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(Zapletal writes ->) This is a REWRITTEN version of my previous 2 posts, which were repeatedly deleted, apparently because of presumed "personal attack".

To those who did the deleting, PLEASE READ THIS THROUGH before deleting again. If you wish to delete again, then please explain why.

(First post from 27 November 2014.) Briefly,

• This issue is not resolved.
• "The Statement" is incorrect.
• Doug McLean is right. Lanchester also explained this position very well in 1894, and then in his book of 1907.
• I suggest the editors who agree with "TS" should study the history of Fluid Dynamic Lift theory.
• The AAPT is negligent in its promotion of "The Statement" (see below), and is most definitely negligent in suggesting that F->dP/dt is Newton's THIRD.
• NII, paraphrased , is "F CAUSES P-dot". Teaching that NII is "F=ma" is plain WRONG, and consequently leads to mistakes.
• IMO "The Statement" should be IN the article, but with an explanation for why it is so WRONG. Else future generations will have an ever worsening understanding of FDL.

(Doug, I may write more in few weeks, if I have time. You are NOT ALONE. "Hourglass" thinking is good. NB the "upwash" always present in front of the aerofoil. FWIW, a single vortex in unbounded fluid is as likely as a magnetic-monopole, because it implies infinite angular-momentum and energy, hence difficulty with calculations. So calcs that include a ground-plane (= image vortex underground) work better. And there is most definitely a "wavelike" motion in lifting flows that explains most of above (see Lanchester, 1907).) (End first post.)

(Second post from 29 November.) Burninthruthesky, are you aware of the particular "Newtonian method" that Lanchester is discussing in your above quote, namely the assumed type of fluid? Are you aware of the "deficiencies" of that method, namely that it gives the wrong results? Are you aware that Lanchester, who was the first to develop the current, accurate, "circulation" theory of lift (in 1894) did so by adopting the "Principle of No Momentum"?

In short, the notion that lift is a direct consequence of "rate of change of momentum of the fluid downwards" was known to be flawed in the 1700s. Some 120 years ago, Lanchester (and then Kutta, Zhoukowsky, Prandtl, et al) fixed this problem, and came to the much more accurate explanation of "circulation theory" by abandoning "The Statement".

So, why do you, together with 0x0077BE and Steelpillow, want to reinstate this flawed model? (End second post, Zapletal.)101.170.42.165 (talk) 10:10, 30 November 2014 (UTC)

Our answers may be found in the long debate which sprawled across many topic headings above. Since you are sufficiently prejudiced against our view to twice post insults to us here and yet a third time at User talk:J Doug McLean, there appears little point in us engaging with your rhetoric. Since you also appear to be new to Wikipedia, I would strongly suggest that you check out WP:Five pillars and especially WP:CIVIL. This will explain why I deleted your insulting posts from here. I reply now and offer my advice only out of politeness, but I am unlikely to respond further unless there is clear evidence that this conversation might not simply rehash the same old same old but actually, and with some semblance of decorum, go somewhere encyclopedic. — Cheers, Steelpillow (Talk) 09:47, 2 December 2014 (UTC)

In posts since 15 November Steelpillow and Burninthruthesky have put forward what amount to new arguments to effect that the classical control-volume analyses are irrelevant. So the following rebuttals are not the "same old same old".

Steelpillow wrote:

[T]he atmosphere does not accelerate down on us more and more with every passing plane, it soon decelerates and swirls back up again. But nobody claims that ma=0 apples to the local airflow over the wing. Yet in claiming that dp/dt=0 you are effectively claiming that it does. No, only once the craft has passed and the trailing vortex brought the air back up again will either ma or dp/dt return to zero. And that does not contribute to the lift. This article is about the lift, not about how the atmosphere restores itself afterwards. OTOH those learned models you quote do address the restoration. Your whole analysis does not belong here.

First, this misrepresents what I claimed, which was only that dp/dt = 0 for a pancake control volume that is very wide compared to its height and thus extends far from the foil. This is not the same as claiming dp/dt = 0 applies to the "local airflow". But are you thinking dp/dt = -L applies to the "local airflow"? That isn't true either. Sources have found dp/dt = -L only for the tall sliver control volume. For practical purposes the height doesn't have to be infinite, but it does have to be quite large. To get 99% of the "right" answer, i.e. dp/dt = -0.99L, the total height must be about 64 widths. So to find the answer advocated in The Statement you have to look beyond the "local airflow".

But the main flaw in your reasoning is the idea that there are two separate processes going on, the imparting of downward momentum by the foil and the "restoration" ("afterwards") by the atmosphere, and that only the first "contributes" to lift. I've not seen any reputable source on aerodynamics that describes lifting flow in those terms. And your two-process model isn't consistent with the following features of the flow:

1) In an integrated sense, half the upward acceleration (positive dp/dt) in the field happens ahead of the foil, in air that has not yet been accelerated downward. Is this part of your purported "restoration" process?

2) There is substantially more downward acceleration (negative dp/dt) in the field than just -L. We can see this by looking at an hourglass-shaped control volume that contains negative dp/dt almost exclusively, i.e. that concentrates on "the air deflected downward". Using the same mathematical velocity-field expressions used in the published classical analyses, it is easy to show that an hourglass-shaped control volume with a total height of about 64 chords contains dp/dt = -1.8L. Based on your model of the flow, to what would you attribute the excess -0.8L? On the other hand, it's easy to explain in terms of the interaction between the pressure and velocity fields, and it's consistent with the citable analyses.

So your two-process concept is seriously flawed, and so is the idea that anything other than downward momentum is irrelevant to lift. All of the fluid accelerations in the field are essential to maintaining the pressure differences acting at the airfoil surface. In a continuum flow these pressure differences at the surface must be accompanied by an extended pressure field that has the two-lobed form sketched in the section "A more comprehensive physical explanation". The lobes of low and high pressure extend beyond the leading and trailing edges of the foil, and the resulting upward accelerations ahead of the foil and behind are essential to sustaining the pressure field, as Lanchester explained in 1907. So your assertion that upward accelerations don't contribute to lift is unfounded.

The momentum balance in the field around a lifting foil is not irrelevant as you claim. Some discussion of it belongs in the article. I intend to draft new subsection "Momentum balance in lifting flows". Then we'll let the community decide whether it belongs or not, based on the detailed merits and on the citable sources. You don't have sole veto authority.

Burninthruthesky wrote:

The total downward momentum imparted to air within the atmosphere is the same whether someone makes an integration which accounts for all of it correctly or not.

and

To reiterate, the other analyses do not account for all of the momentum imparted to the air. The one that does, proves that, "The resulting force upwards is equal to the time rate of change of momentum of the air deflected downwards". The correct interpretation of this statement (The Statement) is true whether proof is stated or not.

Regarding the integrated negative dp/dt in the air, there is no basis for saying that -L is "all of it", or that it represents the "total". The tall sliver control volume doesn't find "all of it". The hourglass analysis finds that considerably more negative dp/dt than -L "exists" in the atmosphere if you look in the right place (see above). No, there is not just one correct "total" that somehow applies to "the air" in general. There are many different correct totals for the "time rate of change of momentum of the air" depending on what part of the air you integrate over. The mainstream published analyses make this clear. And the idea that they are irrelevant isn't consistent with the physics.

Burninthruthesky wrote:

Other interpretations place more weight of meaning on the words "the air" than they can bear. If "the air" meant "an integration region of an arbitrary size and shape", it would be correct to say The Statement is not specific enough. That is not what it says. Integration is not mentioned.

True, "integration" isn't explicitly mentioned, but it is inescapable. The Statement makes a specific mathematical claim about a quantity ("the time rate of change of momentum of the air") that for a continuum fluid in non-uniform motion has no logical definition other than by integration over some fixed volume. The idea that The Statement refers to something other than an integrated quantity defies logic.

Burninthruthesky also cites Lanchester's discussion of "the Newtonian method" and its deficiencies, concluding that it "seems to concur with a lot of what's already been discussed." Actually, Lanchester's "deficiencies" section provides no support for The Statement, but instead supports what I've been arguing all along. The "Newtonian medium" (a hail of projectiles that don't interact with each other) is a poor model for flows of real fluids. In a Newtonian hail of projectiles, pressure exists only where the particles impact a surface. There is no pressure internal to the fluid and thus no pressure field, and as the classical analyses show, the pressure field is crucial to assessing the momentum balance in lifting flows. Your other citation, Bradley Jones. Elements of Practical Aerodynamics, also introduces a Newtonian flow model, but doesn't get the details right (e.g. he finds a sin(alpha) lift curve for an inclined plate, where Newton found sin squared) and is remiss in not discussing the deficiencies.

I'm posting this because it didn't seem right to leave the latest round of erroneous reasoning unanswered. Zapletal's joining the discussion means that in a pure numerical sense the "consensus" is not as "strong" as before. Our opposition is not based on "prejudice", but on the fact that the majority position is inconsistent with established physics.

J Doug McLean (talk) 19:45, 5 December 2014 (UTC)

I'm a bit reluctant to re-engage with this debate since it has gone on so long, but having thought about it some more and re-reading the arguments I'm now persuaded to Doug's position - The Statement is problematic and misleading. (I have to confess to being mislead by it myself) That said, I don't think it is actually wrong but it requires a bit of clarification and specific language to treat momentum transfer in a technically correct manner.

Upthread, Doug suggested including a section on momentum transfer. I support this. If we're going to treat The Statement and momentum transfer in the article we'll need a paragraph or two. My hunch is that if we go about writing it we'll probably be able to reach consensus since we'll have the space to be more nuanced and won't be constrained by an 'up or down' ruling on The Statement.

Thanks to Doug for asking tough questions and making me think this through more thoroughly - I hadn't really given it the thought it deserved. I'll probably have more to say on Monday. The article is fine as it is, and we don't have a deadline. Mr. Swordfish (talk) 20:35, 5 December 2014 (UTC)

What we think, is of no importance. This is:

"Thus the lift of the wing is equal to the rate of transport of downward momentum of this air." — Clancy, L.J.; Aerodynamics, Pitman 1975, page 76.

Wikipedia relies on Verifiability, not truth (WP:NOTTRUTH). Need I say more? — Cheers, Steelpillow (Talk) 20:43, 5 December 2014 (UTC)

Yes, I'm aware of the policy on "verifiability, not truth". But that policy doesn't mean that our job as editors is to take statements from sources out of context, without comparing them with what other sources say, or without exercising some judgment as to what the statement represents.

Clancy's statement, for example, was made in the context of his discussion of a very crude model for the flow around a 3D wing, in which the flow is seen as a stream of circular cross-section, like that from a fire hose (see his fig 5.21), that is uniformly deflected downward by its interaction with the wing. This model is similar to the Newtonian flow model I discussed above in the sense that it takes no account of the non-uniform pressure field around the wing. This deficiency of the Newtonian model has been discussed by Lanchester and other citable sources.

The horseshoe-vortex model is a higher-fidelity model for the flow around a 3D wing. Lissaman (1996) and others have used this model and arrived at the same conclusion as for a 2D foil, i.e. that The Statement is true only for the special case of a tall sliver (tall slab in 3D).

But even if we were to take Clancy's statement at face value, it's only one view among many in citable sources. The classical control-volume analyses I've cited arrive at a more nuanced view, showing that The Statement is valid only for a special case. If we keep The Statement in its current unapologetic form, we'll be presenting a biased view of what the established sources say on this topic. What I'm saying here isn't just my own "truth". It's all verifiable in citable sources.

Thanks, BTW, to Mr. Swordfish. I appreciate the positive feedback.

J Doug McLean (talk) 01:26, 6 December 2014 (UTC)

J Doug McLean, thank you for listening, and addressing the issues I raised. My understanding of the evidence presented is that "lift is accounted for either by pressure or by momentum flux, depending on the proportions of the control volume." We must consider only citable sources, and you said that they do not find more negative dp/dt than -L.

Lanchester says there are "circumstances in which Newtonian theory is applicable and those in which it is not". This is discussed fully in §8. It was suggested above that an isolated airfoil (outside ground effect) is one of those circumstances where the method does give results "within measure of the truth", as Lanchester puts it. Why do you say that 'Lanchester's "deficiencies" section provides no support for The Statement'? Burninthruthesky (talk) 11:23, 6 December 2014 (UTC)

Yes, I know of no citable source for the hourglass analysis. I raised that example only as an argument against other original-research arguments on this page. If discussion of the control-volume results is added to the article, as I advocate, it should of course be limited to the citable sources, all of which have found dp/dt between zero and -L.

At the top of §5 Lanchester says "It is evident from the above that the theory of the Newtonian medium is capable of giving results within measure of the truth, when applied to real fluids." The only thing "the above" refers to, as far as I can tell, is the drag of a plate normal to the flow. I don't see anywhere that Lanchester applies the Newtonian method to the lift of a plate or foil at angle of attack, or where he says it gives reasonable results for that case. Newton's own results for an inclined plate are not "within measure of the truth". Newton's lift curve (proportional to sin squared) has zero slope at zero alpha, where foils in real flows have lift slopes in the neighborhood of two pi.

In §8, the only example he cites where the Newtonian method is "applicable" is the flow through the disc of a screw propeller. My reason for saying that 'Lanchester's "deficiencies" section provides no support for The Statement' is his conclusion of §5: "It is thus apparent that no momentum is imparted to an actual fluid in the sense that it is imparted to the Newtonian medium". That and the fact that nothing else in §5 supports dp/dt = -L.

J Doug McLean (talk) 22:49, 6 December 2014 (UTC)

Lanchester §8 says the Newtonian method is applicable in cases "where there are well-defined conditions on which to compute the amount of fluid dealt with per second". We agree there are well-defined conditions which show dp/dt = -L.

He discusses aerodynamic support of an aerofoil in §112. He says, "Under ordinary conditions" "the weight may be regarded as in no part statically supported." He goes on to clarify the exception of ground-effect.

I support the proposal to add more description of momentum/pressure further down the article, along with keeping a simple description of the Newtonian method at the beginning of the article, in line with WP:UPFRONT. Burninthruthesky (talk) 07:50, 7 December 2014 (UTC)

Yes, there are "well-defined conditions" for which dp/dt = -L. But as I've maintained all along, those conditions are narrow (literally), and The Statement in its unapologetic form is therefore misleading.

Lanchester's §112 amounts to a verbal derivation of the tall sliver control-volume analysis and arrives at the same result published by Lissaman (1996). So it doesn't support an unapologetic version of The Statement any more than Lissaman did.

The simple qualitative flow-deflection explanation based on Newton's laws belongs up front. I think the quantitative statement dp/dt = -L doesn't, whether it comes from the tall sliver control volume or from the "Newtonian flow model". See my response to Steelpillow's post of 7 December.

J Doug McLean (talk) 01:42, 10 December 2014 (UTC)

(Zapletal Writes->) (Just noticed that Doug and others posted while I was writing this. Will read above and may reply tomorrow...)

Steelpillow, the following is a long post covering the above issues. It is broken up with sub-headings to improve readability. Please make yourself comfortable.

1. MY PREVIOUS POSTS HERE. - Yes, I don't spend much time on these Wikipedia Talk pages. This is mainly because I find the formatting very difficult to read, and even harder to write.

The "wall of words" makes it very difficult to know who is writing what. Especially so when one author's long post, with name only at the bottom, is then broken up with many other author's posts. For this reason I have recently got into the habit of bracketing my posts with my name, as above/below here, simply so that I can more easily navigate this alphabet soup.

Regarding entering the text, whatever happened to WYSIWYG!? IMO, most every other forum on the web does "communication" much better than Wiki, ... but that is another matter.

Anyway, I have been here before. First back in Feb 2011, on archived Talk page 5, headings "Is Vicosity Necessary..." and "Correction Required...". Also on archived Talk page 7, July 2013 "This Article is Still Deeply Flawed". And a few other places...

I have not read through all the archived Talk pages yet (for reasons given above), but I noticed that Doug McLean has been here from near the beginning, on page 1. Sadly, it has taken Doug some 8 years, and apparently much, much effort, to improve this article. And still he meets with unreasonable obstruction. I can understand why he hasn't responded recently.

~o0o~

2. "THE STATEMENT" (IE. L = -dP/dt) SO FAR. - Having quickly read Talk page 1, I see that exactly this issue was being argued ad nauseam back then. Both there, and on this page, the pattern is the same.

The posts arguing "against TS" are usually long. They often contain definitions of the terms used, or at least an attempt at such. They are somewhat technical, and appear capable of giving quantitative results (ie. real numbers), though the actual "maths" isn't always included. They are supported by many "Reliable Sources" going back many years. And they appear to be prepared to clarify their case in even more detail, if requested.

Conversely, the posts arguing "for TS", namely that "Lift is fundamentally due to downwash", tend to be much shorter. They are usually bereft of well-defined terms, or detailed maths. They have a decidedly ideological flavour (ie. "...it MUST be so..."). They quote as their RSs bodies such as the AAPT, who are, quite literally, "dilettantes" in this particular field. And they seem to be in a great rush to meet "consensus" (ie. in their favour), and "move on".

I have read all the "for" arguments on this page, and, despite the difficulty of keeping track of who is saying what, I have not found a single convincing "for" argument. More on this below.

~o0o~

3. MY REASONS FOR BEING HERE. - My bluntness in my above, much deleted, post was a result of the above point. Namely, that this issue has been clarified so many times over, that it does not warrant yet another Talk page "wall of words". Nor should the Article revert, yet again, to a version that promotes misleading ideas such as "TS".

My aim in writing these and previous posts here, has always been to improve the educational prospects of future generations. That is, I have tried to encourage a higher standard of this particular Wiki Article. To explain this again, I quote here from my July 2013 post.

Furthermore, the notion that an Encyclopedia is simply "an assembly of information taken from reliable published sources" is codswallop. There are today countless "reliable published sources" offering many and varied explanations of Fluid Dynamic Lift. Unfortunately, a great many of these explanations are pure bulldust. A random sampling of these sources does not constitute an encyclopedia. Worse yet, a biased sampling, which is perfectly acceptable under your definition, is a disservice to society in general.

In short, the editors of good encyclopedias filter out the nonsense. If this does NOT happen, then very soon we will have to believe that the world is flat, voodoo is real, and the star signs predict our future. That is, any and all of the urban myths and superstitions that can be found in some "reliable published source" somewhere, will quickly spread throughout society. This is because these myths are usually easier to understand than the more difficult truths, so are more often repeated. Soon after, the difficult truths become outnumbered, and eventually disappear.

This particular article is a good example of the above process. The "Bernoulli vs Newton" explanations, the "Coanda effect", and "Lift is because of downwash," are all examples of the dumbing-down of this phenomena. An appropriate quote by Theodore Von Karmann is, "When you are speaking to technically illiterate people you must resort to the Plausible Falsehood instead of the Difficult Truth.".

(Extra emphasis added.)§

~o0o~

4. WIKIPEDIA AND EDUCATION. - My general feeling about Wikipedia is that it is hastening our society's descent into The Next Dark Ages. It is doing so by encouraging academic standards that amount to "the lowest common denominator". The fact that anyone, at anytime, can change Articles, or even delete other peoples' Talk posts, without any good reason, means that any notion of eventually achieving high standards is wishful thinking.

To explain by example, in the "Golden Age" of antiquity (~ 6th to 3rd centuries BC) it was widely considered that the Earth is a sphere spinning on its axis, and together with the other Planets it orbits the Sun, with the fixed Stars at a much greater distance. The Pythagoreans believed this. Aristarchus clearly put this case. Eratosthenes even measured very accurately the Earth's diameter, and its distance from the Sun.

Such "difficult ideas" were allowed to spread back then because the national pastime was debating stuff, any stuff, in the town square. In fact, the first subjects taught at school, the "Trivium" of Grammar, Rhetoric, and Logic, were intended to hone those skills. ROBUST DEBATE WAS ENCOURAGED! Others' arguments were not simply deleted. Instead, they were critically analysed, dissected, deconstructed, and ultimately shown to be either bereft of reason, or perhaps, maybe, worth considering...

But all this was hard work. So, within a few centuries the Ptolemaic System of Astronomy took hold, and the great-unwashed were taught that the Earth was flat, and at the centre of the Universe. So much easier for the great-unwashed to learn! And so much easier for the developing Priesthood to teach, especially when embellishments like the Four-Elephants-And-Then-Turtles-All-The-Way-Down could be added willy-nilly.

So, what has this rant got to do with "TS, L = -dP/dt"?

Well, if any supporter of "TS" can point to a single argument in its favour that they think is valid, in all of these walls of words, then I will happily explain where said argument is flawed. Please note that my response may necessarily have to be robust, in order to get the message through. For example, a single flaw in an argument can make the argument, as a whole, INVALID.

~o0o~

5. TWO CASES TO THINK ABOUT. - The following two examples are intended to improve readers' understanding of this issue. These are NOT intended to prove that, in this particular field of Fluid Dynamic Lift (= FDL), "L = -dP/dt" is wrong. So please don't say "Oh, but that's different, so it doesn't count...". Rather, the intent here is that if the reader can understand the following, then they will better be able to grasp why "TS" is wrong.

~o0o~

5.1. Consider a "lighter-than-air" airship, such as a hot-air balloon or zeppelin. (This example also mentioned on Talk page 1.)

Ask yourself whether any downward force acting on such an airship, such as its gravitational weight, or a rope pulling it downwards, needs to be counter-acted (NIII) by an upward inertial reaction force that MUST come from a never-ending "downward rate of change of momentum" of the surrounding atmosphere (NII).

The answer, of course, is that the airship can stay aloft with NO MOVEMENT of the atmosphere at all. It is AEROSTATIC Lift. This works because the amosphere's gravitational mass, in concert with the Earth's gravitational mass and the consequent (hypothesized) gravitational field, creates a PRESSURE GRADIENT in the atmosphere.

That is, the pressure at lower altitudes is greater than the pressure at higher altitudes. As a result of this pressure gradient, the air-pressure forces on the under-surface of the airship are greater than the air-pressure forces on the over-surface. As I hope is obvious, the net sum (or integration) of these surface pressure forces amounts to a Lift force on the airship.

In a similar way, in FDL the Lift force is nothing more than the integration of the fluid pressure forces acting on the surface of the lifting body, typically an aerofoil (2-D) or wing (3-D).

However, a big difference is that in this "buoyancy" example here, the pressure gradient is due to the fluid's GRAVITATIONAL mass embedded in a gravitational field, whereas in FDL the pressure gradients are due to the fluid's INERTIAL mass, and its behaviour in Lanchester's "sustaining wave". More below.

~o0o~

5.2. Consider a wave on the ocean. Better yet, consider a surfer riding such a wave. Or since some readers here are interested in yachts, consider a yacht surfing the wave. (And to be a bit more rigorous, perhaps we should be considering "solitary waves", aka "solitons", travelling along a canal.)

Ask how the wave can "Lift" its massive self ABOVE the natural water-level, whilst also travelling vast distances. Ask how the wave can also Lift its passengers. Ask whether the wave, or its passengers, must constantly be "throwing mass downwards" to sustain these Lifts.

Well, in a sense, yes, the wave does "throw down mass". The wave has mass just aft of its peak that is moving, and indeed accelerating, downward. It even has mass just in front of its peak that is moving upward, but accelerating downward. But further forward and rearward the accelerations, and "changes of momentum", are upwards. Importantly, the net "changes of vertical momentum" are ZERO (not including "unsteady" effects...).

Nevertheless, despite zero net momentum change, the "wave" has an energy that is greater than if the water were still. The wave is also very identifiable as an "entity" (see definition below). And, unfortunately, its behaviour is rather difficult to understand, both physically and mathematically, or at least so say most students who study it.

Perhaps most relevantly here, the wave is almost impossible to understand when viewed in a reference frame that travels with the wave. Here it appears as a body of water that is standing high up above its natural level, in complete defiance of gravity and all common sense! (Looking closer, we see the water particles flowing rapidly through the wave, from one side to the other, but that doesn't help the explanation at all.)

Interestingly, almost all standard explanations of FDL are done in the same reference frame as above, namely moving with the aerofoil. IMO, this is the unique reference frame where it is hardest to make sense of what is happening. But the maths is a bit easier, which is why it is taught that way.

~o0o~

6. LANCHESTER'S "SUSTAINING WAVE" - Much to say here. Perhaps it is most important to note that the essence of this explanation is really very simple, but it is also rather subtle.

For example, the whole issue of "cause and effect of pressure-velocity", much argued on these pages, only really becomes clear when you take it right back to the start. Namely, back when the aerofoil was first stationary, and then started to move, and thus created "wavelike" motions in the fluid around it, with the fluid of these "waves" now having higher energy than the quiescent fluid a moment before. And then there is the issue of "hydrodynamic impulse", which is necessary to understand when doing the detailed maths, but it obfuscates the "gist" of the FDL explanation.

Anyway, keeping in mind that this is just a brief (!) post on a Talk page. My dictionary defines a "wave", amongst many other meanings, as, "14. Physics - an energy-carrying disturbance propagated through a medium or space by a progressive local displacement of the medium or a change in its physical properties, but without any overall movement of matter....

When FDL is viewed in the more natural reference frame of the stationary-bulk-fluid, with the aerofoil moving through it, then the above wavelike nature of the flow becomes startlingly obvious. Well, with the clarification that an FDL wave leaves fluid particles directly under the path of the aerofoil shifted slightly forwards, and those above shifted slightly rearward. Different movements when no Lift, but still significant shifts, EVEN IN INVISCID FLUID. (Other very different "waves" also do these small, permanent, shifts.)

Also obvious in this view is a pressure field that moves with the wave and aerofoil, and looks a bit like Doug's Figure in the Article. Away from the small near-field distortions, the isobars are all circles tangent to the aerofoil, and with centres lying on a vertical line through the aerofoil. Highest positive pressure directly under the aerofoil. Lowest pressure above it. Vaguely similar to the pressure field of point 5.2 above.

But necessary in this moving picture is that the aerofoil CONSTANTLY exerts a downwards force on the fluid, equal to -L. If the aerofoil vanishes, or perhaps disintegrates, and this downforce also vanishes, then the flow pattern changes, and the "bound vortex" starts looping the loop.

Much of this behaviour was explained in Lanchester's 1907 book, and also in other classics such as Lamb's "Hydrodynamics". Simple usage of the circulation/vortex theory equations (ie. due to Kutta and Zhoukowsky for 2-D, or Prandtl for 3-D) confirms these behaviours.

Interestingly, the Lillienthal brothers (two "farm-boys" who decided to fly) also spoke of a wave that supported the wing. And the notion of "vortex lift" was used by Rayleigh in his 1877 paper "On the Irregular Flight of a Tennis Ball", although at that time it was considered somewhat speculative. But it seems quite certain that school-boys (well, tertiary level) in the mid-to-late 1800s where drawing with pen and paper these wavelike motions of fluids, both with and without vortex Lift.

Unfortunately, back then those workers had to work quite hard to make such "dynamic" phenomena visible. The Potential Flow methods (ie. Div.V = Curl.V = 0) are quite straightforward, but neverthless quite arduous with only pen and paper. And a "moving picture" requires many such individual drawings. Perhaps, if I ever get the free time, I will post somewhere on the interweb such visualisations of the above "sustaining wave", showing the particle displacements and velocities, and also the pressure maps. (I have these, but not yet in a form suitable for You-Tubing, or whatever...)

Bottom line here, is that this "wavelike" nature of FDL is what allows flight to be so efficient. In the limit of very long wings (ie. getting close to 2-D), the Lift can be sustained with almost NO ENERGY INPUT. See "Caspian Sea Monster" for a good example. Conversely, any "Lift due to downwash" implies a constant exependiture of energy to maintain the Lift. See helicopter fuel bills for a good example.

In a sense, this Lanchesterian FDL is quite magical, which might be why only a small number of people ever understand it.

~o0o~

7. "DOWNWASH" - Very briefly, in planar-aerofoil-flow (aka "infinitely long wing", or "2-D flow", or REAL WING flying between two real parallel walls), THERE IS NO NET DOWNWASH. More explicitly, the upwash in front of the wing is exactly equal to the downwash behind it. (This covered immediately above, and also throughout these Talk pages.)

In "3-D flow" (ie. a finite-span wing inside a large volume of fluid), there is again no net downwash (as explained in many posts...). BUT, there IS MORE DOWNWASH of fluid directly behind the wing than upwash in front of it. So there is a "delta-of-downwash" from front to rear of wing. Note that there is upwash to the rear-sides of the wing, which gives the zero sum.

But, importantly, this downwash is NOT directly related to FD-LIFT.

In 3-D this delta-downwash is related to DRAG. Specifically "induced" (the old word), or "wing-tip vortex" (newer term) drag.

In a loose sense the wing has to fly in descending fluid. Thus its Lift vector, always perpendicular to the onset flow, is tilted rearward, giving a Drag component. The forwards force required to overcome this vortex-drag x the forwards travel of wing (= force x distance) = work required from engine = extra energy put into the swirling fluid behind the wing (ie. downward directly behind wing, up at the two rear-sides).

As a further brief explanation, consider that for a given amount of Lift, wings of greater span have a lesser difference between the upwash in front, and downwash behind, them (ie. lesser delta-downwash). So the amount of "downwash" can vary, while the Lift stays the same. So it is not possible to quantitatively assign a certain amount of "downwash", to account for a certain amount of lift.

Indeed, for very long wings, as seen on gliders, or Burt Rutan's Voyagers, the amount of delta-downwash "near" the aerofoil is quantifiably MUCH, MUCH TOO SMALL to account for the Lift. Similar considerations explain why large diameter helicopters are much more efficient (ie. require less fuel/sec/Lift-force) than smaller diameter rockets or "jet-packs". (This is usually called "actuator disc theory".)

As a last argument against the idea that "Lift happens because the wing pushes the fluid down". Consider the all too common (and very misleading!) picture of an aerofoil with fluid streamlines approaching it horizontally, then departing with "downwash" behind the aerofoil. According to "TS", or "Downwash Theory", the Lift should be able to be calculated by integrating the vertical momentum in the flow just behind the aerofoil (taken through an infinitely high wall).

As explained many times on these pages, the above calculation only gives about half the Lift, because the other half comes from the UPWASH in front of the aerofoil. And it also gives unrealistically large Drag.

In short, if "TS" were true, then flight would be very expensive.

~o0o~

8. TWO MORE RELIABLE SOURCES. - Other than the writings of the abovementioned founders of this work, and also, of course, Thompson (aka Kelvin), Helmholtz, et al, here are two other references worth reading.

~o0o~

8.1. Felix Klein (eminent German mathematician of the time, and teacher of Prandtl) wrote a short but very important paper in 1910, "Uber die Bildung von Wirbeln in reibungslosen Flussigkeiten.". This is usually referred to as the "Kaffeeloffel", or "coffee-spoon" experiment. It is in German, and I have yet to see a translated version, only English summaries of it.

If anyone knows where to get an English translation, then please advise.

This paper gives a good explanation of how the starting and bound vortexes required for FDL can be created INSIDE an INVISCID fluid domain, albeit with NO fluid particles rotating (ie. no fluid "vorticity", though this depends on definition of the fluid's "boundaries").

~o0o~

8.2. David Bloor has more recently (2011) written a book "The Enigma of the Aerofoil...". This is a sociological study of the contrasting approach to understanding FDL taken by the English "Cambridge School" and the German "Gottingen School" in the early 1900s.

Briefly, despite Lanchester's seminal work, the English ignored him and insisted (almost religiously!) that Stokes' Viscous Equations and the "discontinuous flow" postulated by Rayleigh, MUST BE USED to explain FDL. Conversely, the Germans were inspired by Lanchester's much simpler ideas, and ran with them, eventually arriving at the very accurate 2-D and 3-D equations that describe "vortex Lift".

Keep the above paragraph in mind when reading Lanchester's 1907 book. Lanchester was largely self-taught in this field, and was very much alone in developing his ideas. Sadly, to get his book published it seems he had to sully his main ideas by paying lip-service to viscosity and Rayleigh's "discontinous flow" hypothesis.

In fact, the Cambridge School only accepted the inviscid model in the late 1920s, after Glauert, of German parentage but Cambridge education, visited Prandtl, then wrote his "Elements of Aerofoil..." book. However, even this kept in it a certain amount of the "viscosity" lip-service.

It seems that nothing much has changed in the English speaking world's understanding of FDL. Except that now it might be even worse!

~o0o~

9. AND - ... much more to say. For example, NS-Eqns should NOT feature prominently in this Article because they misleadingly suggest that viscosity is somehow important, even though the much simplified Euler-Eqns can grasp the "essence" of FDL.

But this post is already too long.

So, last request. Please don't edit the above, or put inline comments in it. IMO that makes it much harder for later readers to follow the arguments. "Cut-and-paste" makes it easy enough to extract any of the above, should you want to then criticize it, demolish it, whatever...

(End Zapletal)101.170.170.152 (talk) 05:13, 6 December 2014 (UTC)

As I have said before, there is much to be said about this but a simple sentence in an introductory section on the Newtonian model is the wrong place to try and say it all. Your view that there is a fundamental battle between viewpoints in the history of the subject is a fascinating one and I wonder whether the battle per se has been documented. It it has, then we should present it either here or in an associated article. But if it has not, then Wikipedia cannot present it.

Returning to the dp/dt picture as stated by Clancy, I would suggest that the justification runs as follows:

1. From Newton, every action has an equal and opposite reaction
2. Therefore there must be a reaction on the air, -L
3. From Newton's F=ma, -L = ma or, L = -ma
4. Therefore the air against which the wing acts must accelerate downwards
5. ma = dp/dt
6. Therefore L = -dp/dt

Which step(s) contain flaws? And more importantly for Wikipedia, where are those sources which explicitly say that it is flawed? If any has yet been cited with exactitude, I have missed it. — Cheers, Steelpillow (Talk) 09:55, 6 December 2014 (UTC)

The flaw in the reasoning is assuming that -L is the only force acting on the air. Let's consider the case of a plane flying straight and level at a steady speed: the lift is exactly balanced by the weight (L=-W) so the net force on the plane in the vertical direction (L+W) equals zero. Thus, there is no change in momemtum of the plane and dp/dt=0. Turning our attention to the air, there are forces acting on the air other than -L. If -L were the only force acting on the air then the statement would be correct. But there are other forces acting on the air, and while the total force F equals ma or dp/dt, -L is not the total force, F!=-L, so you can't say -L=dp/dt.

In the above paragraph "the air" means the entire atmosphere. If we restrict ourselves to a subset of the atmosphere, then there is a region for which it is true that dp/dt = -L. But it's not clear from the statement that "the air" refers to that particular subset rather than to the atmosphere as a whole.

Regarding citations, we don't need a citation showing something is false to leave it out of the article. We do have many reliable sources that deal with momentum transfer to the air and we need to look carefully at all of them. Some who make the statement (or something similar) are not very specific about what they mean by "the air", and the ones that do specify what they mean by "the air" are careful to point out that -L=dp/dt only applies to a specific subset of the air, not the entire atmosphere.

I have to say that until recently I was applying a similar line of reasoning to the one you give above and thought that -L was the only force acting on the air or at least that the other forces were negligible. This is not a valid assumption. I also thought that "the air" in the statement was the entire atmosphere. It's not. I'm still optimistic that we can arrive at consensus on how treat the issue in the article - given its own sub-section and a bit more space to describe the assumptions I think we will find language we can agree on. Mr. Swordfish (talk) 15:16, 8 December 2014 (UTC)

Indeed it is not necessary to find a reference refuting an unsupported statement before removing it, but that is beside the point. This statement is now supported by two reliable citations, and it most certainly is necessary to find sufficient references refuting these sources before the statement can be removed. Bear in mind too the points I raise below. I too would be happy to see Doug and Zapletal's approach being given proper encyclopedic treatment - in its own section. Provided we adhere to WP:VERIFICATION and similar, we should be fine. — Cheers, Steelpillow (Talk) 16:06, 8 December 2014 (UTC)

We seem to have a disagreement on policy:

Mr. Swordfish says "Regarding citations, we don't need a citation showing something is false to leave it out of the article."

Steelpillow says "This statement is now supported by two reliable citations, and it most certainly is necessary to find sufficient references refuting these sources before the statement can be removed."

Mr. Swordfish's version seems to me to be more in line with common sense, but what is the actual Wikipedia policy? In my reading of the policy pages I've seen nothing saying that a citable source is needed to justify exclusion or removal of anything from an article, supported or not. Can [User:Steelpillow|Steelpillow]] steer me to where it says that?

J Doug McLean (talk) 01:42, 10 December 2014 (UTC)

(Zapletal Writes->)

Steelpillow, your flaw is in step 3. Doug has covered this before (ie. there is only an "mA" when there is an unbalanced force acting on the body, which in this case is the very large and slippery volume of fluid with a groundplane below it to carry the "-L"). I also hinted at this flaw in my point 5 above "Two Cases..." (eg. the airship exerts a large downward force "-L" on the air, yet there is NO "mA" of the air, anywhere).

Lanchester introduces his "Principle of No Momentum" in section 5, page 5, of his 1907 book. Is he not a reliable enough source?

(Added:) To quote Lanchester (page 9) "As a whole, the fluid, in the previous section, does not gain or lose momentum any more than does a cast-iron pillar supporting a load."

(End Zapletal.) 101.171.127.232 (talk) 12:01, 6 December 2014 (UTC)

We've seen that no net vertical momentum is imparted to the atmosphere as a whole by an airplane in steady level flight. However, there are regions of both upward and downward momentum in the field [McLean p.431]. There can be no doubt this momentum exists, and that it is communicated from region to region. Burninthruthesky (talk) 13:19, 6 December 2014 (UTC)

Lanchester's "Principle of No Momentum" refers to net momentum in the entire field. He wasn't ruling out momentum in local areas.

What you say is correct, but to say that momentum is "communicated from region to region" is potentially confusing in that someone might think you're referring to some kind of action-at-a-distance. Actually, momentum is convected (carried along) by fluid parcels and can thus be carried from one region to another. Otherwise, it can be exchanged only locally, by the pressure or the viscous stress between fluid parcels in contact with each other.

J Doug McLean (talk) 22:49, 6 December 2014 (UTC)

Somewhere in the previous debates I mentioned the distinction between a principle and its application in practice. I do find the airship analogy dangerous, perhaps spurious. The situations are utterly different. Airship lift is static, aerofoil lift dynamic, and this topic is confined to the dynamic situation. Analogy with a static situation can at best confuse. We look at the net force on any mass. In the case of the airship, the downforce exerted locally is counterbalanced by an upward pressure from below, net force is zero and there is no related momentum anywhere in the system. In the case of a dynamic flow over an aerofoil, the downforce is exerted through pressure changes brought on by the passage of the aerofoil through the air. The foil rides a "wave" of higher pressure beneath and of lower pressure above. Momentum circulates around this wave. In the foil, the lift forces generated exactly balance gravity. But in the air there is no such locally counteracting force and -L = ma should in principle apply.

Lanchester's point, that in the long run no net momentum gets transferred, is of course correct. There is no persistent "downwash" (ignoring the inefficiencies of the average helicopter rotor). But unlike a cast-iron pillar, or the underside of an airship, the business end of the air is highly dynamic. The localised downflow is rapidly corrected, but it has by then done its job. And during that local downward deflection, it briefly gained momentum. Only part of the overall flow pattern supports the aerofoil, the rest is an accompanying mechanism imposed by the laws of physics. And in that part that actually supports the wing, the air is being deflected downwards. Depending on which bits of the overall flow one considers, and which specific effects, the net downward momentum will vary substantially. Typically the momentum at the trailing edge will comprise not merely downward momentum imparted by the reaction to lift, but also upward momentum imparted by other mechanisms, some if not all of which have been exhaustively set out. Thus, in practice, the application of dp/dt is quite complex.

So the true debate here should not be, "how does it all work?" but, "what aspects should a simple introduction to the Newtonian model of dynamic lift be talking about?" And should it be discussing the basic principle or the complications we meet in practice?" Depending on one's answer to this last, I would suggest that it should be introducing the basic principle, and to the relevant localised airflow. I would also suggest that from this perspective my Step 3 is valid as a principle. It is only when one moves beyond the basic principle of lift to the more practical analysis of airflow overall that it becomes trite. — Cheers, Steelpillow (Talk) 14:54, 6 December 2014 (UTC)

I think Steelpillow is trying to frame the debate in the wrong terms. The article subsection in question is not about "a simple introduction to the Newtonian model of dynamic lift". It is about the popular qualitative "flow-deflection" explanation of lift, which in its usual form in sources other than the AAPT papers makes no quantitative claim regarding the rate of change of momentum. The flow-deflection explanation has shortcomings, but it belongs here, provided the shortcomings are explained. The Newtonian model of lift has been thoroughly discredited by numerous sources. See my comment above regarding the zero-versus-two-pi discrepancy in lift slope. The Newtonian model doesn't belong in this section. Perhaps some discussion of the Newtonian model and its deficiencies would be appropriate in the "Mathematical theories" section.

No, the imparting of momentum locally to the flow around the foil at the rate -L isn't a "basic principle" unless you accept the grossly unrealistic Newtonian flow model. In a real continuum flow, the non-uniform pressures in the field apply a "locally counteracting force", so that dp/dt = -L is not true in the local flow around the foil. It is true only if you consider a control volume that is slender and very tall, so as to eliminate the pressure force. The pressure field is not just a "complication we meet in practice". It is a basic feature of the flow when realistically modeled. Steelpillow's Step 3 is not valid as a principle. I agree with Zapletal that Step 3 is the flaw.

J Doug McLean (talk) 22:49, 6 December 2014 (UTC)

I cannot fathom this argument at all, it appears full of straw men and patent absurdities. The article section is titled "Simplified physical explanations of lift on an airfoil" and the subsection "Flow deflection and Newton's laws". It is not possible to deflect a flow without invoking Newton's laws. To suggest that a discussion of the Newtonian model does not belong in a section titled "Flow deflection and Newton's laws" is patently absurd. This debate has always been about the content of said section. Zapletal suggested that someone put the Newtonian case so that it could be criticised. I offered my understanding of Clancy's statement of it, focusing as he did on the airflow region in which lift (the topic of the article) is generated. Apparently this is "framing the debate in the wrong terms". I'm sorry, but such rhetoric just heralds a return to the same old same old.

Besides seeking refutations of Clancy's position, I emphasised the importance of relevant citations. I had hoped for verifiable quotations clearly relevant to Newtonian flow deflection and explicitly countering Clancy's position, yet the silence on this point is becoming deafening. No relevant citations, no progress. — Cheers, Steelpillow (Talk) 11:15, 7 December 2014 (UTC)

I think the reason my argument seems "absurd" to you is that you're failing to make the distinction between "the Newtonian model of dynamic lift" and "Newton's laws". They're not the same thing. I apologize if I didn't make that sufficiently clear.

In the aerodynamics literature, "the Newtonian model" refers to a specific flow model, i.e. the modeling of the flowing fluid as a hail of bullets that interact only with the foil and not with each other. Just because Newton's second law is applied to the model doesn't mean the results will be correct. Because the flow model itself is unrealistic, it leads to a wrong answer for dp/dt in the near field of a lifting foil.

Clancy's fire-hose model is wrong about near-field dp/dt in the same way. It isn't a bullet model, but it has a similar failing: It assumes that only a limited part of the flow interacts with the foil and doesn't interact with the rest of the surrounding flow. Thus it doesn't account for the role of the pressure field in the momentum balance, as I've already pointed out. Clancy's model gets dp/dt = -L for the flow in the near field of the foil. We know this is wrong for reasons I've explained several times and Mr. Swordfish explained above. And we have citable sources for the fact that it's wrong, i.e. the classical control-volume analyses I've cited. How are these sources not seen as "countering Clancy's position"? And how are they not "clearly relevant to Newtonian flow deflection"? They clearly show that the Newtonian model's answer for dp/dt in the near field is wrong, and they make it clear why it's wrong.

You are mistaken when you refer to the air that Clancy's statement focuses on as "the airflow region in which lift is generated". In Clancy's statement, "this air" refers to the air inside the fire-hose stream, which is a narrow region of the flow. In the real flow there's not enough momentum imparted to the air in a region of that size to account for all of the lift. In reality, lift is generated by the flow over a much wider region, and the momentum-balance picture is more complicated.

I think this subsection of the article should just be about the popular qualitative flow-deflection explanation based on Newton's laws. This simple explanation has many sources: NASA websites, "Stick and Rudder" by Wolfgang Langewieshe, and others. It avoids getting into the quantitative question of dp/dt, and I think that's the appropriate level of detail for this section of the article. Newton's laws are central to this explanation, but the Newtonian model doesn't belong as part of it. The Newtonian model is unnecessarily quantitative, and erroneously quantitative at that.

If this is "a return to the same old same old", it's because you continue to push for giving a prominent place to the same old discredited model.

J Doug McLean (talk) 01:42, 10 December 2014 (UTC)

(Zapletal Writes->)

Steelpillow, you wrote:

1. "I do find the airship analogy dangerous, perhaps spurious. The situations are utterly different..."

Just before making that analogy I wrote:

"5. TWO CASES TO THINK ABOUT. - ... please don't say "Oh, but that's different..." ..."

The first "airship" example was intended to make clear that a Lift force can be created in a fluid by pressure forces alone, so -dP/dt is NOT absolutely essential. The second "wave" example hinted at how dynamic effects can create such Lifting pressure zones.

~o0o~

2. "Only part of the overall flow pattern supports the aerofoil ... in that part that actually supports the wing, the air is being deflected downwards. [etc...]"

That whole paragraph is wrong, or at the least, very misleading. All parts of the flow pattern depend on all other parts of the flow pattern. That is why it is called "Continuum Mechanics".

Any smallish volume of fluid near the aerofoil (ie. any fluid that might be said to "actually support the wing"), necessarily has very small mass. There is simply NO WAY that this small mass can cause ALL of the Lift via its -dP/dt.

Instead, this small volume of fluid is responsible for a VERY SMALL part of the Lift, via its downward dP/dt. The rest of the Lift comes from the PRESSURE FIELD surrounding this small volume. That pressure field (established when the aerofoil first started to move, or accelerated) is also related to the momentum changes of all the other parts of the fluid, more than half of which are now UPWARD dP/dts. ~o0o~

3. "Thus, in practice, the application of dp/dt is quite complex ... So the true debate here should [be, how do we give] a simple introduction to the Newtonian model of dynamic lift ... introducing the basic principle ... to the relevant localised airflow..."

What you are suggesting is that this article should teach a FALLACIOUS model of Lift, for purely IDEOLOGICAL reasons. (This shouting is just to make this point clear, so I don't have to repeat it.)

Specifically, your qualitative "Newtonian Model" is incapable of giving any quantitative results. To get any results at all, you must first know the Lift, then ARBITRARILY assume an amount of mass to do the Lifting (ie. your "relevant localised airflow"), after which you get an "average" acceleration value, but NO IDEA of what the actual flow field looks like.

This is an utterly useless approach to understanding FDL (ie. it is of zero help in designing aerofoils), that is taken simply to support an ideological viewpoint (ie. that "Lift MUST be due to Downwash..."), with that viewpoint being WRONG anyway (ie. as many others here now agree, there is NO NET change of vertical momentum).

As I wrote earlier,

' "In short, the editors of good encyclopedias filter out the nonsense. If this does NOT happen, then very soon we will have to believe that the world is flat, voodoo is real, and the star signs predict our future." '

To which we might have to add, "... and, because Newton said so, all FD-Lift is due to Downwash". And maybe after that ETT can make a comeback.

~o0o~

4. "Besides seeking refutations of Clancy's position, I emphasised the importance of relevant citations. I had hoped for verifiable quotations clearly relevant to Newtonian flow deflection and explicitly countering Clancy's position, yet the silence on this point is becoming deafening. No relevant citations, no progress."

Again, your deafness seems decidedly ideological in nature.

As already quoted and cited many times, the major part of Lanchester's book is directed at refuting "Newtonian flow deflection". All of the "Circulation/Vortex Theory of Lift", hugely successful for 100+ years, and which has countless citations from umpteen reliable sources, refutes it.

If anyone is seriously interested in this Article, then they should study this body of knowledge more deeply before trying to impose a false ideology upon the next generation.

I will be away for the next week, so not able to respond to any questions for a while.

(End Zapletal) 101.170.255.230 (talk) 11:43, 8 December 2014 (UTC)

Your rant about ideology closes this discussion as far as I am concerned. It is a breach of WP:GOODFAITH, it demonstrates that you do not have a neutral point of view (WP:NPOV) and are therefore WP:NOTHERE to build an encyclopedia and that this discussion remains as utterly pointless as I have suggested all along. — Cheers, Steelpillow (Talk) 15:06, 8 December 2014 (UTC)

This question is in regards to the text, "the flow following the upper surface contributes strongly to the downward-turning action."

To paraphrase, one event - "the flow follows the upper surface" - causes (or more precisely, is a contributing cause of) a second event - "the air turns downward".

Is this in accordance with accepted science? If not, I think that the text should be reworded to convey what was meant.

I think I may understand the important point that the author was trying to convey. I think the author meant to refer to a baseline of 'atmospheric pressure on all subsurfaces'--which applies when there is no flow--and compare that to the conditions of flight, where the deviation from the baseline is greater on the upper surface than on the lower (so the "contribution" relative to the baseline is mostly from the changed conditions on the upper surface, not the lower as intuition would suggest). But that is very different I think than what was said. The fact is that under conditions of lift, the upper flow is following the surface of the wing, more or less, "because of" (if we must allow a causal interpretation) the excess of pressure from the air above over that applied by the wing. And the pressure on the upper surface of the wing under conditions of lift is opposing, not enhancing lift.

Mark.camp (talk) 23:44, 1 December 2014 (UTC)

At some point in the article's history, the idea expressed by this passage was followed by some discussion of airflow on both sides of the wing and the point made that some explanations only involve air being deflected by the bottom of the wing. (sometimes called "bullet theroy" or "skipping stone theory"). This was accompanied by a graph showing the pressure distribution along the top and bottom of a wing where the pressure difference along the top was substantially larger than along the bottom. At some point this was excised, whether by accident or not.

Which is to say that your interpretation of the intent is correct. I can see where what is actually written may be interpreted differently than what was meant. A suggestion for how to reword would be welcome. I'll take a look at earlier versions and see if we edited something out that shouldn't have been. Personally, I don't read the passage as a statement of cause and effect but I can see how someone might interpret it that way. Mr. Swordfish (talk) 00:24, 2 December 2014 (UTC)

Sorry, I didn't say why I thought the current text suggested a causal relationship, so I will provide some examples that clarify why I inferred one. (I address this point of yours before answering your good request for proposed wording, since if I'm off a bit in my reading then no change is needed.)

  The addition of fertilizer to the poor soil common to the region contributes 
  strongly to the higher corn yields.
  (The sentence implies, for me, that "the addition of fertilizer" is a contributing cause of "higher corn yields")

  Having three unusually strong candidates for the lower house contributed strongly to the party's gains in that election.  
  (The sentence implies for me that "having three unusually strong candidates for
  the lower house" was a contributing cause of "the party's gains in that election."

  Adding two extra cylinders to the V6 engine contributed strongly to the increased torque
  in the new engine.  (The sentence implies, in my reading, that "adding two extra 
  cylinders to the V6 engine" was a contributing cause of "the increased torque in the new engine".

In these cases, which are I hope analogous to the text under discussion, it seems that the first event ("addition of fertilizer") is implicitly claimed as being a contributing cause of the second ("increased corn yields").

Does my reading of the original text seem reasonable to you?

Mark.camp (talk) 23:38, 7 December 2014 (UTC)

I am not sure there is a significant problem here:

 The higher yields from fertilizer are predicated on it being poor soil. (this is specifically mentioned in the 
 example sentence)

 The strong election gains are predicated on the election being for the lower house. (this is not exactly 
 mentioned in the example, although the description "that election" might suggest it)

 The increased torque is predicated on the existing cylinder capacities remaining constant. (this is not mentioned 
 at all in the example sentence)

 The contribution of the upper surface flow is predicted on the downward turning of the upper surface itself. (this 
 is not mentioned in the example sentence)

Whether these assumptions are made explicit in the given sentence is neither here nor there since they are, one way or another, trivially evident from the overall discussion. One might write, "the flow following the downward-turning upper surface contributes strongly to the downward-turning action of the flow," but I personally think that this would be unnecessarily pedantic. There comes a point where the sheer amount of word salad begins to confuse. Whatever the present version says in terms of phrasing, the physical mechanism it is explaining is obvious enough, and at the end of the day that is what language is for. Steelpillow 10:54, 8 December 2014 (UTC)

The resulting force upwards is equal to the time rate of change of momentum of the air deflected downwards.

— "The Statement"

Since I don't know quite where to insert this into the wall of text above I'm starting fresh with a new section. I'm also starting more or less from the beginning. Please bear with me, and thanks in advance for your patience.

Let's take a look at a simple model, i.e. a plane flying straight and level at a constant speed. In this model, the only things are the plane, the atmosphere, and the ground. After decomposing the total aerodynamic lift into it's components we have four forces on the plane: lift, drag, weight, and thrust. Lift is opposed by weight and thrust is opposed by drag. Since the plane is flying straight and level L+W=0 and D+T=0. With no net force in either the vertical or horizontal direction, there is no acceleration and consequently no momentum change. For the plane, dp/dt = 0.

The ground, of course, is stationary, so for the ground dp/dt is also zero.

The only other thing in the model is the air, and if its momentum is not constant we have a violation of conservation of momentum - how can the air experience a change in momentum without anything else experiencing an equal but opposite change in momentum? So the air (ie the atmosphere as a whole) must have constant momentum, that is dp/dt for the atmosphere as a whole is zero.

NB. That is not to say that there is no transfer of vertical momentum from the atmosphere as a whole to the foil. On the contrary, if there is a vertical force between wing and air, then there must be a momentum transfer, unless one supposes that there is a non-mechanical force in play, such as gravitation, electrostatic, etc. It is only to say that, since the momentum of the air as a whole is constant, then if the air is transferring momentum to the wing at rate x, then it must be receiving momentum at an equal rate from some other interaction, such as an interaction with the earth)Mark.camp (talk) 03:23, 10 February 2015 (UTC)

We don't need to compute integrals of momentum flux and take the limit as the boundary goes to infinity to arrive at this, although making those calculations gives the same result.

However, there are subsets of the air that experience non-zero dp/dt. And if we take just the right subset, it can be shown that for that subset of the atmosphere dp/dt = -L. It is reasonable to interpret the lift physically as the result of the momentum change of that subset of the atmosphere. (not everyone agrees with or likes that interpretation, but it is supported by many reliable sources)

There's nothing special about the vertical direction in the argument above. Looking at the horizontal component of momentum change, thrust is equal in magnitude to drag so the net force in the horizontal direction is zero. For the plane, the horizontal component of dp/dt is zero as well. The ground is just as stationary as it was a couple of paragraphs ago, so we can conclude that for the air the horizontal component of dp/dt is zero.

This does not contradict the fact that the propeller or jet is pushing a fairly large amount of air backwards. Unlike with lift, there seems to be no controversy over whether air is pushed backwards by the engine. ( NASA has a concise treatment of thrust and momentum change at http://www.grc.nasa.gov/WWW/k-12/airplane/thrsteq.html). The physics in the horizontal and vertical directions is basically the same - if you take a close look at the propeller blades they're just small airfoils generating lift. One can say that the "real" reason the propeller drives the plane forward is the imbalance of pressure between the front and back of the propeller blades, but most folks are satisfied with the 'push air backwards' idea, so much so that for many simple explanations thrust isn't even explained - most people just get it without any explanation. In any case, looking at the Talk page of the Thrust article I don't see any long drawn out discussions about how to explain thrust, the article simply says it's a reaction force and this unremarkable statement has collected few remarks on the talk page.

So what does all this have to do with the statement? Well, one point of the exercise is to show in an easy-to-follow manner that when you consider "the air" as the entire atmosphere then the rate of momentum change of "the air" is zero, not -L. So, if a reader gets the idea that "the air" means the whole atmosphere rather than just a subset then including the statement as previously worded will give the wrong impression and mislead the reader. However, if we provide context then some version of the statement would be appropriate.

Another point is to show that dp/dt=0 is not inconsistent with some subset of air being accelerated - either downward as occurs with lift or backwards as occurs with thrust. Some subset of the air is accelerated downward with dp/dt = -L; some subset is being accelerated backwards with dp/dt = -T. I don't know how important it is to specify exactly what subset(s) meets this criteria, but I do think it's important to specify that it is a subset and not the entire atmosphere, that is if we are going to include it at all.

Moving forward, I'll try to collect in one place the cites that relate lift to momentum change of air. then we can put on our wikipedia editor hats and evaluate the material provided by the various reliable sources and perhaps craft a subsection that reflects that material. Mr. Swordfish (talk) 20:08, 8 December 2014 (UTC)

The analogy with thrust is a good one. Since a propeller is a rotating aerofoil, there's little difference in the physics, except for geometry.

I can see why someone familiar with Lanchester's "Principle of No Momentum" might initially see The Statement as a claim that the atmosphere as a whole is given downwards momentum. The trouble with that interpretation is that for it to be true, the atmosphere would have to fall through the ground. That is a nonsensical assumption, which highlights the straw man in the argument that The Statement is false.

It's true that momentum can only be calculated for a specified portion of air. I think you've expressed the point well, that that subset of air (and the momentum that is communicated^* to the rest of the air) exists whether the location of that subset it is specified or not.

I think we've all agreed from the outset that talking about control volumes at this early stage of the article is more likely to confuse the reader than help them understand how the physical principles expressed in Newton's laws contribute to lift.

I think once some text for the proposed new section is drafted it will be much easier to agree the facts, and decide what changes (if any) should be made to the section on Newton's laws to improve the coherence of the article as a whole.

[* Lanchester's choice of word: When a loaded aerofoil is dynamically supported by a fluid, we know that its weight is eventually sustained by the surface of the earth, and that the transmission of the stress is effected by the communication of momentum from part to part p.148]

Burninthruthesky (talk) 10:15, 9 December 2014 (UTC)

I'd second that gathering and correlating sources is far the best way forward. And do you know, I have clean forgotten what "the statement" said, it was so long ago. Perhaps it is better not to remind ourselves but to just stick with the sources and a clean sheet? — Cheers, Steelpillow (Talk) 11:06, 9 December 2014 (UTC)

"The atmosphere as a whole" isn't the only definition of "the air" for which a reader is likely to mistakenly think The Statement is true. Another potential trap is the idea that The Statement is true for "the local airflow" in the neighborhood of the foil and that it is only when you look farther afield that other effects creep in. This is a misconception that's been expressed by several participants in this discussion and may still be held by some of them.

Burninthruthesky seems to have a strange definition of a "straw man". It's obvious to him that The Statement is false for the atmosphere as a whole, so the mentioning of that as an example is a "straw man"? The Statement is also false for "the local airflow", which is perhaps not so obvious. So I disagree with the idea that it's not important to discuss the "location" where this "subset" with dp/dt = -L "exists". I think it's important to know that "the local airflow" isn't that location.

In terms of basic physics, a propeller is different from a wing in important ways, and the analogy between thrust and lift is a poor one for the following reasons:

• Even in a reference frame moving with the airplane, the propeller blades are moving and doing work on the fluid, leaving behind a slipstream with higher total-pressure than in the rest of the field. In even the simplest model of propeller flow, like Rankine's actuator-disc model from 1859, the boundary of the slipstream is a vortex sheet that has no counterpart in the flow around a 2D lifting foil.

• A propeller has a substantial effect on the part of the flow that passes through the disc and becomes the slipstream, and relatively little effect on the rest of the flow. Thus the kind of model used by Clancy and by Chris Waltham, in which only a limited part of the stream is assumed to be affected, applies reasonably well to propeller flow. It doesn't apply so well to the flow around a lifting foil.

• Cross-stream pressure gradients play only a minor role in propeller flows but play a key role in the momentum balance in airfoil flows. This is to be expected, given that thrust is a streamwise force, and lift is a cross-stream force.

So I don't think analyses of thrust are much help in understanding lift.

I also second Mr. Swordfish's initiative to gather the sources.

That said, I have some reservations about including direct quotes in the article's list of sources. I understand that it makes things easier for the reader in a way. But it also has a downside. It isn't generally practical to provide a long enough quote to avoid the "out-of-context" problem, and the result can be an incomplete and possibly misleading view of what the quote really represents. In a quote of reasonable length you often get only the author's conclusion, not the assumptions he made or the analysis he used to reach that conclusion. I'd propose that instead of a direct quote we should consider paraphrasing the findings, including a brief summary of the assumptions and methods of analysis.

Now that we're collecting sources, I propose that we also collect comments by those who take the time to read the sources, e.g. brief summaries of the models and assumptions that were used, and resulting criticisms etc. My preference would be to append comments directly under each source to make things easy to correlate and to facilitate later discussion.

J Doug McLean (talk) 01:57, 10 December 2014 (UTC)

Yes, I know that there is more than one way to misinterpret The Statement in a way which makes it false. What I'm saying is that the language used is not specific enough to imply anything whatsoever about how to calculate the rate it describes. I still believe the control volume analyses which account partly for momentum and partly for pressure do not answer the question posed by The Statement. I see that you now describe it as "misleading" rather than "false". The former is an opinion to which you are entitled and I thank you for moderating your language.

Personally, I have no problem with the suggestion made above to keep quantitative statements out of the Newtonian section and introduce them later if required. I noticed myself that Langeweische doesn't make any quantitative claims.

I look forward to seeing your suggestions for the structure and focus of the new section you propose. Burninthruthesky (talk) 17:00, 10 December 2014 (UTC)

Doug, I think a big reason why you've received so much pushback here on the talk page about your objection to the statement is due to the lack of direct quotes from the sources you cite. Citations and verifiability are what makes the entire wikipedia party happen. While I agree that we need to be careful to not take a single sentence or two out of context, we need more than just a work and a page number to back-up contentious claims.

Wikipedia can be a funny place sometimes; I'm sure you are quite capable of looking at a page of equations and concluding in words that "these equations clearly show that the time integral of foo is equal to bar". But unless we have a reliable source that draws the same conclusion putting that statement into the article is synthesis or interpretation which is prohibited. If you publish the same statement in a book or a paper we can use it, but if you just say so here on the talk page we can't. Like I say, Wikipedia can be a funny place, but those are the rules of evidence.

So, I'd prefer to see some direct quotes rather than editors' interpretations. Right now, we have an excerpt from your book and the clarifying aside from Waltham about "doing it right" that we can weigh against the imprecise assertions of Smith and the AAPT committee. Another one or two and we're probably there.

Sorry you didn't like the thrust analogy - like any analogy it only goes so far, but I think it serves to illustrate that dp/dt = 0 for the atmosphere as a whole is consistent with non-zero mass flow is some subsets of the atmosphere.

Finally (for now) I'd prefer that the raw material thread not be interrupted by a lot of back-and-forth exchanges amongst the editors. Once that starts happening the thread will become difficult to follow. Instead, I'd suggest a sub-thread for each source below the initial post. I'll start with an example. Mr. Swordfish (talk) 20:45, 10 December 2014 (UTC)

Two examples that may help clarify the discussion

Consider an iceboat oriented so that the wind is perpendicular to its centerline with its sail trimmed in and the brake engaged. The sail generates lift which is parallel to the centerline of the boat and the lift force (L) is opposed by the friction force of the brake (B). We'll assume in this idealized model that the brake is strong enough to hold the boat motionless. L + B = 0, the total force on the boat is zero and therefore it's acceleration and dp/dt are zero.

In this model the boat can't move, the ice doesn't move, and the only other thing is the air. Since momentum is conserved, dp_boat/dt + dp_air/dt = 0 and the net momentum change of the air is zero.

Now, let's release the brake. If we ignore the negligible friction force of the runners (skates), the net force acting on the boat is L. (drag is opposed by the runners that don't move sideways). If F is the total force on the boat we have F = L = ma = dp_boat/dt .

Again, conservation of momentum says dp_boat/dt + dp_air/dt = 0, and in this case dp_air/dt = -L. So in this special case we can say that the lift is equal to the time rate of change of momentum of the air.

When we had the brake engaged, the situation was very similar to a plane in steady level flight, with the brake playing the role of gravity in opposing the lift force. When we release the brake, the situation is similar to the idealized model of a wing in an infinite atmosphere in the absence of gravity. In this second situation, the statement is true even when "the air" is the entire atmosphere. But the usual example when explaining lift is steady level un-accelerated flight in a gravitational field, not a plane flying in the absence of gravity or an iceboat accelerating from a stand still.

To be a bit nit-picky, I should add that in the case of the iceboat, dp_air/dt = -L is only strictly true for a moment - once it begins accelerating the apparent will will move forward and L will not be parallel to the centerline of the boat anymore so L != dp_boat/dt in general. Further, since it is accelerating our usual frame of reference will no longer be an inertial reference frame. And eventually the boat will reach a steady speed at which point dp_air/dt = 0. So I don't think an iceboat accelerating from rest is a good example to place in the article.

Hopefully these two examples (a foil constrained to have no acceleration and a foil that is allowed to accelerate with L being the total net force) will cast a bit of light on how momentum is (or is not) transferred to the air. This thought experiment helped clarify things for me anyway. Mr. Swordfish (talk) 20:52, 15 December 2014 (UTC)

You have changed the statement from the version originally stated (and which I copied above before archiving). This change makes the phrase "the air" more ambiguous and easier to attribute an unintended meaning. Have I missed something or is this effectively a new discussion about a new problematic statement? — Cheers, Steelpillow (Talk) 22:01, 15 December 2014 (UTC)

Apologies. I didn't recall whether the word "downward" appeared in the original, so I went to the talk page archive to find the earliest example. On July 27th, Doug wrote The more specific statement "lift is equal to the time rate of change of momentum of the air" is not correct in general. I recommend deleting this sentence. leaving out the word "downward". I mistakenly took this to be the definitive version of the statement but looking back at the actual draft and subsequent versions of the statement on the Talk page indicates that the word "downward" was in the original. Thank you for restoring it. Mr. Swordfish (talk) 22:15, 15 December 2014 (UTC)

The version I copied also included the word "deflected". This makes a big difference to what one assumes is the air in question. Without it the Statement is ambiguous and requires a suitable preceding remark to give it context. We have lost that context so, if the Statement as now presented is to mean anything at all that can be discussed, it needs that context restoring. — Cheers, Steelpillow (Talk) 11:23, 16 December 2014 (UTC)

Agree that "downward" needs to be part of the statement, otherwise the air deflected in the horizontal direction by the thrust and drag would be included. However, even with "downward" included the statement is still ambiguous. What is meant by "the air"? If it's the entire atmosphere then the statement is false. If parsed narrowly, the statement says that the total momentum change of all the air with a negative vertical deflection is -L and this does not agree with the results of control volume analysis. If "the air" is a carefully defined subset of the atmosphere then the statement is true, but it's not true for arbitrarily chosen subsets and it's not true for most subsets that one would intuitively choose as representative.

Until recently, I was mislead by the statement. Only after reading up a bit on control volume analysis did I realize my intuitive ideas were not supported by rigorous quantitative analysis. I think something like the statement can go into the article if we provide sufficient context, but as it stands it's likely to give the reader the wrong idea. Mr. Swordfish (talk) 16:06, 16 December 2014 (UTC)

Are the sources which convinced you that your ideas were "not supported by rigorous quantitative analysis" listed below? Burninthruthesky (talk) 17:02, 16 December 2014 (UTC)

Yes. Zero net momentum change for the atmosphere as a whole is a fairly standard result. Chapter 8.5 of McLain's book lays it out in words fairly clearly. Google books has a generous excerpt at http://books.google.com/books?id=_DJuEgpmdr8C&q=Manifestations+of+Lift+in+the+Atmosphere+at+Large#v=snippet&q=%22Manifestations%20of%20Lift%20in%20the%20Atmosphere%20at%20Large%22&f=false Here are some quotes:

"...there is no net downward momentum imparted to the atmosphere as a whole and that the lift is reacted by pressure differences on horizontal planes above and below the wing, or on the ground plane, if there is one. We'll also consider how conservation of momentum applies to control volumes that don't encompass the entire atmosphere. ... the lift can show up at the boundaries either as pressure differences on the horizontal surfaces or as fluxes of vertical momentum mainly through the vertical surfaces, or as combinations of the two, depending on the proportions of the control volume."

"Prandtl and Tietjens (1934) showed how in steady level flight the lift is balanced by an overpressure on the ground under the airplane, so that of course there is no need for net momentum transfer."

I've been trying to find the actual passage in Prandtl that supports this, but I haven't yet. In any case, I thought that "the air" in the statement meant the entire atmosphere, or some arbitrary box around the airfoil, but the only interpretation of "the air' that makes the statement true is a tall thin subset of the atmosphere - this is not intuitively obvious. Mr. Swordfish (talk) 21:11, 16 December 2014 (UTC)

Thank you for clarifying. Yes, the net change of momentum of the whole atmosphere is zero, but momentum is necessarily imparted to air within the atmosphere. See my comments on the AAPT paper below. Burninthruthesky (talk) — Preceding undated comment added 10:06, 17 December 2014 (UTC)

Agreed. The net change of momentum of the whole atmosphere is zero. And within the atmosphere there are subsets which experience non-zero momentum change. If one chooses the subset carefully, the rate of momentum change for that subset is equal to -L. But if one chooses a different subset then in general dp/dt != -L. I think the main point of disagreement is over the lack of precision in referring to that particular carefully chosen subset for which dp/dt = -L as simply "the air" or "the air deflected downward". I'm ok with a bit of imprecision in a qualitative introductory section aimed at the lay person as long as it leaves a basically correct impression. Here, I don't think it leaves a basically correct impression. Mr. Swordfish (talk) 16:50, 17 December 2014 (UTC)

It is imprecise to refer to the net momentum of a body of air without defining the body, but we don't do that. What is imprecise about saying that momentum is imparted to air within the atmosphere at a rate equal to lift? Burninthruthesky (talk) 17:48, 17 December 2014 (UTC)

For information, the whole of the disputed section containing what I understand to be "The Statement" can be seen here. Burninthruthesky (talk) 17:24, 16 December 2014 (UTC)

@User:Mr swordfish, I think there is some discussion at cross-purposes here. In saying that "downward" should be included in the Statement, are you implying by omission that "deflected" should not be? That is the word which you removed and which I am more concerned about. To me, the phrase "the air deflected downward" has a very clear meaning which is garbled when any one word is removed. I cannot help but wonder if it is the removal of "deflected" which might have caused the ambiguity which originally confused you. — Cheers, Steelpillow (Talk) 19:30, 16 December 2014 (UTC)

The word "deflected" does not appear in the AAPT version of The Statement or in any other of the sources, as far as I know. Thus adding "deflected" to it is something that has no citable source. And for what it's worth, it's easy to show (though I know of no citable source for this) that adding "deflected" doesn't make The Statement more correct anyway. There is much more negative dp/dt in the region of "the air deflected downward" than just -L. J Doug McLean (talk) 21:15, 16 December 2014 (UTC)

No, I'm not implying anything by omission. And removing whatever word I did was an error on my part for which I apologize (I think I removed "downward' but it doesn't really matter).

I disagree that "the air deflected downward" has a clear meaning. If you take it literally then the statement is false. Mr. Swordfish (talk) 21:24, 16 December 2014 (UTC)

In Clancy's cylinder model (see below) the air which is deflected downwards is described with mathematical precision. If you take "the affected air" to be the air deflected downwards (and what other interpretation is even remotely plausible?) then the Statement is demonstrably true. So I find your assertions to the contrary to be utterly baffling, an absolute failure between us to establish any common use of language. I get the feeling that we agree on the maths but just not on how to describe it. Still, I don't see how we can take this forward between us, so I guess I will have to withdraw from this conversation. — Cheers, Steelpillow (Talk) 23:00, 16 December 2014 (UTC) [Updated 10:01, 17 December 2014 (UTC)]

I have not read Clancy, but I have the book on order. Unfortunately, I have to get it via inter-library loan so probably won't see it until after the new year. It may well be true that in his model the integral of all the air experiencing downward deflection is equal to -L. But from what I've seen in the excerpt posted here, his cylindrical model is not as accurate as the potential flow model. In the potential flow model, a subset of the air experiences dp/dt = -L, but if you add up all the air being deflected downward the magnitude of dp/dt is larger than |L|.

So, perhaps we are just looking at different models? Mr. Swordfish (talk) 16:27, 17 December 2014 (UTC)

Yes, I am sure that we are referencing different models. Some models give dp/dt=0, some 0.5L, some L, some >L. Each model is applicable under different assumptions or conditions, i.e. they are modelling different aspects of the problem, and - crucially to this debate - all are well attested in the literature. Taking a result (or assumption) from one of these aspects of the problem and then complaining that it doesn't match the results derived (or assumed) for a different aspect is at best futile. Asserting that it is therefore "wrong" is nonsensical. If the Statement disturbs you, it is because you and it are addressing different aspects of the problem. — Cheers, Steelpillow (Talk) 17:49, 17 December 2014 (UTC)

I agree. The idea that since these analyses give a numerical value for dp/dt, they all answer exactly the same question is tempting, but wrong.

• Lanchester §112 asks, in effect, how much momentum is transferred per unit time between the foil and the ground, via the atmosphere.
• Prandtl and Tietjens ask how much overpressure is exerted on the ground due to lift.
• The control volume analyses of various other shapes ask how lift can be accounted for by a mixture of pressure and momentum.
• The Statement is only concerned with momentum.

Just to avoid any confusion, I haven't seen any sources saying |dp/dt| > |L|, neither has J Doug McLean. Burninthruthesky (talk) 10:56, 18 December 2014 (UTC)

I think Steelpillow's and Burninthruthesky's line of argument above mischaracterizes the issue.

What we're discussing here is the question of how much integrated dp/dt is imparted to the flow by a lifting foil, and as part of that question we're concerned with how dp/dt is distributed in the field.

Both Clancy's cylinder model and the classical uniform-flow-plus-vortex model address these questions. They are not modeling "different aspects of the problem"; they just model the same flow in different ways. Clancy's model for the velocity field is much more crude than the classical model, and Clancy's model ignores the pressure field, while the classical model models it realistically. Clancy's model assumes dp/dt = -L in the near field (within the cylinder), while finding dp/dt = -L in the classical model requires looking much farther afield (the tall sliver control volume). In this regard, the classical model is realistic, and Clancy's model is not. Comparing the realism of different models in this way is not "futile".

Lanchester's analysis and the other classical analyses don't deal with momentum exclusively, but they do address the question of dp/dt. In that sense they all address the same question, i.e. the value of integrated dp/dt in the flowfield.

True, I have not seen any source saying that control volumes exist for which |dp/dt| > |L|, but it's easy to show that it's true. It's original research and can't be used in the article, but I think it's fair to use as a counterargument against other original research arguments on this page. J Doug McLean (talk) 22:36, 19 December 2014 (UTC)

In this section I'm trying to collect source material for a proposed section on momentum transfer and lift. Additions cheerfully accepted, but let's try to keep extensive discussions out of this thread so we can see what raw material we have to work with.

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"What supports an airplane aloft? ... Newton has given us the needed principle in his third law: if the air is to produce an upward force on the wing, the wing must produce a downward force on the air. Because under these circumstances air cannot sustain a force, it is deflected, or accelerated, downward.

Newton's second law gives us the means for quantifying the lift force:

F_lift = m∆v/∆t = ∆(mv)/∆t .

The lift force is equal to the time rate of change of the momentum of the air."

Bernoulli and Newton in Fluid Mechanics
Norman F. Smith
The Physics Teacher 10, 451 (1972); doi: 10.1119/1.2352317
http://dx.doi.org/10.1119/1.2352317

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"Most of the texts present the Bernoulli formula without derivation, but also with very little explanation. When applied to the lift of an airfoil, the explanation and diagrams are almost always wrong. At least for an introductory course, lift on an airfoil should be explained simply in terms of Newton’s Third Law, with the thrust up being equal to the time rate of change of momentum of the air downwards. See C. Waltham, “Flight without Bernoulli,” Phys. Teach. 36, 457 (Nov. 1998)."

Quibbles, misunderstandings, and egregious mistakes
AAPT Physics Textbook Review Committee
Citation: The Physics Teacher 37, 297 (1999); doi: 10.1119/1.880292
http://dx.doi.org/10.1119/1.880292

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"Birds and aircraft fly because they are constantly pushing air downwards:

L=dp/dt (3)

Here L is the lift force and dp/dt is the rate at which downward momentum is imparted to the airflow...

If we were to do this more correctly, we would box in the wing with a control volume of infinite vertical thickness. "

Flight without Bernoulli
C. Waltham
Phys. Teach. 36,457 (Nov. 1998).
http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/fluids/fly_no_bernoulli.pdf

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"Now let’s move on to conservation of momentum: the force exerted on a fluid equals the time rate of change (derivative with respect to time) of its linear momentum. If you exert a force on something, you change its momentum. If you don’t exert a force on something, its momentum stays unchanged or is conserved. This is Newton’s laws, if you choose to call it that. When an airfoil is producing lift, that force does in fact change the vertical component of the airflow’s linear momentum, and the drag force changes the horizontal component of the airflow’s linear momentum. ...Measuring lift by measuring the increase in downward vertical velocity in the flow coming off the trailing edge of the airfoil is conceptually possible. This downward velocity is definitely there and is known as downwash. I have never heard of anyone actually measuring it with sufficient precision to calculate lift, not because it is physically unsound but because it is not a practical experiment."

An Aerodynamicist’s View of Lift, Bernoulli, and Newton
Charles N. Eastlake
THE PHYSICS TEACHER Vol. 40, March 2002
http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/Bernoulli_Newton_lift.pdf

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"There is a widespread notion that an airplane in steady level flight continuously imparts net downward momentum to the atmosphere. ... Thinking in intuitive physical terms, we might also expect the impulse imposed by the airplane on the air (the product Lt) to produce a net vertical momentum in the atmosphere that grows with time. This expectation is not satisfied by the mathematics, however. ... If we expected to see a net downward momentum equal to Lt, the result comes as a surprise: The value of the integral over the semi-infinite space above the ground is zero, which means that the airplane imparts no net downward momentum to the atmosphere in steady level flight over a ground plane, regardless of height above the ground."

Understanding aerodynamics arguing from the real physics sec 8.5
McLean, Doug
Chichester, West Sussex, U.K. : Wiley, 2013.
http://mirlyn.lib.umich.edu/Record/012482734

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On basic control-volume analysis of the rate of change of momentum in a moving fluid:

The Dynamics and Thermodynamics of Compressible Fluid Flow Section 1.5
Shapiro, A. H. 1953.
New York: The Ronald Press Company.

McLean: "This analysis shows that for a steady flow the integrated time rate of change of momentum of fluid parcels passing through the interior of a control volume is equal to the integrated (net) flux of momentum through the boundary. This is a basic ingredient in the other analyses cited below."

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For the atmosphere as a whole, including a ground plane:

Applied Hydro- and Aeromechanics
Prandtl, L., and O. G. Tietjens. 1934. . New York: Dover Publications. Derivation in connection with figure 150.

McLean: I don't have a copy at hand, so I can't provide a quote, but this is the classic analysis showing that the pressure pattern on the ground constitutes a downward force on the ground, and thus an upward force on the atmosphere, equal to L. The net force on the atmosphere due to the lift, (i.e. the vector sum of the forces exerted by the wing and the ground) is therefore zero, so that the integrated rate of change of vertical momentum for the atmosphere as a whole must be zero.

The Prandtl and Tietjens analysis is for the 3D case. It is easy to show that the same overall conclusion applies in 2D. A citable source for the 2D analysis probably exists, but I don't know of one offhand.

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For a circular region centered on the airfoil:

Aerodynamic Theory, vol. 1. Sections B. V. 6 and B. V. 7.
Durand, W. F., ed. 1932.
New York: Dover Publications.

McLean: This is a control-volume analysis of the flow around a 2D lifting body of arbitrary cross-section in an infinite atmosphere, using a circle of large radius as the outer boundary of the volume. It shows that in the far field the flow is independent of the details of the body, and that significant contributions to the pressure and the momentum fluxes at the outer boundary come only from the combination of the uniform flow and the bound vortex. It arrives at a derivation of the Kutta-Joukowski theorem in equation 7.3. Equation 5.6 shows that the flux of vertical momentum across the outer boundary, and thus the time rate of change of vertical momentum in the air in the interior, is equal to only half the lift. Equation 6.6 shows that the integrated vertical pressure force on the outer boundary is upward and equal to half the lift. The net force on the air due to the lift is therefore downward and equal to half the lift, and Newton's second law is satisfied. It is explicitly stated that this result holds regardless of how large the radius of the circle is made.

Reference added by J Doug McLean (talk) 21:08, 16 December 2014 (UTC):

An Introduction to Fluid Dynamics Batchelor, G. K. 1967 Cambridge University Press

Applying the momentum theorem to incompressible inviscid flow around a 2D body of arbitrary cross-section (a general "cylinder") with circulation, and using a control volume bounded by a circle of large radius, Batchelor finds on p. 407:

"It follows from the calculation of the integral that the side-force exerted by the cylinder appears in the fluid far from the body half as a momentum flux and half in the form of a pressure distribution."

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For rectangular control volumes:

"For a large rectangular control surface, part of the lift is attributable to pressure and part to momentum, depending on the aspect ratio of the surface. For a square control surface the contributions on the surface due to momentum and pressure are equal; for a tall, long vertical surface the contributions are mainly momentum, while for a streamwise long, flat, horizontal surface the lift is primarily due to pressure. This illustrates that it doesn't make much sense to attribute the lift on an airfoil to either pressure or momentum effect, unless one takes a control surface on the actual airfoil surface, when the lift is indisputably due only to pressure!"

The facts of lift. Section titled "Lift in thin slices: the two dimensional case".
Lissaman, P. B. S. 1996.
AIAA 1996-161.
http://arc.aiaa.org/doi/pdf/10.2514/6.1996-161

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For a tall column of air:

"When a loaded aerofoil is dynamically supported by a fluid, we know that its weight is eventually sustained by the surface of the earth, and that the transmission of the stress is effected by the communication of momentum from part to part, and is thereby distributed over a considerable area as a region of increased pressure"

Fig. 62 illustrates the forces on a narrow column of air where W is the weight of the foil acting downwards and the pressure at the base of the column is w. "Consequently the downward momentum imparted per second to the fluid leaving the prism plus the upward momentum received per second from that entering must be equal to W – w."

"When the height at which the aerofoil is sustained is great in comparison with its own dimensions, the area over which the weight is distributed on the earth's surface is obviously also great, and the quantity w becomes negligible. Under ordinary conditions this would usually be the case, so that the weight may be regarded as in no part statically supported."

Aerodynamics. §112 – Aerodynamic support
Lanchester F.W. (1907)
Archibald Constable & Co. Ltd.
https://archive.org/stream/aerodynamicscons00lanc#page/146/mode/2up

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"The downwash also varies in the streamwise direction. It reaches its ultimate value little more than a chord length behind the trailing edge; and its mean value at the wing itself can be shown to be one half of this ultimate value." (Page 75)

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5.15 Lift and downwash

"The lift produced by a wing is imparted to it through the variations in pressure over its surface. This lift force has its reaction in the downward momentum which is imparted to the air as it flows over the wing. Thus the lift of the wing is equal to the rate of transport of downward momentum of the air.

"This downward momentum is measured in terms of the induced downwash described above." (Page 76)

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"Consider, then, this cylinder of air, as illustrated in Fig. 5.21.[longitudinal axis with respect to the foil, bends down to form the downwash] The area of cross-section of the cylinder of affected air is 1/4 πb². The rate of mass flow of affected air past the wing is therefore 1/4 πρVb². The rate of transport of downward momentum is therefore 1/4 πρVb²w, and this must equal the lift, L." (Page 76)

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"If we consider unit span of an infinite wing, however, the air above this unit span forms part of a cylinder of infinite radius, and its mass is therefore infinite. Since the downward momentum imparted to the air in unit time is finite, and since the mass of the air is infinite the induced downwash velocity must be zero." (page 77)

Aerodynamics,
Clancy, L.J.
Pitman Publishing (1973)

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"All attempts to fly in heavier-than-air machines must embody some means of forcing the air downwards so as to provide the equal and opposite reaction which is to lift the weight of the machine."

"...if we reject the idea of flapping wings, we must replace it by some other device which will deflect the air downwards."

Mechanics of flight
Kermode, A.C.
Eighth (metric) edition, 1972.
Pitman Publishing

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Reference added by J Doug McLean (talk) 21:08, 16 December 2014 (UTC):

Elements of Practical Aerodynamics Jones, B. 1939 John Wiley and Sons, Inc.

In the context of an analysis of induced drag on p. 82 he makes the following statement about the downward momentum imparted to "the mass of air affected by the wing":

"It has been proven mathematically that the downward momentum in unit time is equal to one-half the lift".

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Section added by J Doug McLean (talk) 21:08, 16 December 2014 (UTC):

On the popular qualitative flow-deflection explanation based on Newton's laws:

"The main fact of heavier-than-air flight is this: the wing keeps the airplane up by pushing the air down.

Stick and Rudder - An Explanation of the Art of Flying. Langewiesche, W. McGraw-Hill Education

"In momentum-based explanations, it is generally argued that the airfoil produces a flowfield in which some of the air is "deflected" downward and thus has downward momentum imparted to it. To acquire downward momentum, the air must have a downward force exerted on it by the airfoil, and thus, by Newton's third law, the airfoil must have an upward force exerted on it by the air."

Understanding Aerodynamics -- Arguing from the Real Physics sec 7.3.1.7 McLean, D. Chichester, West Sussex, U.K. : Wiley, 2013.

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Section added by J Doug McLean

On the Newtonian theory of lift

"The fluid itself is postulated as a collection of individual particles that impact directly on the surface of the body, subsequently giving up their components of momentum normal to the surface, and then traveling downstream tangentially along the body surface. That fluid model was simply a hypothesis on the part of Newton; it did not accurately model the action of a real fluid, as Newton readily acknowledged. However, consistent with that mathematical model, buried deep in the proof of Proposition 34 is the result that the force exerted by the fluid on a segment of a curved surface is proportional to sin^2 (theta), where theta is the angle between the tangent to the surface and the free-stream direction. That result, when applied to a flat surface (e.g. a flat plate) oriented at an angle of attack alpha to the free stream, gives the resultant aerodynamic force on the plate:

R = rho*V^2*sin^2(alpha)

This equation is called Newton's sine squared law...."

A History of Aerodynamics Anderson, J. D. , Jr. Cambridge University Press

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(work in progress - to be continued) I'll try to track down the cites provided by Doug McLean and see if I can pull out the relevant direct quotes instead of relying on his summaries. Not that I don't believe his summaries, it's just that we'd be remiss as editors if we just took his word for it. Mr. Swordfish (talk) 21:33, 8 December 2014 (UTC)

Please make any comments below here, so that we can keep the listing of sources clean and uncluttered.

• Comments on Prandtl and Tietjens

"...the integrated rate of change of vertical momentum for the atmosphere as a whole must be zero." Thus for the most obvious assumption a reader is likely to make regarding what is meant by "the air" (i.e. the atmosphere as a whole), The Original Statement is false. - DougMcLean (from earlier)

• Comments on Durand

It is explicitly stated that this result holds regardless of how large the radius of the circle is made. Thus a large circle is another example of a region of "the air" for which a reader might reasonably expect The Original Statement to apply, but for which it is in fact false. - DougMcLean (from earlier)

• Comments on Lissaman

According to Lissaman's results, if "the air" is taken to be the air in a rectangular box surrounding the airfoil, The Original Statement isn't even close to being true unless the box is a tall, slender sliver, and even then it isn't strictly true until the vertical dimension of the box is taken to infinity. Steelpillow quotes the section of my book that describes the result for the infinitely tall, slender sliver, the only control-volume shape for which The Original Statement has been shown to be true, and interprets it as being "in support of The Statement". A balanced recounting of what my book says would also quote the discussion in connection with figure 8.5.4, which deals with other control-volume shapes for which The Original Statement isn't true. - DougMcLean (from earlier)

• Comments on the AAPT paper

The quote from the AAPT textbook committee given above is the entire discussion of lift in that paper. The paper itself is a 25 pager devoted to reviewing seven high school physics textbooks, and that's all the space they had to address lift. As such it is quite cursory and lacks context. They suggest seeing Waltham's paper for more details and context. Waltham in turn cautions that to do it "correctly" requires a control volume of infinite thickness.

The AAPT does not explicitly say dp/dt of the entire atmosphere (or the "local flow" for that matter) is equal to -L. By not defining what they mean by "the air" they leave an imprecise statement that can be interpreted in different ways, one of which is correct and most of which are incorrect. If we repeat it with the same imprecision it is likely that our readers will latch on to one of the incorrect interpretations.

In sum, I would not give it the same weight as other more in-depth treatments of momentum transfer. Mr. Swordfish (talk) 21:09, 10 December 2014 (UTC)

The AAPT describe how much momentum is imparted to air within the atmosphere per unit time, consistent with results obtained by Lanchester, Lissaman and others.

I find it hard to think of a better form of words to describe this rate simply and concisely without going into details of a mathematical proof. Burninthruthesky (talk) 09:20, 16 December 2014 (UTC)

I agree with Mr. Swordfish that the AAPT paper doesn't deserve "the same weight as other more in-depth treatments of momentum transfer", and that "to describe this rate simply and concisely without going into details" would be misleading. J Doug McLean (talk) 21:08, 16 December 2014 (UTC)

• Comments on Lanchester

Lanchester §112 says that it is generally possible to show that dp/dt = -L. He goes on to clarify the exception commonly known as ground effect. Burninthruthesky (talk) 10:13, 11 December 2014 (UTC)

Without the use of calculus, he derives the total directly from Newton's laws.

The pressure w is entirely accounted for on the surface of the earth. Burninthruthesky (talk) 07:20, 13 December 2014 (UTC)

Lanchester's §112 does not say "that it is generally possible to show that dp/dt = -L." His analysis only shows that it is possible if you make one particular assumption for the shape of the control volume.

Lanchester's §112 amounts to a verbal version of a control-volume analysis for a tall-sliver control volume in contact with the ground. Lissaman (1996) published the corresponding analysis for the free-air case. The result is the same whether there is a ground plane or not, i.e. that as the height of the sliver goes to infinity the pressure force at the bottom (and top in the free-air case) vanishes, and thus dp/dt = -L for a control volume that is infinitely tall compared to its width.

Lanchester's result is essentially the same as Lissaman's and doesn't support an unapologetic version of The Statement any more than Lissaman did. The pressure is "entirely accounted for", but it's effect vanishes only because the height of the sliver is taken to infinity and the width is kept finite. J Doug McLean (talk) 21:08, 16 December 2014 (UTC)

Lanchester's §112 does not say "that it is generally possible to show that dp/dt = -L."
— User:J Doug McLean

Yes it does. Providing the right physical conditions exist, it is always possible to make the assumptions which show dp/dt is practically equal to -L. Lanchester suggests that when an aerofoil is in ground effect, w may become significant, in which case it would not be possible to show dp/dt = -L. He characterises the former situation as "ordinary conditions" which would "ususally be the case".

I only mentioned the fact that Lanchester accounts for pressure on the surface of the earth in response to your previous comment suggesting Lanchester supports your argument against The Statement.

It is clear from previous discussion and your obvious expertise in the subject that you need no explanation of the physics. So it is a mystery to me why you repeatedly misrepresent what has been written by others. You jest that "chuckling at the mistakes of others" is "part of the fun of being an aerodynamicist". I have not made a mistake here. We are WP:NOTHERE for an exercise in schadenfreude.

I've no doubt that that Lanchester's §112 is essentially the same as Lissaman's result. Both show that momentum is imparted to air within the atmosphere at a rate equal to lift. I don't see anything misleading about describing this rate as a simple fact in an introductory text, as advocated by the AAPT. You may disagree, but they are experts at educating people. Burninthruthesky (talk) 12:07, 17 December 2014 (UTC)

What I've said repeatedly is that the only published sources that use a realistic flow model and find dp/dt = -L to be true are those using a very-tall-sliver control volume. These sources make no claim that dp/dt = -L is true in any more general sense than that. So what, specifically, have I misrepresented?

You still seem to have concluded that The Statement is somehow true in a more general way. To me, this doesn't seem consistent with the physics or the published evidence. Just because dp/dt = -L applies in one particular control volume doesn't mean it applies to "the atmosphere" in any general sense. Yes, the tall sliver control volume "exists within" the atmosphere, but so do other control volumes for which dp/dt is different from -L. I see no basis for thinking one control volume is the "correct" one and the others are not. In general, the force exerted on the air by the foil is manifested as a combination of momentum changes and pressure differences in the flowfield. The one control volume for which the integrated pressure differences happen to vanish isn't in any fundamental way more "correct" than the others.

I know of no published source that uses a realistic flow model and shows that dp/dt = -L is true in the general sense you're proposing. The AAPT paper presents no analysis, and Chris Waltham's paper doesn't count on this score because he uses a simplified flow model that omits the crucial effect of the pressure field, as discussed in my comments on Clancy.

No, the Statement is not a "simple fact". It is a statement that is misleading unless it is accompanied by a somewhat arcane caveat. And I'm not making these arguments for fun. I'm here to improve the article by avoiding the inclusion of a misleading statement. J Doug McLean (talk) 22:52, 19 December 2014 (UTC)

In answer to your question, I have already clarified why I said, "Lanchester §112 says that it is generally possible to show that dp/dt = -L. He goes on to clarify the exception commonly known as ground effect." My comment is supported by the citation above. Your contradiction takes my words out of context.

The earlier comment I referred to said,

Actually, Lanchester's "deficiencies" section provides no support for The Statement, but instead supports what I've been arguing all along. The "Newtonian medium" (a hail of projectiles that don't interact with each other) is a poor model for flows of real fluids.
— User:J Doug McLean

This is a rebuttal for a proposition that was never made. The point of discussion was whether or not The Statement is true.

Several sources clearly explain how to calculate the result dp/dt = -L. As I have explained repeatedly, all of them account only for momentum. There are other calculations which account partly for pressure differences and for a smaller proportion of momentum. Your repeated assertion that other results for dp/dt are different, yet somehow answer the same question defies common sense. Again it is a rebuttal for a proposition that the cited authors did not make.

I'm afraid this is going round in circles again. Hopefully in the New Year there will be some progress on improving the article. Burninthruthesky (talk) 12:26, 20 December 2014 (UTC)

• Comments on Clancy

It is interesting that Clancy sees no contradiction between his Newtonian description and the fact that at the trailing edge, only half the momentum has yet been transferred. — Cheers, Steelpillow (Talk) 09:51, 15 December 2014 (UTC)

As far as I can tell, in the idealised infinite situation he goes on to describe Clancy is arguing that although the downward change of momentum in any finite portion of air is now infinitesimal, the sum of infinitely many such portions remains finite and is in fact still equal to the reaction to the lift. — Cheers, Steelpillow (Talk) 16:11, 11 December 2014 (UTC)

Clancy refers to "the affected air". This compares to the phrase "the air" which has caused so much supposed scope for misunderstanding here. Simply inserting the word "affected" as Clancy does would clear that side issue up. — Cheers, Steelpillow (Talk) 09:36, 12 December 2014 (UTC)

I don't think inserting the word "affected" will solve much of anything. According to the model, the entire atmosphere is affected by the presence of the moving airfoil so the "affected air" is all of it. And we have seen that for the entire atmosphere dp/dt =0. A few months ago we tried inserting "the air deflected by the foil" and that didn't do it either. There is some subset of the air for which dp/dt=-L, but I'm at a loss for how to state this in layman's terms without it being so awkward and convoluted that it distracts from the flow of the simple introductory section. Mr. Swordfish (talk) 13:10, 15 December 2014 (UTC)

It is not true that, as you suggest, "According to the model, the entire atmosphere is affected by the presence of the moving airfoil." Nowhere does Clancy's model address the entire atmosphere. It addresses a certain cylinder of air which he first makes finite and then expands to infinite size. I wonder if you are confusing this infinite cylinder with the whole atmosphere? We can be sure that they are not the same thing because within the interior of Clancy's model infinite cylinder, dp/dt = F while we know that within the even more infinite atmosphere which contains his model, dp/dt = 0. "The affected air" in his model is just the air within the rear part of the cylinder, aka "the air deflected downwards". — Cheers, Steelpillow (Talk) 16:52, 15 December 2014 (UTC)

Apologies for not being clear, but I wasn't referring to Clancy's model - I was referring to solutions to the Navier-Stokes equations, Euler equations, potential flow , etc.

In the very simple case of potential flow, the resulting flow field is the superposition of a steady uniform flow (i.e. what the flow would be like in the absence of the foil) and a vortex flow. While the vortex flow field diminishes as one gets farther away from the foil, at least in theory it is non-zero everywhere. So in the potential flow model the entire atmosphere is affected by the foil. More rigorous models (N-S, CFD, etc) give similar non-zero deviations from uniform flow throughout the entire atmosphere. These mathematical treatments are what I meant by "the model".

It appears that when Clancy says "the air" he means some specific subset of the atmosphere which he has defined beforehand and not the entire atmosphere. Fair enough, but unless we provide such a definition to our readers it is likely that they will interpret "the air" as the entire atmosphere. I think we are in agreement that for a non-accelerated foil dp/dt of the entire atmosphere is zero. If so, we're just arguing over what is meant by "the air". If not, then our disagreement is more fundamental. Which is it? Mr. Swordfish (talk) 19:55, 15 December 2014 (UTC)

Ah, in an item headed "Comments on Clancy", I hope you will forgive my misunderstanding which model you were discussing. The sources certainly bear out that the overall dp/dt is zero, I have no problem with that. Perhaps the best approach to "the air" is simply to write the new section intelligibly and not worry about our past usage. My comment on Clancy's usage was really just a flag to that end, in case it came in useful. — Cheers, Steelpillow (Talk) 20:50, 15 December 2014 (UTC)

Clancy himself admits that his flowfield model is "very crude". It assumes that "the air affected" by the wing in 3D is limited to a stream of circular cross-section with diameter equal to the wingspan (fig 5.21) and that this air is uniformly deflected downward by its interaction with the wing. There is no upward turning ahead of the wing or behind as there is in more-realistic flow models.

His model is unrealistic in another respect, and that is that it completely neglects the pressure field. It is assumed that the only force acting on the affected stream is that exerted on it by the wing, and this force is assumed to show up entirely as a rate of change of momentum of the steam of affected air. Thus dp/dt = -L is not really a result of this analysis; it is more of an a priori assumption.

His model becomes a little less unrealistic in 2D, where the wingspan and the diameter of the affected cylinder have gone to infinity, and the entire flow is thus affected, but it is still unrealistic in assuming the flow deflection is uniform, and in neglecting the pressure field.

Both Durand and Batchelor rigorously show that a uniform flow plus a vortex is a good approximation for the far-field flow in 2D, regardless of the details of the airfoil shape. The classical control-volume analyses I've cited use this model and show that the pressure field exerts significant forces on "the air" except in the case of the infinitely tall sliver.

I would not give Clancy the same weight as I would to the classical analyses I've cited, which use a much more realistic model. And I agree with Mr. Swordfish that adding "affected" doesn't clear up what is meant by "the air". J Doug McLean (talk) 21:08, 16 December 2014 (UTC)

I am quite sure that you would give your own work more weight than you give to those whom you criticise. Yawn. Worse, you cherry-pick from Clancy's full text to support your PoV. It also notes that his simplified model is consistent with a more complex analysis he gives later - and when we turn to that later analysis we find that it embraces the very flow-plus-vortex model you approve of. To selectively quote and then claim that Clancy's simplified model is at odds with the flow-plus-vortex model is somewhat invidious. Turning to the classical analyses you have quoted from, we may note that Clancy also writes that the downwash at the trailing edge is only half of its ultimate value, which it achieves a little over a chord-length further downstream. This is entirely supported by the classical analyses you quote. If I had had a different textbook on my shelf introducing these standard results using the standard introductory model, I am sure you would have laid into them equally. To claim that a standard textbook such as Clancy is at odds with the mainstream is to seriously undermine your own position. — Cheers, Steelpillow (Talk) 11:02, 17 December 2014 (UTC)

All of the quotes attributed to Clancy in the "sources" section above are from chapter 5, and all are based on the simplified flow model he uses there. In criticizing this model, I am not "cherry-picking". I'm sticking to the topic under discussion, i.e. the weight these different sources should be given regarding the question of dp/dt in the flow around a lifting foil.

You say that his results from chapter 5 are "consistent" with his results from the more realistic model in chapter 8. That's simply not true with regard to the question we're discussing here. The issue of dp/dt isn't addressed at all in chapter 8. The only part of the book that deals with dp/dt due to lift is chapter 5. So to criticize the model he uses in chapter 5 is not to "selectively quote" him.

The only thing for which Clancy claims the two models yield equivalent results is in the variation of the downwash from the near field to the far field, which does not address the question we're discussing here. The downwash velocity is a local quantity, while the dp/dt we're discussing is an integrated quantity.

In chapter 8 he uses the horseshoe-vortex model for a 3D wing, for which it is said that both the bound vortex and the trailing vortices contribute to the downwash field. But when he says that the downwash in the near field is only half the value in the far field, he's changed gears and he's referring only to the "3D" part of the downwash, the part associated with the trailing vortex system, and omitting the part of the downwash associated with the bound vorticity. I mention these details only to rebut your claim that "This is entirely supported by the classical analyses you quote." No, the analyses I quote deal with integrated dp/dt in a control volume, not with the variation of the downwash velocity downstream. And all but one of them deal with the 2D case, where the downwash velocity doesn't behave at all as Clancy describes for the 3D case anyway.

I'm not criticizing Clancy's book as a whole. I'm criticizing the applicability of the model he uses in chapter 5, and the statements he derives from it, to the question of dp/dt. And yes, I do find that in neglecting the pressure field he's at odds with the mainstream analyses on this particular issue. If you have any actual specific counterarguments to make in this regard, please let us know what they are. J Doug McLean (talk) 22:52, 19 December 2014 (UTC)

• Comments on Chris Waltham's Flight without Bernoulli

In the section titled "A Simple Model", Waltham uses the same kind ot model Clancy uses in sec 5.15, i.e. the model in which the air is affected only within a stream of limited cross-section. He starts with the assumption that the cross-section is rectangular, but he later says that it could just as well be circular. This model is unrealistic for the same reasons I give in my comments on Clancy. Because the model does not represent the flow realistically, it is wrong on some important details, such as dp/dt in the local flow around the wing. Regarding the question of dp/dt, I would not give Waltham the same weight as I would to the classical sources. J Doug McLean (talk) 21:08, 16 December 2014 (UTC)

• Comments on the popular qualitative flow-deflection explanation based on Newton's laws

I have added new section to the sources list: "On the popular qualitative flow-deflection explanation based on Newton's laws". It lists only two sources so far, but more can be found on NASA websites and elsewhere.

I think this kind of thing is the appropriate level of detail for the "Flow deflection and Newton's laws" section, and that we should not include a quantitative dp/dt statement there. J Doug McLean (talk) 21:08, 16 December 2014 (UTC)

• Comments on the "Newtonian" approach

In the "Sources" section I've added a quote from J. D. Anderson describing Newton's theory of lift, based on modeling the flow as a hail of bullets. The flow models used by Clancy and by Chris Waltham are similar to Newton's model in the sense that they assume that only a limited portion of the flow interacts with the foil, and they take no account of a continuum pressure field. Like Newton's theory, these "fire-hose" models are wrong about important details of the flow, such as dp/dt in the near field. As I argue above, Clancy and Waltham should be given less weight as sources on the topic of dp/dt than the classical sources that use a more realistic model. J Doug McLean (talk) 20:03, 20 December 2014 (UTC)

We've created quite a wall of text arguing about the statement, and don't seem to be getting anywhere. Perhaps some pictures can help clarify things.

Here's a diagram of an airfoil generating lift, with the airflow coming in from the left. Ahead of the airfoil in region A the air is accelerated upwards (upwash), in regions B and C the air is accelerated downward, and in region D the air is accelerated upwards as it returns to horizontal flow.

Let's say we define the regions accordingly, where A is the region in front of the foil where dp/dt>0 (upward acceleration) B and C are the regions above and below the foil where dp/dt<0, and D is the region behind where dp/dt>0.

When I encounter the phrase "the air deflected downwards" I parse that to mean the union of regions B and C. Perhaps there's some other interpretation that can be used, but that's what "the air deflected downwards" means to me. If there are other interpretations floating about I'd be happy to hear them.

What can we say about the net momentum transfer of B ∪ C? I do not know of any source that gives this value dp_B∪C/dt. But we can infer how it relates to L by looking at the following sub-region of B ∪ C:

Region E is a tall thin sliver and if we take the limit of dp_E/dt as the height goes to infinity and the width goes to zero we get dp_E/dt = -L. Since this is a proper subset of B ∪ C and all of B ∪ C has negative dp/dt, E must have a lower magnitude of momentum change than all of B ∪ C. That is, for B ∪ C |dp/dt| > |L|. Earlier, Doug claimed to have calculated it to be -1.6L, which sounds plausible.

Now, I'm not suggesting that the above analysis (along with my crude diagrams) go into the article - it's certainly too arcane for the intro section and it's not ready for "prime time" as a later section. But I hope that my fellow editors can read it and understand why I have a problem with saying "the time rate of change of momentum of the air deflected downwards" is equal to the lift. By my interpretation of 'the air deflected downwards' the statement is incorrect. It took me a while to come around to this view - recall that I actually wrote the statement and included it in my re-draft last summer - but I now see that it's problematic. Comments? Mr. Swordfish (talk) 17:21, 22 December 2014 (UTC)

I am having trouble following your summary:

1. The "width" which goes to zero is not defined - the width of what? Is it of the aerofoil chord or just of the column E, or perhaps the span orthogonal to the screen?
2. Whatever the "width" is, I find it hard to justify the statement that "as ... the width goes to zero we get dp_E/dt = −L" (unless you are also implying that as the width goes to zero, L also tends to zero, which is not very helpful).

If you believe what you wrote, then I can indeed understand why you have a problem with the Statement. But more fundamentally, I think you are still confusing a broad statement of the Newtonian principle with an attempt at detailed analysis. The Statement is expressing the Newtonian principle in a few words, while you are seeking to interpret some of those words ab initio, i.e. without prior acceptance of the principle. That is bound to end in tears. — Cheers, Steelpillow (Talk) 14:51, 23 December 2014 (UTC)

Mr. Swordfish presents a clear, detailed analysis of the problem with The Statement. There is one substantive problem with the analysis as presented, which Steelpillow has picked up on, and that is that it doesn't make sense for the width of column E to go to zero. But this problem doesn't invalidate Mr. Swordfish's conclusion.

In his analysis of the tall sliver control volume, Lissaman took the limit as the height goes to infinity, but not as the width goes to zero. With an actual foil in the picture, a proper control-volume analysis of the lift requires that the control volume be wide enough to bracket the projected chord of the foil. I'm sorry if the word "sliver" confused the issue here. I used it to refer to the control volume's proportions, meaning to convey that the control-volume width is small compared to the height, not that it is small compared to the chord. Anyway, even though the width doesn't go to zero in Lissaman's analysis, the pressure difference between the top and bottom vanishes as the height goes to infinity, and the integrated vertical pressure force vanishes, with the result that dp/dt = -L, independent of the width, as long as the width is kept finite.

For E to be a proper subset of B ∪ C, and to not include part of A ∪ B, the width of E must be restricted compared to what Lissaman assumed, with the vertical boundaries pushed up against the leading and trailing edges of the foil. But Lissaman's analysis still applies, and dp/dt = -L for E.

Steelpillow's point 3 is mistaken. He says "E has a smaller magnitude which means that it is closer to zero and is therefore 'greater than' −L." No, E is the subset with dp/dt =-L, so its dp/dt cannot be "'greater than' −L.". Mr. Swordfish's analysis is correct.

Ah, yes, thank you for pointing that out. Too much Christmas spirit in my glass, I fear. I have now deleted that item. — Cheers, Steelpillow (Talk) 22:59, 23 December 2014 (UTC)

Steelpillow is also mistaken when he says "But more fundamentally, I think you are still confusing a broad statement of the Newtonian principle with an attempt at detailed analysis." No, dp/dt = -L for "the air" can be established as a valid "statement of the Newtonian principle" only after a detailed analysis has shown that -L is indeed the resultant force acting on "the air". And analysis has only shown this to be the case for the tall sliver control volume.

Mr. Swordfish's analysis above clearly shows that dp/dt = -L is false for "the air deflected downward". However, we have no citable source for this argument. On the other hand, even if we thought dp/dt = -L was true for "the air deflected downward", we have no citable source that supports including the word "deflected". To stay within what our sources support, our only choice is The Original Statement from the AAPT paper, without the word "deflected".

I agree that The Original Statement in unapologetic form is unacceptably vague. If we include it in the intro section, we must, at a minimum, also specify that the only definition of "the air" for which it's been shown to be true is "a region that is very tall compared to its width", citing Lissaman. As I said long ago, I think the best option is not to make any quantitative statement in the intro section and to discuss the quantitative momentum balance in a new later section.

I'd like to see something like Mr. Swordfish's ABCDE discussion in this new section, but I know of no citable source for it. From the sources I know of, I think the best we can do is to describe the results for the circular and rectangular (tall, square, and flat) control volumes in free air, and the atmosphere with a ground plane. Here are two possible diagrams I've made for the purpose, and I've started drafting candidate text to go with them.

If we mention the "fire-hose" models at all (Clancy, Waltham), it would only be to point out their deficiencies relative to the more rigorous analyses. I'm proposing that it be a new subsection titled "Analyses of the integrated momentum balance in lifting flows", under "Mathematical theories of lift", just after "Circulation and the Kutta-Joukowski theorem". J Doug McLean (talk) 22:36, 23 December 2014 (UTC)

This is just the same old same old. The article is not going to be amended to support a view unsubstantiated by reliable sources. — Cheers, Steelpillow (Talk) 22:59, 23 December 2014 (UTC)

There is one substantive problem with the analysis as presented ... it doesn't make sense for the width of column E to go to zero. Thanks. I have struck that language.

I look forward to seeing the draft section. Agree that anything we put into the article must have a citable source. Mr. Swordfish (talk) 00:46, 25 December 2014 (UTC)

Mr. Swordfish, I suggest you think about how dt should be handled in these calculations. You may find Lanchester §3 helpful.

When making content decisions, we should be guided more by RS than by OR. The novel, unpublished analysis above will not help anyone understand the relevant physics. If you haven't already, I recommend reading Lanchester §112 for a straightforward explanation. Burninthruthesky (talk) 14:58, 27 December 2014 (UTC)

At this point I would like to ask both Burninthruthesky and Steelpillow to elaborate on what they think "the air deflected downward" means. I think we are in agreement that it doesn't mean the entire atmosphere since dp/dt of the entire atmosphere is zero. So, what does "the air" mean? I've given my interpretation and Doug has given several possible reasonable interpretations (of which only one makes the statement true). What's yours? And is it likely that our readers will have the same interpretation?

Agree that we should value RS over OR discussion on the talk page, and I'll keep trying to chase down a copy of Lanchester and read sec 112. Mr. Swordfish (talk) 21:28, 27 December 2014 (UTC)

Since the Statement is just the application of Newton's laws to lift in words, in this context it means, "the air deflected downwards in reaction to the lift force." Not any other air deflected downwards because of some vortex or some distant pressure distribution or some clever analysis or whatnot. It is simply affirming that if we apply F=dp/dt to L, then there is a mass of air whose dp/dt is in reaction to L. Our clever analysis can then identify the location of this mass for us, and different analytical models will identify different locations (e.g. Clancy's firehose). Crucially, it is not saying that this is the only approach, nor even the best approach, just that it is an approach. Other models based on other approaches, say on pressure, will not even yield dp/dt=L because they have already accounted for much or all of L some other way. The sources can then indicate the due weight that each deserves. This is how pretty much every textbook treats it, and I am not aware of widespread misinterpretation among engineering students. I am confident that our readers will be no different. One can really only misinterpret it once one has gained a good deal of detailed knowledge, well beyond the introductory stage at which it is appropriate. — Cheers, Steelpillow (Talk) 22:10, 27 December 2014 (UTC)

Apologies for taking so long to reply.

I don't have any fundamental disagreement with your position. I do think Doug has a point (made elsewhere) that defining "the air" as the region that makes the statement true is somewhat circular, but the fact remains that there is such a region and I'm comfortable eliding over some of the details in the introductory section. To that end, I've prepared a draft in my user space that may help move us towards consensus. I'll introduce that in a new thread. Mr. Swordfish (talk) 19:56, 7 January 2015 (UTC)

I have posted a proposed revised version of the article in my sandbox User:J_Doug_McLean/sandbox. Changes from the current version are limited to two places:

1) Under "Flow deflection and Newton's laws" I have removed the quantitative statement about momentum and done a bit of rewording of what remains to be sure that both the second and third laws still get their due.

2) At the end of "Mathematical theories of lift" I have added two new subsections: "Analyses of the integrated momentum balance in lifting flows" and "Newtonian theories of lift".

Everything I've included has a citable source and is presented, I think, from a neutral point of view.

I think removal of The Statement is best for the following reasons:

1) In this part of the article and at this level ("Simplified physical explanations..."), the flow deflection explanation is better off without it. This explanation is usually presented in its qualitative form anyway.

2) Without the qualification that it's only been found to be true for the tall sliver, The Statement is open to misinterpretation. Steelpillow and Burninthruthesky still seem to think that it isn't, but I think their confidence that the typical reader will know how to interpret it correctly is unjustified. I think it's just too easy for an uninitiated reader to assume that "the air deflected downward" could refer to the atmosphere as a whole or at least to some sufficiently large subset of it. The atmosphere as a whole may be a "nonsensical" assumption as Burninthruthesky called it, but I wouldn't expect the typical reader to know that unless we tell him. And I certainly don't expect the typical reader to realize that it's true only for a particular shape of region.

3) A general, unapologetic "dp/dt = -L" isn't consistent with what the mainstream literature says about dp/dt.

The two new sections are pretty self-explanatory. I included a paragraph on Newton's bullet model because I think it's interesting in its own right, it had an impact on early assessments of the practicality of heavier-than-air flight, and it helps put the "fire hose" models in perspective, which I also included under "Newtonian theories".

Looking forward to comments and suggestions.

J Doug McLean (talk) 23:53, 30 December 2014 (UTC)

First of all I would like to thank @J Doug McLean: for all the hard work that has gone into this. The only real issue I have with any of it is the well-worn one we are all familiar with.

Given all the quotations we so carefully collected above, quite how anyone can maintain that the mainstream sources do not support the momentum statement - and right at the introductory stage at that - is beyond me. Mainstream sources do include it, and even mandate it there. Ours is not to reason why or to sanitise it out of the article. It is there in the article, it is reliably cited, and there it must stay. Doug McLean makes some other minor textual changes to this section which are generally good.

The bulk of the new section on "Analyses of the integrated momentum balance in lifting flows" is good, though there is a certain residual defensiveness in the last few sentences which can probably simply be omitted. Also, I would shorten the heading to just "Integrated momentum balance in lifting flows".

The next section - the critique of the momentum model - is useful as far as it goes. However I think it needs a balancing critique of the other simple model we introduce, viz. the pressure model. These critiques could better introduce the whole section on "Mathematical theories of lift" rather than conclude it. Alternatively, they could be confined to their respective introductory subsections on "Limitations of ..." — Cheers, Steelpillow (Talk) 10:52, 31 December 2014 (UTC)

I agree with Steelpillow there is no justification for removing the existing momentum statement. I'm also grateful for progress on improving the article.

One minor point - I haven't been able to find Shapiro to reference the momentum equation, but I have found this page which says (in abbreviated terms):

F = dM/dt = F_B + F_S

I understand that in steady flow, F_B = 0, so F = F_S.

In the proposed new section, I read the last two sentences of the first paragraph as F_S = F_B. Is this the intended meaning? Burninthruthesky (talk) 18:06, 1 January 2015 (UTC)

I have now incorporated what I believe to be the bulk of the proposal into the article, save for two parts: I retained the Statement along with its citations, and I have not copied across the subsection on Newtonian theories of lift because I am not yet sure where to put it. — Cheers, Steelpillow (Talk) 14:01, 4 January 2015 (UTC)

I still don't have an answer to my question above. A Google search for "momentum theorem for a control volume" brings back mainly references to Reynolds transport theorem. Is this what is being described? Burninthruthesky (talk) 14:58, 4 January 2015 (UTC) Here is an actual quote from Shapiro:

Eq. 1.13 is usually called the momentum theorem and states that the net force acting instantaneously on the fluid within the control volume is equal to the time rate of change of momentum within the control volume plus the excess of outgoing momentum flux over incoming momentum flux.

— Shapiro

Also, Shapiro's Eq 1.15 is identical to Eq 3.42 in the page I linked above. Burninthruthesky (talk) 17:05, 4 January 2015 (UTC); edited 17:17, 4 January 2015 (UTC) I've left "disputed" tags on these two sentences. I am disappointed they were added to the article despite my unanswered question. Please will someone with more specialist knowledge than myself correct them? Burninthruthesky (talk) 17:36, 4 January 2015 (UTC)

My apologies. I took the citation of Shapiro Section 1.5 at its word, as I was not able to check it and you had referred to it as a "minor point". I do think we need to be clear whether each case is allowing a dynamic flow where the net rate of momentum change within the control volume is non-zero, or restricted to a steady-state flow where the net rate of momentum change within the control volume must be zero. — Cheers, Steelpillow (Talk) 22:17, 4 January 2015 (UTC)

Thank you, and I'm sorry I didn't make myself clear. By "minor", I meant the content probably needed correcting before release, as opposed to not being inherently useful.

I think a link to Reynolds transport theorem may be useful, as I undertsand this momentum theorem directly follows from it.

In this case, I would be a little uncomfortable with adding material to the encyclopedia which I only learned myself yesterday, in the course of verifying another's work. Burninthruthesky (talk) 07:44, 5 January 2015 (UTC)

First to Burninthruthesky's question: Is F_S = F_B the intended meaning of the last two sentences of the first paragraph of the new section? No. That interpretation isn't consistent with what the variables represent.

F_B is the body force acting throughout the volume of the fluid, which for an electrically neutral fluid is just gravity. In aerodynamics we usually neglect both gravity and the background hydrostatic pressure gradient that goes with it, under the assumption that they cancel each other. Thus F_B = 0 results from neglecting gravity. Whether the flow is steady or unsteady has nothing to do with it.

F_S is the sum of the surface forces (pressure and viscous shear stress) acting on the control volume boundaries. In the airfoil analyses I've cited it includes both the -L' imposed by the foil and the integrated pressure force on the outer boundary. The volume integral I refer to in the sentences in question is the integral of the material rate of change (material derivative) of momentum in the interior, which is not at all the same thing as F_B. Note that the two integrals on the RHS of equation 3.42 of this page represent the volume- and surface-integral parts of dM/dt. The fact that dM/dt has two parts has nothing to do with the decomposition of F into F_B and F_S, and the first term on the RHS is not equal to the first term on the LHS.

So yes, F_B = 0, so that F = F_S, but it's because we neglect gravity, and not because the flow is steady. And no, F_S = F_B does not follow, and is not the intended meaning of the last two sentences of the first paragraph of the new section. These two sentences follow from the fact that the first integral on the RHS of Shapiro's Eq 1.15 is zero for steady flow, and that the entire RHS represents the same quantity as the RHS of the first equation (unnumbered) of section 1.5, i.e. the instantaneous time rate of change of the momentum of the material system that occupies the control volume at time t, commonly referred to as the material derivative. The two sentences don't "need correcting". They are consistent with Shapiro, and the "disputed" tags should be removed.

The Reynolds transport theorem as described in the linked article is similar to Shapiro's Eq 1.15, but it uses d/dt to represent a more general kind of time derivative, the total time derivative for some quantity contained within the volume as it evolves in time, including the effects of movement of the boundaries of the volume in the general case. The result is formally the same as Shapiro's only for the special case in which the boundaries of the volume move with the flow as described under "Form for a material element". I think this article is unlikely to help anyone understand Shapiro because it provides less supporting detail than Shapiro does.

Steelpillow wrote:

"I do think we need to be clear whether each case is allowing a dynamic flow where the net rate of momentum change within the control volume is non-zero, or restricted to a steady-state flow where the net rate of momentum change within the control volume must be zero."

Are you saying that The Statement dp/dt = -L can be true only in unsteady flow? That would make no sense. Actually, all of the sources we list that bear on the dp/dt issue analyze the flow in the frame of the foil and assume the flow is steady in that frame. But the rate of change of momentum within a control volume that's stationary in that frame can still be non-zero in Shapiro's sense of the material derivative. And although Chris Waltham and the AAPT don't say so explicitly, dp/dt in their versions of The Statement has to be referring to the material derivative. Otherwise, if it referred to the conventional partial derivative with respect to time at a fixed location, it would be zero for steady flow, as you say, and The Statement would be false for any control volume. And even I'm saying that there's one control volume for which The Statement is true. J Doug McLean (talk) 06:40, 7 January 2015 (UTC)

I am certainly not saying that, as you say that would make no sense. Equations applicable to dynamic momentum distribution will presumably differ from the simpler equations required for steady state. Some of the remarks posted or referenced appeared to encompass the dynamic situation, and that concerned me. For example your new material contains this: "The momentum theorem states that the integrated force exerted at the boundaries of the control volume (a surface integral), is equal to the integrated time rate of change (material derivative) of the momentum of fluid parcels passing through the interior of the control volume (a volume integral).[under discussion] For a steady flow, the volume integral can be replaced by the net surface integral of the flux of momentum through the boundary." Grammatically, the addition of the caveat "For a steady flow" to the second sentence would suggest that the first sentence encompasses unsteady, aka dynamic, flow. Since the momentum theorem is not yet properly defined and cited, I cannot judge whether this is so. Some other materials left me similarly concerned. I have no knowledge of such dynamic situations, nor any references on my bookshelf, or I would be able to comment more sensibly. — Cheers, Steelpillow (Talk) 12:14, 7 January 2015 (UTC)

I see my assumption that each term on the LHS of (3.42) as discussed equates to the same term on the RHS doesn't necessarily follow from what is written, but that's how I read it. Anyway, this equation shows the total force is equal to a volume integral plus a surface integral and it requires some calculation to follow your argument. In shorthand (with the integral contents omitted), Shapiro's Eq 1.15 is ∑F = ∂/∂t ∫_c.v. + ∮_c.s.

As you say, In steady flow the first RHS term disappears, so
∑F = ∮_c.s.

The first equation of 1.5 is a statement of Newton II in the x-direction. In general Newton II is
∑F = d/dt (mV)

So
d/dt (mV) = ∮_c.s.

I'm starting to think this wording may not be incorrect, so I have changed the tags. However, Shapiro 1.5 doesn't directly state any of the three equations above.

The wording in question is:

The momentum theorem states that the integrated force exerted at the boundaries of the control volume (a surface integral), is equal to the integrated time rate of change (material derivative) of the momentum of fluid parcels passing through the interior of the control volume (a volume integral). For a steady flow, the volume integral can be replaced by the net surface integral of the flux of momentum through the boundary.

The idea that either of the relationships derived above for steady flow conditions are "The momentum theorem" is not consistent with any of the sources I have seen.

I don't see where Shapiro says that d/dt (mV) is the "material derivative" or that this term involves a volume integral.

Your assertion that in the discussed (3.42), "the first term on the RHS is not equal to the first term on the LHS" implies that neither term on the RHS is equal to the corresponding term on the LHS. Yet the quotation above seems to imply the opposite: i.e. the second term on the RHS (a surface integral) is equal to the surface forces, "the integrated force exerted at the boundaries of the control volume" and "the net surface integral of the flux of momentum through the boundary".

Anyway, this discussion has already taken up far more of my time than I wish. I am not going to embark on an undergraduate course in Fluid Mechanics just so I can continue to protect this article from dubious and misleading information, as I have done for many months now. Burninthruthesky (talk) 12:09, 7 January 2015 (UTC); last edited 06:54, 9 January 2015 (UTC)

Also, this page says,

Physically, the linear momentum equation states that the sum of all forces applied on the control volume is equal to the sum of the rate of change of momentum inside the control volume and the net flux of momentum through the control surface.

Burninthruthesky (talk) 15:46, 7 January 2015 (UTC)

From a reader's perspective, all he needs to know in this context is that in steady flow, momentum changes to air passing through the control volume can be accounted for at its boundaries. I think a simpler form of words would be more understandable. Burninthruthesky (talk) 07:43, 8 January 2015 (UTC)

Looking at other sources, as far as I can tell the momentum theorem states that the integrated rate of change of momentum within the control volume equals the sum of the integrated forces acting on the internal volume plus the integrated forces acting on the surface. (e.g. George Emanuel; Analytical Fluid Dynamics, Second Edition, pp447-448 [1]) That is rather different from the definition currently given in the article. One can add that for a steady state flow where the force acting on the interior is zero, the integrated rate of change of momentum within the control volume equals the integrated forces acting on the surface, like this:

The momentum theorem states that the integrated rate of change of momentum within the control volume equals the sum of the integrated forces acting on the internal volume plus the integrated forces acting on the surface.[cite] For a steady state flow where the force acting on the interior is zero, the integrated rate of change of momentum within the control volume simply equals the integrated forces acting at the boundary.

I would be happy for this to replace the "wording in question" quoted above. Any objections? — Cheers, Steelpillow (Talk) 16:35, 9 January 2015 (UTC) [Updated — Cheers, Steelpillow (Talk) 16:59, 9 January 2015 (UTC)]

Thanks for suggesting a new wording and for the further reference. All the sources I've seen have presented the momentum theorem in the same form [Shapiro (1.15), Emanuel (14.3)]. I see this equates a force to the sum of volume integral and surface integral components of momentum, but I'm not sure how to express it accurately in words. Burninthruthesky (talk) 07:01, 10 January 2015 (UTC); edited 07:06, 10 January 2015 (UTC)

If the suggested wording can be reliably cited, I've no objection to its addition to the article. Burninthruthesky (talk) 11:55, 10 January 2015 (UTC)

Specific wording does not need to be cited verbatim (or we would fall foul of plagiarism), however their meaning needs to be clear and that meaning needs to be cited properly. This is what I have tried to do. — Cheers, Steelpillow (Talk) 12:35, 10 January 2015 (UTC)

Without plagiarising, we must somehow present the facts which are directly supported by the sources. Does Emanuel say the Momentum Theorem is:

• the splitting of momentum into surface and volume components of force (14.1)
• the splitting of momentum into surface and volume components of momentum (14.2)
• the splitting a force into surface and volume components of momentum (14.3)
• something else derived later?

I'm pretty certain some of those bullets are not the correct answer, but I'm not sure which is. Burninthruthesky (talk) 13:11, 10 January 2015 (UTC)

Emanuel gives the equation of integrals. I paraphrased that equation in words. The LHS is the momentum-change integral, the RHS is the sum of the two force integrals, effectively your 14.1. One could write the equation, which is not plagiarism but equally is not especially helpful unless one explains it in words as well. It would be better included in an article on fluid dynamics in general. — Cheers, Steelpillow (Talk) 13:31, 10 January 2015 (UTC)

I was attempting to describe Emanuel's 14.1, not make my own. I agree the suggested text above is also a verbal description of that equation. My question is whether that equation is in fact "The Momentum Theorem", since Emanuel describes it as "Newton's second law". Burninthruthesky (talk) 14:49, 10 January 2015 (UTC); edited 15:39, 10 January 2015 (UTC)

Ah, silly me. My apologies. I'll have to find time to digest Emanuel a bit more carefully. We also have 14.9 to consider. — Cheers, Steelpillow (Talk) 16:56, 10 January 2015 (UTC)

A lot of issues to deal with here. To begin: Burninthruthesky wrote:

"I don't see where Shapiro says that d/dt (mV) is the "material derivative" or that this term involves a volume integral."

Good point. He doesn't explicitly use the term "material derivative", though that is the widely accepted term for the kind of time derivative he refers to as d/dt(mV). He also doesn't explicitly say the term involves a volume integral, but he does define it as "the time rate of change of the total x-momentum of the system", which for non-uniform flow can be quantified only in terms of a volume integral. Shapiro's notation is confusing in this regard, and Emanuel would be a better source to cite. The RHS of his eq 14.2 is the same quantity as Shapiro's d/dt(mV). It is clearly a material derivative (for which the capitalized D/Dt is the common notation), and it is clearly a volume integral. So I think my wording is correct and well supported by Emanuel, just not well supported by Shapiro. Thanks for pointing this out.

Burninthruthesky wrote:

"The idea that either of the relationships derived above for steady flow conditions are "The momentum theorem" is not consistent with any of the sources I have seen."

I don't understand your basis for saying this. Your relationship
∑F = ∮_c.s. is identical to Shapiro's eq 1.15, for the case of steady flow, where the first term on the RHS is zero. And this is the final equation in a section headed "Working Form of Momentum Theorem".

Burninthruthesky wrote:

"Your assertion that in the discussed (3.42), "the first term on the RHS is not equal to the first term on the LHS" implies that neither term on the RHS is equal to the corresponding term on the LHS. Yet the quotation above seems to imply the opposite: i.e. the second term on the RHS (a surface integral) is equal to the surface forces. "

You're right about what is implied, but that doesn't mean it's contradictory. The two second terms are equal only in the special case in which the flow is steady, for which the first term on the RHS is zero, and the body force (the first term on the LHS) is neglected, as it usually is in aerodynamics. This is the special case used in all of the airfoil analyses.

Burninthruthesky wrote:

"From a reader's perspective, all he needs to know in this context is that in steady flow, momentum changes to air passing through the control volume can be accounted for at its boundaries. I think a simpler form of words would be more understandable."

This is also a good point. I originally included the wording about the volume integral of the material derivative because that's the form of the momentum theorem that relates to the "time rate of change of momentum of the air" in The Statement in the intro section, and I think I had the editing community in mind more than the general reader. I agree that the simpler form is better for the article, and I've made the change in my sandbox User:J_Doug_McLean/sandbox.

Steelpillow proposed replacing "the wording in question" with the following:

"The momentum theorem states that the integrated rate of change of momentum within the control volume equals the sum of the integrated forces acting on the internal volume plus the integrated forces acting on the surface.[cite] For a steady state flow where the force acting on the interior is zero, the integrated rate of change of momentum within the control volume simply equals the integrated forces acting at the boundary."

There are two reasons this isn't satisfactory:

1) As I explained before, setting the body-force term ("the sum of the integrated forces acting on the internal volume") to zero comes from neglecting gravity and has nothing to do with whether the flow is steady or unsteady.

2) This version doesn't mention the surface-integral form for the momentum term, which is the form used in the airfoil analyses that follow.

Burninthruthesky asks which of the equations is actually the "momentum theorem". I think a reasonable reading of the sources is that the "momentum theorem" can be expressed in several forms and that it can be any of the equations that relate the integrated force to the integrated rate of change of momentum and/or momentum flux. In Emanuel that would be eq 14.1, 14.3, 14.4, or 14.9. It is not eq 14.2, 14.5, 14.6, 14.7, or 14.8 because they deal with forces or momentum changes separately, not with the second-law relationship between them.

In light of the above discussion I have changed the words in question to the simpler form suggested by Burninthruthesky, and cited both Shapiro and Emanuel. See in my sandbox User:J_Doug_McLean/sandbox. J Doug McLean (talk) 00:19, 11 January 2015 (UTC)

I take on board much that has been said, and apologise again for looking at the wrong equation. But I am still puzzled by a couple of points in Doug McLean's latest proposal. It says, "For a steady flow, the momentum theorem states that the integrated force exerted at the boundaries of the control volume is equal to the integrated flux of momentum through the boundary." But in explaining his equation 14.3 Emanuel remarks, "the left side represents the sum of all the applied forces that act on the fluid inside the control volume." and later in explaining 14.9, "the force is therefore provided by a volumetric integral plus an integral over a stationary surface." i.e. Emanuel's generic analysis of fluid flows does not support two aspects of the new version:

• Emanuel describes the force as acting within the control volume, McLean as acting at its boundary.
• Emanuel does not observe that in air, gravity may be ignored and the momentum volume integral is zero.

I am not saying that Doug's analysis is necessarily wrong, only that Emanuel does not appear to support it fully. Does Shapiro? — Cheers, Steelpillow (Talk) 13:28, 11 January 2015 (UTC)

That is a good question. There is also the question of whether it is correct to refer to a degenerate case of Shapiro's eq 1.15, with the first RHS term set to zero for steady flow, as "the momentum theorem". By way of comparison, if one described a relationship derived from Newton's second law where F = 0, it would look very much like Newton's first law.

If I was mistaken to say, 'The idea that either of the relationships derived above for steady flow conditions are "The momentum theorem" is not consistent with any of the sources I have seen', I ask J Doug McLean to specify where the evidence is. Failing that, he may wish to clarify or strike out his comment. Burninthruthesky (talk) 09:37, 13 January 2015 (UTC)

After looking again, I don't see anything in Shapiro 1.5 which says that the first RHS term of Eq 1.15 is zero in steady flow, although I've no doubt it's true. I don't see anything saying gravity may be excluded from the sum of body forces. In fact the paragraph headed BODY FORCES includes "gravitational attraction" in the description. I don't see Shapiro make any attempt to combine those terms in a single equation as Emanuel (14.4) does. I stand by the comment I quoted. Burninthruthesky (talk) 16:37, 13 January 2015 (UTC)

You're both questioning whether my summary of the momentum theorem is correct and uses the term correctly, and whether it is fully supported. First, let's look at the apparent contradiction between me and Emanuel, as raised by Steelpillow:

"Emanuel describes the force as acting within the control volume, McLean as acting at its boundary."

There's actually no contradiction here. Note that Emanuel defines the RHS of eq 14.1 as "the vector sum of the applied forces that act on the system, which here is the fluid inside V." The force acting on the boundary (the second integral on the RHS) is part of that sum, along with the body force acting throughout the interior. So Emanuel considers the force acting at the boundary to be part of the total force acting "on the fluid inside V". Then if you neglect gravity, the first integral on the RHS (the volume integral) is zero, and only the second integral (the force acting at the boundary) remains. So my description is identical to his when gravity is neglected.

True, Emanuel doesn't say that gravity can be neglected, and neither does Shapiro's section 1.5, but gravity is neglected in every application of the momentum theorem to aerodynamics that I've ever seen, including the ones I cite in the article. Clancy's firehose analysis also neglects gravity. And in the rest of Shapiro's book, when he uses Newton's second law, he leaves the gravity force out without explaining why. So does every other aerodynamics book on my shelf, except Batchelor. On p. 176, in a section headed "Modification of the pressure to allow for the effect of the body force", Batchelor shows that gravity does not affect the dynamics of a constant-density flow because the body force (the weight of a fluid parcel) is canceled by a background gravitational-hydrostatic pressure gradient that always accompanies it. Thus neglecting both the body-force term and the gravitational-hydrostatic part of the pressure gradient is rigorously justified for constant-density flow.

So neglecting the effect of gravity on the flow is something everyone does in aerodynamics applications, and most take it for granted. In my quick check of the sources, Batchelor is the only one who takes the time to justify it rigorously. Neither Shapiro nor Emanuel mentions the simplified form of the momentum theorem with the gravity terms omitted, so I see now that it's misleading for me to cite them when I state the simplified form. I'll propose a fix for this problem below.

Now to the matter of steady flow. Burninthruthesky wrote:

"I don't see anything in Shapiro 1.5 which says that the first RHS term of Eq 1.15 is zero in steady flow".

True, he doesn't say it in 1.5. He defines steady flow in 1.2 as "a condition where at each point in space there is no variation of any property with respect to time", and writes it as the partial derivative of any property with respect to time equals zero, using density as an example. So I'd say that Eq 1.15 with the first RHS term set to zero for the case of steady flow is fully supported by Shapiro.

On this same topic Burninthruthesky also wrote:

"If I was mistaken to say, 'The idea that either of the relationships derived above for steady flow conditions are "The momentum theorem" is not consistent with any of the sources I have seen', I ask J Doug McLean to specify where the evidence is."

I said that I didn't understand your basis for saying this because it seemed to me at the time, and it still does, that your relationship
∑F = ∮_c.s. is identical to Shapiro's eq 1.15, for the case of steady flow, and is thus consistent with Shapiro. This version of the equation requires only steady flow; it doesn't require neglecting gravity. So I think that in addition to being consistent with Shapiro, it is fully supported, though as I point out above, you have to look in section 1.2 in addition to 1.5. The short answer to your question is that the evidence regarding the unsteady flow term is in Shapiro.

Whether it is correct to refer to it as "the momentum theorem" is the next question. Burninthruthesky wrote:

"There is also the question of whether it is correct to refer to a degenerate case of Shapiro's eq 1.15, with the first RHS term set to zero for steady flow, as "the momentum theorem". By way of comparison, if one described a relationship derived from Newton's second law where F = 0, it would look very much like Newton's first law."

In general I think it's fair to use the name of a theorem or law to refer to a special case, provided you also make it clear what special case you're talking about. To use your example, I see nothing wrong with saying "For F = 0, Newton's second law states that dp/dt = ma = 0". Yes, it looks like the first law, but nothing logically forbids having a special case of one law look like another law. And in the case of the "momentum theorem", the special cases don't have their own separate names anyway, as far as I know. So I'd say that special cases of the momentum theorem are still examples of "the momentum theorem".

A proposed fix: I'm confident that my summary of the momentum theorem is correct for the case of steady flow when gravity is neglected. And it's well supported, except for the problem, as I discussed above, that you need to look beyond Shapiro and Emanuel, e.g. to Batchelor, to find formal justification for neglecting gravity. That said, however, the fact is that the sources I'm citing for the momentum analyses all use the form of the momentum theorem in which gravity is neglected. So I'm not really on the hook to justify it; I really only have to observe that that's the form they use. I've moved the Shapiro and Emanuel citations and changed the wording to reflect this in my sandbox User:J_Doug_McLean/sandbox. I think this addresses the issues you've raised here. Thank you for raising some interesting questions. I also propose simplifying the introductory discussion of control volumes by eliminating the mention of the momentum volume integral and the material derivative (first paragraph), and providing further clarification of the lifting flow results (new fourth paragraph). J Doug McLean (talk) 20:46, 23 January 2015 (UTC)

Regarding the proposed deletion of The Statement, I see nothing in Wikipedia policy that says that something "must" remain in an article just because it's already there and has a citable source. Nor do I see anything that says that removal of something that has a citable source requires a direct and citable refutation. No, it looks to me like we as editors are free to make changes based on weighing the sources available to us, even if those sources don't explicitly refer to each other. So it appears to me that Steelpillow's contention that The Statement "must stay" is unfounded. If I'm wrong, show me the specific policy wording.

When Steelpillow insists that "mainstream sources" support The Statement, he's being unduly selective. Yes, some of the sources support The Statement in unapologetic form, but all of the sources taken together, on balance and weighted according to the quality of their analyses, clearly show that The Statement is true only with qualifications. If we present The Statement without the qualifications, we're presenting a biased and misleading impression of what sources on this topic actually say.

The only published analyses we have that support The Statement in unapologetic form are based on the "firehose" model for the flow (Chris Waltham and Clancy). In my posts of 17and 19 December I presented detailed arguments as to why these sources should be accorded less weight than those that use the classical model based on uniform flow plus a vortex. I invited specific counterarguments and so far there have been none.

Likewise, Mr. Swordfish invited Burninthruthesky and Steelpillow to elaborate on what they think "the air deflected downward" means. Only Steelpillow responded, and his answer amounted to "It means whatever it has to mean to make The Statement true, depending on what flow model you prefer". That's an unsatisfactory answer in general, but especially when one of the models we're considering (the "firehose") assigns an unrealistic spatial distribution to dp/dt, as Clancy himself admits.

This is not a question of a choice between a "momentum model" and a "pressure model", as a matter of style or personal taste. No, a proper application of the momentum theorem requires that all of the forces exerted on the air be taken into account, including the pressure force. The "firehose" analyses ignore the pressure force, while the classical analyses properly include it. Thus in terms of the basic physics, these two types of analysis are not of equivalent quality. Steelpillow suggests that the new section on Newtonian models "needs a balancing critique of the other simple model we introduce, viz. the pressure model." No, there is no "balancing" of that kind to be done. The classical model is not just a "pressure model". It accounts for both momentum and pressure, and assigns them their realistic locations in the field. It has no faults that rise to the same level as the faults of the "firehose" model. If you disagree with this assessment, please state your specific counterarguments.

The classical analyses (Durand, Batchelor, and Lissaman) clearly deserve more weight than the "firehose" analyses. And they clearly show that The Statement in unapologetic form is misleading. Thus it should either be deleted or properly qualified. This is not "a view unsubstantiated by reliable sources". It is a conclusion supported by an appropriately weighted and balanced consideration of all of the sources. Nor does it constitute synthesis, though I would also argue that the (WP:SYNTH) policy doesn't apply to a decision to omit something.

I agree with shortening the heading to "Integrated momentum balance in lifting flows". Regarding the overall organization of "Mathematical theories of lift", I think it's best just as it is, starting with the basic principles, followed by the predictive theories (the ones that actually predict lift starting with the airfoil shape). Those that merely relate one thing to another but don't make actual predictions, such as the Kutta-Joukowski theorem, the momentum-balance analyses, and the Newtonian theories, are not theories at the same level as the predictive theories and should not precede them. This is an ordering that befits an encyclopedia article as opposed to a textbook.

The "Newtonian theories of lift" belongs where I proposed putting it, at the end of Mathematical theories....". None of it should be moved to the introductory section.

J Doug McLean (talk) 06:40, 7 January 2015 (UTC)

Doubters of Wikipedia's policies and guidelines may find it useful to read WP:REMOVAL and, on the matter of neutrality, WP:NPOV. — Cheers, Steelpillow (Talk) 12:14, 7 January 2015 (UTC)

Re-reading the proposed section on Newtonian theories of lift, it is really two unconnected parts. The first is a summary of early theories and would go better as the start of a "Historical development" of theories of lift, the second is a critique of the firehose model and while that might be a useful topic to work in somewhere, frankly I find the treatment presented to be unbalanced. Neither part is fit to be moved into the present article as it stands, nor do I intend to engage with the author on their improvement. — Cheers, Steelpillow (Talk) 12:47, 7 January 2015 (UTC)

Your feedback that you don't see the connection between the two parts of "Newtonian theories...." is useful. Thank you. I have revised the second part to make the connection clearer. See User:J_Doug_McLean/sandbox. Beyond that, I have already explained why I struck the balance I did in my criticism of the firehose model. If you have specific suggestions for improving the balance, let's hear them. Simply calling the treatment "unbalanced" isn't helpful.

You are the only one who has expressed opposition to including "Newtonian theories...." in the article, so at this point yours would seem to be a minority view. Does anyone else oppose my adding this new subsection? J Doug McLean (talk) 00:26, 11 January 2015 (UTC)

Yes. Burninthruthesky (talk) 08:08, 12 January 2015 (UTC)

To explain the message a little more clearly. The first part is not current but historical. It has no place in an exposition of current theory. The second part discusses a model still to be found in the text books. No matter how one wraps words around them or applies other creative fixes, for encyclopedic purposes they are not linked. Rather, the flavour of your discussion - and of your response to my considered rejection - makes it clear that your purpose is to push your PoV that the Newtonian approach is flawed in comparison to your favoured approach, and that is your motivation for linking them. That PoV is not backed up by the sources. "Verifiability, not truth" is an old watchword of Wikipedia and no amount of yardage in filling this talk page is going to change that. I have absolutely no interest in conrtibuting any more than necessary to that yardage, in order to terminate it. If you wish for wider consultation on WP:VERIFICATION and its application here, then there are plenty of avenues to follow. Flogging a dead horse here is not one of them. Poor User:Burninthruthesky has suffered enough and I too have a life. If this endless charade persists I shall take it higher to seek a topic ban on this talk page. I trust that all is now clear. — Cheers, Steelpillow (Talk) 10:47, 12 January 2015 (UTC)

Steelpillow, I do not think this hostile tone and threats is conducive to building consensus. I understand the frustration with a topic that has gone on for too long without resolution, but it is imperative that we keep cool heads and refrain from impugning the motives of fellow editors. Threatening a topic ban over a good-faith disagreement over emphasis is over the top. Please consider retracting those comments.

Regarding the section on "Newtonian theories..." My take is that it's not the place of this article to go into every historical failure. It is true that Newton tried to calculate lift using a flawed model and produced inaccurate results. Unfortunately, some authors use this to confuse things - Newton's (flawed) model and using Newton's laws to explain lift are two distinct things with similar names. If we are going to address Newton's (flawed) model we should be clear to make that distinction, and my take is that the best place for it would be to take a page from NASA and treat it alongside the Equal Transit Time (see http://www.grc.nasa.gov/WWW/k-12/airplane/wrong2.html ) under the heading Alternative explanations, misconceptions, and controversies.

Although we shouldn't go into every historical failure, my feeling is that the ETT is sufficiently widespread that we would be remiss in not including it in the article. I'm not so sure about the "Skipping Stone" explanation, so I can go either way on whether we should include such a subsection.

Regarding the second paragraph, I've managed to borrow on a copy of Clancy and have read the short section 5.15 on page 76 introducing what is sometimes called the "firehose model". To my eyes, it just looks like an example of a spherical cow analysis. I don't think it is sufficiently noteworthy that we need to treat it in the article. Mr. Swordfish (talk) 19:18, 12 January 2015 (UTC)

My thoughts and feelings on the matter are very similar to Steelpillow and I thank him again for his support. Given the level of activity in this discussion, if there were any objections to his decision to omit that content from the article, there has been ample opportunity for them to be voiced.

I agree with Mr. Swordfish's comment that going into every historical failure is out of place in the article. It is very similar to what I wrote but decided not to post because I'm tired of repeatedly defending practically everything I have written since I joined this discussion in August. Burninthruthesky (talk) 07:49, 13 January 2015 (UTC)

I've said it before, but I would again like to provide a pointer to WP:LISTEN. Thank you. Burninthruthesky (talk) 11:04, 13 January 2015 (UTC)

In reply to Mr Swordfish, it is not in my power to threaten sanctions, only - as I said - to seek them. The disruption and distress are real and they need to be dealt with. I stand by all that I said. — Cheers, Steelpillow (Talk) 13:36, 13 January 2015 (UTC)

Regarding the firehose model, my "PoV", as Steelpillow calls it, is supported by the sources, but that's perhaps beside the point. Mr. Swordfish has a good point that the firehose model is an example of a "spherical cow" analysis, and as such isn't sufficiently noteworthy for inclusion in the article. So I withdraw the second paragraph of my proposed subsection on "Newtonian theories....".

And I propose renaming the subsection "Newton's theory of lift" and moving it to "Alternative explanations, misconceptions, and controversies", after "Misconception regarding 'pulling down' of the flow". See User:J_Doug_McLean/sandbox. Newton's theory isn't as prominent these days as EET, but it was quite influential in the early discussions of the practicality of heavier-than-air flight, and so I think is noteworthy for that reason. J Doug McLean (talk) 23:21, 13 January 2015 (UTC)