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Increased flow speed and Bernoulli's principle

There is a cycle: "For any airfoil generating lift, there must be a pressure imbalance" → "an increase in speed" → "a lower pressure". It needs a correction. Probably without "False explanation based on equal transit-time" this explanation lost sense (not Bernoulli's principle itself, of course). --109.174.113.181 (talk) 18:29, 12 June 2021 (UTC)Serg

I'm trying to understand the nature of the confusion here, but I can't make sense of the above comment. Perhaps others can explain. I'll give it a few days and then remove the confusion tag if no further comments. Mr. Swordfish (talk) 15:30, 3 July 2021 (UTC)

Now, having read the comment several times and also the article it appears that the comment author 'is' confused. They seem to think that the article states that "an increase in speed" → "a lower pressure". But it doesn't say that. However, given the prevalence of "explanations" that say the pressure differences are caused by speed differences I can see how one might think our article says that. I propose the following language, which might help clear things up:

Bernoulli's principle states that there is a relationship between the pressure at a point in a fluid and the speed of the fluid at that point, so if one knows the speed at two points within the fluid and the pressure at one point, one can calculate the pressure at the second point, and vice versa. For any airfoil generating lift, there must be a pressure imbalance, (i.e., lower average air pressure on one side than on the other). Bernoulli's principle implies that these changes in the air pressure must be accompanied by changes in the air speed. In the case of an airplane wing, air flows faster and at a lower pressure over the top of the wing than under it.

Mr. Swordfish (talk) 13:12, 6 July 2021 (UTC)

If we have "a pressure imbalance", then we have the lift. So if it states "there must be a pressure imbalance", we don't need speeds and Bernoulli's principle to explain the lift. On the other hand, the actual contribution of Bernoulli’s principle to the lift theory is not required for a simple explanation. 109.174.113.183 (talk) 20:04, 8 July 2021 (UTC)Serg

I disagree with the comment above from 109.174.113.183. The occasion when we must make use of Bernoulli's principle is not when we begin "there is a pressure imbalance"; it is when we begin "the air flows faster past one side of the airfoil than past the other side." That demands an explanation as to why a difference in flow speed leads to a pressure imbalance - and the answer is "Bernoulli's principle!"

I agree that it is possible to point to the existence of lift in airfoil action and accurately state that there is a pressure imbalance whenever the airfoil meets the oncoming air at an angle of attack greater than zero; Bernoulli's principle is not required because it is a simple but accurate description of airfoil action. This is an explanation that is reasonable and sufficient for many people, but for others it is too simple and completely fails to relate lift to the known kinematics of the flow field - why does the air flow faster past one side than the other etc.? For this latter group of people a sufficient explanation is available when they begin to take into account the Kutta condition and the Kutta-Joukowski theorem, and these two concepts ultimately require that use is made of Bernoulli's principle. Dolphin (t) 07:41, 9 July 2021 (UTC)

In the text, it starts from "For any airfoil generating lift, there must be a pressure imbalance". After that we don't need "air flows faster ..." since we have "a pressure imbalance". Moreover, this explanation doesn't describe a source. It can be based on cause-and-effect misunderstanding only.

I don't think this explanation is simple. Probably it is habitual (rather than clear) for people who heard about "equal transit time" theory. As an example, in comparison to the flow turning explanation:

• it doesn't explain a source (this leads to misunderstandings).
• it's impractical and unsafe. For example:
  • the stall warning is based on low pressure sensor. So we have low pressure over the wing, but the airplane falls.
  • it doesn't explain why it is dangerous to fly behind an airliner.
• it doesn't explain wingtip vortices (and this can be observed in contrast to speed difference of the airflows).
• this doesn't help to understand wing configuration (e.g. aspect ratio) because it is based on wing area.
• it is harder to explain Bernoulli's principle rather than Newton's third law.

Bernoulli's principle can be useful in advanced practices (e.g. KTAS vs. KIAS calculation).109.174.113.178 (talk) 14:39, 11 July 2021 (UTC)Serg

I agree with you that the flow turning explanation is both simpler and more useful than the Bernoulli explanation, especially for an audience that is not mathematically inclined. I also agree that you don't need to know that the air is going faster in order to have a basic concept of lift. However, the changes in speed are a very real phenomenon and just about every reliable source includes a treatment of Bernoulli's principle, so we would be remiss as wikipedia editors if we didn't include something about it. So, I'm not sure what you are asking for here. Do you want us to remove all references to Bernoulli's principle in the article? Something else? Do you think the material is incorrect or misrepresents the reliable sources it's based upon? Mr. Swordfish (talk) 17:32, 11 July 2021 (UTC)

Yes, there are a lot of incorrect explanations based on misinterpretation of Bernoulli's principle. For example, FAA PHAK describes lift via venturi tube and refers to NASA at the same time (I guess this is not a mistake because NASA published description about Venturi nozzle in 2000). So I propose to mark the current section "Increased flow speed and Bernoulli's principle" as false explanation in addition to "False explanation based on equal transit-time" (this should be clear enough, since we have already references to McLean about correct usage of Bernoulli's principle). For example, the seminar from University of Michigan Engineering has a good structure for a simplified explanation. It even explains the pressure imbalance (same as Holger Babinsky) [however, 13:45 - "you don't need to go into pressure in order to explain lift"]. According to this seminar or NASA we have three false explanations wrong1 "Equal transit time", wrong2 "Particle kinetics" based on Newton's third law, wrong3 "Venturi tube", and correct one.

In regards to Bernoulli's principle description in a comprehensive explanation, I think the current picture of the pressure field around an airfoil could mislead. Color gradients (like this ) could help to understand that the lowest pressure is not at the trailing edge. The current picture shows the same (almost), but it requires more attention to understand.109.174.113.177 (talk) 15:53, 12 July 2021 (UTC)Serg

Serg, you propose to mark the current section "Increased flow speed and Bernoulli's principle" as false explanation. To do so, you will need to find a reliable source that declares it to be false, and also convince the other editors that the reliable sources that the article is based on are wrong. I sincerely doubt that you will be successful.

There is nothing incorrect about the current section. I'm willing to entertain the notion that it may be confusing, or that it could be written in a more easily understood manner. But it's not wrong and marking it as a false explanation would itself be false. Both Bernoulli's principle and Newton's laws can be used to correctly explain lift. Both have also been used to incorrectly explain lift - that doesn't mean that every explanation using one or the other is wrong. If you read past the small section under discussion, I think you will see that most of your concerns are addressed later in the article. Mr. Swordfish (talk) 20:06, 12 July 2021 (UTC)

I see three discussion points about the section:

1. I agree, the section properly describes Bernoulli's principle. No issues here.
2. The explanation is false because it is based on cause-and-effect misunderstanding.
3. Probably it is not easy to explain this misunderstanding simply. Thus in regards to your "we would be remiss as wikipedia editors if we didn't include something about it", I propose to add popular false explanation about Venturi tube (instead of the current section). It mentions Bernoulli's principle, and no problems with refs.

A comprehensive explanation could require both Newton's laws and Bernoulli's principle (and maybe mention of adverse pressure gradient). A simplified explanation don't need Bernoulli's principle or pressure imbalance.109.174.113.177 (talk) 11:25, 13 July 2021 (UTC)Serg

1. Good. We have agreement that the section correctly describes Bernoulli's principle.
2. Where does this section say anything about cause-and-effect? If you think it does, then either you are reading something into it that is not there, or I'm missing something. Could you be more specific?
3. Agree that it's not easy to explain. I have no issues with adding a subsection on the venturi tube false explanation, as long as we point out that it is false. However, I don't think removing the four sentence introduction that simply states Bernoulli's principle and how it applies to an airfoil is the right approach. If we're going to discuss BP then we have to say what it means first. I'll propose a redraft.

As for whether BP should be part of a simplified explanation, I'm inclined to agree with you. If we hadn't had a century of the false equal-transit-time explanation being the more or less standard explanation then my preference would be to move the BP material further down in the article as part of the mathematical treatment and only give the flow-turning Newton's 3nd law explanation in the "simplified" section. But, the reliable source material treats BP prominently (often incorrectly, although the more reliable sources treat it correctly) so I think as editors we are bound to reflect that in the article. That said, if there is consensus to pull BP out of the simplified section I will readily agree. I doubt there will be. Mr. Swordfish (talk) 14:00, 13 July 2021 (UTC)

2 and 3 are addressed below.

By "misrepresents the reliable sources it's based upon". There are two references #12 and #13 that could be refined. The 13th doesn't seems to be reliable source. It mixes statements e.g. it refers to FAA PHAK and Jeppesen’s PPM (that use Venturi tube to describe lift) as to textbooks with a valid Bernoulli-based explanations and manifest Venturi tube as a false base at the same time. The 12th states the following:

• "Newton’s laws may be a simpler description as long as one does not need to evaluate the details of the flow field."
• "conservation of mass and conservation of energy, Bernoulli’s law" and "conservation-of-linear-momentum principle, Newton’s laws" are "mathematical models that correctly calculate the force".

I have two concerns here:

1. I think it could be helpful to point that BP is not enough for classic Bernoulli-based explanations (disregarding unexplained reasons mentioned in the limitations section). In pilot schools BP is manifested as a complete explanation. In fact it requires conservation of mass and conservation of energy including BP.
2. Regarding mathematical models we have already "This explanation is largely mathematical, and its general progression is based on logical inference, not physical cause-and-effect." with ref to McLean at Lift (force)#Circulation and the Kutta–Joukowski theorem section. Probably this source is not enough to proof equivalence of simplified physical explanations.

109.174.113.170 (talk) 06:28, 15 July 2021 (UTC)Serg

I agree that it is possible to explain aerodynamic lift without including a discussion of Bernoulli's principle. However, a description of the physics would be incomplete without saying that as the air flows from a region of ambient pressure to a region lower pressure it must speed up. More pressure behind than in front accelerates the air. That's Bernoulli's principle, and at least one of our sources claims that the change in pressure causes the speed increase, rather than the other way around. It's the [speed increase] -> [pressure drop] causality so common in the incorrect explanations that causes the confusion. We've tried to avoid that in the article. Mr. Swordfish (talk) 16:03, 9 July 2021 (UTC)

Airflow acceleration is a part of a comprehensive explanation. So, the airflow turning is a simple explanation , and as an extension we have the acceleration and conservation of momentum.109.174.113.178 (talk) 14:39, 11 July 2021 (UTC)Serg

I don't find the paragraph confusing, but I concede it does little to clarify the relationship between Bernoulli's principle and the phenomenon of aerodynamic lift, and therefore could be confusing to many readers. I will give some thought to some words that might be an improvement. Dolphin (t) 13:24, 6 July 2021 (UTC)

The way I explain it to my sailing students is:

The air flows around the sail and changes direction. That means that the sail has exerted a force on the air, and according to Newton's 3rd the air must exert a force on the sail that is equal in magnitude and opposite in direction. How does the air do this? The only way it can: through air pressure. (I elide over shear stress to keep it simple). So there is a region of reduced pressure on the outside surface of the sail and a higher pressure on the inside. As the air flows along the outside surface it moves from a region of ambient pressure to a region of lower pressure. Since there is more pressure behind than in front, the air speeds up and goes faster as it travels along the outside surface of the sail. Is this important? Not really; I can't think of a single practical implication that is useful for trimming your sails. But it has to happen. You can't have the force without the pressure difference, and you can't have the pressure difference without the speed change. Sometimes this algebraic relationship between speed and pressure is used in the mathematical analysis of how sails work, but it doesn't do much for you out on the water.

Putting this into the article would probably be categorized as synthesis, but perhaps we could use it as a starting point for a rewrite to better "...clarify the relationship between Bernoulli's principle and the phenomenon of aerodynamic lift." Mr. Swordfish (talk) 12:49, 10 July 2021 (UTC)

The discussion here has highlighted some problems in the existing presentation of this sub-topic. Rather than trying to patch up the existing presentation I want to propose a complete re-write. Please see my proposed re-write in my sandbox. All comments will be welcome. Dolphin (t) 07:28, 12 July 2021 (UTC)

I do not think introducing the concept of circulation and the Kutta condition at this point in the article will reduce confusion. Just the opposite IMHO. The main section is titled "Simplified physical explanations of lift on an airfoil" That's should not include circulation and the Kutta condition.

My take is that the problem with the current sub-section is that we studiously avoid making any concrete statements regarding cause and effect. While the bulk of the incorrect Bernoulli-based explanations say that the air speeds up for some reason and this causes the pressure to be lower, our presentation is much more passive - "an increase in speed must accompany any reduction in pressure". My sense is that most lay readers are looking for some cause-and-effect language and when they don't get it don't feel like the article has answered their question. I think the section taken in it's totality eventually clears this up, but not until somewhat later. I'm thinking that perhaps re-ordering the material might help, but thus far I haven't come up with a coherent approach. My thought is that he conservation of mass explanation could wait until later since it's not so "simple" (and really is not much of an explanation either). But as it's discussed in the following section, we'd need to move that too and I'm not seeing a simple way to do that. I'll give it some more thought. Mr. Swordfish (talk) 20:30, 12 July 2021 (UTC)

I agree, it seems complex for an introduction. I also agree, cause-and-effect language will work better for a simplified explanation. The article has a good start: propeller, helicopter rotor, wing share the same physical principles and work in the same way. Thus fans, propellers, helicopter rotors and wings generate lift and produce airflow in the same manner. Airflow is evident for fans, propellers and helicopter rotors; it is also observable as wingtip vortices for wings. The following section about flow turning describes how it happens.109.174.113.177 (talk) 11:25, 13 July 2021 (UTC)Serg

@ Mr swordfish We are talking about the section titled "Simplified physical explanations of lift on an airfoil". On close examination, the explanation under scrutiny uses Bernoulli's principle to explain why the air flows faster over one side of the airfoil than over the other. It isn't using Bernoulli to provide an explanation of lift on an airfoil, but rather the other way around. Perhaps this is why the originator of the thread (Serg) found it confusing. I take your point that my first proposal isn't a simplified explanation and is therefore inappropriate. I have revised my proposal to simplify it. Please peruse it at my sandbox.

As has been discussed many times on these Talk pages, no-one has ever claimed that Bernoulli's principle can be applied to an airfoil section at a particular angle of attack in order to determine the lift. Bernoulli's principle can only be applied once the kinematics of the flow field are known. Bernoulli's principle reveals nothing about the kinematics but critics of Bernoulli seem invariably to dismiss it on the grounds that it fails to provide the complete solution of the lift problem from A to Z. First, the kinematics of the flow field must be determined and that is typically done by such methods as the Kutta condition and the Joukowski airfoil or similar.

I suspect a rigorous "cause-and-effect" explanation will prove elusive. We have seen debates about which occurs first - the increase in speed or the reduction in pressure. As happens in so many areas of physics, two or more quantities are observed to change simultaneously, and it is naive to imagine that one changes first and drives the change in the second. (In the cases of a venturi or an airfoil, it is the shape of the solid body and its orientation to the flow that causes flow speed and pressure, and sometimes also density and temperature, to change simultaneously.) Dolphin (t) 13:19, 13 July 2021 (UTC)

I don't think this revision is an improvement. The first sentence ("When an airfoil is inclined to the oncoming flow at a non-zero angle of attack, the flow on one side of the airfoil moves at a faster speed than the flow on the other side.") is crying out for a tag. While it is technically true, some readers may think it implies the pressure differences are caused by the speed differences. A decade or so ago, after the equal transit time fallacy (ETTF) had been well publicized, many lay-person explanations changed their materials to say "the wing is designed to make the air go faster over the top..." to avoid ETTF. While this is a technically true statement, it's misleading and doesn't begin to explain how one would go about designing such a wing.

Let me give it another try, providing context and building on the previous subsection:

As stated in the previous subsection, the air exerts an upward force on the wing when the air is deflected downward. This upward force manifests itself as air pressure with a lower air pressure on the top of the wing than on the bottom. Bernoulli's principle states that there is a relationship between the pressure in a fluid and the speed of the fluid, with lower pressure implying higher speed and vice versa. For any airfoil generating lift, there must be a pressure imbalance, (i.e., lower average air pressure on one side than on the other). Bernoulli's principle implies that these changes in the air pressure must be accompanied by changes in the air speed. In the case of an airplane wing, air flows faster and at a lower pressure over the top of the wing than under it.

I think this revision avoids the pitfalls of cause-and-effect or "which happens first" while providing some logical reasoning as to why the pressure is lower. The current article "buries" the reason there are pressure differences in the second sentence, which may be the source of the confusion. Mr. Swordfish (talk) 14:34, 13 July 2021 (UTC)

Mr swordfish, by our conversation about cuase-and-effect misunderstanding above, I agree with you that the current text can be interpreted differently. For example, by the version in the sandbox one might think it manifests [speeds]→[pressure imbalance]→[lift]. The current text of the subsection ends with "a lower pressure over the top of the wing than under it" that implies lift. Note, this subsection is intended to explain the lift force. I guess you read it as explanation of speeds only. In that case it is correct. I think that "As happens in so many areas of physics, two or more quantities are observed to change simultaneously" from Dolphin51 sounds better than "accompanied". Since the pressure and speed are changed at the same time and this change doesn't produce energy, it cannot explain the force. But we need BP to construct a wing (or to calculate the airspeed by the pressure using pitot tube).109.174.113.177 (talk) 06:15, 14 July 2021 (UTC)Serg

Serg, yes I read this little four sentence subsection as explaining why the air speeds up, not why there is lift. Conceptually, it's [lift]->[pressure differences]->[speed differences]. I'm not really seeing how to read it differently. And I don't think it was intended to explain the lift force - explanations based on pressure differences follow the subsection, along with another subsection discussing their limitations. This subsection is merely an introduction to what follows. Mr. Swordfish (talk) 15:39, 14 July 2021 (UTC)

I think it will better to end with "[speed differences]" e.g.:

For any airfoil generating lift, there must be a pressure imbalance, i.e., a lower-than-ambient pressure accompanied by higher airflow speed over the top of the wing and a higher-than-ambient pressure accompanied by lower airflow speed under it.

, and rename the subsection to "Conservation of mass and Bernoulli's principle" (and one more link to McLean to the limitations)109.174.113.170 (talk) 04:48, 15 July 2021 (UTC)Serg

@Serg - it is incorrect to imagine that the air under the wing is at a pressure significantly higher than ambient pressure. Underneath the wing the pressure is close to ambient and the airspeed is close to that in the free-stream. At the stagnation point the pressure coefficient is 1, and in the free-stream it is 0. Underneath the wing the pressure coefficient is between 0 and 1, but much closer to 0; at the top surface of the wing the pressure coefficient is less than 0 for example -1, -2, -3, even -4 etc. Dolphin (t) 06:17, 15 July 2021 (UTC)

Agree. I used this picture as ref.109.174.113.170 (talk) 06:48, 15 July 2021 (UTC)Serg

@Mr Swordfish: Your proposal begins “… the air exerts an upward force on the wing when the air is deflected downward.” I see two objections to this proposal:

Firstly, “an upward force … when the air is deflected downward.” This is the explanation of lift based on Newton’s 3rd law! If we were to use this approach it would imply that the role of Bernoulli’s principle in explaining lift is only as an appendage to the explanation based on Newton’s 3rd law. Overall, it would imply that the explanation based on Newton’s 3rd law is complete without Bernoulli, but the explanation based on Bernoulli is not complete without Newton. That would seriously devalue the role of Bernoulli and would be unacceptable.

Secondly, we appear to agree that Bernoulli alone cannot explain the lift on an airfoil – it works in conjunction with some other information. (Reference 30 is from Resnick & Halliday and states "There is no way to predict, from Bernoulli's equation alone, what the pattern of streamlines will be for a particular wing.") Some extra information is required; and in the interest of simplicity that extra information cannot be explained – too confusing. So that extra information must be presented without explanation – “stated without proof”. In the alternative in my sandbox I state without proof that “the flow on one side of the airfoil moves at a faster speed than the flow on the other side.” You have pointed out that this will be challenged because it “is crying out for a WHY tag.” In your proposal you state without explanation or proof that “the air is deflected downward.” This can also be challenged – why is the air deflected downward? Who said it is? Etc.

It appears that the key issue to be decided at this point is what extra information should be presented, without proof, to support the simplified Bernoulli explanation of lift? (Should it be some information about the kinematics of the flow field; or some information about Newton’s 3rd law?)

I have adjusted my proposed alternative wording in my sandbox. Dolphin (t) 09:28, 14 July 2021 (UTC)

Dolphin, I think there are basically three approaches to explaining lift via Bernoulli's Principle (BP):

1. A mathematical approach involving partial differential equations, vector fields, line integrals, boundary conditions, etc.
2. Starting with Newton's 3rd law and using the obvious fact that the air is deflected downward to establish a force, then noting that force implies a pressure difference, and finally using BP to conclude that the air goes faster on the top of the wing.
3. Magical thinking involving non-physical reasons for why the air speeds up e.g. equal transit time.

The first option is not simple. The third is not correct. That seems to leave option 2, assuming we want to explain things rather than just make assertions. e.g. "the wing is designed to make the air go faster over the top". And I think that it is obvious why a wing at an angle of attack will deflect the air downward, so I don't think saying so will make readers wonder "why" in the same manner that asserting "air goes faster on top" will.

As for implying that the Bernoulli explanation is merely an appendage to Newton's 3rd law, well, it is. Look at the derivation of BP as originally published - it assumes pressure changes, uses the pressure change to calculate the net force, then uses F=ma to calculate the acceleration, and finally integrates the acceleration expression to obtain speed. BP is a direct consequence of Newton's laws. (Granted, BP can be derived by applying conservation of energy, but conservation of energy is itself derived from Newton's laws.)

The subsection in its current form basically uses option 2 when it says "For any airfoil generating lift, there must be a pressure imbalance..." I suggested stating that idea first to make the section more readable; I don't think it really changes the content (and I'm not sure it actually makes it more readable).

Serg is correct to point out above that one way to read this little four sentence sub-section is that it does not explain how lift comes about. It merely explains that lift requires a pressure imbalance and this pressure imbalance implies changes in airspeed. i.e. it explains why the air speeds up, not why there is lift. The "explanations" that follow are flawed, as we state clearly in the "Limitations" subsection. I'm not sure that we can do better without dragging a bunch of math into it, and I don't think that's appropriate for a "Simplified" explanation. Mr. Swordfish (talk) 15:22, 14 July 2021 (UTC)

@Mr Swordfish: I see that the simplified Bernoulli explanation I am looking for is actually included in the sub-section titled Conservation of mass. (It includes “Starting with the flow pattern observed in both theory and experiments, the increased flow speed over the upper surface can be explained in terms of streamtube pinching and conservation of mass.” It ends with “From Bernoulli's principle, the pressure on the upper surface where the flow is moving faster is lower than the pressure on the lower surface where it is moving slower.”) This is satisfactory as a simplified explanation using Bernoulli.

The sub-section that we are discussing (titled Increased flow speed and Bernoulli's principle) is actually a simplified explanation of the flow speed being faster beside the top surface and slower beside the lower surface. As Serg has suggested, a change in the titles of these sections might be warranted. Dolphin (t) 13:33, 17 July 2021 (UTC)

We all agree that the explanation under discussion doesn't satisfactorily explain lift. It avoids saying anything that's incorrect, but also avoids identifying any actual cause-and-effect relationships. It also falls short on sourcing. It cites reliable sources only for separate pieces, but cites none for the overall explanation. And I don't know of any source that supports the overall approach. So in addition to not explaining lift, it's also guilty of synthesis.

So far in this discussion we seem to be trying to figure out how to repair our version, so as to make it coherent in a cause-and-effect sense. I happen to think that this isn't logically possible. But whether it's possible or not isn't the issue, in my opinion. Our job isn't to fix an inherently faulty explanation of lift; it's to report what the sources actually say. And the classic Bernoulli-based explanations actually purport to explain lift, not just to explain why the upper flow is faster.

True, the traditional Bernoulli-based explanations in the old sources are wrong. But I also agree with Swordfish that they deserve a place in the article because they're prominent historically and likely familiar to many readers. So it seems to me that our reason to include a Bernoulli-based explanation at all is primarily historical. It thus needs to be rewritten so as to faithfully present what the classical sources say, right or wrong. It should present the three major purported reasons why the flow speeds up (equal transit time, half-Venturi, and streamtube pinching) and then present all the reliably reported objections. I don't think it needs a separate subhead for "Conservation of mass".

Giving "False explanation based on equal transit time" separate billing in its own subsection implies that equal transit time is the only thing false about the Bernoulli explanations. The material in that subsection should be moved up and placed with the other objections to the Bernoulli explanations.

And I think we should rethink the "Limitations..." subsection. For one thing, the "Limitations" heading is polite to a fault. It sounds like we're talking about limits on the range of applicability of a mathematical theory, while what we're really talking about are shortcomings or outright errors in all the qualitative explanations, including the one based on flow deflection. In what I propose below, I would eliminate the separate "Limitations..." subsection and fold the discussion of shortcomings and errors into the headings and explanations themselves.

After reading about all the shortcomings and errors, an attentive reader will have noticed that everything under "Simplified explanations..." is pretty weak and likely wonder why it's all featured so prominently.

To head off such questions, I think we should do more up front to put the simplified explanations in perspective relative to our understanding overall. I'd suggest adding a brief new section just ahead of the simplified explanations and changing some of the headings within. Something like this:

"Understanding lift as a physical phenomenon (New section)

The flow around a lifting wing is a complex fluid-mechanics phenomenon that can be understood on essentially two levels:

1) The level of the mathematical theories (link to that section), which are based on established laws of physics and represent the flow accurately, but which require solving partial differential equations, and

2) The level of qualitative physical explanations without math. Correctly explaining lift is difficult because the cause-and-effect relationships involved are subtle. A comprehensive explanation (link to that section) that captures all of the essential aspects is rather long. There are also many simplified explanations, and most readers will likely already have been exposed to one or more of them. But simplifying the explanation of lift is inherently problematic, and no simplified explanation is completely satisfactory. Each simplified explanation presented below is therefore accompanied by a discussion of its shortcomings or errors.

Simplified physical explanations of lift (Existing heading)

Over the last hundred years or so, many different simplified explanations have been proposed. Most follow either of two basic approaches, being based either on Newton's laws of motion or on Bernoulli's principle. Both approaches have positive aspects, but neither approach, by itself, is a completely satisfactory explanation.

Incomplete explanation based on flow deflection and Newton's laws (revised heading)

(Revised subsection combines material from "Flow deflection and Newton's laws" and "Limitations...")

Incorrect explanations based on an increase in flow speed and Bernoulli's principle (revised heading)

(Revised subsection combines a major rewrite of "Increased flow speed and Bernoulli's principle" and "Conservation of mass" with material from "Limitations...")"

Altogether this approach may seem harsh, but I think it more accurately reflects the status of the simplified explanations. I haven't filled them in, but there are plenty of sources to cite. And we don't have to cite all the sources we currently cite.

If the group thinks this is a promising approach, I could be persuaded to draft it in in my sandbox.

The changes I've listed above would improve things, I think. But there may be more we should do. Serg has raised the issue of Weltner's (also Babinsky's) streamline-curvature explanation, which has definite virtues, but which isn't currently treated anywhere in the article. I'd support adding it to the "Simplified explanations...". I think it qualifies as "simplified" because it explains lift based only on the cross-stream components of the pressure gradient the fluid acceleration. If we decide to add it, we should also describe its shortcomings, for which I know of some citable sources.

J Doug McLean (talk) 22:26, 27 July 2021 (UTC)

Thanks Doug, and welcome back! I think it is a promising approach and I encourage you to draft it in your sandbox, Dolphin (t) 02:34, 28 July 2021 (UTC)

I also agree that this is a good approach. Presenting each "simple" explanation and immediately following it with clear statements of the "limitations" is preferable to lumping the limitations into it's own section that the reader may not even get to. I also agree that it is overly polite to describe explanations that are simply wrong as "limited". "Incomplete" and "incorrect" are more accurate labels, and I think the sources support this.

Doug suggests adding material about the half-venturi non-explanation, which is currently not treated by the article. I have no objection to that; we might want to consider including the skipping-stone explanation as well.

As for the streamline curvature theorem approach, we already include that in the article - see https://en.wikipedia.org/wiki/Lift_(force)#Basic_attributes_of_lift. I'm not convinced that moving it up to the simplified section would be an improvement - for some audiences saying "it's really simple - just take a look at this differential equation" is appropriate, but I don't think most of our audience would think an explanation based on a differential equation is simple. But I could be persuaded otherwise if we can explain it with a careful choice of language.

I look forward to seeing Doug's draft; I may take a stab at it myself. Mr. Swordfish (talk) 17:04, 28 July 2021 (UTC)

I have a draft almost done, and I'll post it shortly.

I've run into a bit of a surprise with sourcing for equal transit time. Above, I was advocating citing original sources that seriously presented equal transit time as being correct. Now I find I don't have any. All the relevant sources in the current article are "second-hand", describing equal transit time only to debunk it. The second-hand sources I've looked at so far don't cite any original source, but offer only vague references to "text books" and such. So I currently have no original source. Of course the second-hand sources are correct and reliable, and we'll definitely cite them for the objections to equal transit time, but for the explanation itself I was hoping for something closer to "the horse's mouth". Does anyone here know of a source that presents equal transit time as true?

Our treatment of streamline curvature under "Basic attributes of lift" deals only with the equation relating streamline curvature to pressure gradient. The Weltner paper and Babinsky paper I was thinking of present a coherent explanation of lift based on the equation. Still, I'm okay with not adding it to the "Simplified explanations...". J Doug McLean (talk) 23:58, 29 July 2021 (UTC)

See https://en.wikipedia.org/wiki/User:Mr_swordfish/List_of_works_with_the_equal_transit-time_fallacy Cheers! Mr. Swordfish (talk) 01:32, 30 July 2021 (UTC)

Thank you, Mr. Swordfish. This is an impressive list indeed. I wasn't aware that the fallacy was as common as this, even into recent years. Judging by the numbers through 2009, I'm guessing that the only reason there are no later entries is that you stopped gathering them.

For my draft of my proposed revisions I tentatively chose three of Mr. Swordfish's references spanning the decades and limited to authors involved in the aeronautical community. I'm open to other suggestions. My draft is now posted in my sandbox. J Doug McLean (talk) 00:03, 31 July 2021 (UTC)

I can't take credit for the list; it was a collaborative effort among wikipedia editors when it was a full-on page. At some point, around 2009 it was nominated for afd (articles for deletions) and consensus was to remove. I requested that the page be "userfied" so it still exists on my user page. Glad to see that it is of some use.

My sense is that although the list stopped being updated in 2009, there are actually fewer works that present ETT as truth. It really slowed down when Glenn Research Center started calling it "Incorrect Theory of Flight #1". Perhaps this article has helped too.

Looking forward to reading the draft. I'll post whatever minor detail suggestions there and reserve or this space whatever bigger picture concerns I may have. Mr. Swordfish (talk) 21:19, 31 July 2021 (UTC)

References

Section headings using the word lift

I tried [1] to remove the word "lift" from the section headings, as it certainly seems unnecessary for an article that is already named that. It is also in the Wikipedia manual of style WP:HEADINGS. @Mr swordfish: which sections title do you wish to keep?--ReyHahn (talk) 14:13, 17 August 2021 (UTC)

"Simplified physical explanations on an airfoil" didn't make much sense to me. The others are fine without the word lift. We should probably keep the lift in "Lift Coefficient". Other than that I think the section headers read fine without the word lift. Mr. Swordfish (talk) 22:27, 17 August 2021 (UTC)

One issue with re-titling sections is that it may break links that point to that subsection. There's a workaround, which I'm looking into for the proposed changes to the "simplified explanation" section. We should make sure we do the same for these changes. Mr. Swordfish (talk) 20:47, 20 August 2021 (UTC)