Talk:Lift (force)

The diff is here: https://en.wikipedia.org/w/index.php?title=Lift_%28force%29&diff=1228641725&oldid=1227711027

I don't read the previous version as claiming that equal transit time never happens, only that it cannot be assumed. The "offending" passage is:

This is because the assumption of equal transit time is wrong. There is no physical principle that requires equal transit time and experimental results show that this assumption is false.

By way of analogy, regarding flipping a coin we could write:

This is because the assumption of it always landing heads-up is wrong. There is no physical principle that requires a coin to always land heads-up and experimental results show that this assumption is false.

I don't think that anyone would read that as claiming that coins never land heads-up, only that they don't always land heads-up. Likewise, ETT is not a general physical principle, but that doesn't imply that it never happens. I don't think we need this level of clarification and the recently added/changed language seems to me to make the section more difficult to read. Perhaps we could simply add a sentence to the effect of "ETT does occur in some situations, but when it does there is no lift." But I don't know that it's really necessary. I'll wait for other editors to weigh in before reverting the edit. Mr. Swordfish (talk) 14:24, 12 June 2024 (UTC)

Prior to my recent edit, Wikipedia’s emphasis was that equal transit time (ETT) is wrong, false, incorrect, misleading etc. In fact, the opposite is true. ETT represents the flow past most solid bodies. Airflow past a power line, past each strand of a wire fence, past every flag pole, satisfies the description of ETT. Every rain drop and hail stone that have ever fallen have experienced the 3-dimensional equivalent of ETT. It is only lifting flows that don’t exhibit ETT. Let’s say 99% of flows around solid objects can be described as exhibiting ETT; and only 1% of flows cannot be described in this way. Saying “the assumption of equal transit time is wrong” is a statement that can be soundly challenged unless it is clear that it is confined to lifting flows.

ETT is a very simple 3-word expression. Doug McLean describes it as “an argument that is widespread in explanations aimed at the layman.” (See Understanding Aerodynamics, section 7.3.1.4) A more sophisticated way of saying ETT is “the circulation is equal to zero”. There are many reliable sources that talk about flows where circulation is equal to zero.

Prior to my recent edit, Wikipedia said there is no physical principle that requires equal transit time ... This statement can be soundly challenged unless it is clear that it is confined to lifting flows. The Kutta–Joukowski theorem is a fundamental theorem in the field of aerodynamics and it clearly implies that a non-lifting flow around a body must have a circulation of zero! Similarly it implies that if the circulation is zero, the lift will also be zero. For circulation equal to zero, the layman may read ETT.

Wikipedia needs to say that ETT does not exist around a lifting body or around an airfoil experiencing lift but we need to be careful to avoid versions of this statement that are so universal in their applicability that they can be readily challenged. It can be challenged if Wikipedia implies that ETT is inherently false, or universally inapplicable. ETT is the usual state of affairs, and it is only in the very narrow field of lifting flows that it does not prevail and cannot be assumed. Dolphin (t) 06:15, 13 June 2024 (UTC)

> Airflow past a power line, past each strand of a wire fence, past every flag pole, satisfies the description of ETT. Every rain drop and hail stone that have ever fallen have experienced the 3-dimensional equivalent of ETT.

Is this true? Usually power lines, wires in fences, and flagpoles sway and move in the wind. What force is causing that movement? Do raindrops always fall straight down, or is there sometimes asymmetrical airflow that causes a horizontal force?

Flows with zero circulation are nice simple models so there are lots of textbook examples of that idealized condition. I'm highly skeptical that they occur in nature as the rule rather than the as a first order model in theory; for it to occur, I think you'd need to have the solid object be perfectly symmetrical, not rotating, and the airflow non-turbulent. Perhaps you can provide a reference for your 99% claim? Regardless, this tangent distracts from the main thrust of the section i.e. ETT is not a physical law like conservation of momentum, energy, or mass so it can't be assumed.

The previous version states that "the assumption of ETT is wrong". That's correct. And "There is no physical principle that requires ETT" That is also correct. We should stick by that. Mr. Swordfish (talk) 12:56, 13 June 2024 (UTC)

Interesting article that addresses the history of ETT. It's not peer reviewed so we can't cite it as a reliable source, but worth a read.

https://arxiv.org/pdf/2110.00690

On the Origins and Relevance of the Equal Transit Time Fallacy to Explain Lift

Graham Wild

School of Engineering and Information Technology, UNSW ADFA, Canberra, Australia

[email protected]

1st of October 2021

Preprint

Not Peer Reviewed

Abstract

Recently, aerodynamics syllabi have changed in high schools, pilot ground training, and even

undergraduate physics. In contrast, there has been no change in the basic theory taught to

aeronautical or aerospace engineers. What has changed is technology, both experimentally and

computationally. The internet and social media have also empowered citizen science such that

the deficiencies in the legacy physics education around flight and lift are well known. The long-

standing equal transit time (ETT) theory to explain lift has been proven false. If incorrect, why

was it ever taught? Through a historical analysis of relevant fluid and aerodynamics literature,

this study attempts to explain why ETT theory is part of our collectively lower-level cognitive

understanding of lift and flight. It was found that in 1744 D’Alembert himself assumed this to

be a feature of moving fluids, and while this initial intuition (ETT 1.0) was incorrect, the

property of ETT (ETT 2.0) was derived in 1752 when applying Newton’s laws of motion to

fluids. This incorrect result was independently confirmed in 1757 by Euler! The conclusion is

that an over simplified treatment of fluids predicts ETT, along with no lift and drag. This then

leads to the open question, can ETT be taught at an appropriately low level as an explanation

for lift? Mr. Swordfish (talk) 12:51, 14 June 2024 (UTC)

I don’t accept your arguments. I explained my arguments in significant detail but you haven’t engaged with that detail or responded to it adequately. For example, I have written about non-lifting flows and you have responded with a little original research suggesting that flows with zero circulation are non-existent or rare.

If you wish, you could make a reasonable defence of the sentence I amended by arguing that the surrounding context makes it clear to all readers that the entire section, and the article, apply exclusively to lifting flows so if Wikipedia says the assumption of ETT is wrong it is not referring to non-lifting flows. I won’t automatically buy that argument but perhaps I will eventually if it is explained persuasively. It is an argument that has much greater potential than the arguments you put forward in your previous edit.

You have written “the assumption of ETT is wrong. That’s correct.” No, it’s not correct in the case of non-lifting flows. I have explained that in detail.

You have written “There is no physical principle that requires ETT. That is also correct.” No, it isn’t correct. The Kutta–Joukowski theorem is a physical principle and it requires ETT in non-lifting flows. I have explained that in detail. Dolphin (t) 13:13, 14 June 2024 (UTC)

I think we both agree that ETT is not a valid assumption for an airfoil with lift. I think we also both agree that there is a body of scholarship that does make the simplifying assumption of ETT in some specific examples. That doesn't imply to me that ETT is the usual state of affairs any more than the assumption of a spherical cow implies anything about the shape or real-world cows.

You assert that "ETT represents the flow past most solid bodies". But you have not provided a citation for that. I'm highly skeptical that this is true since just about everything moves and flutters in the wind. As Norman Smith's paper states:

...the claim that the air must traverse the curved top surface in the same time as it does the flat bottom surface...is fictional. We can quote no physical law that tells us this.

That is, in general there is no physical law that requires ETT. That's not to say it never happens, or that no physical models ever make that simplifying assumption (and when they do, the result is zero lift). Whether "most solid bodies" exhibit ETT is somewhat orthogonal to this section, so perhaps we don't need to settle that here. I do think that the recent additions and changes are a distraction and make the section less readable. I'll take a look at improving the readability while keeping your concerns about overstating the invalidity of ETT. Mr. Swordfish (talk) 16:04, 14 June 2024 (UTC)

You and I both have a thorough understanding of the Kutta–Joukowski theorem. I believe the expression “equal transit time” may be a layman’s way of saying the circulation is equal to zero; I hope we agree on that.

A small part of the problem is that ETT is not a well-defined or rigorously defined expression. To the best of my knowledge this expression is only used by authors who are repudiating this attempt at an explanation of aerodynamic lift. To the best of my knowledge none of the authors and institutions that resort to this naïve explanation of lift actually use the expression “equal transit time“; no-one actually asserts that “ETT” is true or correct. There are only people like us who assert that ETT is not correct (when applied to a body generating lift.)

Your quote from Norman Smith describes a body with “the curved top surface” and “the flat bottom surface.” He is not referring to “most solid bodies” - he is describing an airfoil!

I can supply a quotation from Anderson’s “Fundamentals of Aerodynamics” that will help on this topic. I expect to get access to my copy of Anderson within 7 days. Dolphin (t) 14:30, 15 June 2024 (UTC)

Agree that ETT is not well defined, and that it doesn't appear to be used other than by those repudiating it. Searching for the phrase (or even the word "equal") on my user page collection of works presenting ETT as correct only finds that in the references, not the actual works themselves. Similarly, the obstruction explanation is sometimes derisively referred to as "hump theory" but it's proponents don't use that phrase.

A typical turn of phrase is "The air moving on the top has to travel a greater distance in the same amount of time." or "Air flowing over the top has a greater distance to travel in the same time; that's why it flows faster."

I don't know that the expression “equal transit time” is a layman’s way of saying the circulation is equal to zero, since I would surmize that those advancing the idea probably don't know what circulation is. That said, here's a source basically confirming that ETT and Γ=0 are the same idea.^[1]

Regarding whether most flows around solid objects exhibit ETT, if that were true than vortex shedding and Vortex-induced vibration would not pose problems for engineers to overcome.

References

Mr. Swordfish (talk) 16:20, 15 June 2024 (UTC)

Edits finished. Hopefully that addresses the concerns above. Mr. Swordfish (talk) 16:36, 14 June 2024 (UTC)

Your recent edit to the article is an acceptable alternative to my edits. Thank you for making those changes.

The article now avoids giving readers the impression that ETT is inherently false. Hopefully readers can now see that the only falsehood is suggesting ETT exists in the flow around a lifting body. Dolphin (t) 14:46, 15 June 2024 (UTC)

Thanks for the reference to “Flight Physics:Essentials ...” I was not aware of that publication. It looks like it might be essential!

Vortex induced vibrations are an oscillatory phenomenon. They become a problem in structures that have inadequate stiffness or inadequate damping. In our article on lift we are talking about steady flows with zero viscous effects, or only minor viscous effects. We use a reference frame attached to the airfoil or solid body so the consequences of oscillations of a solid body are way beyond the level of analysis we are using in this article, and related articles.

Could it be that after half a lifetime of believing that ETT is false, the work of the devil, it will take a major change of direction to accept that there is nothing false or distasteful about ETT? Could that be why you are finding reasons to deny the inevitability of flows in which circulation is zero, ETT prevails and lift is zero? Dolphin (t) 03:46, 16 June 2024 (UTC)

It's not that I don't believe lift can be zero (and that implies ETT). I just don't think it occurs as often as you seem to think it does i.e. 99% of the time a solid body is immersed in a moving fluid. That's because almost all real world objects are not perfectly symmetrical and that implies an asymmetrical air flow hence non-zero circulation.

Stated another way, ETT is not a valid assumption in general. If you assume ETT, you will get zero lift. I don't have a cite for this and I am willing to consider evidence to the contrary, but real-world airflows around solid objects with zero circulation are the exception rather than the rule. For instance, consider a symmetrical airfoil in a steady flow - it is well established that the lift varies by the angle of attack. For the special case of zero AOA, the lift is zero and ETT occurs (in this simple 2-d model). For all the other values there is lift, circulation is non-zero, and ETT is false. In mathematical terms, the set of values for which ETT holds has measure zero. That's about as rare as you can get without it being never.

Perhaps there is some area of aerodynamic research that assumes ETT or decides that lift is small enough that lift is negligible - many treatments ignore viscosity, or compressibility for example - I'm not aware of any that assume zero lift, but maybe there are. Let me know if you know of any. Mr. Swordfish (talk) 13:00, 16 June 2024 (UTC)

There are several elements of your edit on which I can comment but at present I only have time for one. I will comment on others later.

You write about “real-world solid objects with zero circulation ...” Then you make a sneaky gear change and write about “a symmetrical airfoil ...” The two are very, very different in aerodynamics so your gear change doesn’t go unnoticed. Yes, a well-designed airfoil will produce lift (and lift coefficient and circulation) that varies approximately linearly with angle of attack. The feature of a well-designed airfoil that yields this desirable property is the sharp trailing edge. Clancy’s book Aerodynamics addresses the role of the sharp trailing edge and the way it causes vortex shedding to adjust the strength of the bound vortex to maintain the Kutta condition. I don’t have Clancy with me but I think it is Section 4.5 and/or 4.8 that contains good explanatory diagrams.

In the absence of a sharp trailing edge, any change in orientation of a body is not accompanied by a change in lift (or lift coefficient or circulation.) For example, a cylinder with elliptical cross section, immersed in a flow produces little or no lift; altering the orientation of the cylinder doesn’t produce much change. What lift might be produced is due to asymmetric boundary layers and separated flow, rather than due to the primary flow predicted using an inviscid fluid. If a body doesn’t have a sharp trailing edge, and the orientation of that body is changed, the fluid flow adjusts itself so that circulation remains zero. Circulation greater than zero requires the Kutta condition, and the Kutta condition requires a feature resembling a sharp trailing edge. Airfoils have sharp trailing edges, but real-world solid objects don’t. That is why the only circulation and lift that are observed on bodies without sharp trailing edges is the small amount caused by asymmetric boundary layers on the two sides of the body, separated flow and possibly other minor viscous effects.

Scientists and engineers have to work hard to generate circulation and lift. Typically they use airfoils with thin, sharp trailing edges even though this feature is structurally weak and vulnerable. Flowing fluids are uncooperative - as they flow around bodies their natural state is doing so with zero circulation. Any change in orientation of a real-world solid body causes the fluid to change its flow pattern to avoid circulation developing. If it were not so, aircraft designers would use wings with thick, generously rounded trailing edges so they could get more fuel into the wings, use deeper and lighter spars, and have more room into which to retract the undercarriage. Dolphin (t) 16:18, 16 June 2024 (UTC)

On the matter of the sharp trailing edge there is a very useful quotation by George Batchelor in the short article Trailing edge.

There is also a useful quotation by Richard von Mises at Airfoil, reference number 4. Dolphin (t) 00:38, 17 June 2024 (UTC)

The conventional wisdom is that fluid flow around a real-world solid body experiences zero circulation. Picture the wind blowing around such a body, and then the wind changes direction. Imagine that this change causes a circulation to begin in the flow. This circulation causes a lift force to act on the solid body. Newton’s 3rd law tells us that an identical lift force acts on the flowing air. When a fluid that is free to flow or change shape is subjected to a force or pressure it responds in whatever way will cause that force to diminish. Consequently the lift force on the air flowing around the solid body causes the streamlines, velocities and pressures to change to diminish the circulation that has just begun. This process can be expected to continue until all circulation has been eliminated. Only then has equilibrium been achieved within the flow pattern around the body.

Any residual circulation and lift is not related to the primary flow as would exist in a geometrically similar situation but with an inviscid fluid. It is related to the secondary flow caused by viscous effects such as flow separation. Any residual lift is still accompanied by the original drag force. The lift to drag ratio is so small that this solid body doesn’t qualify as an airfoil. I believe this is an explanation for the operation of oddly shaped lifting bodies which glide without conventional wings. Dolphin (t) 05:22, 17 June 2024 (UTC)

I'm continuing this discussion since I think I may learn something. I'm not trying to be "sneaky", just trying to understand what evidence there is that zero-circulation/zero-lift/ETT is the usual or normal state of affairs rather than a rare exception.

>Circulation greater than zero requires the Kutta condition, and the Kutta condition requires a feature resembling a sharp trailing edge.\

Agree that Kutta condition requires a sharp trailing edge, because without one it's not obvious where the rear stagnation point occurs. And without that it's not clear how much circulation to apply to model the fluid re-joining at the rear stagnation point. But you don't need a sharp trailing edge to have an asymmetrical airflow with non-zero circulation, you just can't apply the Kutta contidion. As Gale Craig states, (paraphrasing) you don't need an airfoil shape to get lift, as anyone who has ever handled a sheet of plywood in the wind knows. Of course, if you want enough lift to fly a plane of propel a sailboat, you'll want something with more lift than a non-arifoil can provide. That doesn't mean only airfoils with sharp trailing edges can generate lift.

I have sailed boats with rudders that have a rounded trailing edge. Performance is sub-optimal, but the rudder most definitely provides enough lift to steer the boat. When I look at leaves on trees or flags on a flagpole in the wind, they never settle down into an equilibrium of zero lift as you describe above. Spinning balls have lift, as any tennis player understands. Here in the US, there's a baseball pitch called the knuckleball where the ball is thrown with a little spin as possible, with the effect that it's impossible to predict which direction the lift will take the ball making it very hard to hit. So, my experience is quite at odds with your assertions.

You say that "The conventional wisdom is that fluid flow around a real-world solid body experiences zero circulation." but don't provide anything to back that up. Along with your 99% figure, I would need some more to go on than your assertion.

Agree that my examples above are anecdotal or original research. Here's an interesting treatment of bluff bodies which seems to be in conflict with your assertion that Circulation greater than zero requires the Kutta condition...

For bluff bodies, the interest is usually in the drag on that body, mainly because experiments have found that drag is the dominant force. This observation, however, does not imply that bluff bodies cannot produce lift because many do. Nevertheless, examining just the drag characteristics of such bodies is convenient in the first instance. Furthermore, bluff bodies may also produce pitching moments, which sometimes need to be known for certain types of engineering work, e.g., to determine torsional loads.

Mr. Swordfish (talk) 13:56, 17 June 2024 (UTC)

Here's an excerpt from another paper BLUFF-BODY AERODYNAMICS

Bluff bodies are obviously also subjected to forces in the across-wind direction and to

moments around the various axes due to non-symmetries of the pressure distribution on their

surface. Therefore, these loads depend fundamentally both of the body shape and on the

orientation of the incoming freestream. Particularly in the two-dimensional case, the force

component in the across-wind direction is often called lift force, in analogy to the

corresponding force acting on an aeronautical wing section (airfoil).

(elision of details about the starting vortex and consequential circulation around an arifoil)

Coming back to bluff bodies, the above described mechanism does not apply in all its

details, particularly because the boundary layer cannot remain attached to their surface even

after the end of the initial transient. However, if the body is sufficiently elongated (like an

ellipse), a starting vortex is shed anyway (even if not as strong as that of an airfoil), and the

asymmetry of the final flow configuration for non-symmetrical wind orientations may be

sufficient for producing significant lateral forces.

Seems to me that if it were the case that almost all bluff bodies experience zero lift the paper would say that at some point. Mr. Swordfish (talk) 14:32, 17 June 2024 (UTC)

One of the frustrating aspects of discussing this subject is the variation in meaning given to the word “airfoil”. On these Talk pages I see the word used with three different meanings:

1. A two-dimensional shape that can be employed in three-dimensional bodies to generate lift. For example, the shape known as NACA 2412 is an airfoil section commonly used for the wings of low-speed aircraft.
2. A three-dimensional body that generates at least a little lift. Some Users point to an irregular body or a sheet of plywood or a sycamore seed and, noting that it experiences a small lift force, say “see, it is an airfoil!”
3. A three-dimensional body that, over a usable range of angle of attack, is capable of generating significantly more lift than drag. With this meaning, airfoils are manmade structures that have the generation of lift as their primary purpose. Airfoils are carefully designed and manufactured structures to ensure the lift-to-drag ratio is high enough to achieve its intended purpose.

Wikipedia’s current definition of airfoil closely matches No 3 above. Airfoil says:

When the wind is obstructed by an object such as a flat plate, a building, or the deck of a bridge, the object will experience drag and also an aerodynamic force perpendicular to the wind. This does not mean the object qualifies as an airfoil. Airfoils are highly-efficient lifting shapes, able to generate more lift than similarly sized flat plates of the same area, and able to generate lift with significantly less drag. Airfoils are used in the design of aircraft, propellers, rotor blades, wind turbines and other applications of aeronautical engineering

The layman imagines that the essential feature of an airfoil (meaning No 3) is its generously rounded leading edge, or its curved surface. In fact it is the trailing edge. That is partly the explanation of why a flat sheet of plywood will experience lift in a flow of air - it has a sharp trailing edge.

Since the days of Joukowski and Kutta, mathematicians and physicists have been able to model the flow of an inviscid fluid around suitable geometric shapes. With a sharp trailing edge it is possible to determine the lift and pitching moment on the shapes. Tests on real models of wings in wind tunnels show there is close agreement between the math and the real world for these shapes with sharp trailing edges. For bodies without a sharp trailing edge, the math shows that an inviscid fluid imparts no lift or pitching moment to the body.

Wind tunnel tests on bodies without sharp trailing edges, and anecdotal evidence, show that these bodies can experience a little lift. This does not mean they qualify as airfoils under meaning No 3 above. Engineering, and most science, have little interest in these bodies. What lift they develop is not due to airfoil action - exploiting the Kutta condition to generate lift. It is due solely to viscous effects such as flow separation. These bodies, at best, have a very low lift-to-drag ratio. Little is written about them in mainstream science or engineering publications. This type of lift has little or no engineering application.

We know that eating a tablespoon of salt a day won’t cure cancer, but it is probably impossible to find a reliable published source that confirms eating a tablespoon of salt a day won’t cure cancer! Similarly it is probably impossible to find a reliable published source that confirms that no bluff body has ever been found that is capable of a high lift-to-drag ratio.

We use the Kutta condition to determine, mathematically, the circulation around a 2-D shape with a sharp trailing edge edge. There is no similar model, theory or equation to determine circulation around a 2-D shape with no sharp trailing edge. I suspect that wind tunnel tests would not show a usable relationship because, being reliant entirely on viscous effects, the results would be strongly influenced by the surface conditions of each model being used - roughness, smoothness, manufacturing imperfections etc.

When I say that bodies without sharp trailing edges do not generate circulation in fluid flows around them, I am speaking as an aerodynamicist applying the model of the inviscid fluid. There is no doubt that my statement is true for inviscid flows, which admittedly are fictitious, but this is usually a good, simple guide to the reality of high Reynolds number flows. When you say that all bodies in a fluid flow experience viscous forces and these forces will provide at least a very small amount of circulation that cannot be eliminated by the flow pattern adjusting itself you are possibly speaking as a scientist focussed on observing the complex realities of the real world. You aren’t able to determine how much circulation there will be, or say exactly how that circulation is sustained. What circulation exists is small and I say it is zero. You possibly describe the same situation by saying circulation is not zero. That might be as close to consensus as we can hope to reach. Dolphin (t) 15:39, 17 June 2024 (UTC)

Agree that I am sometimes a bit loose with the terminology re: airfoil. One other possible avenue of miscommunication here is that when I see the word "lift" in this context I think of the definition used in the first sentence of the article:

When a fluid flows around an object, the fluid exerts a force on the object. Lift is the component of this force that is perpendicular to the oncoming flow direction.

and as a mathematician rather than an aerodynamic engineer lift=0 means actually zero, as opposed to "too small to be useful or significant." One of the arts of engineering is to figure out what things can be ignored, and for most non-airfoil applications the fact that there is some component of the aerodynamic force perpendicular to the airflow is negligible. I'm sure that there are many situations where we would agree that whatever small amount of lift might be present, it's too small to matter so let's assume it is zero. This would imply ETT in that situation.

Other situations I wouldn't agree that it's too small to matter, for instance, a leaf on a tree in a breeze - the leaf repeatedly flutters back and forth in a direction perpendicular to the airflow and this implies to me that there is some force making it move that way and the obvious one is that there is some non-zero component of force transverse to the airflow. I would call that "lift" according to the definition above. But since I doubt either of us will be hired as an engineer to design tree leaves any time soon we can leave it there. Mr. Swordfish (talk) 17:56, 17 June 2024 (UTC)

Thanks. I agree with most, if not all, of what you have written. I now realise that the concepts of streamlines, time slices, circulation and ETT are all concepts that rely on steady flow. When we are talking about a turbulent wake, separated flow, oscillatory flow, the erratic dancing of the leaves and branches of a tree, we can’t claim the protection offered by retreating to steady flow. Debating about streamlines, time slices and ETT in a non-steady flow is deeply flawed.

The dancing of leaves on a tree is definitely caused by the interaction of aerodynamic forces and elastic forces within the highly flexible structures of a tree. This kind of motion could be caused entirely by drag, so I’m not persuaded that the dancing motion of a leaf necessarily shows the presence of lift.

The concepts of lift and drag rely on knowing the direction of the local velocity of the fluid. The air moving through the branches and leaves of a tree is highly disorganised and the velocity at each point is changing rapidly so it is probably true to say that while we can possibly identify aerodynamic forces acting on branches and leaves, the concepts of a drag component and a lift component are not applicable. The distinction between a lift component and a drag component seems to be reliant on steady flow, and flow in which the speed and direction at one point is almost identical to the speed and direction at all nearby points.

The Kutta-Joukowski theorem is remarkably similar to Newton’s 1st and 2nd laws. Scientists and engineers say Newton’s laws are valid. Perhaps a mathematician and philosopher might say Newton’s 1st law is redundant because there is no such thing as a body whose acceleration is truly zero; and no such thing as a body experiencing a net force that is truly zero. Dolphin (t) 00:30, 18 June 2024 (UTC)

In my edit dated 15 June 2024 (14:30) I wrote “I can supply a quotation from Anderson’s Fundamentals of Aerodynamics that will help on this topic.” See the diff. In section 3.16 Anderson writes about the Kutta-Joukowski theorem:

"Although the result given by the equation ${\displaystyle L^{\prime }=\rho _{\infty }V_{\infty }\Gamma }$ was derived for a circular cylinder, it applies in general to cylindrical bodies of arbitrary cross section."

This confirms that the Kutta-Joukowski theorem is not confined to airfoils. It applies to all cylindrical bodies regardless of their cross sectional shape. If a cylinder of arbitrary cross section causes no circulation in the flow in which it is immersed the cylinder will experience no lift.

It is not too great a leap to say that, just as airfoils are associated with the Kutta condition to explain when they will generate lift, and when they won’t, cylindrical bodies of arbitrary cross section also rely on a feature resembling a sharp edge to obtain a well-defined lift. If these bodies of arbitrary cross section experience lift in the absence of a sharp edge, it is due to viscous effects such as flow separation and asymmetric boundary layers, rather than due to airfoil action.

My mention of a well-defined lift is from "sharp trailing edge to obtain a well-defined lift" as written by Richard von Mises. See citation No. 4 in Airfoil. Dolphin (t) 12:44, 30 June 2024 (UTC)

The picture/diagram used to show the incorrect "equal transit time" theory does not actually show the equal transit time theory.

The most important point (that makes the theory wrong) is that molecules, or two points in the streamline before the wing, and then after the wing, must meet again at the end.

The diagram in this section, doesn't include the molecules or points in the streamline starting together and then coming back to together at the trailing edge. This just shows what does happen, faster fluid on top = higher pressure; lower velocity on bottom = higher pressure. This part is true. Its equal transit time explanation of WHY that occurs that isn't. The image should be updated to show the points meeting again. KarmaKangaroo (talk) 03:12, 16 March 2025 (UTC)

Yes, the current picture does not adequately show equal transit time, only faster air, lower pressure, and longer distance.

We used to have a picture something like this.

I'll take a look at the archives and see if I can restore the better diagram. Mr. Swordfish (talk) 15:35, 24 May 2025 (UTC)