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Limits of current human knowledge

Looking over the article and all the archived discussions, one basic thought occurs to me: Humans do not fully and clearly understand why airfoils generate lift. There are various competing explanations, and there is no broad, general, and complete consensus among scientists as to why airfoils generate lift. This is an astounding fact. I think this aspect of current human understanding should be mentioned in the introduction to the article. It is remarkable with the wide-spread use of airfoils throughout history (age of sail, age of flight) that humans do not fully and clearly understand why the airfoil works. --Westwind273 (talk) 18:06, 20 March 2013 (UTC)

I rather strongly disagree with the assessment that "there is no broad, general, and complete consensus among scientists as to why airfoils generate lift." In fact I would say just the opposite, that the science and engineering of airfoils and lift is a mature subject that is well understood and "settled" science. If you have gotten the opposite impression from the article, I apologize.

Where there is disagreement is in how to explain these rather complicated and sophisticated ideas in layman's terms. This disagreement over pedagogy is quite distinct from any controversy over the underlying science.

I am now more inclined to agree with J Douglas McLean's statement upthread that "the quote by John D. Anderson gives the misleading impression that there are disagreements over the science itself, not just the qualitative explanations" and will remove that material. Mr. Swordfish (talk) 19:02, 20 March 2013 (UTC)

I agree that when read by a layman, the article certainly gives the impression that lift is not "settled" science. To the layman, it certainly reads as if there are various competing explanations for the underlying science. For example, this introductory section definitely gives the impression of various competing explanations of the underlying science: "There are several ways to explain how an airfoil generates lift. Some are more complicated or more mathematically rigorous than others; some have been shown to be incorrect. For example, there are explanations based directly on Newton’s laws of motion and explanations based on Bernoulli’s principle. Either can be used to explain lift." Does the Newton explanation conflict with the Bernoulli explanation? Newton and Bernoulli are not alternative explanations of lift; rather they are both in effect simultaneously to create lift, aren't they? Then why present them as two alternatives? It is relatively easy for the layman to understand the Bernoulli effect, but the key question that the article never explains clearly to a layman is: Why does the air on the top flow faster than the air on the bottom? This is the key point. Later the article says "Explaining lift while considering all of the principles involved is a complex task and is not easily simplified." To me, this is a cop out as far as Misplaced Pages is concerned. The article is basically saying "We're going to punt on any attempt to explain this to a layman, and instead divert into scientific mumbo-jumbo that you will never understand." Is it really so hard to explain why the air on top is flowing faster than the air on bottom? Overall I am quite disappointed in this Misplaced Pages article. --Westwind273 (talk) 19:29, 21 March 2013 (UTC)

I think the whole concept of "multiple explanations" is the wrong way to approach this topic. It leads to deep confusion in the layman. If it is settled science, there should be one explanation which can be presented in greater or lesser levels of depth. --Westwind273 (talk) 19:38, 21 March 2013 (UTC)

I think that the problem being described here is the one about the way science is taught (in some schools). First there are phenomena in the real world, then there are scientific theories and mathematical models that attempt to explain the phenomena. There's nothing after that - no point at which physical phenomena stop being what they were and start following the dictates of the mathematical models, rather than their own inscrutable processes. That does not mean that science is wrong or badly understood, but that the scientific models and equations we have, are all we have, apart from the mysterious wonders of nature itself. People try to use similar arguments to rubbish climate science - "If this is all just a theory, then let's wait until it's been sorted out", etc. Lift is settled science - jet airliners fly every day to within tolerances very close to those their designers intended - but there isn't one simple explanation. We just have to get used to that. --Nigelj (talk) 20:35, 21 March 2013 (UTC)

>... there should be one explanation which can be presented in greater or lesser levels of depth.

Alas, the world is not that simple. Almost every scientific principle admits multiple explanations. For instance, there are at least nine ways to prove the fundamental theorem of algebra, and this is an area that has been "settled" for centuries. As another example, many problems in Newtonian physics can be approached in multiple ways - conservation of energy, conservation of momentum, direct application of newton's laws, the principle of least action, etc. These are just different ways of looking at the same problem.

Much of the controversy surrounding lift is due to some individuals thinking that there is "one true explanation" that is correct and therefore all other explanations must be incorrect. Unfortunately, one of the most common explanations actually is incorrect; were this not the case I surmise that the differing explanations would simply sit quietly side-by-side as they do in most topics.

I agree that the sentence "Explaining lift while considering all of the principles involved is a complex task and is not easily simplified." adds little to the article, and we have contemplated removing it. Maybe its time has come? Opinions form other editors?

Finally, to answer your question "Why does the air on the top flow faster than the air on the bottom?" there's a very simple answer:

When air follows a path that is curved, the pressure is lower on the inside of the curve than on the outside. So, there's a region of lowered pressure on the top side of the wing. When the air flows from atmospheric pressure into this lower pressure region, there is more pressure behind than in front resulting in a net force on the air which speeds it up. (the last sentence is basically Bernoulli's principle in a nutshell)

Perhaps something like this should be added to the article. I've never considered "why does the air speed up" to be a "key point" since lift can be explained (albeit incompletely) without even mentioning the speed changes. But if our readers are coming here looking for the answer to that question, perhaps we should present it. Mr. Swordfish (talk) 20:42, 21 March 2013 (UTC)

I agree with Mr Swordfish, and I disagree with Westwind273 when he writes Humans do not fully and clearly understand why airfoils generate lift. I disagree for two reasons. Firstly, science does not address questions about why the universe operates the way it does. That is a question for theology. Science merely observes the universe and attempts to determine principles and laws which describe these things. As a simple example, scientists understand and apply Newton's first law of motion but science does not bother with the question of why a force is necessary to cause an object to accelerate. Theologians might explain that a force is necessary because God dictated that it would be so, but scientists find Newton's observations, and his laws of motion, to be entirely adequate. Similarly, Bernoulli observed the flow of fluids and the interchange of speed and pressure and described it all in his famous principle; but he didn't bother to include any speculation about why it is so. That would not be science.

Secondly, Westwind273 has grasped John Anderson's statement that scientists and engineers disagree over what is the most fundamental way to explain the phenomenon of aerodynamic lift. Westwind273 has misunderstood Anderson to be referring to some remarkable mystery about aerodynamic lift. If it is true that humans do not fully and clearly understand these things, then that is equally true of any scientific phenomenon. Westwind273 should also be writing that humans do not fully and clearly understand magnetism, electricity, meteorology, thermodynamics, and so on. There is nothing specially intractable about aerodynamic lift which is a splendid application of Bernoulli's principle, Kutta's observations, Newton's third law of motion, the principle of momentum and so on. Each person contemplating the phenomenon of aerodynamic lift, whether that person is a student pilot, college student, professional engineer or research aerodynamicist, must choose whichever of these scientific principles is most satisfactory for him. There is no one true explanation for any scientific phenomenon, and certainly not aerodynamic lift. Dolphin (t) 23:28, 21 March 2013 (UTC)

I think it's understandable that Westwind273 got the mistaken impression from the current article that there is a lack of consensus on the science of lift. And I largely agree with the responses by Mr. Swordfish, Nigelj, and Dolphin, but with some quibbles below. I have a suggested revised version of the article in my sandbox User:J_Doug_McLean/sandbox that I think would avoid the mistaken impression that Westwind273 got. It sets the record straight on the science and also answers the question of why the flow over the upper surface speeds up a little differently from the way Mr. Swordfish did. I'd appreciate it if Westwind273 would read my suggested version and provide feedback.

The answer by Mr. Swordfish to the question "Why does the air on the top flow faster than the air on the bottom?" is a good start, but it needs to be added that the cause-and-effect relationship between the pressure field and the velocity field is circular, as explained in my suggested revision. Both flow curvature and changes in flow speed are caused by differences in pressure, and the differences in pressure are sustained by the changes in flow direction and speed.

The issue of cause-and-effect and "why" has come up before, and I still don't entirely agree with the hard-line take on that topic by Dolphin. I agree that for some fundamentals like Newton's second law we don't understand the "why". But at other levels, I think it's perfectly reasonable to talk about causation and "why", as in saying that a force causes an acceleration. So "why" does something accelerate? Because of a force. "Why" are force and acceleration related the way they are? We don't know. J Doug McLean (talk) 02:07, 6 April 2013 (UTC)

My opinion is that this article has long suffered from the fact that we editors are sometimes too close to the subject matter and get caught up in meta-discussions about the material instead of just presenting the material in a srtraightforward manner. We've all read the great Bernoulli/Newton debates of the 90s, and while this is interesting to folks who already know quite a bit about the subject I do not think it is helpful to re-hash that debate here. Perhaps it belongs in its own wikipedia article, but the purpose of this article is to introduce the basic ideas in a manner understandable to the lay reader. It seems to me that when we write about how we're we're going to explain the actual subject, we've made the artcle harder to understand by encapsulating it in a second layer of meta-analysis.

The result is that some readers, such as Westwind, get the mistaken impression that there is a lack of scientific consensus. Doug has suggested that we add language to correct that impression, eg; The mathematical theories are scientifically rigorous, are supported by empirical observations, and have been agreed upon by the scientific and engineering communities since the early 20th century. My take is that this should go without saying, of course the theories are rigorous and well accepted - having to state it explicitly seems like we "doth protest too much".

To put a finer point on it, everything in science has multiple explanations; all science is rigorous (otherwise it wouldn't be science). There is no need to apologize for choosing one explanation over another, or to have to make assurances that the science is actually science.

So, I would advocate editing the article to downplay the Bernoulli/Newton "controversy", and to avoid giving the impression that these are two or more competing theories. As an example, take a look at the Bernoulli's_principle article itself - it states that BP can be derived from either conservation of momentum or by directly integrating newton's 2nd law. To my eyes, it does so without implying that one is correct and the other is wrong, or that there's any controversy over which derivation is correct. The subtext is that both are correct; somehow that subtext seems to be missing in this article. I do think that this article should present both explanations, but I think we can do so without making such a fuss over it. In fact, the more I think about the subject, the more I am persuaded that it's really one big explanation that fits together in harmony, rather than multiple competing theories.

By way of analogy, this subject reminds me of the blind men and the elephant. It's a great parable, but here we're writing an article describing elephants, not the arguments of the blind men. Statements like "some say the elephant is like a snake and some say it is like a wall" doesn't really advance the article.

In other matters, Doug has pointed out a definite shortcoming of the current article - the airfoil affects the flow over a wide area around it - and this fact along with the reasons why it occurs (ie the self re-enforcing interplay between pressure and fluid motion) should be incorporated into the article. I'll take a swat at this in coming days, most likely just stealing Doug's text. Mr. Swordfish (talk) 21:20, 8 April 2013 (UTC)

The blind men and the elephant is spot on. Avoid the arguments between the blind men, and ignore those who ask "Why is there an elephant in the room anyway?" This is an article about lift, and the main conceptual and mathematical models that enable pilots and engineers to understand and manipulate lift. People who want to know why, or how did we get here, are looking for different topics, for which there may or may not be articles at this time. --Nigelj (talk) 22:33, 8 April 2013 (UTC)

I understand the urge to simplify things by downplaying the "meta-analysis", but I think it would be a mistake.

If we were the only ones who had ever discussed alternate explanations of lift, and if the controversies were limited to our little talk-page circle, then I'd agree that those discussions would be out of place in the article. But that's not the situation. The public folklore on this topic is full of misconceptions and erroneous explanations. And the controversies have been out there in public view for decades. I'll bet many of the potential readers of this article have already read a Bernoulli explanation (likely based on longer path length) or deflection explanation of lift and have probably also read somewhere that one or the other is wrong. And they're also very likely to have already gotten the impression from somewhere that the science is unsettled.

So the fact that the science on this particular topic is in good shape doesn't speak for itself. It needs to be spelled out. And given what's out there in the popular culture, we'd be short-changing the reader if we left out discussion of the pros and cons of the alternate explanations (and the outright errors in some versions). Whether we like it or not, these issues are now part of the topic of lift. Just the straight facts will not be enough to enable a reader to see through the fog.

Mr. Swordfish (Mr. Swordfish), you suggest that we should present "both explanations" of lift in the same way that the Bernoulli's_principle article presents its two alternate derivations. I don't entirely agree. Both derivations of Bernoulli are actually correct and self-sufficient. Our two simpler explanations of lift are both correct to some extent but also have significant shortcomings. The shortcomings shouldn't be swept under the rug.

Mr. Swordfish, you also say you're persuaded that the two simpler explanations really amount to "one big explanation that fits together in harmony". If you follow that idea to its logical conclusion and try to write it out as an explanation of lift, including the ideas of flow influence over a wide area and mutual interaction between pressure and velocity, what you arrive at is my "more comprehensive explanation" in my proposed revised version in my sandbox User:J_Doug_McLean/sandbox. The hard work is already done, including integrating the "one big" explanation with the simpler ones in the pedagogically favored order.

My proposed revision also attempts to put the mathematical theories and the various qualitative explanations in perspective in the new sections "The understanding of lift as a physical phenomenon", "Popular physical explanations of lift" and "Shortcomings of the popular explanations". Not all the material in these sections is new, but I think organizing it in this way makes things clearer. It explains the science in a way that would prevent misunderstandings like the one expressed by Westwind273, and it provides the necessary "meta-analysis" of the qualitative explanations. J Doug McLean (talk) 22:33, 17 April 2013 (UTC)

I get the science vs theology thing. For example, we know a lot about how gravity works, but we don't actually know why it works. We feel confident that there are such things as photons, but are there such things as gravitons? We don't know. But I think the explanation of lift should be much closer to science than theology. I strongly agree with the statements above that the article's explanation bends strongly toward circular reasoning: Why does the air move faster on top? Because there is lower pressure. Why is there lower pressure? Because the air is moving faster. This circular reasoning really turns off the layman reader, and I think it is reasonable to ask science to avoid this kind of circular reasoning without resorting to theology. The air on top is being made to both go faster and become lower pressure, but why? The best I can figure is that it is some sort of combination of surface cohesion for the molecules closest to the top of the wing, and a whiplash effect for the molecules a bit further away from the wing. This surface cohesion and whiplash combo creates both the lower pressure and faster airflow on top. Is this correct?

I think the authors of this article need to realize how uniquely odd this article is in beginning the explanation with the "There are several ways to explain..." paragraph. I challenge you to find any other scientific article on Misplaced Pages that starts an explanation in this way. For example, look at the Misplaced Pages articles on nuclear fission or freezing. The explanation is straightforward and does not wade into this "several different ways" explanation. --Westwind273 (talk) 04:50, 30 January 2014 (UTC)

I was not saying that the current article "bends strongly toward circular reasoning", and I don't think it does. What I was saying is that the article should be revised so as to state explicitly that the cause-and-effect relationship between pressure and velocity in an airfoil flow is circular. Circular cause-and-effect is not the same thing as "circular reasoning", which generally refers to a false argument that purports to establish something that was assumed a priori and for which there is no support other than a circular argument. The circular cause-and-effect relationship between pressure and velocity in fluid flows isn't in the circular-reasoning category because it's the way the physics actually works.

Of course Newton's second law is the key physical principle here. In many applications of Newton's second law, it's appropriate to think of the force as the "input" and the motion as the "output", but that way of thinking misses part of the picture in continuum fluid flows. The motion of a local parcel of fluid does depend on the net force exerted on it by all the adjacent parcels in contact with it, consistent with Newton's second law. But that force depends on the motions of the adjacent parcels, which depend on the motions of the parcels adjacent to them, and so on. Because we're dealing with the motions of many parcels, all interacting with their adjacent neighbors, we effectively have a situation in which the motions depend on the forces, and the forces depend on the motions, i.e. circular cause-and-effect.

So of course science should avoid circular reasoning, but circular cause-and-effect between pressure and velocity is a fact of life in aerodynamic flows, and a good qualitative explanation of lift needs to make that clear.

One way to summarize the relationship between pressure and velocity is as follows: The pressure gradient causes a fluid parcel to accelerate (consistent with Newton's second law), and the combination of the parcel's inertia and acceleration causes the pressure gradient to be sustained. The necessity of acceleration to sustain the pressure gradient involves Newton's third law. When the pressure gradient is nonzero, a fluid parcel experiences a net pressure force exerted by it's neighbors. A net force on a fluid parcel can exist only if the parcel pushes back, consistent with Newton's third law. In the effectively inviscid flow outside the boundary layer, a fluid parcel can push back only through the combination of its inertia and acceleration.

I'll admit that the idea that the parcel's acceleration "sustains" the pressure gradient isn't that east to grasp intuitively. Does "sustain" mean the same thing as "cause" in this case? I think the answer is yes, but a bit indirectly. I found it helpful to think of a simple example from solid mechanics.

Think of a square block of wood, a couple of inches on a side, resting on a rigid table. Center your thumb on the top of the block and press downward. The forces exerted on the external surface (your thumb pushing down on the top and the table pushing up on the bottom) cause the stress field throughout the interior of the block to be altered. For one thing, there will be a non-uniform distribution of vertical compression stress, likely more concentrated directly under your thumb and more spread out at the bottom of the block where it presses on the table. This will be balanced by a non-uniform distribution of shear stress such that the net force on any parcel of material in the interior is zero, consistent with Newton's second law. At the local level at any point in the interior, the only cause we can identify for the compression-stress gradient is the shear-stress gradient. Locally, the two stresses are engaged in a mutual interaction, i.e. circular cause-and-effect. At the global level (the whole block), the cause of the whole non-uniform compression-stress field is the forces applied at the surface. There is circularity at this level as well because the distribution of compression stress applied by your thumb depends on the deformation of your thumb, which depends on the distribution of stress. This is not circular reasoning, just circular cause-and-effect associated with a mechanical interaction.

We can apply the same line of reasoning to an airfoil flowfield. Because the shear stress in most of the field is insignificant, the compression-stress gradient (i.e. the pressure gradient) acting on any fluid parcel must be balanced by fluid acceleration instead. At the local level, the interaction between the pressure gradient and the acceleration is mutual, or circular, just as it was with the two interacting stress gradients in the solid. At the global level, the cause of the non-uniform pressure field (and thus also of the non-uniform velocity field) is the force applied to the flow by the airfoil, acting at the airfoil surface. As in the case of the wood block, the pressure field in the flow is just a state of stress in the interior of the domain, resulting from the application of forces at the boundaries, and distributed in a manner consistent with the laws of motion throughout the field.

I think this answers the questions that crop up a little later in the exchange between Westwind and Swordfish: Why does the flow above the upper surface follow a curved path? And why is there a pressure gradient associated with that curvature? At the local level, the answer is in the mutual interaction between pressure and velocity that I've already described. At the global level, the ultimate cause of the non-uniform pressure and velocity fields is the force exerted on the flow by the airfoil. This sounds unsatisfyingly circular because that force is just the equal-and-opposite reaction to the lift force that we're trying to explain. But that's how the physics works. The force exerted by the airfoil makes the flow non-uniform, and the non-uniform flow exerts force on the airfoil. The cause-and-effect is circular even at this global level, but it's all tied together by the facts that the airfoil shape and angle of attack impose a boundary condition on the velocity at the surface and that Newton's second law applies throughout the field. This is circular cause-and-effect, but not circular reasoning.

On a related issue raised by Westwind273, the following of the curved surface by the flow has nothing to do with "surface adhesion". Air molecules don't adhere in significant numbers to solid surfaces, and air can't be put in tension. The background atmospheric pressure is high enough that the pressure at the airfoil upper surface, though lower than ambient, is still strongly positive in an absolute sense. So the flow follows a curved path and is able to follow the convex upper surface because it is pushed from above by higher pressure. There is no pulling from below. And the following of the curved surface has nothing to do with viscosity either. J Doug McLean (talk) 19:45, 3 April 2014 (UTC)

If readers see circular reasoning when they are trying to find a satisfying explanation for lift, it is most likely because the question "Why does the air move faster on top?" is not a particularly serious scientific question. (I think the best answer to this question would be "Because air observes the laws of physics"; but this is unlikely to satisfy many of the people who ask "Why does the air move faster on top?") It is a bit like Kepler's laws of planetary motion. Science is absolutely fascinated that the planets move in such a regular, repeatable and predictable manner that Kepler was able to postulate three laws that accurately summarise their motion; but science is not at all interested in the question "Why do the planets obey Kepler's laws of planetary motion?" If someone (presumably a layman) set about trying to give a fundamental explanation as to why the planets move in a regular, repeatable and predictable manner, it is my guess that he would end up presenting circular reasoning.

Similarly, the air moves around an airfoil in such a regular, repeatable and predictable manner that we can see its motion is consistent with Newton's laws of motion, the Kutta condition, Bernoulli's principle etc. If the air did not move faster across the top of an airfoil, it would demonstrate a flaw in these fundamental laws of physics.

The scientific approach to lift is firstly to select Newton's laws of motion or the Kutta condition or Bernoulli's principle, explain it in some detail and then present the phenomenon of lift on an airfoil as a practical example of Newton or Kutta or Bernoulli. If it is done in this way, the question "Why does the air move faster on top?" doesn't arise because the air moving faster on top is exactly what the Kutta condition predicts for airfoils and lots of other bodies with sharp edges.

If Lift (force) attempts to answer this question, or give the impression it is attempting to answer this question, there is grounds for amending the article to avoid that impression. Dolphin (t) 05:48, 30 January 2014 (UTC)

Dolphin, I'm going to disagree with you here. Why does the air move faster on top? is perfectly reasonable scientific question, and the article does explain it, although in a somewhat roundabout (but not circular) manner. It's not presented in this order in the article, but the pieces are there to fit together the following explanation:

Why does the air move faster on top?

Because there is a region of low pressure along the top of the wing. According to Bernoulli's principle when air flows into a region of low pressure it speeds up. This is because there is more pressure behind than in front which results in a net force on the air molecules. Consequently they accelerate to a higher speed.

Ok, so why is there a region of low pressure on top of the wing?

So, why does the air follow a path that is curved?

It is deflected by the wing, with the geometry of the flow path dependent on the shape of the wing and the angle of attack. It's obvious why it is deflected downward by the bottom the wing - the wing is solid and there is nowhere else for the air to go. Along the top, the air follows the surface of the foil, resulting in a curved path.

Why does the air follow the surface of the foil instead of just continuing on in a straight line?

At this point we're getting beyond the scope of the article, but this is usually explained using viscosity.

I don't think Why does the air move faster on top? is central to the topic of lift, so I wouldn't re-structure the article to answer it. But the answer is there if the reader is willing to hunt for it. And the reasoning is not circular.

Regarding Kepler's laws of planetary motion, they can be derived from Newton's laws (including the law of gravity), although since Kepler died a dozen years before Newton was born he obviously didn't derive them that way. So a reasonable non-circular explanation of Kepler's laws would be to start with Newton and proceed from there - Kepler's laws are true because they are a logical extension of Newton's laws. Of course, this begs the question of Why are Newton's laws true?, and the answer to that is that you've got to start somewhere and the reason we accept them (without a logical proof starting from more fundamental assumptions) is the millions of observations and experiments confirming them.

All this said, I do agree that the various physical phenomenon surrounding lift (a net force, pressure differences, speed differences, air changing direction etc.) can be explained starting from basic principles. And I think the present article does this. Mr. Swordfish (talk) 15:54, 30 January 2014 (UTC)

Mr Swordfish wrote: Because the air is following a path that is curved. Euler's equation, which is derived directly from Newton's laws says that whenever a fluid follows a curved path there are pressure differences, with lower pressure on the inside of the curve and higher pressure on the outside. The flow turning causes a region of low pressure along the top of the wing.

This is what I don't understand. Your explanation of the first and third questions here helped me a lot, but it is this middle second one that still seems unexplained to me. Specifically, why does air that follows a curved path have lower pressure on the outside? I know that Euler's equation says that it does, but why? Is it simply that the outside path is longer and therefore the molecules get spread out over a greater distance? This seems remarkably close to the equal-transit-time theory, which we know is false. Is the answer to this theology? I think it should not be. I read the Misplaced Pages article on Euler's equation for fluid dynamics, and it did not help me. --Westwind273 (talk) 20:37, 30 January 2014 (UTC)

Sorry, I was being a bit imprecise. When I said "Euler's equation" I meant the one referenced in this article, which is different than the one treated at Euler's_equations_(rigid_body_dynamics). So, it's unsurprising that that article didn't shed much light on it. Mathematically, the equation in question (dp/dr = rho*v^2/R) is derived by just writing an expression for centripetal force, applying F = ma and doing a bit of algebra. Babinsky's paper ( http://iopscience.iop.org/0031-9120/38/6/001/pdf/pe3_6_001.pdf ) has a concise derivation at the very end.

To get an intuitive notion of why it's true, ie why there is less pressure on the inside of the curve, imagine riding on a train between two cushions pressing equally on you from the sides - as the train goes around a curve, your body will press on the outside cushion and pull away from the inside cushion; less pressure on the inside and more pressure on the outside. The tighter the turn and the faster the train is moving, the greater these pressure differences become. The analogy only goes so far, but air following a curved path experiences the same forces. It's just a consequence of the centripetal force necessary to make the air follow a curve. Mr. Swordfish (talk) 22:28, 30 January 2014 (UTC)

Yes, this is what I was trying to understand. It is quite similar to what I was saying before. The overall airflow follows the curve of the wing on top because of the tendency of the air molecules to adhere to the wing, once they come in contact with it. But at the same time, there is a kind of whiplash centripetal force that is throwing the air molecules away from the top of the wing. The result is a powerful spreading out of the air molecules in the area above the wing, resulting in lower pressure there and the resulting lift. Does this sound right? Could the article be modified to give some kind of explanation like this to the layman? --Westwind273 (talk) 00:38, 31 January 2014 (UTC)

There is no force "throwing the air molecules away from the top of the wing". However, there is inertia which would make the air follow a straight line in the absence of any force. Since there is a force pulling the air down towards the wing surface, the air changes direction.

I'm not sure what you mean by "a powerful spreading out of the air molecules in the area above the wing", but if you mean the air becomes less dense (fewer air molecules per unit volume) that is incorrect. In a first approximation, the air is incompressible meaning the density remains constant throughout the airflow. This is not strictly true since air does compress at sufficiently high airspeeds, but trying to explain lift via changes in air density is barking up the wrong tree. Mr. Swordfish (talk) 14:58, 31 January 2014 (UTC)

I think the authors of this article need to realize how uniquely odd this article is in beginning the explanation with the "There are several ways to explain..." paragraph. I challenge you to find any other scientific article on Misplaced Pages that starts an explanation in this way.

Two that come to mind immediately are derivation of Bernoulli's principle which states: "The Bernoulli equation for incompressible fluids can be derived by either integrating Newton's second law of motion or by applying the law of conservation of energy" and the proofs of the fundamental theorem of algebra. Granted, the latter doesn't call a lot of attention to the fact that there are dozens of different lines of reasoning that can be used to arrive at the result, it just presents them. The phrases "yet another" and "still another" occur numerous times.

A quick search or two ( https://en.wikipedia.org/search/?title=Special%3ASearch&profile=default&search=several+ways+to+explain&fulltext=Search , https://en.wikipedia.org/search/?title=Special%3ASearch&profile=default&search=multiple+explanations&fulltext=Search ) turns up thousands of wikipedia articles that present multiple explanations. Which is unsurprising, since there are usually several ways to explain any phenomena. Insisting on only presenting one when the literature presents several would violate WP:NPOV Mr. Swordfish (talk) 16:25, 30 January 2014 (UTC)

Hi Mr Swordfish. Thank you for taking the time to write such detailed explanation on the subject. I don’t have any major objection to what you have written. I think my only objection is that your explanations, regardless of their correctness, are not answering the question “Why does the air move faster on top?” but that is not because there is anything wrong with your answer; it is because the question is not a good one.

Let me illustrate my thinking. Person A might ask “Why do ripe apples fall to the ground?” Person B might answer “Because of Newton’s law of universal gravitation.” Person A might be entirely satisfied with this answer, but I don’t find it a satisfying answer at all. Ripe apples were falling to the ground for many millions of years before Newton was born so Newton cannot possibly be part of the explanation of falling apples. (Science is fascinated that ripe apples, and all other unrestrained objects, always fall towards the center of mass of the Earth with predictable initial acceleration, but science has little or no interest in why.)

I would prefer the conversation go like this: “We observe that ripe apples always fall to the ground. Is Newton’s law of universal gravitation consistent with this observation?” To which the answer is “Yes, Newton’s law of universal gravitation appears to be consistent with this observation.” (Albert Einstein made some observations and found that Newtonian mechanics were not consistent with the observations, so Einstein developed a replacement system of mechanics that more closely match his observations. The universe does not change its ways in order to behave in accordance with our laws!)

In your explanation of why there is lower pressure on the inside of a curve than on the outside, you have strayed too close to suggesting it is because of Euler’s equation. The pressure gradient across curved streamlines existed for millions of years before Euler’s birth so Euler’s equation is not an explanation of why this pressure gradient has always existed. However, it is reasonable to say “We observe a pressure gradient across curved streamlines. Is there any scientific principle that matches this observation?” To which the answer is “Yes, Euler’s equation is consistent with these observations”. Euler’s equation has stood the test of time and we confidently use it to predict pressure gradients and the curvature of streamlines, but we should not imagine Euler or his equation is an answer to the question “Why is there a pressure gradient across curved streamlines?” That is not a sound question for a scientist. Dolphin (t) 06:23, 31 January 2014 (UTC)

My background is mathematiics, so I'm used to working with axiomatic systems. To me, Newton's laws of motion are like axioms, and if I can deduce that something logically follows from the axioms I'm satisfied - "why does X happen? because it's logical consequence of Newton's laws" - is a perfectly acceptable explanation of why in my book. I understand that not everyone will agree, and that I'll never get an answer to why the axioms (Newton's laws) are correct.

If someone asks me "why is the sky blue" or "why are there infinitely many prime numbers" or "why is a catamaran harder to tack than a monohull?" I'll try to give them an answer based on scientific principles and logic. I don't scold them for asking an unsound question, or say that we can never know why about anything. Agree that we can never really know why, but we can explain complex things in terms of simpler, easier to understand concepts. Anyway, we've kind of gotten away from discussing the article, so I'll let you have the last word if you care to. Mr. Swordfish (talk) 15:47, 31 January 2014 (UTC)

I have been grappling with the difficulty I see whenever Misplaced Pages pretends to answer scientific questions that begin with “Why” such as "Why does an airfoil generate lift?"

It is true that Misplaced Pages (and others) give answers in response to these questions but I don’t believe the question they are answering is the one beginning with “Why”. Superficially, it appears that an answer has been given to the Why question, but philosophically I doubt it.

I would prefer it if Misplaced Pages answered the question “How does an airfoil generate lift?” It is easy to give a genuine answer to this question by referring to the flow pattern:

When a symmetric airfoil is moving relative to the surrounding air but it isn’t generating lift, the flow patterns above and below the airfoil are identical. At each point in the atmosphere above the airfoil, the flow speed and air pressure are identical to the flow speed and air pressure at the corresponding point below the airfoil. The force of the air pressure acting on the top surface of the airfoil is equal to the force acting on the bottom surface. The two forces balance and no lift is generated. But when a symmetric airfoil is generating lift, the air is approaching the airfoil with a non-zero angle of attack and the flow pattern above the airfoil is significantly different to the flow pattern below the airfoil. At each point in the atmosphere above the airfoil, the flow speed and air pressure are different to the flow speed and air pressure at the corresponding point below the airfoil. In particular, the streamlines adjacent to the top surface are closer together than the streamlines adjacent to the bottom surface. The air is moving past the top surface faster than it is moving past the bottom surface and the force of the air pressure acting on the top surface is less than the force acting on the bottom surface. The two forces don’t balance and the resultant is called lift.

I think this kind of response is an answer to the question “How does an airfoil generate lift?” rather than the question “Why does an airfoil generate lift?” Everyone agrees on the answer; it is the question that still perplexes us! Dolphin (t) 06:31, 26 February 2014 (UTC)

++++ The OP stated that humans do not understand why airfoils generate lift.

Now, "Humans understand lift" could mean several different things. The answer depends upon the meaning assigned to the proposition.

But the common interpretation in the scientific community isn't at all that vague. It might be stated: "broadly accepted scientific theory (in this case, mainly the laws of Newtonian fluid dynamics) accounts for the all the salient observed facts concerning lift, without arbitrary ad hoc assumptions, as confirmed by repeatable experiments." If we were to accept this interpretation, then it would remain only to ask ourselves, do we agree or not? I think that all experts on fluid dynamics would agree that the proposition is true. If so, then the article should reflect that accepted dogma, until and unless it is superseded by a new paradigm.

It is understandable that some participants in the discussion are not experts: they don't know Napier's equation, they don't understand what it does and doesn't say about causality, they don't understand the relationship in science between theoretical models and experiments, etc. But the article should not reflect their ignorance...it should reflect humankind's current best understanding of the subject.

That's just my opinion. Do you agree? Mark.camp (talk) 00:33, 27 March 2014 (UTC)

I agree.

There is a temptation to imagine that to fully and clearly understand why airfoils generate lift, the explanation must be esoteric, complex, with lots of advanced math. There is no reasonable ground to imagine that. Different people will prefer different explanations of lift, and all those different explanations can be legitimate. For example, in one of John D. Anderson's books he goes looking for the simplest explanation of lift and concludes that it is based on the observation that the pressure on the upper surface of an airfoil is different to the pressure on the lower surface, resulting in an aerodynamic force; lift is the component of the aerodynamic force perpendicular to the vector representing the relative motion between the airfoil and the free stream of fluid moving past it. That is a simple explanation but it is entirely legitimate as an explanation of how (or why) airfoils generate lift. Many people, including those who embrace Anderson's simple explanation, are entitled to object to the OP's suggestion that Humans do not fully and clearly understand why airfoils generate lift. Dolphin (t) 05:41, 27 March 2014 (UTC)

+ + + + + + I agree that the science allows multiple formulations of explanation or presentation. This an inherent characteristic of Newtonian physics; it is a set of definitions, assumptions, and equations, and the equations can be transformed mathematically without changing their meaning. Often, for example, one can present the predictions of science, in a given case, in terms of forces, or alternatively in terms of energies. You can present Newton's original way of describing the evolution of a system, or you can use the form developed later, the law of least action, to describe the very same system evolution. As a final example, you can present Maxwell's laws in differential form or in integral form. Same science, same math, different presentation.

But that is an entirely different question from that of presenting the explanation of lift as the result of net force on the body, as Anderson does. This is a *stage* in the explanation, not a *form* of the explanation. I think we would all agree that it is a necessary introductory stage. But it is only the beginning. Any curious reader will be happy to understand at this simple level but will immediately want an explanation of the pressure field and velocity field itself: "OK, I understand that if that is the velocity field, then that is the pressure field, and the conclusion is that there is lift. But now I want to know WHY those are the fields". The next stage, I think all of us would perhaps agree, is to proceed to a very simple model (called ironically "complex" potential) that accounts for a particular solution for the two fields that is consistent with lift (and an infinite number of others consistent with the boundary condition but NOT consistent with the observed lift!). But again a persistent reader will say, "ok, I see how ONE of the infinite number of possibilities yields the observed lift, but you have not explained why nature always settles on JUST THAT ONE, the one that happens to produce the observed lift." The next stage, I think you will agree, is to allow a slightly more realistic model...still far from the truth, still no turbulence, no separation, no chaos...but one which can account for the solution (Kutta condition, other approximations concerning effective shape of the foil rather than its actual shape) which nature has been proven experimentally to choose, very approximately.

A good explanation for this article, I think, would allow the reader to pick his own level of advance. If he didn't understand the first stage about net force, he could understand just that much and be satisfied to stop. If he had the next obvious question, he could get a clear exposition of that. If he still were curious, he could pursue the next level, which allows for friction and thus the Kutta condition. If he were still curious, he could move on to boundary layer, and then to turbulence, and then to separation, and then to chaos....

Mark.camp (talk) 00:36, 29 March 2014 (UTC)

A major revision proposed to be installed soon

Some of us have been saying for some time that this article needs revisions, to clarify the relationship between the mathematical theories and the qualitative physical explanations, to make clear the incomplete nature of the popular explanations, to offer a better explanation that emphasizes the spread-out nature of the flowfield and the reciprocal nature of the interaction between pressure and velocity, and so on. Over a year ago Mr. Swordfish offered to take a "swat" at incorporating these last two points into the article, but it hasn't happened yet, so I'm proposing adoption of my own revisions, which do essentially the same thing Mr. Swordfish proposed, among other things.

A draft of my proposed revised version is in my sandbox User:J_Doug_McLean/sandbox. I've just made major revisions to it, and I think it's now worthy to replace the current article, but I hope others will suggest corrections and improvements, so I'll leave it for a few weeks before I install it in place of the current version.

The reasons revisions are needed have been discussed at length on this page, by me and several others (Zapletal recently made some very good points), so I'll touch on them here only in summary form.

The proposed new version is longer than the current one, but I would argue that the additional material is needed to clarify the issues and avoid confusion on the part of the reader. If you don't think this kind of clarification is needed, just read the discussion on this page. The typical reader of the article is likely to be puzzled by some of the same questions that puzzle the participants in this discussion. Questions such as why the flow speeds up over the upper surface, why the flow follows a curved path, and why the pressure changes in the ways that it does. My draft attempts to make the answers to such questions clearer than they are in the current article. Read my draft carefully. If you find it leaves you with questions unanswered, let me know, and I'll try to fix it.

The proposed new version cites my own book, but I think the citations are relevant and not excessive, and thus in keeping with Misplaced Pages guidelines.

The proposed revision preserves some later sections of the current article, with minor changes: "Pressure integration", "Lift coefficient". and "Lift forces on bluff bodies". Otherwise, the changes are major, and the headings are new.

The title is proposed to be changed to "Lift (aerodynamic force)" to be less ambiguous. The introductory section and a new section, "Lift is a result of pressure differences and depends on airfoil shape, angle of attack, air density, and airspeed", describe what lift is and its general behavior, i.e. the "what" of lift, but without explanation of "how" or "why".

Next, "The understanding of lift as a physical phenomenon" is an all-new section that tries to establish a key distinction that isn't clear in the current article, i.e. the settled status of the science compared with the less settled status of the qualitative physical explanations, to set the stage for going into the details in following sections.

"Popular physical explanations of lift, and their shortcomings" covers much of the same ground as the current article, but the organization and most of the words are new. It integrates the explanations and their shortcomings into a single section to make the shortcomings more prominent. The "blind-men-and-the-elephant" problem is part of the folklore of explaining lift and thus should not be swept under the rug. I think this section, combined with the discussion in "The understanding of lift as a physical phenomenon", puts it all in perspective and equips the reader with enough background to avoid the common misunderstandings.

"A more comprehensive physical explanation" is a shorter version of the explanation in my book, but with different graphics to avoid copyright issues. It does not incorporate Zapletal's suggestion to adopt Lanchester's "wave of sustenance" metaphor, because I don't regard the wave idea as helpful. To understand Lanchester's "wave", you have to go into the details of the interaction between the pressure and velocity fields, as my explanation already does. Once you've done that, I don't think the "wave" idea adds anything. The resemblance of an airfoil flow to a wave is superficial, not fundamental, it seems to me.

"Mathematical theories of lift" attempts to make the nature of the theories clearer without going into too much detail. It does not incorporate Zatletal's suggestion to get into the history of fluid mechanics. That might be a good topic for another article, but it would be out of place in this one. In this article I think it's appropriate to explain the physical principles involved, as currently understood, not the history of their discovery.

"Lift of three-dimensional wings" is an all-new section that tries to remedy the current article's lack of information on lift in 3D.

"Viscous effects: Profile drag and stalling" explains how viscosity produces profile drag and limits the lift curve (stalling) in more detail than the current version. "Coandă effect is not relevant to explaining lift" takes a firmer stand on the relevance of Coandă and debunks the idea of a role for viscosity in the flow's ability to follow the upper surface. It also debunks the idea that the flow "sticks" to the upper surface and is "pulled down" toward it.

The "Further reading" and "External links" sections have been shortened by the deletion of a few items that were less than helpful for one reason or another or already in the reference list.

I look forward to constructive feedback and to getting these revisions installed.

J Doug McLean (talk) 19:19, 23 May 2014 (UTC)

My apologies for not following through my promise to incorporate your proposed changes. I have not forgotten, but other matters have garnered my attention and this one went on the back burner.

I have not had a chance yet to review your latest revision. I will do so in the coming week and give my feedback. Thanks for contributing; I think it is great that we have someone with your knowledge and expertise on the edit team. I am optimistic that we can come to a consensus that improves the article. Mr. Swordfish (talk) 22:27, 24 May 2014 (UTC)

Doug,

I have now had a chance to read the proposed revision in some detail.

I think the revision is much improved from the one from last January and it is clear that you have put quite a bit of thought and effort into it. However, I still do not think it is an improvement on the current article, and would not support changing it out wholesale. Apologies for repeating myself, but the current article's structure is based on the work educators who have written about the pedagogy of explaining lift. As the American Association of Physics Teachers states:

"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."

The decision to present the material the way it is currently ordered was informed by the AAPT and other peer-reviewed articles addressing pedagogy. My strong preference is to state early and explicitly that "lift is a reaction force" and explain it in terms of Newton's 3rd law. Any revision that presents a more complicated explanation first will not have my support.

I do recognize that a pressure based approach is favored by aerodynamic engineers, and surely that approach should appear in the article. We just need to start with the simpler Physics 101 explanation such as provided in Halliday and Resnick.

You have written much that is of value that should be incorporated into the article. I have been remiss in not following through with my promised integration. I hope to have a first pass up in my sandbox in a week or so. Mr. Swordfish (talk) 21:45, 30 May 2014 (UTC)

I think the proposed change has lost the focus on explaining what lift is and why it happens - the proposed changes seem to focus more on giving a critique of various "simplified explanations". While there might be a case for having an article on that topic, putting it at the top of this article seems likely to add to the confusion of the typical reader of this article, rather than reducing it. Djr32 (talk) 22:43, 31 May 2014 (UTC)

First for the response from Mr. Swordfish (talk). Thank you for the encouraging words. But I don't see the basis for your objection that my draft "presents a more complicated explanation first". I don't think it does. In "Lift is a result of pressure differences and depends on airfoil shape, angle of attack, air density, and airspeed" I do say that lift is a result of differences in pressure, but that's just part of describing what lift is; it's not explaining lift in terms of the physical principles involved. The first explanation presented in my draft is "Flow deflection", the same one advocated by the AAPT.

In the quote from the AAPT, they advocate explaining lift "simply in terms of Newton's third law", but then they equate the force to a "time rate of change of momentum". This is the domain of the second law, not the third. When you use both laws you should explicitly mention both, as my draft and the current article do.

So it seems to me that we've both followed the AAPT recommendation in spirit, if not to the letter.

Regarding the structure of the article, I think it's important to present a sufficient description of "what" lift is before presenting explanations of "how" it works, i.e. how the principles of physics apply to it. The fact that lift is exerted in the form of differences in pressure is a key part of an adequate description, independent of any physics-based explanation as to how the pressure differences come about.

The current article muddles the distinction between description and explanation by presenting its explanations under headings that bill them as "description", i.e. "Description of lift on an airfoil" and "A more detailed physical description".

Pedagogically speaking, describing something adequately before you present the physics-based explanations is just common sense. I doubt that the educators at the AAPT would object to the way I've structured things.

As for explicitly stating that lift is a "reaction force", I don't think it's a good idea. It seems to me that the term is either misleading or practically meaningless, depending on how it's couched and understood. The first sentence of the current article's "Deflection" section, i.e. "Lift is a reaction force—an airfoil deflects the air as it passes the airfoil", is misleading because it implies that causing an acceleration is part of the definition of a "reaction force". After this misleading introduction, one has to study the subsequent sentences to get the straight story. Of course the correct definition of a reaction force has nothing to do with causing acceleration, as is clear in the article "Reaction (physics)" to which the reader is redirected in that first sentence. When "reaction force" is properly understood as simply a force that has an action/reaction partner in accordance with Newton's third law, the statement "Lift is a reaction force" is practically meaningless because the same can be said of any other force. If we were to keep this section of the current article, I would at least delete the first clause, "Lift is a reaction force". Then you'd have something close to my draft, but I think my draft is more clearly worded.

So it doesn't seem to me that your objection to my proposed structuring of the article is justified, or that you've suggested any real improvement to my draft, at least so far. I think my draft represents a marked improvement over the current article, in both structure and content. Unless you or someone else suggests improvements soon, I'll go ahead and make the replacement. BTW, I've changed the proposed title to "Lift (fluid-dynamic force)" to be consistent with identifying "aerodynamic force" as a special case, as is done in the current article.

I disagree with the response by Djr32 (talk). Just focusing on a straightforward explanation sounds appealing in its simplicity. But given the history of multiple, mostly flawed explanations that have been presented to the public over the years, just presenting yet another explanation, without discussion of the earlier ones, would cause confusion. Given the history of this topic, context-setting is essential if confusion is to be avoided. Again, just look at the confusion manifested in the discussion on this talk page. My proposed revisions are intended to reduce this kind of confusion by providing context.

J Doug McLean (talk) 22:35, 3 June 2014 (UTC)

J Doug McLean wrote: Unless you or someone else suggests improvements soon, I'll go ahead and make the replacement.

I'm sorry, Doug, but that is not the way wikipedia works. The objective is to arrive at a consensus that the proposed changes to the article are an improvement. Thus far, I have not seen any evidence of such a consensus here on the talk page, either with this iteration or the one you proposed last January. To issue an ultimatum that you will "go ahead and make the replacement" unless certain terms are met is at variance with the wikipedia processes.

I agree with Djr32's criticism above.

Moreover, the proposed revision has other problems at the moment:

• Major sections have no citations at all. (e.g. A more comprehensive physical explanation)
• Other sections have insufficient citations.
• Controversial assertions are made in a somewhat opinionated manner, with the only reference being to your book. This violates both WP:NPOV and WP:COI (e.g. Coandă effect & viscosity)
• In many places it reads more like a personal opinion than a neutral encyclopedia piece.

I think it is a good article, but I don't think it is a good wikipedia article. I would like to continue to work towards incorporating some of it, and I'm hoping that you, I, and the other editors can work together to improve the current article .

At this point I'd like to solicit the opinions of other editors. What's your take? Mr. Swordfish (talk) 14:44, 4 June 2014 (UTC)

Thanks for the response. I'm sorry about the ultimatum. I am appropriately chastised and won't let it happen again. Still, there's a lot about the current article that needs changing, and I'm eager to get things off top-dead-center. And I still intend to push for large parts of the article to be replaced, either by me or by others.

I can see now how I got on the wrong side of WP:NPOV regarding Coanda and viscosity, and possibly on the popular explanations of lift. I've reworked those parts to take a more neutral point of view in the writing, while still making clear that there are reliable sources whose position is that some arguments are incorrect. When there are two opposing views on something, there is by definition a "controversy". But it doesn't follow that both views should be labeled "controversial". When one view is supported by the science (and can be verified as such by reliable citations), and the other is not, the physically sound view isn't controversial, to my way of thinking. In the case of the Coanda effect, the primary issue is the questionable use of a term, so I've labeled it "controversial". In the case of the purported role of viscosity in flow turning, it's not just semantics. On this one the science is clear, so I've labeled the "pro" statement a "misconception" and provided a citation of Milton Van Dyke, a leading authority on fluid-flow theory, whose mathematical analysis convincingly supports the "con" statement, i.e. it shows that viscosity plays no significant role in supporting flow curvature in boundary layers. In contrast, the sources for the pro side of this argument (Anderson and Eberhardt, and Jeff Raskin) provide only arm-waving statements with no mathematical support. In a case like this, it seems to me that not all sources should be given equal weight.

I don't see how I've violated WP:COI. As I've said, I think the citations of my book are relevant and not excessive. Boeing, with which I now have no relationship, holds the copyright, and I have no financial interest in the book's sales. And my book is not the only source I cite for the argument that Coanda is not relevant to lift. There are three others. So I think the citations are OK there, but I have revised that section to take a neutral point of view.

You wrote "Major sections have no citations at all. (e.g. A more comprehensive physical explanation)". I'm sure there are places where more citations would be good, but I found no section that had none at all. "A more comprehensive physical explanation" cited my book in the opening paragraph. In one sense that should be sufficient, since everything in the section can be found in that reference. This explanation of lift is my original work, but it is not "original research" by Misplaced Pages's definition because it has a citable source. I know of no other source that has put all of these ideas together in one explanation, so if we're to include this explanation I think we have no choice but to cite my book. The constituent ideas (e.g. the spread-out effects of the airfoil on the flow, the reciprocal relationship between pressure and velocity, and the acceleration of fluid parcels by the pressure gradient), on the other hand, are all well established in fluid mechanics, and there are other sources that can be cited for them. I've added some and continue to look for more. If you see other places that could benefit from more citations, I'd appreciate it if you'd point them out specifically.

J Doug McLean (talk) 22:48, 5 June 2014 (UTC)

I now have a first pass at integrating the proposed changes into the current article. It's at https://en.wikipedia.org/User:Mr_swordfish/Lift

I don't claim that it is perfect, or even ready (yet) to replace the current article. Since it is a mash-up of two different articles the writing style varies a bit. It would be nice to address that. In particular, the cites from the current article are very "web friendly' with hyperlinks where available and brief quotations of the relevant supporting text. In the main article space the reader can mouse-over the footnote and see for him or herself the supporting material without having to go find a book in a library (unfortunately, the mouse-over feature doesn't work in a sandbox). It would be nice to flesh out the citations in the new material to take advantage of this feature.

Regarding WP:COI, I did not mean to accuse anyone of ethical lapses or attempting to profit off our efforts here. Merely that Misplaced Pages's COI policies are rather strict - an author citing his own work and unilaterally editing an article over the objections of other editors would be a problem. As long as it is a group effort with other editors involved we should be in the clear.

Not everything from both articles made it into the integration. Arguments in favor of "restoring" certain sections cheerfully accepted. But when combining two rather long articles it's inevitable that some material would be cut. Perhaps more should be cut or moved to a separate article.

Some material is repeated. Since we're not making a set of mathematical axioms or constructing a normalized database, repetition in itself is not a problem. But there are redundancies that probably should be removed.

So, I'm soliciting comment on this draft. Whether that happens here on this talk page or the talk page in my sandbox shouldn't matter. Since the proposed revision is a release candidate, edits in place are welcome. I'll continue to make edits over the next few days, then I'm on vacation for a while. I'm thinking maybe a target date of July 1 to get it in order and replace the current article, subject to reaching consensus here, of course. Mr. Swordfish (talk) 21:11, 10 June 2014 (UTC)

Integration of McLean's proposed changes and current article

The integration is up in my user space at https://en.wikipedia.org/User:Mr_swordfish/Lift. Please make general comments here, and please start a new section for each specific topic so that we can discuss unrelated issues one at a time. Mr. Swordfish (talk) 21:49, 10 June 2014 (UTC)

After spending only a few minutes looking at in-line citations I noticed that some merely nominate an author and a year; no page or section number, no title, no publisher etc. That standard does not meet Misplaced Pages's guidelines. For complex referencing tasks, I recommend Misplaced Pages:Harvard citation template examplesDolphin (t) 01:08, 11 June 2014 (UTC)

Note that the author/date citations in the "Notes" section refer to entries in the alphabetized "References" list that give the title and publisher. True, some of them need to have a page or section number added. This is a format I've seen in the article on Navier-Stokes equations and in the Journal of Fluid Mechanics. I think the alphabetized list makes some things much easier for the reader, such as answering questions like "does this article cite Lanchester?" The "Notes" section is now a mixture of this new format and the original format. In the original entries that include quotes out front, author information is deeply buried and thus not so easy to find in a quick visual scan. A change that would be helpful, but would take some work, would be to put all the notes in a name/date/section/quote format and put all the all the other information on the references in the "References" list. J Doug McLean (talk) 20:01, 20 June 2014 (UTC)

Proposed changes to early sections of the integration

This integration is a good start. With this as a starting point, I'm proposing some moves and revisions for the early sections. I've installed them in my sandbox User:J_Doug_McLean/sandbox for your review, and I'll explain my rationale here.

I propose moving my new section "The understanding of lift as a physical phenomenon" back to a prominent position, just after the overview. It doesn't fit with the rest of the material in the "A more comprehensive physical explanation" section and would be much less effective there. Discussions over the years on this talk page have convinced me that there's widespread misunderstanding of the status of the hard science and how the qualitative explanations relate to it, so I think this context-setting section should come before the explanations start. I also propose adding words to the effect that the qualitative explanations cannot provide quantitative information for engineering. That's a property of all qualitative explanations, so I think it belongs here rather than in its current place as a limitation of flow deflection.

The integration's "Description of lift on an airfoil" section seems to me to mix explanation and description in a way that's not coherently organized and thus not as easy to follow as it could be (e.g. several of the subheadings under "Newton's laws: lift and the deflection of the flow" don't fit there.). I think the whole section could benefit from reorganization.

So I'm proposing rearranging this as two main sections. The first is "Simplified physical explanations of lift on an airfoil", which gives the deflection explanation first, in keeping with the AAPT advice. I put the points covered by the current "Flow on both sides of the wing" in with the deflection explanation. I kept separate headings for limitations of deflection and Bernoulli, but I'm proposing changes to what's included in those sections. Failure to produce quantitative information is no longer a limitation of deflection, as it's been covered above. I also propose a change under the limitations of Bernoulli (see below).

I propose putting everything else in the current "Description..." section under "Basic attributes of lift", with the current "Summary" statement moved to the front, and keeping the subheadings other than "Flow on both sides of the wing", the main points of which are would now be covered under flow deflection. I'd really prefer to put this section between "Overview" and "The understanding of lift as a physical phenomenon", but putting it after the simplified explanations, so that flow deflection can come earlier, is a compromise I can live with.

I look forward to feedback on these proposed changes. J Doug McLean (talk) 20:01, 20 June 2014 (UTC)

Apologies for taking some time off from this article. We didn't make the July 1st deadline, but hopefully we can get things moving again in the next several weeks.

I think the section https://en.wikipedia.org/User:J_Doug_McLean/sandbox#The_understanding_of_lift_as_a_physical_phenomenon is a fine section and don't disagree with anything in it. However, I do not think it deserves to be the opening section fight after the overview. I recognize that opinions may vary about this, but my issue is that the section is rather meta- that is, it talks about the explanation rather than simply giving it. At some point some amount of meta-analysis about the explanation is in order, but I prefer to cut to the chase and go right in to the explanation. Mr. Swordfish (talk) 20:29, 22 July 2014 (UTC)

I have integrated this section into my draft later in the article. Mr. Swordfish (talk) 19:42, 23 July 2014 (UTC)

Proposed change to limitations of Bernoulli

Under limitations of Bernoulli, I propose deleting the third bullet item because it implies that the assumptions behind the steady incompressible Bernoulli equation are invalid for "real world airfoils" in general. Actually, for low-Mach-number steady flow outside the boundary layer in the reference frame of the airfoil, the Bernoulli equation is highly accurate, contrary to what this paragraph and its sources imply. Significant limitations to the Bernoulli equation apply only in circumstances different from those of the usual airfoil explanations (e.g. accelerating flow or high-speed flow). The arguments in the four cited sources are seriously flawed, and I can give you my detailed reasons if you wish to see them.

I look forward to feedback on this proposed change. J Doug McLean (talk) 20:01, 20 June 2014 (UTC)

I have no objections to this. I've implemented this proposed change in my version of the draft. https://en.wikipedia.org/User:Mr_swordfish/Lift#Limitations_of_explanations_based_on_Bernoulli.27s_principle Mr. Swordfish (talk)

Proposed changes to "Mathematical theories"

The integration makes some changes to the new section "Mathematical theories of lift". The added explanation of getting velocity vectors from CFD and then the pressure from Bernoulli isn't applicable to CFD in general, only to potential-flow methods. I've taken a crack at fixing that and at dealing with the repetition regarding the Kutta condition.

I look forward to feedback on these proposed changes. J Doug McLean (talk) 20:01, 20 June 2014 (UTC)

I'm ok with this. I've replaced this section in my draft with the version from your draft. Mr. Swordfish (talk) 20:42, 22 July 2014 (UTC)

Proposed deletion or substitution of two figures

The figure currently illustrating streamtube pinching, with the caption "Streamlines around an airfoil in a wind tunnel. ..." seems to me to be contradictory. The horizontal bars appear to be intended to represent wind-tunnel walls, but the streamlines don't appear to be constrained by the walls. And wind-tunnel walls are not relevant to the explanation anyway. I propose, as I show in my sandbox, replacing this figure with the flow animation, with a caption tailored to the streamtube pinching explanation.

The figure caption "Uniform flow plus vortex flow (circulation) gives the total flow below" is not technically accurate. To get the flow around the NACA 0012 you would need to add a particular distribution of vortex strength along the chord (not just simple circulation), as well as a distribution of sources and sinks to represent airfoil thickness. I propose just deleting this figure. J Doug McLean (talk) 06:13, 21 June 2014 (UTC)

I agree that the diagram depicting streamtube pinching leaves something to be desired, but it is what's available in the public domain. That said, I think it does a better job of depicting streamtube pinching than the animated picture (https://upload.wikimedia.org/wikipedia/commons/9/99/Karman_trefftz.gif). Ideally, we'd find a better diagram. I'll see what I can turn up.

Agree that the other diagrams are not ideal either. The idea was lifted from one of Anderson's books, but I did the graphics and I'm a terrible graphic artist. I've deleted them from my draft since they may give a too-simplified impression. I do think that a picture representation of the idea of vortex flow + steady flow == total flow helps with a layman's understanding of circulation. But maybe it doesn't need to be in this article.

In coming days I hope to take a good look at both versions of the opening sections and attempt further integration. What would be nice would be to get a third (or fourth or more) editor(s) to help with this. Mr. Swordfish (talk) 20:58, 22 July 2014 (UTC)

I found a better picture for the streamtube pinching.

I think this depicts it better than the animated diagram, and it doesn't have the issues you mention that the old/current picture have. Mr. Swordfish (talk) 14:14, 23 July 2014 (UTC)

Release candidate?

I've spent some time further integrating Doug's draft into my draft, adopting much of his organizational structure and copying entire sections. At this point I think we have a release candidate.

The immediate question is whether it is an improvement over the current article. If so, we should replace the current article now and move forward with further improvements in-place. No article is ever "done" on wikipedia; refinements, additions, and improvements will likely be made in coming months and years.

If the draft is not an improvement then let's discuss how to improve it so that it is better than the current article.

My own opinion is that it's a stronger article. Many thanks to Doug for his effort and patience.

The draft is at https://en.wikipedia.org/User:Mr_swordfish/Lift Please take a look and share your opinion here. Mr. Swordfish (talk) 14:02, 25 July 2014 (UTC)

Great work! I have had a quick look at the release candidate and left a couple of comments at User talk:Mr swordfish/Lift. I will try to do more in coming days. Dolphin (t) 06:38, 26 July 2014 (UTC)

I agree that it's a stronger article, and by that criterion it qualifies for release. But I'd still like to advocate for some further changes that I think would improve it further, if you'll bear with me.

The first has to do with the section "The understanding of lift as a physical phenomenon". We have agreement that it should be included, but not on where to put it. I still think it should precede the qualitative explanations because it seems to me that when things aren't put in perspective at the start, the article ends up giving a misleading impression. If you just "go right in to the explanation" as you prefer, the article gives the impression, intended or not, that that's how lift is understood, and that the rest, including the mathematical theory, is just filling in the details. I think that's a misleading picture of how we really understand lift. And I don't think that reading the meta-analysis later in the article, assuming the reader even gets that far, will be very effective in undoing the impression. Better, I think, not to give the impression in the first place.

The mathematical theory is the bedrock of human understanding of lift. The qualitative explanations are secondary, really just attempts to square the theory with our intuition. And that's a hard thing to do, given that the continuum flow in effect consists of innumerable little parcels of fluid moving in concert to get around the airfoil, each one obeying the 2nd law in a mutual interaction with its neighbors. The theory handles this complexity correctly by requiring the solution of a set of PDEs, but our intuition doesn't do so well when faced with an entire flowfield. For one thing, how the pressure field comes about in such a flow is very difficult to grasp intuitively. The popular explanations either avoid the question altogether (the deflection explanation) or do it badly (the Bernoulli explanations), and even my "more comprehensive explanation" is shaky on this point.

So I feel strongly that before we dive into the qualitative explanations, we owe the reader a heads-up on where such explanations stand in the overall scheme of things, and why. "The understanding of lift..." attempts to do this, but it may not be entirely satisfactory as it stands. It should perhaps be beefed up to make it clear that the difficulty of the problem dooms the qualitative explanations to fall short of being completely satisfying, not just that they don't produce numbers and that there's been disagreement on what to include in them. In my sandbox User:J_Doug_McLean/sandbox I've added a sentence to try to do that.

There are times when some meta-analysis up front makes things better for the reader, and I think this is one of those times.

And the section heading should remain "The understanding of lift as a physical phenomenon", not "Understanding lift as a physical phenomenon". The former implies we're talking about the understanding held by the community at large (which is what this section is doing), while the latter implies a concentration on changing the understanding held by the reader. I think the difference is significant.

Next are a couple more issues with headings:

The content in "Description of lift on an airfoil" isn't really description; it's explanation. I think "Simplified physical explanations of lift on an airfoil" is more consistent with the content.

I think the heading "Methods to determine lift on an airfoil" promises more than we deliver. To apply either "Lift coefficient" or "Pressure integration" you have to know something a priori that's tantamount to knowing the lift. So these are really just relationships for converting one form of knowledge about lift to another; they don't really "determine" lift. I propose deleting the heading "Methods to determine lift on an airfoil" and promoting "Lift coefficient" and "Pressure integration" to sections in their own right.

Most of the material in the section "Kutta-Joukowski theorem" is now covered in "Circulation and the Kutta-Joukowski theorem" in the "Mathematical theories of lift" section. I propose integrating some material from "Kutta-Joukowski theorem" into "Circulation and the Kutta-Joukowski theorem", moving the description of the Magnus effect to "Lift forces on bluff bodies", and deleting "Kutta-Joukowski theorem". I've taken a crack at this in my sandbox User:J_Doug_McLean/sandbox.

Then a few technical issues:

Under "Flow deflection and Newton's laws", the statement "The resulting force upwards is equal to the time rate of change of momentum of the air downwards" is problematic on two counts, in spite of the fact that it has a citable source.

The first problem with the statement is that for it to be true, the downward force exerted by the airfoil on the air surrounding it would have to be the only force being exerted on "the air". There are many possibilities for how we can define the body of air we're considering, and this condition (no other force but the lift) isn't met in general. The airfoil exerts a downward force on the inner boundary of the body of air surrounding it (at the airfoil surface), but the surrounding environment exerts unbalanced pressure forces on the outer boundary of the body of air. This problem cannot be eliminated just by increasing all the dimensions of the "box" of air we consider, even to the limit of infinity. As the box is made larger, the pressure disturbances at the outer boundary get weaker, but the area over which they act gets larger, and the integrated force remains comparable to the lift. How much of the lift is accounted for by this pressure force rather than by momentum change depends on the proportions of the box. For example, for a box that is very large horizontally compared to its vertical dimension, practically all of the lift is accounted for by pressure at the outer boundary, and practically none by momentum changes. Only in the limit as the vertical dimension of the box becomes large relative to the horizontal is it true that lift is accounted for by momentum changes.

The other problem is that most such analysis in fluid mechanics deals with boxes whose boundaries are fixed in space. The time rate of change of momentum in such a box is zero in steady flow, and momentum changes must be assessed in terms of fluxes in and out, not the time rate of change.

Thus the simple explanation in terms of flow deflection is correct only if it's couched in vague terms such as "for the airfoil to deflect the flow downward, it must exert a downward force on the air". 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.

Under "Limitations of deflection/turning", the only limitation mentioned is that this explanation doesn't produce numbers. This limitation is a characteristic of all of the qualitative explanations and is now included in "The understanding of lift as a physical phenomenon". I recommend substituting the paragraph under "Limitations of the flow-deflection explanation" in my sandbox version User:J_Doug_McLean/sandbox, which discusses some limitations specific to deflection.

Under "Increased flow speed and Bernoulli's principle", the first paragraph needs to stipulate that Bernoulli's principle requires steady flow.

In that same section, I recommend deleting the second paragraph. The statement "Bernoulli's principle does not explain why the air flows faster over the top of the wing" isn't true. On the contrary, Bernoulli's principle tells us that if the air flows faster, it is because of the lower pressure. It's just that that didn't help the originators of the Bernoulli explanations in boot-strapping their way toward an explanation of where the low pressure comes from, and they had to find other reasons for the faster flow.

We're getting close, but I'd appreciate it if you'd consider the above changes. Thank you for your patience.

J Doug McLean (talk) 01:58, 27 July 2014 (UTC)

A lot to respond to at once, so I'll break it up into bullet points;

• Placement of the "The understanding of lift as a physical phenomenon" section - As I've stated before I think it s a good addition to the article, but leading with it seems off-putting to the general audience. And really, fundamentally I think our disagreement here stems from a different idea of who the intended audience is. For the layperson who knows little about the subject (i.e. the vast majority of wikipedia readers) the section would make little sense without first providing some context. I am open to moving it up in the article, say, between "Basic attributes of lift" and "A more comprehensive physical explanation."

• Section heading - I don't see a big difference in meaning between "The understanding of lift as a physical phenomenon" and "Understanding lift as a physical phenomenon" to my eyes, the former merely has two extraneous words. But I can see how you would parse it differently than I, so I've reverted the heading to your original.

• Section heading - "Simplified physical explanations of lift on an airfoil" is fine by me, I'll implement that change too.

• Section heading - propose deleting the heading "Methods to determine lift on an airfoil" and promoting "Lift coefficient" and "Pressure integration" to sections in their own right. that sounds reasonable. I'll do it and see how it looks.

• "The resulting force upwards is equal to the time rate of change of momentum of the air downwards" is problematic - I'm gong to punt on this one for now. Let me give it some thought and attention and I'll get back to you.

• "Limitations of deflection/turning" - I think you make a reasonable criticism, but I also think there's a bit of strawman there - the basic deflection explanation does not refer only to forces "exchanged at the airfoil surface, where the air and the airfoil are actually in contact". The diagrams clearly show air being deflected at some distance from the foil, not just at the surface.
  
  Agree that it doesn't explain why the air is deflected a distance away from the foil, or how the force manifests itself as a pressure difference, but my take is that it doesn't have to. For instance, it also doesn't explain why the air moves faster over the top or any of a hundred other related phenomena. It does explain where the lift force comes from and that's the point of the exercise.
  
  We have to be careful that we don't give the misleading impression that deflection is wrong or incorrect and I think the typical wikipedia user could get that impression from what you have written. I'll take a stab at addressing your concerns by adding some of these issues to the list of limitations.

• Redundancies in K-J theory section. Your proposal sounds fine. I'll take a look at integrating your changes into my version.

• Under "Increased flow speed and Bernoulli's principle", the first paragraph needs to stipulate that Bernoulli's principle requires steady flow. Ok, I'll add something to that effect.

• "Bernoulli's principle does not explain why the air flows faster over the top of the wing" isn't true. Yeah, that sentence has always bothered me too. Once you know that the pressure is reduced, BP tells you that the speed is faster. So it does explain why. Equal transit time doesn't explain why the air goes faster, and most explanations based on BP do not explain (correctly anyway) why the air goes faster. I'll look at changing that sentence.

It's now Friday, August first, and I think we are close enough that we can go live with the revision as-is. We can continue to discuss outstanding issues afterwards. I'll make the changes outlined above and unless I hear objections I'll replace the current article with the draft early next week.Mr. Swordfish (talk) 15:19, 1 August 2014 (UTC)

UPDATE: I've now completed the above edits. One issue I see is in response to I propose deleting the heading "Methods to determine lift on an airfoil" and promoting "Lift coefficient" and "Pressure integration" to sections in their own righ... I propose integrating some material from "Kutta-Joukowski theorem" into "Circulation and the Kutta-Joukowski theorem", moving the description of the Magnus effect to "Lift forces on bluff bodies", and deleting "Kutta-Joukowski theorem".

I've done this in my draft (with the exception of the treatment of the Magnus effect - will take a look at that next) A question: does it make sense for Lift Coefficient and Pressure Integration to have their own sections, or does it make more sense for them to be sub-sections under "Mathematical theories of lift"? I'm in favor of the latter, but could be convinced otherwise. I'm going to move them under the math section pending further discussion. Mr. Swordfish (talk) 18:29, 1 August 2014 (UTC)

Doug McLean wrote: ...the statement "The resulting force upwards is equal to the time rate of change of momentum of the air downwards" is problematic...

I have to say that I was surprised by this, so much so that I needed to take a few days to think about it before responding. And the reason for the surprise is that the statement is merely a combination of Newton's 2nd and 3rd laws with dp/dt replacing ma. This should be about as uncontroversial as it gets. In the simple model where all we consider is the air flow and the foil, it follows directly from Newton's laws. Of course, if the air is being accelerated by something other than its interaction with the foil then that additional acceleration will not contribute to the lift force, but it seems clear to me from the context that we're not talking about that scenario. I've added some language to clarify:

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

Agree that this total momentum change is difficult to calculate or measure. But in theory at least it must be equal to the lift force.

BTW, there's not just one cite for it, three others are included elsewhere: https://en.wikipedia.org/User:Mr_swordfish/Lift#cite_note-7 https://en.wikipedia.org/User:Mr_swordfish/Lift#cite_note-23 https://en.wikipedia.org/User:Mr_swordfish/Lift#cite_note-32

Mr. Swordfish (talk) 18:33, 4 August 2014 (UTC)

I'm also surprised by Doug's comment. Perhaps he is alluding to the idea that the time rate of change of momentum is equal to the aerodynamic force and not just its vertical component, lift. Dolphin (t) 22:28, 4 August 2014 (UTC)

No. The problem has nothing to do with whether we consider the total force exerted by the foil or only the lift component. See my response to Mr. Swordfish above. J Doug McLean (talk) 00:19, 7 August 2014 (UTC)

Your reasoning regarding placement of "The understanding of lift as a physical phenomenon" puzzles me. You argue that leading with it would be "off-putting to the general audience" and that it would "make little sense without first providing some context". But providing context is what this section is intended to do. It seems to me that launching directly into the deflection explanation without the context provided by "The understanding of lift as a physical phenomenon" gives a mistaken impression to the reader, to be remedied only later in the article: "Oh, by the way, those explanations we gave you early on aren't the real story on how lift is understood."

As for making "little sense" to an audience without prior knowledge, I don't see it that way. The section is brief and to the point, and, I think, easy to understand. I assume the target audience of an article in a general encyclopedia is literate adults, not children. If I were the reader, I'd welcome the context-setting up front. This is an encyclopedia article, not a mystery story.

So how do we decide this? Let's try a little meta-analysis of the arguments pro and con. I've argued that logical exposition of the subject matter favors having "The understanding of lift as a physical phenomenon" precede the simplified explanations, so as to put them in context with general understanding of lift. You haven't offered a counter-argument to this but have instead brought up other issues: "It's -meta." "It's potentially difficult for an audience without prior knowledge to understand." I think I've offered effective rebuttals to these arguments.

Regarding my proposed passage in "Limitations of deflection/turning", I think your argument that there's a strawman there is unjustified. I do say that the only forces referred to are those "exchanged at the airfoil surface, where the air and the airfoil are actually in contact", which is true. I don't say that those forces are all that the explanation refers to. I think the passage should be included. It doesn't imply that deflection is incorrect, just that it leaves a gap in that it doesn't explain how a deeper swath of flow is deflected than is touched by the airfoil.

Regarding "The resulting force upwards is equal to the time rate of change of momentum of the air downwards", I thought I made it clear in my previous posting what the problem with this statement is, but your response indicates that you don't agree that the force exerted by the airfoil is not generally the only force exerted on "the air" as a result of the lift. Let's look at this further.

A crucial question raised by the statement is what is meant by "the air". Again, any body of air that you choose to define as "the air" surrounding the airfoil must have both an inner boundary where the airfoil contacts it and an outer boundary where the surrounding environment contacts it. As a result of the lift there is generally an unbalanced pressure force on the outer boundary, so that the force exerted by the airfoil on the inner boundary isn't the only force resulting from the lift. With some detailed bookkeeping this pressure force can be quantified. If we put the outer boundary far enough from the foil, the idealized model of a uniform flow plus a vortex suffices, and we can draw general conclusions. Please read my previous comments where I explain how the percentage of the airfoil's force that is offset by the pressure force on the outer boundary depends on the proportions of the outer-boundary box.

Anyway, for most ways of defining what is meant by "the air", the statement is untrue. For example, the reader might reasonably assume that "the air" refers to the whole atmosphere. Given this definition of "the air", the downward force exerted on the air by the airfoil is completely offset by a distribution of over-pressure on the ground (see the famous figure 150 in Prandtl and Tietjens for what this pressure footprint looks like in 3D), so that the net force exerted on the air as a result of the lift is zero. Then the time rate of change of the integrated vertical momentum of the air must be zero as well. It's just Newton's second law, as you say. So again, the problem with the statement in the current draft is that it's not generally true, because it doesn't account for all the forces.

Your proposed clarification, i.e. limiting the statement to "the air deflected downwards by the foil", doesn't fix the problem. The subset of the air that's actually experiencing downward acceleration is still a body of air that an outer boundary can be drawn around. That body will still in general have a net pressure force on its outer boundary, so that the downward force exerted by the foil will not be the only force acting on that body of air. Thus even your clarified version of the statement isn't generally true.

There is one way to define "the air" so that the statement is true, but I think it's too specialized and complicated to be appropriate for this article. Draw the outer boundary of the box so that the vertical dimension is much larger than the horizontal dimension. In the limit as the vertical dimension goes to infinity relative to the horizontal dimension, the net vertical pressure force on the outer boundary vanishes. Then all of the lift is accounted for by the momentum transfer and none by the outer-boundary pressure force. But we're not done yet. To observe the momentum transfer as a time rate of change, we have to take another special step. The outer boundaries of the box must be assumed to be moving with the flow so that the box is not gaining or losing fluid anywhere along the boundary (This is different from the usual approach to control-volume analysis, in which box boundaries are fixed in the reference frame of the body). Only for this very special definition of "the air" can we make the statement that the lift is equal to the time rate of change of the integrated downward momentum of "the air". Unless we're willing to add these specialized qualifications to the statement (along with an appropriate citation), I think we should delete it.

This isn't just a quibble about rigor. The statement L = dp/dt is actually untrue for many reasonable ways of defining what is meant by "the air", i.e. it's untrue for anything other than an infinitely tall vertical sliver with boundaries that move with the flow.

The three sources you mention all make an error that's easy to make, i.e. applying the second law to a body of air, but without adequately defining what is meant by "the air" and without identifying all the relevant forces. The idea that "the air" generally has lift-related forces acting on it other than that exerted by the foil seemingly didn't occur to them. J Doug McLean (talk) 00:19, 7 August 2014 (UTC)

There seem to be three remaining areas of disagreement;

• Placement of the "The understanding of lift as a physical phenomenon" section. At this point, I don't think either of us are going to be swayed by the others opinion. My sense is that we have a disagreement over the intended audience and how best to serve that audience. My view is that the section makes a lot of sense to those who are already familiar with the material, but that it's "inside baseball" for 99% of the audience. My editorial sense is that we shouldn't lead with it.
  This will have to be resolved by seeing what the other editors think or getting a third opinion.
  I do take exception to your characterization "Oh, by the way, those explanations we gave you early on aren't the real story on how lift is understood." The simplified explanations are every bit as "real" as the more thorough explanations. Replace real with full and I'll agree with you. But the article is quite upfront about the fact that the simplified explanations are not the "full story".

• "Limitations of deflection/turning" I've added a few lines reflecting the issues you bring up. Please take a look.

• "The resulting force upwards is equal to the time rate of change of momentum of the air downwards" I have to say that I am not able to follow your line of argumentation. And even if I could and agreed with it, it wouldn't matter for our purposes here as editors. Discussions on this page are not citable. Our job as editors is to reflect what is published in reliable sources. In reading literally hundreds of articles on this subject, I have never run across a single one refuting this assertion. Meanwhile, there are several reliable sources that support the statement. Perhaps if there was some disagreement in the literature we could present it as a controversy. But unless we have some reliable published source we are bound to present what's been published. See WP:TRUTH for more details.

Mr. Swordfish (talk) 18:33, 7 August 2014 (UTC)

My arguments on the "rate of change of momentum" statement are all supported by citable sources. A minimal but sufficient set of them will be quoted below. I didn't bring them up before because I was advocating for deleting the statement, and I didn't think that would require citations.

Because the statement doesn't specify what it means by "the air", a reader would and should expect it to be true for any reasonable assumption as to what "the air" encompasses. However, it is well established in the aerodynamics literature that the statement is false for most of the assumptions the reader might make, i.e. it is false if "the air" refers to the whole atmosphere or to any subset of it that isn't very tall compared to its width. If the statement failed only in exceptional circumstances I wouldn't press the issue. But it fails for the most obvious assumption the reader is likely to make, i.e. that "the air" refers to the whole atmosphere. So the problem is serious.

Because the statement has been shown by reliable sources to be contradicted in relevant situations, it has been effectively refuted, and letting it stand "as is" would be inaccurate and inconsistent with "what's been published". I think that leaves us two options:

1) Delete the statement and the citation. It isn't crucial to the deflection explanation, which is most often stated without the quantitative assertion " is equal to...." anyway. We have ample evidence from the mainstream aerodynamics literature that the statement is faulty, justifying our deleting it.

2) Keep the statement but add the clarification that's needed to make it clear when it's true and when it's not. Here's a rough draft of what I think that would have to look like:

In the text of the deflection explanation:

The resulting force upwards is equal to the time rate of change of momentum of the air downwards. This statement assumes that all of the lift can be accounted for by a momentum change in "the air", which is true only if "the air" refers to a region that is very tall relative to its width. For the atmosphere as a whole, or for a subset of it that is not tall compared to its width, part or all of the lift is accounted for by pressure differences on the top and bottom of the body of air in question, reducing the proportion accounted for by the momentum change.

In the notes section:

For the atmosphere as a whole, the integrated time rate of change of vertical momentum due to the lift on a wing is zero , and the lift is reacted entirely by a pattern of overpressure on the ground. For regions that are subsets of the atmosphere, the proportions of the lift that are accounted for by momentum change and by pressure differences depend on the size and shape (vertical dimension compared to horizontal dimension) of the region. Only if the vertical dimension is very large relative to the horizontal dimension are the pressure differences negligible, leaving the lift entirely accounted for by the change in momentum. (Section numbers and quotes would be added to these citations, and other citations could be added. I mention only the ones that come immediately to mind, but I think even just these would be sufficient.)

I expect you'll agree that the second option is too complicated and technical to be appropriate for this article. I'd argue that deleting the statement and the citation is the better option.

I wouldn't advocate presenting this as a "controversy" because I don't think it amounts to one. The "con" arguments are from the mainstream aerodynamics literature, where they are supported by rigorous math. The "pro" statements you've cited are not supported by rigorous analysis and are all from "The Physics Teacher", which is not a mainstream source of information on aerodynamics. The error made by the statement isn't something esoteric about which experts might disagree; it's basic: It is wrong to apply Newton's second law to just a subset of the forces exerted on a body. In addition to the force exerted by the foil, the air around an airfoil generally has unbalanced pressure forces acting on it. Not being aware of these pressure forces is understandable in this case. Authors of articles in "The Physics Teacher" are not typically mainstream experts on aerodynamics.

A relevant quote from WP:TRUTH: "To know where we have a dispute and where a simple mistake, consider whenever the author is really an expert on the topic (and not an expert on another topic, making a brief reference to something beyond his area of expertise)...." So we editors are not just cyphers. We are expected to exercise judgment as to the relative authoritativeness of our sources. Weighing what's been published in the mainstream aerodynamics literature against the statement in question, I think we'd be on firm ground deleting the statement and the citation.

Your proposed changes to "Limitations of deflection/turning move in the right direction, but not far enough, in my opinion. And the first and second sentences have a jarring relationship. The first sentence deals with the failure to produce quantitative results. The second begins with "In particular," implying it is about to home in on a particular aspect of that issue, but then deals only with the incompleteness of deflection as a qualitative explanation, which is a separate issue. I'd replace "In particular" with "Furthermore". The third sentence deals with issues that are treated further later in the article, so some tie-in would be good. Here's a shot at fixing the whole paragraph, with some rearranging to keep the quantitative and qualitative issues separate:

This simple explanation, while correct in as far as it goes, is not sufficiently detailed to support the precise calculations required for engineering. Quantitative predictions require a mathematical theory as described below under "Mathematical theories of lift."

Furthermore, this explanation does not explain pressure and velocity variations in the vicinity of the airfoil or how the airfoil can impart downward turning to a much deeper swath of the flow than it actually touches. "A more comprehensive physical explanation" given below attempts to address these issues in a qualitative way.

On an earlier question, I don't see "Pressure integration" and "Lift coefficient" as belonging in the mathematical-theory section. I think they would fit well in "Basic attributes of lift", with the material in "Pressure integration" merged into the current "Pressure differences", and the material in "Lift coefficient" merged into the current "Air speed and air density". I've tried this out in my sandbox User:J_Doug_McLean/sandbox, and I think it works well.

J Doug McLean (talk) 06:44, 10 August 2014 (UTC)

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