Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Lift (force)
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
===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>
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)