” body and are to be used not only to explain but also to compute the lift force but assumption that the Coanda “effect” “explain” lift force is simply fallacy. Because of that I would propose to move the Coanda out from the article or at least to move it to the misconception section.

Best regards andrzejmat 12:45, 24 March 2006 (UTC)

I don't think anyone is claiming that Coanda "explains" lift, but it is possible that it does have a lot to do with the efficacy of aerofoils. How else do you explain how the air across the convex surface stays attached? The effect may or may not be simple, that has nothing to do with whether it has a special name or not; lots of simple principles have names. Having said that, the Coanda effect may not be that simple - the equations for fluid flow are actually too difficult to solve for anything other than a very basic approximation, so nobody really knows exactly what is going on at the microscopic level. It can't be said that fluid attachment to the convex surface is unimportant in explaining lift - the attachment is vital to 'turn' the airflow, where Newton is then sufficient to explain the rest. But if you can explain how every molecule of air behaves as it crosses a wing, then you will probably make yourself very famous. We have some models that help us visualise where lift comes from, and we have many empirical results so we can predict the lift for a given set of parameters, but we still do not really know what is going on beyond this level of haziness. So to call it a misconception is wrong - it may turn out to be important, we just don't really know yet. We have to separate the practical (predicting lift) from the truth of the physics, which may be academic in that not knowing it doesn't stop engineers designing aeroplanes, but is important if we value true and complete knowledge of the real universe. Graham 13:08, 24 March 2006 (UTC)

Still, such claims (Coanda explains,,,) can be found... and secondly please do not exaggerate the difficulty of solving the Navier- S, even not speaking about classical approach of two dimensional flow of perfect fluid, solved analytically for foils 90 or so years ago, and now there are Cray – like machines and numerical computation.

I don’t think we would be famous predicting a molecule behavior. It is the matter of statistical approach, let us stay with continuous medium and finite element method.

You ask how can I explain that the air across the convex surface stays attached? The air stays attached across the convex surface simply because it has “no choice”: the continuity “forbids” voids, such a void would create zero pressure place. So the pressure gradient normal to the surface that has radius R is to be dp/dn=ro x V^2/R x n, where n is distance from surface and ro is air density when V is the flow velocity. You can see, for 100m/s, reasonable dp/dn the radius of 1m order is easily obtainable. Above of course is not any kind of mathematical proof, just a coarse calculation with the help of my fingers, I’m just sitting in my car in a horrible traffic jam.

I absolutely agree with you that it is important if we value true and complete knowledge of the real universe.

andrzejmat 17:26, 24 March 2006 (UTC)

The phenomenon you are talking about above, where the air has "no choice", etc, has a name: the Coanda effect. It's not magic or anything very remarkable, but since the phenomenon has a name, why not refer to it? If a bouncing ball was called "the Maradona effect" then no doubt that term would be commonly used. It's easier to say "the Coanda effect" for short than go into an explanation of what that means every time - that's why things are given names, to save time. Graham 04:04, 25 March 2006 (UTC)

What do you mean "no choice?" Aren't you familiar with boundary layer detachment and "stall," where the air "chooses" a path which no longer follows the convex surface? The usual textbook example is a sphere immersed in a fluid flow, where the flow either follows the trailing surface and converges behind the sphere, or instead it detaches and doesn't converge behind the sphere. (And no, a void does not appear behind the "stalled" sphere. --Wjbeaty 01:02, 31 March 2006 (UTC)

Sure I'm familiar, believe me. But I'm writing here about the range where the potential flow model is applicable and "no choice" words were used as a kind of a joke; in fact there should be said, that zero divergence (find the term if you do not know it, sorry if I'm in a mistake) conditions govern such flow. Outside this range such model should not be used, stall will arrive but such stall does not mean creating voids, but "vortex filled" area with pressure increased. But, again, I am speaking about potential model and range of flow, very close to reality. BL does nor change that flow in its most important range. andrzejmat 18:49, 31 March 2006 (UTC)

You obviously are not familiar. You're arguing that boundary layer detachment or stall is impossible; that air has no choice but to remain attached, that in order for Stall to exist, there would have to be a vacuum between the airfoil's surface and the detached flow. But such an argument is disconnected from reality! Stalls are not impossible, instead they are very common, and the flow across the upper surface of a wing becomes easily detached. During boundary-layer detachment (stall,) the region between the detached flow and the airfoil surface is full of turbulent air, and is not an empty void. You say you're "familiar," but a person who does understand basic aerodynamics would never argue that flow-detachment must form a void ...and therefore air has no choice but to remain always out of stall.

Boundary layer attachment is critical for normal airfoil function, and it's very strange that someone has given it an alternate name and put it in the "Misconceptions" section. As for the conventional explanation ...the usual explanations are simplified, and they assume a non-stall condition (since stall is a second-order effect which interferes with normal airfoil operation.) Unfortunately, by assuming that the boundary layer must "stick" to the airfoil, the conventional explanation says nothing about the micro-scale physics involved in boundary-layer attachment. It says nothing about the forces keeping the air flow in contact with the upper wing surface, nor about the forces producing streamline curvature causing the air above the wing to be deflected downwards. According to the conventional explanation, the boundary layer is always attached, and a barn door flys just fine. --Wjbeaty 00:39, 30 May 2006 (UTC)

Of course it would be unwise to be against giving names to things and phenomena…and using them to make some text short.

But – please agree – there are traps from a didactic point of view, and maybe even not only didactic, as the practice shows. I’m meaning the situation, when the wording, the form – camouflages the matter.

Let us take this article about lift as an example: for a untrained reader (the “target” reader, I’d assume and name him or her) it maybe looks like a hypermarket trolley, in which can be found newtons, bernoullis, coandas, circulations, downwashes - all of them together but individually lifting the plane over his head…

In my view it would be much better to show the reader an UNIFORM PICTURE, simplified as far as defined by the level of interest and capability of this target reader – but still not false. Maybe it would be reasonable not even mention any names but writing in terms of conservation, continuity ect. laws of physics? Or try to find a compromise?

Difficult? Impossible? Sure difficult and never ideal from the didactic point of view, but worth the effort, do not you agree? andrzejmat 09:02, 25 March 2006 (UTC)

keeping it simple?

First off.. I didn’t see any other way to get the attention here than to create a new heading.

I believe it’s mainly just a big misunderstanding on almost everyone’s part.. not so much about lift as about what others say about it.

I might be wrong and I will be very general and un-theoretical, here goes;

The angle of attack of a symmetrical wing is defined as the angle between the airflow and the geometrical centre line of the profile/airfoil.. This gives the airfoil a positive angle of attack when the lower surface is parallel to the airflow (if facing the right direction). The lower surface could then, as it is parallel to the airflow, not invoke any force on it related to physically diverting it. Air IS however diverted, this through the lower pressure created on the upper side of the airfoil effectively “sucking” air down from above. (as I said, very un-theoretical…)

This effect is explained with Bernoulli, it is because of the lower pressure that the air is accelerated (downwards), and the force/lift can be calculated using Newton’s Third..

This is a misunderstanding of the Bernoulli principle. In simplified terms the B principle says that an increase in velocity of air and a reduction of pressure will coincide as air flows through a diverging or converging path. What you have described is the Newtonian effect F=ma. the force on the air applied as a pressure, causes the air (a mass) to accelerate.

This will of course change with higher angles of attack, but it is true in this case..

Also, I have a grudge against all people having such an agro with this “fallacy” of "equal transit-time". (stop frowning and read on..) It is of course true that there is no need for particles that separate at the front end of the airfoil to rejoin at the rear. But when I had it explained to me it was used to explain how the particles on the upper side of the wing are accelerated more than those on the lower side. If you only think of vertical acceleration this is true (particles deflected upward will travel further than those below due to the shape of the airfoil.) to the point that not entirely all particles will return to their original vertical position. Seen like this (disregarding the need for all particles to hold hands before and after) it does make sense as to how the low pressure on top of an airfoil is achieved.

except that it isnt even close to being true. Do you want the truth, or a comfortably acceptable falacy that seems to explain reality.

I would like to see this explained in the article instead of rebuked with a “If you believe that you’re a freaki’n moron!” attitude.

Also (#2), I think it’s kind of ignorant to say that a symmetrical wing couldn’t fly inverted using this theory, as it is based on the symmetrical wing having a positive angle of attack. The angle of attack is most certainly positive while flying inverted and so the statement is false. The author himself claims the air is moving faster on what is now the upper side of the wing, this is due to the angle of attack being positive.. [edit] ok.. I missread the article, it says normal wings shouldn't be able to fly inverted.. but again, angle of attack.. same explaination for symmetrical and non symmetrical wings, allthough if you want to fly inverted you're better of with a symmetrical wing.. [edit]

I don’t have the audacity to actually edit the article, mainly as I’m Swedish and we have our own version to worry about.. but please consider what I’ve written.. BE SURE to point out any factual errors, but know that I’m quite aware that “sucking” is not a term widely used in the engineering profession.

In closing, why not describe both theories Bernoulli/Newton and discuss how they interact. At the moment you get the impression that anybody believing in low-pressure-lift on the upper side of an airfoil is simultaneously writing letters to Santa clause.

Of cause there is low pressure on the upper surface and higher pressure on the lower surface. This is accepted by anyone who has any understanding of lift. The argument about Bernoulli is that this version of the explanation of lift says that air goes faster over the wing(with no explanation of WHY that happens) and this then by Bernoulli causes lower pressure. There are two pieces of this version that are not acceptable. 1) why did the air accelerate so that it was going faster over the wing... what caused this. There is never an explanation for this in the bernoulli version. and 2) The Bernoulli equation does not state that high velocity causes low pressure. It states that they co-incide. Detailed consideration of the Bernoulli effect from first priciples shows that it is always the pressure difference that causes the gas to change speeds, not visa-versa.

(Also (#3), I’ve never heard of Albert Einstein building airfoils with huge humps on them, but it is about as related to the subject as if Monica Lewinsky was. His failure in practise is in no way related to the validity of the theory.)

no but the theory using good maths and physics demonstrates that such a hump would be necesary under those conditions.

Mangemang 16:04, 30 March 2006 (UTC)

hey.. I just got my head turned 90 degree to the side.. I've never seen such a good explanation before.. really good explanation I still feel/think that the real acceleration of the air takes place above the wing..(ok.. it's a religion to me..) but it gives a real nice analogy of how to "see" the "downwash"..

Ok, so now I’ve read even more of this page.. and I intend to use the “Bernoulli sucks” peoples own links against them..

First an analogy;

A normal balloon is filled with air.. it takes a force to expand the balloon and keep it expanded/inflated (as it is made of elastic rubber that wants to contract..). anyone would call me a fool for saying that it is the reference system, the surrounding air, that is keeping the balloon expanded by “sucking” its surface outwards, right? Of course it’s the relative pressure inside the balloon that is doing this..

Now, if we have an airfoil with a RELATIVELY lower pressure above, it’s equally not being “sucked” upwards by this low-pressure-air, but rather pushed upwards by the air below. Therein lies the problem, the air below is at the same(almost) pressure as the reference system (the atmosphere). At the same time as I can state that the air below the wing is lifting it, I would be mistaken in thinking that this same air has generated the relative pressure difference. The “lift” is in fact “produced” above the wing.. it is only “acted out” below.. To support this idea I would like to reinsert a link used under the chapter “Question about history of explanation-debunking”

It isnt one or the other... A wing if lifted by the difference in pressure above and below, not one or the other of them.

"yay, there is no Bernoulli lift.."

Please open this link in a new window and place this to be viewed simultaneously as reading this text. Scroll down to Figure 4. (the above pictures are not related to the point I’m trying to make. I’m NOT trying to refute the ability of an angled surface to create lift in an airflow!)

Now, figure 4. depicts the changing of a symmetrical airfoil into an unsymmetrical and how your eyes can “fool” you into thinking it’s still symmetrical. What the author is trying to prove here is that a symmetrical airfoil can’t produce lift if the angle of attack is zero. He is very right to do so but manages to show how lift can be produced seemingly without any surface deflecting air downwards. The 4:th picture within figure 4. shows an airfoil that will produce lift at this angle of attack. It is true that it can not be said to be zero angle of attack.. but it is also true that there is a greater surface deflecting air upward than downward. (if you look at picture 4. the curved surface facing the airflow above the new “invented” centre line is greater that the surface below.) This would/should according to any action/reaction theory I’ve ever heard of induce a net force downward. But the author goes on to talk about trailing edge as more important to lift due to deflection. Well, lets look at the trailing edge.. it’s still tilted UPWARDS on the lower side.. the only way to explain how particles below the airfoil could be “pushing” against this surface involves the Coandă effect and from what I hear, it’s not popular amongst the action/reaction people.. that is if you don’t want to bring Bernoulli’s theory in to this section.. (you can say it now, there IS a relatively higher pressure below the wing than above, only the pressure below is a lot closer to the absolute pressure of the reference system..)

So we move along to Figure 5. and what do we find..? Well, it’s a simulation performed by the nice people at SAAB. We are told that the air moves MUCH faster over the top of the airfoil and is deflected downwards.. hmm.. what are we not told..?

For one thing, there are colours assigned to the “parcels” in the picture. If FEM-analysis using simulation has taught me anything, it is that the scale follows this order, RED-YELLOW-GREEN-BLUE, or reversed naturally.. and as plainly seen, “parcels“ moving faster (above) are red, that colour then represents a lower pressure.. Yellow seems to be the speed/pressure of the reference system and green is a lower speed/higher pressure.. Any observation in this picture supports this. If the yellow parcels at the bottom of the screen are used as reference, we can observe the following, one column at the time, starting from the left:

The very first column seems to be accelerated somewhat ABOVE the centre of the airfoil, perhaps even slightly below ( it is slightly tilted to the right)..

The second column is even more accelerated ABOVE the airfoil and seems, if anything, to have slowed down below it (well, hard to tell, but it appears a bit more vertical).

The third column is really picking up speed ABOVE the airfoil and is actually showing green (tilting to the left as well) below which would mean a HIGHER than reference pressure (good for the action/reaction people)

This pattern is then pretty much the same across the length of the airfoil until the parcels meet at the end (note that there are no more green parcels below the airfoil). Here, the 7:th column of the upper parcels meet the 9:th of the lower (time across surface IS unequal). At the same time we can observe a small pressure increase below the airfoil in the 8:th and 9:th column (this time not HURRAY for the action/reaction people if we watch the angle of the lower surface).

As stated, the air IS also deflected downwards. However, if we study the parcels it can be noted that they seem to curve a lot more downwards above the airfoil than below. It also seems to happen a lot more BEHIND the airfoil than under it. Incidentally this is where the UPPER parcels, that seem to have a greater vertical velocity, meet the lower parcels. Slightly behind the trailing edge a green parcel can even be observed in the UPPER part of the flow, indicating perhaps a higher pressure “pushing” equally up and down but in this case acting DOWNWARDS ON THE AIRFLOW behind the trailing edge..

Many things can be said about this simulation. But to use it to rebuke the “Bernoulli theory explanation” I find impossible. If anything it supports it.

(actually, to refute the low-pressure-above-airfoil lift theory, shouldn't there be AT LEAST an equal or higher relative-high-pressure below the airfoil..??)

Basically, it could be said that air is deflected downwards and that a lift could therefore be calculated with Newton’s Third, yes. But it is in no way proven to be the lower side of the wing that is deflecting the air, it could just as well be the upper side.

Returning to the analogy of the balloon, the airfoil can be viewed as an incompressible solid, much as the rubber of the balloon (the balloon-shells thickness is so small that any compression is negligible). Basically the air below the airfoil is pushing the wing upwards as there is nothing holding it back from above.. this is pretty basic stuff if you’ve done elementary physics or studied engineering mechanics.

There are a lot of people on this site presenting their views with the “support” of this and that doctor of whatever subject.. I will present this only as my own theory, although I have the support of doctor as well, for anyone to refute or heckle.. Best regards //m4ng4

Eek!! That's a lot to plough through - if you really want to "keep it simple" it might be better to build an argument in more digestible chunks... but let's take up a few points. You say let's give the equal transit time theory a fair go - but in the next sentence you say it's the angle of attack that matters. It's perfectly possible to construct an aerofoil section that has a cambered upper surface, a flat lower surface, and zero angle of attack - the camber itself doesn't necessarily confer an angle of attack though in many designs it does. But lets keep it simple and separate out the variables. How much lift will we get from this aerofoil at this AoA? Almost nothing, because the curve of the upper surface in itself doesn't cause the air to accelerate very much, or rather, there is no downward deflection of the airflow so there is no reason for the air over the upper surface to accelerate. As we increase the AoA, there will be more and more downward deflection as the foil turns the airflow. The problem as I see it comes in determining at this stage what is cause and what is effect (or rather, in trying to force one of them to be cause, and one to be effect, whereas in fact they are inseparable). What we observe is that the air over the upper surface accelerates more and more as the AoA increases, and there is more and more downward acceleration leading to lift. Some prefer to say that the acceleration causes a decrease in pressure, creating lift by "suction"; others prefer to see this as an effect of the downward deflection - the air must accelerate in order to balance out the forces. In fact you can't have one without the other - each effect is the other's natural consequence, and must always be present in any functional foil. Thus it is my view that trying to "settle" the argument in favour of one or the other is unhelpful, and leads to an incomplete picture either way. Mathematical descriptions such as Bernoulli's equation describe the phenomenon only from one perspective, but you can use Newton to describe it from the other. This doesn't mean one is wrong and the other is right, but that they are alternate views of the same thing. That's why the article is right to give both explanations equal space and explain that they are describing the same thing. So where does that leave the equal transit time explanation? Nowhere, it doesn't come into it because it doesn't happen. It's true that the upper surface airflow accelerates, it's true that the pressure observed here is lower, etc, but (as you rightly point out) it says nothing about parcels of air joining hands front and back. So it's really not helpful to try to say that the acceleration/pressure change IS the equal transit time theory, because it's not. Personally I feel that the article is really pretty good overall. The fact that this talk page is vastly larger than the article, full of the same arguments being passed back and forth over and over again, and also full of everyone's pet theories shows that a) the phenomenon is actually quite hard for many people to get their heads around, b) that in reality the phenomenon of lift is a lot simpler than people assume and c) there are a lot of misconceptions nevertheless. If we could somehow agree that the Newton/Bernoulli explanations are in fact two sides of the same coin and that the pressure/downwash viewpoints are not separable we could probably make some progress. Graham 01:35, 31 March 2006 (UTC)

Well, Graham, I’m sorry you found my post such an utter mess.. but thanks for the very articulate and polite answer..

To separate the variables, as you put it, I would like to address a post you’ve made earlier.

You wrote that, and I’m quoting, “..What we can say with absolute certainty is that it takes a force to keep an aircraft in the air - it is a force exactly equal to the weight of the aircraft. So where does this force come from? Force is mass x acceleration. So what mass is being accelerated that creates an upward force equal to the aircraft's weight? Well, it MUST LOGICALLY be a mass of air accelerated downward. It is the only thing that CAN give rise to this force, since there is no physical contact with any other supportive medium, and anti-gravity doesn't exist, as far as we know.” Long quote, I know..

Well it’s true that force = mass x acceleration, but is it the only truth? Is not Δp x A also a force? (relative pressure x Area) Try removing the glue holding a standard fish tank together and I’ll show you a force (note, the water in this tank can be perfectly still, no relative acceleration). As a matter of fact, the walls of this fish tank could be slanted inwards and they would still be forced outwards. Has this “new” force just negated gravity..? No, it arises from gravity, as gravity is an acceleration. This is how you can measure the force under your feet when you stand, it’s Your mass x the gravitational acceleration.. (I'm drunk and I get confused.. but gravitation IS an acceleration, right?)

Now, air IS a supportive medium, Δp x A = F says nothing about the density, mass or absolute pressure of the fluid, it is entirely up to the relative pressure variation and Area.

Having straightened that out I would like to continue by saying you probably already knew that, you just chose to look away when it comes to lift..

I will ad a new explanatory edit to my post and I would like for you to read and comment.. as you did not really comment on any of the material (links and so forth) of my last post.. Mangemang 14:42, 31 March 2006 (UTC)

The ”second coming” of Bernoulli..

I will start this by saying it might be a long assay of lift, but if you’re interested in “killing” the Bernoulli theorem, you’ll have to/should go on..

My first intention is to create the final “debunking” of the “equal transit time” idea.. totally different from the one found in the article.

The theory argues that lift will be created as the parcel of air on the upper side of an airfoil will have travelled longer in the vertical direction than parcels on the lower side of the airfoil, thus creating a relative acceleration. (given an airfoil with positive angle of attack)

It, the “equal transit time theory”, seems to only take vertical acceleration into account and this is its flaw. What we should be looking for is not so much a “net acceleration” as a “net work”. (if an object is accelerated upwards and then equally downwards, no “net work” has been done.. (I should be careful here though, as I imply that acceleration is equal to lower pressure which is what causes lift in the Bernoulli theorem)) Work is defined as force x displacement. And if at the end of the airfoil the parcels meet again, the “net work” will be zero (as their relative displacement will be zero).. effectively nothing has happened. (This is where the action/reaction people say “Hurray!!!”. But they should not, if they think of action/reaction only as an airfoil “physically” (by standing in the way of the air) is deflecting air downwards..)

Let me make an example:

Imagine an endlessly thin and endlessly strong rectangular surface. Put this surface in a wind tunnel at zero degree angle of attack (= parallel to the airflow). It would produce NO lift. Only at an angle of attack it could.

Now look at this.. single picture or take a look at the full web page with comments.. full article

At zero degree angle of attack, the lift is zero.. (I , partially supported by the “equal transit time theory”, consider producing zero lift to be the definition of “Zero degree angle of attack”). But above zero degrees the lift is proportional to the angle of attack (limited by “too high” angles of attack). I would like to concentrate on the 5° angle of attack depiction. (I know this is a simulation done by “someone”, but it is descriptive and not far off a real wind-tunnel)..

Looking at this depiction we can see an airflow that is quite affected above the airfoil and quite unaffected below. What really stands out is that the “parcels” above the airfoil seem to move faster then those below. This, in contradiction to the “equal transit time” theory, is producing a net work, as work is defined by force x displacement. (force = acceleration x mass, in this case) We could now say that there is work done above the wing.

If we carefully study the leading edge we find that the Area that COULD deflect air is greater on the upper side than on the lower.. this is also clearly shown by the parcels as they seem to CURVE on their way above the airfoil as supposed to the parcels below, supporting the theory that the parcels are deflected more above the airfoil than below.. in the “Newtonian third” sense of this there should be a net force produced DOWNWARDS. Still the airfoil is quite happily producing a lift. Now how could that be?

Well if we think about what this net work is doing on the upper side of the wing we could find a plausible solution. If there is a local low-pressure produced on this side we could look at it this way:

Any low pressure produced in a fluid will soon be equalized due to particles “rushing in” from all sides (this is what would happen in a fluid such as air). In the case of the airfoil, with the low-pressure concentrated above it, the particles would rush in from all sides but from beneath. This is because of the physical barrier separating the particles below the airfoil from those above it. Now if particles are rushing in from all directions but from beneath, the net velocity of those particles would be directed downwards. And as the airfoil is moving away at a quite rapid velocity, it would be plausible to assume they could continue in this direction once the airfoil has removed itself (this is inverted in case of a wind tunnel where the airfoil is stationary, but equally true).

Moving to the lower side of the airfoil now; There is no evidence, after the assumption that the leading edge is producing a net down force, to assume that a surface parallel to the airflow could deflect it. (you could talk at length about the Coandă effect but, as the surface doesn’t curve, it’s invalid.)

This is where I would like to reconnect with the initial imagination. The lower surface of the airfoil, as it is basically parallel to the airflow, is now equal to that of the lower side of the “endlessly thin, endlessly strong” rectangular surface. That surface did not “magically” induce any deflection of air downwards when at zero degree angle of attack. So why would the lower surface of our airfoil do that???

I have now, at least the way I see it, proven the Bernoulli side of lift. (if there is an area and a difference in pressure, there MUST be a force) I really hope that a lot of people have taken the time to read through this and created their own ideas about the subject..

I equally wish that anyone who sees a flaw in my description would be so kind as to point it out to me.. I am in no way educated in aerodynamics (although I’ve taken a few related courses, under professors who really could throw their weight about (meaning they have several years of research in the field behind them)). I am in fact doing Composite Design, and that is more of a static-mechanic area.. unless you want to calculate strength/durability, where it becomes very much dynamic.. Also, as I’m a native Swede, I hope you have had no major problems understanding my English..

I intend for this to be my final BIG input on this page and hope that you have not been offended..

Mangemang 23:55, 31 March 2006 (UTC)

Who says that Bernoulli's Equation doesn't apply to airfoils? There's no need to prove that Bernoulli works, since it was never in doubt. What was in doubt was the "conventional explanation" otherwise known as the "equal transit time fallacy." Bernoulli explains lift if you know the value of circulation (so you know the average difference in velocity of air above and below the wing.) But the conventional explanation appearing in most textbooks is wrong because it doesn't tell us the circulation, instead it says that parcels must recombine at the trailing edge after moving at two different speeds. Wrong. The divided parcels DO move at two different speeds, i.e. there is circulation. But why does this occur? If you can figure out what the two different speeds are, then you can calculate the lifting force with Bernoulli (and knowing the force, you can also calculate the downward acceleration of air via F=mA, and add numbers to the reaction-force explanation of lift.)--Wjbeaty 01:32, 30 May 2006 (UTC)

Is the circulation only a mathematical construction?

"A third way of calculating lift is a mathematical construction called circulation" states the article. It is not true. The circulation is described by mathematic formula, sure, but the description relates to the as real phenomena as a typhoon,and even mathematical description is alike typhoon's to the some degree. andrzejmat 16:28, 7 April 2006 (UTC)

Circulation isn't just a mathematical construction as it is derived from basic physical principles and is clearly demonstrated by experiment. --131.111.226.61 00:15, 14 April 2006 (UTC)Thilee

Indeed, but no pilot every learns to fly an airplane properly by making computations involving circulation. That's the point of the "only" remark. If you'd like to reword this bit to be more clear, then, of course, do so. Regards. --Blimpguy 10:09, 14 April 2006 (UTC)

circulation and lift c.

If pilot have to make the lift force computations, he/she should use the formula supplied by an airplane manufacturer, or use just aeroplane lift/stall characteristics; he also shold know about much greater importance of the upper surface of his/her wings in comparition with lower surface. But if he/she would like to understand fully aerodynamics, she/he should study aerodynamics, not any encyclopedia, even as exellent as Wiki... By the way: look at this simple (but not quite formally true) way of bridging circulation with the "lift cooficient" and obtain the same result as Cutta -Zukowski theory gives - look at the picture:

I wonder if the image and the approach would be of any use in the article (after - maybe - correcting my language errors), from the "didactic' point of view? --andrzejmat 15:11, 16 April 2006 (UTC)

But, but

The wing vortex system, the way it's set up on initial motion of the wing, and the way the tip vortices reach back to the very real starting vortex on the ground, make the circulation concept seem pretty real and useful to me! (see the classic prictures of Prandtl & Tietjens 1934, reproduced in G. K. Batchelor's Fluid Dynamics, plate 13, and p 580) --Linuxlad 21:23, 2 July 2006 (UTC)

The vortex system is real, but it is quite different from the inviscid version described in textbooks. After all, the starting vortex dies away within minutes. So does the vortex-wake after the aircraft has passed by. If regions of high vorticity were visible to human eyes, we wouldn't see a starting vortex sitting forever on the airstrip. But even in viscous fluids, these lines of vorticity are circles, so whenever the starting vortex dies away, we'd see its lines of vorticity leaking "forwards" towards the aircraft. The vorticity from the starting vortex would end up as a fast-moving sheet of vortex-lines which connect the pair of vortex filaments in the aircraft wake. At the same time as the lines of vorticity fly forwards towards the aircraft, the rotating wake is being slowed by viscosity. This sheet of "starting vortex" would eventually follow the aircraft at the same speed as forward flight.

And just to be fully accurate, I must point out that the pair of vortex filaments in the aircraft wake are not actually coming from the wingtips, and are not really filaments. Instead, the entire wing generates a "sheet of vorticity" which extends back from the trailing edge of the wing. But because the air motion associated with this vorticity resembles a pair of counter-rotating cylinders, the air motion causes the wing's trailing-edge vortex-sheet to wrap up in a pair of opposite spirals centered on the edges of the vortex-sheet. It may look like "wingtip vorticies" but it's actually "vortex-sheet-edge vorticies!" <grin> --Wjbeaty 17:39, 5 July 2006 (UTC)

'True, but not relevant' - the starting vortex is there for long enough to embarass other aircraft, as are the effects of the trailing vortices. We all expect the real world to dissipate vortices (cf stirring my tea) but that doesn't make the concept too arcane for 'the layman' (of whom, in this area, I'm one). Bob aka Linuxlad 17:46, 5 July 2006 (UTC)

Rereading this all after a (rather traumatic) 6 month, I see we really need something in the article about 'loading', especially 'elliptical loading' Bob aka Linuxlad 17:55, 24 January 2007 (UTC)

I've started a horseshoe vortex article, with reference to the varying loading/circulation and the shed vortex sheet, which i cognoscenti can now attack. Bob aka Linuxlad 11:59, 25 January 2007 (UTC)

Article content RfC re Coanda-Effect

Please see Talk:Coandă effect#Article_content_RfC. Also, the second paragraph of the Coanda-Effect-Subsection here reads like gibberish to me. --Pjacobi 00:20, 25 May 2006 (UTC)

In the Misconceptions section under "Coanda", we find this statement: "However, the conventional explanation of lift makes verifiable predictions of lift using the lift equation, without invoking the Coandă Effect." But this is very misguided because such a conventional explanation assumes that the Reynolds number is right for flight, and the boundary layer therefore remains attached to the upper surface. Or in other words, in the conventional explanation, the assumption is silently made that "coanda effect" is already there. As I understand it, if instead we assumed an extremely high R, then the wing would always be in the stall regime at all angles of attack, and we would no longer see "Coanda effect," and we could not use the "conventional explanation."

So that statement is incorrect. I'll remove it unless someone can say why I shouldn't. --Wjbeaty 01:58, 30 May 2006 (UTC)

Another problem. The misconceptions section states that "The practical applications of Coandă effect, such as blown flaps and other lift augmentation devices, create conditions different from the normal airflow over a wing." This is very misleading, since the "Coanda effect" itself only involves the attachment of flows to a curved surface, and doesn't require any actively-pumped jets of fluid. The statement in the WP article looks to me like a rhetorical ploy: an insinuation that the Coanda Effect only involves actively-pumped jets. In reality the clinging of the boundary layer flow against any airfoil surface... that is the Coanda Effect, so why pretend otherwise? I'll remove that misleading statement. --Wjbeaty 02:09, 30 May 2006 (UTC)

Different Flow Regimes

An impressive discussion on basic Kutta-Joukowski flow using trailing edge separation! However lift may also be generated by leading edge separation on low aspect ratio wings (notably Concorde taking off and landing) and by shock waves (Ackeret aerofoil theory). Slender body theory is another curiosity, which calculates the lift from the velocity potential term which doesn't contain the circulation, but arbitrarily doubles the cross flow component. Gordon Vigurs 12:00, 28 June 2006 (UTC)

"Transit time" fallacy continues

In Scientific American for April 2006, in the "Working knowledge" column, the author carefully teaches ...the fallacy! He says that "because the wing top is curved, air streaming over it must ravel farther and thus faster than air passing underneath the flat bottom. According to Bernoulli's principle" ...etc. The fallacy is also illustrated by a very clear (and misleading) diagram.--Wjbeaty 16:42, 28 June 2006 (UTC)

Venturi Nozzle

It is mentioned in the article that it is incorrect to analyze the wing as a venturi nozzle to explain the acceleration of the airflow around the wing. The argument is that since a venturi nozzle requires the fluid to be squeezed between two surfaces and the wing is only a single surface, that the venturi nozzle explanation does not apply. However, there is a second surface: the relatively undisturbed relative airflow some distance away from the surface of the airfoil. The air that is accelerated is the air that is deflected around the airfoil and squeezed between the airfoil and the "undisturbed" airflow some distance from the airfoil. Comments?? --Sancho McCann 04:36, 27 July 2006 (UTC)

The undisturbed streamlines above the airfoil are empty air: they are not a wall, and they cannot block any flow. In other words, if other nearby streamlines needed for some reason to deflect upwards, then those "undisturbed" streamlines would instantly become disturbed, while an actual wall would not. An actual wall can support a pressure distribution without moving. If we want to understand why the streamlines above a wing are closer together than those below, we must look for an explanation elsewhere, rather than pretending that some empty air can behave as a wall.

To understand airfoils, it greatly helps to analyze a rotating cylinder (or just a vortex summed with a uniform flow.) A rotating cylinder will "grab" incoming streamlines from well below itself, then deflect them up and over its top. It does so without needing any second wall as venturies do. (Then all we need to do is to explain why a cambered or tilted airfoil will behave as a rotating cylinder!) --Wjbeaty 18:32, 27 July 2006 (UTC)

Why does an airfoil behave like a rotating cylinder? This is easy to explain visually. First look at this diagram of the very slow flow surrounding a tilted flat plate: barn door, slow. At very low speeds, the inertia of the air is insignificant, and viscous effects dominate. In that diagram the flow is symmetrical and the lifting force is zero. Especially note that the flow near the leading edge looks like a mirror-image of the flow near the trailing edge. (BTW, there is no circulation.)

Now look at this diagram where the flow is much faster: barn door, fast. It looks much like the flow diagram for a wing. In this diagram the inertia effects are strong. They cause the flow to reorginize itself so the air will move smoothly off the trailing edge. The flow no longer looks symmetrical: the flow near the leading edge looks very different from the flow near the trailing edge. Now the big question: how is the "fast flow" diagram different from the "slow flow" diagram? There's one big difference: the fast diagram has a large circulation! So ...airfoils cause circulation because they use inertia to "fling" air smoothly off their tilted trailing edge. If the inertia effects should become insignificant, then air will whip sudddenly around the sharp trailing edge and no longer depart smoothly ...and in that case both the circulation and the lifting force go to zero. (Both diagrams are on J. Denker's site)--Wjbeaty 01:09, 28 July 2006 (UTC)

From equal transit time section

The explanation also fails to account for airfoils which are fully symmetrical yet still develop significant lift.(Dubious: a symmetric aerofoil can only create lift if its has a angle of attach on the incoming fluid flow. If the angle of attack was reversed it creates a force in the opposite direction)

Although I don't understand lift verywell, I deleted the above from the article. If it really is a shortcoming of the equal transit time explanation, someone can put it back, but from the "dubious" label, it looks like it might not be a shortcoming. --Kjoonlee 15:42, 29 July 2006 (UTC)

But the equal transit-time theory says nothing about angle of attack! The books which use this theory to explain the lifting force do not have a separate section where they explain lift in terms of tilted flat airfoils. According to equal transit-time theory, AOA has no effect (since changing the AOA does not change the shape of the wing.) According to equal transit-time theory, only a cambered wing can generate lift. --Wjbeaty 08:55, 30 July 2006 (UTC)

The continuing myopia needs to end. It is large quantities of air flow, emphasis on "large" as in "heavy" and "massive", being deflected downwards that creates lift. Focusing on the flow immediately adjacent to the wing surfaces and what it is doing means little. Whether the large volumes of air some distance above and below the wing conserve their mass and do or do not take an equal amount of time to reach the trailing edge is (a) something normally observable only in wind tunnels and (b) means next to nothing toward the creation of lift compared to their deflection downwards. AnthonyChessick 14:01, 30 July 2006 (UTC)

Anthony, your explanation is POV. Have you ever encountered the story of the Lilliputian war in Gulliver's Travels? The big-endians, little-endians, and mass murder over the one true way to crack an egg for morning breakfast? It is a warning. Whenever someone describes their side of an argument in glowing terms, and describes their opponents' argument in derogatory terms, that person has lost their objectivity. They've become emotionally entangled in a single exclusive viewpoint, and they've started pursuing a "religious war" in support of the One True Way.

For example, if I wanted to fight with you, I'd simply point out that all the lifting force can only be created by pressure upon the wing surface. The wing surface area experiences direct collisions with molecules, and the wing doesn't know anything about moving masses which are nearby. That's the "opposite religion" from your own. It's the belief system of the enemy, and needs to be stamped out and replaced by the moving-masses explanation, right? No way! Both viewpoints are WRONG, because any correct explanation incorporates both of them. Or in other words: "If you don't have many separate ways to explain something, then you don't really understand it."

Here's a close analogy. In a rocket engine, is the thrust produced by the ejected exhaust, and calculated with F=mA? Or is the thrust really produced by hot gas molecules colliding with the inner surface of the engine bell, with thrust being created by gas pressure imposed over a surface? Which explanation is pure and good and right, and which one is evil garbage produced by misinformed minds and needing to be silenced in order to protect our children? Neither. BOTH EXPLANATIONS ARE CORRECT. Or said better: if we chose a single explanation as being the "One True Way," and then we try to silence the other competing explanations, then we've started fighting an emotion-based "religious war" and have fallen into error.

The Newtonian mass-flow explanation does need more emphasis though. Far too many textbooks describe only the pressure-based Bernoulli explanation. (Perhaps they're looking for the One True Explanation themselves, and have decided that the Bernoulli explanation is "better" and must win out?)

--Wjbeaty 08:55, 30 July 2006 (UTC)

WJBeaty, please see the entry near the end below entitled, "The Missing Piece of the Puzzle: Air Mass?" AnthonyChessick 16:31, 1 August 2006 (UTC)

No winners. No losers. No fights. Richard Feynman the Nobel Laureate said, "The behavior of fluids is in many respects very unexpected and interesting." It is an evidently unexpected fact here that the mass of air as stated in the title of this contribution is not being adequately accounted for almost universally throughout these detailed explanations. The mass density is incomplete as a vehicle by which this issue can be covered. It is tons of air per second moving across a wing from leading edge to trailing edge not only adjacent to it but some distance above and below it and being deflected downwards that is not being mentioned. I have no quarrel with the pressure considerations introduced and observed at the surfaces. I do say, on the other hand, that it is short-sighted to look at the flows at the surface only such as by means of the Venturi Effect, the Bernoulli Principle, temporary velocity changes, boundary layers, induced turbulences and vorticies, and the Circulation Parameter and this is not disputable. Tons of air per second even for small aircraft. The overlooking of this important consideration places analysts in the position of hunting for what can only be described as largely untenable answers as I have listed above, falling in the category otherwise as something called in the books "kinematics" and useful but for other reasons. Air in quantity is heavy, massive. Isolated POV? Air in reasonable volumes is as heavy in terms of mass content as the largest ships afloat. Entire railroad trains including the locomotives. Hundreds of thousands of tons. Some ideas take time to be understood - are imponderables. But this is not at all difficult to digest. Wind energy in particular is subject to the confusion that results when this science is not carefully developed. To provide explanations of these terms that are not complete is of some concern. Thanks. AnthonyChessick 14:01, 30 July 2006 (UTC)

From Reaction due to accelerated air section

It is important to note that the acceleration of the air does not just involve the air molecules "bouncing off" the lower surface of the wing. Rather, air molecules closely follow both the top and bottom surfaces, and so the airflow is deflected downward. The acceleration of the air during the creation of lift has also been described as a "turning" of the airflow

and occurs up to large distances away from the surfaces. (Air in large quantities has much more mass than that for which it is often given credit since its buoyancy masks what is typically mass flows affected by wing surfaces in the tons of air mass per second.)

I deleted the deeply-indented part from the article; it's very difficult to understand the sentence structure. --Kjoonlee 09:21, 30 July 2006 (UTC)

Kjoonlee, it is a necessary addition that balances out the triviality of the "molecules of air bouncing off the surface" content and so please see the paragraph below, entitled, "The Missing Piece of the Puzzle: Air Mass?" I need your support for my not adjusting the article to provide even more simplistic parallels instead, such as that the so-called "complex phenomenon" of "Lift" is really, really, truly and really, the same as flow going through a downward bend in a pipe and putting upward stress on the pipe supports. AnthonyChessick 16:31, 1 August 2006 (UTC)

That's true (about downward deflected mass.) However, when a wing is infinitely long, there is no downward-deflected mass, and instead the wing remains in "ground-effect mode" where it indirectly pushes upon the floor or ceiling of the wind tunnel. Unfortunately most textbooks illustrate this 2-dimensional situation while claiming that they are explaining flight. A 2D airfoil diagram is also called an "infinite wing diagram." 2D airfoil diagrams depict ground-effect mode, and do not show the downward-deflected mass in the aircraft wake, the moving mass which all real-world wings employ in order to remain aloft. (Yet these diagrams also neglect to show the floor and ceiling, and they never mention that the lifting force in 2D systems is always paired with another force on the floor/ceiling!) --Wjbeaty 03:30, 2 August 2006 (UTC)

This and previous comments have an honest intent to set things right. By "infinite" here you clearly mean the wing chord and not its span and the point seems to be that wind tunnels have their limitations.

No. Two-dimensional airfoil diagrams are also called "infinite wing" diagrams. Go search Google if you don't believe it. They are named this way because their flow pattern is not that of an aircraft, instead it is that of a wing of infinite span. In any 2D airfoil diagram the induced drag is exactly zero, and the upwash ahead of the wing exactly equals the downwash behind the wing. 2D airfoils do not fling air downwards; they work by ground-effect. It's different with a real-world aircraft. With non-infinite wingspan there is a "net downwash." The downwash behind the wing is greater than the upwash ahead of it, and the air in the downstream wake far behind the wing is left with a permanent downward motion. This has been photographed when small planes move in level flight over a layer of ground fog, and their descending wake carves a slot in the fog. See this photo, plus my animation at rotating disk balloons. Note also that my animation depects Anderson and Eberhardt's "scoop," the region which extends to great distance above and below an aircraft wing. Lifting force is proportional to (span)^2 for good reason. 2D airfoil diagrams don't show any of this. 2D airfoil diagrams depect WIG or "ground effect flight" where there is no net deflection of air, where the ground surface is a part of the system and where the aircraft presses down on the ground below. These diagrams do not explain how airplanes fly. Or in other words, if your span is infinitely wide, you can never fly high enough to escape from the WIG-mode flight regime. This issue appears in the real world in wind tunnels where the tips of the wings are against the tunnel walls. But it also is a critical issue in nearly all textbook explanations, since the authors rarely mention that their 2D diagrams are in fact depicting how WIG works. (A 2D airfoil diagram is in fact much like a venturi flow diagram. But a real aircraft with finite span is different, and the "venturi" aspect is gone.) Neither do textbooks mention that in 2D diagrams the airfoil creates instant forces on the distant floor and ceiling (since the pattern of circulation extends infinitely, all the way to any floor and ceiling.) The opposite end of the force-pair giving lift, gives a force-footprint upon the floor and ceiling which is equal and opposite to lift. If we try to get rid of the floor and ceiling, we end up with an infinite-span wing where we've pulled the floor and ceiling out to a distance that is... greater than infinity?!! This is another way of saying that the floor and ceiling is necessarily a part of any 2D airfoil diagram, and it's a bit disingenuous to not depict it in the textbook diagrams. Yet no floor and ceiling is needed when a real world aircraft is flying. In that situation the aircraft flings air downwards, and the air in the wing's downstream wake remains moving downwards. See also my large website on the lifting-force misconceptions, http://amasci.com/wing/airfoil.html --Wjbeaty 23:33, 6 August 2006 (UTC)

I am deeply distressed by this analysis and, as the initiator of this title on this page, intend to remove it soon unless there is a good reason presented why it should not be. Attempts to send an e-mail off-line from Wikipedia proved to be incompatible with your e-mail workload as stated on your website and so it is all that I can do to register my complaint. Anthony Chessick 03:11, 8 August 2006 (UTC)

Well. The analysis up there is a load of bullocks. But it is generally considered bad practice to erase other user's comments. However distressingly wrong they may be (2D wing == no drag !!! WTF ?). You may however as an admin to archive the talk page and start with a clean slate.CyrilleDunant 06:00, 8 August 2006 (UTC)

On second thought and with the support of this kind remark, maybe not. Wikipedia seems to have infinite patience with these infinitely long discussions. User Wjbeaty just discovered the "edge effect" in aviation wing design, wherein the incident air flow doesn't just trail off behind and below the wing at the wing tips but is diverted out to the side of them as well since it has the freedom to do so. The source of the mystery of why momentum seems to be conserved in one case and not the other is the scope of the system being considered. Granted, momentum is not changed over the whole earth including its atmosphere and the earth is not shifted in its orbit due to the passage of one airplane but no one can determine a lift force this way. This, I take it, is what is meant by infinitely long wings. It is only in limiting the system to just the elements causing the initial disturbance to it where one can understand flight.

The phrase you are looking for is control volume. And no, what is meant by "infinitely long wings" is really "2D approximation". The absence of drag comes from the further simplification assuming the flow derives from a potential, and thus has zero vorticity ($\nabla \times \mathbf {v} =\mathbf {0}$). This also leads to the "equal transit time".CyrilleDunant 16:48, 8 August 2006 (UTC)

More generally, even Shakespeare complained in one of his sonnets (66) about the tendency for some to look for irrelevant exceptions and unusual values in parameters rather than acknowledgeing the veracity of the guiding principles. His lasting words, directed against this failing, were "And simple truth miscalled simplicity". The compounding of this tendency with the power of the computer to produce, as above, animations only proves how well the computer can be misused to confuse as well as elucidate. No one need fear that the "simple truth" here can be expounded upon to produce a wealth of complexity when it comes time to actually make use of it in determining the Lift Force with appropriate formulations and in providing solid logic clarifying the responses of the airfoil in different operational situations. Not to be unmindful of the breadth of the scientific mind in exploring many fields, but Wjbeaty's page emphasizes a background in electronics and electricity rather than fluid dynamics and it is supposed that other discoveries await as well. This talk page is unwieldy as a proper vehicle for providing for its intended purpose but it sends a message just from its length that the dispute tag on the subject entry of Lift Force need not be "lifted" soon. How this all is to be resolved is not for me to decide. I have only provided within a website of my own responsibility some discussion of this subject at www.integener.com with a focus on wind energy. Anthony Chessick 14:21, 8 August 2006 (UTC)

I hope you will excuse me from being blunt, but laconism is a quality.CyrilleDunant 16:48, 8 August 2006 (UTC)

In his well-referenced textbook, G. K. Batchelor introduced the idea of vorticity by saying that vortex-lines may be described and followed in exactly the same way as streamlines of flow velocity, such as the solutions to:

${\frac {dx}{u(\mathbf {x} ,t)}}={\frac {dy}{v(\mathbf {x} ,t)}}={\frac {dz}{w(\mathbf {x} ,t)}}$ (Secs. 2.6, 2.1)

This has often turned Fluid Dynamics into a search for vortices, something worth while and beneficial. But to place fluid rotations, circulations, and vortices into such a prominent place as to obscure the readily accessible concepts of Lift and Induced Drag (not viscous drag) is, again, a hunt for exceptions to the general rule. Eberhardt and Anderson have made it possible to regain a sense of proper perspective on this issue. Enough abruptness on my part. I look forward to seeing and understanding more of the insights that have been introduced here. Anthony Chessick 16:50, 9 August 2006 (UTC)

I refrain from anything further on this but just to say that kinematics and the study of flow fields is important - and quite a challenge as must be clear by now - but let's get on with observing the averaged values up to large distances above and below the wing instead, what is actually going on that is of some significance. When they get down to following each of the molecules of air flowing adjacent to the airfoil profile and how they do or do not twirl about (and I have the Batchelor reference cited with its studies from the early years of aviation) it is time to stop this and let the basic facts of Newton's Laws speak for themselves. Please understand that this is a worthwhile objection. Some serious arguments involving the Circulation Parameter may be seen as well in its subject article elsewhere. Anthony Chessick 14:15, 3 August 2006 (UTC)

With respect to the subject article itself, corrections are suggested to immediate affronts in it at the very top. We all can live under the Newton's "Third" Law - equal and opposite reactions - here but it is the Newton "Second" Law which has the teeth in it and provides F = ma, the vehicle by which the value of the lift force may be found. Another problem is the direction of the lift force being stated as being perpendicular to the flow. In the Newton's Law explanation of Lift, the Lift Force is directed at 90 degrees plus, in addition, one half of the angle of attack to the flow. This can be seen readily on a graphical drawing showing the incident and as-deflected or "downwash" air flows. The difference is important in wind energy wherein the angles of attack are much greater than in the case of aviation. Even commercial aviation pilots have been known to express a not-quite-true belief that the Lift Force is always strictly perpendicular to the horizontal flow from the aircraft flight through the air. Anthony Chessick 14:43, 4 August 2006 (UTC)

The Missing Piece of the Puzzle : Air Mass?

Note - while issues may be taken with these thoughts, unsigned comments are transferred to my User Talk pages for detailed discussion and may be found there instead. Thanks.

A continual source of error and misconception in these discussions is the lack of a good understanding of the mass of air. Air is about one and a quarter ounces of mass per cubic foot, readily dismissed as anything that can, without the help of unusual pressures or velocities, generate much force at all. Thus the continual "clutching at straws" such as the Bernoulli Principle or viscosities or the Coanda Effect or the Venturi Effect or mysterious flow velocity differences or the even more mysterious Circulation parameter to explain, for example, how a 500 ton aircraft can support itself. Commonly not understood is that airfoils affect air flows not just adjacent to and near their surfaces but up to large distances away from them and that in larger volumes air has substantial mass.

A cubic yard of air "weighs" almost exactly two pounds, the same as a quart of water. A hot air balloon of 37 feet in diameter contains air of about one ton of mass, reduced somewhat by the lower density maintained by heat for its buoyancy. The rate of mass flow through the rotor blades of a 1.5 Megawatt wind turbine at rated capacity with its 75 meter diameter rotor is no less than 80 tons per second, about the same as a hypothetical freight train moving through the blades.

The clouds in the sky contain air masses in the hundreds of thousands of tons. With this kind of mass in sufficient quantities to fly through, aircraft of such large weights have no trouble supporting themselves with just a little coaxing of the air they see ahead of themselves into a downwash that needn't have much velocity downwards at all for the large volume of it that then trails below and behind the aircraft. This is Lift.

What is still missing is a mathematical description of Lift that eschews some of the fancy kinematics (study of flow fields) handed down by the honored names involved with the literature of aerodynamics. It is readily supplied in some of the material by recent names such as Eberhardt and Anderson referenced in the article. A brief summary can be described as follows: the lift force in a straightforward vector equation equal to no more than the rate of mass flow seen by the airfoil times the vector difference representing the change of direction of the flow vector before and after the encounter with the airfoil. This equation is immediately derivable from the Newton Third Law. In solving this, even graphically, it can be seen that a small component of the resulting lift force is in the direction opposite to the velocity of the aircraft and this, of course, is the induced drag, otherwise known as the "drag penalty of lift". Having the basic idea, first and foremost, of the substantial mass of air as described above simplifies this problem and all its related controversies hopefully acceptably for everyone. AnthonyChessick 14:07, 30 July 2006 (UTC)

Is this well-documented somewhere? If it's original research, there's a Wikipedia policy against it. Wikipedia:No original research. --Kjoonlee 16:55, 1 August 2006 (UTC)

As stated, it is the substance of the Eberhardt and Anderson paper referenced in the text of the subject article. I approach this material from the standpoint of wind energy, not aviation, and it is of importance that it be complete for this evolving technology with its differences not accounted for otherwise. Missing previous to these statements are the basic formulations on computing the Lift Force from the Newton's Law deflected flow mentioned repeatedly in all the talk above. Here they are, extracted from the cited paper. AnthonyChessick 21:14, 1 August 2006 (UTC)

This is still just blatantly wrong. First, you're using the term downwash in a completely inapropriate way, and assuming that the calculations given for it are something they are not. Downwash is ONLY present on a 3-d wing (not an airfoil which is, essentially, infinitely long). 2-d airfoils, as they're called, are set up in windtunnels with both edges of the airfoil connecting to the walls of the test section. These airfoils generate MORE lift than their 3-d counterparts, and do not produce a downwash. A downwash is generated by the tips of the wing, where the high pressure air underneath rolls out around the tip, and mixes with the low pressure air above. This generates, depending on the design of the wing, a downward flow of air out and behind the wing. It should be noted that this is a NONBENEFICIAL effect, and engineers do everything they can to eliminate these vortices, which rob lift and create more drag. It should also be noted that the lift a wing will produce is accurately predicted by the Bernoulli model, and that the only effective way of testing an airfoil is by comparing Cp (relative point pressures) above and below the wing, the integral of which is equal to lift. 164.107.199.93 17:00, 30 January 2007 (UTC) Jason M.

I think, if you employ our friend G, you will find he is NOT the first person to use downwash in this way (ie to changes in 2-d momentum flows). Bob aka Linuxlad

Has anyone heard of lifting line theory for lift generation (refer here) ? Downwash is not just related to wing tip vortices as pointed out earlier. -Myth (Talk) 12:10, 31 January 2007 (UTC)

Sorry for the misleading comment. I checked on the definition of downwash and the given by Jason M. (164.107.199.93) is perfectly fine. btw the lifting line theory is still valid and it does not contradict with the pressure distribution, just another way to explain lift generation. -Myth (Talk) 04:05, 1 February 2007 (UTC)

On speaking with the professors at OSU, one finds that the explanations of lift are all pressure related, with some citing circulation, Γ as an important factor, particularly Dr. Gregorek. Regardless, should we not exlain lift to the general public with that explanation which best models the behaviors seen? The problem with airmass is how far in front of the wing to project the 'airmass deflection'. It (airmass deflection) may or may not exist (I still stand firmly on my definition of downwash, as it is backed up in many reliable sources, such as Anderson's textbook) but the lift generated by pressure is absolute verifiable FACT. A pressure difference between the upper and lower surfaces of an airfoil DOES exist (we measure it in wind tunnel and real-life tests every day). This simply can't be ignored in favor of another theory when all the instruments available to us indicate pressure as the supporting force. Also, I'd like to make a note to those on both 'sides' of this argument: we need to at the VERY LEAST make a distinction between low-speed, transonic, and supersonic flight. The way lift is generated on the practical side changes DRASTICALLY as the critical mach number is reached, and some of the flow goes supersonic. 164.107.199.93 19:11, 31 January 2007 (UTC) Jason M.

Some figures that may be interesting

This article was contributed by --JayJayPlant 12:57, 5 August 2006 (UTC)

Interesting article that goes against what has been commonly taught and makes a case for what seems obvious, but maybe the simple physics should be shown....

The impulse of an air mass by the wings would be a large transfer of energy. Rough figures for an aeroplane with 100m wing span and a frontal area of lets say 200m² at say 80m/s (take off speed) would encounter ( an atmospheric density of 1.29kg/m³) approx 20 tonnes of atmosphere each second, The impulse that this mass would give is F=mv (actually Ft=mv-mv₀, but we're looking at 1s and an initial velocity of zero for the air), if the wings were able to give the air encountered a velocity of 80m/s (and that would be optimistic) then

20640kg_air X 80m/s= 1.65 megaNewtons of force

on the wings(this is the best case).

The force of gravity on this 400tonne aircraft is F=mg :-

400,000kg X 9.81ms^-2 = 3.92 megaNewtons.

(NOTES: Only the frontal area of the wings can carve out the atmosphere to impel downwards, so the surface area of the wings are irrelevant for moving air masses, and it should be noted that only the atmosphere that comes in direct contact with the aerofoils can have an effect in a momentum interaction.)

So how can this aircraft leave the ground?

Um? How indeed?

It is very easy to never notice what 1 atmosphere of pressure is. It is 14 pounds/ sq inch,or approx 1kg/cm². This is alot, and I really mean a lot. But, because we have evolved to be happy in this atmosphere we never notice this pressure.

So how does this help an aeroplane? Some one mentioned that a 747 had a wing area of 500m², okay. If you had a vacuum above the wings, then the atmosphere below the wings( and everywhere else around the vacuum) would exert 1 kg/cm² trying to fill the vacuum. On 500m² that would be a weight equivalent of 5 million kg, or 5000 tonnes. To keep a 747 of 400 tonnes in the air would require a mere 8% pressure drop above the wings to maintain altitude.(400/5000 =0.08)

The reason for laminar flow over the top of the wings is to stop the atmosphere above the low pressure volume getting in, so having the atmosphere exert its force on the underside of the wings only. A stall is when the laminar flow breaks down and the low pressure volume is filled from elsewhere.

As you can see there is a good reason that they claim that low pressure above the wing is what gives lift.--JayJayPlant 12:57, 5 August 2006 (UTC)

Anonymous, extemporaneous thoughts like this tend to display what is commonly held. The above comments are appreciated. For the record, though, notice the "clutching at straws" mentioned earlier seen here again, since air is so "insubstantial experienced up close as anything that can support heavy aircraft". What this is missing is an understanding of how large a quantity of air is given an impulse by the wings. The frontal area mentioned of only 200 m^2 for a wing span of 100 m is off. Conservation of mass, a requirement even for this most readily dismissible of substances, air, requires a much larger frontal area that is affected by the wings and given the impulse downwards. The value of the velocity downwards at 80 m/s need not be assumed to be so great either but merely about one tenth of that or 8 m/s. A frontal area adjusted to a value of 5000 m^2 readily puts everything in proper perspective and makes it all come out to be about right. This is air that is not just flowing within a meter nearby the wing surfaces but up to 25 meters both above and beneath them on average that is being affected by them and being given the "shove" downwards. Makes sense, no? This is quite a large amount of air and therefore quite a large amount of mass.

Much more than the 35 grams or so of one cubic foot of it, hopefully not mixing measurement systems more than necessary. No need to try to somehow find a "convenient vacuum" somewhere (I believe the laminar flow logic here does not hold - someone correct me if I am wrong), in pertaining to which something of this sort many have tried to do, to apply to the upper wing surface!!! Anthony Chessick 15:50, 3 August 2006 (UTC)

How does a fluid behave?

Contributed ny--JayJayPlant 13:14, 5 August 2006 (UTC) It has to be understood that the particles( atoms or molecules) that make up a fluid generally do not have a force component linking themselves to each other (See gas). A liquid is just a gas that has particles that are moving to slowly to escape gravity. (Note a liquid that can form a miniscus will behave differently to a gaseous fluid, because of the van de Waals force.)A particle of gas moves in its own little vacuum and occasionally hits something, either another particle or a surface, when it hits another particle it changes direction. If it hits a surface the surface experiences what is known as pressure. If the container is expanded the gas can only fill the newly created volume at the speed the particles are travelling at.

The Coanda effect must rely on surface friction to divert particles in the spin direction. But those particles that never contact the surface can only behave like a gas. The reason the ball diverts is because on the side spinning forwards, with its surface texture, will be hit/ and hit particles in the direction that the texture is moving, there will an increase in the number of particles collecting forward on this side, so building up pressure. The side spinning backwards is batting particles backwards , so reducing the number of particle of the front of this side. If you put more particles into a volume you have an increase in pressure, if you remove particles you have a decrease in pressure. I have never suggested that the low pressure is sucking, because a gas particle cannot pull, it can only push as it hits something, so the Coanda ball is being pushed by the atmosphere; which does not like the dis equilibrium of a local high pressure spotonto this high pressure zone. The low pressure side puts up less resistance to the gas trying to be in equilibrium, and so the ball gains a sideways component to its travel.

Now why would a fluid flow seem to attach to a curved surface:, because if the fluid flow took a tangential path there would then be a vacuum created between the surface and the straight lining fluid, that vacuum is going to have to be filled. It can be filled either by internal pressure within the flowing fluid , or the fluid and/or the surface is going to be pushed towards the vacuum by external pressures. I have been a bit shocked to discover that it might be thought that the fluid particles are some how rolling along the surface; all the particles can do is bounce and have their direction changed by collision.

A fluid's behaviour is just a generallisation of what many individual particles are doing on a microscopic scale, the fluid flow is just a macroscopic collection. As a flow passes a curved surface the mean free path of some particles have the opportunity to lengthen in the direction of the surface,so filling the void, but leaving a void behind them that will be filled when another particle happens to travel into the new void(now remote from the surface)and then that particle will leave another void, and so on. The fluid flow acts like a flow because most of the particles happen to be flowing in roughly the flow direction and as ; dare I say, a faster flowing fluid is at lower pressure so the flow column( if you like)will be contained, if it happens to be within another fluid, by that stationary fluid. If the flow is in a vacuum, it will disapate as the particles on the edge travel without collision to send them back into the flow, away from the others.

So why is there so much air affected above the wing, because as the flow over the wing leaves the curve(or the leading edge of a flat wing) in a tangent(macroscopically speaking), it will result in a vacuum that has to be filled, either by the surface/wing, or the surounding air, more likely and easier for the air to fill the void, hence the coanda effect, and this will have a knock on effect away from the wing surface, so a large volume of air will move towards the upper surface of the wing, remember this is filled just by the air particles that happen to travel into the void/ lower pressure zone, they do not pull particles with them. Now as these particles move towards the wing, the wing moves on, leaving air behind that has been effected by the lower surface of the wing, in most cases showing a deflection of paths downwards. This will effectively also leave a lower pressure region behind the trailling edge of the wing, that the upper particles are already moving towards, so the air will actually have downwards motion well behind the wing, but ....

The problem with the article is that it is, and can only be, the particles that hit the wing that can have an effect on the wing, (see gas), the particles of a gas do not interact except to bounce of each other or a surface. Granted the movement of air is a manifestation of just how much energy is being expended.

If you wish to see how this conflict in hypothesis has arisen and been maintained, look at the first link on the article page "How airplane fly", In the section "Wing Votices" there is a picture of an F-14 in high G , and the author has used this to support the air movement argument, to demonstrate the effect that the wings are having in moving so much air above the wing. What the picture is also showing, and not been appreciated (in what has been written, anyway) is that the condensation is produced by extremely low pressure above the wing, cooling the air above the wing so much that the gaseous water vapour condenses into liquid water. It is a visual showing of how large the low pressure zone is above the wing.

Because particles cannot pull on another particle, the apparent Coanda effect that creates streamlines over the wing, cannot pull a wing up, anymore than the wing is "sucked" into the low pressure area. A fluid can only push with pressure it cannot pull.--JayJayPlant 13:14, 5 August 2006 (UTC)

"Ne sutor supra crepidam" "Stick to your (and our) knitting here" An unsigned piece of some length on molecular movement in fluids only peripheral to the subject on an overly lengthy talk page (with a warning to this effect) is at risk for removal as I am sure is the consensus! A problem spotted with this is the need to understand inertia. Even molecules of gas have weight. Another problem is the need to understand differential pressures, that is, pressures relative to one another. You haven't even gotten yet to viscosity and other characteristics of fluids. Fluids are just a collection of bouncing molecules but they are much more than this as well. Anthony Chessick 03:31, 5 August 2006 (UTC)

Okay so now I've registered. The knowledge of how a fluid works is of vital importance to aerodynamics, and a little background in the discussion page has to be helpful, it gives readers an insight to where they may look if they want to get a fuller picture of the dynamics of the system as a whole. The air mass hypothesis requires a mass of air to be moved so an eplanation of how this may or may not happen is vital.

One of the reasons why the downwash hypothesis has a problem, is that in level flight there is no momentum change, so how does the aircraft stay in level flight? Could it be the bounacy of a low pressure zone created above the wing? It is going to interesting to see how this conflict turns out. I dont mind if my present view turns out to be wrong, but I will require a proper description of the fluid mechanics to support the air masses/ downwash hypothesis.--JayJayPlant 13:14, 5 August 2006 (UTC)

JayJayPlant, your User page does not tell us anything about yourself. I am not a perfect person, especially not a perfect teacher and readily back away from "conflicts", if there is one here. Another concept needing some thought is "average". Within the downwash is some faster moving molecules and some slower ones. They all have been given a push down as a result of the passage of the wing even though most did not contact it. This pursuit of level of detail is not helpful to understanding Lift but only gets into infinitely long discussions of flow details that are exceptions and not the rule and flow segments that fall outside of the average. Sorry to be so abrupt but it is simply incorrect to say that in level flight there is no momentum change! Please address these ideas to someone a little smarter than I am. Anthony Chessick 14:19, 5 August 2006 (UTC)

As a postscript here, the salient edge of the Newtonian view of Lift comes into focus with the following facts. The above example of the 747 taking off at 80 m/s on the airport runway with the wings seeing a frontal air flow of about 5000 m^2 that is given a momentum change downward into a "downwash" of an average velocity means that the air mass flowing over and under the wings is:

(80 x 5000 x 3.2808^3 x .0765) / 2000 = 540 tons per second

The weight of a 747 is less than 500 tons and so the wings are deflecting downwards an air flow that is significantly greater than its own weight every second. How much force is provided can readily be found by means of this fact together with how fast the air is moving downwards on average in the resulting downwash.

In the field of wind energy, the air mass flow seen by the 75 meter diameter rotors of the 1.5 megawatt turbines at the rated wind speed of 30 mph comes to 80 tons per second. The modest wind turbines sold for use by home owners rated at 10 kilowatts with 10 foot long blades and seeing just a 15 mph breeze (about half its rated wind speed) are being driven by about a quarter of a ton of air mass flow each second.

There is no mystery to these facts. It is time to make abundantly clear just what is happening that provides the Lift Force in no uncertain terms and, indeed, to actually calculate it using math based on Newton's Second Law, F = ma. Anthony Chessick 12:57, 6 August 2006 (UTC)

JayJayPlant, you suffer from a typical misconception: the idea that air behaves like a hail of bullets. No, air behaves like a fluid; very much like water, but of course with 1.2KG/M^3 density rather than 1000. And simple fluid mechanics is based on this central concept: for good reason it deals with fluids and not with clouds of flying bullets. Fluid behavior is an "emergent property" which by definition can never be seen if we examine populations of whizzing molecules. (In other words, we must deal only with "forests," and anyone who starts dealing with "trees" has lost sight of the fluid mechanics behaviors.) Any aerodynamics explanation which is based on visual pictures of gas molecules will often suffer from this "hail of bullets" fallacy, a fallacy which leads us away from seeing the "fluid" aspect of the air. If instead we imagine that all our explanations take place under water, it greatly helps fight the "bullets" misconception. (And if any aerodynamics explanation can't handle the underwater environment, yet works well for clouds of moving air molecules, then that explanation is almost certainly not based on fluid behavior, and is almost certainly wrong.) --Wjbeaty 22:50, 6 August 2006 (UTC)

Sorry, this is wrong. Gasses behave exactly like humongous amounts of billiard balls. And proper statistical analysis will yield the same results as those predicted by fluid dynamics. Except, of course for control volumes so small the continuity hypothesis is no longer valid -- and that is pretty small indeed. Thermodynamics are derived from considering gases as large amounts of molecules.CyrilleDunant 16:37, 7 August 2006 (UTC)

Read it carefully before commenting. (Perhaps I should have said hail of non-interacting bullets.) I'm discussing the difference between airfoils in gas at 760 Torr versus airfoils at 0.01 Torr. Do you know how a fluid behaves? Are you aware that gas at 0.01 Torr no longer acts like a fluid, but instead acts like a molecular beam? It acts like a hail of individual bullets which don't collide with each other. The effects of molecule-molecule collisions become insignificant at low pressure, but at 1ATM their effects are extremely significant, and it causes gas to take on fluid characteristics similar to that of water. At 0.01 Torr the inviscid/incompressible fluid model used in fluid dynamics fails. Crookes Radiometer starts spinning at that low pressure because the gas acts like non-interacting bullets, but Crookes Radiometer won't spin at high pressure because gas then behaves as a fluid. Gas at 1ATM acts like water because it acts like strongly-interacting billiard balls where any individual ball cannot move very far without being reflected back by a collision and thus communicating momentum change to other molecules. In other words, in a fluid-like gas, the billiard balls are essentially vibrating back and forth, and rapidly transferring momentum throughout the array of balls. No stats are needed to understand this, it's the "vibrating back and forth" which holds the key concept. (Of course an animation would help greatly!) But as I said above, it also helps if we move our explanations under water. That way the fluid nature of the medium is so obvious, that it becomes difficult to fall into misconceptions. (Or in other words, water is not like a hail of non-interacting bullets!) --Wjbeaty 02:25, 9 August 2006 (UTC)

Well, yes, you should have said "non-interacting". Because bullets interact. In a fascinating way. And not at all like billiard balls, I should say. What I was trying to say is that you can derive fluid behaviour from considering it like a statistically large amount of billiard balls. Note "statistically". Note that if "statistically" is not true anymore, the rest of my sentence drops. And "vibrating back and forth" is very incomplete: what about rotation? What about complex moecules having many degrees of freedom? BTW, yes, I know how a fluid behaves.62.167.50.249 05:50, 9 August 2006 (UTC)

Of course there is a situation where gases really do behave like a hail of bullets: when pressure is less than a fraction of a Torr and the mean free path is a significant percentage of the size of containers or of wings. Explanations based on the motions of separate air molecules are explanations of aerodynamics up in the Ionosphere. But down here near the surface of the Earth, air molecules rapidly and repeatedly collide with their neighbors, and this instantly transfers both momentum and viscous force. The repeated collisions act almost like chemical bonds, or better, like compressed springs connecting all the air molecules. And that's a good way to see the difference between fluids based on gas, versus fluids based on liquid: liquids have chemical bonds between the molecules, while gases behave as if there were compressed springs connecting all the neighboring molecules. The air is like a liquid, but a liquid which can only push. --Wjbeaty 22:50, 6 August 2006 (UTC)

Or push differentially. It is a temptation to try to understand the pressure distributions across the profile and all around it although aircraft wing designers rightly have a need to do so. For example, this is generally not necessary in wind energy technology and certainly finding the Lift Force, the subject of this Wikipedia entry, need not take this detour into the complexities of doing so. It is like starting in the middle of the flow problem (building up from a molecule by molecule analysis at the profile surface) rather than from the beginning - the averaged momentum change of a large quantity of air flow mass being applied to a deflecting surface. Even optimizing the Lift Force by means of profile designs can proceed without understanding the detailed pressure distributions but only how well the air flow mass deflection is being obtained. Anthony Chessick 14:46, 7 August 2006 (UTC)

It is strange that the defenders of the air mass movement hypothesis are so willing to insult those who they are trying to convince, and also to say that it is pointless to examine the mecanics of the system.

It is not a hypothesis, in the sense that conservation of momentum is not a hypothesis. It simply is a fact. Lift is produced because of the reaction of air.

If the mass air movement hypothesis dependes on inter-particle atraction to generate lift, then it means that lift cannot be experienced in a perfect fluid, which has no inter-particle forces.--JayJayPlant 11:51, 13 August 2006 (UTC)

1) There exists no such thing as a "perfect fluid". It is a hypothetical construct. A perfect fluid is one for which the behaviour law $pv=rT$ stands. This assumes not no interaction between molecules, but a) an infinitely small size for the molecules and b) no attractive behaviour between the molecules. It is a hypothesis valid for air around an airplane, for example.

2) If you write the Navier-Stokes equations for a fluid, the first thing you do is write the conservation of momentum equation. Which involves pressure.

3) The difference of pressure "above" and "under" the wing causes lift.

4) The difference of pressure "above" and "under" the wing is caused by the variation of speed. The variation of speed is caused by the deflection of the air by the wing. Because of the boundary condition introduced by the wing.

5) For the above to be true you need not make any assumption on the fluid other than continuum. If the pressure is so low that the continuum hypothesis is no longer valid -- well, you have so little fluid that lift is not really in order anyway :)

6) I suggest you go read Navier-Stokes Equations CyrilleDunant 15:11, 13 August 2006 (UTC)

I think you are on my side Cyrille, The last two sub sections of this discussion were started by me argueing against the air masses movement, which is an hypothesis that effectively abandons the notion that the pressure differential between the upper and lower surfaces of a "wing" is the source of lift.

This is playing on words: the pressure differential is caused by the variantion of the momentum of the air. Of course, the "direct" cause of lift is differential pressure, but the "engineered" cause is the wing shaped so as to displace the air in a suitable fashion.CyrilleDunant 10:16, 14 August 2006 (UTC)

I am trying to find out if the Coanda effect actually occurs for a fluid flowing through a vacuum to see if the "attachement" of a fluid flow to a surface is only possible if the flow and the surface exist within an environment with an ambient pressure. As yet I have found no periodical that has any info on an experiment such as this. ???--JayJayPlant 16:49, 13 August 2006 (UTC)

This is bacause you ccan't have a fluid flowing in a vacuum ? Because it would boil and make the vacuum not a vacuum anymore.CyrilleDunant 10:16, 14 August 2006 (UTC)

A Math Formula As Per Eberhardt and Anderson For Determining The Lift Force

It is briefly stated in the Eberhardt and Anderson reference of this subject article that an actual calculation of the lift force may be made (independent of formulas based on Bernoulli's Equation, the Batchelor Circulation Parameter, various Venturi considerations, Wing Edge Effect Vortices, Unequal Transit Times, and all the rest) by using a formula based on what these authors call the "rocket thrust" formula. This is correct but rockets are only a special application of this more general formula. Newton's Second Law, F = ma, may be rewritten in a different form for the case of all fluid flows as follows:

${\overline {F}}=\left({\frac {dm}{dt}}\right)\nabla {\overline {V}}$

This is a vector equation as is indicated by the over lines above the F and the V. It may be considered to be a short form of Navier-Stokes that has been integrated over the control volume and made applicable to the presence of a boundary condition - the wing or blade profile surfaces. The (dm/dt) factor in effect says, "the rate of fluid mass flow". For the case of rockets, of course, this is just the rate of burnup of the rocket fuel that is then propelled through the rocket nozzle. In some cases where, for example, flow in a pipe is involved this is just the same as $\rho \mathrm {AV}$ but for wings or blades the A is an undefined value. So an assumption that may be made is that a proportionality constant is used instead of A and this constant is left for other work, usually empirical (wind tunnels, etc.). In general it may be said that the rate of mass flow for air passing over a wing or blade is quite a bit higher than generally realized when taking into consideration that the value of A may encompass distances that are large both above and below it, reflecting the substantial incident area where flow is affected by its passage through it.

The second factor, $\nabla {\overline {V}}$, is the vector difference between the average flow vector before and after the passage of the wing or blade. Vector algebra is useful and vector subtraction (as here) is done by just placing both vectors at the same starting point and finding a new vector that extends from the tip of one vector to the tip of the other. In the case of rockets, the beginning vector is zero and so the result is just the same as the vector of the flow out of the nozzle. In the case of wings and blades, in general the magnitude of the vectors (the actual flow velocity) is unchanged but the directions are altered in a process called flow deflection. The new vector, then, is found by placing both the starting flow vector and the deflected flow vector at the same beginning point on a graph and drawing a line between the two tips (extending as they do in two different directions), which is a vector nearly at right angles to both of these vectors. This becomes the direction of the force vector, F. Note that sometimes the vector, F, has both a lift and a drag component to it - but this can be discussed elsewhere.

Notice also the parallel with bends in pipes where forces are seen by the pipe supports as a result of fluids flowing within them.

Notation is sometimes confusing. The upside down Greek letter delta used here is often also used to indicate a differential over space especially in dot or cross products of vectors as made clear with a dot or "x". Here no differential is intended and a simple "vector that is the difference vector" is meant.

Notice how quick and easy this is, using math to powerfully make the complex more understandable and to simplify calculations. No need to view what is happening at the airfoil surfaces either in terms of flow velocity bumps or pressure distributions or flow transit times. All that is needed is the beginning flow vector and the ending flow vector of the averaged flow mass seen by them. In wind energy, this is especially important because some of these details hold little interest compared to how much forces are being generated.

Then this formula can be worked to produce calculations making predictions of how changes in profile shape or attack angle create changes in performance of various parameters of interest. It is, in other words, just the beginning of lengthy computations that bear upon further design efforts.

It is important that this be mentioned here irrespective of any rules or policies of Wikipedia involving the handling of disputes over what are the correct formulas for the lift force. In effect, this is additional material upon which debate is taking place. Anthony Chessick 16:46, 21 August 2006 (UTC)

Er by my reading of Professor B, you need to account explicitly for the pressure variation in the momentum flux expression in at least two important cases 1) when taking the control surface directly over the wing (where the mass flux is zero, see eg Batchelor eqn 6.4.20) and b) in a 2-d system, evaluating momentum flux at large distances, where the pressure and momentum flux integrals are in fact equal (Batchelor, eqn 6.4.27 et seq.. And of course, it helps if you've got a technique to actually find the velocity variation, which the Kutta condition gives you. Linuxlad 20:27, 22 August 2006 (UTC)

It is with reluctance that I dismiss these thoughts and hold firm to what has been stated above. Batchelor and, before him, Prandtl, Joukowski, and Kutta are not saying anything earth-shaking, just trying to follow the flows on a streamline-by-streamline basis, even, sometimes, making use of the interesting variation of vortex-lines. The Kutta condition means only that the air mass "flux" turns a corner (in his terms, "circulates") at the trailing edge and then heads downwards by a small angle equal to an "effective" angle of attack that is often not determined as well as it might be. Further, it is plain wrong to say, as he does, that pressure variations of the necessary significance occur at distances far removed from the airfoil when in fact, for aircraft as well as wind turbines, we know they don't. (He also misidentifies his "airfoil" profile of Figure 6.4.1 as a "cylinder", a proof-reading error perhaps but a telling one in those earlier days when the Magnus Effect was such a byword.) Anthony Chessick 01:36, 23 August 2006 (UTC)

I think the reference to an airfoil as a "cylinder" is no "proof-reading error". Any 2D airfoil is a cylinder in the sense that it is a surface defined by an array of parallel lines ("generators") passing through a curve in 3D space. Anthony Chessick must think it referred to a "circular cylinder", which is a special case in which the defining curve is a circle in a plane perpendicular to the generators. --J Doug McLean 22:50, 30 October 2006 (UTC)

Some basic physics, and other missing pieces of the puzzle

Explaining lift qualitatively, without computation, has been an interesting topic to me for some time. It's a difficult problem, and prone to being misunderstood, so it's not surprising that this discussion generates so much disagreement. After years of mulling it over, I think I understand some of the reasons why it is so difficult, which I'll get to below.

I agree with Anthony Chessick that the fact that air has mass is an essential factor that is missing from much of the discussion. I will propose two other essential factors that I think help explain the difficulties we face and that suggest what we need to do to surmount them. But before I do that, I want to establish a couple of basic facts that I think are incontrovertible but that don't seem to be agreed upon by all our participants:

The available physical theory in principle "explains" everything nearly perfectly. It just doesn't make it easy to understand.

I'm not referring here to higher-level derived concepts like circulation and the Kutta-Joukowski theorem or to things that show up in phenomenological observations, like the existence of the starting vortex. I'm referring to the fundamental physical theory. Here is a very brief summary:

Air consists of mostly empty space with only a small percentage occupied by molecules flying around in random thermal motion. The kinetic theory of gasses provides a highly-accurate probabilistic description of these motions, not only when the gas is in thermodynamic equilibrium, but when some deviation from equilibrium is present. But in aerodynamics we needn't concern ourselves with the details of these motions. In ordinary air, the mean free path of the molecular motions is very small, and on a practical scale, air acts like a continuous material. Furthermore, its properties and behavior as a continuous material are relatively simple. In ordinary aerodynamic flows, local deviations from equilibrium are small, and under these conditions we can rigorously derive, from the kinetic theory, the continuum description of the physics that we call the Navier-Stokes (NS) equations. Historically, the NS equations weren't first derived this way, but we now know how to do it. So our continuum description of the physics is firmly tied to our understanding of the molecular physics, but it allows us to proceed to describe and analyze flows without having to know the details of the molecular motions.

In the NS equations the representation of molecular transport processes (transport of momentum by viscous "stresses", and the transport of heat by conduction) is highly simplified compared to the general possibilities, but for ordinary aerodynamic flows this simplified representation is highly accurate. For a complete definition of the physics governing the flow around an airfoil, all we need to add is the condition of no slip and no temperature jump at the interface with the solid surface (another approximation of the molecular physics, but highly accurate). Then if we could solve the full NS equations for the flow around an airfoil or wing, in sufficient detail to resolve the time-dependent details of the turbulence in the boundary layer and wake, I'm confident that the time-averaged flow would be predicted with an accuracy that would exceed that of the experimental measurements. We don't have the computing power to do this now, but a few decades from now we should be able to calculate the flow around a 2D airfoil this way, and maybe 70 years from now we'll be able to do a whole airplane. For now, we must settle for "modeling" the effects of turbulence. But even with turbulence modeling, the accuracy of predictions based on the NS equations is beginning to rival that of the experiments, if we limit our attention to the attached-flow regime. When separation is present, the accuracy of our current turbulence models is not that good, the effects of these inaccuracies on the predicted flow are larger, and the resulting predictions of lift and drag are not very accurate. We should view this not as a deficiency in the basic physics, but just as a result of the lack of computing power that forces us to model the effects of turbulence rather than compute them directly.

So in a quantitative theoretical sense the physics of lift is perfectly understood: Lift happens, and we can in principle predict it accurately, because the flow obeys the NS equations with a no-slip condition. There is no mystery or fuzziness in the basic physics. The fuzziness and misunderstandings arise when we try to explain things qualitatively.

The pressure is the only way the lift force can be transmitted to the airfoil.

An electrically neutral fluid can transmit force to a body only through direct contact in which the internal stress in the fluid is transmitted directly to the surface. At any point on the surface, the force transmitted to the surface can be visualized as a force vector, the force per unit area transmitted to the surface. This vector can be resolved onto a component parallel to the surface (the shear component) and a component perpendicular (the normal component). The shear component is of direct viscous origin, while the normal component generally has both viscous and non-viscous contributions. But in ordinary air flows, according the NS equations, the direct viscous contribution to the normal component is negligible, and the normal component is equal to the local hydrostatic pressure. The displacement effect of the boundary layer is often significant, but it is an indirect viscous effect and is felt as a change in the pressure, not as part of the direct viscous contribution to the normal component.

If we integrate these local forces over the whole body surface, we get the total aerodynamic force, which can be resolved into a drag component parallel to the freestream and a lift component perpendicular. On a 2D airfoil with attached flow, typically about 75% of the drag comes from the integrated local shear contributions, and about 25% of the drag (the form drag) comes from the integrated pressure, through the displacement effect of the boundary layer and wake. 100% of the lift comes from the integrated pressure, with only a negligible contribution from shear.

So whatever the deeper origin of the lift force is (and it must include the transfer of momentum that is going on throughout the field), the force is, for all practical purposes, transmitted to the airfoil only through the pressure acting at the surface.

The science is clear on these two issues, so I hope we can stop arguing about them. Now here are two key elements that have been missing from the discussion so far and that I think are crucial:

A flow field is a distributed, or "global", phenomenon, while the equations of motion (the NS equations) explicitly address only local interactions.

The NS equations are a set of field partial-differential equations (PDEs) that explicitly express only local relationships between the flow variables. Forces are exchanged only through direct contact between adjacent fluid parcels or with bounding surfaces, and there is no "action-at-a distance", as there would be if we had significant electromagnetic or gravitational forces.

A flow field, on the other hand, is a global entity in which the local physical balances expressed in the equations must be satisfied everywhere simultaneously. Determining what flow-field does this requires solving the equations for the particular situation at hand. This is a huge obstacle to intuitive understanding because we humans are not well equipped to solve PDEs in our heads. Nor is it easy for us to deal with corresponding problems of a qualitative nature, as for example in applying Newton's second law locally at points in a flow field and then trying to deduce what the overall flow pattern must be.

The equations enforce only implicit relationships between flow variables, not one-way cause-and-effect relationships. In particular, the cause-and-effect relationship between the pressure and the velocity is circular. Likewise, the cause-and-effect relationship between the flow field and force it exchanges with the airfoil is circular.

So it is obviously wrong to try to reason what the velocity will do first, without reference to the pressure, and then to deduce the pressure from Bernoulli's principle. Likewise it is wrong to invoke one-way causation in the other direction. Any argument based one one-way causation between pressure and velocity is at least partly wrong. A correct argument must acknowledge that causation runs in both directions simultaneously. In my attempts to deal with this issue, I've found that resolving circular causation requires looking not just at what is happening locally, but looking at what is happening over the extended flow field. Thus the issue of circular causation leads naturally back to the previous issue, that of a global flow field governed by local physical balances.

Because circular cause-and-effect is much more difficult to grasp than one-way causation, we tend to go to great lengths to find one-way causation relations, even when they don't exist. "Bernoulli-based" explanations of lift are obvious examples. Another example, in which the error is not so obvious, is the line of argument put forward by Dave (B.E.Mech) on this talk page, and by Weltner and Ingelman-Sundberg on their web site. It is noteworthy because it explicitly rejects the one-way causation from velocity to pressure that is usually invoked in Bernoulli-based explanations, but then it turns around and invokes one-way causation in the other direction. The argument goes as follows:

It is wrong to argue that the high flow speed over the upper surface of an airfoil "causes" the low pressure there because the pressure difference whose existence we're trying to justify must have been there in the first place to accelerate the flow to higher speed. So where does the pressure difference come from? It arises because the airfoil deflects the flow, or causes it to change direction. So the change in flow direction causes the reduction in pressure, which in turn causes the increase in flow speed.

This argument says, in effect, that it is not correct to invoke a longitudinal acceleration (a change in speed) as the sole reason for a pressure change, but in the case of an airfoil flow it is correct to invoke a normal acceleration (a change in flow direction). The implied justification is that the primary effect of the airfoil surface is to force the flow to change direction and that it is therefore logical for the normal acceleration to "precede" the pressure change in the chain of cause-and-effect. This idea has considerable intuitive appeal, but it is not entirely correct. The problem is that the interaction of most of the flow with the solid surface is not as direct as this argument implies. Only one vanishingly thin streamtube (the stagnation streamline) actually comes into contact with the airfoil surface, and the normal accelerations of all other streamtubes happen out in the field, just like the longitudinal accelerations do. For most fluid parcels there is no direct interaction with the airfoil surface, only with adjacent parcels, and in this situation there is no basis in the physics for making a distinction between the normal and longitudinal components of the acceleration. They are both just accelerations, and neither one has a one-way causal link to the pressure. We can correctly apply the same argument to the normal acceleration as the original argument applied to the longitudinal acceleration: The only thing that can cause a change in the velocity vector is a pressure gradient, so that for the normal acceleration to happen, the normal pressure gradient must already be there. And then if we incorrectly limit ourselves to one-way causation, we leave unanswered the question of what causes the pressure gradient.

These two issues, global behavior governed by local physical balances, and circular causation, are resolved naturally when we actually solve the equations: Global behavior arises naturally, and circular causation relationships are properly taken into account by the equations. But these issues do make the task of explaining lift qualitatively a difficult one. Our failure, so far, to face these issues has naturally led to errors and confusion.

We'd like to be able to start from first principles (the properties of air and the laws of physics), and using nothing else, predict that lift exists and explain what features of the flow contribute to the lift. But I've concluded that this is not a realistic expectation, and that we'll have to settle for something less ambitious.

As I've already argued, the flow around an airfoil must obey the basic laws of physics, in the form of the NS equations. These equations can be used to predict what the flow around an airfoil will do, including how much lift is produced and the detailed flow pattern that accompanies the lift, but to make such a prediction, we must solve the equations for each particular airfoil shape and flow condition we're interested in. Because the flow around an airfoil is a complicated phenomenon, this requires lengthy calculations that are practical only on a high-speed computer. So starting from first principles and predicting what happens requires solving a complicated set of equations on a computer, and is not something we should expect to be able to do in our heads.

To cut the problem down to size, so that we can approach it with simple words and diagrams instead of laborious calculations, we'll have to assume some things ahead of time, things that are consistent with the theory and that can be observed in real flows. There may be more than one viable approach to this, but the only satisfactory one I have found is to assume from the start that lift exists and that it is felt as a pressure difference between the airfoil's upper and lower surfaces. Then, applying the Newton's second law in a qualitative way that doesn't require calculations, I can deduce what the flow pattern looks like that accompanies and supports the lift, a flow pattern that is consistent with what is actually observed.

To summarize my proposed approach to a correct explanation: I start by noting that air has mass and exerts pressure. I then assume that the lift force exists and is transmitted to the airfoil by a pressure difference between the upper and lower surfaces. Then I explain the circular cause-and-effect relationship between pressure and velocity in as layman-friendly terms as I've been able to devise. This is not easy, but if I leave it out, I'm left with an explanation that is incomplete and, to my mind, not entirely correct. Now, with the correct local physics in hand, I am able to argue that an airfoil produces lift essentially by pushing air downward, turning part of the air stream downward and imparting downward momentum to it. To do this, the airfoil must exert a downward force on the air, and since every action has an equal-and-opposite reaction (Newton's third law), the air exerts an upward force (lift) on the airfoil. The pressure difference that transmits the lift is sustained by the changes in flow direction and speed associated with the downward turning of the stream. Both the momentum transfer and the pressure difference are necessary parts of the picture (not alternative ways of explaining the same thing, as has been suggested by some).

I've drafted a somewhat detailed explanation along these lines. It's longer and more detailed than the current version of the lift article (this page). I'd be happy to share the draft with anyone who's interested. --J Doug McLean 20:02, 30 October 2006 (UTC)

It suffices here to say in reply that the essential bones of this discussion are what are important, not lengthy - leading to book length - expostulations making more of this than is necessary here. The highly deductive approach from Newtonian theory vs. the more inductive traditional teachings handed down from aviation pioneers as characterized by correlations and graphs. If you favor one or the other, please say so. Your vote will be counted along with those of the others. In wind energy, which is the basis from which I come, the pressure, necessary though it may be, is almost meaningless and no one worries about pressure distributions across the profile rather than just skipping from descriptions of the airflow - before and after its encounter with the airfoil - right to the resulting forces in total generated on the blade. As far as deliberating whether a figure of a roundish object cross section in the book does or does not represent that of a cylinder, to what lengths does this go? If the figure were that of a square or a proper wing profile ( which it should have been ) could this still be referred to by Batchelor as a "cylinder"? One way or the other, it is an error. It is telling that minor errors such as this create comment but the larger error of outdated - and, by now, generally accepted as misleading - theories in the book does not. Anthony Chessick 16:19, 21 November 2006 (UTC)

We seem to have a disagreement as to what kind of explanation this article should provide. To design a turbine blade it suffices to know what happens when air flows over an airfoil section, but I think that when people look up lift force in Wikipedia, they probably want to know how it happens. To me, explaining the how of a complicated physical phenomenon requires breaking it down into pieces that can be related back to first principles, and showing how the pieces fit together, not so much how they might be logically related through the mathematics ("the highly deductive approach"), but what the physical cause-and-effect relationships between them are. This is my idea of what an "essential bones" explanation requires, and anything less is condescending to the reader.

Explaining lift correctly is treacherously difficult, as demonstrated by the numerous attempts at it that have gotten it wrong and by the confusion that characterizes much of the discussion on this page. An accessible explanation that meets my definition above and gets everything right would be a first, and developing one is going to take some work. The current Wikipedia article is better than most, but it has significant deficiencies that we should try to fix (see below). Given the almost unique difficulty of this topic, I don't think I was "making more of this than is necessary here". I think everything in my admittedly long posting above was relevant to the task at hand, and I'd appreciate some specific feedback on the issues that I raised. In any case, the problem certainly doesn't boil down to an either/or choice between "deductive" and "inductive" approaches.

So, what are the deficiencies of the current article? First, "Reaction due to accelerated air", "Bernoulli's principle", and "Circulation" are presented as separate, equivalent ways of explaining lift, the implication being that any one of them can stand alone as a logically complete explanation. The problem with this is that none of these can stand alone in that way. A complete explanation must include both reaction and pressure, at the least.

Most of what is said in the "Reaction" section is right, as far as it goes, but it fails to convey the idea that the airfoil influences a lot more air than just what flows close to the upper and lower surfaces. And this section by itself doesn't tell you that the pressure is what transmits the force or how the pressure difference arises as a result of the reaction.

The "Bernoulli's principle" section has several problems. Overall, it is confusingly vague. It describes Bernoulli's principle and makes an oblique reference to solving for the velocity and imposing the Kutta condition, but it does not make clear how Bernoulli's principle is supposed to explain lift. To do this it would need to describe and explain what actually happens in the flow around an airfoil. Then for the lay audience it does something unnecessarily intimidating: using a vector integral equation just to convey the idea that we get the total force by adding up local pressure contributions. And several things it says about the pressure integral are incorrect. The integral does not suffice "to predict both lift and drag". It doesn't "predict" anything; it just defines the total force in terms of contributions distributed over the surface. And it is not "always exactly true". For that to be the case, it would have to include the shear contribution, which is a major part of the drag and even makes an insignificant, but not exactly zero, contribution to the lift. Finally, saying that it excludes the "form drag" isn't consistent with the usual definition of form drag as the pressure drag due to the displacement effect of the boundary layer. This is separate from the direct shear contribution to the drag, usually called "skin-friction drag".

For a lay audience, the "Circulation" section contributes nothing to understanding, as the article itself admits. The article's discussion of circulation, the Kutta-Joukowski theorem, and the Kutta condition is too cursory to do anything but cause confusion. It would be better just to mention these things by name, informing the reader that they are elements of the mathematical theory, and to refer interested readers the technical sources.

The so-called "lift equation" is not really an equation in the sense of expressing an independent physical relationship. It is really just the definition of the conventional lift coefficient, which, among the many possible ways of non-dimensionalizing the lift, is the one that is usually most convenient. The lift coefficient represents the lift with the effects of speed, density, and area approximately removed, and is therefor more "portable" in a practical sense, but it is not somehow a more fundamental physical quantity than the lift itself. The lift equation doesn't "predict" anything, unless you consider scaling from one situation to another to be a form of prediction.

The "Coanda effect" section is right where it belongs, under misconceptions, but it too contains significant errors. The conventional explanation of lift does not make "verifiable predictions of lift using the lift equation" (see above). And it is not correct to say that "the effect is not fully understood". A correct and detailed understanding of it is available, though apparently there are many people who misunderstand it. It is also incorrect to say that "Coandă effect's force actually pushes in the opposite direction of the main lifting force". The fact is that the Coanda effect is not applicable to ordinary airfoil flows. We need to make clear the distinction between the Coanda effect and ordinary boundary-layer attachment, and to clarify these issues I am posting a separate entry in the discussion of the Coanda effect article.

Regarding Batchelor's "error", I agree it's a minor issue, but I stand by my statement that it wasn't an error at all. In Section 6.6 of An Introduction to Fluid Dynamics he uses "cylinder" to refer to any 2D body (constant cross-section), including a flat plate at angle of attack, which is mathematically correct usage, just not in line with current American vernacular. I agree that some things in the old books are misleading, for example the Prandtl and Tietjens explanation, which is repeated by Batchelor, that implies that the shedding of a starting vortex somehow causes the establishment of circulation around the airfoil. This is an example of establishing a connection that follows logically but gets the cause-and-effect backwards. J Doug McLean 20:23, 4 December 2006 (UTC)

Opening Illustration

Hello to everyone, As a flight instructor (but still learning a lot) I'd like to add something to the disscussion regarding the graphic on lift near the top of the main article. Where is the relative wind? And since when did lift have a forward component to the vector diagram? If anything, it has a slight rearward component, which contributes to induced drag. I think we could come up with a better diagram explaning lift. Anyone else feel the same way? Joe "Jetman"

Yeah, it isn't the greatest diagram. It takes the frame of reference of the airmass rather than the airfoil. So the airfoil is shown moving through the airmass rather than the airmass moving past the wing. It also is drawn with the wing in a "downward glide" rather than "straight and level." This give the forces their "funny" angles. I presume this choice was made in order to illustrate the fact the lift is not always opposite weight but is defined as being the force perpendicular to the relative motion of the fluid and body. I agree that it's a confusing picture. If you can find or draw a better one, I'd be more than happy to have this one replaced. Blimpguy 23:14, 16 November 2006 (UTC)

I wanted to comment on that image. There are many like it in many books (Including many basic ME textbooks), and there are some fundamental flaws. Primarily, it needs to be noted that lift is generated perpendicular to the chordline. If lift were generated forward of that perpendicular, as illustrated, then the total thrust of an aircraft would, in fact, be increased by the presence of lift. The reverse is actually the case, where lift induces a second vector, induced drag. and I'll agree that marking V(infinity)would be helpful

How do gliders overcome drag? Rolo Tamasi 21:23, 30 September 2007 (UTC)

Someone misspelled "angle of attack" in the illustration.

Thrust in diagram

Why is a thrust vector shown in the diagram of an airfoil at the top? This does not belong there. Dhaluza 13:57, 4 February 2007 (UTC)

It is okay to include the thrust vector, because the figure is trying to show the force balance on an airfoil. There is no reason for the thrust vector to be oriented such that it points in the direction of motion or is parallel to the chord of the airfoil. -Myth (Talk) 00:24, 5 February 2007 (UTC)

No, the thrust and weight vectors do not belong at all. These are not aerodynamic forces generated or acting on the wing, the force balance only applies to the whole aircraft. Dhaluza 11:06, 5 February 2007 (UTC)

Well, without the extra vectors showing force-balance the diagram violates Newton's Third. And in a 3D aircraft those vectors still are not aerodynamic forces, so the wing-vs-aircraft argument is not relevant --Wjbeaty 21:00, 18 February 2007 (UTC)

I think Dhaluza is right. The purpose is to explain the lift force on the airfoil. How it might be balanced, or not, by other forces on the airplane is a separate topic. The forces needn't always be balanced. Unbalanced forces just result in acceleration of the airplane.

Leaving the extra forces out of the diagram does not violate "Newton's Third". The balance or imbalance of separate forces on an object is not what Newton's third law is about. The third law deals with the individual forces that are exchanged between two objects, and states that the objects experience them as equal-and-opposite forces. If we wanted to show vectors illustrating this, we would have to show both the lift exerted on the airfoil by the air and the equal-and-opposite force exerted on the air by the airfoil. But this would be confusing unless we put the two vectors on separate diagrams showing the force on the airfoil and the force on the air. J Doug McLean 21:03, 19 February 2007 (UTC)

I have added the figure back (the reason that it is confusing is not clear to me). Without the figure it is even more difficult to follow the definition of lift. If you have a better figure please replace it, but till then let this figure be here.

I am fine if we do not show the force balance, but then atleast show the net aerodynamic force and its components perpendicular and parallel to the direction of motion and change the caption appropriately. That way it will be easier to explain that the component of the aerodynamic force perpendicular to direction of motion is lift. -Myth (Talk) 20:43, 22 February 2007 (UTC)

I am removing the image again. It does not support the definition of lift in the intro, which only refers to fluid dynamic forces. The diagram is actually specific to a heavier than air aircraft, and not generally applicable. Dhaluza 10:48, 28 February 2007 (UTC)

Instead of removing the figure, you can just add a comment in the caption. Its always better to explain with a figure. If you do not like the figure, replace it with a better one. No figure is not much useful. -- Myth (Talk) 21:15, 28 February 2007 (UTC)

Jef Raskin article is "controversial?"

User 80.221.34.208 added the word "controversial" to the Raskin external link. I've temporarily removed it for discussion. Besides contradicting the many supporters of "equal transit time" misconception, is Raskin'g writing actually controversial? If so, why? (If the controversy is over "equal transit time," then there is no controversy, just a widespread misconception which some authors have the temerity to point out.) --Wjbeaty 21:10, 18 February 2007 (UTC)

In an ideal world, Raskin's article would be labeled "not recommended". While debunking "equal transit time" is a good thing to do, much of the rest of Raskin's article is more confusing than enlightening. Specifically:

1) He devotes too much attention to demonstrations that involve blowing jets of air over pieces of paper or "airfoil" models. The pressure differences in these demonstrations are between flows with different Bernoulli constants, i.e. higher total-pressure in the jet than in the surrounding air. The pressure difference on an airfoil, on the other hand, comes largely from a flow with a single Bernoulli constant, i.e. the flow outside the boundary layer and wake. To really understand the jet demonstrations correctly one needs to take the jet total-pressure difference into account, which is an unnecessary complication and potential source of confusion when the objective is to understand the lift on an airfoil.

2) He refers to ordinary flow attachment (to an airfoil or a baseball) and to the water-faucet demonstration as examples of the Coanda effect. All of these are misleading (see my posting dated 4 December 2006 and the ensuing discussion on the Coanda talk page).

3) He mischaracterizes explanations of the Coanda effect when he says that "the airstream is 'entrained' by the surface". The Coanda effect is a result of the tendency of jets to entrain surrounding fluid. Solid surfaces don't entrain anything.

4) His "MENTAL MODEL OF HOW A WING GENERATES LIFT AND DRAG" is questionable on several counts. He refers to air molecules being "attracted to the surface" and being "pulled down" toward the upper surface. Air actually has no significant attraction to surfaces (The no-slip condition is not a result of attraction), and the air is pushed down by the air above it. His analogy of the air being "attached to the wing with invisible rubber bands" that pull the wing upward is a poor one because it encourages seeing the air as being under tension, which is not possible. J Doug McLean 21:26, 19 February 2007 (UTC)

Incorrect Lift Theory

I came across a few pages that provide a fairly lucid debunking of some of the incorrect theories regarding lift (equal transit, skipping stone, etc). They also have some helpful java apps that you can play with--nice. I plan to integrate some of the content one way or another at my first opportunity, but that may be a while. If anyone else would like to do it, feel free to. The site is http://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html Click the "next" buttons at the bottom to continue viewing each successive incorrect theory and the respective rebuttals. Hope that helps. Davidmhaley 20:12, 21 February 2007 (UTC)

presence of force implies mass and acceleration?

It seems like a lot of people argue that airfoil lift is entirely caused by downward deflection of air according to f = ma. Their reasoning is that there is a force holding up the plane, so by f = ma it must come from mass under acceleration. But that's necessarily the case. Force can exist without mass under acceleration. A book sitting on a table is not held up by mass under acceleration. Nor is a hot air balloon, nor is a boat on the water.

I find the buoyancy arguments compelling. Force can also be created by differences in pressure, without accelerating masses, right? If we measure the air pressure above a 747 wing and find it to be 8% lower than the air pressure below, that fully accounts for the force holding up the plane (though I won't venture as to what causes that, perhaps the partial vacuum created by the shape of the airfoil).

I imagine that there's truth to many of the arguments laid out here. Some of the force holding a plane up comes from pressure differences, some of it comes from downward deflection of air. Is it the case that in a plane weighing 1500N, the pressure differences on the wing account for 1200N of upward force and the acceleration of air accounts for 300N of upward force? Is it the case that a plane can fly upside down only with much more drag because it relies more on deflection caused by extreme angle of attack and less on pressure differences (which might in fact be working against it)?

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- Not correct. A book sitting on a table is mass under acceleration - away from the earth at 10m/s/s. That's why it stays on the table. Don't argue against f = ma. It is fact. (Nothing to do with the theory of lift here - just the physics). --Grinning Idiot 17:51, 15 April 2007 (UTC)

A book sitting on a table is not accelerating unless you want to bring some sort of relativistic equivalence in to this discussion which would be entirely irrelevant. We're dealing with Newtonian mechanics here. The velocity of the book is zero. The derivative of the velocity of the book is zero. I'm not arguing against f = ma, I'm arguing against the idea that f implies ma. Force can exist without acceleration. Let me give another example since you didn't see my point- consider a spring pushed to half of its rest length. It's causing a force on whatever is holding it back, right? Is there anything under acceleration? no. The fact that there is a force holding an airplane up does not imply that air is being accelerated downwards to keep it afloat.Jhhays 01:59, 25 April 2007 (UTC)

Jhhays, I'm assuming the previous post was yours (you didn't sign) but you are right. Downward deflection is not the explanation of lift. This discussion page is very good though. I think some people here might know what they are talking about. --Grinning Idiot 15:24, 4 May 2007 (UTC)

Wow. I have now read all the posts on this discussion page. They range from amazing to common sense to psychotically incorrect. Not getting involved - have fun!--Grinning Idiot 15:07, 5 May 2007 (UTC)

Lie-to-children

I think this article is begging for a link somewhere to the "lie-to-children" article. The reason there are half-correct theories out there concerning lift is that initial explanations to aviation students are simplified so they don't run away screaming. If they don't continue their aeronautical theory beyond the basic stages (beyond what is required to operate an aircraft) they will believe they have the whole story because they haven't heard any different and it sounds right. Check out the above mentioned article and give thoughts on whether it might be a relevant addition.--Grinning Idiot 19:58, 1 April 2007 (UTC)

The difference between "wrong" versus "lies to children" is that lies to children are easily recognized by adults (or at least by the experts.) Here's a common example: In grade school we are taught that atoms are little solar systems, with electrons orbiting the nucleus. Any chemistry student recognizes this lie, and probably sees why it's necessary. Chem instructors certainly recognize the lie. Yet the airfoil misconceptions were (until very recently) taught to pilots, and appeared on license exams. And in my experience, when I discussed these fallacies on newsgroups starting in ~1996, it created huge flamewars because most aviation people simply could not accept that the fallacies could contain any errors. The entire airfoil controversy caught fire only in the 1990s (though "Stick and Rudder" by Langewiesche is an early rare example of the correct, non-fallicious explanations.

Is there a concept called "lies to adults?" I'd say no, because if we must give misleading oversimplifications to advanced students, the teachers recognize the oversimplifications. And we also tell the students about the oversimplifications. It's a matter of respect. But if a textbook explains lift to student pilots by using the equal transit time fallacy, and if the textbook author really believes that fallacy is true, and if the pilot licence exams require fallicious answers on test questions, then it has nothing to do with "lies to children." Instead it's called "being wrong." Or its called "errors as infectious disease" where textbooks spread the errors to teachers. Think about it: if you gave a correct answer on a pilot exam, you'd be marked wrong. They REQUIRED the wrong explanation.

If the textbooks and authors and exam-creators all realized that equal-transit-time (etc.) is an error, then things would be different. They didn't. Instead they angrily defended it as being correct. If they told their students "this is extremely oversimplified and doesn't work well, but it's the only understandable explanation..." then things would be different. They didn't. Instead they really believed that parcels divided by the leading edge are required to join at the trailing edge. I watched over the last ten years as the physics teaching community and the aviation community confronted this error and slowly developed better explanations. But the errors still appear in older textbooks, so they won't rapidly vanish.

Apparently even Prandtl believed the equal transit time fallacy, and a diagram in an early aero math paper may have been one cause of this particular galloping error. Jeff Raskin points out that even Albert Einstein believed the same fallacy, and based a (failed) airfoil design upon it. --Wjbeaty 22:35, 1 July 2007 (UTC)

It is very difficult to believe that Albert Einstein believed in equal transit time. We can be pretty confident that he understood the theory of conservation of energy and that he could see that the only two energy variables with any significant part to play are pressure and velocity. It is therefore immediately apparent that lower pressure regions will have higher velocity. As the average pressure above the wing has to be lower than below the wing it would be obvious to him that the transit time above the wing must be less than below the wing.

I believe the observation that it is a “lie to children” is extremely valuable and accurate. I don’t regret that the “lie” may cause some to believe that the airflows have equal transit times as it is a misunderstanding that is unlikely to have any consequence (any more than thinking that atoms have valence “hooks” on them). However I do regret that fact that it causes many to believe that shape is the cause of lift rather than angle of attack. This misconception can be a barrier to understanding many things we may come across (e.g. How can a boats rudder work? How can anything fly upside down? etc.)Rolo Tamasi —Preceding unsigned comment added by Rolo Tamasi (talk • contribs) 13:16, 10 September 2007 (UTC)

--- Just to clarify, the shape (camber) is an important part of the lift and combined with the Angle of attack sets the lift. Tzickuhr 02:37, 12 September 2007 (UTC)

Just to clarify even further, camber is not important in generating lift in wings that have no camber and is even less important than that in the case of cambered wings flying inverted! Rolo Tamasi 14:58, 16 September 2007 (UTC)

Basic ideas

Here is a simple explanation for lift which I think most people will agree with. First of all what does a wing do to the air? The answer is the air flowing over one side of the wing is forced to follow a curved path. The greater the angle between wing’s path and the relative airflow the smaller the radius of the curve path the air will follow, up to a certain point after which, the smooth flow of air breaks down. This has been shown in wind tunnels and is easy to observe as passenger in an aircraft flying in cloud or humid air. Form basic physics we know that to make something move in a circle we need to apply a force towards the centre of the circle. The wing is providing that force by in effect pulling down on the air above the wing and in turn being pulled up in the process (Newtons 3rd law).

This is in complete accord with Bernoulli’s principle which states that if we accelerate a parcel of air the pressure will drop. The air follows a curved path as its passes over the lifting surface of the wing and therefore is accelerating for the full chord of the wing. From the equation F=MV²/R we know that the force must related to the velocity squared. Note that while we know that the speed of the air over the top surface does in fact increase it is only necessary for the air to follow a curved path for it to be defined as accelerating.

On the bottom of the wing the air for the most part will just collide with the under side of the wing and be defected down. The lift will be equal to air mass times the velocity which in the case of my aircraft would be only 10 % of the lift needed to sustain level flight. The important difference here is the velocity is not squared and so the lift produced is only a small part of that needed.

Now if we consider a wing as just a flat plate at an angle to the air flow. We can see that the only air which is directly affected is a rectangular block of air of which the wing chord becomes the diagonal. The block of air will be divided into two equal parts. We can determine the volume of the whole block and what its mass will be from the air density, the area of the wing, and the vertical height of the block of air. You can then derive the well know equation for lift.

Lift =Cl * ½ ρV²*S Using the metric system Lift will be in Newtons Cl is the coefficient of lift which is a number between 0 and about 2. ρ is the air density which is about 1.225 kg/cubic meter at sea level. V is air velocity in meters a second. S is aerofoil surface area in sq meters. Cl will be related to the amount of air moved and how much the air is forced to bend not to mention a host of other minor factors.

Now we get to the bit where lots of people will disagree. A popular site refers to physical description of lift .I am of the view that this particular physical description of lift is just plain wrong. I think for it to be correct the equation for lift would have to be proportional to the velocity not velocity squared. Below are some of the problems I see with the idea.

If you really think that the physical description of lift is correct try and use it to explain how the tail plane produces a strong down force despite the fact that under certain conditions it may have a positive angle of attack of as much as 12 degs!

A biplane's a lower wing which would be just about useless!

The idea that downwash is the cause of lift was disproved way back in the 1930’s by experiment. It was found that the speed and angle of the up flow in front of the wing was the same as the down flow at the trailing edge.

So where does all the turbulence from a large aircraft come from. A simple analogy is what happens at the start of a game of pool. You hit the white ball which in turn transmits its momentum to all the other balls causing them to go all over the place. The force applied to the system all comes from the single blow to the white ball. Trying to work out the amount force applied to the system by just adding up the mass of all the balls will not yield any useful information. In other words the wing may well disturb a large mass of air but the bit that matters is the air that directly interacts with the wing. PR 27 July 07

I have had a careful look at the above link to the physical description of lift. It appears to be full of errors and mistakes. There are too many to list but here are a few examples. The picture of the Cessna flying over the fog is claimed to be an example of a wing producing a large downflow. I think not, there are two jet turbines blasting 1000's lbs of hot air at the fog bank.

The article also claims that power is needed to generate lift, as an aircraft in level flight is not gaining or losing height this is not true. In physics for work to be done a force must move its point of application in the direction of the force. If the plane is flying level the lift force is not moving in the direction of the force and so work is not being done. This is a serious error. On the other hand a plenty of work is being done overcoming drag. This is an important distinction and negates much of what is claimed in the article.

Under conclusions he states that lift is proportional to the amount of air diverted times the vertical velocity of the air. I don’t know where any one has proved that, it seems to be an unwarranted assumption. I also don’t think that it can be reconciled with the fact lift is proportional to the amount of air moved times the square of the horizontal speed.

Is there any reason why the lift force has to be solely generated by an exchange of linear momentum? I would argue that it is in fact mostly generated by giving the air angular momentum. Remember we only need to generate a force to balance the weight of the plane not a force to accelerate the plane higher.

Further to the above I would add that the explanations of how ground effect and winglets work are also very dubious and certainly not the accepted view. PR 5 Aug 07

There are to my mind two areas in which the main article could be improved.

The first is to get rid of what I call the rocket engine analogy of lift. That is the idea that the wing must accelerate an amount of air directly downwards to balance the weight of the aircraft. In fact lift for the most part is generated by changing the direction of the air flow by making it take a curved path. This again should be obvious from experimental results. In a wind tunnel the amount of lift from an aerofoil can be found by measuring the up force on the tunnel itself. If air moving vertical down was the cause of lift it would push the floor of the wind tunnel down and so make it impossible to get a reading for the lift force.

The next area which needs attention is the section on the Coanda effect. The way in which wing generates lift was fairly well understood before Coanda noticed that the hot exhaust from the engine was some how increasing the amount of lift that wing produced. He was then given the credit for finding and explaining this phenomenon. If you are to claim that Coanda effect is the source of lift you are in effect saying he did not discover anything. The Coanda effect specifically requires a source of high pressure air to be injected into the air flow.

In the Coanda effect energy has to be added to the airflow and the air flows along the curved surface due to various forces of attraction between the surface and the air molecules. On the other hand in ordinary lift the air follows the curved surface at first because it has no choice and subsequently in order to fill the void that the wing would otherwise create on the lifting side of the wing. In both cases the lift force is generated by the air being forced to change direction but the reason the air follows a curved path is quite different. The forces can be added together so the can hardly be considered one and the same.

I think the section on the Coanda effect should be restricted to explaining that it is way to increase the amount lift a wing produces, or if you like another way of producing lift. It should not be under the heading of misconceptions.

I would also suggest the section referring to Raskin be removed. The Coanda effect is a separate phenomenon and not a generally accepted explanation of ordinary lift. PR 24 Aug 07

Question to PR

Quoting PR: The idea that downwash is the cause of lift was disproved way back in the 1930’s by experiment. It was found that the speed and angle of the up flow in front of the wing was the same as the down flow at the trailing edge.

Dear PR. Can you provide any reference to the experiment you mentioned? Wouldn't it seem that the case of generated lift without net downwash violates Newton't 3rd law? Integrate total momentum flux of air along the vertical planes some distance ahead and behind the wing. If there is no total change of vertical momentum of the air (i.e. no net downwash), then there is no total vertical force acting on the air as it passes the wing, or, from Newton't 3rd law, no vertical force by the air on the wing. N.P. Aug 07

I will answer this question in some detail later as I don't have time just at the present, but in the mean time I would like you to think about this. The Earth stays at pretty much the same height above the sun so where is the change in vertical mommentum coming from and will it upset Newton ? PR 29 Aug 07 —Preceding unsigned comment added by 124.180.147.246 (talk) 22:37, August 28, 2007 (UTC)

Newton's 3rd law is not violated.

The pressure field of the wing is reacted. Recall the 2 dimensional case mentioned earlier. The upwash in front of the airfoil is exactly the same as downwash behind the airfoil. The force on the airfoil is reacted against the wind tunnel walls by pressure. I verified this with a 2-d Navier-Stokes CFD code. As I moved the walls further from the airfoil, the pressure change on the walls was lower, but acting over a larger region. Each time I integrated the pressure on the airfoil (the lift) and the pressure on the walls, they were the same in opposite directions.

From a very far distance, the vortex structure of a wing is somewhat like a doublet, so I realized that a 3 dimensional wing must do the same thing (I'll explain this better later if you're interested). So I set up a 3 dimensional wing and did the same N-S analysis, again changing the outer boundaries to solid surfaces instead of far-field conditions. I got the same result. When I integrate the lift on the wing (by integrating the pressure on the surface) and then I integrate the pressure on the top and bottom walls I get the same number (in opposite directions). The lift of the wing is reacted against the wind tunnel walls. I moved the walls further from the wing and got the same results, with a smaller pressure over a larger area.

So, the lift of a wing is reacted against the ground and against the outer boundary of the atmosphere. This took a little thought, but I would compare it to a hydrofoil in water. The low pressure on the upper surface of the hydofoil causes a wave on the surface of the water. A wing will do the same on the outer boundary of the atmosphere, causing a wave. The distances are so large relative to the wing that these disturbances will be imperceptible.

An equal and opposite force, so no violation of Newton's 3rd law. TZ 29 Aug 07

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Hmmm, interesting. What about hypersonic flight in upper atmosphere? Before disturbances reach any distance in the vertical direction, the vehicle will be long gone. By the way, to calculate lift numerically it is sufficient to do 3-D Euler simulation, without wind tunnel.

That the downwhash exists in situations of realistic Reynolds number flows can easily be observed from experiments; for example, see visualizations in the following paper: Aircraft Trailing Vortices and Downwash Phenomenon by Hiroshi Higuchi; the paper can be downloaded from Physics of Fluids Journal at http://pof.aip.org/pof/gallery/1993toc.jsp.

The lift still can exist without downwash, however, provided that trailing vortices are shed from the tip -- a process which generates circulation around the wing. N.P. 30 Aug 07 —Preceding unsigned comment added by 128.186.104.222 (talk) 15:39, August 30, 2007 (UTC)

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With hypersonic flight the pressure still reacts against the ground and space. There's just a delay due to the pressure wave (shock). I don't see a problem here.

Yes, I could have done an Euler calculation, but I already had the N-S model complete, so I just changed the boundary conditions on the outer box. It was easier. If you don't change the boundary conditions to be solid walls like a wind tunnel, there will still be a disturbance at the computational boundary, so you will not have reacted the force. The walls must be solid to understand how the force is reacted.

More on the downwash later. TZ 30 Aug 07 Tzickuhr 02:46, 31 August 2007 (UTC)

Newton 3rd law and lift

Here are my views on Newtons 3rd law and how it applies to lift.
It is necessary to be clear on the definitions of the following terms:-
Velocity is speed in specific direction that is to say a vector quantity.
Acceleration is a change velocity over time that means a change in speed or direction is acceleration.
Mass is a measure of how difficult it is to accelerate an object.
Momentum is the product of Velocity and Mass and is therefore also a vector quantity.
Force is a directly related to any change in momentum a body undergoes.

Newtons 3rd law is normally stated as follows:

A/ To every action there is an equal and opposite reaction.

This only covers a dynamic situation that is where both bodies are moving so an alternative definition which includes the static situation is typically stated as follows:

B/ For every force acting on a body there is an equal and opposite force acting on another body.

If we apply definition A to an aircraft in level flight we know that the vertical velocity is Zero and the product of Mass times velocity must also be zero which in turn leads us to conclude that the net vertical momentum of the air must also be zero and therefore we can not account for lift by considering vertical movement of the air.

On the other hand if we apply Definition B to an aircraft in level flight we can say that there is a force of mass times gravity pulling the aircraft down and the air must be providing an equal and opposite force on the wing. If we accept that the air flowing over the wing follows a curved path, then the wing must be producing a centripetal force on the air, which is equal and opposite to the weight force of the aircraft.

To help clarify the above I will quote some numbers for an aircraft.
Weight 350 Kgs
Stall speed 20 meters /sec (40 knots)
Force required to support aircraft =Mg = 350 * 9.8 =3430 newtons
If force provided by turning airflow then F=MVh²/R where M will be the amount of air moved and Vh is the true airspeed over the wing.
Assume r =1 (this is guess but it is in the right ball park)
Using Newton 3rd and solving for air mass required to provide lift
3430=MVh²/1
M=3430/Vh² = 3430/20*20
M=8.5 Kgs of air or about 6.9 cubic meters of air

If we think that the vertical momentum of air is responsible for lift then F=½MVd² where Vd is the net vertical velocity of the air and will be no greater than .25 of the horizontal airspeed. Using Newton 3rd and solving for air mass required to provide lift
3430=.5*M*5*5 =12.5*M
M=274 kgs of air or 220 cubic meters of air at sea level

Now I will leave to those who are interested to calculate what happens when the lift has to be doubled as in a 2 g turn. PR 10 Sept07. PatRobot 02:10, 26 September 2007 (UTC)

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Ooohh, a trick question and you almost got me. If you're already at the stall speed you can't pull 2g in a turn!

I see no aerodynamics in your equations. It looks more like the equation for a ball on a string. Can you please show the force and moment diagram that includes a centripetal force? What about the upwash in front of the wing?

Are you saying the air is only disturbed one meter from the wing (r=1)? Even for an A380?

How did you determine that Vd=0.25*Vh? That's a lot of downwash!

So is it 6.9 or 220 cubic meters of air? How can there be two different answers?

Tzickuhr 03:30, 12 September 2007 (UTC)

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Sorry it was not meant to be a trick question. In a 2 g turn the new stall speed can be easily be determined knowing that the lift goes up by the square of the airspeed. The stall speed will typically occur at about 15 degrees angle of attack and just before the stall occurs is the maximum lift the wing can produce at any given speed.
This implies that air mass moved must remain constant at any given angle of attack, and moves across the wing in a shorter time at higher speeds. If we base our calculations on vertical movement of air we get an impossible answer for air mass on the other hand if we base our calculations on the curved airflow we get an acceptable answer that is the air mass moved remains constant at the stall angle regardless of speed.
The justification for saying that the vertical speed of the air can be no more than .25 of forward speed is that airflow from the highest part of the of the wing to the trailing edge represents the maximum vertical height that the air has to move in unit time and is Tan 15 degs just before the stall angle is reached.
If Vh=30 m/s and angle =5 degs then Vd=2.6 m/s or 5 knots which might be more typical for a light aircraft in cruise mode.

I'm slightly confused by this working, it appears not to recognise that the air is accelerating all the time it is in the pressure gradient and that it is the final speed that is important, not the average as this appears to estimate. 11:01, 29 September 2007 (UTC) —Preceding unsigned comment added by Rolo Tamasi (talk • contribs)

The values calculated by me under Newton 3rd and lift are simply to demonstrate the scale of the problem and may well be off by some margin. The results showed I hope how improbable it was that vertical momentum could account for lift especially as I ignored up flow upwash in front of the wing which of course makes the vertical calculation invalid.
Applying the principle that bending the airflow causes lift then we can say that up flow upwash contributes to the overall lift. So the answer is much closer to 7 cubic meters of air than it is to 220 as in the example given previously.
The value I used for the radius should I think be of the same order of magnitude as the chord of the wing in use. The radius does not determine how far above the wing the air is disturbed. Of course to get the correct answers you would have to integrate the various radii over the whole wing but using F=mv2/r does give an idea the much greater forces involved in bending the flow rather than just pushing air vertically down.
As a pilot my main interest is to explain how lift works to others in a way that I hope complies with conventional aerodynamics and physics.PR 13 sept 07 PatRobot 02:10, 26 September 2007 (UTC)

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It was a joke.

It's obvious by your description that you don't have a clue how a wing works. You're just making up numbers and plugging them in equations that have nothing to do with aerodynamics. Your ability to pilot an airplane does not lead to any understanding in how a wing works. I've read that many pilot training programs use incorrect descriptions of lift. You haven't even acknowledged that you understand what upwash is.

A wing lifts because the surface curvature and angle of attack cause the pressure on one side to be lower than on the other side. And this has nothing to do with the bogus equal transit time nonsense. It's physics.

When we do a CFD analysis, we integrate the pressure on the surface to calculate the lift. If we want loads distributions from a wind tunnel model or an airplane, we measure the surface pressures and integrate them to calculate the lift. The only forces that can be applied to an object by a fluid are the pressure normal to the surface and the shear stress tangential to the surface.

We never use the vertical velocity in any way to calculate the lift of the wing.

As a professional aerodynamicist who designs wings for a major business jet manufacturer, my main interest is to explain how lift works that is correct. If you have any questions, please ask.

Tzickuhr 02:16, 14 September 2007 (UTC)

Do I see a possibility that you may agree with each other? PR says that the total lift cannot be explained only by vertical acceleration of the air (whether or not you agree with his maths). I think that below Tzickuhr says something similar viz. “The lift is the integral of the rotational velocity (the vorticity) of the wake, not the integral of the vertical velocity.” Rolo Tamasi 23:51, 14 September 2007 (UTC)

Absolutely correct Rolo. Oh and by the way as pressure is force per unit area what is the origin of the lift force Tzickuhr? Pr 16 Sept 07 PatRobot 02:10, 26 September 2007 (UTC)

I’m surprised you don’t understand that PR. The answer is that the origin is the relative movement between the wing and the air. That creates pressure differences that have the equal and opposite effects of lift on the wing and acceleration of the air. Rolo Tamasi 09:38, 16 September 2007 (UTC)

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It is the airflow changing direction that is the origin of lift force.

I disagree, I would say that the acceleration of the air and the lift have a coincidental rather than a causational relationship. For me there is a clear, undeniable, logical sequence. The origin is the relative movement between the wing and the air, angle of attack is a condition and pressure differences are the result. The pressure differences in turn cause two coincident effects, lift on the wing and acceleration of the air.Rolo Tamasi 20:12, 1 October 2007 (UTC)

The mistake that is made by a number of people on these pages is their failure to understand that acceleration is a vector quantity. When an object moving at speed changes direction, large forces are produced and that acceleration is often greater than either it’s starting speed or its final speed.

I suggest it is safer to assume that people in here have an intimate understanding of acceleration and of vector mathematics.

A speed cannot be smaller or larger than an acceleration, they have different dimensions and are therefore incomparable.Rolo Tamasi 20:12, 1 October 2007 (UTC)

If we consider an object moving horizontally at 16 meters/sec and 1 second later it is moving vertically at 9 meters/sec what is the acceleration? If you really understand acceleration you will know the answer straight away. If you have difficulty working this out you will have to study up on vectors.

If we consider an object moving at 16 metres/sec and 1 second later it is moving at –9 metres/sec what is the acceleration it has experienced? Rolo Tamasi 20:12, 1 October 2007 (UTC)

When you have worked out the acceleration you can then find the size of the force that caused the change by multiplying it by the mass.
In the case of air flowing over a wing we need to know the acceleration at every point around the wing and the mass of air involved then we can determine the total lift force. It sounds simple, but is difficult to actually calculate, for this reason an easier method is used to calculate the lift forces. That is to measure the different pressures at a large number of points around the wing and add them all together to find the total lift force.
If you want to demonstrate the effect next time you are at supermarket push a loaded trolley directly away from you and let go, you will notice you can not get much of a push force in the opposite direction. On the other hand try to swing the trolley through an arc of say 180 degs and you will find that the pull force you have to provide is large and lasts much longer than the simple push case. Now suppose instead of swinging the one trolley through 180 degs we swing a succession of trolleys through say 30 degs of arc we would experience a powerful and continuous force pretty much in one direction. I don't need to point out that the trolley has to allow all wheels to steer for this to work. That it I’m going shopping! PR note name change last name got cancelled by Wiki PatTwace 05:56, 1 October 2007 (UTC)

The secret of the difference here is the instruction to let go in one and not the other. This does not demonstrate that it is possible to transfer more energy by continuingly changing the direction of acceleration. It only shows that you can you transfer more energy if you are able to hold on longer!

The only difference between the curved flow of air and a linear flow of air is the viewpoint of an observer (you are in the aircraft, I am on the ground). The same energy is required in both and the maths for both is essentially identical other than the approach needs to be consistent throughout the frame of reference.

This is a classical example of why it is important to ensure an understanding of the principles informs the use of the maths and why it is dangerous to allow the maths to inform your understanding of the principles.Rolo Tamasi 20:12, 1 October 2007 (UTC)

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The lift is due to the pressure on the wing. The wing pressure (due to the circulation) extends out to the walls so that the integrated pressure on the walls equals the wing lift. F=F. The summation of the forces equals 0. I have proven this with a CFD calculation. If anyone else does this calculation and gets a different answer, please let me know.

The lift is related to the downwash behind the wing based on the circulation. However, the circulation also induces an upwash in front of the wing that is equal to the downwash. There is no net downwash. The air is not accelerated in the way this page describes F=ma. This "physical description of lift" ignores the upwash in front of the wing and is wrong and is in no way equivalent to pressure. There is not an "equal and opposite" acceleration of the air. I'm going to try to do this calculation in the next couple weeks by integrating the vertical velocity on a cut plane in front of the wing and behind the wing and showing that they are equal and opposite.

The pressure on the wing is due to the curvature of the surface. This is hard to explain, which is why there are so many incorrect explanations. I'll see if I can put together some pictures that explain this visually.

I'm working with a professor to complete my understanding of a few details of the far field lift derivation, but I'm confident I'm right. If anyone would like to discuss these details, please let me know.

PR, I do not understand your question. The origin of the lift is the pressure.

Tzickuhr 02:22, 19 September 2007 (UTC) TZ

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TZ The statement “The pressure on the wing is due to the curvature of the surface” is meaningless what I hope you are trying to say is “the air flowing over the curved surface of the wing causes a reduction of pressure” in which case we would seem to agree on number of the relevant points.

I can’t go along with the repeal of Newtons second law as pressure is simply an example a force spread over an area therefore we are stuck with F=ma. Please explain A why it is not applicable or B how it should be applied PR 20 Sept 07.PatRobot 02:10, 26 September 2007 (UTC)

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This appears to be a problem about definitions rather than a difference of substance.

I prefer to ditch the jargon in a public forum as it confuses rather than informs and is unnecessary.

For example, air does not circulate around an aerofoil when it generates lift. The variable named “circulation” in the Kutta-Joukowski equation may well be non-zero but that does not mean that there is any pattern of flow that could be called circulation in any normal meaning of the word. It is a little like the difference between saying “For some purposes all the mass of a body can be considered to be acting at the centre of gravity” and “All the mass of a body is at the centre of gravity” – lazy use of jargon that could lead to a big misunderstanding.

Likewise, while it may be important to take account of any curvature of a wing in order to accurately calculate lift, curvature is not required in order to generate lift.

I am always surprised that some people’s curiosity is satisfied by the explanation that lift is caused by accelerating the air. That, as Basil Faulty would say, is a statement of the bleeding obvious. It explains no more than saying the air is accelerated because there is lift. Neither of them gives any indication at all what the mechanism actually is – and that mechanism is the formation of pressure differences. Rolo Tamasi 15:43, 20 September 2007 (UTC)

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Acceleration of air over an aerofoil.
In the following discussion my remarks apply to aerofoils moving at speeds below about 300 meters per second.
Air molecules at room temperature are moving at speeds in the range of 500 m/sec or close to 1000 knots.
When an object moves through the air there is a relationship between the speed of the object and the speed of the air molecules. Suppose we have a wing moving at 50 m/sec then any air moved out the way by the wing will be replaced by air from the immediate surroundings and not from some more distant location. In other words the potential void at the back of the wing will not be filled by air from the front of the wing; it will fill from close by long before it can have any influence over the more distant air near the front of the wing.

The question then arrises as to the reason the air flow accelerates over the front section of the wing. To keep it as simple as possible let us consider an aerofoil which is a curved plate, (and part of the arc of a true circle) where the chord is at zero degrees to the air flow. A small parcel of air striking the top surface of the leading half aerofoil will attempt to leave at a tangent this will produce an area of lower pressure both below and ahead of the parcel, thus causing an acceleration of the air along the surface of the wing but only up to the mid point of the aerofoil beyond this point the horizontal component is reversed. The air then starts to slow down which in turn causes the air pressure to rise. A similar situation occurs on the underside of the wing but the situation is reversed so that the net result is an increase in pressure in the first part of the aerofoil and the pressure starting to fall towards atmospheric after it passes the mid point of the aerofoil. You can understand this in terms pressure differences, Bernoulli or acceleration as you wish. These effects take place over very short distances, not over longer distances as the air molecules are just too quick.

As they are taking place instantaneously along the entire pressure gradient and the pressure gradient is propagating at close to the speed of sound they are actually taking place over quite large distances (typically expressed at between 1 and 2 wing spans).Rolo Tamasi 17:32, 12 October 2007 (UTC)

The acceleration I referred to was in the vertical plane not the horizontal (I was contrasting the deflection explanation of lift and the pressure explanation), the accelerations in the horizontal plane broadly cancel out and thus their effects do also. Many people have, from an early understanding, been seduced into the trap of perceiving that horizontal speed increases create lower pressures and thus lift. It is just a perceptual fallacy, the relationship is coincidental not causational. Rolo Tamasi 17:32, 12 October 2007 (UTC)

Now I hope it will be clear why the nose of an aeroplane or airship is rounded and the tail tapered to a narrow point.

A flat plate at an angle to the air flow produces lift because the airflow changes direction and as it is impossible for it to change direction instantly it follows a curved path. --PatTwace 07:37, 12 October 2007 (UTC)

I think the above sentence illustrates the problem perfectly. Whether the air is moving or stationary is merely a matter of the frame of reference of the observer. Most see aircraft moving in stationary air – the perception of curved path caused by the acceleration is a purely matter of choice. It is possible to accelerate along a straight path if it starts as stationary. It is thus confusing to say that lift is caused by the path being curved. Rolo Tamasi 17:32, 12 October 2007 (UTC)

The frame of reference is unimportant the air flow is still curved the air is accelerated both backwards and vertically thus giving a curved path compared to the more distant air.--PatTwace 22:36, 14 October 2007 (UTC)

It is only because of a particular frame of reference that you were able to say "it is impossible for it to change direction instantly". In any event, the air is accelerated backwards and then decelerated. Both of these events are perpendicular to the plane of the lift and thus have no effect on lift. In addition the horizontal acceleration and deceleration cancel out, there is no residual horizontal momentum. Rolo Tamasi 18:57, 15 October 2007 (UTC)

In any event, the air is accelerated first upwards and then downwards. Both of these events are in the same plane as the lift and thus have no effect on lift. In addition the vertical acceleration and deceleration cancel out; there is no residual vertical momentum.--PatTwace 03:09, 19 October 2007 (UTC)

So you don’t believe that fans work?

Consider, for example, the high-pressure region on the under surface of the wing. This creates pressure gradient from the high-pressure to the ambient with a component that inevitably accelerates the air downwards, where is the reverse gradient that decelerates it back to stationary?

Pressure works equally in all directions, if part of the pressure works on the wing as upwards lift, there must be a reverse net effect working on the air accelerating it downwards. Rolo Tamasi 11:59, 20 October 2007 (UTC)

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Yes, it is the curvature of the air flow that creates the low pressure, but the curvature of the surface causes the air to turn. I tend to focus on the surface because that is what I have to change to get the air to turn to get the pressure I want. You are correct in that the physics is all about the air.

But wings with no curves also generate lift. There is no need for the air to turn, just for it to accelerate. I find it far clearer to consider that the pressure difference causes the acceleration of the air rather than the other way round. The pressure difference is caused by the wing moving and vacating space. Rolo Tamasi 18:33, 24 September 2007 (UTC)

A simple aerofoil can be made by taking a flat sheet and bending it into an arc of a circle. An aerofoil made like this works fine but once the camber exceeds a value of about 7% the aerofoil will only work at positive angles of attack. Such a wing will not produce lift at negative angles of attack or if you like it will not allow the aircraft to maintain level inverted flight. So curvature is kinda important. I will leave it to the reader to figure out why.--PatTwace 06:20, 8 October 2007 (UTC)

Rolo

I will try to explain why the idea that the void that you think should form over the back section of the wing is not responsible for lift. First of all when you move an object through the air it simple flows around it and no voids are formed. The next point to consider is this, if a void were indeed formed in this region, the air would fill it from the rear of the wing not the front and would slow the air down over the top of the wing not speed it up. The air does in fact start to slow down once it passes over the thickest part of the wing, but this has more to do with fact that the air is no longer turning so quickly and therefore the acceleration is less. This all shows up clearly when you look at the pressure around a wing at least half of the lift is generated by the first ¼ of the wing. That’s why they put mainspar around that position.

To understand circulation think of it this way suppose we take a hollow cylinder and spin it. The air on the outside of the cylinder will be flung outwards thus creating and area of low pressure right around the outside wall, on the other hand the air on the inside will be flung from the centre of the cylinder to the wall creating a higher pressure on the inside wall.PR PatRobot 02:10, 26 September 2007 (UTC)

I don’t think a void should form over the back of a wing, but it would if the air did not flow. The reason the air accelerates is because of a pressure gradient. In steady state conditions equilibrium is established where the pressure gradient is sufficient to cause the flow rate necessary to maintain the pressure gradient. This is the mechanism by which any fluid flows round any body.

On the top of a wing the pressure gradient exists in all directions but the horizontal accelerations cancel out. I would be interested to understand why you feel the air would accelerate from the back and not the top. The air accelerates horizontally before the maximum low pressure and decelerates horizontally after it.

The simple answer is that it that’s not what happens anyway, but even if it did the air would fill the potential void from all available directions but as the wing is in the way some of the area to the front is unavailable and we are left with a net acceleration of the air towards the front of the wing and by newton 3rd a net rearward force on the wing.PR PatTwace 05:42, 1 October 2007 (UTC)

You appear to believe that the air on top of the wing is slower than the free stream speed and that it gets relocated forwards (and indeed continues moving forwards). I have never come across these ideas before. Can you explain? Rolo Tamasi 21:25, 1 October 2007 (UTC)

Which proves the reason the air speeds up is not due to a low pressure area behind the wing. The air speeds up because it has to follow a longer path around the curve than the straight line path. Just like the water skier who moves out the side of the boat will move much faster. If you have ever flown a plane you will be very familiar with consequences of the air trying to move from the back of the wing to the front it’s called a stall.

I am afraid I don’t see that is an attempt answer to my question.

The air velocity is not due to the longer path. It is due to the curvature of the path. The length of the path for the air around a sail is the same on both sides, but the pressure on the concave side is higher and the pressure on the convex side is lower. Tzickuhr 03:21, 11 October 2007 (UTC)

I agree point taken --PatTwace 07:37, 12 October 2007 (UTC)

However, I have two issues with what you do say: -

1)You don’t need a curved surface to generate lift (as you said yourself).

The benefit of a curve is an optimisation of the acceleration along the aerofoil; it is not an essential element for lift. My concern is that any definition of lift that says it is caused by the curvature of a wing will confuse the reader, as they will take it to imply that wings have to be curved and also that inverted flight is impossible.

2)Only a pressure gradient can cause a fluid to accelerate.

I am exceptionaly familiar with the behaviour of a wing at the stall. I see no value in describing a stall in the terms you do. As long as there is a low pressure region the air is "trying" to flow towards it. In most real life stalls the air is not flowing backwards. Rolo Tamasi 16:21, 8 October 2007 (UTC)

See this link http://www.youtube.com/watch?v=zrwlpHE7P8Q It shows the air flowing forward at the stall and its fun.PatTwace 03:04, 10 October 2007 (UTC)

You are confusing the issue with separated flow. That is a very complicated subject and is beyond the scope of this topic. It's hard enough to get people to understand lift with attached flow. Let's stick with that.

I dont agree that it is hard to get people to understand lift. It is just hard to get those who don't understand it to stop confusing people! Rolo Tamasi 17:32, 12 October 2007 (UTC)

Likewise, when you say you don't need to have a curved surface. True, it's the curvature of the air flow path that generates the pressures that create lift, but if the surface is not curved, you will not get much lift before the flow separates. Again, more complicated than needed for this topic. Tzickuhr 03:21, 11 October 2007 (UTC)

Agreed! Rolo Tamasi 17:32, 12 October 2007 (UTC)

To quote from a Martin Simons a well know aerodynamics professor “Every diversion from the straight path is associated with interdependent velocity and pressure changes.” --PatTwace 06:20, 8 October 2007 (UTC)

Obviously, a change of direction is an acceleration, which can only be created by a pressure difference. I don’t se any reference to curve. Rolo Tamasi 16:21, 8 October 2007 (UTC)

I understand circulation very well thanks. It’s a shame that name was used for the variable as it confuses so very many people. If you are saying that the layman would see any pattern of flow with a non-zero line integral around the shape as a circulation I must disagree with you.

A curved acceleration can be resolved into two perpendicular linear accelerations. There is little point in arguing that there is a substantial difference between the two. If you consider a vertical acceleration of the air from a moving wing frame of reference you will see a straight line. If you consider it from a stationary wing frame of reference you will see a curve. They are both the same.

The simple world of lift is being completely confused by people who believe that mathematical models define the principles. They don’t, it is the other way round. There are many ways of mathematically modelling the same lift.Rolo Tamasi 23:15, 28 September 2007 (UTC)

Personally I find it very disappointing when a perfectly good theory has to be discarded because of the failure of the facts to cooperate.In the above case the facts are as follows:-

The pressure above the wing drops to near its minimum value in the first 5 % of the wing chord and remains close to the minimum until it reaches about the half way point on the wing and then starts to rise rapidly. In fact a pressure higher than normal is reached before the air the leaves the trailing edge of the wing. This has been measured countless times in wind tunnels.

I can’t see a logical reason for a low pressure zone to relocate to any place other than where it was created. I add these comments with some trepidation as I have not fully digested your comments above EG A curved acceleration can be resolved into two perpendicular linear accelerations.PatRobot 01:00, 30 September 2007 (UTC)

We appear to failing to communicate effectively. – I have not made any reference to the nature of the pressure profile along the top of the wing, that changes significantly on shape, speed, angle and chord length. But in all cases when a wing is generating lift it is, on average, below the ambient pressure that exists before and after the wing. What is the relevance of its profile?

I am interested to understand why some consider there to be a significant difference to the energy input required to accelerate air along a curved path rather than a linear one. I suggest that this is just an artefact of a particular mathematical approach and, in particular, the frame of reference that happens to be chosen. It may be misleading to call it a theory. Rolo Tamasi 14:35, 30 September 2007 (UTC)

I'm not trying to repeal any of Newton's laws. The pressure (force/unit area) on the surface area of the wing integrates to the lift force. This has nothing to do with F=ma. The pressure on the upper and lower walls of a wind tunnel also integrate to the lift force in the opposite direction. Pressure acts on an area to create a force.

A book on a table applies a pressure (force/unit area) on the table. The table applies a pressure back on the book. F=F. Or more technically, Fbook-Ftable=0. Fwing-Fwalls=0

Rolo, air does circulate around a wing, but it is superimposed by an onset flow and therefore does not look like the circulation you mention. Picture a spinning cylinder, with and without an onset flow. A wing needs the onset flow to create the circulation.

Tzickuhr 22:47, 20 September 2007 (UTC)

Hi, Tzickuhr. My point is that Wikipedia is here to inform rather than to confuse.

Some of us in here have a thorough understanding if lift but Wikipedia has far more to offer those who do not and have looked up Wikipedia in order to learn. They have to be the primary target audience.

Unfortunately, while the former group understand the substantial difference between circulation and circulation, to the target audience the two words appear identical and thus they can only be confused, it has to be avoided.

Your justification is subject to two fundamental flaws in logic.

Just because Γ is non-zero when the air is circulating it does not mean that whenever Γ is not zero the air must be circulating (all men are human but not all humans are men). It is a shame it was ever given that name – rotation would have been better but has different conflicts.

(Modified on re-reading my reply.) When you say the flow “does not look like the circulation you mention.” You are recognising that the flow does not at all resemble circulation in any normal use of the word, i.e. that the actual flow is not circulating.

By subtracting the free stream speed and direction from every part of the flow you are changing it hugely from that which actually takes place. Once you do that I accept that you would have a flow pattern that might be said to look more like a circulation than the actual flow does but even then I would say it is not even close to what most laymen would consider to be circulation.

Why cant people just accept that Γ can have a value without the flow actually being a circulation?

And why are there so many contradictory and flawed diagrams all over the Internet struggling to demonstrate the impossible?

I understand the concept of circulation; it is straightforward but is continually presented in a way that completely confuses people who are trying to understand lift a little better. Let us not add to the confusion. Rolo Tamasi 11:55, 22 September 2007 (UTC)

Correction required to Coanda Effect opening sentence

The opening sentence currently reads: 'A common misconception about aerodynamic lift is that the Coandă effect plays a no part.' What's being said?? This obviously requires correction, please! —Preceding unsigned comment added by 206.47.191.132 (talk) 12:20, August 29, 2007 (UTC)

Lift Equation only provided as algerbraic restatement of Lift Coefficient

Since this article's intent is to explain and define 'Lift', I believe it would be preferable to have a short review of the Lift Equation near the start of the article which defines lift in the classical formula: L =0.5*Cl*r*V^2*A. The restatement of this formula in the latter part of the article as the definition of Lift Coefficient should be secondary to the principle definition of lift i.m.h.o. —Preceding unsigned comment added by 206.47.191.132 (talk) 13:03, August 29, 2007 (UTC)

Thoughts on downwash

As Mr. McLean mentioned earlier, the equations of motion are simplified to get the Navier-Stokes equations, which is the best flow simulation used on a regular basis. By eliminating viscosity, the N-S equations are simplified to the Euler equations. Eliminating the rotational terms yield the Full Potential equations and eliminating compressibility finally gives the Potential flow equation.

The Potential Flow (Laplace) equation does a wonderful job of predicting the lift of a wing. It is typically solved using a Panel Method or a Vortex Lattice method.

Working with the simplest form, the Vortex Lattice method uses a series of vortices to simulate the flow over a wing. These are arranged as a series of horseshoe vortices to model the spanwise lift distribution. Each vortex induces a symmetric flow field which results in an equal and opposite velocity distribution on each side of the vortex (see Figure 3 of http://web.mit.edu/2.016/www/handouts/2005Reading4.pdf). Therefore, looking at the vertical component of velocity, each individual element of the vortex lattice model will induce an equal and opposite vertical flow. The upwash in front of each wing element will be equal to the downwash behind the element. The upwash outside of each wake element will be equal and opposite of the downwash on the other side of the element. The Superposition principle says that the effect of each of these vortex elements can be summed together to calculate the velocity at any point in the flow field.

There can be no net downwash.

Everywhere there is downwash in the flow field, there is a corresponding equal and opposite upwash due to the other side of each vortex element. If you look closely at the pictures in <http://pof.aip.org/pof/gallery/pdf/1993/S5_1.pdf>, you will see the upwash extending outward from the wing tips. Note the location of the core of the vortex in Figure 2. Note how the smoke line outboard of the tip vortex is completely above the core.

The lift force (the pressure on the wing) is reacted against the walls (ground and space). The lift force cannot be reacted out in two different ways.

One more thought experiment. When an element of fluid is displaced downward, what fills the space that it used to occupy? How did it get there? Are those forces equal and opposite?

TZ 30 Aug 07 Tzickuhr 03:18, 31 August 2007 (UTC)

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> The lift force (the pressure on the wing) is reacted against the walls (ground and space)

Thinking out loud here... I believe we need some thought experiments to help zero in on critical concepts.

When a ship's prop suddenly starts turning, it experiences a thrust force... but where is the "wall" upon which it reacts? The narrow jet of water being created by the prop becomes longer over time. But must it strike a "wall" in order for the ship to begin accelerating? Does an aircraft require such a "wall," or could it still produce a lifting force if the distant Earth's surface was not present? Or do you believe that an underwater propeller obeys fundamentally different physics than a wing in flight?

This line of thinking demonstrates that you do not understand pressure. The "narrow jet" you speak of is the downwash behind the propeller due to the spiraling trailing vortices. The force that accelerates the boat is due to the pressure on the surface of the propeller. The downwash behind the propeller does not have to reach a wall but the pressure field created by the flow over the propeller will. Tzickuhr 10:41, 3 October 2007 (UTC)

Another example: a water-filled rubber balloon can accelerate forwards via F=mA, by ejecting a jet of water out the rear. If we immerse this balloon in a large water tank, is the physics fundamentally different? (In the water tank all the flow lines are closed, but does the balloon suddenly STOP being a reaction engine?!!

If I'm sitting in a rowboat, I can scoop up a bucket full of water from the lake. In doing so, I take water in from all directions. I then fling that water rearwards in order to accelerate the boat forwards. By injecting momentum into the water, I inject opposite momentum into the rowboat, just as with a rocket engine. Is this fundamentally different than using a paddle or a propellor immersed in the water? (Flinging a bucket full of water does not require any distant "wall" to react against... but is a propellor or a paddle or an airplane wing somehow different?)

In all these examples all streamlines must be closed, so in a global sense "upwash" must always equal "downwash." Yet if a pump should draw in mass-bearing fluid parcels from all directions, but eject the fluid in a narrow jet, that pump will accelerate itself as a reaction engine, and it will experience a reaction force proportional to the momentum-change given to those parcels over time. Isn't it similar to a rocket with momentum deposited into the "exhaust?" Or do you believe it's like a venturi problem where the force cannot exist unless there is a distant "wall" upon which an equal opposite force appears? --69.29.211.201 04:48, 24 September 2007 (UTC)

These cases are irrelevant to the lift on a wing. A fluid can only exert force on a body in one of two ways. A pressure acting normal to the surface and a shear stress acting tangential to the surface. Tzickuhr 10:41, 3 October 2007 (UTC)

It is an example of taking something simple and making it appear complex through muddled thinking. Of course a force can be reacted more than once. I am sitting on a chair; my weight is being reacted by the chair. The floor is reacting the weight of the chair and also my weight. Imagine a tall beaker of water on some scales. Then introduce an object heavier than water and with a very "draggy" shape, the scales will register the additional weight of the object as soon as it is placed in, long before it reaches the bottom of the beaker. The weight is being reacted by the drag as well as by the scales. The air exerts a pressure on the ground representing the air plus everything in it (adjusted for any acceleration effects of course). Rolo Tamasi 18:26, 24 September 2007 (UTC)

A force cannot be reacted in more than one way. This is fundamental physics. If a body is not accelerating, the sum of the forces must equal zero. You have combined two different control volumes. The chair reacts your weight. When you include the floor in your control volume, then the floor reacts the weight of the chair and you. Your weight is always being reacted through the chair. In all cases the sum of the forces must equal zero since there is no acceleration.

The drag force of the object dropped in the beaker is due to the pressure field in the fluid, which gets reacted against the walls of the beaker. It is always the pressure. Tzickuhr 10:41, 3 October 2007 (UTC)

Hi Tzickuhr, I was agreeing with you and your reply is agreeing with me! (worrying eh?)

As an aside, it is interesting to consider what the mechanism is that transfers the weigh of my object to the pressure on the floor and walls of the beaker. Clearly once the object reaches terminal velocity the pressure difference between the top and bottom of it equals its weight. However this pressure difference is due to an increase underneath it and a decrease above it. It is easy to see how the increased pressure below it has the effect of increasing the pressure in the entire beaker.

Would anyone like to explain if and how the decreased pressure above the object results in and increased pressure in the bulk of the beaker??? Rolo Tamasi 18:40, 3 October 2007 (UTC)

PS to get back to disagreeing, I believe my chair example is a useful illustration of multiple reactions to a single force. I also agree with you that if all the reactions don’t balance you will get acceleration. However, as the air is accelerating why are you unhappy with the multiple reactions? Rolo Tamasi 18:40, 3 October 2007 (UTC)

Do you understand control volumes? This is sophomore engineering. For your chair example, there is no acceleration therefore the sum of the forces must equal zero for any control volume. The chair reacts the weight of the person. The floor reacts the combined weight of the chair and the person. These are two different control volumes. The weight of the person is not reacted out in two different ways.

For the control volume we really care about of a wing in air, the induced drag is reacted out by the angular momentum (what you seem to be calling acceleration but is more accurately called conservation of momentum) in the wake and the lift on the wing is reacted out by the pressure on the upper and lower walls. The lift cannot also be reacted out with a change in vertical momentum. The far field momentum derivation proves this. Please read the paper by Cummings (AIAA-96-2482, purchase at www.aiaa.org) and tell me where they are wrong. The "downwash" theory is wrong ("Lift is generated when an object turns a fluid away from its direction of flow." and the whole section on "Reaction due to deflection" need to be removed). Tzickuhr 02:43, 4 October 2007 (UTC)

Please Tzickuhr, don’t allow your frustration to turn into personal remarks. I was trying to tease the discussion out in a direction that would lead to a resolution of our little conundrum.

Yes I believe I understand what you mean by control volume.

Following your red herring for a moment - Are you saying that a change of angular momentum does not involve acceleration? (Before you ask, I am familiar with the conservation of energy principle.)

Wow, how many times can I indent? Of course any change in momentum involves an acceleration, but when you're working with a fluid in a control volume you use the conservation of mass, momentum and energy equations to determine what's happening. For a control volume as described in Cummings' AIAA paper, there is no acceleration on the boundaries. You only look at the pressure and momentum on the boundaries. The only momentum being angular momentum (vorticity) on the downstream face. Tzickuhr 03:10, 5 October 2007 (UTC)

I am a free man. YOU may choose to use conservation of momentum but, when I describe my point of view, I use the terms I feel best help my point to be understood. We will find at the end of this journey that the conundrum you struggle with is all about clear understanding of language and not about physics at all.Rolo Tamasi 08:47, 5 October 2007 (UTC)

Let us just keep it simple.

Your hypothesis is that all lift forces on an aerofoil are explained by pressure differences (I agree, in a friction free environment it is the only way a fluid can have any influence on a solid body). You then go on to say that these pressure differences are reacted on the walls/floor and there cannot be any other reaction and thus it is not possible for an aerofoil to also result in a movement of the air.

This isn't a hypothesis. It has been proven by Maskell, Cummings, Kusunose and others. I never said there is no movement of the air, just that there is no _net_ change in vertical momentum. And I'm just passing on what these others have proven. Tzickuhr 03:10, 5 October 2007 (UTC)

For you it is an absolute truth that, even though you cannot fully explain it, you accept as such. A little like religion and no the less valid an approach for that. I, on the other hand, see an idea being described with a stated conclusion clearly at odds from my experience. You say we must stop talking about downwards deflection because it is impossible but I still feel the breeze from my propeller. Please excuse me for calling it an hypothesis until you have explained.Rolo Tamasi 08:52, 5 October 2007 (UTC)

I ask,if that is so why can I feel the air moving under a helicopter rotor, a fan, an aircraft propeller and I can see and feel the movement of water from a ships propeller?

Treat me as a dumb 14 year old physics student and explain it to me simply please. I am here to learn. Rolo Tamasi 08:13, 4 October 2007 (UTC)

This is a much different control volume than a wing in steady flight. I have never studied helicopter aerodynamics, so I can't be definitive, but I can point out the obvious differences. The wing wake extends (mostly) straight to the downstream face. The rotor wake spirals down below the rotor. Because the wake spirals down, the tip vorticies have an additive effect which creates a higher velocity below the rotor. However, there is still air moving up outside of the wake. Put your ceiling fan on high and hold a thread outside of the blade tips. The air is moving up. If the same amount of air doesn't move up as down, you would have to compress the air below the rotor, which is impossible.

I think we begin to see the end of the tunnel! A force can be reacted more than once but, at any boundary, the total net effect must equal the original force. You started by implying there can be no acceleration of the air as it is “all pressure”. You then become happy to accept a rotational acceleration and now your description clearly includes a linear one!

What you are describing includes a downward deflection of the air. So why do you say we should drop it?

No one is saying that every time an aircraft flies there is a permanent downward movement of the air so that the top of the atmosphere is getting lower and the air more dense.

The conundrum is in your understanding of the meaning of the words used. You pray to your god and deny the existence of other peoples gods. The truth is we are praying to the same god but describing him in different, yet equally valid ways.Rolo Tamasi 08:57, 5 October 2007 (UTC)

In the end the lift on the rotor is because the pressure on the upper side of the blades is lower than the pressure on the lower side. The control volume for a rotor is very complicated and mathematically may have problems with the wake. It's not even steady. I understand wings, not rotors. Let's stick with wings. Tzickuhr 03:10, 5 October 2007 (UTC)

Both you and I agree that, for a large number of reasons, the “Lift is caused by Pressure” conceptual model is far move valuable than the “Lift is caused by Deflection” conceptual model which tells us very little and is, in the end analysis, totally tautological. However that does not mean that the pressure does not cause a deflection. You cannot have a pressure differences in a fluid without causing the fluid to accelerate. Rolo Tamasi 08:59, 5 October 2007 (UTC)

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Rolo,

Here is what I hear from you. I explain myself but you don't understand, therefore I am wrong. I cite references that prove my point but you don't read them much less understand them, therefore I am wrong. I do calculations to prove my case and you do nothing but say "F=ma is true" but I am wrong.

Please tell me your background that explains why it is me, an Engineer, who does not understand the meaning of technical words explaining aerodynamics, but you do.

You do not even seem to understand the simple concept that a force cannot be reacted out in two different ways. You do not understand that the complicated flow of a moving rotor is not the same as a steady level wing.

I have explained upwash but you have not acknowledged that you understand what it is much less that you believe that it exists. I explained the wake structure of a rotor but you just say "I feel air moving" so I am wrong and you are right. If you reverse the ceiling fan, how come you don't feel the same strong air movement going into the fan? Because the wake structure is on the other side. Do you understand any of this? Everywhere in the room, outside of the fan wake, the air is moving the opposite direction. Do you know why? It's the pressure. Air moves toward low pressure.

Please show some proof that a wing deflects air down to create lift (don't forget the upwash). Find a reference. Show me the math. Use your "F=ma" to prove your case, don't just say it must be.

Have you studied far field momentum theory? Where am I wrong? Please read Cummings' paper and tell me where they are wrong. Prove something.

Tzickuhr 00:06, 6 October 2007 (UTC)

Dear Tzickuhr. I am impressed by your infallible engineer status and reading list. However this is a discussion and an ability to offer clear explanation is the only relevant qualification.

If you are unable to answer the relevant questions I don’t think we should agree with your proposal (that “Lift is generated when an object turns a fluid away from its direction of flow." and the whole section on "Reaction due to deflection" need to be removed.).

Those questions remain-

If there is no deflection why can I feel it? (Helicopter rotor, propeller etc etc)

If the pressure regions can have no other reaction except the pressure on the ground how is the air within the pressure gradients prevented from accelerating?

I think these are perfectly reasonable questions to ask. I am not trying to persuade anyone of anything, you are. Rolo Tamasi 19:44, 6 October 2007 (UTC)

Reasonable, but not relevant. And I already explained why a propeller is different, but you don't understand. This should be a discussion area for experts, not for a 14 year old to argue about things he doesn't fully understand. You still have not acknowledged you understand what upwash is. You don't understand that a force cannot be reacted out in two different ways.

Tzickuhr, you appear frustrated by my sluggishness in agreeing to your proposal and clearly attribute my reluctance to assumptions about my capability, knowledge base and experience. There are alternative possibilities.

You attempted to describe why a propeller is different but failed because what you did was to describe different behaviours but not to explain “why”. I continue to suggest we are lost in interpretation and fear the use of undefined jargon is not helping.

You claim there is no deflection at a wing but accept that a desk fan causes the air to circulate round a room. What is it that causes this difference in the behaviour of the two aerofoils? If the fan aerofoil can exhibit this behaviour why do I have to accept your proposition that a wing cannot? Rolo Tamasi 18:05, 11 October 2007 (UTC)

I'll try that one again. The complete equation is $\sum F=ma$ so if the sum of the forces on a control volume of air is zero, as I have calculated, there can be no NET acceleration. Obviously, the air accelerates as it moves around the wing, but the wing causes just as much upward acceleration (upwash) as it does downward acceleration (downwash). Tzickuhr 03:22, 11 October 2007 (UTC)

I suggest the problem may lie in the following areas – Your use of the word “if”; the definition and application of “control volume”; the definition of “upwash” and “downwash”; and, possibly, some missing factor. Rolo Tamasi 18:28, 11 October 2007 (UTC)

If I'm holding a book and let go, one of two things will happen. If I let go after setting it on a table, the table will exert a force on the book so that the sum of the forces is zero and therefore there is no acceleration. If it is not on a table, then the sum of the forces is not zero and the book will accelerate based on F=ma. Both cannot happen at the same time. Tzickuhr 17:32, 11 October 2007 (UTC)

This is because a book cannot be both touching the table and not touching the table at the same time, they are mutually exclusive. However you have already accepted that there are pressure differences at the wing, lift, air accelerating downwards, air accelerating upwards, air circulating in the room (fan example), and pressure and momentum changes at the boundary to the system. No mutual exclusivity here. Now, which of these do you consider deflection in reaction to lift and which do others consider deflection in reaction to lift? Rolo Tamasi 18:28, 11 October 2007 (UTC)

---

Fluid dynamics text books would give you the quantitative expression of the lift force as directly proportional to the integral of vertical velocity component actoss the laminar/tubulent wake behind the body (e.g. Landau and Lifshitz, par. 21). The wake with flow caracteristics different from those of the incoming mean flow (e.g. vortices or downwash) is what makes possible the lift. I would like to end my posts here. N.P.

---

The lift is the integral of the rotational velocity (the vorticity) of the wake, not the integral of the vertical velocity. Kusunose of Boeing integrates the vorticity in the wake region of a wind tunnel model to calculate the lift, and actually shows that the contribution of vertical momentum is a small correction that decreases the calculated lift. (Kusunose, K., "Lift Analysis Based on a Wake-Integral Method," AIAA-2001-0420, January 2001.) TZ Tzickuhr 12:56, 31 August 2007 (UTC)

That is interesting. I have difficulty comprehending it but I am not arguing with it. Surely (irrespective of the relative proportions of energy between vertical and rotational) if the impact of the vertical momentum decreases the calculated lift the air must be deflected upwards from the wing on average? I can confirm that the fan in my office and the propellers on aircraft work in the reverse sense. What am I misunderstanding? 15:38, 10 September 2007 (UTC) —Preceding unsigned comment added by Rolo Tamasi (talk • contribs)

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First let me clarify that there is downwash behind the wing. There is also an equal amount of upwash in front of the wing. I believe the correction term in the Kusunose paper is a slight decrease in the downwash due to the viscous wake momentum deficit. I'll try to look at the paper again to see if I have explained it correctly. Tzickuhr 02:51, 12 September 2007 (UTC)

---

In answer to the last part of the above question. Most ceiling fans use flat blades and reverse the flow by reversing the direction of the blade which is the same thing as picking the whole fan up and turning it upside down. On an aircraft the flow from the prop can be reversed by changing the angle of the blade to the airflow from positive to negative. An aerofoil is designed to work with the airflow only flowing across it in one direction i.e. from the front which has a obvious radius on it to the back which tapers to a sharp edge. PR 14 sept 07

Indeed but no one was contemplating reversing the pitch and thus it cant be the answer. Rolo Tamasi 18:03, 24 September 2007 (UTC)

Major flaw in the downwash/momentum theory

I have copied this from the article – it appears to have been posted there by mistake as it is clearly a discussion item. Rolo Tamasi 12:25, 20 October 2007 (UTC)

There is a major flaw in the downwash/momentum theory of lift. Whilst downwash and downward momentum may be produced as a consequence of lift (through induced drag for instance), it is however not the cause of lift. In two dimensional airfoil theory (potential flow), there is no net momentum produced in the fluid by the airfoil. Anecdotally, there can be no net flow of fluid in any direction because fluid cannot accumulate anywhere. The flow that goes down, must circulate upward somewhere else, hence zero net momentum. Since there is no net momentum produced in the fluid by the action of the airfoil, there can be no lift generated by this mechanism. There must be another explanation of lift other than the "downward momentum or deflection-reaction theory". I am apparently not permitted to publish the "Curvature Theory of Lift" in this forum because it is classed as Original Work by Wikipedia. It is a faily simple theory and only takes ten lines of simple mathematics to prove. The result however is the same as produced by the Bernoulli Equation.Markosvincios 05:53, 20 October 2007 (UTC)

I agree that whenever any air is displaced, by whatever mechanism and in whichever direction, it must eventually result in flows so that the atmosphere recovers to its original condition. (With the added complexity of a net energy increase due to the work done.)

The same is true of the air in a closed room being propelled by a desk fan; the water in a lake being propelled by a boat’s engine and even a cup of coffee being stirred with a spoon.

However I do not accept that these flows have no momentum, they all do. Rolo Tamasi 12:53, 20 October 2007 (UTC)

I suggest to those who believe that there is a net momentum developed by a 2d airfoil in potential flow - to calculate the net linear momentum produced over a control volume containing the airfoil. A simple equivalent mathematical model can be contructed by the superposition of a uniform velocity field (representing the freestream velocity), and a point vortex velocity field (representing the airfoil with circulation).

Furthermore, an airfoil in 2d potential flow does not perform any work on the flow. The net force (lift) of the airfoil is perpendicular to the freestream velocity. The dot product of the lift vector and the motion vector is zero. Therefore no work is performed by the airfoil on the fluid, or by the fluid on the airfoil.'Markosvincios 13:27, 21 October 2007 (UTC)

There is no net change in momentum in any closed system. The action of firing a gun does not change the net momentum in the system but it does change momentum.

Consider a fan on a desk in a sealed room with stationary air. Turning the fan on will cause the air to circulate around the room. The total kinetic energy in the air will increase, the total net momentum will remain the same, the centre of mass of the air will remain the same and there will be a resultant force on the fan, which will be reacted through the desk. Rolo Tamasi 14:56, 21 October 2007 (UTC)

PS a 2D aerofoil does nothing. Rolo Tamasi 18:02, 21 October 2007 (UTC)

I am confining my discussion to the 2d theory of lift for an airfoil. The concepts I am discussing refer to a single airfoil moving in a straight line. The same kind of airfoil motion that is representative of aircraft wings and lift. These concepts can be extended to three-dimensional flows, and for ease of understanding are limited to 2d. Why be concerned about complex flow situations when a satisfactory theory of lift has not been arrived at even by using a simple flow situation such as 2d potential flow. As a Professional Mechanical Engineer, I have put some thought into what I am saying, and its not my job to lecture others who have unsupported arguments or questions which have not been thought out very well. I am trying to be informative, however, if I am wrong about something then provide the solution for others to see in the discussion section.Markosvincios 11:03, 22 October 2007 (UTC)

It could be confusing if we were to describe the behaviour of 2D systems without explaining how these may be different to real life. Particularly if your conclusions are that no work needs to be done in order to generate lift and that lift generating aerofoils do not deflect the air. 2D systems only exist in order to help us understand.

I am interested in your comment “Since there is no net momentum produced in the fluid by the action of the airfoil, there can be no lift generated by this mechanism.” Can you justify this statement? After all, there can be no net momentum change in any closed system. It appears to be implying that it is impossible to support a body in a fluid by accelerating the fluid downwards by any mechanism at all.

Of course the mechanism has other elements as well (notably pressure differences) but I am quite happy that, in my desk fan example, the reaction from the fan is equal to the acceleration the fan imparts to the air and yet there is no net momentum change in the room. Rolo Tamasi 12:50, 22 October 2007 (UTC)

I plan to elaborate on the Curvature Theory soon, but I want it make sure it can be explained fairly clearly. The theory does involve first year University level calculus and it should be understandable in principle to high school level physics students. So, I will be justifying the theory.

Basically, the source of lifting forces on an airfoil is the "centrifugal acceleration" of fluid particles as they move along the curved path of the streamlines. The "centrifugal lines of force" act at right angles to the flow streamlines and cause a net lifting force on the airfoil. Because the lifting forces act at right angles to the flow, there is no mechanical work being performed.

That is all I will say for the time being.Markosvincios 15:56, 23 October 2007 (UTC)

I have never come across the term "centrifugal acceleration" before and presume your reference to centrifugal force is in the real sense rather than the more usual fictitious sense.

While I’m sure your maths will be just fine I look forward to the justification that the air moves only along the arc of a perfect circle in an inertial frame of reference and does not change speed. Rolo Tamasi 18:21, 23 October 2007 (UTC)

---

In the curvature theory posting in the article the use of equation 3 appears to be unjustified. It only addresses force components normal to the streamline and we know that, as pressure and speed changes occur along the streamline, that there are parallel components.

It is interesting to consider that, if there were to be no components of force parallel to the free stream flow then the motion of the air particles in the inertial air frame of reference would be linear and vertical. Rolo Tamasi 10:15, 28 October 2007 (UTC)

Streamlines Curvature and lift (Removal of Article)

Thanks to the vandalisation of my contribution from (Personal attack removed). Others may revert or review the article if they care to do so. I have other dragons to slay.

It appears the Bernoulli Theory has had 300 years of publicity and it still wrong, yet someone proposes a mathematically sound theory which provides a better explaination of lift, and its then taken down from Wikipedia in a day. Fools.

You may want to follow up with a cited reference from an independent source which was also removed.

See http://www.scribd.com/doc/247213/How-do-wings-work-Babinsky

The abstract quotes:

" The popular explanation of lift is common, quick, sounds logical and gives the correct answer, yet also introduces misconceptions, uses a nonsensical physical argument and misleadingly invokes Bernoulli’s equation. A simple analysis of pressure gradients and the curvature of streamlines is presented here to give a more correct explanation of lift."

Now, two quotes from me

[1] "If some people choose to be ignorant, let them be"

[2] "Whilst some people go to church on Sunday to be closer to God, others study Physics."

Markosvincios 08:26, 29 October 2007 (UTC)

For Your Information: Wikipedia is not a place to advertise your own research (a). It has a (fairly extensive) style manual (b). Your explanation of lift is for example, not truer than, say, solving NS for free surfaces (c). It is not done to sign your contributions on main articles (d). Personal attacks are not accepted (e).CyrilleDunant 09:48, 29 October 2007 (UTC)

Hi, I just found the article on the theory of lift with streamline curvature, on google. The overall results looks correct but for some small mathematical errors in the calculations presented. The sign conventions in the middle of the "proof" need to be rationalised. The static pressure equation in line 2 needs to be made negative. There may be another negative arising with respect to the conventions for the positive direction of radial acceleration, curvature, radius of curvature, or velocity gradient along the line integral. Its a tricky bit of calculus.

I also note that one external link on the article for lift(force) "Physics of Flight-Reviewed" http://user.uni-frankfurt.de/~weltner/ , attempts to prove the same thing, but they stop short by stating "Curved streamlines within a flow are related to pressure gradients. Unfortunately this equation cannot be integrated directly. The integration requires the knowledge of the total flow field." Apparently the deleted "proof" did integrate the pressure gradient without knowledge of the total flow field. Its a shame this article was pulled down. Luckily it will live on in googles database.

JohnBono 14:45, 29 October 2007 (UTC)

Related edit war

Looks like an edit war is breaking out over this issue, and I'd like to nip it in the bud. While the curvature of lift section that's been repeatedly added and removed is malformed, I'd like to see some discussion here as to its actual merits and legitimacy. It contains a citation, which I checked out and which seems to me to back the concept, so as cited material, it is properly discussed here as to its inclusion. Let's keep it civil, free of personal opinion, and focus on whether the material has legitimate source backing. Remember, NPOV requires that even if we disagree with something personally, if it is a cited viewpoint, it can be represented in an article. Having looked over the material in question, its length leads me to ask, additionally, whether it would be better for this material to be contained in its own article and referenced from here with a {{main}} template. AKRadecki^Speaketh 17:17, 29 October 2007 (UTC)

I have several things against this section, most of them being of an aesthetic nature. But I also object to the explanation.

1. it is not widespread (and thus is not really a candidate for WP)
2. it is not, as claimed "true". "True" is solving Navier-Stokes around the wing and integrating the stress on the surface. But then, no model is "true"...
3. Bernouli assumes a potential flow, incompressible and irrotational, true, but when those hypotheses hold, it is a good model. It will model the flight of a paper airplane, for example, but not that of a jet.

I don't believe I need to explain why the shape of the section in unacceptable.CyrilleDunant —Preceding comment was added at 17:44, 29 October 2007 (UTC)

I appreciate your comments, but they seem to revolve around you opinions of what is true and not true. The point here is: do others (ie, published references) discuss this as one of the explanations for lift? There is at least one reference, the one included in the edit, that does. Rather than express your opinion of its truthfulness, it would be more helpful for you to point us to external references that say such an explanation isn't valid. As to "widespread", that is not the same as "notable". If the aesthetics can be cleaned up, is there any policy reasons for not including the information? AKRadecki^Speaketh 18:27, 29 October 2007 (UTC)

No, no, my point was that this "theory" is presented as an explanation for lift. Which assumes that lift needs to be explained (in the sense "proven") somehow. This is not the case: lift stems from the conservation of momentum, the constitutive law of the fluid, and the boundary conditions set by the lifting body and the relative airspeed thereof. This yields the Navier-Stokes equations, which can be solved numerically, and the integral of stress over the surface of the lifting body projected along x and z axes yields drag and lift.

There is no mystical reason for lift, or mathematical demonstration to be made except perhaps to establish the NS equations. This is not my opinion of what is true, that is the state of the art since more than a century -- except then there where no computers and solving such equations was impractical.CyrilleDunant 20:15, 29 October 2007 (UTC)

But to someone who's not familiar with lift, it does need to be explained. That's what an encyclopedia is for, after all. You still haven't pointed to any refs that discount this theory. AKRadecki^Speaketh 20:25, 29 October 2007 (UTC)

I don't need to. There are many models for fluids, they do not all predict lift. Those that do not predict lift do not predict lift because in those models the integral around a closed boundary is always nil. This stems from the following two assumptions 1) the complex function describing the flowlines derives from a potential, 2) there are no singularities in the integration domain.

This is interesting from a mathematical, abstract point of view. But it is not rooted in physics (it is more a kind of "hmmm, what can we solve analytically" kind of reflection). None of those models, however "explains" lift. Lift is a feature of (some) of those models.

The purpose of an encyclopedia is to explain stuff, not wave equations around and pretend they explain something. So basically, there is lift because momentum is conserved, and that is all. CyrilleDunant 21:12, 29 October 2007 (UTC)

You are missing the point. You are approaching this from a philosophy/opinion point of view, not from a Wikipedia policy/guideline point of view. Actually, from a policy point of view, you do have to. You've removed cited material and provided no other reason than your own opinion that it is unnecessary. If style is an issue, fix it. If OR is an issue, either remove only the OR parts or tag those parts with {{fact}} tags and give the contributor a chance to further back up his/her points. This looks like a case of WP:OWN, with you deciding what can and what cannot be in this article, with your opinion being the only guide. One person does not have final authority as to the content of an article, and if you're going to remove cited material, you have to provide a valid reason for doing so. Your opinion by itself is not a valid reason for removal, that is acting in a POV manner. If you don't provide a valid reference stating that the cited material is a hoax, fraud or in some other way inappropriate here, I will work out the presentation issues and re-add it. AKRadecki^Speaketh 23:07, 29 October 2007 (UTC)

No, I am approaching this from the "this has to fit somehow in what is known of fluid mechanics", which is the majority point of view. This section gives undue weight to something that is not useful or interesting or even relevant to understanding lift. It is WP policy not to give undue weight to minority point of view. And I can tell you it is minority point of view because no aircraft is designed today without being modelled using NS, and guess what, they actually fly -- so much for "proving" lift... It is not a question of removing only the OR (which would be all of it), or because the layout is so bad (which would be sufficient grounds for removal as vandalism, even if well meaning vandalism). As for OWN, I'll have you note this is my first foray on this page in over a year, and it is not like it is not the seat of heated debates. Question: what do you think about the presented theory? Does it work? is it physically and mathematically sound? is it intelligible? can you design a wing profile with it? CyrilleDunant 06:50, 30 October 2007 (UTC)

Yes, it is WP policy to not put undue weight on minority theories, but that's not the same as including minority theories. If this was the lead explanation, you would have a point. But it isn't, so you don't. How can it be OR if it is referenced to an outside source? And who are you to judge what it helpful or interesting, two very subjective and opinion-based conclusions? Have you forgotten that we have a broad range of readers here, and not everyone fully understands fluid mechanics the way you do? Have you not considered that multiple math models that demonstrate lift are actually a good thing when it comes to teaching someone? Again, you still have not justified, by WP policies or guidelines, why a section of sourced text should be deleted, other than it isn't interesting to you, and it doesn't fit your view of things. AKRadecki^Speaketh 13:53, 30 October 2007 (UTC)

Because it puts undue weight on a minority point of view. That is WP policy. The pasting of extremely badly formated stuff on pages is also against WP policy. You have not provided a "well-formated" version of the text, as far as I know, which renders any discussion moot. From an encyclopedic point of view, explaining lift with potential flow as a starting point is a Bad Idea™(fluid modelling yes -- for historical reasons, lift no). As for fluid mechanics, I believe less people actually understand what potential flow is than have an intuitive grasp of fluid mechanics. CyrilleDunant 14:09, 30 October 2007 (UTC)

(reset indent)Akradecki, I would encourage you to step back and take another look at this. The introduced content was equivalent in length to the rest of the entire article. A google search of "Babinsky + lift" produces an entirely underwhelming 1,000 hits. There are not many cases where one could make such a clear determination of undue weight. Also note that this was added by a SPA; it sure looks like POV pushing. Maralia 14:43, 30 October 2007 (UTC)

I feel the article should not have been removed although clearly it would have benefited from some editing. However it is better dealt with here until we have some degree of consensus. Anyone who cannot site references and has to ask others to either find some or remove the posting cannot possibly be posting incompliance with Wiki rules. But once others had cited references we moved into the area of substance and style – a more subjective realm and good faith should have been assumed.

I suggest there is a substantial point that needs addressing in the post, that the method ignores all components of force parallel with the streamlines. If the justification is insufficient than it should not be included.

However there remains a further, far more significant issue. There is a view, stated by several in here and very more widely, that lift does not involve a net deflection of the air (upwash=downwash). This view is not expressed within the article. Should it be? If so, how should we address the conflict with the current content? While I would argue against the hypothesis (at least to start with) I do feel that there is sufficient reason to consider a reference to it. Rolo Tamasi 19:40, 30 October 2007 (UTC)

In respect of upwash versus downwash, refer to http://www.arvelgentry.com/origins_of_lift.htm "Origins of Lift"

"And on the 'deflecting the air downward' idea, that is a three-dimensional effect. In our 2-D case, the circulation flow field causes the air out in front of the airfoil to be directed upward around the airfoil and then back down to about the same level as it started out in front. Yet due to viscous effects and resulting circulation, lift is generated. Yes, we can't fly with a two-dimensional wing and, therefore, are influenced by three dimensional effects caused by a complex trailing vortex system. We can reduce these 3-D effects by using very long wings such as on gliders or the around the world aircraft design by Bert Ruttan. On an infinitely long wing, the 3-D effects are gone and we are essentially back to looking at two-dimensional airfoil aerodynamics. If we can reduce the 3-D effects, then 'deflecting the air downward' is not essential to the origins of lift."

The problem with this reference is that it has little authority. It is a private webpage merely asserting something to be the case while providing no argument as to why. Further, the links it provides are to sources that disagree with the notion that there is no net downwash. Rolo Tamasi 11:39, 4 November 2007 (UTC)

It appears to me, as a casual observer, there is a case for discussing the merits or otherwise of streamline curvature and the generation of airfoil lift. Firstly there are credible cited references for the material. This is not new thinking. Secondly, there is debate of style over substance. Not all new contributors to wikipedia are knowledgeable or experienced in its requirements, nor are they necessarily interested in providing a polished article initially. I would rather see substance than puff, and I would like to see the curvature/streamline theory given a proper forum for expansion. The principle that individuals can censor public knowledge because that information is not consistent with their internal beliefs, goes back to the middle ages. Consensus means exactly that.

If the same critical appraisal of this article were extended to all the other contributor articles, then there would be nothing left to read. Lets be fair and consistent in standards.

Which credible cited references do you have in mind? Rolo Tamasi 11:40, 4 November 2007 (UTC)

Circulation Lift Theory and Momentum Reaction/Downwash/Deflection Theory are Incompatible

I do not know why anyone has not seen this contradiction before.

In the derivation of the Lift equation for circulation, $L=\rho V\Gamma$, there are certain assumptions made.

The key assumptions are:

1. The Bernoulli equation is correct, and

2. No contribution to lift arises from momentum effects, because there is no change in momentum across the control volume containing the airfoil.

So, anyone who says that changes in momentum cause lift cannot say circulation causes lift too - because the derivation of the lift circulation equation, (not shown here), says so.

Alternatively, and correctly so, anyone who says the circulation theory of lift is correct cannot say the momentum theory of lift is correct too.

It appears the momentum theory of lift is based on false concepts or false assumptions. —Preceding unsigned comment added by 58.110.94.188 (talk) 17:05, 13 November 2007 (UTC)

Calculation of the momentum equation (not shown here) DOES show a contribution to lift force from momentum effects. Although not obvious, or intuitive, the momentum equation does show that half of the total lift force is developed from the rate of change of momentum across the control volume, and the other half of the lift contribution is from static pressure forces acting externally on the control volume.

What is harder to understand, is what this really means in practice.

Why?

1. If the control volume is drawn around the surface of an actual airfoil then all of the lift force arises from pressure effects and no momentum effects.

2. If the control volume is taken out toward infinity then there is no net circulation, because the starting vortex and bound vortex around the airfoil cancel out. Therefore there seems to be no far-field lifting force in so far as circulation is concerned.

3. Where does momentum actually produce lift? The momentum equation as applied to circulation is vague about the connection between airfoil lift and the rate change of momentum in the flow causing it. Something very important is missing from these arguments .... —Preceding unsigned comment added by 58.106.36.163 (talk) 15:38, 5 December 2007 (UTC)

Whether or not momentum produces lift is moot. That they absolutely always occur at the same time is undoubted.

Lift is a force on a wing, the only way a fluid can exert a (non frictional) force on a solid is by pressure differences.

The existence of a pressure difference in a fluid will always cause the fluid to accelerate (momentum change) down the pressure gradient.

Pressure in a fluid always works equally in all directions, if there is no wing present the fluid accelerates equally in all directions – no net effect.

If part of the pressure acts on a wing as part of the lift, that part does not act on the air. Thus, in this case, there is a net acceleration on the air equal and opposite to the pressure effect on the wing. If the lift effect is upwards, the acceleration of the air is downwards.

The downwards-flowing air displaces other air upwards. The net pressure and fluid momentum effects result in the pressure differences at the boundary. Thus the sum total of the air pressure on the ground is equal to the total weight of the air plus the lift being applied to the aircraft.

None of this describes the mechanism by which the pressure differences are created, only the inevitable consequences once they do.

The pressure differences are created by an inevitable need for the air to move out of the way of the oncoming wing and to flow into the void left behind after it passes. If the air did not flow the inevitable result would be a rapit tendency towards infinite pressure immediately ahead of the wing an a total vaccum immediately behind it.

In fact a steady state is reached in these two regions where the pressure gradients are sufficient to accelerate exactly the quantity of air away and towards the wing in order to maintain exactly the pressure gradients causing the acceleration.

There are many and varied ways of mathematically modelling the different parts of the flow. The so-called different theories of flight are just different approaches to creating mathematical models. They are not mutually exclusive.

Rolo Tamasi (talk) 19:24, 5 December 2007 (UTC)

Control-volume analysis and momentum transfer

In recent exchanges there is a lot of confusion as to whether lift involves momentum transfer or not, culminating in the entry by Mr. Tamasi, 5 December 2007, which finds a non-existent contradiction between the Kutta-Joukowski theorem (lift per unit span = rho*V*Gamma) and the presence of any momentum transfer. Of course lift involves momentum transfer, and the Kutta-Joukowski theorem is correct. I think the confusion over momentum transfer in general arises because the momentum is either visible or not, depending on where you look. However, if you include all the right pieces in the analysis and do the sums right, it all works out, and there is no mystery or contradiction. The purported contradiction found by Mr. Tamasi is the result of leaving out one of the pieces, as I hope to make clear below.

I don't think I described any contradiction at all. I certainly see none.

I believe you are referring to contradiction seen by 58.106.36.163, to whom I was responding. The sense of my response was, I believe, similar to yours other than I question the value of attempting to attribute causational relationship. Within the system you can inevitably find pressure differences that equate to the lift and you can find momentum changes that equate to the lift. Equally you can net off both all pressures and all momentum changes to zero if you wish. These are just simple principles that we would not waste any time discussing in the dynamics of solids but once lift becomes involved we appear to make the simple mechanism appear as complex as possible. Most of the discussion tends to be about artefacts of a particular analytical model chosen to apparently assist in an explanation rather than features of lift. Why do we do it? Rolo Tamasi (talk) 00:37, 16 January 2008 (UTC)

Control-volume analysis is a powerful tool, and using control volumes of different shapes and sizes can provided insights into different aspects of the problem. In fact, if you want to gain a full understanding of what happens in the flow field when lift is generated, you have to look at multiple views that slice the atmosphere in more than one way.

Control-volume analysis can be applied to either 2D or 3D flow, and the outer boundaries of the volume can be either flow-through or solid walls. Correct results can be derived for any of these situations, and if things are done right there will be no contradiction between them. Some have insisted that only a closed system makes sense, but whether you enclose the atmosphere in a box or not needn't alter any general conclusions. If I assume the box is large, I can draw a control volume around a small subset of the interior and have an open system that isn't significantly affected by the walls. In the real atmosphere, the only real wall is the ground. If the height above the ground is large compared to any dimension of my control volume, it is as if the ground weren't there. And if there is a starting vortex, I can put it out of the picture by assuming that my airfoil or wing has been in flight over a large distance compared to the altitude, so that the effect of the starting vortex is cancelled by that of its image in the ground.

To do a momentum analysis in a control volume you have to take into account the time rate of change of the total momentum in the interior and the forces (pressures, if we ignore viscosity) and momentum fluxes at the boundaries. For my discussion I'll assume steady flow, for which the time rate of change of total momentum in the interior is zero. For analyzing lift, we take the surface of the airfoil or wing as the interior boundary of our control volume, where we need only to consider the pressure, whose integral gives the lift. The outer boundary encloses the airfoil or wing, and if the boundary is flow-through, we must consider both the pressures and the momentum fluxes.

Consider the 2D flow around an airfoil of infinite span. More than a few chord lengths away in any direction, the only flow disturbance outside the viscous wake looks as if there were a point vortex located somewhere on the airfoil (If you're far enough away, it doesn't matter exactly where), superimposed on the uniform freestream.

Now consider a tall, skinny rectangular control volume with vertical (front and back) faces far enough ahead and behind the airfoil so that the point vortex is a good approximation to the flow. In the vertical force/momentum balance that will tell us the lift on the airfoil, the pressures on the vertical faces make no contribution. If we move the horizontal (top and bottom) faces far enough away, keeping their lengths the same, the pressure contributions on them become negligible. The final result is independent of exactly how far ahead and behind we place the front and back faces, as long as the vertical dimension of the box is large compared to the horizontal. What we find is a flux of upward momentum through the front face that accounts for half the lift and a flux of downward momentum through the back face that accounts for the other half. If we calculate the circulation on the outer boundary, we get lift = rho*V*Gamma, and we have just carried out the simplest derivation of Kutta-Joukowski that I know of.

So in a tall, skinny control volume we find the lift totally accounted for by momentum fluxes at the outer boundaries (and to be consistent with Kutta-Joukowski). This disproves Gentry's (Origins of lift) contention that "deflecting air downward" is significant only in 3D flows. It also contradicts assumption 2 in Tamasi, 5 December 2007. I think where Mr.Tamasi went wrong is that he considered only the momentum content in the interior and left out the fluxes at the boundaries.

Now for a different view, consider a thin, flat rectangular control volume. Put the top and bottom just far enough away so that the vortex approximates the flow well, and move the front and back much farther away, but still a small fraction of the height above the ground. Now the fluxes of vertical momentum through the front and back effectively vanish, and fluxes through the top and bottom cancel by symmetry. Half the lift is now accounted for by overpressure on the plane below the airfoil, and the other half is accounted for by underpressure on the plane above, even though these planes are flow-through boundaries.

So for a tall, skinny control volume the lift is accounted for by momentum fluxes, and for a thin, flat control volume it is accounted for by pressures in the field. For situations between these two extremes, the lift is accounted for by combinations momentum fluxes and pressures that depend on the proportions of the control volume. Of course both the pressures and the momentum fluxes are always there at the same time. Which accounts for the lift just depends on how we choose to slice up the atmosphere.

Now for another view, to pacify those who insist that the ground is an essential part of the picture. If we take the thin, flat control volume that we just considered and increase either of its dimensions so that it is no longer a small fraction of the distance to the ground, the effect of the vortex at the airfoil no longer dominates over the effect of its image under the ground. The integrated pressures that account for the lift then shift toward more than half being accounted for by the overpressure under the airfoil. If we move the bottom boundary to the ground and make the control volume much longer than it is high, the lift is completely accounted for by the overpressure on the ground. Note that this doesn't contradict anything we concluded before. We can still account for lift in terms of momentum fluxes, and we can still find the underpressure above the airfoil to be significant, if we look in the right places.

This kind of analysis can be extended to 3D, with the wing and its wake modeled by a horseshoe vortex. The starting vortex doesn't last long in the real world, and in the ideal world where a vortex never dies, we can always put it out of the picture as I argued earlier. There are additional details to take care of and mathematical traps that some classical texts fell into, but if you do it right you find that lift can be accounted for by varying combinations of momentum fluxes and pressures, including pressures on the ground, very much like the above examples in 2D.

So considering only the pressures or only the momentum fluxes can lead you astray. To understand the relationship between the lift and the flow field that goes with it, you must consider both the pressure field and the momentum fluxes. --J Doug McLean (talk) 22:35, 14 January 2008 (UTC)

Possible sources of the Lifting Force Controversy: Vortex-shedding, Ground Effect, etc.

I've been observing the long-running battle over the Lifting Force explanation. I notice that certain unstated concepts are the source of distorted conceptions, and may provide the driving force for various sides in the battle. But these concepts are rarely highlighted or brought out for explicit discussion. Let me list some of them.

1. Flight in ground-effect mode is somewhat different than flight at higher altitude. Most importantly, all two-dimensional "infinite wings" remain forever in ground-effect mode. Perhaps infinite wings provide misleading examples for explaining the flight of real-world aircraft. The mathematics of 2D infinite wings is the mathematics of ground-effect flight, where the ground is an essential component of the system, and where the distance to the ground is much shorter than the (infinite) wingspan. This differs from the conventional flight of aircraft, where the wingspan is much smaller than the distance to the ground, and where some of the obvious "venturi" phenomena associated with infinite-wing descriptions are missing.

2. An airfoil in constant-altitude flight against a gravity force is a special case, and may be a misleading example. Alternatively, if we consider the accelerated-trajectory flight of neutrally-bouyant submarines, or aircraft moving in a "zero-G" environment, or if we examine the horizontal "lifting forces" created by sailboat hulls and ships' rudders, this may help remove some of the conceptual distortions which produce long-running "Swiftian battles," and which block our understanding of flight.

3. The creation and ejection of ring-vortices can supply a force useful for fluid propulsion. For example, a ring-vortex launcher produces a strong reaction force which drives the launcher backwards relative to the ejected ring-vortex. In recent years, detailed consideration of the forces involved in vortex-shedding provided key insights into the functioning of flapping insect wings. I remain convinced that the same insights also apply to fixed finite-wing aircraft, and a good explanation of the lifting force must involve the forces produced by vortex-shedding. Let me say it differently: airplanes can fly in ground-effect mode, or they can fly via vortex-shedding. Our most common mistake is to analyze the ground-effect flight required in a 2D world, then assume that we've explained the vortex-shedding flight of a 3D real-world aircraft. The lifting force will be difficult to understand as long as flapping-wing insect flight remains poorly explained.

4. The rudders on ships and the blades of rotary fluid pumps are airfoils which produce fluid mechanical forces. If our explanations of the lifting force apply only to fixed-wing aircraft in constant-altitude flight against gravity, but contains no obvious application to rowboat oars or to helicopters, then our explanations are deeply flawed. The best explanation should offer general connections to many different cases, rather than explaining only narrow special cases. --Wjbeaty (talk) 20:58, 18 January 2008 (UTC)

The Article does primarily address lift in the general form.

Just because some people don't understand lift does not mean that it has not been well understood for a few hundred years and is not extremely simple. Rolo Tamasi (talk) 01:02, 19 January 2008 (UTC)

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