Talk:Lift (force)/Archive 10

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Rotary wings

Thinking about helicopters, it occurs to me that "the air deflected downwards" is unusually easy to identify. A rotary wing is just an ordinary wing moving in a circle. Most noticeably when hovering, a helicopter's rotor creates a strong downdraught in the form of a cylindrical column of air. The effect is readily visible as a characteristic texturing of waves when over water. This downwash evidently carries a good deal of momentum, which is constantly replenished by the rotary wings. But of course, the no momentum theorem cannot be violated. How can this be? The downwash splats against the ground and spreads out - low over water, spume is often thrown up to show this flow. The air then rises again, creating a toroidal vortex kept spinning by the rotor. The net momentum of the vortex is zero, but to argue that the rotor is not supporting itself by imparting momentum to the downwash appears absurd. Considering a short span of a single rotary blade or wing, we can treat it like any other short section of any other wing. We are forced to conclude that it is contributing to the downwash. Therefore, a normal wing also contributes to a downwash. Furthermore, in neither case is the no momentum theorem violated: the difference lies only in the geometry of the induced vortex. Is there a flaw in this picture? — Cheers, Steelpillow (Talk) 21:40, 25 March 2015 (UTC)

"Is there a flaw in this picture?" Yes, several flaws. The biggest is when you say "We are forced to conclude that [the short section of wing] is contributing to the downwash.". There is nothing "forcing" you to this conclusion other than your belief that it must be true, combined with a lack of rigour in your initial assumptions and development of the argument. I could explain all the Fluid Dynamic details of rotary wings at length here (I have covered some of it before), perhaps by mentioned that the "downwash" is a direct consequence of the inefficiencies that result from the "wing-tip vortices" and is not central to understanding the Lift generated by rotary wings, or that the more simplified "actuator disc theory" requires a consideration of both the momentum AND ENERGY in the flow before it can produce any useful results. But, previously when Doug tried such thoughtful and patient explanations you described his efforts as "... vast screeds of techno-verbiage and tenacious persistence [to] swamp every discussion ... a perfect case of long-term WP:DISRUPTION", and "It will only be when this editor is removed from the discussion and can no longer drown it out that the content issue can be properly addressed.". So I won't bother spelling out these details here. Instead, if you want to properly address the content issues, then I suggest you study more deeply the RSs yourself, which for this subject begin in early 1800s. In doing so, it is worth considering a rotary wing in a sealed duct. (Zapletal) 101.170.255.232 (talk) 03:19, 26 March 2015 (UTC)

The idea that I a priori believe that it must be true is absurd. I have argued all along that it is to be found in sufficient reliable sources that it must be given due weight. I have also tried to present that case as best I understand it, that is all. — Cheers, Steelpillow (Talk) 11:45, 28 March 2015 (UTC)

Without going into a lot of detail, I'd just say the situation is similar to what we've been discussing for a stationary foil with air flowing past. The simple actuator-disc theory for a rotor or propeller treats the flow in a time-averaged sense (averaging out the effects of individual blade passages) and ignores viscosity and compressibility. The rotor disc itself doesn't directly impart any change in vertical momentum because that would require a jump in vertical velocity, which would violate conservation of mass. Thus in the immediate vicinity of the disc the lift is manifested entirely as a pressure difference between the air below the disc and the air above. There is vertical momentum in the air passing through the disc, but it was imparted by the extended pressure field above the disc. The pressure jump imparted by the disc is what is needed to make the whole flowfield consistent with the equations of motion. To see the lift accounted for entirely by a change in momentum flux requires a control volume for which the integrated vertical pressure force on the outer boundary vanishes. which essentially requires looking at the equivalent of the tall, slender control volume we've been discussing in connection with airfoils. I think the upshot is that this example doesn't tell us anything we didn't already know. J Doug McLean (talk) 22:12, 26 March 2015 (UTC)

I take your point that the imparting of downward momentum is indirect. Nevertheless it is imparted, and tertiary sources in particular give a lot of weight to the momentum model (I just found another, from Sikorsky ca. 1960s, but I won't clutter this discussion unless asked). The problem has always been to follow that momentum, to identify "the air deflected downwards". It just seems to me that the cylindrical downwash of a helicopter disc is a rare case of easy visualisation. I'd add that the classic disc model imparts half the momentum above the disc and half below. I'd suggest that this helps picture how the momentum model works and consequently also to see its limitations. — Cheers, Steelpillow (Talk) 18:32, 27 March 2015 (UTC)

Readers wondering about good theoretical models for explaining "Rotary wings" might want to think about this particular case. Consider a helicopter in a very tall circular room, such that the blade-tips are spinning very close to, but not quite touching, the walls. It should be apparent that this helicopter can, indeed, hover above the ground (ie. it can sustain Lift, and thus fly). Big questions - Where is "the downwash"? Where is the air that has "downward momentum imparted" to it, in order to generate the required Lift, per "TS"? And what happens to this supposed downward moving air, given that the bottom of the room is sealed (ie. it has walls and a floor, but no open doors, etc.!)? This hypothetical problem is, of course, no different to the extremely common "fan in a duct". That is, it is VERY REAL. Any good model of "Lift" should, at the very least, be able to explain this simple and very real case. (BTW, the main difference between this case and the "helicopter in free air" is that one has wing-tip-trailing-vortices and the other does not.) (Zapletal) 101.170.85.82 (talk) 01:51, 28 March 2015 (UTC)

• For a helicopter in a tall cylinder, instead of downwash, the rotors maintain a pressure differential within the tall cylinder sufficient for the helicopter to hover. For a more general situation, consider the case where an electric powered model helicopter is enclosed inside a large sealed chamber (the rotors are not close to the walls). First note that the external weight of sealed chamber with just air (no helicopter) equals the weight of the chamber and the air inside the chamber. Following the Bernoulli equation gravitational potential, gh = constant - pressure / density, the pressure decreases linearly with height, and the pressure gradient results in a net downwards force exerted onto the interior of the sealed chamber, exactly equal to the weight of the air inside the chamber. Now add the helicopter into the chamber. The total weight of the system is the weight of the chamber, air, and helicopter, regardless if the helicopter is at rest or hovering (as long as there's no vertical component of acceleration of the center of mass of the system). If the helicopter is hovering it increases the pressure gradient so that the net downforce exerted onto the sealed chamber exactly equals the weight of the air and the hovering helicopter. Rcgldr (talk) 16:00, 3 December 2015 (UTC)

An underlying assumption of the simple model, ISTR given explicitly by some sources, is that the air extends indefinitely and so cannot sustain a unidirectional force. This is the reason that F=ma has to be invoked. The sealed chamber breaks this assumption and is not comparable: its rotary wing is not in "free flight" and so does not invoke F=ma. Come to think of it, this assumption of free flight is not stated in the article - it might be useful to do so, and to explain that this is why F=ma gets invoked in the first place.

This is in fact the main difference between the chamber and free flight, not the tip vortices as suggested. Consider an open-ended duct, which is also common enough: there are no tip vortices here, yet there is a downwash. In fact the downwash is even stronger than that of the same rotor spinning freely: the inefficiencies of the tip vortex do not create the downwash, they do the opposite and reduce it - in proportion as they reduce the lift. What I have mainly been discussing is the well-established actuator disk model. In this theory the individual blades and their tips are ignored. A fuller treatment, including the individual blades and their tip vortices, describes a rather different downwash, which is perhaps where some of the confusion in the above reply lies. Unfortunately it leaves the deflection of air as complicated and un-intuitive as before. I do not see how a discussion of tip vortices can clarify the present example.

— Cheers, Steelpillow (Talk) 11:45, 28 March 2015 (UTC)

Steelpillow, there are numerous errors in your above post.

1. On a technical point you say "... the inefficiencies of the tip vortex do not create the downwash, they do the opposite and reduce it - in proportion as they reduce the lift." This is completely at odds with established Fluid Dynamic thinking (as was first developed by Lanchester and Prandtl). Completely back-to-front. Stronger tip vortices = more downwash. I suggest you study this subject more deeply. Also other technical errors, but...

1. Take a look at faa_helicopter. Tip vortices, especially when in a hover, reduce downwash, and require more collective (more angle of attack) in order to produce the same downwash. Rcgldr (talk) 16:17, 3 December 2015 (UTC)

@Rcgldr: I did take a look at the web site, and searched for the word "downwash". This word doesn't appear on the web site. Please quote the actual sentence you are alluding to, or the first sentence in the paragraph you are alluding to. Saying "Tip vortices, ..., reduce downwash" defies comprehension. Perhaps you have found a source that says ground effect reduces downwash. Dolphin (t) 11:53, 4 December 2015 (UTC)

It is probably closer to the truth to say that downwash spills out around the blade tips, thus causing or increasing wingtip vortices: allowing those vortices to increase for a constant loading involves greater spillage and this leaves less downwash behind. It would be even more correct to describe it in terms of the pressure and momentum distributions which cause both effects. OTOH if the vortices are increased through increasing the loading then yes of course the downwash will also increase. So it depends on the assumptions behind such statements. But really, this particular detail is too far from the subject matter of this article to be worth pursuing here. — Cheers, Steelpillow (Talk) 12:49, 4 December 2015 (UTC)

@Dolphin51 - It's poorly worded: When the helicopter gains altitude vertically, with no forward airspeed, induced airflow is no longer restricted, and the blade tip vortices increase with the decrease in outward airflow. As a result, drag increases which means a higher pitch angle, and more power is needed to move the air down through the rotor. The statement is backwards, drag increases because a higher pitch angle is required to generate the same amount of lift (downwash). The key point is more power is needed when blade tip vortices increase. This is a side effect of induced flow cycling to increase tip vortice size when in a hover. In forward flight, at sufficient speed, the induced flow doesn't cycle, tip vortice size is smaller, and less power / pitch angle is required for level flight. The worst case scenario for a helicopter is a vertical descent into its own downwash, as some helicopters don't have enough power to compensate and the only way to recover is to transition into forward flight. Rcgldr (talk) 19:01, 6 December 2015 (UTC)

2. On a more general point, "What I have mainly been discussing is the well-established actuator disk model. In this theory the individual blades and their tips are ignored. A fuller treatment, including the individual blades and their tip vortices, ... leaves the deflection of air as complicated and un-intuitive as before." This Lift article is mainly about explaining aerofoil and wing-Lift, NOT rocket propulsion or other forms of Lift. Actuator disc theory (which I mentioned on these Talk pages several months ago) is a dumbed-down averaging of the effects of a rotary-wing AND its tip-vortices. As such it misses most of the interesting parts of aerofoil/wing Lift theory. For example, it is of no practical use in the fan-in-sealed-duct case I gave above, which thus makes it an inferior model to CToL (eg. the CToL model allows accurate predictions to be made of flows around the fan-blade sections, even in a sealed duct).

3. Most generally, "Come to think of it, this assumption of free flight is not stated in the article - it might be useful to do so, and to explain that this is why F=ma gets invoked in the first place." The article is about Lift, NOT "free flight". As such it should explain BOTH wing-between-walls (= fan-in-duct) and wing-in-unbounded-fluid-domain models of Lift. The simpler of these is the former (ie. the "planar", or "axisymmetric", or ~2-D model), and the latter "free-flight" 3-D model is simply an extension that builds on this initial model (again, read Lanchester's and Prandtl's early work). It follows that the simplest model, namely planar-CToL, should be introduced first and given the clearest explanation, with no unnecessary distractions.

On a final note, I read the Actuator-Disc Wiki-article, and many of the other Fluid Dynamic Wiki-articles linked to it. They are all RIDDLED WITH ERRORS! I guess this should come as no surprise, given the extreme difficulty there has been in getting this article into reasonable shape (ie. in accordance with GOOD RSs, and as per proven GOOD Fluid Dynamic theory). (Zapletal) 101.171.255.248 (talk) 02:26, 30 March 2015 (UTC)

Zapletal - Stop shouting. It is offensive, and is not a way to address content disputes in Wikipedia, and it certainly is not a way for an unregistered anonymous editor who apparently doesn't have the courage to use a pseudonym and a consistent editing history to address a content dispute. You have made no constructive contributions to this article. All that you do is to insult other editors. If you don't have anything useful to say, you don't need to say anything. Robert McClenon (talk) 02:40, 30 March 2015 (UTC)

Robert, your above post is extremely offensive on many levels (in particular, read all the constructive contributions that I have made on this Talk-page, and on at least three other archived Talk-pages). Please strike-through your above offensive comments (including the one further up). If you have anything to contribute to these content issues, then please do. Meanwhile, stop your personal attacks. (Zapletal) 101.171.255.250 (talk) 02:34, 31 March 2015 (UTC)

I have no intention of striking anything. You, Zapletal, stop the personal attacks. Robert McClenon (talk) 02:58, 31 March 2015 (UTC)

One possibly useful technical point does arise. If a given (e.g. square-tipped) rotor is shrouded in a short open-ended duct, this reduces the tip vortices. Are you saying that it consequently also reduces the net downwash from the rotor disc? That is contrary to my understanding, though I have no source to hand. What do Lanchester and Prandtl say about this? Or is this just another of those claims that on investigation turn out to be unsupported? — Cheers, Steelpillow (Talk) 10:44, 30 March 2015 (UTC)

Steelpillow, this is all covered by Helmholtz's "Vortex Laws" (given in H's seminal paper of middle 1800s). The "Bound Vortex" belonging to each rotary-wing (ie. to each fan-blade, and giving it Lift via CToL) cannot just disappear into the "short open-ended duct". So all of the BVs of all of the rotary-wings (ie. fan-blades) ultimately emerge at the trailing edge of the duct and form a tubular vortex-sheet extending downward. An unducted propellor has a helical arrangement of blade-tip trailing vortices that approximate the tubular vortex sheet (this helix is often seen "cavitating" in underwater propellor flows). The BVs at the hub-end of all the blades also all combine and result in a power-sapping swirl to the flow. This swirl can be largely overcome with counter-rotating blades, but the outer tubular vortex sheet cannot be made to disappear in unbounded 3-D flows. As to "...another of those claims that on investigation turn out to be unsupported?", I must assume you are referring to TS? The established body of Fluid Dynamics knowledge that Doug and I have been putting forth here is rock-solid. It has been most thoroughly tested. If you can find any genuine flaws in it, then please write up a paper and go through the usual peer review process (there is a Nobel prize in it for you, IF you are right). Meanwhile, Wikipedia is supposed to be about giving due weight to the genuinely reliable sources, and NOT about promoting wacky fringe ideas such as in the "One Minute Physics..." cartoon currently at the end of the article. (Zapletal) 101.171.255.250 (talk) 02:34, 31 March 2015 (UTC)

The only people claiming to have found flaws are those who continuously argue that the cited material in the article is wrong/misleading. Nobody will win a Nobel prize out of this discussion, because nobody has found a "genuine flaw" in anything. That's the whole problem with this discussion. I note Steelpillow's simple direct question, "What do Lanchester and Prandtl say about this?" hasn't been answered. Burninthruthesky (talk) 08:35, 31 March 2015 (UTC)

Indeed. Nor was any attempt made to answer my question, "Are you saying that it consequently also reduces the net downwash from the rotor disc?" A simple yes or no would suffice. Instead we get an irrelevant and inconclusive diversion about the inner workings, along with the evident rejection of my good faith when I say that I have no a priori beliefs about these issues. — Cheers, Steelpillow (Talk) 22:57, 31 March 2015 (UTC)

Clarifications:

1. "If a given (e.g. square-tipped) rotor is shrouded in a short open-ended duct, this reduces the tip vortices." No it does not (as per H's Vortex Laws). The question that followed this quote is thus baseless.

2. "What do Lanchester and Prandtl say about this?" They have a great deal to say about wing-tip vortices in 3-D flows. Please read their works.

3. "... nobody has found a "genuine flaw" in anything." The words used to explain "...how wings actually generate Lift..." in the "One Minute Physics" cartoon at the end of the article are TS, pure and simple, ie. "... the key is the wing must deflect the air downward...". The picture drawn in that cartoon is typical of many other images that accompany these dumbed-down (ie. ETT-like) TS explanations of Lift. That picture is entirely inconsistent with the streamlines of real Lifting flows, which are well represented by the animation near the top of the article. The TS picture is unrealistic, and is thus genuinely flawed. (Zapletal) 101.171.213.66 (talk) 01:06, 1 April 2015 (UTC)

The assertion that such rotor shrouds to not reduce tip vortices runs counter to widely-held belief. Similarly, in the design of fixed-wing aircraft, devices such as endplates and winglets are widely believed to reduce tip vortices - see for example Wingtip_device#Winglet. To the question, "What do Lanchester and Prandtl say about this?", "lots" is not an adequate answer. I may have missed it but I am not aware that Lanchester or Prandtl denies this belief. The editor's claims to the contrary are now clearer, but they appear unusual and I see nothing in the above to support them. — Cheers, Steelpillow (Talk) 09:52, 2 April 2015 (UTC)

Steelpillow, if you read your link more thoroughly you will see that "winglets" are used to reduce induced drag whilst adding only small structural loads on the wing. They do this by moving the core of the tip-vortex a short distance above or below the outer section of the wing. (To restress this, the core of the tip-vortex is "moved away from", not "reduced in strength".) A small increase in wing-span can give the same (or much greater) reduction in drag, but it increases structural problems (ie. much more bending stress at wing-root). Importantly, Helmholtz's Vortex-Laws are non-negotiable. Good Fluid Dynamicists know this, and seek only to distribute the unavoidable vorticity as best suits the problem. For example, the main rationale for ducted-fans, or winglets-on-propellor-blade-tips, is to allow the "circulation" (ie. the bound vorticity) around the blades to be increased, thus allowing greater thrust from smaller diameter propellors, and thus also allowing greater craft speed before blade-tip-flow compressibility problems arise (ie. tip goes sonic and makes too much noise). But the blades' bound vorticity must inevitably emerge somewhere, typically at the trailing-edge of the duct or winglets. This is undeniable.

Of course, reading my link more thoroughly - which is to say at least as far as the second paragraph - reveals the remark that "Another potential benefit of winglets is that they reduce the strength of wingtip vortices." One may be forgiven for taking the rest of Zapletal's comments to be as well-resarched as this one. — Cheers, Steelpillow (Talk) 10:40, 3 April 2015 (UTC)

To repeat yet again, moving the core of the tip-vortex further away from the wing reduces the strength of the vortex's EFFECT at the wing, but it does NOT reduce the vortex's inherent strength. Study the Biot-Savart equation. But given that the depth of your research seems to be to pick the first quote from a Wikipedia article (!) that, when misunderstood, supports your mistaken view, I guess Biot-Savart is a step too far. (Zapletal) 101.170.42.142 (talk) 02:43, 4 April 2015 (UTC)

Now the big question is whether the above explanation will be described again as "... an irrelevant and inconclusive diversion about the inner workings..."? Given that this was your offensive response to my earlier post, I will leave it to you to find out what Helmholtz, Lanchester, Prandtl, et al, say on the issue. (PS. Have you managed to explain how the "helicopter-in-a-circular-room" (= fan-in-a-sealed-duct) can sustain Lift, given that there is no possible continuous "downwash", as is required by TS?) (Zapletal) 101.170.42.159 (talk) 01:33, 3 April 2015 (UTC)

Yes. Evidently you read it as thoroughly as you followed up my link. — Cheers, Steelpillow (Talk) 10:40, 3 April 2015 (UTC)

Your previous explanation concluded with "A fuller treatment, including the individual blades and their tip vortices [ie. CToL], ... leaves the deflection of air as complicated and un-intuitive as before...". In both the helicopter-in-free-air case, and the helicopter-in-circular-room case, the CToL model gives an entirely accurate description of the "deflection of air" and its consequent generation of Lift. It is, in fact, essentially the same description as that presented (by Doug) in the body of the article. However, as you seem to acknowledge in your previous explanation, the TS model is incapable of describing the Lift of the helicopter-in-circular-room (ie. for some reason you seem to believe that the air in the circular room has somehow developed different properties, namely ''is not comparable", to the air outside). The TS model is thus in no way a fundamental description of Lift (as per "the wing MUST deflect the air downwards"), and it should be expunged from the article. (Zapletal) 101.170.42.142 (talk) 02:43, 4 April 2015 (UTC)

Raskin

The following reference may not be useful:

• Raskin, J. (2007), Coanda Effect: Understanding Why Wings Work http://jef.raskincenter.org/published/coanda_effect.html, archived from the original on September 28, 2007 {{citation}}: External link in |title= (help); horizontal tab character in |title= at position 44 (help)

It was removed. Anyone that can shape it up may replace it. — Rgdboer (talk) 22:13, 12 June 2016 (UTC)

They all had tab characters in, now removed. The problem with the Raskin cite was the url and comment in the title field, now fixed. There are probably fields for them in the template, perhaps somebody can put them back in the right places. — Cheers, Steelpillow (Talk) 09:04, 13 June 2016 (UTC)

 Done. Burninthruthesky (talk) 09:20, 13 June 2016 (UTC)

Misconception regarding "pulling down" of the flow

One simple explanation for why a flow follows a convex surface is that the convex surface sweeps out a volume of a flow leaving what would otherwise be a void if the flow didn't follow the convex surface as either an attached flow or a detached flow with a turbulent (vortices) boundary layer to fill in what would otherwise be a void. I'm not sure if this explanation could be considered as a type of Coandă effect Rcgldr (talk) 02:43, 23 June 2016 (UTC)

Theories for this mechanism are quite contentious. The article tries to follow only what reliable sources say and to avoid original research by its editors. If you can find a reliable source which explains it all clearly, please weigh in! — Cheers, Steelpillow (Talk) 08:19, 23 June 2016 (UTC)

There are multiple sources on web sites that include the common phrase what would otherwise be a void in this simplified explanation for how wings work, but I'm not qualified to claim these are reliable sources. Rcgldr (talk) 09:26, 23 June 2016 (UTC)

There are a good few myths about aerodynamics that crop up all over the place. Such web sites are not always reliable, and must be regarded as unreliable unless we are confident their content is properly peer-reviewed. — Cheers, Steelpillow (Talk) 12:04, 23 June 2016 (UTC)

• A reference that includes the phrase "otherwise there would be voids ..." lift.htm - an article by David Anderson, Fermi National Accelerator Laboratory, and Scott Eberhardt, formerly of the Department of Aeronautics and Astronautics, University of Washington. Also "what would otherwise be a void": new world encyclopedia aerodynamics of gliders pdf. "sweep out a space behind the top" avweb . Rcgldr (talk) 05:26, 24 June 2016 (UTC)

  Looks OK to me. Go for it. — Cheers, Steelpillow (Talk) 08:53, 24 June 2016 (UTC)

Material written by David Anderson and Scott Eberhardt cannot be regarded as reliable for the purposes of Wikipedia or any other encyclopedia. Anderson and Eberhardt write about flight and lift for a non-scientific audience such as trainee pilots, young people and others new to the field. Their objective is to avoid mathematics and an overly scientific approach, and to make use of day-to-day language that will be readily comprehended by a wide audience. In pursuit of their objective they have written some things that cause dismay to scientists and aviation professionals. See Talk:Bernoulli's principle/Archive 2#Understanding Flight. They have attracted a fair amount of criticism for some of their sweeping generalisations. Dolphin (t) 12:33, 24 June 2016 (UTC)

"Their objective is to avoid mathematics and an overly scientific approach, and to make use of day-to-day language that will be readily comprehended by a wide audience". That is pretty much what Wikipedia is for. We do need to provide an accessible treatment at this kind of level, even if we also provide a more specialised treatment where the mainstream technical jargon and equations are presented. The question then is, at which level should the present article be presenting the subject? Has it got too technical too soon, and if so then how do we fix that? — Cheers, Steelpillow (Talk) 18:29, 24 June 2016 (UTC)

That was their objective but I'm not saying they succeeded. They suggest that flow around a convex shape, including flow around an airfoil, is caused by the Coanda Effect. That is not avoiding an overly scientific explanation. Application of Coanda to aerodynamic lift is highly controversial. Anderson and Eberhardt say "Bernoulli's principle has mistakenly become linked to the concept of flight." Where reliable published sources acknowledge two or more different explanations Wikipedia aims to give due weight to them all. Anderson and Eberhardt deserve no more than a little weight. Dolphin (t) 22:51, 24 June 2016 (UTC)

It seems clear that a convex surface sweeps out a volume of air (per unit time), which would introduce a void if the air didn't somehow fill in that volume (per unit time) swept out by the convex surface. The same principle applies to a flat plate at an angle of attack, and I assume that Coanda effect doesn't apply to flat plates. If the curvature of the convex surface is gradual enough or if the angle of attack of the flat place is small enough, then in what could be called the principle of least action, the air tends to mostly accelerate inwards (perpendicular to the flow (lift)) and only somewhat accelerate forwards (drag). If the curvature of the convex surface is too great, or the angle of attack of a flat plate is too great, the flow detaches, and what would be a void is filled by turbulent vortices. A similar and well known concept applies to streamlining high speed land vehicles with a gradually tapered tail, so that the "void" is gradually introduced, which results in the affected air accelerating mostly inwards (no drag), and only a bit forwards (drag), which is essentially attached flow. Rcgldr (talk) 02:43, 25 June 2016 (UTC)

The "otherwise a void" explanation lacks power, because flow-attachment isn't a permanent feature of the leeward side of airfoils (and spheres, etc.) Stall and flow separation exist but without creating a void, and this reveals the flaw in "otherwise a void" reasoning. The flow need not attach, see Flow_separation. So, I think we're actually trying to answer two questions: 1) What causes flow attachment? 2) Are "Coanda Effect" and Flow Attachment just names terms for the same phenomenon, or if they're distinct, what's the central feature which forces us to declare them distinct? (No, the presence of a jet-orifice or slot-jet is not a central feature, not if we can smoothly widen that slot until it's wider than wingspan, yet flow-attachment still arises.) 205.175.118.146 (talk) 06:59, 28 June 2016 (UTC)

Aren't we talking about simplified inviscid case? There is no separation in inviscid case, only at the trailing edge, by a singular radius of curvature (Kutta condition). Strictly in this sense, "pulling down" does seem correct, since separation, stall do destroy lift, don't they? Separation caused by an adverse pressure gradient pushing the boundary layer's slowed velocity profile bottom into the negative, thus producing backflow. Without viscosity, there is no sensitive low velocity part of the flow next to the body. Stall and flow separation do exist without void, but in the irrotational flow sense, stall, separation, free shear layer aren't considered part of the flow, but rigid body surfaces around the vortices.Even the separated flow follows the body surface without gap, with all its vortices.The "otherwise a void" explanation in a general sense is used widely when explaining physics, when people note that a system takes a state with the lowest energy, unless potential barriers present in the classical sense. Of course there's a pressure gradient working to close that hypothetical "void". It need not to be "pulling", it's just negative pressure difference to ambient pressure. In reality, the wing is pushed up by the bottom side pressure, but this is equivalent to saying that the upper pressure deficit pulls up the wing. It's equally valid to say that the wing pulls down air, even if it's because it doesn't provide enough reaction force against ambient pressure above it. The continuity of the hydrostatic stress component through the air and the body, which stems from the volume infinitesimal principle of action-reaction, or the conservation of momentum , so this all makes the air to follow the shape of the body. In other words, the "otherwise void" is the everyday term describing perturbing a system in equilibrium and showing that the restoring force is greater than and opposite to the perturbing one, so the system is stable in that state. The whole fluid path deforming effect of a wing can be explained by the continuity. The curvature (angle of attack) of the wing deforms the fluid path (streamlines) around the body, bending the air, and the reaction force cause lift. So I think the "pulling down" is pretty adequate after all, or maybe "letting down" is more appropiate. Actually, air is penomenologically fairly rigid in compression and - effectively - tension in this incompressible and inviscid case, especially perpendicularly to a flat object, like a wing. Air can only take no shear stresses. I just stood next to a curtain, and pulled swiftly a wooden plate away from it, the curtain followed it without contact. It's nitpicking to argue that it was the pushing of the ambient air pressure, because in pressure differences, it doesn't matter. I think the air parcels' force (momentum change) equilibrium with their neighbours is enough to see that "letting down" is correct, and when there is ambient pressure, this is effectively "pulling".

Why curved flow forms over the upper surface of a wing

No where in the entire article is an accepted explanation for why curved flow (acceleration perpendicular to flow) forms above a wing. Coanda is considered controversial. So is void theory - that the air fills in what would otherwise be a void. So there's no accepted theory offered anywhere in the entire article, yet the mathematical models include curved flows as part of the process to calculate velocity fields. In mathematical models and simple observation, curved flows are formed, but no accepted explanation is offered. I prefer void theory, since it's seems obvious and simple to understand, and applies to angled flat plates as well as convex surfaces (which may also be angled). The explanation and math behind boundary layers is more complex. Principle_of_least_action would at least partially explain when flows remain attached or become detached (stall condition). Rcgldr (talk) 23:57, 25 June 2016 (UTC)

The literature attests the controversy over Coanda. I think the void theory, or perhaps more correctly a pressure-induced theory, lacks coherent sourcing: it is controversial only among Wikipedia editors. I have just checked out a few sources (e.g. Clancy), and the idea is taken as such a basic feature of fluid physics that it is assumed rather than explained. So perhaps what we need is something like this:

"Basic fluid mechanics
Throughout any fluid there exists a static pressure. When a solid body is immersed in the fluid and moves relative to it, the fluid therefore flows around it. The notional path of an individual particle of fluid past the body is called a streamline.
These principles apply whether the body is moving through the fluid, as with a aircraft, or whether the fluid is flowing past the body, as in a flow sensor, and any particular analysis will take whichever of these is the more convenient for its frame of reference.

Any good? — Cheers, Steelpillow (Talk) 09:58, 26 June 2016 (UTC)

I must admit to being puzzled why people wonder why the air flows around the convex surface of a moving body, thereby preventing a void from forming behind the moving body. Why focus on moving bodies? Voids don't form in the stationary atmosphere so why would they form behind a moving body? Atmospheric pressure (at sea level) is about 100,000 pascals so any tendency for a void to form would promptly disappear under the influence of this substantial pressure.

Newcomers to the field of fluid mechanics might say "Sure, voids don't form in the stationary atmosphere but what about behind an object that is moving?" The kinetic theory of gases tells us that gas molecules in the atmosphere move at very high speed. Very high indeed! I have done a simple calculation regarding molecules of nitrogen at a temperature of around 20 deg Celsius and my result suggests the RMS speed of this population of molecules is about 1800 km per hour, or about 40% faster than the speed of sound at the same temperature. This is the RMS speed so a significant proportion of the nitrogen molecules are moving even faster than this. When we consider an airfoil in a wind tunnel, or a propeller-driven aircraft, or even a transonic jet airliner, its speed is much, much lower than the speeds of the molecules in the atmosphere. So when we think of a moving body it is really just standing still when compared with the speeds of the gas molecules that move in behind to fill the void.

Voids don't form in a stationary atmosphere and there is no reason to imagine they might form behind moving bodies because moving bodies are barely moving at all. Dolphin (t) 10:30, 26 June 2016 (UTC)

The basic principle of "void theory" is that since a fluid has momentum and viscosity, it has to accelerate to fill in "what would otherwise be a void", and this acceleration coexists with a reduction in pressure behind a moving object (not that a void is actually created). By using an asymmetrical shape and/or angle of attack, the net acceleration can be directed perpendicular to the flow, resulting in lift, although some of the acceleration will be in the direction of the moving object, resulting in drag. Why lift can be much greater than drag is probably related to airfoils that take advantage of the Principle_of_least_action. Rcgldr (talk) 15:51, 26 June 2016 (UTC)

Our intuition often suggests there should be a reduction in pressure behind a moving object. Up until a century ago, most people believed a reduced pressure existed and it was the cause of drag. In fact, this reduction in pressure behind a moving object doesn't exist - potential flow theory shows that a stagnation point will exist at the extreme rear of the body and the pressure there will be equal to the stagnation pressure at the front of the body. Losses in the boundary layer, and separation, mean the pressure at the rear of the body doesn't quite reach stagnation pressure but it gets fairly close. I think it was Ludwig Prandtl in the first quarter of the 20th century who determined the significance of the boundary layer in determining drag, thereby putting an end to the theory that said drag was due solely to reduced pressure at the rear of the body.

The point of lowest pressure on an airfoil is somewhere between the leading edge (at high AoA) and the quarter chord point (at low AoA), wherever the relative airspeed is highest.Dolphin (t) 00:24, 27 June 2016 (UTC)

Although it would be mathematically difficult to model, I would assume that drag is related to forward acceleration air. In the case of a bus it's pretty clear that what could be called a stagnation zone at the flat trailing edge of a bus has significantly reduced pressure, even though it's moving at nearly the same speed as the bus. Since most wings have thin trailing edges, most of the forward acceleration of air and associated drag occurs well in front of the trailing edge. Rcgldr (talk) 08:30, 27 June 2016 (UTC)

I'm not conversant with the principle of least action. Our article on the subject suggests its current application is primarily in quantum mechanics and other modern physics. Dolphin (t) 00:24, 27 June 2016 (UTC)

Principle of least action also applies to Newtons laws. Although I've saw this term used before at some web site, I can't find that web site anymore, and now I'm not sure it is a proper use. The premise is that if an interaction between a moving object and a fluid causes the fluid to accelerate, the fluid will tend to accelerate in the direction (or along the path) that requires the smallest magnitude of acceleration. Rcgldr (talk) 08:22, 27 June 2016 (UTC)

@Dolphin See http://www.feynmanlectures.caltech.edu/II_19.html for a good intro to the principle of least action. Interesting stuff, and it's probably possible to cast the theory of lift in terms of the princiople of least action, unless we find a reliable source that does it we shouldn't put it into the article. Mr. Swordfish (talk) 20:21, 28 June 2016 (UTC)

This is getting into detail that I wasn't considering. My point for this section was to see if there can be a reasonably simple and acceptable explanation for why air flow is curved (accelerates perpendicular to flow) above a wing. Rcgldr (talk) 08:34, 27 June 2016 (UTC)

I think we'd have to ask physics educators to hammer out a clarified simple version. I've yet not seen it done. In fluid mechanics, the difference between attached flow versus separated flow has little to do with ambient pressure or "otherwise a void would form" reasoning. Instead, we note that separated flows only exist when fluid has high inertia and low viscosity, then take the attached flows as a given, even though we've not explained why it occurs. I think characterizing all this a "Flow Attachment" is a step forward. Because objects don't naturally accelerate to follow a given surface, and the origin of the force isn't clear, we shouldn't be sweeping it under a rug by labeling it as "lack of flow-separation." Ask specifically about the origin of the forces on each moving parcel which leads to attached flows, rather than to separated flows. 205.175.118.146 (talk) 07:39, 28 June 2016 (UTC)

My point for this section was to see if there can be a reasonably simple and acceptable explanation for why air flow is curved (accelerates perpendicular to flow) above a wing.

I don't know that there is one. Dolphin's idea that we shouldn't expect voids behind a (slow moving) body any more than we would expect a void behind a stationary object sounds reasonable, but I'm not aware of a reliable source for it. And it has the drawback that sometimes there is a void (or something like it anyway) in the case of cavitation

I've never liked the "Coanda effect" explanation because it's not an explanation at all - it just gives it a fancy name, with the implication that the reader should already be familiar with something that they probably aren't.

When I present lift to my sailing stucents, I sidestep the question by simply stating that we observe that it does. (i.e. the air follows the outside curve of the sail, or the top side of the wing)

If pressed for an explanation, I'd point to the mathematical model that is the Navier-Stokes equation and that they model conservation of mass, momentum, and energy plus a few other things, and that solutions to the N-S equations have the air flowing along a curve. But this doesn't really get at the why in an elementary manner.

So, since this is wikipedia, I would suggest that unless we can find a reliable source that explains this in a way that we can agree on (consensus) let's not try to write one of our own. Mr. Swordfish (talk) 20:14, 28 June 2016 (UTC)

Refocusing of the introductory sections

The above discussions have led me to a broader idea: to present the introductory ideas not as alternative "explanations" but as compatible "principles" of lift. This gets round the whole problem of the inadequacy of each individual principle to explain the whole picture.

Besides a bit about basic fluid mechanics, as above, Clancy (Aerodynamics, 1975) also introduces a basic circulation theory of lift at this early stage. I would agree with him that this is a good idea. Does that seem sensible? — Cheers, Steelpillow (Talk) 09:49, 26 June 2016 (UTC)

In my opinion, you can start off with diverted flows (effective angle of attack), and Newtons laws (like F = ma). Then noting that the diverted flows are curved, Euler relates the curved flows (speed, density, radius of curvature, ...) to pressure gradients, which in turn relate to velocity and pressure variations. Although this explains the basic idea, trying to mathematically model this is complex, such as Navier Stokes equations. Rcgldr (talk) 15:40, 26 June 2016 (UTC)

User:Mr swordfish did a lengthy and comprehensive re-write of the introductory sections about 18 months to 2 years ago. A number of other Users contributed their thoughts, comments and suggestions. Hopefully he will contribute to this latest suggestion because there is a possibility it has been tried before. Dolphin (t) 00:31, 27 June 2016 (UTC)

I seem to recall that I was one of those other users. We were all distracted by a different issue at the time and lots of nit-picking counter-edits which led to much duplication of wording and ludicrous numbers of citations. I just did a fair amount of rewriting, which I regard as continued cleaning-up after the mess, building on Mr. Swordfish's efforts rather than chewing them up all over. @Mr swordfish: I hope this is OK by you. @Rcgldr: I have started by trying to be more explicit about flow deflection (in fluid mechanics) before tackling Newton, as you suggested, so I hope it's OK by you too, at least so far. — Cheers, Steelpillow (Talk) 12:03, 28 June 2016 (UTC)

General comments. Viscosity resists differences in velocities of adjacent streamlines, I'm not sure it always ultimately results in drag, as one alternative is that it affects curvature of flow. Variations in pressure and speed are coexistent, rather than cause and effect (technically changes in pressure propagate at the speed of sound, so pressure changes slightly lead changes in accelerations and velocity field (there are also some feedback issues)). The standard Bernoulli correlation between pressure and speed only applies in the frame of reference of the wing. From the air's frame of reference, work is performed on the air, mostly as a pressure increase (with little change in speed) as air flows across the plane swept out by a wing, that results in the air starting with zero velocity and after a wing passes by, having a non zero "exit" velocity (the velocity of the affected air when it's pressure returns to ambient). The Newton perspective is mostly frame independent. I'm not sure how to organize this information. Rcgldr (talk) 17:02, 28 June 2016 (UTC)

I expect there will always be local regions where viscosity is transferring forward momentum to the air, but the net effect is to create drag. Remember, in superfluids there is no viscosity and hence no drag. One might even define drag as the dissipation of forward momentum from the airfoil and into the surrounding fluid, as this is equivalent to the usual force-based definition (f=dp/dt where p is the momentum). There will always be readability issues over a choice of phrase such as "causes" vs. "is equivalent to", "may be seen as", etc. If the facts have been clearly stated, some minor looseness of language in the interests of readability can sometimes keep things clearer. I will take another look at my own phrasing, though. I checked my wording and can find no issues over cause and effect. [previous para updated 18:06, 28 June 2016 (UTC)] From the free stream's frame of reference, the wing actually causes a circulation - up past the leading edge, back over the wing, down behind the trailing edge and forwards underneath to (nominally) reach its starting point again. Without this circulation, lift cannot be generated. I think this "circulation theory of lift" needs bringing out sooner in the article, just as Clancy does. Discussions of exit velocity and pressure are usually fraught with misunderstandings, for example the static pressure remains constant throughout while almost by definition the dynamic pressure returns to zero only when the air finally stops moving, while half the downward momentum of the rear circulation is imparted after the air has passed below the trailing edge. — Cheers, Steelpillow (Talk) 17:57, 28 June 2016 (UTC)

By cause and effect, I meant an implied order of events in the wording of "Bernoulli's principle states that within a steady airflow of constant energy, when the air flows through a region of lower pressure it must speeds up and, vice versa, when such a flow speeds up it must experience reduced pressure." The cited reference states this as "where the velocity increases the pressure decreases and vice versa". I'm not sure how to word this, but the concept is that changes in speed occur as air travels through pressure gradients, air accelerates from higher pressure zones to lower pressure zones and decelerates if moving from a lower pressure zone to a higher pressure zone. Bernoulli's equation relates the instantaneous pressure to instantaneous speed during transitions through pressure gradients. Lower pressure coexists with higher speed, higher pressure coexists with lower speed. Rcgldr (talk) 22:47, 28 June 2016 (UTC)

The "tit for tat" reversibility of the explanation is enough to demonstrate that neither "causes" the other as such. From this point of view, the wording is adequate if a little clumsy. I think the "where the velocity increases the pressure decreases and vice versa" is a little too brief, but as it is more a matter of taste than of substance. I have no strong preference. — Cheers, Steelpillow (Talk) 09:23, 29 June 2016 (UTC)

Viscosity - I though most of the effects of viscosity occur in the boundary layer. There's a skin friction drag related to viscosity, but what about form drag, isn't some of the form drag related to momentum (forward acceleration of air)? I struck out my comment about viscosity and curvature, that was based on an article's description of what happens in a laminar boundary layer, not air flow in general. Rcgldr (talk) 22:47, 28 June 2016 (UTC)

By Newton's Second and Third laws, all drag is accompanied by forward acceleration of air - there is nothing else for the retarding force to react against. The acceleration is balanced out by the backwards acceleration against which the thrust reacts: in steady flight, net horizontal acceleration of the air is zero. — Cheers, Steelpillow (Talk) 09:23, 29 June 2016 (UTC)

I was away for the weekend and missed a whole bunch of edits. I haven't had time to digest it all yet. My initial take is that I agree wholeheartedly with many, but overall I do not think the article has been improved. I would suggest that before we do a comprehensive re-write of the basic organization of the article (which was arrived at by several months of consensus building), we slow down see if there is consensus for these changes. To that end, I'd like to see the article restored to last week's version and for the proposed revisions to be transferred to a sandbox for evaluation and commentary. Once we reach consensus on a new organization, we can transfer that version to the live article. Mr. Swordfish (talk) 20:01, 28 June 2016 (UTC)

I have done the first main change that I had in mind. Yes, I am happy to wait and see how it gets received before I try any more. If you want the version before I started in on that change, it is here. Personally I see no reason to break out a sandbox as one can already see the old and new side by side, but if you find it worthwhile I have no objection as such. — Cheers, Steelpillow (Talk) 20:50, 28 June 2016 (UTC)

The advantage of making the changes in a sandbox or user space is that we can all review it and discuss changes and arrive at a consensus before changing the live article. I'm going to restore the previous basic structure while leaving most of the more incremental changes. We can proceed from there, but let's try to reach consensus first on major changes. Mr. Swordfish (talk) 21:04, 29 June 2016 (UTC)

OK. Can you post a link to the sandbox/wherever with the last article state that you undid? — Cheers, Steelpillow (Talk) 21:14, 29 June 2016 (UTC)

I've moved it to my user space. https://en.wikipedia.org/wiki/User:Mr_swordfish/Lift Please note that I removed the categories at the bottom so that the sandbox article won't be included in the autogenerated lists. We'll need to restore them when we move to production. Mr. Swordfish (talk) 21:26, 29 June 2016 (UTC)

Here's my take on things: user Rcgldr has joined us and has a reasonable request - that we cover the interaction of curved airflow and pressure earlier in the article. The present order is something like:

1. A brief nod to the Newton/Bernoulli "controversy" and an assertion that either can be used to explain lift
2. A very simply presentation of the explanation using Newton's laws i.e. "air goes down, plane goes up" (no discussion of air pressure )
3. A presentation of the Bernoulli's principle explanation, together with a discussion of its limitations
4. Discussion of pressure differences and how they arise from curved flow
5. Further qualitative discussion about angle of attack, airfoil shape etc.
6. Mathematical models

Rcgldr's observation is that a Newtonian explanation is sufficient to explain pressure differences and so we should incorporate item #4 into item #2. I can't say I disagree with this. But I also think that for most people the simple pressure-less explanation is good enough and presenting it succinctly and clearly early on is the right idea. As the AAPT puts it:

"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."

My hesitancy is how to simply explain the relationship between curved streamlines and pressure gradients to an intended audience that probably doesn't know what a "gradient" is. For me, the simple formula:

${\frac {\operatorname {d} p}{\operatorname {d} R}}=\rho {\frac {v^{2}}{R}}$

clearly expresses the relationship between between pressure differences and curved fluid flow, but it's a differential equation that's beyond most of the intended readership. That doesn't mean we can't include it, but we need to be circumspect about how early in the article we break out the calculus.

But, hey, maybe we don't need to recapitulate the Bernoulli vs Newton drama that raged a decade ago. That seemed to be the right way to structure the article a few years ago, but maybe not now. Opinions? Mr. Swordfish (talk) 21:55, 29 June 2016 (UTC)

My point was to provide a tie between the Newton and Bernoulli explanations, as long as the Newton explanation mentions diversion or curvature of flow (the basis of how wings work). Then it could be pointed out that Euler was able to start with Newton's laws, and determine a relationship between curved flow and variations in pressure (avoiding usage of the term pressure gradient). The details of this would be explained later in the article. Rcgldr (talk) 16:10, 30 June 2016 (UTC)

One issue is frame dependencies. Newton, at least the acceleration aspect, is frame independent. Bernoulli's equation requires using the wing as a frame of reference (from a free stream frame of reference, a wing performs work on the air, violating Bernouolli, mostly with a pressure increase with little change in speed as air flows past the plane swept out by a wing). Circulation normally uses the free stream frame of reference. Rcgldr (talk) 16:10, 30 June 2016 (UTC)

Section 4.3 (A more comprehensive.../Pressure differences... )

this is not the right place to draft article content, only to discuss it. A personal sandbox is recommended. — Cheers, Steelpillow (Talk) 09:19, 10 December 2016 (UTC)

About the image "Pressure distribution with isobars around a lifting airfoil" The distribution seems wrong, meaning the number and the position of the local extrema of the pressure field, and the arrows which represent the pressure gradient field. The position of the global maximum pressure should be at the leading edge, coinciding with the frontal stagnation point. From there "arrows" should point up and down, in a diverging way, unlike the two front arrows of the image in question. Depenting on leading edge radius of curvature, there is a strong minimum of pressure right next to the front stagnation point on the bottom side, and there is another on the opposite side of the front stagnation point, that's the global pressure minimum on the top side. The next local maximum on the positive pressure side is where the image places it. Then there is another local maximum at the rear stagnation point, which, in an inviscid case, should be of around the same magnitude as that of the front stagnation point. (No pressure drag in inviscid case.) That's three local maxima - with the associated different pressure gradients - not one. Also the suction side's pressure minimum is much closer to the leading edge. (Search for detailed images or simulations, I did the simulations myself, too.) [1] About the reasoning The section warns that the velocity increase and the pressure decrease are mutually interdependent (Bernoulli equation). I agree, but for this very reason one shouldn't attempt to use this circular reasoning. Instead, take an axis symmetric rigid body in fluid flow with zero angle of attack. Take a streamline arbitralily close to both the front and rear stagnation point, on one side of the body. According to Bernoulli's equation, the fluid parcel's energy content is conserved along the streamline. The free stream dynamic pressure converts to static pressure increase entirely when the fluid parcel approaches the front stagnation point. Then the fluid parcel turns sideways around the body, and the dynamic pressure builds up again from the static pressure, but this is not the exact time reversal of the slowing down, because the curvature induced centrifugal force (or negative pressure gradient from Euler's equation ) provides additional static pressure drop below the ambient, thus more room for pressure-velocity conversion. The work of speeding up the parcel above ambient velocity is not done by the centrifugal force, but the static pressure. (The centrifugal force is a fictitious force.). So there are symmetrical low pressure-high velocity regions around the body. Now fix the rear stagnation point at place by the Kutta condition, and move the front stagnation point by changing the angle of attack or the symmetry of curvature of the airfoil. Then the general amount of curvature (total angle deflection on the surface from front to rear stagnation point) changes to asymmetrical, that is, the pressure gradients and the velocity field will be asymmetric, too, and there is net lift on the body. So, in nutshell, the centrifugal force makes it possible for the pressure to drop and to convert to more velocity. Implicitly assumed are the smoothly changing velocity field (streamlines), and the boundary condition imposed by the body. — Preceding unsigned comment added by 188.143.50.215 (talk) 23:50, 7 December 2016 (UTC) I agree it would be nice to have a more accurate pressure distribution picture, maybe File:Airfoils_-_pressure_diagrams.svg ?-Eio (talk) 07:27, 8 December 2016 (UTC) That detailed picture would be nice. It wouldn't be consistent with paragraphs 1 to 4, where they derive the speedup (in a bad way from a bad picture), IMHO those should be deleted . In paragraphs 5-6, they write about the interdependence, that part is circular, vague and incomplete, but right and has citations. Since my last comment, I've thought it over, and I think this whole explaining thing in layman terms boils down to saying the three conservation laws precisely but in a plain language. I don't think anymore that the runaway self-reinforcing effect is real, but the velocity-pressure relation is still true. 1. Simple: Body flies through fluid, makes room for itself by displacing its own volume in fluid. Relative velocity exceeds body velocity at wide parts, because side motion adds to body velocity. 1. Technical: Continuity (conservation of mass, or in incompressible case, volume) + Initial Conditions 2. Simple: The displaced air also displaces air around itself, and so on, and so on. As this effect goes away from the body, it spreads on a bigger and bigger imaginary surface, so smaller and smaller displacement is enough for the same volume to be displaced (the body's volume). The displacement changes and vanishes smoothly away from the body in every direction, so does the altered fluid path relative to the body. This way, the body copies its shape into the surrounding fluid path in a smoothly vanishing way with distance. 2. Technical: Streamlines + Continuity + Boundary Conditions 3. Simple: If a wing's overall curvature and/or its angle relative to the oncoming air copies a bend into the surrounding fluid path, like an invisible pipe bend, then the relative fluid motion undergoes direction change, and pushes (pulls) the wing back, perpendicular to the wing's velocity. This is lift. 3. Technical: Newton Third Law or Euler's equation. Asymmetric curvature or angle of attack induced asymmetric streamline curvature causes certain pressure gradients around the airfoil with vertical component, which integrates to lift. Bernoulli equation: Fluid relative motion comes to halt in front of the airfoil, the dynamic pressure converts to static pressure increase, then the fluid parcel moves to the side of the airfoil, opposite happens. Euler equation predicts a pressure gradient at the wider curved sides, that pressure drop (which is the lift) accounts for the additional velocity increase above the ambient.