Editing Lift (force) (section)

==Simplified physical explanations of lift on an airfoil==
[[Image:Airfoil cross section.jpg|thumb|240px|right|A cross-section of a wing defines an airfoil shape.]]
An [[airfoil]] is a streamlined shape that is capable of generating significantly more lift than drag.<ref>Clancy, L. J., ''Aerodynamics'', Section 5.2</ref> A flat plate can generate lift, but not as much as a streamlined airfoil, and with somewhat higher drag.
Most simplified explanations follow one of two basic approaches, based either on [[Newton's laws of motion]] or on [[Bernoulli's principle]].<ref name="ReferenceA">Doug McLean ''Aerodynamic Lift, Part 2: A comprehensive Physical Explanation'' The Physics teacher, November, 2018</ref><ref>{{cite book |last=McLean |first=Doug |date=2012 |title=Understanding Aerodynamics: Arguing from the Real Physics |page=281 |publisher=John Wiley & Sons |isbn=978-1119967514|quote=Another argument that is often made, as in several successive versions of the Wikipedia article “Aerodynamic Lift,” is that lift can always be explained either in terms of pressure or in terms of momentum and that the two explanations are somehow “equivalent.” This “either/or” approach also misses the mark.}}</ref><ref>"Both approaches are equally valid and equally correct, a concept that is central to the conclusion of this article." Charles N. Eastlake ''An Aerodynamicist's View of Lift, Bernoulli, and Newton'' The Physics Teacher Vol. 40, March 2002 {{cite web|url=http://www.df.uba.ar/users/sgil/physics_paper_doc/paperse_phys/fluids/Bernoulli_Newton_lift.pdf|title=Archived copy|access-date=10 September 2009|url-status=dead|archive-url=https://web.archive.org/web/20090411055333/http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/Bernoulli_Newton_lift.pdf|archive-date=April 11, 2009}}</ref><ref>{{citation|url=http://www.planeandpilotmag.com/component/zine/article/289.html|last=Ison|first=David|title=Bernoulli Or Newton: Who's Right About Lift?|magazine=Plane & Pilot|access-date=January 14, 2011|url-status=dead|archive-url=https://web.archive.org/web/20150924073958/http://www.planeandpilotmag.com/component/zine/article/289.html|archive-date=September 24, 2015}}</ref>

===Explanation based on flow deflection and Newton's laws===
[[File:AirfoilDeflectionLift_W3C.svg|thumb|240px|right|When a wing generates lift, it deflects air downward, and to do this it must exert a downward force on the air. Newton's third law requires that the air must exert an equal upward force on the wing.]]

An airfoil generates lift by exerting a downward force on the air as it flows past. According to [[Newton's third law]], the air must exert an equal and opposite (upward) force on the airfoil, which is lift.<ref>"...the effect of the wing is to give the air stream a downward velocity component. The reaction force of the deflected air mass must then act on the wing to give it an equal and opposite upward component." In: {{citation|first1=David|last1=Halliday|first2=Robert|last2=Resnick|title=Fundamentals of Physics 3rd Ed.|publisher=John Wiley & Sons|page=378}}</ref><ref name="Anderson and Eberhardt 2001">Anderson and Eberhardt (2001)</ref><ref name="Langewiesche 1944">Langewiesche (1944)</ref><ref>"When air flows over and under an airfoil inclined at a small angle to its direction, the air is turned from its course. Now, when a body is moving in a uniform speed in a straight line, it requires force to alter either its direction or speed. Therefore, the sails exert a force on the wind and, since action and reaction are equal and opposite, the wind exerts a force on the sails." In: {{citation|first1=John|last1=Morwood|title=Sailing Aerodynamics|publisher=Adlard Coles Limited|page=17}}</ref>

As the airflow approaches the airfoil it is curving upward, but as it passes the airfoil it changes direction and follows a path that is curved downward. According to Newton's second law, this change in flow direction requires a downward force applied to the air by the airfoil. Then Newton's third law requires the air to exert an upward force on the airfoil; thus a reaction force, lift, is generated opposite to the directional change. In the case of an airplane wing, the wing exerts a downward force on the air and the air exerts an upward force on the wing.<ref>a. {{cite web|publisher=NASA Glenn Research Center|title=Lift from Flow Turning|url=https://www.grc.nasa.gov/WWW/K-12/airplane/right2.html|date=May 27, 2000|access-date=June 27, 2021|archive-url=https://web.archive.org/web/20110705131653/http://www.grc.nasa.gov/WWW/K-12/airplane/right2.html|archive-date=July 5, 2011|quote=Lift is a force generated by turning a moving fluid... If the body is shaped, moved, or inclined in such a way as to produce a net deflection or turning of the flow, the local velocity is changed in magnitude, direction, or both. Changing the velocity creates a net force on the body.}}<br />
b. {{cite web|quote=Essentially, due to the presence of the wing (its shape and inclination to the incoming flow, the so-called angle of attack), the flow is given a downward deflection. It is Newton's third law at work here, with the flow then exerting a reaction force on the wing in an upward direction, thus generating lift.|author=Vassilis Spathopoulos|title=Flight Physics for Beginners: Simple Examples of Applying Newton's Laws ''The Physics Teacher'' Vol. 49, September 2011 p. 373|url=http://tpt.aapt.org/resource/1/phteah/v49/i6/p373_s1|access-date=June 29, 2021|archive-date=June 18, 2013|archive-url=https://archive.today/20130618032326/http://tpt.aapt.org/resource/1/phteah/v49/i6/p373_s1|url-status=dead}}<br />
c. {{cite book|quote=The main fact of all heavier-than-air flight is this: ''the wing keeps the airplane up by pushing the air down.''|author=Langewiesche|title=Stick and Rudder, p. 6}}</ref><ref>
a. {{cite web |quote=Birds and aircraft fly because they are constantly pushing air downwards: L = Δp/Δt where L= lift force, and Δp/Δt is the rate at which downward momentum is imparted to the airflow.|title=Flight without Bernoulli|author= Chris Waltham |publisher=The Physics Teacher Vol. 36 Nov. 1998 |url=http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/fly_no_bernoulli.pdf|access-date=4 August 2011|url-status=live|archive-url=https://web.archive.org/web/20110928200519/http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/fly_no_bernoulli.pdf|archive-date=September 28, 2011}}<br />
b. {{cite book |author=Clancy, L. J.|title=Aerodynamics|publisher= Pitman 1975, p. 76|quote=This lift force has its reaction in the downward momentum which is imparted to the air as it flows over the wing. Thus the lift of the wing is equal to the rate of transport of downward momentum of this air.}}<br />
c. {{cite journal|quote=...if the air is to produce an upward force on the wing, the wing must produce a downward force on the air. Because under these circumstances air cannot sustain a force, it is deflected, or accelerated, downward. Newton's second law gives us the means for quantifying the lift force: F<sub>lift</sub> = m∆v/∆t = ∆(mv)/∆t. The lift force is equal to the time rate of change of momentum of the air. |last1=Smith|first1=Norman F.|year=1972|title=Bernoulli and Newton in Fluid Mechanics|journal=The Physics Teacher|volume=10|issue=8|page=451|doi=10.1119/1.2352317|bibcode=1972PhTea..10..451S}}</ref>
The downward turning of the flow is not produced solely by the lower surface of the airfoil, and the air flow above the airfoil accounts for much of the downward-turning action.<ref>"...when one considers the downwash produced by a lifting airfoil, the upper surface contributes more flow turning than the lower surface." ''Incorrect Theory #2'' Glenn Research Center NASA https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/foilw2/ {{Webarchive|url=https://web.archive.org/web/20230209111605/https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/foilw2/ |date=February 9, 2023 }}</ref><ref>" This happens to some extent on both the upper and lower surface of the airfoil, but it is much more pronounced on the forward portion of the upper surface, so the upper surface gets the credit for being the primary lift producer. " Charles N. Eastlake ''An Aerodynamicist's View of Lift, Bernoulli, and Newton'' ''The Physics Teacher'' Vol. 40, March 2002 [http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/Bernoulli_Newton_lift.pdf PDF] {{webarchive|url=https://web.archive.org/web/20090411055333/http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/Bernoulli_Newton_lift.pdf|date=April 11, 2009}}</ref><ref>"The pressure reaches its minimum value around 5 to 15% chord after the leading edge. As a result, about half of the lift is generated in the first 1/4 chord region of the airfoil. Looking at all three angles of attack, we observe a similar pressure change after the leading edge.
Additionally, in all three cases, the upper surface contributes more lift than the lower surface. As a result, it is critical to maintain a clean and rigid surface on the top of the wing. This is why most airplanes are cleared of any objects on the top of the wing." ''Airfoil Behavior: Pressure Distribution over a Clark Y-14 Wing'' David Guo, College of Engineering, Technology, and Aeronautics (CETA), Southern New Hampshire University https://www.jove.com/v/10453/airfoil-behavior-pressure-distribution-over-a-clark-y-14-wing {{Webarchive|url=https://web.archive.org/web/20210805181210/https://www.jove.com/v/10453/airfoil-behavior-pressure-distribution-over-a-clark-y-14-wing |date=August 5, 2021 }}</ref><ref>"There's always a tremendous amount of focus on the upper portion of the wing, but the lower surface also contributes to lift." ''Bernoulli Or Newton: Who's Right About Lift?'' David Ison Plane & Pilot Feb 2016</ref>

This explanation is correct but it is incomplete. It does not explain how the airfoil can impart downward turning to a much deeper swath of the flow than it actually touches. Furthermore, it does not mention that the lift force is exerted by [[#Pressure differences|pressure differences]], and does not explain how those pressure differences are sustained.<ref name="ReferenceA"/>

====Controversy regarding the Coandă effect====
{{Main|Coandă effect}}

Some versions of the flow-deflection explanation of lift cite the Coandă effect as the reason the flow is able to follow the convex upper surface of the airfoil.  The conventional definition in the aerodynamics field is that the ''Coandă effect'' refers to the tendency of a [[Jet (fluid)|fluid jet]] to stay attached to an adjacent surface that curves away from the flow, and the resultant [[Entrainment (hydrodynamics)|entrainment]] of ambient air into the flow.<ref name="auerbach">{{Citation|last=Auerbach|first=David|journal=Eur. J. Phys.|volume=21|issue=4|year=2000|page=289|title=Why Aircraft Fly|doi=10.1088/0143-0807/21/4/302|bibcode=2000EJPh...21..289A|s2cid=250821727 }}</ref><ref>{{Citation|url=http://www.av8n.com/how/htm/spins.html#sec-coanda-fallacy|last=Denker|first=JS|title=Fallacious Model of Lift Production|access-date=18 August 2008|url-status=dead|archive-url=https://web.archive.org/web/20090302153902/http://www.av8n.com/how/htm/spins.html#sec-coanda-fallacy|archive-date=March 2, 2009}}</ref><ref>{{Citation|title=Report on the first European Mechanics Colloquium, on the Coanda effect|last1=Wille|first1=R.|last2=Fernholz|first2=H.|journal=J. Fluid Mech.|year=1965|volume=23|issue=4|page=801|doi=10.1017/S0022112065001702|bibcode=1965JFM....23..801W|s2cid=121981660 }}</ref>

More broadly, some consider the effect to include the tendency of any fluid [[boundary layer]] to adhere to a curved surface, not just the boundary layer accompanying a fluid jet. It is in this broader sense that the Coandă effect is used by some popular references to explain why airflow remains attached to the top side of an airfoil.<ref name="scotteberhart">{{Citation|url=http://www.allstar.fiu.edu/AERO/airflylvl3.htm|last1=Anderson|first1=David|last2=Eberhart|first2=Scott|title=How Airplanes Fly: A Physical Description of Lift|year=1999|access-date=June 4, 2008|url-status=live|archive-url=https://web.archive.org/web/20160126200755/http://www.allstar.fiu.edu/aero/airflylvl3.htm|archive-date=January 26, 2016}}</ref><ref name="raskin">{{Citation|url=http://jef.raskincenter.org/published/coanda_effect.html|archive-url=https://web.archive.org/web/20070928072421/http://jef.raskincenter.org/published/coanda_effect.html|archive-date=September 28, 2007|title=Coanda Effect: Understanding Why Wings Work|last=Raskin|first=Jef|year=1994}}</ref> This is a controversial use of the term "Coandă effect"; the flow following the upper surface simply reflects an absence of boundary-layer separation, thus it is not an example of the Coandă effect.<ref>Auerbach (2000)</ref><ref>Denker (1996)</ref><ref>Wille and Fernholz(1965)</ref><ref>{{citation|last=White|first=Frank M.|title=Fluid Mechanics|year=2002|edition=5th|publisher=McGraw Hill}}</ref> Regardless of whether this broader definition of the "Coandă effect" is applicable, calling it the "Coandă effect" does not provide an explanation, it just gives the phenomenon a name.<ref>McLean, D. (2012), Section 7.3.2</ref>

The ability of a fluid flow to follow a curved path is not dependent on shear forces, viscosity of the fluid, or the presence of a boundary layer. Air flowing around an airfoil, adhering to both upper and lower surfaces, and generating lift, is accepted as a phenomenon in inviscid flow.<ref>McLean, D. (2012), Section 7.3.1.7</ref>

===Explanations based on an increase in flow speed and Bernoulli's principle===

There are two common versions of this explanation, one based on "equal transit time", and one based on "obstruction" of the airflow.
[[File:Equal transit-time NASA wrong1.gif|thumb|right|586px|An illustration of the incorrect equal transit-time explanation of airfoil lift.
<ref name="nasa_equal_transit"/>]]

====False explanation based on equal transit-time<span class="anchor" id="False explanation based on equal transit-time"></span>====

The "equal transit time" explanation starts by arguing that the flow over the upper surface is faster than the flow over the lower surface because the path length over the upper surface is longer and must be traversed in equal transit time.<ref>Burge, Cyril Gordon (1936). Encyclopædia of aviation. London: Pitman. p. 441.  "… the fact that the air passing over the hump on the top of the wing has to speed up more than that flowing beneath the wing, in order to arrive at the trailing edge in the same time."</ref><ref>Illman, Paul (2000). The Pilot's Handbook of Aeronautical Knowledge. New York: McGraw-Hill. pp. 15–16. ISBN 0071345191. When air flows along the upper wing surface, it travels a greater distance in the same period of time as the airflow along the lower wing surface."</ref><ref>Dingle, Lloyd; Tooley, Michael H. (2005). Aircraft engineering principles. Boston: Elsevier Butterworth-Heinemann. p. 548. ISBN 0-7506-5015-X. The air travelling over the cambered top surface of the aerofoil shown in Figure 7.6, which is split as it passes around the aerofoil, will speed up, because it must reach the trailing edge of the aerofoil at the same time as the air that flows underneath the section."</ref>  [[Bernoulli's principle]] states that under certain conditions increased flow speed is associated with reduced pressure.  It is concluded that the reduced pressure over the upper surface results in upward lift.<ref>"The airfoil of the airplane wing, according to the textbook explanation that is more or less standard in the United States, has a special shape with more curvature on top than on the bottom; consequently, the air must travel farther over the top surface than over the bottom surface. Because the air must make the trip over the top and bottom surfaces in the same elapsed time ..., the velocity over the top surface will be greater than over the bottom. According to Bernoulli's theorem, this velocity difference produces a pressure difference which is lift." ''Bernoulli and Newton in Fluid Mechanics'' Norman F. Smith ''The Physics Teacher'' November 1972 Volume 10, Issue 8, p. 451 [http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHTEAH000010000008000451000001&idtype=cvips&doi=10.1119/1.2352317&prog=normal] {{dead link|date=January 2018|bot=InternetArchiveBot|fix-attempted=yes}}</ref>

While it is true that the flow speeds up, a serious flaw in this explanation is that it does not correctly explain what causes the flow to speed up.<ref name="ReferenceA"/>  The longer-path-length explanation is incorrect.  No difference in path length is needed, and even when there is a difference, it is typically much too small to explain the observed speed difference.<ref>Craig G.M. (1997), ''Stop Abusing Bernoulli''</ref>  This is because the assumption of equal transit time is wrong when applied to a body generating lift. There is no physical principle that requires equal transit time in all situations and experimental results confirm that for a body generating lift the transit times are not equal.<ref>"Unfortunately, this explanation [fails] on three counts. First, an airfoil need not have more curvature on its top than on its bottom. Airplanes can and do fly with perfectly symmetrical airfoils; that is with airfoils that have the ''same'' curvature top and bottom. Second, even if a humped-up (cambered) shape is used, the claim that the air must traverse the curved top surface in the same time as it does the flat bottom surface...is fictional. We can quote no physical law that tells us this. Third—and this is the most serious—the common textbook explanation, and the diagrams that accompany it, describe a force on the wing with no net disturbance to the airstream. This constitutes a violation of Newton's third law." ''Bernoulli and Newton in Fluid Mechanics'' Norman F. Smith ''The Physics Teacher'' November 1972 Volume 10, Issue 8, p. 451 {{cite web|url=http://tpt.aapt.org/resource/1/phteah/v10/i8|title=Browse - the Physics Teacher|access-date=4 August 2011|url-status=dead|archive-url=https://web.archive.org/web/20120317075304/http://tpt.aapt.org/resource/1/phteah/v10/i8|archive-date=March 17, 2012}}</ref><ref>
{{Citation|last=Anderson|first=David|title=Understanding Flight|publisher=McGraw-Hill|location=New York|year=2001|isbn=978-0-07-136377-8|quote=The first thing that is wrong is that the principle of equal transit times is not true for a wing with lift.|page=15}}</ref><ref>{{cite book|last=Anderson|first=John|title=Introduction to Flight|publisher=McGraw-Hill Higher Education|location=Boston|year=2005|isbn=978-0072825695|page=355|quote=It is then assumed that these two elements must meet up at the trailing edge, and because the running distance over the top surface of the airfoil is longer than that over the bottom surface, the element over the top surface must move faster. This is simply not true}}</ref><ref>{{cite web|url=https://www.telegraph.co.uk/science/science-news/9035708/Cambridge-scientist-debunks-flying-myth.html|title=Cambridge scientist debunks flying myth - Telegraph|access-date=10 June 2012|url-status=dead|archive-url=https://web.archive.org/web/20120630121849/http://www.telegraph.co.uk/science/science-news/9035708/Cambridge-scientist-debunks-flying-myth.html|archive-date=June 30, 2012}} ''Cambridge scientist debunks flying myth'' UK Telegraph 24 January 2012</ref><ref>{{cite AV media|url=http://web.mit.edu/hml/ncfmf.html|title=Flow Visualization|publisher=National Committee for Fluid Mechanics Films/Educational Development Center|access-date=January 21, 2009|url-status=live|archive-url=https://web.archive.org/web/20161021122939/http://web.mit.edu/hml/ncfmf.html|archive-date=October 21, 2016}} A visualization of the typical retarded flow over the lower surface of the wing and the accelerated flow over the upper surface starts at 5:29 in the video.</ref><ref>"...do you remember hearing that troubling business about the particles moving over the curved top surface having to go faster than the particles that went underneath, because they have a longer path to travel but must still get there at the same time? This is simply not true. It does not happen." Charles N. Eastlake ''An Aerodynamicist's View of Lift, Bernoulli, and Newton'' ''The Physics Teacher'' Vol. 40, March 2002 [http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/Bernoulli_Newton_lift.pdf PDF] {{webarchive|url=https://web.archive.org/web/20090411055333/http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/Bernoulli_Newton_lift.pdf|date=April 11, 2009}}</ref> In fact, the air moving past the top of an airfoil generating lift moves ''much'' ''faster'' than equal transit time predicts.<ref>"The actual velocity over the top of an airfoil is much faster than that predicted by the "Longer Path" theory and particles moving over the top arrive at the trailing edge before particles moving under the airfoil." {{cite web|url=https://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html |date=Aug 16, 2000 |title=Incorrect Lift Theory #1 |author=Glenn Research Center|publisher=NASA |access-date=June 27, 2021| archive-url=https://web.archive.org/web/20140427084226/http://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html|archive-date=April 27, 2014}}</ref>  The much higher flow speed over the upper surface can be clearly seen in [[#The wider flow around the airfoil|this animated flow visualization]].

====Obstruction of the airflow====
[[File:Streamlines around a NACA 0012.svg|thumb|300px|Streamlines and streamtubes around an airfoil generating lift. The flow is two-dimensional and the airfoil has infinite span. Note the narrower streamtubes above and the wider streamtubes below.]]

Like the equal transit time explanation, the "obstruction" or "streamtube pinching" explanation argues that the flow over the upper surface is faster than the flow over the lower surface, but gives a different reason for the difference in speed.  It argues that the curved upper surface acts as more of an obstacle to the flow, forcing the streamlines to pinch closer together, making the streamtubes narrower.  When streamtubes become narrower, conservation of mass requires that flow speed must increase.<ref>"As stream tube A flows toward the airfoil, it senses the upper portion of the airfoil as an obstruction, and stream tube A must move out of the way of this obstruction. In so doing, stream tube A is squashed to a smaller cross-sectional area as it flows over the nose of the airfoil. In turn, because of mass continuity (ρ AV = constant), the velocity of the flow in the stream tube must increase in the region where the stream tube is being squashed." J. D. Anderson (2008), ''Introduction to Flight'' (6th edition), section 5.19</ref>  Reduced upper-surface pressure and upward lift follow from the higher speed by [[Bernoulli's principle]], just as in the equal transit time explanation.  Sometimes an analogy is made to a [[venturi tube|venturi nozzle]], claiming the upper surface of the wing acts like a venturi nozzle to constrict the flow.<ref>"The theory is based on the idea that the airfoil upper surface is shaped to act as a nozzle which accelerates the flow. Such a nozzle configuration is called a Venturi nozzle and it can be analyzed classically. Considering the conservation of mass, the mass flowing past any point in the nozzle is a constant; the mass flow rate of a Venturi nozzle is a constant... For a constant density, decreasing the area increases the velocity." ''Incorrect Theory #3'' Glenn Research Center NASA https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/venturi-theory/ {{Webarchive|url=https://web.archive.org/web/20230209112230/https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/venturi-theory/ |date=February 9, 2023 }}</ref>

One serious flaw in the obstruction explanation is that it does not explain how streamtube pinching comes about, or why it is greater over the upper surface than the lower surface.  For conventional wings that are flat on the bottom and curved on top this makes some intuitive sense, but it does not explain how flat plates, symmetric airfoils, sailboat sails, or conventional airfoils flying upside down can generate lift, and attempts to calculate lift based on the amount of constriction or obstruction do not predict experimental results.<ref>"The problem with the 'Venturi' theory is that it attempts to provide us with the velocity based on an incorrect assumption (the constriction of the flow produces the velocity field). We can calculate a velocity based on this assumption, and use Bernoulli's equation to compute the pressure, and perform the pressure-area calculation and the answer we get does not agree with the lift that we measure for a given airfoil." NASA Glenn Research Center {{cite web|url=https://www.grc.nasa.gov/WWW/K-12/airplane/wrong3.html |title=Incorrect lift theory #3|date=Aug 16, 2000 |access-date=27 June 2021 |archive-url=https://web.archive.org/web/20120717222459/http://www.grc.nasa.gov/WWW/k-12/airplane/wrong3.html|archive-date=July 17, 2012}}</ref><ref>"A concept...uses a symmetrical convergent-divergent channel, like a longitudinal section of a Venturi tube, as the starting point . . when such a device is put in a flow, the static pressure in the tube decreases. When the upper half of the tube is removed, a geometry resembling the airfoil is left, and suction is still maintained on top of it. Of course, this explanation is flawed too, because the geometry change affects the whole flowfield and there is no physics involved in the description." Jaakko Hoffren ''Quest for an Improved Explanation of Lift'' Section 4.3 American Institute of Aeronautics and Astronautics 2001 {{cite web|url=http://corsair.flugmodellbau.de/files/area2/LIFT.PDF|title=Archived copy|access-date=26 July 2012|url-status=dead|archive-url=https://web.archive.org/web/20131207102746/http://corsair.flugmodellbau.de/files/area2/LIFT.PDF|archive-date=December 7, 2013}}</ref><ref>"This answers the apparent mystery of how a symmetric airfoil can produce lift. ... This is also true of a flat plate at non-zero angle of attack." Charles N. Eastlake ''An Aerodynamicist's View of Lift, Bernoulli, and Newton'' {{cite web|url=http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/Bernoulli_Newton_lift.pdf|title=Archived copy|access-date=10 September 2009|url-status=dead|archive-url=https://web.archive.org/web/20090411055333/http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/Bernoulli_Newton_lift.pdf|archive-date=April 11, 2009}}</ref><ref>"This classic explanation is based on the difference of streaming velocities caused by the airfoil. There remains, however, a question: How does the airfoil cause the difference in streaming velocities? Some books don't give any answer, while others just stress the picture of the streamlines, saying the airfoil reduces the separations of the streamlines at the upper side. They do not say how the airfoil manages to do this. Thus this is not a sufficient answer." Klaus Weltner ''Bernoulli's Law and Aerodynamic Lifting Force'' The Physics Teacher February 1990 p. 84. [http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHTEAH000028000002000084000001&idtype=cvips&prog=normal] {{dead link|date=January 2018|bot=InternetArchiveBot|fix-attempted=yes}}</ref> Another flaw is  that conservation of mass is not a satisfying physical reason why the flow would speed up. Effectively explaining the acceleration of an object requires identifying the force that accelerates it.<ref>Doug McLean ''Understanding Aerodynamics'', section 7.3.1.5, Wiley, 2012</ref>

====Issues common to both versions of the Bernoulli-based explanation====
A serious flaw common to all the Bernoulli-based explanations is that they imply that a speed difference can arise from causes other than a pressure difference, and that the speed difference then leads to a pressure difference, by Bernoulli's principle.  This implied one-way causation is a misconception.  The real relationship between pressure and flow speed is a [[#Mutual interaction of pressure differences and changes in flow velocity|mutual interaction]].<ref name="ReferenceA"/> As explained below under [[#A more comprehensive physical explanation|a more comprehensive physical explanation]], producing a lift force requires maintaining pressure differences in both the vertical and horizontal directions.  The Bernoulli-only explanations do not explain how the pressure differences in the vertical direction are sustained.  That is, they leave out the flow-deflection part of the interaction.<ref name="ReferenceA"/>

Although the two simple Bernoulli-based explanations above are incorrect, there is nothing incorrect about Bernoulli's principle or the fact that the air goes faster on the top of the wing, and Bernoulli's principle can be used correctly as part of a more complicated explanation of lift.<ref>"There is nothing wrong with the Bernoulli principle, or with the statement that the air goes faster over the top of the wing. But, as the above discussion suggests, our understanding is not complete with this explanation. The problem is that we are missing a vital piece when we apply Bernoulli's principle. We can calculate the pressures around the wing if we know the speed of the air over and under the wing, but how do we determine the speed?" ''How Airplanes Fly: A Physical Description of Lift'' David Anderson and Scott Eberhardt {{cite web|url=http://www.allstar.fiu.edu/aero/airflylvl3.htm|title=How Airplanes Fly|access-date=26 January 2016|url-status=live|archive-url=https://web.archive.org/web/20160126200755/http://www.allstar.fiu.edu/aero/airflylvl3.htm|archive-date=January 26, 2016}}</ref>