Talk:Lift (force)/Archive 6

This is an archive of past discussions about Lift (force). Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Archive 1

←

Archive 4

→

Planing lift

An editor recently added discussion of Planing to this article. What's the consensus about this change? My take is that it's a separate topic that should be covered in it's own wiki article. I definitely don't think it belongs in the overview, as it's only somewhat related to the main thrust of the article. Introducing the term "Submerged Foil Lift" seems like it would confuse the reader.

I'm going to undo the edits pending consensus here on the talk page. Mr. Swordfish (talk) 20:08, 28 October 2011 (UTC)

I obviously think youre mistaken as LIFT is the topic and planing is obviously a type of lift wherein: "A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction.[1] ." There are obviously a LOT of shared aspects. The omission of planing lift and discussion of its relation to submerged lift are simply an omission due to the fact that aero guys are largely editing the copy. Please revert the page.Juanguzman1967 (talk)LOTS of examples of obvious, visible "flow-turning" here: http://www.google.com/search?rlz=1C1_____enUS424US424&gcx=w&q=surfing&um=1&ie=UTF-8&hl=en&tbm=isch&source=og&sa=N&tab=wi&biw=1440&bih=815&sei=%20URerTs_zNc7MrQfIkpjWDA Juanguzman1967 (talk) 20:59, 28 October 2011 (UTC)

Hopefully you'll take the occurrences of Lift in discussion of planing hulls in numerous books as evidence that planing hulls do exist and Lift per the definition above absolutely belongs in the article here. If I need to cite particular works I will, however it would be in bad faith to disregard the truth of the matter. Certainly we could situate the sub-discussions of both submerged and planing lift under respective headings though. Please refer : http://www.google.com/search?tbm=bks&tbo=1&q=planing+hull+lift&btnG=

Juanguzman1967 (talk) 00:59, 29 October 2011 (UTC)Further: http://www.scribd.com/doc/39037195/3/Savitsky-Method Juanguzman1967 (talk) 01:59, 29 October 2011 (UTC)

@Juanguzman1967 - You have written If I need to cite particular works I will ... Of course you need to cite your sources. We all have to cite our sources. No-one contributing to Wikipedia should ever ask if it is necessary to cite sources. Please read, very carefully, WP:Verifiability. Dolphin (t) 03:56, 29 October 2011 (UTC)

Oh please Miss, Ms or Mrs "Dolphin," pray don't scold me. I am but a novice wikinerd. But the fact is, the existence of planing lift is common knowledge. Vastly more people have caused, played with, and otherwise experienced planing lift than the much more complicated submerged flow-turning lift which overwhelms this article. You should research how many people have actively caused planing lift for recreation by skipping stones, surfing, skimboarding, waterskiing, wakeboarding, windsurfing, sticking their hand out car windows, flying kites, for that matter, vs. how many have piloted an aircraft, driving submerged foils. In fact, planing lift is the most elemental and common type of lift man deals with and as it's strictly Newtonian, it's quite arguably a much better starting point for understanding lift than discussing foils. (And by the way, in fact, billions of animals worldwide do far more -- exponentially, galactically more lifting with foils than we do. You gave them short shrift here, too. This article was a joke when I arrived.) You can force me to start a new article I suppose as there's really no accountability on the likes of you two around here, but a Planing Lift article will trample all over this one as it is the most elemental lift.Juanguzman1967 (talk) 04:57, 29 October 2011 (UTC)

I'm not scolding you. I'm asking you to read WP:Verifiability. On Wikipedia, when someone writes It is a known fact or Everybody knows or It is common knowledge it will be assumed that they believe it to be true but can't actually cite a source to allow independent verification. Material that is unsourced is likely to be removed. That is the way encyclopedias operate. Dolphin (t) 05:40, 29 October 2011 (UTC)

> In fact, planing lift is the most elemental and common type of lift man deals with and as it's strictly Newtonian, it's quite arguably a much better starting point for understanding lift than discussing foils.

That's an interesting opinion, and I'm not going to argue that it's incorrect. But even if I agreed with you, wiki is not the place to air our opinions; we're here to present a summary of the published sources and I'm unaware of any treatment that proceeds from planing to "submerged lift" as a pedagogic method. So what would be the justification for doing it here?

There's already an article on planing sailboats. Much of what you have written could go there. Perhaps a more general article on the phenomenon of planing lift (as applied to motorboats, surfboards, skipping stones, etc ) would be in order as well. Mr. Swordfish (talk) 14:33, 29 October 2011 (UTC)

Planing lift is Lift itself -- the most elementary phenomenon of Lift. It's the lift youre talking about when you talk about foils, but without foil-side attachment, flow-turning, turbulence, stalling etc. "There's already an article on planing sailboats. Much of what you have written could go there." It's the lift of kiteflying. Would you have it subsumed to the "kite-flying" page because it "crowds" this article inconveniently? Wiki articles don't have a word-limit -- why impose this argument on an honest, good-faith contributor? I don't have a monetary or cynical interest here. Planing lift simply belongs in an article on the broader subject "Lift (force)." Consider the complexity and controversy around how lifting foils work. Consider how elemental planing lift is. They are two heavily- (and hierarchically-) related phenomena of Lift that are studied and practically utilized by two different groups, but it seems to me encyclopedias cover broad fields that have sub-aspects that don't talk to each other much, often. In my opinion Webster's definition of Lift itself in the most general terms and then a discussion of planing lift should lead the article, with the vastly more complicated and controversial subject of foils following. It should be included and this is the proper hierarchy, which positions the simple form above discussion of the complex. Planing is Lift exactly per the definition at the top of the page. Juanguzman1967 (talk) 00:01, 30 October 2011 (UTC)

"Lift occurs when a moving flow of gas is turned by a solid object." - NASA. (Whoever wrote the article does go on to negate all lift not utilizing 3D engineered foils with curved surfaces on top, but that's an error many aero guys make apparently.) A kite is obviously utilizing lift. A kite operates without the benefit of a 3D foil body's upper surface being optimized to enhance flow-turning but the inconvenient fact is that it simply doesnt need it. So the kite, of all things, exists outside the discussion of the Lift article. Because it is so elementary and fundamental --in other words, common knowledge-- planing lift is totally overlooked and omitted even after it's been illustrated. The trees are the forest, gentlemen. Quite so, in spite of my charming demeanor.Juanguzman1967 (talk) 22:27, 3 November 2011 (UTC) http://dictionary.reference.com/browse/plane Juanguzman1967 (talk) 20:21, 5 November 2011 (UTC)

The Oxford English Dictionary definition of "plane" is as follows: verb [no object] (of a bird or an airborne object) soar without moving the wings ; glide: a bird planed down toward the water below

(of a boat, surfboard, etc.) skim over the surface of water as a result of lift produced hydrodynamically. -- http://oxforddictionaries.com/definition/plane?region=us&rskey=AtuBt9&result=1#m_en_us1278560.008. I rest my case, gentlemen and trust I may revert the page with this definition providing all the support anyone should need. Juanguzman1967 (talk) 20:29, 5 November 2011 (UTC) As I believe the material will just be deleted again if I revert the page, I guess I have no choice but to continue providing citations until the body of evidence I'm accumulating here reaches a tipping point sufficient to sway the judges who seem to hold final control of this material, Dolphin51, and MrSwordfish? https://docs.google.com/viewer?a=v&q=cache:YT8S6ziu3DQJ:aerade.cranfield.ac.uk/ara/arc/rm/2998.pdf+&hl=en&gl=us&pid=bl&srcid=ADGEESgFxTWHHivkjuqAdtzGl12eG--9bOkof0gmaK6p4yta_KqIJd_JsBIQuJSISJD9IZSZFTUNrTwPv5RIqMHFZGFENV16jzINuQK_hZh7R7S0IIWDoGFOls7MmCKePJHOq3uZHpeR&sig=AHIEtbTF5gBSfl0v23oyK5yqDOFwvHoAlw&pli=1 Juanguzman1967 (talk) 22:16, 5 November 2011 (UTC) I am looking here http://www.grc.nasa.gov/WWW/k-12/airplane/bernnew.html and here http://en.wikipedia.org/wiki/Aerodynamic_force and conclude that Lift appears to have been completely misappropriated as the page now is completely concerned with the Aerodynamic_force. Lift is the article. Please address this. Juanguzman1967 (talk) 23:18, 5 November 2011 (UTC) NASA video equating hydroplaning with "lift" at http://www.youtube.com/watch?feature=player_detailpage&v=90mj4Fh5MrU#t=37s Juanguzman1967 (talk) 01:10, 6 November 2011 (UTC) NACA study of "planing lift of a flat plate": http://crgis.ndc.nasa.gov/crgis/images/7/77/1957_Investigation_of_The_Planing_Lift_of_a_Flat_Plate_at_the_Langley_High-Speed_Hydrodynamics_Tank.pdf This oughta do it: http://www.waveequation.com/NACA-TN-3233.pdf Juanguzman1967 (talk) 01:26, 6 November 2011 (UTC) http://naca.central.cranfield.ac.uk/reports/1958/naca-tn-4251.pdf Juanguzman1967 (talk) 03:24, 6 November 2011 (UTC) http://www.flyingmag.com/technicalities/technicalities-short-history-airfoils Juanguzman1967 (talk) 03:26, 6 November 2011 (UTC) http://naca.central.cranfield.ac.uk/reports/1958/naca-report-1355.pdf This page needs to be drastically edited -- obviously Lift has been recanted here and my research bears me out. What this page is currently displaying is a specific realm of Lift, not the thing itself. I feel I've cited the matter sufficiently using NASA and NACA and will revert the [page tomorrow, providing these sources in the proper format. http://naca.central.cranfield.ac.uk/reports/1958/naca-tn-4168.pdf Thanks. Juanguzman1967 (talk) 03:40, 6 November 2011 (UTC) etymology of "plane": http://www.etymonline.com/index.php?term=plane&allowed_in_frame=0 Juanguzman1967 (talk) 04:16, 6 November 2011 (UTC) http://en.wikipedia.org/wiki/Wikipedia:Vandalism#What_is_not_vandalism Juanguzman1967 (talk) 04:21, 6 November 2011 (UTC)

@ Juasguzman:

Nobody is disputing the fact that planing lift is a real phenomena worthy of study and inclusion in wikipedia. (FYI, my nym is a reference to the Swordfish - a planing dinghy designed in the 50's by Uffa Fox). However, planing lift where the fluid only contacts one side of the foil is a different but related topic to the much more mainstream "submerged" lift treated in this article. The overwhelming majority of texts on "lift" concern themselves with this phenomena, not planing lift. Where a text addresses planing lift, it almost always includes the modifier "planing" whereas ordinary unmodified "lift" is assumed to be submerged lift.

I understand that you would like it to be otherwise, but wikipedia is supposed to reflect the broader body of published works, not be a place for us to push our own agendas.

I fully support the creation of an article on planing lift, and linkage to it from this article. I think your energies would be better placed there than trying to fundamentally change the topic of this article. Mr. Swordfish (talk) 16:44, 7 November 2011 (UTC)

I thoroughly disagree. My interests comprise my agenda, but this discussion about topics regarding Lift is not a matter of agenda. It is a discussion of proper hierarchy. Surveying basic Lift phenomena in a reasonable hierarchy from basic to more complex is not "fundamentally changing the topic" which is Lift (force). I and any reasonable user of Wikipedia take the word at the top of the page to be the topic, and we often discover that what we "always think of" is not at all the entirety of the thing -- that is all to the point. I think letting one field's jargon overwhelm the real topic is anti-educational and counterproductive to the goal of any encyclopedia.

As to your argument regarding published works, I would refer you to the NACA papers I cite above and the planing/lift formulae in them.

The article as it stands is completely overwhelmed by discussion of issues, facets, controversies, etc of aerodynamic force relating solely to submerged lifting foils, solely given over to manmade lifting foils at that. I've noted before my exception to the scant-if-any mention of naturally-occurring lifting foils. The topic at the top of this page is "Lift (force)."

Lift's most general definition and phenomena (whence the "flat plate" example?) should be at the top, followed by more complicated phenomena. This is a matter of standard hierarchy.

Most of the foil material on the page now should be moved to "aerodynamic force" and Foil pages. The Wiki guidline I cite above gives me the right to "edit boldly," as long as I cite the NACA and other evidence. I encourage you to move the aero foil material which crowds this parent topic to appropriate subordinate pages.

I've made this case as reasonably as I wish to with you -- who is the higher authority I request review from? Juanguzman1967 (talk) 17:48, 7 November 2011 (UTC)

Again: "A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction.[1] It contrasts with the drag force, which is the component of the surface force parallel to the flow direction.

Furthermore:

"plane (1) "flat surface," c.1600, from L. plantum "flat surface," properly neut. of adj. planus ::"flat, level, plain, clear," from PIE *pla-no- (cf. Lith. plonas "thin;" Celtic *lanon "plain;" ::perhaps also Gk. pelanos "sacrificial cake, a mixture offered to the gods, offering (of meal, honey, and oil) poured or spread"), suffixed form of base *pele- "to spread out, broad, flat" (cf. O.C.S. polje "flat land, field," Rus. polyi "open;" O.E., O.H.G. feld, M.Du. veld "field"). ::Figurative sense is attested from 1850.

The verb meaning "soar, glide on motionless wings" is first recorded 1610s, from M.Fr. planer (16c.), from L. planum on notion of bird gliding with flattened wings. Of boats, etc., "to skim over the surface of water" it is first found 1913.

plane

(2) 1908, short for aeroplane (see airplane).

http://www.etymonline.com/index.php?term=plane&::allowed_in_frame=0 Juanguzman1967 ([[User ::talk:Juanguzman1967|talk]]) 17:56, 7 November 2011 (UTC)

Also, I note your terms used here:

"Nobody is disputing the fact that planing lift is a real phenomena worthy of study and inclusion in wikipedia. (FYI, my nym is a reference to the Swordfish - a planing dinghy designed in the 50's by Uffa Fox). However, planing lift where the fluid only contacts one side of the foil is a different but related topic to the much more mainstream "submerged" lift treated in this article. The overwhelming majority of texts on "lift" concern themselves with this phenomena, not planing lift. Where a text addresses planing lift, it almost always includes the modifier "planing" whereas ordinary unmodified "lift" is assumed to be submerged lift.

Please note the generic term in your argument.Juanguzman1967 (talk) 18:18, 7 November 2011 (UTC)

I missed the noun form of Plane, which Oxford defines as

" 1 a flat surface on which a straight line joining any two points on it would wholly lie:

the horizontal plane

an imaginary flat surface through or joining material objects:

the planets orbit the sun in roughly the same plane

a flat or level surface of a material object:

the plane of his forehead

a flat surface producing lift by the action of air or water over and under it.

Juanguzman1967 (talk) 18:21, 7 November 2011 (UTC)

Select "plate:" http://www.grc.nasa.gov/WWW/K-12/airplane/lift2.html Juanguzman1967 (talk) 03:47, 8 November 2011 (UTC)

I fully agree with Mr. Swordfish: leave the subject of this article as it is -- lift force on a body (primarily foils) in a homogeneous medium (air, water). The article is long enough (see WP:SIZE). Planing lift can go into a separate article, and be referred to from Lift (and here). -- Crowsnest (talk) 14:02, 8 November 2011 (UTC)

Juanguzman: ...who is the higher authority I request review from?

Editing decisions on Wikipedia are done by consensus of the editors involved, i.e. the people who take the time and trouble to participate in the discussion on the talk page. On this issue, four editors have weighed in so far. Perhaps others editors will also voice their opinions.

The closest thing to "higher authority" I'm aware of is the mechanism at Wikipedia editor assistance. You might want to check out that resource.

BTW, this discussion would be much easier to follow if you adhered to the indentation conventions when you post.

Mr. Swordfish (talk) 14:42, 8 November 2011 (UTC)

Then the title of the article should be changed to disambiguate the subject and specify that it is talking about submerged foils and that this is only one type of fluid-dynamic Lift. NACA and NASA agree, of course, that of course Planing is Lift, as does the Oxford English dictionary. To not more specifically title this article would be misleading.

(I would respect the minutiae of Wikiconventions such as indentation guidelines only if the editors present had dealt with this issue and others relating to it much differently.) Juanguzman1967 (talk) 16:45, 8 November 2011 (UTC)

No one is claiming that Planing lift isn't an example of lift. It's just that it's sufficiently different than the more commonly studied lift-in-a-homogeneous-fluid that it should be broken out into it's own article. Sort of like how an open-face sandwich is sufficiently distinct from an ordinary Sandwich that it deserves separate treatment in a separate article. This is a judgment call about organization and the common usage of language, not something that is "right" or "wrong".

If you want your view to prevail, you'll need to convince some other editors. The best way to do that is to familiarize yourself with the talk page guidelines and try to persuade people to your point of view. Your other recourse is to avail yourself of the resources at Wikipedia:Dispute_resolution. Mr. Swordfish (talk) 20:54, 8 November 2011 (UTC)

The introductory paragraph in Lift (force) is sufficiently generic that it covers planing lift. It would be appropriate to add a new section to the article, dedicated to planing lift. If there is another article dedicated to planing lift, that section could link to that other article.

It would not be appropriate for details of planing lift to be added to the existing introductory paragraph.

At present, Lift (force) is supported by 62 in-line citations related to use of the word lift to mean a component of the force generated by a body submerged in, and moving through, an homogenous fluid. None of those citations use an expression other than lift so there are no good grounds to adopt a new expression such as submerged lift.

If Juan wants to challenge some aspect of the content of Lift (force) he could ask for assistance at Wikipedia:Third opinion. If he wants to challenge the behaviour of any of the Users who created the article, or who contribute to this Discussion page he could ask for assistance at Wikipedia:Wikiquette assistance. Dolphin (t) 06:57, 9 November 2011 (UTC)

I've cited plenty of sources and the whole of naval architecture uses the term in studying planing lift of hulls. Those folks just dont show up here. Wonder why. I've got better things to do than this though. This whole thing -- the blatant bias, the huge omission, and your tyranny of small minds--in the face of my citation of the Oxford dictionary, NASA, NACA... this is exactly why Wikipedia is a joke. And it is a joke. Nobody would cite Wikipedia in seriousness in any venue that mattered at all, and anyone relying on Wikipedia is sanctioned. Because it's full of this kind of ... 'substance.' — Preceding unsigned comment added by 206.16.109.32 (talk) 20:17, 9 November 2011 (UTC)

Here's a Google result that shows pretty clearly that the aforementioned tunnel-vision is simply wrong: association of https://www.google.com/search?q=flat+plate&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a#sclient=psy-ab&hl=en&client=firefox-a&hs=vhJ&rls=org.mozilla:en-US%3Aofficial&source=hp&q=flat+plate+planing+lift&pbx=1&oq=flat+plate+planing+lift&aq=f&aqi=&aql=&gs_sm=e&gs_upl=10291l12318l0l12496l13l9l0l0l0l0l612l1973l3-1.1.2l4l0&bav=on.2,or.r_gc.r_pw.r_cp.,cf.osb&fp=bb50f3788b2ebeea&biw=1200&bih=696 Juanguzman1967 (talk) 20:54, 11 November 2011 (UTC)

Here's a very interesting paper that found a "streamlined" airfoil to have worse lift/drag/stall than a flat plate at a variety of AoAs. I was interested in the flat wings of insects. They actually are corrugated, but they are certainly not the airfoils this page has boxed all Lift up with. The paper looks at the effects of the corrugated flat wings too. https://docs.google.com/viewer?a=v&q=cache:6o7zWANicIEJ:www.public.iastate.edu/~huhui/paper/2007/AIAA-2007-0483.pdf+&hl=en&gl=us&pid=bl&srcid=ADGEESg--3Zr8674jhSGEdeXOCBzwzGEK4pjKnHfIaUZG3xD7brOSWE7GluZcOlKAfM89WEcwNrgVGGncyRmEa-jFo792rTsGwi6sIgHurof0s83trWjz9rF9MhgQbKqvShoHMsPp6hv&sig=AHIEtbQhPKShlkE-umy2U-FMcakjxcUklQ Juanguzman1967 (talk) 21:11, 11 November 2011 (UTC)

Lift by Rotors

I would like to see a section of the article dedicated to lift created by rotors, i.e. by helicopter propellors. I've been researching this for, well, almost a day, and so far I haven't been able to find barely anything on the internet, and I've begun to start reading actual books for the information =) If anyone has any resources, or could help me just to gather information and sources to write a section describing lift by rotor, that would be awesome. Thanks. BriEnBest (talk) 08:38, 14 January 2012 (UTC)

Oh and by the way, I'm hypothesizing that the normal "airfoil" approach won't work because (I'm hypothesizing) that the fast-moving propeller blade will change the pressure of the air after a few spins by an as-yet-unknown-by-me amount. BriEnBest (talk) 08:40, 14 January 2012 (UTC)

Agree that this would be a useful addition to Wikipedia. But probably best as a separate article. Mr. Swordfish (talk) 16:47, 16 January 2012 (UTC)

@BriEnBest: A conventional helicopter has two rotors - the main rotor and the tail rotor. The blades on both these rotors are airfoils and they generate lift in the same way as the wing of a fixed-wing aircraft. A helicopter's rotors generate lift by exactly the same process as the propeller of a fixed-wing aircraft generates thrust. In both cases, each blade operates in the downwash from the preceding blade but this has only a very small effect on the lift generation, and this effect can be ignored for most purposes. Dolphin (t) 21:34, 16 January 2012 (UTC)

"Bluff Body" is not explained

I've no idea what this is, either. — Preceding unsigned comment added by 99.41.68.19 (talk) 19:21, 5 February 2012 (UTC)

As I understand it, a Bluff Body is a non-aerofoil shape that can be used to generate lift. A plane's wing could be a piece of flat bar, but it would have significantly more drag. I came to this talk page to request an illustration to show how a Bluff Body can also create lift, albeit with more drag than an aerofoil. OberonViking (talk) 03:31, 7 April 2012 (UTC)

My understanding of bluff body is that it is a non-streamlined shape rather than a non-aerofoil shape. For example, a sphere is not an aerofoil but it would not be described as a bluff body. However, I concede that my explanation is still not ideal because non-streamlined shape and streamlined shape are also not well defined. A streamlined body is one whose shape conforms closely to the shape of the streamlines surrounding the body when it is moving relative to a fluid. It is not a precisely defined term. Dolphin (t) 06:01, 7 April 2012 (UTC)

Hmmm. It seems even people who think they know what it means disagree. Are there any good references that use that specific term, and define it? If not, perhaps we should drop it from the heading and the opening of that sentence, and just describe what the section is about in ordinary language as we go? --Nigelj (talk) 22:04, 7 April 2012 (UTC)

"Bluff" is just an adjective to indicate a non-streamlined body, see e.g. wikt:bluff#Adjective.

Or: bluff bodies are "... bodies whose aspect is not small compared with the streamwise dimension ...", in: Paīdoussis, Michael P.; Price, Stuart; De Langre, Emmanuel (2010). Fluid-Structure Interactions: Cross-Flow-Induced Instabilities. Cambridge University Press. p. 1. ISBN 9780521119429. In this article it is explained as a body "... without a streamlined shape ...", which seems to be an adequate description, as far as I am concerned. There are so many terms which are not very strictly or uniquely defined, or differently by different authors. That should not hinder us in using it, since "bluff body" is a very common phrase in fluid dynamics. -- Crowsnest (talk) 12:28, 8 April 2012 (UTC)

Can aeroplanes fly upside down?

if lift is 'up' on an airplane, and allows it to fly, why can planes fly upside-down? — Preceding unsigned comment added by 98.69.160.44 (talk) 01:43, 2 January 2012 (UTC)

Lifting force on a body acts perpendicular to incoming flow. Coefficient of lift (CL) is a function of Angle Of Attack of the body that can pitch in both positive and negative direction. Note how CL is +1.0 and -1.0 for +10 deg and -10 deg AoA respectively in the following picture for a symmetrical aerofoil. This means that even if the aerofoil were to be flipped upside down (in the case of an aircraft, positioned top-face-down during flight having a NACA 0012 wing section), it would generate the same component of lift when pitched upwards. tldr; Cl vs. AoA chart gives you component of lift (+ve/-ve) with respect to AoA (+ve/-ve) accordingly. 146.87.52.53 (talk) 02:25, 29 April 2012 (UTC) Anon.

Fundamental physics

Comment here only, I am not going to edit the actual W. page. The fundamental generator of force is inertia, the acceleration of a mass (remember the old unit named Slug?), air in this instance but is the same for a liquid. A brick can fly but aerofoils are about how to achieve least energy loss for whatever regime they are designed to operate in. Hence I am amused at the hand waving, the detail processes surrounding the elephant. — Preceding unsigned comment added by Tchannon (talk • contribs) 14:18, 28 May 2011 (UTC)

Welcome to this talk page. You say The fundamental generator of force is inertia. I haven't heard that before, and I disagree with it. Who, or what source, are you quoting when you say that?

Your final sentence suggests you think lift should be explained only in simple, basic terms. Many people are very happy with simple, basic explanations of things. I think we cater for those people in the article Lift (force). Wikipedia aims to reflect the sum of knowledge to be found in reliable, published sources. On the subject of lift, reliable published sources go far beyond a simple, basic explanation so it would be inappropriate for Wikipedia to omit the more comprehensive, science-based explanations found in those sources. Dolphin (t) 00:57, 29 May 2011 (UTC)

'The fundamental generator of force is inertia.' is i suppose a confusing way of stating Newton's second law, 'force is the rate of change of the momentum.' — Preceding unsigned comment added by 81.141.165.139 (talk) 19:50, 29 October 2011 (UTC)

The article (and nowhere else I have read) does not seem to give an explanation of where the FORCE comes from in a fundamental way. See if this makes sense (an explanation then a question): The lift is caused by a pressure difference between the upper and lower surfaces. Pressure is due to gas molecule impacts. These impacts are slightly more on the lower surface, and significantly less on the upper surface, than if the airfoil was stationary relative to the air mass. The lower pressure on the upper surface is due to acceleration of the air over it. But acceleration requires force (F = ma). What's the force? I do not see any agent that will CAUSE the air to be accelerated backwards or downwards (Bernoulli is not a force or a cause, only a description). The analysis is simpler with a flat inclined plane (which will create lift at an angle of attack). There is going to be a void on the upper surface if air does not move down to fill it. What makes the air come down? Is it "drawn" down? If so is this due to intermolecular attraction as you get with water? I doubt this. Does it EXPAND down? This would make sense. I understand the lift equations treat air as an incompressible (and presumably non-expandable fluid) but there must be some elasticity otherwise the acceleration forces would be huge in some situations. I understand that the air mass up about 2 metres above a small Cessna's wing is deflected down. I hope readers see my point. I would like to see an explanation of WHAT MAKES THE AIR DEFLECT, in terms of funadamental forces, not just descriptions of how fluids behave. Nelsonpom (talk) 19:55, 28 April 2012 (UTC)

In physics, forces do not come from somewhere. Forces are exerted by one body on another body. In the case of lift on an airfoil, the lift force is exerted by the surrounding fluid. Consistent with Newton's third law of motion, the airfoil simultaneously exerts a force of equal magnitude but opposite direction on the surrounding fluid. It is this latter force that causes the surrounding fluid to accelerate downwards.

You are correct in proposing to say that lift is related to the difference in pressure between the upper and lower surfaces of the airfoil. It would be incorrect to say that the increase in pressure on the lower surface is similar in magnitude to the decrease in pressure on the upper surface - the pressure on the lower surface is similar to the pressure in the surrounding fluid so there is very little increase in pressure on the lower surface. However, there is a significant and substantial decrease in pressure on the upper surface - particularly near the leading edge of the airfoil.

You are correct in talking about the number and energy of the impacts by gas molecules, but this is equally true of pressure in general and is not in any way unique to the pressure on an airfoil. Consequently, explanations of the lift on an airfoil should not get distracted by explanations about gas molecules or the nature of pressure.

Finally, you have asked a very valid question about why the air is drawn downwards across the upper surface of the airfoil. My answer is that it is due to the vortex in the fluid surrounding the airfoil - in particular the bound vortex, not the trailing vortices. This bound vortex exists because of the angle of attack and the sharp trailing edge of the airfoil - if there was no angle of attack, or the trailing edge of the airfoil was rounded like the leading edge, there would be no lift. All this is consistent with the Kutta condition and the Kutta-Joukowski theorem. Dolphin (t) 02:01, 1 May 2012 (UTC)

I did recognise that the the pressure change (relative to surrounding air) was greater on the upper than lower surface.

I believe the vortex is the result, not the cause, of the acceleration of the air over the airfoil. The question remains: for a previously stationary block of air (some distance) above the airfoil "does it accelerate due to expansion on response to a void being formed below it, or does it accelerate due to intermolecular attraction/adhesion with surrounding air (i.e. being "pulled" - I do not believe we can accept "suction" as a valid force) ?" Nelsonpom (talk) 08:04, 3 May 2012 (UTC)

There are many situations in physics where two or more things can be observed to occur simultaneously; and where there is a temptation to contemplate which comes first and which second - which is the cause and which is the effect. Bernoulli's principle is a good example - in those regions in the fluid where the speed is increasing the pressure is also decreasing, and where the speed is decreasing the pressure is increasing. It is tempting to contemplate which is cause and which is effect, but that is not a valid line of thought. The truth is that they are both effects. The causes are the shape of the bodies at the boundaries of the fluid, and the driving force that is causing the fluid to move.

The vortex system in the fluid surrounding a working airfoil is an effect of the relative movement of airfoil and fluid. However, there is a precise mathematical relationship between the vortex system and the speed of the fluid at every point in the flow field; and the precise nature of that mathematical relationship allows us to say the vortex system induces a velocity at every point in the flow field. The velocity induced by the vortex system must be added vectorially to whatever velocities already exist as the result of other causes.

It is sufficient to say the fluid above the airfoil accelerates due to the vortex system in the surrounding fluid. Any comment about intermolecular attraction/adhesion may be true but it is universally true and not unique to the flow about an airfoil. When I read someone trying to explain the lift on an airfoil in terms of molecular attraction or kinetic theory of gases I find myself thinking that someone doesn't know much about aerodynamics but is striving to sound knowledgeable on the subject. Dolphin (t) 08:39, 3 May 2012 (UTC)

I fear we are straying beyond what may be editorially useful comment. I am not "striving to sound knowledgable..." - I am trying to find if there is an intuitively cause-and-effect description that I can explain to high school physics students. The usual equal-transit-time stuff won't do. And sorry but I do not find it "sufficient" to say "the fluid above the airfoil accelerates DUE TO the vortex system". I think I will give up because I am out of my depth in the complexity that is being presented, but I can't help feeling the intelligent enquirer is being fobbed off. Nelsonpom (talk) 09:52, 3 May 2012 (UTC)

When I wrote about someone trying to explain the lift on an airfoil in terms of molecular attraction or kinetic theory of gases I was not alluding to you. I apologise sincerely if I gave that impression. You are genuinely enquiring about the possibility of using that as an explanation whereas I have encountered others who boldly assert that they can provide the true explanation of lift by invoking ideas of molecular interaction and collisions with the walls of containers etc. (Ludwig Prandtl and Frederick Lanchester successfully explained the phenomenon of lift without resorting to kinetic theory.)

There are numerous different explanations for the phenomenon of lift - there is one for every "age group". None of them is entirely correct and none is entirely incorrect. The equal-transit-time theory is one that worked for many people for many years but it has been thoroughly de-bunked in the last decade, often with religious fervour. Sadly, those who revile the equal-transit-time theory usually replace it with something that is no better. (For example, the ETT theory is often replaced with the "lift is caused by Newton's third law of motion" explanation, which isn't an explanation at all because Newton's third law applies to all forces, all the time.)

For high school physics students I suggest you focus firstly on Bernoulli's principle. The air is moving much faster over the upper surface of the airfoil than the lower surface, and the lower pressure over the upper surface is consistent with Bernoulli's principle. Next comes the difficult bit - how to provide an intuitive explanation of why the air moves much faster over the upper surface. The most rigorous explanation is probably achieved by using the Kutta condition but that is perhaps unnecessarily esoteric. It might be sufficient to show students the sort of animated diagram available at Lift (force)#A more detailed physical description, and leave it at that. As you know, in physics we observe what happens in our world and frame laws and principles that summarise what we observe; but we don't attempt to explain WHY those things happen. For example, Newton explained that every action has an equal and opposite reaction, but he made no attempt to explain WHY it is so. I'm happy to continue our discussion, particularly if you find it useful. Dolphin (t) 12:36, 3 May 2012 (UTC)

I am trying to find if there is an intuitively cause-and-effect description that I can explain to high school physics students. The usual equal-transit-time stuff won't do...

Well, a very good place to start is the simple intuitive explanation that "the shape of the arifoil deflects the air downward; since the foil deflects the air downward, the air deflects the foil upwards" Then you could show/derive that the net force on the foil is equal to the total momentum change (F = dp/dt) Then you could calculate the average pressure difference implied by this net force. Then you could look at actual pressure distributions and see that the pressure is not uniformly distributed, that there is a small region of very low pressure on the upper side near the leading edge.

This region of low pressure could then be explained by the fact that the turning radius of the air is much smaller than elsewhere, that a tighter turning radius implies higher acceleration, hence more force/pressure. If your students have had calculus, then you might want to introduce the equations describing pressure gradients across and along curved streamlines as contained here: http://iopscience.iop.org/0031-9120/38/6/001/pdf/pe3_6_001.pdf In short, curved streamlines cause pressure gradients and this can be derived from first principles in a straightforward manner.

Granted, such a presentation elides over a lot of rigorous analysis - deriving and then solving 3 dimensional partial differential equations (Navier-Stokes or Euler), applying bounday conditions (Kutta) to obtain a vector field that describes the fluid flow in the vicinity of the foil, and finally applying Bernoulli's law to the vector field to get the pressure distribution. I think this is a bit much for high school, moreover it's easy to get lost in the mathematical details and lose sight of the underlying physics IMHO.

I don't think introducing Bernoulli's law is necessary, and if it didn't appear in so many other treatments I'd probably advocate leaving it out altogether. If you're going to use it in an intuitive explanation, you have to explain why the air speeds up and I have yet to see a simple correct explanation of that (Or I should say that I haven't seen one that doesn't rely on the existence of the pressure differences you're trying to explain.)

HTH. The Babinsky article linked above should be a good resource. Maybe just present that and stop listening to me. Mr. Swordfish (talk) 19:31, 9 May 2012 (UTC)

The article (and nowhere else I have read) does not seem to give an explanation of where the FORCE comes from in a fundamental way.

If nowhere else gives such an explanation then it would violate the Wiki policy of no original research to give one here.

What makes the air come down?

This is a difficult question and I understand your frustration in not seeing a simple explanation. There are several attempts out there to provide one - eg the Coanda effect, the air is "sticky" etc. but there is not widespread agreement that any are correct. When I'm explaining it (since I teach sailing I'm talking about sails, but it's the same principle) I merely state that the air follows the curve of the sail and leave it at that without trying to explain why the air flows that way. We can observe that it does, and that's a good starting point for a practical understanding of how to adjust the sail controls.

If I were pressed for a more complete explanation, I'd probably refer to the equations of fluid flow (Euler, Navier-Stokes) which are based on Newton's Laws and note that that the vector fields that solve these equations all "make the air come down" (non-stalled, lifting scenarios anyway). I don't expect you to find this explanation very satisfying. I know I don't. Mr. Swordfish (talk) 20:22, 9 May 2012 (UTC)

What makes the air come down? If it did not, there would be a vacuum from the leading edge backwards. Clearly the air 'rushes in' from above to fill this and in doing so picks up momentum that it can't easily lose again after the wing has passed. The immediate fluid that 'rushes in' to fill the space behind (and above) the leading edge (at a positive angle of attack) also would leave a space above it, so more air from above needs to move down too, and so on. I don't know why people have so much trouble visualising this. Maybe I was lucky that no one tried to explain it to me at school using badly formed theories. --Nigelj (talk) 20:41, 9 May 2012 (UTC)

Sails are interesting. If you sit and look at them for many hours, wondering how they are pulling the boat along (which I have done), another explanation is that every square inch of sailcloth can only create a force at right angles to itself, and it can only do that if there were no drag on its surface. In fact, every square inch is feeling a force slightly abaft the perpendicular. This explains why tall, narrow sails are more efficient on the wind - really only the strongly curved bit near the luff is pulling the boat to windward, and the rest is only there to keep this forward bit nicely curved. Any cloth parallel with the centre-line is just contributing to heel. Those are all my theories anyway, so probably not much use here unless a source exists. --Nigelj (talk) 20:49, 9 May 2012 (UTC)

Mr swordfish, Nigelj and I all agree that there is great difficulty in finding an intuitive explanation of what makes the air come down? Unfortunately, it is not sufficient to say the air is merely flowing along the upper surface of the airfoil to avoid a vacuum forming. The truth is that the speed at which the air flows around the leading edge and along the upper surface of an airfoil is much greater than necessary to satisfy continuity and avoid a vacuum forming. Indeed, it is possible to build a streamlined body that is basically a rectangular cylinder but with rounded leading and trailing edges and show that, even with a significant angle of attack, this body with its rounded trailing edge does not generate significant lift. Part of the reason why it doesn't generate lift is that the speed of the fluid around the leading edge and along the upper surface is not fast enough to cause the pressure to be lower than the pressure on the lower surface.

Part of the problem of explaining why airfoils generate lift is to explain why the flow around the leading edge and along the upper surface is so much faster than one would expect - so much faster than in the case of the streamlined body with the rounded trailing edge. The solution to this problem is attributed to Martin Wilhelm Kutta who identified the significance of a sharp trailing edge. His solution is now known as the Kutta condition and it explains why all airfoils have sharp trailing edges, in contrast to the generously rounded leading edges on subsonic airfoils. Any complete explanation of why the fluid flows around the leading edge and along the upper surface so much faster than it flows along the lower surface must point out the necessity of having a sharp trailing edge and acknowledge the work of Kutta in explaining that the flows along both upper and lower surfaces leave the body at the trailing edge. The flow along the lower surface does not flow around the sharp trailing edge. The flow along the upper surface persists all the way to the trailing edge because a vortex of sufficient strength is established in the fluid to ensure the flow does not leave the body until it reaches the trailing edge. It is this vortex, the bound vortex, that quantifies the extraordinary speed of the flow around the leading edge and along the upper surface. Any attempt at a complete explanation of fluid dynamic lift that doesn't incorporate:

1. the necessity for a sharp trailing edge,

2. the bound vortex necessary to achieve the Kutta condition,

is doomed to ultimately fail. Dolphin (t) 22:47, 9 May 2012 (UTC)

Since I was a child I remember putting my flat hand out of a car window - fingers extended straight and together, palm down. The slightest rotation, thumb side up or thumb side down, and the lift is sufficient at about 30 - 40 mph to deflect the extended arm with force. Any flatish shape angled in an air or water flow is deflected. I have sailed wooden work boats where the keel, daggerboard or leeboards are only very slightly champhered at both the leading and trailing edges of what is otherwise a simple rectangular section. They are not as efficient as a carbon fibre aerofoil section, but they do create lift at some angle of attack to the water flow, as it is possible to sail to windward using them. I don't think lift is half as magical or precarious a phenomenon as you make it out to be. (Although the mathematical description of it may be) --Nigelj (talk) 20:15, 10 May 2012 (UTC)

The force you observe on your flat hand is the force that undoubtedly occurs at very high angle of attack on any flat plate. It is similar to the force that keeps a water skier on top of the water. (See planing lift, as discussed in the thread immediately following this one.) Very high angles of attack are not practical for aircraft because they are accompanied by very high drag, and they exceed the stall angle. The ratio of lift-to-drag on your flat hand is about 1:1 or worse - that is why your hand is blown upwards and backwards at about 45°. The ratio of lift-to-drag on an aircraft wing needs to be about 5:1 or better. Gliders typically have lift-to-drag ratios better than 20:1 and sometimes up to 30:1. The mystery confronting the early aerodynamicists was not to explain why a flat plat could generate planing lift that was about equal to the drag. It was to explain why certain designs of airfoil would generate five to ten times as much lift as drag, and remain stable in the process. They soon found that angles of attack greater than about 15° were impractical because of excessive drag and instability (stall). Progressively they refined the design of airfoil sections to reach the large number of efficient, practical sections now available to serve a broad range of purposes. Dolphin (t) 23:43, 10 May 2012 (UTC)

Our definition is, "Lift is any component of this force that is perpendicular to the oncoming flow direction." I don't see anything about aircraft, stability or efficiency in that, and quite rightly so. --Nigelj (talk) 22:52, 11 May 2012 (UTC)

You are right. That is what the sources say. In the next thread, immediately below this one, you will see a debate about planing lift. In particular it is about how to distinguish between aerodynamic lift of the kind used to keep aircraft flying, and planing lift. Most sources deal with one or the other and nothing much has been found that distinguishes between the two. Aircraft rely on lift, and hydrofoils rely on planing lift. Some people simply say they both rely on lift and there is no difference in principle between the two. From an engineering perspective there is clearly a lot of difference. The wings on an aircraft are nothing like the foils on a cross-channel hydrofoil. When you hold your hand out the window of a moving car and feel the up, down and backwards forces that can be generated I would say you are simulating the foil on a hydrofoil because of the high angle of attack and large amount of drag. However, you are welcome to say you are simulating the lift on an aircraft wing. Dolphin (t) 02:06, 12 May 2012 (UTC)

What I'm saying is that they are fundamentally the same thing, just to a different degree. We cannot take it upon ourselves (without a single reference) to say, for example that L/D ratios better than 5:1 are lift, and if worse (or if we don't like the section design) are not lift. Lift begins with an angled flat plate in a flow and gets better from there.

As a series of side notes, I think you are confusing a few things to do with marine applications. The submerged foils on a commercial hydrofoil will have a very well designed hydrodynamic lifting section - they will be far from crude rectangle sections. Secondly, regarding the topic below, I think there is a special case of lift that can only happen at a medium boundary, and where the flow of the denser medium only passes on one side of the foil or of the lifting body. This is planing lift. The term is not applicable to other cases where the flow is on both sides; whether the foil is thick or thin, flat or curved, and whatever the angle of attack. Lastly, I think that we must, as authors of this article, remember that readers coming here may be researching many different things, and we should not at any point in the prose discount what may be their topic of interest. Lift as a force may be produced by an aerofoil, but it may also be produced by a very thin sail (fore-and-aft, spinnakers and square sails - which all work in very different modes), by a modern efficient daggerboard, rudder or keel underwater, by the wings on a racing car, by lifting bodies from the space shuttle landing to a speedboat rising out of the water to come onto the plane, by the heavy rectangular section leeboards on a Dutch barge beating to windward, by the submerged foils on a hydrofoil or those controlling the attitude of a submarine. If we define lift so generally and then write an article about only one aspect of it, we have not finished the job. If it turns out that there is too much detail here about aerodynamic lift, as strictly applied to modern commercial and military fixed-wing aircraft, then per WP:SPLIT, some of it may have to go into a specialist article on that topic. In short, I think there's a lot of work to do here. --Nigelj (talk) 09:05, 12 May 2012 (UTC)

The current activity on this thread began when User:Nelsonpom asked for an explanation of what causes the air to flow along the upper surface of an airfoil. If we wish to include flat plates operating at very high angle of attack we would have to tell him the air doesn't flow along the upper surface - behind the airfoil there is a turbulent mixture of air that forms a broad wake.

Wikipedia is still a work in progress so there is much work still to be done on most articles, including Lift (force). If you are inclined to provide some coverage of lift on flat plates and sails, and you have reliable sources, you are most welcome to start immediately. Dolphin (t) 12:44, 12 May 2012 (UTC)

My take is that the present article is a bit airplane-centric for my tastes, but the body of literature on the subject is also quite airplane-centric, so the article is probably a fair representation of the general body of knowledge. One thing that took me awhile to internalize when researching the subject is that airplane wings are usually operated at an angle of attack far away from the stall angle, while sailboat sails are usually set very near the stall angle (or way past the stall angle for downwind sailing). Perhaps the article should mention this? I'm not sure if it would create more confusion than it clears up.

Flat plates and sails set very near the stall angle are definitely within the scope of this article. That said, the bulk of the literature is about airplane wings far away from the stall angle, so it makes sense to give that application a more detailed treatment. Mr. Swordfish (talk) 14:47, 14 May 2012 (UTC)

Thanks Mr swordfish. As usual, I agree with everything you have written! A year ago I gave a little assistance in splitting the article Propeller into Propeller (aircraft) and Propeller (marine). It may be that we are approaching the time when Lift (force) can be split into Lift (aircraft) and Lift (sailing) or some similar pair of articles. Dolphin (t) 23:05, 14 May 2012 (UTC)

I would not agree with splitting the article in this manner. My preference is to keep a general article about the physics of Lift, and expand the specific treatment of wings and sails under their respective pages (or in a dependent article). For instance, Wing#The_aerodynamics_of_wings refers to this article for more information when it probably should be the other way around. In particular, the section Lift_(force)#Methods_to_determine_lift_on_an_airfoil would make more sense in the context of a different article specifically about airfoils or wings.

Unfortunately, the Forces on Sails article is currently somewhat of a muddle - I think that improving that article is a higher priority than adding sail-specific info to this one, or creating a new Lift(sail) page. Mr. Swordfish (talk) 15:04, 15 May 2012 (UTC)

Very sound ideas. Dolphin (t) 22:20, 15 May 2012 (UTC)

I thought this was the "main" article on aerodynamic lift and didn't notice there was a separate one on "wings". However it is titled, surely the "lift" provided by wings, rotors and propellors in air is a discrete topic. Once you start on planing and other forms of fluid transmitted forces you could digress into hydraulic rams, and even solids. "lift force" is not a good title IMO. Nelsonpom (talk) 09:04, 18 May 2012 (UTC)

Difference in areas redux

There was quite the spirted discussion of the "alternative" explanation "In terms of a difference in areas" a little over three years ago on the talk page. I'd like to revisit that, since I don't think is was resolved successfully.

In particular, a Google search for '"difference in areas" lift' turns up zero relevant hits other than this article (and the numerous wiki clones out there on the web) and shudder articles citing this article as their source. As this seems to be the only source for that terminology it would seem to violate the prohibition on OR. So at the very least, we should retitle the section with something more appropriate. JD Anderson uses the term "squashes" to describe the reduced stream tubes. NASA uses the term "constriction". The Smithsonian Air and Space Museum uses the term "squeeze". I do not currently have access to the other two sources, but have them on order and will peruse them in coming days.

Once I get my hands on the Smith and Brandt titles I'll take a stab at crafting a better treatment in my user space. Meanwhile I'd appreciate any pointers to other articles that explain lift in this manner - Googling for it is difficult since there appears to be no standard name for the explanation. Mr. Swordfish (talk) 14:08, 7 June 2012 (UTC)

Ooh, yes, that section does grate. What is that about 'zero angle of attack', then going ahead and getting lift anyway? And it goes straight for Bernoulli's principle too, without there being any deflection, turning or circulation of the flow. It is a sub-section under the heading 'Other alternative explanations for the generation of lift', alongside 'equal transit-time'. What's not clear in that whole section, is are these subsections all right? wrong? helpful? confusing? We can't have a big section including discredited theories without making the distinctions completely clear. --Nigelj (talk) 22:23, 7 June 2012 (UTC)

I've now read the relevant sections of Brandt et al and Smith. I've also turned up several other expositions of this explanation. What all of them have in common is lack of anything that I recognize as physics or engineering - there's no math or anything quantitative in any of the treatments - and the treatments are all quite brief. For instance, Brant et al devote all of two short paragraphs to it in a book spanning over 500 pages.

NASA's Glen Research Center is quite critical of this explanation, calling it flat-out "wrong".

My takeaway is that this is not a "scientific" theory, but rather a crude analogy that gives the right answer in some situations, while leading to misconceptions in others. For instance, while it makes intuitive sense that a conventional airfoil (i.e. flat on the bottom and curved on top) will "obstruct" more air on the top than the bottom, this idea cannot explain why lift occurs for flat plates, sailboat sails, symmetric airfoils, or for cambered airfoils that are upside down. It also fails to explain why lift increases with angle of attack, since as the AOA increases it's the bottom that's presenting the larger obstruction. Moreover, it might give one the false impression that a wing with a hump on top will generate more lift since it presents a bigger obstruction.

So, what to do about the article? This idea shows up twice, once at the end under "alternative" explanations, but it also appears under "A more rigorous description of lift" in the subsection "Lift in an established flow". I think this is misleading, since there's nothing rigorous about this idea. To be clear, it is rigorous to say that smaller streamlines imply faster flow and that faster flow implies lower pressure. What is not rigorous is to deduce smaller streamlines from "constriction" or "obstruction". To be fair, the section doesn't actually claim this, but a cursory reading might give some readers the wrong impression. I think some clarification is in in order and I'll try to take a stab at it in coming days.

Actually, after rereading the entire article several times, I think it has a serious flaw in its presentation: we say early on that lift can be explained by either Newton or Bernouilli, but don't ever take the bull by the horns and explain it with Bernoulli in a straightforward manner. We should. I think a good structure would be:

Intro (more or less what's there now)

Newton explanation (more or less what's there now)

Bernoulli explanation in layman's terms (which would be a new section)

The more rigorous explanation w/ math

Alternate explanations

Again, I'll try to craft something in my user space for review. The new section could conceivably encompass the "obstruction" explanation meaning we could remove the "Difference in areas" section altogether. But I'm not wed to that idea. Other thoughts?Mr. Swordfish (talk) 17:43, 17 June 2012 (UTC)

I agree that the difference in areas explanation of aerodynamic lift is a crude analogy. When explaining the concept of aerodynamic lift it has the advantage that it is intuitively satisfying, probably because it enables the kinematics of the flow field around the airfoil to be presented in a simple, easily comprehended, visual format.

It is not a fundamental observation. The fundamental observation is that the fluid surrounding the airfoil exerts a resultant force on the airfoil. From that, we can deduce that the mean pressure of the fluid on one side of the airfoil is different to the mean pressure on the other. From that, we can apply Bernoulli's principle and deduce that the mean speed of the fluid is different on one side of the airfoil than on the other. From that, we can apply the continuity equation and deduce that the mean separation of streamlilnes adjacent to one side of the airfoil is different to the mean separation adjacent to the other.

Your offer to write some words to incorporate the Bernoulli explanation in layman’s terms is appreciated. Go for it. I look forward to seeing it.

Here is a brief summary of a personal view of mine, although I know there are many others who share it. Science does not attempt to explain things, or to say why things happen the way they do. Science observes, always looking for patterns, repeatability, predictability etc. so that principles, theorems, laws can be formulated to describe what is observed. Once a principle (or theorem or law) has been formulated we can make other observations and say they are consistent with the principle. Science doesn’t say the universe is good or bad, or attempt to explain why the universe is the way it is. Science merely observes and describes. For this reason, science observes that aerodynamic lift can occur on a body moving relative to a fluid, and science can point to a number of principles (or theorems or laws) and say the phenomenon of lift is consistent with those principles, and therefore an example of each of those principles in action. The phenomenon of aerodynamic lift is consistent with a number of principles so it is unsound to contemplate which is the correct one – they are all correct. Our objective with this article should be to show that the phenomenon of aerodynamic lift is consistent with a number of scientific principles – Bernoulli’s principle, Newton’s laws of motion, Joukowski’s circulation theorem and so on. We shouldn’t be attempting to explain lift, or say why it occurs. Dolphin (t) 23:26, 17 June 2012 (UTC)

I now have an alpha version of the revised article in my user space: http://en.wikipedia.org/wiki/User:Mr_swordfish/Lift I invite comments and suggestions. I realize that much of it is uncited at this point - that will change before it goes live, but it may take me a few weeks to get it to the point where it meets wiki standards for sourcing. I'd also like to get some more pictures and diagrams into the article. Let me know your thoughts about the new material and organization. Mr. Swordfish (talk) 21:13, 26 June 2012 (UTC)

lift

please move lift-section to dedicated article. -paul — Preceding unsigned comment added by 188.25.109.9 (talk) 16:25, 21 June 2012 (UTC)

I need to verify final results in lift-section.Let someone verify it thx!

188.25.109.9 (talk) 16:28, 21 June 2012 (UTC)

July 2012 Article reorg

Hello,

Per the discussions under Difference in areas redux, I have been working on a reorganization of the article in my user space. It's at the point now where it's a release candidate. http://en.wikipedia.org/wiki/User:Mr_swordfish/Lift

Since this is a substantial overhaul, I'm going to allow a week for comments and suggestions. Since it's an almost live wiki article I have no objection to edits in place before transferring it to the live site. Have a go at it - no point in waiting until it's live.

In about a week I'll transfer it to the live site. Mr. Swordfish (talk) 21:47, 17 July 2012 (UTC)

I have no objection to the reorganised version going live. Just one observation - the diagram Airstreams around an airfoil in a wind tunnel is used twice. If that was a deliberate decision I have no problem with it. Dolphin (t) 04:26, 18 July 2012 (UTC)

Yes, this is deliberate. One reason is that I don't want to make the user scroll up to see the diagram; I want it to be right next to the text. Another reason is that using the same picture but interpreting it differently re-enforces ~~the primary~~ a major theme of the article that there are multiple ways to explain lift. If you look at the picture with Newton's 3rd law in mind you see the air being deflected; if you have Bernoulli in mind you'll see the size of the streamtubes. It's almost like one of those optical illusions where some people see a vase and others see two faces. A third reason is that I don't have ready access to another picture - this is probably the biggest reason. I'm not wedded to the idea of reusing the same picture, so if someone can come up with a better graphic I won't object. Mr. Swordfish (talk) 13:23, 18 July 2012 (UTC)

I agree with your reasoning. Dolphin (t) 01:55, 19 July 2012 (UTC)

Sails

I know you guys have done, and are doing a good job here. Can I drawn your attention to the comments I just made at Talk:Forces on sails#Expert attention? I don't know if any of you have the time/inclination/expertise to want to help there? --Nigelj (talk) 13:04, 12 August 2012 (UTC)

A more complete explanation of lift and suggested major revision of the article

The current article presents explanations based on downward deflection of the flow and on Bernoulli, and states that either can be used to explain lift. I would argue that neither of these is complete by itself and that a complete explanation not only requires both downward deflection and Bernoulli, but also a more detailed discussion of the flowfield and of the interaction between pressure and velocity. My proposed explanation has some novel elements, but it has a citable source. Bear with me while I explain the physical basis for this more complete explanation.

Two questions have been asked but not answered in earlier pages of this discussion:

1) What causes air passing above the airfoil to be deflected downward to follow the downward-sloping upper surface?

2) What causes air passing above the airfoil to accelerate to higher speed?

The answer to both questions is to be found in the nature of the pressure field around the airfoil, and when this is followed to its logical conclusion it suggests a more complete way to explain lift.

Both the downward deflection and the increase in speed reflect accelerations of fluid parcels in a vector sense. Newton's second law (F = ma, where the force F and the acceleration a are vectors) tells us that the proximate cause of any acceleration must be a net force. (I regard F = ma as a cause-and-effect relationship. F can always be thought of as causing a, though the causation needn't always be one-way.)

So what is the force that causes these changes in velocity? Outside the thin viscous boundary layer and wake, the viscous and turbulent stresses are negligible, so that the pressure is the only force of any significance in most of the flowfield. And to exert an unbalanced (net) force on a fluid parcel, the pressure must be non-uniform (i.e. it must have a nonzero gradient, in math terms). When pressure is non-uniform, a fluid parcel experiences an unbalanced force in the direction from higher pressure to lower pressure (i.e. "down" the pressure gradient).

The flow is in the continuum domain, where the fluid flows as if it were a continuous material that deforms and changes course to flow around obstacles instead of just flying into them. The airfoil affects the velocity and the pressure over a wide area. In the flow around a lifting airfoil there is generally a diffuse cloud of low pressure over the upper surface, and if the airfoil is thin enough there will be a diffuse cloud of (usually weaker) high pressure under the lower surface. I've sketched the gross aspects of these clouds using notional isobars in the field (The minus sign doesn't mean the pressure is negative in an absolute sense, only that it is lower than ambient). The differences from ambient are generally largest somewhere on the airfoil surface and die away gradually away from the surface.

Fluid parcels passing through different locations in this non-uniform pressure field (the low-pressure and high-pressure clouds) experience unbalanced forces in the directions indicated by the block arrows in the sketch. The result is that flow above and below the airfoil is deflected downward, flow above the airfoil is speeded up, and flow below is slowed down, as seen in the current article's flowfield animation. Thus the answer to both our questions above is that all the changes in flow direction and speed in the flowfield are directly caused by the non-uniform pressure field.

Dolphin argues that these changes in vector velocity are "due to" or "induced by" the bound vortex and that they can be calculated by a "precise mathematical relationship." Well, yes, the Biot-Savart law allows you to infer velocity from vorticity, but calling the relationship "induction" is a misnomer in this case. Biot-Savart is just a vector-calculus relation between a vector field and its curl. When it is applied to an electric current and a magnetic field, it reflects actual physical cause and effect, for which "induction" is the appropriate term. When it is applied to vorticity and velocity in fluid mechanics, it is just kinematics, not dynamics, and thus doesn't reflect cause and effect. If you want to explain physically how a velocity change comes about, you have to get into the dynamics, which means identifying the force that causes the acceleration. Biot-Savart and the idea of "induction" in aerodynamics have caused a great deal of confusion, with many commentators, including some of the sources cited in the current article, promoting the erroneous idea that vortices cause changes in velocity. Nelsonpom is right in saying that the vorticity is not a cause of the velocities elsewhere, but a result.

So the changes in flow speed and direction are caused by differences in pressure. But what causes the differences in pressure? This part is more difficult for our intuition to grasp. In the mathematical theory, the cause-and-effect relationship between pressure and velocity in steady aerodynamic flows is implicit, described by multiple partial-differential equations (conservation equations for mass, momentum, and energy in the case of the NS or Euler equations) that must be satisfied everywhere in the field simultaneously. The only way I know to explain this nonmathematically is to say that the cause-and-effect relationship between pressure and velocity is mutual, or reciprocal. Pressure differences cause the accelerations in the flowfield, and the pressure differences are sustained by the combination of the accelerations and the inertia of the fluid, in a manner consistent with Newton's second law. One intuitive way to look at it is that a pressure difference can exist only if something is there to "push back," and what pushes back is the inertia of the fluid, as the fluid is accelerated by the pressure difference.

The pressure field and the velocity field thus support each other in a mutual interaction. This circular cause-and-effect is not "something for nothing" or "perpetual motion." The details of the pressure field and the velocity field are dictated by the combination of the airfoil shape and angle of attack and by the fact that Newton's second law must be satisfied throughout the field. As long as the flow doesn't separate ahead of the trailing edge (i.e. as long as the airfoil has a reasonable shape and the flow isn't stalled), the flow next to the surface naturally follows the airfoil contour. The continuum nature of the fluid then requires that the pressure and the speed and direction of the flow are affected over a wide area. The mutual interaction between the pressure field and the velocity field is just nature's way of making it all happen.

To me, it's clear from the above that sustaining the clouds of non-uniform pressure requires sustaining pressure differences in both the vertical and horizontal directions. This requires accelerations of the flow in both the vertical and horizontal directions. Thus sustaining the pressure differences requires both downward turning of the flow and changes in flow speed according to Bernoulli's principle.

As opposed to just a "Newton" or "Bernoulli" approach, the above arguments lead to what I would call an "Euler" approach to explaining lift. For a 2D flow, the Euler momentum equation is a vector equation with two components that must both be satisfied. And, after all, an airfoil flow is at least a 2D flow, not 1D, and we shouldn't expect a 1D approach ("Downward deflection" or "Bernoulli") to suffice. A complete explanation really needs both.

So the stance taken by the current version of the article, i.e. that things can be explained adequately with either "downward deflection" or "Bernoulli" by itself, isn't quite right. The idea that either of these very-different-sounding explanations can be correct and complete by itself is something many people have been uncomfortable with, and it has been a source of a lot of unnecessary controversy. I think the recognition that a complete explanation needs both downward turning and changes in flow speed solves this problem. And explaining the spread-out nature of the pressure field and explaining that the cause-and-effect relationship between pressure and velocity is reciprocal would also be helpful additions.

The physics behind these arguments isn't new, but this particular way of combining the arguments into an explanation of lift seems to be novel, which raises the question of a citable source. As far as I know, the only one is my own book, Understanding Aerodynamics -- Arguing from the Real Physics, recently published by John Wiley and Sons. It contains a long section devoted to physical explanations of lift. In it, I critique all the existing explanation approaches I could find and present my own explanation, based on more detailed versions of the arguments above.

In my personal sandbox User:J_Doug_McLean/sandbox I have posted a proposed draft of the text for a revised version of the article that attempts to meet Wikipedia content and style guidelines (It still needs to have citations and graphics added). This draft applies only minor changes to the introductory paragraph and the Overview, but it makes substantial changes to the sections on physical explanations and the mathematical theories. I'll leave it there a while for feedback before I attempt any editing of the article itself.

J Doug McLean (talk) 00:53, 31 January 2013 (UTC)

Doug, thanks for taking the time to read our article Lift (force) carefully, and to propose ways of improving it. After reading your post immediately above I can make a couple of comments that might help you and others anticipate what reaction you will receive from other readers.

In referring to a complete explanation of lift, you appear to be alluding to the existence of One True Explanation Of Lift. There is no One True Explanation Of Lift. Many contributors to this Talk page promote their favourite explanation of lift as the correct one, and then conclude that all other explanations must be at least partly incorrect. Different people will find different explanations of lift to be satisfactory – an explanation of lift that is satisfactory for a student pilot will be different to one that is satisfactory for a professional aerodynamicist, and vice versa, even though both explanations may be scientifically sound. The questions for the Wikipedia community are: what level of complexity is appropriate for an encyclopedia, and do reliable published sources exist to support each element of the explanations provided in Lift (force)?

You have made many references to a cause-and-effect relationship. Be aware that even though many situations can be described accurately by identifying a cause and an effect, there is no scientific principle that says all situations can be described as a cause-and-effect relationship. We have seen inconclusive debates on Bernoulli's principle about whether changes in pressure are the cause, and changes in velocity the effect, or vice versa. (I would argue that Bernoulli correctly identified the relationship between static pressure and dynamic pressure but he was wise enough to avoid speculating about which was the cause and which the effect.) The notion of cause-and-effect is not a scientific principle so it should not be used in any attempt to explain phenomena in the field of science.

You have written Dolphin argues that these changes in vector velocity are "due to" or "induced by" the bound vortex. Yes, there is an advanced mathematical model based around the notion that fluid motion is induced by a vortex field. (This notion is essential if we are to make use of the Kutta condition when quantifying lift.) The language accompanying this model talks of the flow around a wing being induced by a bound vortex and at least two trailing vortices. Anyone who finds this language unconvincing, or the mathematical model too complex, should simply ignore the model and find another explanation that satisfies their needs.

You are proposing citing as your source a book written by yourself. This presents a potential problem. There is a conflict of interest when the author of a book cites his book as a reliable published source. See WP:COI and WP:SELFCITE for guidance.

I hope to add more ideas in the days to come. Dolphin (t) 07:00, 31 January 2013 (UTC)

Doug,

Can you post a link to your draft of the changes to the article? I can't find it on your user page and I'd like to read it first before commenting further. Mr. Swordfish (talk) 13:13, 31 January 2013 (UTC)

Done. See last paragraph of my posting. --J Doug McLean (talk) 17:10, 31 January 2013 (UTC)

Dolphin, thanks for the thought-provoking comments, some I agree with and that I hope we can use to improve my draft, and others indicating that we have philosophical differences.

I didn't mean to imply that my proposed explanation is the last word on the subject, the "One True Explanation Of Lift". We should be careful that nothing we put in the article implies that it is. That said, however, I think value judgments are possible and appropriate. Some explanations are more complete than others (assuming "complete" can be a matter of degree), and we shouldn't hesitate to say so. In the heading of my talk post I refer to my proposed explanation as "more complete", and the heading in my proposed text refers to it as "A comprehensive explanation", using "A" rather than "The" on purpose to avoid implying that it's the final word. If more care is needed, I'd welcome suggestions.

Any one of the simpler explanations, Bernoulli only, for example, might be satisfactory for some people's purposes, but I think it's still fair to call it incomplete if it leaves a physically necessary part of the phenomenon unexplained. For lift to exist, a pressure difference is physically necessary. For a pressure difference to exist on a finite body, pressure gradients in both the horizontal and vertical directions are physically necessary. A Bernoulli-only explanation doesn't explain how the vertical gradient is sustained and is thus incomplete by this standard.

Given the history of lift explanations, I think an encyclopedia article should survey the whole landscape of published explanations, or at least the major categories. My new explanation is the most comprehensive published so far, as far as I know, and thus I think it belongs in the article along with the older ones. As far as a reliable source is concerned, I think my book is at least as reliable as many of the sources already cited in the article. It is self-written, but it is not self-published. Wiley submitted it to its usual review process and sent sample chapters to several academic experts. The sample chapters included the one with the lift explanation. The experts made many comments that chapter, but not one criticized the lift explanation, in spite of its novelty. WP:COI says that citing yourself is acceptable if it is relevant and conforms to content policies, which I think my book is and does.

Still, I must admit to feeling a bit awkward having to cite my own work, which is one of the reasons I'm seeking the buy-in and help of this community.

I agree that "there is no scientific principle that says all situations can be described as a cause-and-effect relationship." But I disagree with your statement that cause-and-effect "should not be used in any attempt to explain phenomena in the field of science." Fluid mechanics involves many relationships, some reflecting direct physical cause-and-effect and some not. When constructing a physical explanation of a fluid phenomenon one should always try to make the cause-and-effect relationships clear. And if there is a choice of different ways to explain something, an explanation that is based on direct physical cause-and-effect is preferable to one that isn't.

And the cause-and-effect question brings me back to "induction" of velocity by vorticity. It's not that the term "induction" is "unconvincing"; it's that it's misleading. To me, to induce something is to cause it, and that's not what's happening here. Several of the classical sources (e.g. Milne-Thomson, Theoretical Aerodynamics, Dover, 1966) talk about how the causation implied by the term "induction" isn't real. So I would say that the use of Biot-Savart in fluid mechanics is based on the notion that the velocity field is associated with the vorticity field, not induced by the vorticity field. I think it's an important distinction. J Doug McLean (talk) 23:10, 31 January 2013 (UTC)

Doug, thanks for your prompt and well-considered reply.

You have written A Bernoulli-only explanation doesn't explain how the vertical gradient is sustained and is thus incomplete by this standard. I would say Bernoulli's principle doesn’t explain any of the pressure gradients around a wing – vertical or horizontal. Bernoulli merely relates changes in static pressure to changes in speed. Information about changes in speed must come from knowledge of the kinematics of the flow field.

I think we agree that the lift on a wing can be explained using two steps – firstly we must consider the kinematics of the flow field around the wing; and secondly we must use Bernoulli’s principle to translate changes in flow speed to changes in pressure acting on the wing, resulting in a net upward component of aerodynamic force which we call lift. The second of these two steps, Bernoulli, is relatively simple. The first, kinematics of the flow field, is relatively complex. I believe the reason most literature in the fields of aviation and aerodynamics focusses almost exclusively on Bernoulli when explaining lift is because Bernoulli’s principle is relatively simple whereas the kinematics of the flow field is not.

A number of well-informed contributors to this Talk page, and other similar forums, have asked the question “Why does the air flow faster across the upper surface of the wing than across the lower surface of the wing?” A wide variety of attempts have been made to explain this aspect of the flow field, including the notorious Equal Transit Time Theory. In my opinion, most of these attempts fail to satisfactorily explain why the air flows faster across the upper surface than the lower surface. One satisfactory explanation makes use of the Kutta condition and the concept of the horseshoe vortex to identify the strength of the bound vortex. Either the Kutta-Joukowski theorem or the Lanchester-Prandtl Lifting-line theory can then be used to determine the velocity of the flow field at any point. Whether we say the flow field is induced by the vortex line, or is associated with the vortex line, is unimportant. I think to accept, in a rigorous way, that air flows faster across the upper wing surface, we need to have an understanding of the Kutta condition and the horseshoe vortex. Anyone who takes the view that Kutta and the horseshoe vortex are too esoteric or complicated, and who seeks to explain the kinematics of the flow field from a more elementary perspective will end up with an unsatisfactory explanation, even though many readers might find it attractive. So that is the reason I have written about the bound vortex inducing a flow field around the wing. I have no objection to the word “inducing” being replaced by another word, providing it is supported by the cited sources. Dolphin (t) 07:23, 1 February 2013 (UTC)

Doug,

Thanks for the stimulating and very interesting article. I always enjoy reading different perspectives on this fascinating subject, and I particularly like your idea that a mutual interaction between pressure and velocity is what sustains the pressure difference. I would like to incorporate that into the article, and hopefully when I obtain a copy of your book we can add that with a proper citation to meet wiki standards.

But while I find your take on lift interesting and a very good read, I do not think it is an improvement on the current article. The current article's structure is not haphazard; instead it owes a lot to 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 by Hoffren, Smith, Weltner, Babinsky amongst others.

Here are some links to the articles:

Hoffren: http://corsair.flugmodellbau.de/files/area2/LIFT.PDF (see especially section 4)

Smith: http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHTEAH000010000008000451000001&idtype=cvips&doi=10.1119/1.2352317&prog=normal

Weltner: http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000055000001000050000001&idtype=cvips&doi=10.1119/1.14960&prog=normal

Babinsky: http://iopscience.iop.org/0031-9120/38/6/001/pdf/pe3_6_001.pdf

Not only that, wikipedia style guides recommend proceeding from the simpler to the more complex within an article, and avoiding assumptions that the reader is already familiar with the material. While I enjoyed your version of the article, I can't imagine someone who isn't already familiar with the material fighting their way through it and getting much out of it.

All that said, I do think there is material that can be incorporated into the article under the "more detailed physical description" section. As Dolphin points out, citing your own book is problematic, so I think it is best if you let other editors do that integration. — Preceding unsigned comment added by Mr swordfish (talk • contribs) 16:10, 1 February 2013‎

Doug,

Wikipedia articles are expected to be written in an impersonal, business-like tone appropriate to an encyclopedia. Wikipedia is not a textbook, instruction manual or guide-book. See WP:NOTGUIDE.

Much of your proposed text at User:J Doug McLean/sandbox is written in a tone that is not particularly appropriate to an encyclopedia but would be appropriate to a student textbook or guide-book. Following are some examples:

Imagine riding on an airplane as it flies through the air
One way to imagine that lift happens is to think of the airfoil shape and angle of attack as working together so that the airfoil pushes downward on the air as it flows past.
But we still have to explain how the moving air is able to push back. As we saw above, it pushes back in the form of a pressure difference
But to understand how the pressure difference is produced, we must understand what the flow does over a wider area
Newton's second law tells us that a force causes air to accelerate in the direction of the force.
To be sure to see the speed difference in the animation correctly, you must take care to keep track of corresponding columns of markers on the upper-and lower-surface streamlines. Over the length of the airfoil the upper markers nearly catch up with the lower markers one column ahead, which can be confusing.
The pressure difference can exist only if something is there to “push back.”

All text in an article should be in a tone appropriate to an encyclopedia. Guidance is provided at WP:TONE.

Wikipedia’s desired standard in content, quality and tone can be seen in the daily Featured Article – this is presented each day on the Main Page. All Wikipedia’s Featured Articles are catalogued HERE. Dolphin (t) 05:34, 3 February 2013 (UTC)

This discussion illustrates why this topic is so difficult. Here we have three people who have obviously thought a lot about the issue, and we still have significant areas of disagreement.

Dolphin, you say "I think we agree that the lift on a wing can be explained using two steps", first kinematics to infer increased speed over the upper surface and then Bernoulli to infer lower pressure. In the next paragraph you go on to say that the preferred way to infer the increased speed is through a combination of circulation and Kutta-Joukowski, with possible help from knowledge of the Kutta condition. Assuming you intend this as a qualitative explanation for a nontechnical audience, I think this general approach has two serious disadvantages:

1) Whether it's intentional or not, the general implication of this explanation is one-way causation from increased speed to reduced pressure. The real cause-and-effect relationship is reciprocal.

2) Circulation and Kutta-Joukowski are mathematical abstractions that belong in the "Mathematical theories" section, not in an explanation for a nontechnical audience. Besides, the direct physical cause of the increased speed is the low pressure. Why not appeal to the direct physical cause when we know what it is?

I think I understand the rationale for wanting to start with other aspects of the flow and then to deduce the pressure difference. Pressure is the quantity most directly associated with lift, and by arriving at the pressure difference last, it feels more like we're predicting the existence of lift. But qualitative explanations in aerodynamics can't actually predict; the best they can do is explain. And since explaining is what we're really doing, why not start with the quantity most closely tied to the lift, i.e. the pressure, and show how the other things support it?

Your comments on the tone of my draft are well taken. I've revised it to try to fix these issues.

Mr swordfish, thanks for the comments and the links to articles on pedagogy. My book references the papers by Hoffren, Weltner, and Babinsky and discusses their lift explanations.

Hoffren's paper, by the way, does not really qualify as peer-reviewed. While AIAA Journal papers are subject to rigorous peer review, AIAA meeting papers are not. AIAA meeting papers are accepted based on short abstracts, which are generally too cryptic to support a rigorous review and are used just to decide what meeting sessions the papers belong in. As long as your abstract sounds relevant to the subject of the meeting, the AIAA will accept your proposed meeting paper. Then you can go ahead and write just about anything you like. So with regard to reliability, an AIAA meeting paper might as well be self-published. Hoffren's paper offers an interesting explanation of lift that is correct as far as I can tell, but his supporting discussion of potential-flow theory makes significant errors that would probably have been caught by a peer review.

In terms of the progression from simpler to more complex, the current article is well organized. But I think there are some key things that it doesn't quite manage to get across, such as that the quantitative theories are well established and have great predictive power, while the qualitative explanations have essentially none. This is the kind of thing I'd look for in an overview, but the current "Overview" merely defines a couple of key terms. My proposed new section, "The scientific understanding of lift versus qualitative physical explanations or descriptions" tried to do this, but I can see now that I made it too long, including discussion that belonged in the "Mathematical theories" section. In the currently posted version, I've tried reorganizing it, integrating this background material into the "Overview" and trying to keep it short enough to fit there. I also moved the definition of an airfoil from the "Overview" to the explanations section because it seems to me to fit better there.

Having the explanations section start with a downward-turning explanation and then Bernoulli, as the current article does, makes sense if you regard these as alternative explanations, each one satisfactory in its own right. However, I think I've made a strong argument that hadn't occurred to the authors of the pedagogy articles you cite, i.e. that as opposed to alternative/satisfactory explanations, these classics are really complementary/partial explanations. Neither one makes it clear that lift requires both downward turning and changes in flow speed, or that the interaction between pressure and velocity is mutual. So I would ask whether it still makes sense to lead off with them.

In the revised version of my draft comprehensive explanation, I've rearranged the early part so that action-and-reaction and flow deflection are pretty much up front, and someone with a short attention span could stop reading there. But I still propose leaving the details of the older deflection and Bernoulli explanations until after mine, given their incomplete nature.

My draft also suggests replacement of some of the farther-down sections, but if you end up keeping the old versions there are some problems that I think should be addressed:

Under "Angle of attack", flow separation at the stall is blamed on the flow becoming "turbulent". Actually, a turbulent boundary layer is a necessity in the pressure-recovery region under attached-flow conditions because it resists separation better than a laminar boundary layer. When separation does happen, it's not a result of turbulent flow.

The discussion of Bernoulli's principle misses some key points. First, it says "Bernoulli's principle does not explain why the air flows faster over the top of the wing; to explain that requires some other physical reasoning." I think that's true only if you don't know anything else about the flow. If you know that the flow speeds up, Bernoulli's principle explains precisely why: It speeds up because of reduced pressure. Bernoulli is really just a specialized integrated form of F = ma, and when we see that something has accelerated, F = ma tells us that the cause was a force.

Under "Limitations of explanations based on Bernoulli's principle", the failure of Bernoulli to apply in the case of an airplane in level flight is attributed to "adding energy to the flow". Actually, in the reference frame of the airplane, the drag doesn't add energy to the flow. In the reference frame of the air mass, energy is being added to the flow, but that's not the reason Bernoulli fails in this reference frame in the irrotational parts of the field. The usual form of Bernoulli's equation is valid only for steady flow, and the flow around an airplane is unsteady in the reference frame of the air mass. Think of the classical potential flow around a circular cylinder. That flow has zero drag, so that no energy is being added to the flow in any reference frame. Yet in the reference frame of the air mass, that flow violates the steady form of Bernoulli. For example, the pressure at the stagnation points is higher than the pressure in the farfield, but Bernoulli says it should be lower. I don't see Bernoulli's limitation to steady flow mentioned anywhere in the current article.

The section on the NS equations doesn't mention that the effects of turbulence cannot ordinarily be computed directly, but must be modeled, as in the RANS equations. This is an essential distinction in practical calculations of lifting flows.

The current description of the Kutta condition seems overly cryptic to me, so in my current draft I've added one with more detail on why lift in potential flow is indeterminate in the first place. Also, describing the Kutta condition in terms of the stagnation point introduces a new term that is unnecessary and not always applicable. An airfoil with a cusped trailing edge doesn't have a trailing-edge stagnation point, so in that case the Kutta condition doesn't just move the stagnation point to the TE, it makes it disappear. Better just to say that the right amount of circulation is the amount that results in the flow leaving the TE smoothly.

I think the quote by John D. Anderson gives the misleading impression that there are disagreements over the science itself, not just the qualitative explanations. And I think his statement that "the debate centers on which explanation is the most fundamental" is also a bit off the mark. I had an email exchange with him a couple of years ago, and he stated his criterion in a stronger form, i.e. that in choosing what physical principle to start with in an explanation of lift, the most fundamental principle is to be preferred. He preferred starting with conservation of mass because he regarded it as more fundamental than conservation of momentum. I begged to differ, saying that the criterion should be which physical principle is most relevant to the phenomenon we're trying to explain. Lift is a force, and what could be more relevant to a force than conservation of momentum? But I don't think I convinced him.

Thanks again for the thought-provoking discussions. J Doug McLean (talk) 20:08, 6 February 2013 (UTC)

I hear what you're saying - three editors, four opinions! That's par for the course for this topic. That said, I think the three of us can agree that when an airfoil is generating lift the following phenomena occur:

1 The foil experiences a net force

2 The air follows a path that is curved with a net deflection downward

3 There is a region of lower pressure above the foil

4 The air speeds up in this region of low pressure

These four things occur simultaneously, so no one is the cause of the others in the sense of "first A happens and then B happens as a result". Instead, all four phenomena must be present - you can't have any one without the other three.

Where we seem to disagree is how to present it. In the article, we're trying to explain item 1. My take (and it's not mine alone, but is reflected in numerous reliable sources) is that it is easy for a human to see item 2 from the geometry of an airfoil at non-zero angle of attack. One intuitively expects the air to follow a curved path and be deflected downward, and if smoke is injected into the airstream one can see this directly. Likewise, the downwash can be readily observed. So a simple explanation that starts with something readily observable and then applies a simple physical principle (newton's 3rd law or conservation of momentum, both of which are within the experience of most readers) to explain the lift force is readily digestible by almost anyone.

By contrast, we can't directly observe regions of low pressure or regions of higher speed. One needs specialized instruments to detect those phenomena directly. If air changed color or something when the pressure dropped then using pressure as a starting point might make sense; instead pressure is an abstract concept not directly detectable. This makes it harder for a lay-reader to internalize a pressure-based explanation. Moreover, attempts at simple pressure-based explanations are often butchered to the point of being actually false (eg equal-transit-time) This is why the current article starts with the deflection/flow turning instead of a pressure oriented approach. It's why NASA and AAPT advocate this approach. Of course, the simple deflection /flow turning explanation is, well, simple and not the full story; I think the current article is quite clear about this, and it goes on to present more complete explanations. So, to answer your question about whether it makes sense to lead the article the way it is now, the answer is yes.

The approach taken in your book - start with the NS equations and proceed from there - is a good one for it's intended audience. But it's not a good approach for the general lay reader of wikipedia. Our job as editors is to explain in terms that the average reader can follow, and the truth is that as soon as you say 'partial differential equations' you lose 99% of readers. That doesn't mean we can't include the mathematical treatment of the subject, but starting there is not a good approach. From WP:NOTGUIDE:

A Wikipedia article should not be presented on the assumption that the reader is well versed in the topic's field. Introductory language in the lead and initial sections of the article should be written in plain terms and concepts that can be understood by any literate reader of Wikipedia without any knowledge in the given field before advancing to more detailed explanations of the topic. While wikilinks should be provided for advanced terms and concepts in that field, articles should be written on the assumption that the reader will not or cannot follow these links, instead attempting to infer their meaning from the text.

So, while I think the latest draft in your sandbox is an improvement over the last one, I do not think it is an improvement over the current article. I do think there are parts that can be applied to the current article and that you have made some helpful criticism of items in the current article in your comments above. I don't have time to address them right now, but I do plan on addressing them at some time.

In sum, the structure of the current article was arrived at through a weeks-long consensus-building discussion involving multiple editors and is based on many reliable sources. I think it's a good one, and not something that we should change as a result of one new book that takes a different approach. I know that it is your book, but as wikipedia editors that shouldn't factor into the decision of how to balance the various reliable sources. Mr. Swordfish (talk) 16:16, 7 February 2013 (UTC)

I agree that we should start with the concrete (i.e. deflection and flow turning) and proceed to the more abstract later. By way of an analogy, there is often a confusion in the language in the opening sentences of articles, and from what I can understand Wikipedia articles are not about the word or words of the title (such an example here would be if the article started, "Lift is a term that is used to describe..."), but about the thing to which the words refer. Following this logic into technical articles, I have seen other debates about whether the article is about the phenomenon, or about the mathematical model or models that describe the phenomenon. Many will argue, for example, that the difference between positive and negative feedback is entirely down to the sign of the loop gain. I would argue that the opening of an article should describe the concrete phenomenon (in everyday language as far as possible) whenever that is possible, and then proceed to introduce mathematical models and their concomitant equations later. Analogously, articles do often include an etymology section about the words of the title, but they do not begin with it. --Nigelj (talk) 21:23, 7 February 2013 (UTC)

Mr swordfish,

Thanks again for more comments. I agree with your list of four phenomena that accompany lift and that none can exist without the other three. The four phenomena are obviously related, but you seem to be saying that the relationships between them aren't cause-and-effect because the phenomena are simultaneous, not sequential, and the relationships aren't one-way. But cause-and-effect relationships don't have to be sequential or one-way. For example, in Newton's second law the force causes a simultaneous acceleration. That's what's happening here, with the added twist that it isn't one-way. The non-uniform pressure field causes the accelerations in the flow field per Newton's second law, and the existence of the pressure gradients is supported by the accelerations, as I explained in my first post.

I understand the principle behind the ordering of the items in the current article, so I agree that in one sense the article is well organized. But I think you'd have to agree that the article reads like a shopping list of separate items (Try scanning just the headings, and I think you'll see what I mean). It offers very little in the way of explaining how things fit together in a big-picture sense, such as the difference between the mathematical theories and the physical explanations, and between prediction and explanation. To get any sense of the big picture a reader would have to read the entire article, and even then she'd have to work most of it out for herself. That's the void I'm trying to fill with my expanded "Overview" section. I'm not proposing that we "start with the NS equations and proceed from there". My proposed overview doesn't mention "NS equations" or "partial-differential equations"; that's left to the "Mathematical theories" section. My overview just explains what the mathematical theories represent and what their status is as science. If I were a lay reader, that's the kind of big-picture stuff that I'd want to know, and I wouldn't find it in the current article. I think my proposed overview does it in terms any "literate reader" can understand, so I think it's completely in line with the WP:NOTGUIDE paragraph you quote.

I don't think that bringing the mathematical theories in at the overview level is premature, as Nigelj seems to. The what of lift is pretty basic: It is a force. It depends on airfoil shape, angle of attack, and airspeed. But once you get into explaining how or why it happens, you're no longer just describing the phenomenon; you're talking conceptual models, and you should make it clear that the bedrock of our understanding in that sense is the mathematical theories. — Preceding unsigned comment added by J Doug McLean (talk • contribs) 06:56, 8 February 2013 (UTC)

I've gradually come around to not objecting to putting the two popular explanations ahead of mine, provided we expand the overview as I've proposed. So in my revised draft I keep the expanded overview, make "Airfoil shape and angle of attack" an introductory section to the explanations, go to the popular explanations and their limitations, and then go to my explanation. The citations would be essentially the same as in the current article, with citations of my book added in the appropriate places.

Of course my book is just "one new book". But I think technical issues should be settled on the merits of the arguments, not by voting or counting citations. I think I've made strong new arguments regarding the deficiencies of the older explanations and how to remedy them. Specifically, my main points, i.e. that it's important to consider the extended flowfield, that both downward deflection and changes in flow speed are essential, and that the interaction between pressure and velocity is reciprocal, make for a much-improved physical explanation of lift. So my explanation isn't just a "different approach"; it's a substantial improvement over the older approaches. If you disagree, show me specifically where I've gone wrong.

My current draft User:J_Doug_McLean/sandbox retains nearly all of the content and ordering of the current article, and addresses some of its deficiencies, in addition to adding my new explanation. I think that at this point its a substantial improvement over the current article, not just because it includes my explanation, but because it adds a much-needed overview. What do you think? If you don't have time to do the edit, and no one else volunteers, I'll do it.

By the way (and this addresses a point also raised by Nigelj), I think the idea that flow deflection is somehow more "concrete" than pressure (or force?) is a stretch. True, you can make flow deflection directly visible with smoke. But you can also make pressure visible, albeit graphically, by drawing the isobar pattern. Anyway, how many readers will have seen a smoke-flow visualization first-hand? Most will only see pictures, and most of those will be drawings of streamlines, as in the current article, not photos of smoke streams. As pictures, I don't think streamline patterns are fundamentally more compelling than isobar patterns. I think that pressure, being the thing that actually pushes on the airfoil, is quite concrete.

Thanks again for the discussion. J Doug McLean (talk) 06:38, 8 February 2013 (UTC)

Doug, If you are still around, be assured that I have not forgotten or ignored this discussion; I do intend to incorporate some of your suggestions into the article. This may take some time. Please be patient. Thanks. Mr. Swordfish (talk) 19:12, 20 March 2013 (UTC)

I'm still around, and I'm not in a hurry. I've made further changes to my suggested revised article in my sandbox User:J_Doug_McLean/sandbox. Instead of an "Overview" following the introductory section, I now lead off with the "what" of lift in "Lift depends on airfoil shape, angle of attack, air density, and airspeed" and then explain how the theories and explanations are related in "The understanding of lift as a physical phenomenon", which I think would go a long way toward avoiding the kind of misunderstanding raised by Westwind273 in the new string below. That leads into the popular explanations and then my more comprehensive one. I've installed some graphics, but not all, and only a few of the links and citations. J Doug McLean (talk) 01:20, 6 April 2013 (UTC)

where they got the idea of that airfoil shape

Nice article.

I was thinking - how about grounding the article in terms of where they got the idea of that airfoil shape. I discovered that sailors have been talking about lift and that airfoil shape since Egypt ruled, it's really a basic principle of sailing. For wings you just point the lift up, in sailing the lift goes to the side. I think I'm going to copy this to the wiki reference on wing as well.

When I started looking into this I thought these guys like George Cayley were pretty esoteric thinkers to just sit there with Bernoulli's Equation in the 1700's and come up with the airfoil. If you look at it, he was just describing a long-known phenomenon in the lab. In fact I'm a little shocked at how long it took to develop the airplane wing, historically speaking. We've known this for a real long time. This may be obvious you folks on the coast, but it wasn't obvious to this land lubber.

Just a sentence in the intro like...

Pb8bije6a7b6a3w (talk) 21:00, 12 February 2013 (UTC)

It would really help if you had a link to a reference where it says that "sailors have been talking about lift and that airfoil shape since Egypt ruled". Then we could look at this in a little more detail. --Nigelj (talk) 23:36, 12 February 2013 (UTC)

Improvements

I visited this site recently. It's improved fantastically since a couple years ago, from the point of view of those who view Wikipedia's mission as the advancement of honest curiousity, science, and reason. Back then we were losing the battle. All who are responsible deserve our thanks. — Preceding unsigned comment added by Mark.camp (talk • contribs) 03:20, 6 March 2013 (UTC)

Recent additions by ‎Completeaerogeek

There are many problems with the material recently added.

1) Completeaerogeek has provided no sources.

Completeaerogeek:(First of all I apologise for an formatting errors I may have made but I am new to editing Wiki).

However, the above is not correct. I have cited Babinsky source material which was put into the public domain by the author and as such is fair use for educational purposes. material on Wikipedia must be cited byreliable sources; material lacking this is subject to immediate removal.

2) The physics is identical whether one expresses it in the reference frame moving in the direction of the foil or the reference frame of the air. This is basic Newtonian physics. While I agree that this sometimes causes confusion, the nature of the confusion is not what Completeaerogeek represents it to be.

Completeaerogeek:I am clearly referring to conceptual understanding and not mathematical explanations.Most discussion of lift generation in the public domain occurs at the conceptual level. I lecture in this subject at University so I see this regularly.Further, if confusion is not that great, please explain why so-called experts are still quoting Equal Transit Time as the source of lift. If that is not confusion I am not sure what is.'

Completeaerogeek:The point clearly here was that erroneous assumptions arise from attributing kinetic energy to the static air.

3) Completeaerogeek's comments on Babinsky's photo constitute original research which is prohibited in Wikipedia.

Completeaerogeek:The comments directly relate to observation of the video content and the events contained within and as such does not constitute original research.Anyone viewing the content will see the evidence and as such it is not an interpretation much as "The Eiffel Tower is in Paris" is unlikely to be disputed if you are in Paris standing in front of it.

4) Completeaerogeek's comment "the air does not accelerate" is simply false, and contradicted by every reliable source.

Completeaerogeek:Watch the Babinsky video and if you can show me where it accelerates in relation to the static streamlines I will withdraw the comment.

5)The edits have been marked as "minor" when they are anything but. Please see wikipedia's definition of minor edit.

I do think there is some material worth adding - in particular the notion that angle of attack is more of a factor than foil shape - but statements like this must site reliable sources.

Completeaerogeek:That is why I cited NASA's FoilSim where this can be demonstrated to be the case. I believe that NASA is a reliable source.

Happy to discuss further if you like.

We can't just write whatever we feel like writing. So, let's work to improve the article via discussion here on the talk page and avoid further edit warring. Please do not make major changes to the article without first reaching consensus on the talk page. That's the process that has made wikipedia the success that it is.

Other comments? Mr. Swordfish (talk) 12:52, 22 April 2013 (UTC)

Hello, Completeaerogeek,

Welcome to Wikipedia! Contributions by editors knowledgable in their fields are always welcome on wikipedia.

Wikipedia can be a confusing place at first, and it is not uncommon for new editors to have trouble understanding the rules, standards, and conventions here. Editing wikipedia is a process that is fairly well established and has produced very good results when it has been allowed to work. I hope that you will take some time to familiarize yourself with this process and the conventions so that your edits are better received in the future.

One of the pillars of the process is discussion on the talk page. Please see the help section on talk pages and try to follow the guidelines outlined there. In particular, it is not a good idea to edit other people's material on the talk page. Instead, place your replies below, use the indentation conventions, and optionally insert quotes to make clear what you are replying to. This is preferable to responding in-line with bold text.

The objective of discussion on the talk page is to reach consensus. Please follow that link to read up on how that process works. A key point is that if a change will modify a matter resolved by past discussion the editor should propose that change by first discussing it on the talk page rather than simply editing the article. For an article like this with a long history of discussions and consensus, it helps a lot to be familiar with past discussions. Please spend some time reading the talk archives for this article, I think you'll find that many of the issues you raise have been discussed and resolved. That doesn't mean you can't re-raise an issue here on the talk page with the objective of reaching a new consensus, but please avoid editing the article without first checking the archives to see if it goes against the current consensus.

One way the process can work is the BOLD, revert, discuss cycle. That is, try an edit. If another editor reverts your edit, then the next step is to go to the talk page to resolve it through discussion. Simply re-reverting is frowned upon as edit warring.

Here are my replies to your recent comments:

>I have cited Babinsky - yes, you have provided a link to a video, but you have added several statements that are not supported by the link. For instance the following is unsupported by a link to a reliable source: "Confusion about the nature of flow over a wing is sometimes created by representation of air 'moving' over a static wing..."

>please explain why so-called experts are still quoting Equal Transit Time as the source of lift There are no experts in the field of aerodynamics advocating the Equal Transit Time Fallacy. This incorrect notion appears in popularizations, but never in "expert" writing other than to debunk it. Agree that there is a lot of confusion here, but it is unrelated to the choice of co-ordinate system as you assert.

> erroneous assumptions arise from attributing kinetic energy to the static air. I don't understand this comment. Kinetic energy is dependent on the reference frame. In the coordinate system stationary with respect to the air, the air has zero kinetic energy. But in any other coordinate system the air will have non-zero kinetic energy. There is no error in using a coordinate system other than the one stationary with respect to the air. Anyway, unless you can provide a reliable source stating this it can't go into the article.

>Watch the Babinsky video and if you can show me where it accelerates in relation to the static streamlines I will withdraw the comment Watching a video and drawing your own conclusions is original research. Claiming that the Eifel Tower is in Paris because you've been there personally and seen it is a classic example of original research. Please read that section of the help pages and try to assimilate it. If you want to assert "the air does not accelerate", you need to find a reliable source making that claim and provide a cite.

>That is why I cited NASA's FoilSim where this can be demonstrated to be the case. I believe that NASA is a reliable source. Yes, NASA is a reliable source, and their foil sim app is an excellent way to experiment to learn about lift. However, playing with foil sim and drawing your own conclusions is original research.

I hope you can now see why your edits were problematic and why I reverted them. If you don't follow me, please refer to reliable source, original research, verifiability, and verifiability, not truth which explain it better than I can. I'm going to put the article back to where it was on 18 April. We can continue to discuss your proposed changes here. Thanks for your understanding. Mr. Swordfish (talk) 12:22, 23 April 2013 (UTC)

Picture with dotted stream line

Hello, very nice article. I think that in the picture with the dotted moving streamline there is an error. On the upper surface, the black dots that are near the airfoil shall move faster than those of the free stream, thus resulting on a curve of the opposite direction. The pressure near the upper part of the airfoil is smaller than the pressure of the stream, indicating that the air travels faster. isn't this correct? — Preceding unsigned comment added by Stelios19781111 (talk • contribs) 08:22, 16 January 2012 (UTC)

If you watch the picture carefully, you will see that the dots on the top of the airfoil speed up as they pass over the wing and momentarily exceed the free-stream velocity. However, they first slow down as they approach the wing and the the momentary increase in speed is not enough to compensate for the slowdown as they approach. Thus, all the air in the vicinity of the wing is delayed. Mr. Swordfish (talk) 16:16, 16 January 2012 (UTC)

The animation is a massive failure. The very top line and the very bottom line do not track together, thus, above the wing the whole top half of 'air' is moving faster than the whole bottom half of the picture when in reality the only influenced air should be near the aerofoil. Its actually so wrong that is will make students confused! — Preceding unsigned comment added by 115.70.80.179 (talk) 17:43, 29 July 2012 (UTC)

The animation correctly depicts the fact that air flow is affected some distance from the wing, not just that "near" the airfoil. A rough rule of thumb is that air flow is affected to about a distance equal to the wingspan. Mr. Swordfish (talk) 14:03, 30 July 2012 (UTC)

The animation was made by User:Crowsnest, lets just see if we can get him to make an animation that shows points far enough away that the most outer points do track together — Preceding unsigned comment added by 198.82.93.203 (talk) 21:07, 4 December 2012 (UTC)

The animation would seem to be original research. It is a model that does not correspond with reality, and is clearly in need of speedy deletion. Jack 203.106.160.221 (talk) 02:05, 28 April 2013 (UTC)

Please see the policy on original images. This image is within that policy, since it represents the same ideas as presented in the source material. I do not know what you mean by " does not correspond with reality" since it is an accurate representation of the airflow according to the potential flow model. Mr. Swordfish (talk) 11:50, 28 April 2013 (UTC)

Opening paragraph

The opening paragraph was recently changed from:

A fluid flowing past the surface of a body exerts surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction.^[1] It contrasts with the drag force, which is the component of the surface force parallel to the flow direction. If the fluid is air, the force is called an aerodynamic force.

to

Lift is the component of the surface force exerted by a fluid flowing past the surface of a body.^[2] Lift is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the surface force parallel to the flow direction. If the fluid is air, the force is called an aerodynamic force.

My view is that this the kind of sentence that makes the general reader's eyes glaze over and I do not think it improves the article. Also, stating that "lift is the component of the surface force..." is imprecise - it's the component perpendicular to the flow. I'm going to restore the previous opening pending consensus here on the talk page. Mr. Swordfish (talk) 12:15, 1 September 2013 (UTC)

Agreed. Good catch. --Nigelj (talk) 12:48, 1 September 2013 (UTC)

I have long been suspicious about the value of mentioning surface force. It would simplify the opening if the concept of surface force was omitted, and I don't see that the article would be any poorer. What do you think? Dolphin (t) 13:57, 1 September 2013 (UTC)

My opinion would be to remove the word "surface" and just say "force", linking to the article force rather than the poorly sourced and stub-like surface force. I do think it's important to say that we are dealing with a force, but the overly technical "surface force" is a distraction. Mr. Swordfish (talk) 21:36, 1 September 2013 (UTC)

Looks like 100% agreement on that point! I made the change - see my diff. Dolphin (t) 05:54, 2 September 2013 (UTC)

^ "What is Lift?". NASA Glenn Research Center. Retrieved March 4, 2009.
^ "What is Lift?". NASA Glenn Research Center. Retrieved March 4, 2009.

[1] "What is Lift?". NASA Glenn Research Center. Retrieved March 4, 2009.

[2] "What is Lift?". NASA Glenn Research Center. Retrieved March 4, 2009.

[1]

[2]