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Does this event really cause the other event, according to accepted theory?

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)

Why I now find "The Statment" to be problematic

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

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.

Misplaced Pages 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, Misplaced Pages 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)

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)

sources relating momentum transfer and lift

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.

"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

"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

"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

"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

"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

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."

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.

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."

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

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

"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)

...

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)

...

"Consider, then, this cylinder of air, as illustrated in Fig. 5.21. The area of cross-section of the cylinder of affected air is 1/4 πb. The rate of mass flow of affected air past the wing is therefore 1/4 πρVb. The rate of transport of downward momentum is therefore 1/4 πρVbw, and this must equal the lift, L." (Page 76)

...

"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)

"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

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".

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.

(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)

Comments on the sources above

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)

• 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)

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