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[[File:Annular box wing.svg|thumb|right|An annular closed wing]] |
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{{Other uses|Lift (disambiguation)}} |
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A '''closed wing''' is a [[wing]] that effectively has two main planes which merge at their ends so that there are no conventional [[wing tip]]s. Closed [[Wing configuration|wing designs]] include the annular wing (commonly known as the '''cylindrical''' or '''ring wing'''), the joined wing, the box wing and spiroid tip devices.<ref name="Kroo" /> |
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[[File:Boeing 747-8 N747EX First Flight.jpg|thumb|right|275px|The wings of the [[Boeing 747-8F]] generate many tonnes of lift.]] |
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Like many [[wingtip device]]s, the closed wing aims to reduce the wasteful effects of [[wingtip vortices]] which occur at the tips of conventional wings. However such benefits are difficult to realize. Many closed wing designs do offer structural advantages over a conventional [[cantilever wing|cantilever]] [[monoplane]]. |
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A [[fluid]] flowing past the surface of a body exerts a [[force]] on it. '''Lift''' is the [[Vector (geometric)#Vector components|component]] of this force that is perpendicular to the oncoming flow direction.<ref name="What is Lift">{{cite web |publisher = NASA Glenn Research Center |title = What is Lift? |url = http://www.grc.nasa.gov/WWW/K-12/airplane/lift1.html |accessdate = March 4, 2009 |deadurl = no |archiveurl = https://web.archive.org/web/20090309130515/http://www.grc.nasa.gov/WWW/K-12/airplane/lift1.html |archivedate = March 9, 2009 |df = mdy-all }}</ref> It contrasts with the [[drag (physics)|drag]] force, which is the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of [[gravity]], but it can act in any direction at right angles to the flow. |
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==Characteristics== |
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If the surrounding fluid is air, the force is called an [[aerodynamic force]]. In water or any other liquid, it is called a [[Hydrodynamic|hydrodynamic force]]. |
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[[Image:Spiroids.png|thumb|right|The Spiroid winglet is a closed wing surface attached to the tip of a conventional wing.]] |
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[[Wingtip vortices]] form a major component of [[wake turbulence]] and are associated with [[induced drag]], which is a significant contributor to total drag in most regimes. A closed wing avoids the need for wingtips and thus might be expected to reduce wingtip [[drag (physics)|drag]] effects. |
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Dynamic lift is distinguished from other kinds of lift in fluids. [[Aerostatics|Aerostatic]] lift or [[buoyancy]], in which an internal fluid is lighter than the surrounding fluid, does not require movement and is used by balloons, blimps, dirigibles, boats, and submarines. [[Planing (boat)|Planing lift]], in which only the lower portion of the body is immersed in a liquid flow, is used by motorboats, surfboards, and water-skis. |
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In addition to potential structural advantages over open cantilevered wings, closed wing surfaces have some unique aerodynamic properties: |
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==Overview== |
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[[File:Airfoil lift and drag.jpg|thumb|right|300px|Lift is defined as the component of the total aerodynamic force perpendicular to the flow direction, and drag is the component parallel to the flow direction.]] |
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1) For a lifting system constrained to fit within a rectangular box of fixed horizontal (spanwise) and vertical dimensions as viewed in the freestream flow direction, the configuration that provides the absolute minimum [[Lift-induced drag|induced drag]] for a given total vertical [[Lift (force)|lift]] is a closed system, i.e. a rectangular boxplane with lifting surfaces fully occupying all four boundaries of the allowed rectangular area.<ref name="Durand"/> However, the induced-drag performance of the ideal closed boxplane can be approached very closely by open configurations such as the C-wing discussed below.<ref name="Kroo" /> |
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A [[fluid]] flowing over the surface of a body exerts a [[surface force|force]] on it. It makes no difference whether the fluid is flowing past a stationary body or the body is moving through a stationary volume of fluid. '''Lift''' is the [[Vector (geometric)#Vector components|component]] of this force that is perpendicular to the oncoming flow direction.<ref name="What is Lift"/> Lift is always accompanied by a [[drag (physics)|drag]] force, which is the component of the surface force parallel to the flow direction. |
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2) For any lifting system (or portion of a lifting system) that forms a closed loop as viewed in the freestream flow direction, the optimum lift (or circulation) distribution that yields the minimum induced drag for a given total vertical lift is not unique on the closed-loop portion, but is defined only to within a constant. This is because, regardless of what the circulation distribution is to start with, a constant circulation can be added to the closed-loop portion without changing the total lift of the system or the induced drag.<ref name="Kroo" /> This is the key to explaining how the [[C-wing]] produces nearly the same induced-drag reduction as the corresponding fully closed system, as discussed below. |
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Lift is most commonly associated with the [[wing]]s of [[fixed-wing aircraft]], although it is more generally generated by many other [[streamlined]] bodies such as [[propeller]]s, [[Kite types|kites]], [[helicopter rotor]]s, [[wing (automotive)|racing car wings]], maritime [[sail]]s, and [[wind turbine]]s in air, and by [[sailboat]] [[keel]]s, ship's [[rudder]]s, and [[hydrofoil]]s in water. Lift is also exploited in the animal world, especially by [[bird]]s, [[bat]]s, and [[insect]]s, and even in the plant world by the seeds of certain trees.<ref>Kulfan (2010)</ref> |
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The upshot is that although closed systems can produce large induced-drag reductions relative to a conventional planar wing, there is no significant aerodynamic advantage that uniquely accrues to their being closed rather than open.<ref name="Kroo"> |
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While the common meaning of the word "[[wikt:lift#English|lift]]" assumes that lift opposes weight, lift in general can technically be in any direction with respect to gravity, since it is defined with respect to the direction of flow rather than to the direction of gravity. When an aircraft is [[cruise (flight)|cruising]] in straight and level flight, most of the lift opposes gravity.<ref>The ''amount'' of aerodynamic lift will be (usually slightly) more or less than gravity depending on the thrust level and vertical alignment of the thrust line. A side thrust line will result in some lift opposing side thrust as well.</ref> However, when an aircraft is [[climb (aeronautics)|climbing]], [[Descent (aircraft)|descending]], or [[Banked turn#Aviation|banking]] in a turn the lift is tilted with respect to the vertical.<ref>Clancy, L. J., ''Aerodynamics'', Section 14.6</ref> Lift may also act as [[downforce]] in some [[Aerobatics|aerobatic manoeuvres]], or on the wing on a racing car. Lift may also be largely horizontal, for instance on a sailing ship. |
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The Lift discussed in this article is mainly in relation to airfoils, although marine [[hydrofoils]] and propellers share the same physical principles and work in the same way, despite differences between air and water such as density, compressibility, and viscosity. |
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==Simplified physical explanations of lift on an airfoil== |
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[[Image:Airfoil cross section.jpg|thumb|240px|right|A cross-section of a wing defines an airfoil shape]] |
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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. |
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There are several ways to explain how an airfoil generates lift. Some are more complicated or more physically rigorous than others; some have been shown to be incorrect.<ref name="NASA_Incorrect_Theory1">"There are many theories of how lift is generated. Unfortunately, many of the theories found in encyclopedias, on web sites, and even in some textbooks are incorrect, causing unnecessary confusion for students." NASA {{cite web |url=http://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html |title=Archived copy |accessdate=2012-04-20 |deadurl=no |archiveurl=https://web.archive.org/web/20140427084226/http://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html |archivedate=April 27, 2014 |df=mdy-all }}</ref><ref name="swartz">"Most of the texts present the Bernoulli formula without derivation, but also with very little explanation. When applied to the lift of an airfoil, the explanation and diagrams are almost always wrong. 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." Cliff Swartz et al. ''Quibbles, Misunderstandings, and Egregious Mistakes - Survey of High-School Physics Texts'' THE PHYSICS TEACHER Vol. 37, May 1999 pg 300 http://aapt.scitation.org/doi/abs/10.1119/1.880274</ref><ref name=Gentry>"One explanation of how a wing of an [[airplane]] gives lift is that as a result of the shape of the airfoil, the air flows faster over the top than it does over the bottom because it has farther to travel. Of course, with our thin-airfoil sails, the distance along the top is the same as along the bottom so this explanation of lift fails." ''The Aerodynamics of Sail Interaction'' by Arvel Gentry Proceedings of the Third AIAA Symposium on the Aero/Hydronautics of Sailing 1971 {{cite web |url=http://www.arvelgentry.com/techs/The%20Aerodynamics%20of%20Sail%20Interaction.pdf |title=Archived copy |accessdate=2011-07-12 |deadurl=no |archiveurl=https://web.archive.org/web/20110707172946/http://www.arvelgentry.com/techs/The%20Aerodynamics%20of%20Sail%20Interaction.pdf |archivedate=July 7, 2011 |df=mdy-all }}</ref><ref name="ReferenceA">"An explanation frequently given is that the path along the upper side of the aerofoil is longer and the air thus has to be faster. This explanation is wrong." ''A comparison of explanations of the aerodynamic lifting force'' Klaus Weltner '' Am. J. Phys. Vol.55 No.January 1, 1987</ref><ref name="alphatrainer.com">"The lift on the body is simple...it's the re-action of the solid body to the turning of a moving fluid...Now why does the fluid turn the way that it does? That's where the complexity enters in because we are dealing with a fluid. ...The cause for the flow turning is the simultaneous conservation of mass, momentum (both linear and angular), and energy by the fluid. And it's confusing for a fluid because the mass can move and redistribute itself (unlike a solid), but can only do so in ways that conserve momentum (mass times velocity) and energy (mass times velocity squared)... A change in velocity in one direction can cause a change in velocity in a perpendicular direction in a fluid, which doesn't occur in solid mechanics... So exactly describing how the flow turns is a complex problem; too complex for most people to visualize. So we make up simplified "models". And when we simplify, we leave something out. So the model is flawed. Most of the arguments about lift generation come down to people finding the flaws in the various models, and so the arguments are usually very legitimate." Tom Benson of NASA's Glenn Research Center in an interview with AlphaTrainer.Com {{cite web |url=http://www.alphatrainer.com/pages/corner.htm |title=Archived copy |accessdate=2012-07-26 |deadurl=no |archiveurl=https://web.archive.org/web/20120427005906/http://www.alphatrainer.com/pages/corner.htm |archivedate=April 27, 2012 |df=mdy-all }}</ref> For example, there are explanations based directly on [[Newton’s laws of motion]] and explanations based on [[Bernoulli’s principle]]. Either can be used to explain lift.<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/papers_phys/fluids/Bernoulli_Newton_lift.pdf |title=Archived copy |accessdate=2009-09-10 |deadurl=no |archiveurl=https://web.archive.org/web/20090411055333/http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/Bernoulli_Newton_lift.pdf |archivedate=April 11, 2009 |df=mdy-all }}</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|accessdate=January 14, 2011|deadurl=no|archiveurl=https://web.archive.org/web/20150924073958/http://www.planeandpilotmag.com/component/zine/article/289.html|archivedate=September 24, 2015|df=mdy-all}}</ref> |
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===Flow deflection and Newton's laws=== |
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[[File:AirfoilDeflectionLift_W3C.svg|thumb|240px|right|When an airfoil deflects air downwards, Newton's third law requires that the air must exert an equal upward reaction on the airfoil.]] |
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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 the lift.<ref name=HR_378a>"...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 |
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|first1=David |
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|last1=Halliday |
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|first2=Robert |
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|last2=Resnick |
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|title=Fundamentals of Physics 3rd Edition |
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|publisher=John Wiley & Sons |
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|pages=378 |
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}}</ref><ref name="Anderson and Eberhardt 2001">Anderson and Eberhardt (2001)</ref><ref name="Langewiesche 1944">Langewiesche (1944)</ref><ref name=Morwood`> |
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"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 |
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|first1=John |
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|last1=Morwood |
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|title=Sailing Aerodynamics |
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|publisher=Adlard Coles Limited |
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|pages=17}}</ref> |
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The air flow changes direction as it passes the airfoil 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, according to Newton's third law, the air must exert an upward force on the airfoil. The overall result is that a reaction force, the 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>"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." {{cite web |
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|publisher = NASA Glenn Research Center |
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|title = Lift from Flow Turning |
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|url = http://www.grc.nasa.gov/WWW/K-12/airplane/right2.html |
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|accessdate = July 7, 2009 |
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|deadurl = no |
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|archiveurl = https://web.archive.org/web/20110705131653/http://www.grc.nasa.gov/WWW/K-12/airplane/right2.html |
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|archivedate = July 5, 2011 |
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|df = mdy-all |
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}}</ref><ref>"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, as shown in Fig. 2. 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." Vassilis Spathopoulos Flight Physics for Beginners: Simple Examples of Applying Newton’s Laws ''The Physics Teacher'' Vol. 49, September 2011 pg 373 http://tpt.aapt.org/resource/1/phteah/v49/i6/p373_s1{{dead link|date=January 2018 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref name=Langewiesche_6_10>"The main fact of all heavier-than-air flight is this: ''the wing keeps the airplane up by pushing the air down.''" In: {{citation |
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|first1=Wolfgang |
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|last1=Langewiesche |
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|title=Stick and Rudder: An Explanation of the Art of Flying |
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|publisher=McGraw-Hill |
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|year=1990 |
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|isbn=0-07-036240-8 |
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|pages=6–10}}</ref><ref>"Birds and aircraft fly because they are constantly pushing |
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air downwards: |
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L = d''p''/d''t '' |
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Here L is the lift force and dp/dt is the rate at which |
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downward momentum is imparted to the airflow." ''Flight without Bernoulli'' Chris Waltham ''THE PHYSICS TEACHER'' Vol. 36, Nov. 1998 {{cite web |url=http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/fly_no_bernoulli.pdf |title=Archived copy |accessdate=2011-08-04 |deadurl=no |archiveurl=https://web.archive.org/web/20110928200519/http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/fly_no_bernoulli.pdf |archivedate=September 28, 2011 |df=mdy-all }}</ref><ref>Clancy, L. J.; ''Aerodynamics'', Pitman 1975, page 76: "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."</ref><ref>"...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." {{cite journal | last1 = Smith | first1 = Norman F. | year = 1972 | title = Bernoulli and Newton in Fluid Mechanics | url = | journal = The Physics Teacher | volume = 10 | issue = | page = 451 | doi = 10.1119/1.2352317 }}</ref> |
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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. |
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===Increased flow speed and Bernoulli's principle=== |
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[[Bernoulli's principle]] states that within a steady airflow of constant energy, when the air flows through a region of lower pressure it speeds up and vice versa.<ref>"A complete statement of Bernoulli's Theorem is as follows: "In a flow where no energy is being added or taken away, the sum of its various energies is a constant: consequently where the velocity increases the pressure decreases and vice versa." {{cite journal | last1 = Smith | first1 = Norman F | title = Bernoulli, Newton and Dynamic Lift Part I | url = | journal = School Science and Mathematics | volume = 73 | issue = 3| pages = 181–186| doi = 10.1111/j.1949-8594.1973.tb08998.x | year=1973}}</ref> Thus, there is a direct mathematical relationship between the pressure and the speed, so if one knows the speed at all points within the airflow one can calculate the pressure, and vice versa. For any airfoil generating lift, there must be a pressure imbalance, i.e. lower average air pressure on the top than on the bottom. Bernoulli's principle states that this pressure difference must be accompanied by a speed difference. |
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====Conservation of mass==== |
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[[File:Streamlines around a NACA 0012.svg|thumb|300px|Streamlines and streamtubes around an airfoil generating lift. Note the narrower streamtubes above and the wider streamtubes below.]] |
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Starting with the flow pattern observed in both theory and experiments, the increased flow speed over the upper surface can be explained in terms of streamtube pinching and [[conservation of mass]].<ref name="Anderson_Flight_5.19">Anderson (2004).</ref> |
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Assuming that the air is incompressible, the rate of volume flow (e.g. liters or gallons per minute) must be constant within each streamtube since matter is not created or destroyed. If a streamtube becomes narrower, the flow speed must increase in the narrower region to maintain the constant flow rate. This is an application of the principle of [[conservation of mass]].<ref>"The effect of squeezing streamlines together as they divert around the front of an airfoil shape is that the velocity must increase to keep the mass flow constant since the area between the streamlines has become smaller." 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/papers_phys/fluids/Bernoulli_Newton_lift.pdf |title=Archived copy |accessdate=2009-09-10 |deadurl=no |archiveurl=https://web.archive.org/web/20090411055333/http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/Bernoulli_Newton_lift.pdf |archivedate=April 11, 2009 |df=mdy-all }}</ref> |
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The upper stream tubes constrict as they flow up and around the airfoil. Conservation of mass says that the flow speed must increase as the stream tube area decreases.<ref name="Anderson_Flight_5.19" /> Similarly, the lower stream tubes expand and the flow slows down. |
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From Bernoulli's principle, the pressure on the upper surface where the flow is moving faster is lower than the pressure on the lower surface where it is moving slower. This pressure difference creates a net [[aerodynamic force]], pointing upward. |
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===Limitations of the simplified explanations=== |
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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, and thus requires both downward turning of the flow and changes in flow speed consistent with Bernoulli's principle. The simplified explanations given above are therefore incomplete because they try to explain lift in terms of only one or the other. And depending on the details, they have other shortcomings as well. |
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The explanation based on [[#Flow deflection and Newton's laws|Flow deflection and Newton's laws]] is correct as far as it goes, but is incomplete. First, it doesn't explain how the airfoil can impart downward turning to a much deeper swath of the flow than it actually touches. Further, it doesn't explain how the pressure differences in the horizontal direction are sustained. That is, it leaves out the Bernoulli part of the interaction.<ref> McLean 2012, Section 7.3.3.12 </ref> |
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Explanations based on [[#Increased flow speed and Bernoulli's principle|Increased flow speed and Bernoulli's principle]] first try to establish that there is higher flow speed over the upper surface, but they fail to explain correctly what causes the flow to speed up: |
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*The [[#Conservation of mass|Conservation of mass]] explanation that relies on narrowing of the streamtubes over the upper surface does not explain why the streamtubes change size. To see why the air flows the way it does requires more sophisticated analysis.<ref>"There is no way to predict, from Bernoulli's equation alone, what the pattern of streamlines will be for a particular wing." Halliday and Resnick ''Fundamentals of Physics'' 3rd Ed. Extended pg 378</ref><ref>"The generation of lift may be explained by starting from the shape of streamtubes above and below an airfoil. With a constriction above and an expansion below, it is easy to demonstrate lift, again via the Bernoulli equation. However, the reason for the shape of the streamtubes remains obscure..." Jaakko Hoffren ''Quest for an Improved Explanation of Lift'' American Institute of Aeronautics and Astronautics 2001 pg 3 {{cite web |url=http://corsair.flugmodellbau.de/files/area2/LIFT.PDF |title=Archived copy |accessdate=2012-07-26 |deadurl=no |archiveurl=https://web.archive.org/web/20131207102746/http://corsair.flugmodellbau.de/files/area2/LIFT.PDF |archivedate=December 7, 2013 |df=mdy-all }}</ref><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=Archived copy |accessdate=2016-01-26 |deadurl=no |archiveurl=https://web.archive.org/web/20160126200755/http://www.allstar.fiu.edu/aero/airflylvl3.htm |archivedate=January 26, 2016 |df=mdy-all }}</ref> |
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*Sometimes a geometrical argument is offered to demonstrate why the streamtubes change size: it is asserted that the top "obstructs" or "constricts" the air more than the bottom, hence narrower streamtubes. 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 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=http://www.grc.nasa.gov/WWW/K-12/airplane/wrong3.html |title=Archived copy |accessdate=2012-07-26 |deadurl=no |archiveurl=https://web.archive.org/web/20120717222459/http://www.grc.nasa.gov/WWW/k-12/airplane/wrong3.html |archivedate=July 17, 2012 |df=mdy-all }}</ref><ref>"A concept...uses a symmetrical convergent-divergent channel, like a longitudinal section of a Venturi tube, as the starting point. It is widely known that, 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 |accessdate=2012-07-26 |deadurl=no |archiveurl=https://web.archive.org/web/20131207102746/http://corsair.flugmodellbau.de/files/area2/LIFT.PDF |archivedate=December 7, 2013 |df=mdy-all }}</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 |accessdate=2009-09-10 |deadurl=no |archiveurl=https://web.archive.org/web/20090411055333/http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/Bernoulli_Newton_lift.pdf |archivedate=April 11, 2009 |df=mdy-all }}</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 (Fig. 1). 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> |
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*A common version that relies on equal-transit-time is simply wrong, as explained below under [[#False explanation based on equal transit-time|False explanation based on equal transit-time]]. |
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Bernoulli-only explanations imply that a speed difference arises 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 cause-and-effect relationship between pressure and velocity is reciprocal. Finally, Bernoulli-only explanations don't explain how the pressure differences in the vertical direction are sustained. That is, they leave out the downward-turning part of the interaction.<ref> McLean 2012, Section 7.3.3.12 </ref> |
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===Alternative explanations, misconceptions, and controversies=== |
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Many alternative explanations for the generation of lift by an airfoil have been put forward, most intended to explain the phenomenon of lift to a general audience. Although the explanations may share features in common with the explanations above, additional assumptions and simplifications may be introduced. Some explanations introduce assumptions which proved to be wrong, such as ''equal transit-time'', and some used controversial terminology, such as "Coanda effect". |
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====False explanation based on equal transit-time==== |
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[[File:Equal transit-time NASA wrong1.gif|thumb|right|586px|An illustration of the incorrect equal transit-time explanation of airfoil lift.]] |
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Basic or popular sources often describe the "equal transit-time" theory of lift, which incorrectly assumes that the parcels of air that divide at the leading edge of an airfoil must rejoin at the trailing edge, forcing the air traveling along the longer upper surface to go faster. [[Bernoulli's principle]] is then cited to conclude that since the air moves slower along the bottom of the wing, the air pressure must be higher, pushing the wing up.<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, pp. 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> |
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However, there is no physical principle that requires equal transit time and experimental results show that this assumption is false.<ref>"Unfortunately, this explanation falls to earth 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, pp. 451 {{cite web |url=http://tpt.aapt.org/resource/1/phteah/v10/i8 |title=Archived copy |accessdate=2011-08-04 |deadurl=yes |archiveurl=https://web.archive.org/web/20120317075304/http://tpt.aapt.org/resource/1/phteah/v10/i8 |archivedate=March 17, 2012 |df=mdy-all }}</ref><ref name=Anderson> |
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{{Citation |last = Anderson |first = David |title = Understanding Flight |publisher=McGraw-Hill |location = New York |year = 2001 |isbn = 0-07-136377-7 |quote = The first thing that is wrong is that the principle of equal transit times is not true for a wing with lift. |pages = 15–16}}</ref><ref>{{cite book | last = Anderson | first = John | title = Introduction to Flight | publisher = McGraw-Hill Higher Education | location = Boston | year = 2005 | isbn = 0072825693 | 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=Archived copy |accessdate=2012-06-10 |deadurl=no |archiveurl=https://web.archive.org/web/20120630121849/http://www.telegraph.co.uk/science/science-news/9035708/Cambridge-scientist-debunks-flying-myth.html |archivedate=June 30, 2012 |df=mdy-all }} ''Cambridge scientist debunks flying myth'' UK Telegraph 24 Jan 2012</ref><ref>{{cite video |
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|url = http://web.mit.edu/hml/ncfmf.html |
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|title = Flow Visualization |
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|publisher = National Committee for Fluid Mechanics Films/Educational Development Center |
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|accessdate = January 21, 2009 |
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|deadurl = no |
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|archiveurl = https://web.archive.org/web/20161021122939/http://web.mit.edu/hml/ncfmf.html |
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|archivedate = October 21, 2016 |
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|df = mdy-all |
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}} 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 over the top of an airfoil generating lift moves ''much'' ''faster'' than the equal transit theory predicts.<ref name=NASA_Incorrect_Theory2>"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 |
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|url = http://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html |
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|date = March 15, 2006 |
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|title = Incorrect Lift Theory |
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|author = Glenn Research Center |
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|publisher = NASA |
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|accessdate = August 12, 2010 |
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|deadurl = no |
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|archiveurl = https://web.archive.org/web/20140427084226/http://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html |
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|archivedate = April 27, 2014 |
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|df = mdy-all |
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}}</ref> Further, the theory violates [[Newton's laws of motion#Newton.27s third law|Newton's third law of motion]], since it describes a force on the wing with no opposite force.<ref>"...the air is described as producing a force on the object ''without the object having any opposite effect on the air''. Such a condition, we should quickly recognize, embodies an ''action'' without a ''reaction'', which is, according to Newton’s Third Law, impossible." Norman F. Smith ''Bernoulli, Newton, and Dynamic Lift Part I'' School Science and Mathematics, 73, 3, Mar 1973 {{cite web |url=http://eric.ed.gov/?id=EJ075197 |title=Archived copy |accessdate=2015-01-19 |deadurl=no |archiveurl=https://web.archive.org/web/20150119214246/http://eric.ed.gov/?id=EJ075197 |archivedate=January 19, 2015 |df=mdy-all }}</ref> |
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The assertion that the air must arrive simultaneously at the trailing edge is sometimes referred to as the "equal transit-time fallacy".<ref>A false explanation for lift has been put forward in mainstream books, and even in scientific exhibitions. Known as the "equal transit-time" explanation, it states that the parcels of air which are divided by an airfoil must rejoin again; because of the greater curvature (and hence longer path) of the upper surface of an aerofoil, the air going over the top must go faster in order to "catch up" with the air flowing around the bottom. Therefore, because of its higher speed the pressure of the air above the airfoil must be lower. Despite the fact that this "explanation" is probably the most common of all, it is false. |
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It has recently been dubbed the "Equal transit-time fallacy".{{cite web |
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|url = http://www.aviationexplorer.com/fixed_wing_aircraft.htm |
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|title = Fixed wing aircraft facts and how aircraft fly |
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|accessdate = July 7, 2009 |
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|deadurl = no |
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|archiveurl = https://web.archive.org/web/20090603043832/http://aviationexplorer.com/fixed_wing_aircraft.htm |
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|archivedate = June 3, 2009 |
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|df = mdy-all |
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}}</ref><ref>...it leaves the impression that Professor Bernoulli is somehow to blame for the "equal transit time" fallacy... {{cite web |
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|url = http://www.av8n.com/fly/lift.htm |
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|author = John S. Denker |
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|year = 1999 |
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|title = Critique of "How Airplanes Fly" |
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|accessdate = July 7, 2009 |
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|deadurl = no |
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|archiveurl = https://web.archive.org/web/20091120184040/http://www.av8n.com/fly/lift.htm |
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|archivedate = November 20, 2009 |
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|df = mdy-all |
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}}</ref><ref>The fallacy of equal transit time can be deduced from consideration of a flat plate, which will indeed produce lift, as anyone who has handled a sheet of plywood in the wind can testify. {{cite web |
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|url = http://regenpress.com/ |
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|author = Gale M. Craig |
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|title = Physical principles of winged flight |
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|accessdate = July 7, 2009 |
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|deadurl = no |
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|archiveurl = https://web.archive.org/web/20090802062641/http://regenpress.com/ |
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|archivedate = August 2, 2009 |
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|df = mdy-all |
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}}</ref><ref>Fallacy 1: Air takes the same time to move across the top of an aerofoil as across the bottom. {{Citation |
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|url = http://www.scienceeducationreview.com/open_access/eastwell-bernoulli.pdf |
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|author = Peter Eastwell |
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|title = Bernoulli? Perhaps, but What About Viscosity? |
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|accessdate = July 14, 2009 |
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|year = 2007 |
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|journal = The Science Education Review |
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|volume = 6 |
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|issue = 1 |
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|postscript = . |
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|deadurl = no |
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|archiveurl = https://web.archive.org/web/20091128103103/http://www.scienceeducationreview.com/open_access/eastwell-bernoulli.pdf |
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|archivedate = November 28, 2009 |
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|df = mdy-all |
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}}</ref><ref>"There is a popular fallacy called the equal transit-time fallacy that claims the two halves rejoin at the trailing edge of the aerofoil." Ethirajan Rathakrishnan ''Theoretical Aerodynamics'' John Wiley & sons 2013 section 4.10.1</ref> |
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====Controversy regarding the Coandă effect==== |
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{{Main article|Coandă effect}} |
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In its original sense, 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. The effect is named for [[Henri Coandă]], the [[Romania]]n aerodynamicist who exploited it in many of his patents. |
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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 to explain why the air flow remains attached to the top side of an airfoil.<ref name="scotteberhart">{{Citation|url=http://www.allstar.fiu.edu/AERO/airflylvl3.htm|last=Anderson|first=David|last2=Eberhart|first2=Scott|title=How Airplanes Fly: A Physical Description of Lift|year=1999|accessdate=June 4, 2008|deadurl=no|archiveurl=https://web.archive.org/web/20160126200755/http://www.allstar.fiu.edu/aero/airflylvl3.htm|archivedate=January 26, 2016|df=mdy-all}}</ref> [[Jef Raskin]],<ref name="raskin">{{Citation |
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|url=http://jef.raskincenter.org/published/coanda_effect.html |
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|archiveurl=https://web.archive.org/web/20070928072421/http://jef.raskincenter.org/published/coanda_effect.html |
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|archivedate=September 28, 2007 |
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|title=Coanda Effect: Understanding Why Wings Work |
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|last=Raskin |
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|first=Jef |
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|year=1994}}</ref> for example, describes a simple demonstration, using a straw to blow over the upper surface of a wing. The wing deflects upwards, thus demonstrating that the Coandă effect creates lift. This demonstration correctly demonstrates the Coandă effect as a fluid jet (the exhaust from a straw) adhering to a curved surface (the wing). However, the upper surface in this flow is a complicated, vortex-laden mixing layer, while on the lower surface the flow is [[wikt:quiescence|quiescent]]. The physics of this demonstration are very different from that of the general flow over the wing.<ref name="auerbach">{{Citation| |
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last=Auerbach| |
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first=David| |
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journal=Eur. J. Phys.| |
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volume=21| |
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issue=4| |
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year=2000| |
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pages=289–296| |
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title=Why Aircraft Fly| |
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doi=10.1088/0143-0807/21/4/302 |
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|bibcode = 2000EJPh...21..289A}}</ref> The usage in this sense is encountered in some popular references on aerodynamics.<ref name="scotteberhart" /><ref name="raskin" /> This is a controversial use of the term "Coanda effect." The more established view in the aerodynamics field is that the Coandă effect is defined in the more limited sense above,<ref name="auerbach" /><ref> |
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{{Citation |
{{Citation |
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| last = Kroo |
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|url = http://www.av8n.com/how/htm/spins.html#sec-coanda-fallacy |
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| first = I. |
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|last = Denker |
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| title = Nonplanar Wing Concepts For Increased Aircraft Efficiency |
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|first = JS |
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| journal = VKI lecture series on Innovative Configurations and Advanced Concepts for Future Civil Aircraft June 6–10, 2005 |
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|title = Fallacious Model of Lift Production |
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| year = 2005 }}</ref> |
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|accessdate = 2008-08-18 |
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|deadurl = no |
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|archiveurl = https://web.archive.org/web/20090302153902/http://www.av8n.com/how/htm/spins.html#sec-coanda-fallacy |
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|archivedate = March 2, 2009 |
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|df = mdy-all |
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}}</ref><ref>{{Citation |
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|title = Report on the first European Mechanics Colloquium, on the Coanda effect |
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|last = Wille |
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|first = R. |
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|last2 = Fernholz |
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|first2 = H. |
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|journal = J. Fluid Mech. |
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|year = 1965 |
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|volume = 23 |
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|issue = 4 |
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|pages = 801–819 |
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|doi = 10.1017/S0022112065001702 |
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|url = http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=370712 |
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|bibcode = 1965JFM....23..801W |
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|deadurl = no |
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|archiveurl = https://web.archive.org/web/20090823114754/http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=370712 |
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|archivedate = August 23, 2009 |
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|df = mdy-all |
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}} |
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</ref> and the flow following the upper surface simply reflects an absence of boundary-layer separation and is not an example of the Coandă effect.<ref>Auerbach (2000)</ref><ref>Denker (1996)</ref><ref>Wille and Fernholz(1965)</ref><ref name="fmw_fluid">{{citation|last=White|first=Frank M.|title=Fluid Mechanics|year=2002|edition=5th|publisher=McGraw Hill}}</ref> |
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===Configurations=== |
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==Basic attributes of lift== |
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Various types of closed wing have been described: |
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* Box wing |
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* Rhomboidal wing |
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* Flat annular wing |
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* Concentric wing and fuselage |
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Lift is a result of pressure differences and depends on angle of attack, airfoil shape, air density, and airspeed. |
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==History== |
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===Pressure differences=== |
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===Pioneer years=== |
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[[Pressure]] is the [[Stress (mechanics)#Normal and shear stresses|normal force]] per unit area exerted by the air on itself and on surfaces that it touches. The lift force is transmitted through the pressure, which acts perpendicular to the surface of the airfoil. The air maintains physical contact at all points. Thus, the net force manifests itself as pressure differences. The direction of the net force implies that the average pressure on the upper surface of the airfoil is lower than the average pressure on the underside.<ref>A uniform pressure surrounding a body does not create a net force. (See [[buoyancy]]). Therefore pressure differences are needed to exert a force on a body immersed in a fluid. For example, see: {{Citation |first=G.K. |last=Batchelor |authorlink=George Batchelor |title=An Introduction to Fluid Dynamics |year=1967 |publisher=Cambridge University Press |isbn=0-521-66396-2 |pages=14–15 }}</ref> |
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[[Image:Bleriot III.jpg|right|thumb|The [[Blériot III]], with its two annular closed-surface wings]] |
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[[Image:Bleriot IV.jpg|right|thumb|The [[Blériot IV]] replaced the forward annular wing with a conventional [[biplane]] wing]] |
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An early example of the closed wing was on the [[Blériot III]] aircraft, built in 1906 by [[Louis Blériot]] and [[Gabriel Voisin]]. The lifting surfaces comprised two annular wings mounted in tandem. The later [[Blériot IV]] replaced the forward annular wing with a biplane and added a [[canard (aeronautics)|canard]] foreplane to make it a [[three-surface aircraft]]. It was able to leave the ground in small hops before being damaged beyond repair. |
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Based on the work of G.J.A. Kitchen, Cedric Lee and [[G. Tilghman Richards]] built and flew several [[Lee-Richards annular monoplane|annular-wing aeroplanes]] in which the fore and aft segments were on the same level. The first was a biplane. It was followed by a series of monoplanes, the last of the line remaining in use until 1914.<ref>Lewis, P.; ''British Aircraft 1809-1914'', Putnam, 1962, pages 340-343,</ref> |
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These pressure differences arise in conjunction with the curved air flow. Whenever a fluid follows a curved path, there is a pressure [[gradient]] perpendicular to the flow direction with higher pressure on the outside of the curve and lower pressure on the inside.<ref name=Babinsky>"''...if a streamline is curved, there must be a pressure gradient across the streamline...''"{{citation |
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|journal=Physics Education |
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|first=Holger |
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|last=Babinsky |
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|date=November 2003 |
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|url=http://www.iop.org/EJ/article/0031-9120/38/6/001/pe3_6_001.pdf |
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|title=How do wings work? |
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|doi=10.1088/0031-9120/38/6/001 |
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|bibcode=2003PhyEd..38..497B |
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|volume=38 |
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|pages=497–503}}</ref> This direct relationship between curved streamlines and pressure differences was derived from Newton's second law by [[Leonhard Euler]] in 1754: |
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===World War II=== |
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:<math>\frac{\operatorname{d}p}{\operatorname{d}R}= \rho \frac{v^2}{R} </math> |
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In 1944, the [[Nazi Germany|German]] designer [[Ernst Heinkel]] began working on an annular-wing [[VTOL]] multirole single-seater called the ''[[Heinkel Lerche|Lerche]]'', but the project was soon abandoned.{{Citation needed|date=February 2014}} |
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===Postwar=== |
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The left hand side of this equation represents the pressure difference perpendicular to the fluid flow. On the right hand side ρ is the density, v is the velocity, and R is the radius of curvature. This formula shows that higher velocities and tighter curvatures create larger pressure differentials and that for straight flow (R → ∞) the pressure difference is zero.<ref>Thus a distribution of the pressure is created which is given in Euler's equation. The physical reason is the aerofoil which forces the streamline to follow its curved surface. The low pressure at the upper side of the aerofoil is a consequence of the curved surface." ''A comparison of explanations of the aerodynamic lifting force'' Klaus Weltner Am. J. Phys. Vol.55 No.January 1, 1987 pg 53 http://aapt.scitation.org/doi/pdf/10.1119/1.14960</ref> |
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During the 1950s, the French company [[SNECMA]] developed the [[SNECMA Coléoptère|Coléoptère]], a single-person [[VTOL]] annular wing aircraft. The aircraft proved dangerously unstable despite the development and testing of several prototypes, and the design was abandoned. Later proposals for closed-wing designs included the [[Convair]] Model 49 Advanced Aerial Fire Support System (AAFSS) and the 1980s [[Lockheed Martin|Lockheed]] "Flying Bog Seat" concept.{{Citation needed|date=February 2014}} |
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Dr. [[Julian Wolkovitch]] continued to develop the idea in the 1980s, claiming it was an efficient structural arrangement in which the horizontal tail provided structural support for the wing as well as acting as a stabilizing surface.<ref>{{cite web|url=http://adg.stanford.edu/aa241/intro/futureac.html |title=Future Technology and Aircraft Types |publisher=Adg.stanford.edu |date= |accessdate=2012-07-04}}</ref><ref>Wolkovitch, Julian, [http://pdf.aiaa.org/jaPreview/JA/1986/PVJAPRE45285.pdf The Joined Wing: An Overview]{{dead link|date=January 2018 |bot=InternetArchiveBot |fix-attempted=yes }}, AC A Industries, Inc., Torrance, California, 1985</ref> |
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===Angle of attack=== |
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[[Image:Airfoil angle of attack.jpg|thumb|300px|Angle of attack of an airfoil]] |
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The Spiroid [[winglet]], a design currently under development by [[Aviation Partners Inc.|Aviation Partners]], is a closed wing surface mounted at the end of a conventional wing. The company announced that the winglets fitted to a [[Gulfstream II]] reduced fuel consumption in the cruise phase by over 10%.<ref>{{cite web |title=Blended Winglets and Spiroid Technology |url=http://www.aviationpartners.com/future.html |publisher=aviationpartners.com |accessdate=2009-09-25}}</ref><ref>Gratzer 1999.</ref> |
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The [[angle of attack]] is the angle between the [[Chord (aeronautics)|chord line]] of an airfoil and the oncoming air. A symmetrical airfoil will generate zero lift at zero angle of attack. But as the angle of attack increases, the air is deflected through a larger angle and the vertical component of the airstream velocity increases, resulting in more lift. For small angles a symmetrical airfoil will generate a lift force roughly proportional to the angle of attack.<ref>"You can argue that the main lift comes from the fact that the wing is angled slightly upward so that air striking the underside of the wing is forced downward. The Newton's 3rd law reaction force upward on the wing provides the lift. Increasing the angle of attack can increase the lift, but it also increases drag so that you have to provide more thrust with the aircraft engines" ''hyperphysics'' Georgia State University Department of Physics and Astronomy {{cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/angatt.html |title=Archived copy |accessdate=2012-07-26 |deadurl=no |archiveurl=https://web.archive.org/web/20121014185450/http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/angatt.html |archivedate=October 14, 2012 |df=mdy-all }}</ref><ref>"If we enlarge the angle of attack we enlarge the deflection of the airstream by the airfoil. This results in the enlargement of the vertical component of the velocity of the airstream... we may expect that the lifting force depends linearly on the angle of attack. This dependency is in complete agreement with the results of experiments..." Klaus Weltner ''A comparison of explanations of the aerodynamic lifting force'' Am. J. Phys. 55(1), January 1987 pg 52</ref> |
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The Finnish company [[FlyNano]] flew a prototype of a closed wing [[ultralight aircraft]], the [[FlyNano Nano]] on 11 June 2012.<ref name="Grady12Jun12">{{cite news|url = http://www.avweb.com/avwebflash/news/FlyNanoGoesElectricStartsAirborneTestFlights_206813-1.html|title = FlyNano Goes Electric, Starts "Airborne Test Flights"|accessdate = 7 July 2012|last = Grady|first = Mary|date = 12 June 2012| work = AVweb}}</ref><ref name="Nanoblog12Jun12">{{cite web|url = http://flynano.blogspot.ca/2012/06/first-flight.html|title = Airborne|accessdate = 7 July 2012|last = [[FlyNano]]|date = 12 June 2012}}</ref> |
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As the angle of attack grows larger, the lift reaches a maximum at some angle; increasing the angle of attack beyond this [[Angle of attack#Critical angle of attack|critical angle of attack]] causes the upper-surface flow to separate from the wing; there is less deflection downward so the airfoil generates less lift. The airfoil is said to be [[Stall (flight)|stalled]].<ref>"The decrease of angles exceeding 25° is plausible. For large angles of attack we get turbulence and thus less deflection downward." Klaus Weltner ''A comparison of explanations of the aerodynamic lifting force'' ''Am. J. Phys.'' 55(1), January 1987 pg 52</ref> |
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An aircraft was also designed and constructed with a closed wing in [[Belarus]].<ref>{{cite web | title=Planes with ellipse wings, creative oddity of the past | url=http://www.gizmowatch.com/entry/planes-with-ellipse-wings-creative-oddity-of-the-past/ | publisher=gizmowatch.com | accessdate=2010-01-06 | deadurl=yes | archiveurl=https://archive.is/20130124053440/http://www.gizmowatch.com/entry/planes-with-ellipse-wings-creative-oddity-of-the-past/ | archivedate=2013-01-24 | df= }}</ref> |
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===Airfoil shape=== |
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[[Image:Airfoil camber.jpg|thumb|right|300px|An airfoil with camber compared to a symmetrical airfoil]] |
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Miscellaneous modern examples include: |
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The lift force depends on the shape of the airfoil, especially the amount of [[Camber (aerodynamics)|camber]] (curvature such that the upper surface is more convex than the lower surface, as illustrated at right). Increasing the camber generally increases lift.<ref> Clancy (1975), Section 5.2</ref><ref>Abbott, and von Doenhoff (1958), Section 4.2</ref> |
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* Stanford study<ref>{{cite web|url=http://aero.stanford.edu/reports/nonplanarwings/ClosedSystems.html |title=Nonplanar Wings: Closed Systems |publisher=Aero.stanford.edu |date= |accessdate=2012-07-04}}</ref> |
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* [[Lockheed Ringwing]] |
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Closed wings remain mostly confined to the realms of studies and conceptual designs, as the engineering challenges of developing a strong, self-supporting closed wing for use in the large airliners which would benefit most from increases in efficiency have yet to be overcome. |
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Cambered airfoils will generate lift at zero angle of attack. When the chord line is horizontal, the trailing edge has a downward direction and since the air follows the trailing edge it is deflected downward.<ref>"With an angle of attack of 0°, we can explain why we already have a lifting force. The air stream behind the aerofoil follows the trailing edge. The trailing edge already has a downward direction, if the chord to the middle line of the profile is horizontal." Klaus Weltner ''A comparison of explanations of the aerodynamic lifting force'' ''Am. J. Phys.'' 55(1), January 1987 p. 52</ref> When a cambered airfoil is upside down, the angle of attack can be adjusted so that the lift force is upwards. This explains how a plane can fly upside down.<ref>"...the important thing about an aerofoil (say an aircraft wing) is not so much that its upper surface is humped and its lower surface is nearly flat, but simply that it moves through the air at an angle. This also avoids the otherwise difficult paradox that an aircraft can fly upside down!" N. H. Fletcher ''Mechanics of Flight'' Physics Education July 1975 http://iopscience.iop.org/0031-9120/10/5/009/pdf/0031-9120_10_5_009.pdf</ref><ref>"It requires adjustment of the angle of attack, but as clearly demonstrated in almost every air show, it can be done." ''hyperphysics'' Georgia State University Department of Physics and Astronomy http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/airfoil.html#c2 {{webarchive|url=https://web.archive.org/web/20120708102756/http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/airfoil.html |date=July 8, 2012 }}</ref> |
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The closed wing is also used in water, for [[surfboard]] fins of the type also known as the [[tunnel fin]]. |
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===Flow conditions=== |
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The ambient flow conditions which affect lift include the fluid density, viscosity and speed of flow. Lift is proportional to the density of the fluid and approximately proportional to the square of the flow speed. The density, in its turn, may be affected by temperature and, at high speeds approaching or exceeding the speed of sound in the fluid, by compressibility effects. Lift also depends on the size of the wing, being generally proportional to the wing's area projected in the lift direction. |
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===Lockheed Martin Environmentally Responsible Aviation Project=== |
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===Air speed and density=== |
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[[File:AOK Spacejet at Paris Air Show 2013.jpg|thumb|Right|AOK Spacejet at Paris Air Show 2013]] |
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The flow conditions also affect lift. Lift is proportional to the density of the air and approximately proportional to the square of the flow speed. Lift also depends on the size of the wing, being generally proportional to the wing's area projected in the lift direction. In aerodynamic theory and engineering calculations it is often convenient to quantify lift in terms of a "Lift coefficient" defined in a way that makes use of these proportionalities. |
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During 2011, the Environmentally Responsible Aviation Project at [[NASA]]'s Aeronautics Research Mission Directorate invited study proposals towards meeting NASA's goal of reducing future aircraft fuel consumption by 50% compared to 1998. Lockheed Martin proposed a box wing design along with other advanced technologies.<ref>{{cite web | url=http://www.nasa.gov/topics/aeronautics/features/greener_aircraft.html | title=New Ideas Sharpen Focus for Greener Aircraft | publisher=NASA Langley Research Center | work=www.nasa.gov website | date=2012-01-27 | accessdate=December 17, 2012 | author=Barnstorff, Kathy}}</ref><ref>{{cite web | url=http://www.popsci.com/technology/article/2012-04/jets-future | title=The Jets of the Future | publisher=Popular Science magazine | date=2012-05-01 | accessdate=December 17, 2012 |author1=Rosenblum, Andrew |author2=Pastore, Rose }}</ref> |
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=== |
===Prandtl Box Wing=== |
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[[File:Artistic view of a PrandtlPlane freighter.png|thumb|PrandtlPlane airliner concept (University of Pisa, Italy)]] |
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[[File:1915ca abger fluegel (cropped and mirrored).jpg|thumb|300px|Airflow separating from a wing at a high [[angle of attack]]]] |
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No matter how smooth the surface of an airfoil seems, any real surface is rough on the scale of air molecules. Air molecules flying into the surface bounce off the rough surface in random directions not related to their incoming directions. The result is that when the air is viewed as if it were a continuous material, it is seen to be unable to slide along the surface, and the air's tangential velocity at the surface goes to practically zero, something known as the [[no-slip condition]].<ref>White (1991), Section 1-4</ref> Because the air at the surface has near-zero velocity, and air away from the surface is moving, there is a thin [[boundary layer]] in which the air close to the surface is subjected to a shearing motion.<ref>White (1991), Section 1-2</ref><ref name="Anderson 1991, Chapter 17">Anderson (1991), Chapter 17</ref> The air's [[viscosity]] resists the shearing, giving rise to a shear stress at the airfoil's surface called [[Skin friction#Skin friction|skin-friction drag]]. Over most of the surface of most airfoils, the boundary layer is naturally turbulent, which increases skin-friction drag.<ref name="Anderson 1991, Chapter 17"/><ref name="Doenhoff 1958">Abbott and von Doenhoff (1958), Chapter 5</ref> |
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In 1924 the German aerodynamicist [[Ludwig Prandtl]] suggested that a box wing, under certain conditions, might provide the minimum induced drag for a given lift and wingspan.<ref>Prandtl, L. "Induced Drag of Multiplanes", National Advisory Committee for Aeronautics, Technical note No. 182, from Technishe Berichte, Volume III, No. 7, 1924, pp. 309-315</ref> In his design two offset horizontal wings have vertical wings connecting their tips and shaped to provide a linear distribution of side forces. The configuration is said to offer improved efficiency for a range of aircraft. |
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Under usual flight conditions, the boundary layer remains attached to both the upper and lower surfaces all the way to the trailing edge, and its effect on the rest of the flow is modest. Compared to the predictions of inviscid-flow theory, in which there is no boundary layer, the attached boundary layer reduces the lift by a modest amount and modifies the pressure distribution somewhat, which results in a viscosity-related pressure drag over and above the skin-friction drag. The total of the skin-friction drag and the viscosity-related pressure drag is usually called the [[Profile drag#Form drag|profile drag]].<ref name="Doenhoff 1958"/><ref>Schlichting (1979), Chapter XXIV</ref> |
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In the 1980s, the [[Ligeti Stratos]] used this approach.<ref>[https://web.archive.org/web/20130917021549/http://lgtaerospace.com/index.php/lgt-stratos/ligeti-stratos-history Ligeti Stratos History (archived)]</ref><ref>[http://projetplaisir.free.fr/a02.html Ligeti Stratos joined wing aircraft (in French language)]</ref> The name "PrandtlPlane" was coined in the 1990s in research by Aldo Frediani ''et. al.'' of the [[University of Pisa]].<ref>Frediani A., "The Prandtl wing". VKI lecture series: Innovative Configurations and Advanced Concepts for Future Civil transport Aircraft, June 06–10, 2005</ref> It is currently also used in some [[Ultralight aviation|ultralight aircraft]],<ref name="idintos"/> |
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===Stalling=== |
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The maximum lift an airfoil can produce at a given airspeed is limited by [[Boundary layer separation|boundary-layer separation]]. As the angle of attack is increased, a point is reached where the boundary layer can no longer remain attached to the upper surface. When the boundary layer separates, it leaves a region of recirculating flow above the upper surface, as illustrated in the flow-visualization photo at right. This is known as the ''stall'', or ''stalling''. At angles of attack above the stall, lift is significantly reduced, though it is not zero. The maximum lift that can be achieved before stall, in terms of the [[lift coefficient]], is generally less than 2.0 for single-element airfoils and can be more than 3.0 for airfoils with high-lift slotted flaps deployed.<ref>Abbott and Doenhoff (1958), Chapter 8</ref> |
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[[File:IDINTOS project exposition at Creactivity 2013 (Pontedera, Italy).jpg|thumb|Full-scale prototype of an ultralight amphibious PrandtlPlane, developed during IDINTOS project and presented at Creactivity 2013 (Pontedera, Italy).]] |
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===Bluff bodies=== |
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IDINTOS<ref name="idintos">http://www.idintos.eu/</ref> (IDrovolante INnovativo TOScano) is a research project, co-funded by the regional government of Tuscany (Italy) in 2011 in order to design and manufacture an amphibious ultralight PrandtlPlane. The research project has been carried out by a consortium of Tuscan public and private partners, led by the Aerospace Section of the Civil and Industrial Engineering Department of Pisa University, and has resulted in the manufacturing of a 2-seater VLA prototype.<ref>V. Cipolla, A. Frediani, F. Oliviero, M. Pinucci, E. Rizzo, R. Rossi . "Ultralight amphibious PrandtlPlane: the final design", Proceedings of Italian Association of Aeronautics and Astronautics XXII Conference, Naples (Italy), 2013.</ref> |
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{{further information|Vortex shedding|Vortex-induced vibration}} |
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The flow around [[:wikt:bluff#Adjective|bluff]] bodies – i.e. without a [[:wikt:streamline|streamlined]] shape, or [[stall (flight)|stall]]ing airfoils – may also generate lift, besides a strong drag force. This lift may be steady, or it may [[oscillation|oscillate]] due to [[vortex shedding]]. Interaction of the object's flexibility with the vortex shedding may enhance the effects of fluctuating lift and cause [[vortex-induced vibration]]s.<ref name=Williamson>{{citation |journal=Annual Review of Fluid Mechanics |volume=36 |pages=413–455 |year=2004 |doi=10.1146/annurev.fluid.36.050802.122128 |title=Vortex-induced vibrations |first1=C.H.K. |last1=Williamson |first2=R. |last2=Govardhan |bibcode = 2004AnRFM..36..413W }}</ref> For instance, the flow around a circular cylinder generates a [[Kármán vortex street]]: [[vortex|vortices]] being shed in an alternating fashion from each side of the cylinder. The oscillatory nature of the flow is reflected in the fluctuating lift force on the cylinder, whereas the mean lift force is negligible. The lift force [[frequency]] is characterised by the [[dimensionless]] [[Strouhal number]], which depends (among others) on the [[Reynolds number]] of the flow.<ref>{{citation |title=Hydrodynamics around cylindrical structures |first1=B. Mutlu |last1=Sumer |first2=Jørgen |last2=Fredsøe |edition=revised |publisher=World Scientific |year=2006 |isbn=981-270-039-0 |pages=6–13, 42–45 & 50–52 }}</ref><ref>{{citation |title=Flow around circular cylinders |first=M.M. |last=Zdravkovich |publisher=Oxford University Press |year=2003 |isbn=0-19-856561-5 |volume=2 |pages=850–855}}</ref> |
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The configuration is also claimed to be theoretically efficient for wide-body jet airliners. The largest commercial airliner, the [[Airbus A380]], must make efficiency trade-offs to keep the wingspan below the 80-meter limit at most airports, but a closed wing with optimal wingspan could be shorter than that of conventional designs, potentially allowing even larger aircraft to use the current infrastructure.<ref>Frediani A., Cipolla V., Rizzo E., "The PrandtlPlane Configuration: Overview on Possible Applications to Civil Aviation", Variational Analysis and Aerospace Engineering: Mathematical Challenges for Aerospace Design, Springer US, 2012, 66, 179-210</ref> |
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For a flexible structure, this oscillatory lift force may induce [[vortex-induced vibration]]s. Under certain conditions – for instance [[resonance]] or strong spanwise [[correlation]] of the lift force – the resulting motion of the structure due to the lift fluctuations may be strongly enhanced. Such vibrations may pose problems and threaten collapse in tall man-made structures like industrial [[chimney]]s.<ref name=Williamson/> |
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==C-wing== |
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In the [[Magnus effect]], a lift force is generated by a spinning cylinder in a freestream. Here the mechanical rotation acts on the boundary layer, causing it to separate at different locations on the two sides of the cylinder. The asymmetric separation changes the effective shape of the cylinder as far as the flow is concerned such that the cylinder acts like a lifting airfoil with circulation in the outer flow.<ref>Clancy, L. J., ''Aerodynamics'', Sections 4.5 and 4.6</ref> |
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The C-wing is a theoretical configuration in which much of the upper centre section of a box wing is removed, creating a wing that folds up and over at the tips but does not rejoin in the centre. A C-wing can achieve very nearly the same induced-drag performance as a corresponding as a box wing, as shown by the calculations illustrated below.<ref name="Demasi Luciano 2014">Demasi Luciano, Dipace Antonio, Monegato Giovanni, and Cavallaro Rauno; "An Invariant Formulation for the Minimum Induced Drag Conditions of Non-planar Wing Systems", ''AIAA Journal'' (2014), in press</ref> |
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Each of the first three rows in the illustration shows a different C-wing configuration as it is taken through a sequence of theoretical induced-drag calculations in which the wingtips are brought closer together, culminating in the limiting case on the right, where the gap has been taken to zero and the configuration has become a closed box wing (referred to as the "Quasi-closed C-wing" because the calculations were carried out in the limit as the gap went to zero). |
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==A more comprehensive physical explanation== |
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The parameter ε is the optimal aerodynamic efficiency ratio{{Citation needed|date=February 2014}} and represents the ratio between the aerodynamic efficiency of a given non-planar wing and the corresponding efficiency of a reference classical cantilevered wing with the same wing span and total lift. Both efficiencies are evaluated under their respective optimal conditions. Values of ε greater than 1 indicate lower induced drag than that of a classical cantilevered wing for which ε = 1.{{Citation needed|date=February 2014}} |
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As described above under "[[#Simplified physical explanations of lift on an airfoil|Simplified physical explanations of lift on an airfoil]]", there are two main popular explanations: one based on downward deflection of the flow (Newton's laws), and one based on pressure differences accompanied by changes in flow speed (Bernoulli's principle). Either of these, by itself, correctly identifies some aspects of the lifting flow but leaves other important aspects of the phenomenon unexplained. A more comprehensive explanation involves both downward deflection and pressure differences (including changes in flow speed associated with the pressure differences), and requires looking at the flow in more detail.<ref name="McLean 2012, Section 7.3.3">McLean (2012), Section 7.3.3</ref> |
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Note that all of the C-wing configurations have ε greater then 1 and that there is little difference (no difference to the two decimal places shown in two of the cases) between a configuration with a substantial gap (the second entry in each row) and the corresponding closed configuration (the third entry in each row). This is because the optimum lift loading calculated for the quasi-closed cases is very small over the upper centre section, and that part of the wing can be removed with little change in lift or drag. |
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===Lift at the airfoil surface=== |
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The lift distributions shown here for the quasi-closed cases look different from those typically shown for box wings in the classical literature (see Durand, figure 81, for example).<ref name="Durand">Durand, W. F., ed., "Aerodynamic Theory", Volume II, Julius Springer, 1935. Also New York, Dover Publications</ref> The classical solution in Durand was obtained by a conformal-mapping analysis that happened to be formulated in a way that led to equal upward loadings on the horizontal panels of the box. But the optimum loading is not unique.<ref name="Kroo" /> A constant inward loading (corresponding to a constant circulation) can be added to a classical loading like that shown by Durand to obtain a loading like those in the quasi-closed cases below. The two methods of analysis give different-looking versions of the optimum loading that are not fundamentally different. Except for small differences due to the numerical method used for the quasi-closed cases, the two kinds of loading are in principle just shifted versions of each other. |
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The airfoil shape and angle of attack work together so that the airfoil exerts a downward force on the air as it flows past. According to Newton's third law, the air must then exert an equal and opposite (upward) force on the airfoil, which is the lift.<ref name="Anderson and Eberhardt 2001"/><ref name="Langewiesche 1944"/> |
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==References== |
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The net force exerted by the air occurs as a pressure difference over the airfoil's surfaces.<ref name="Milne-Thomson 1966, Section 1.41">Milne-Thomson (1966), Section 1.41</ref> Pressure in a fluid is always positive in an absolute sense,<ref name="Jeans 1967, Section 33">Jeans (1967), Section 33.</ref> so that pressure must always be thought of as pushing, and never as pulling. The pressure thus pushes inward on the airfoil everywhere on both the upper and lower surfaces. The flowing air reacts to the presence of the wing by reducing the pressure on the wing's upper surface and increasing the pressure on the lower surface. The pressure on the lower surface pushes up harder than the reduced pressure on the upper surface pushes down, and the net result is upward lift.<ref name="Milne-Thomson 1966, Section 1.41"/> |
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The pressure difference that exerts lift acts directly on the airfoil surfaces. But understanding how the pressure difference is produced requires understanding what the flow does over a wider area. |
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===The wider flow around the airfoil=== |
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[[File:Karman trefftz.gif|frame|right|Flow around an airfoil: the dots move with the flow. The black dots are on [[Streamlines, streaklines, and pathlines|time slices]], which split into two – an upper and lower part – at the leading edge. A marked speed difference between the upper-and lower-surface streamlines is shown most clearly in the image animation, with the upper markers arriving at the trailing edge long before the lower ones. Colors of the dots indicate [[Streamlines, streaklines, and pathlines|streamlines]].]] |
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[[File:Airfoil isobars.jpg|thumb|right|300px|Pressure distribution with [[Isobar (meteorology)|isobars]] around a lifting airfoil. The plus sign indicates pressure higher than ambient, and the minus sign indicates pressure lower than ambient (not negative pressure in the absolute sense). The block arrows indicate the directions of net forces on fluid parcels in different parts of the flowfield.]] |
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An airfoil affects the speed and direction of the flow over a wide area, producing a pattern called a ''velocity field''. When an airfoil produces lift, the flow ahead of the airfoil is deflected upward, the flow above and below the airfoil is deflected downward, and the flow behind the airfoil is deflected upward again, leaving the air far behind the airfoil in the same state as the oncoming flow far ahead. The flow above the upper surface is sped up, while the flow below the airfoil is slowed down. Together with the upward deflection of air in front and the downward deflection of the air immediately behind, this establishes a net circulatory component of the flow. The downward deflection and the changes in flow speed are pronounced and extend over a wide area, as can be seen in the flow animation on the right. These differences in the direction and speed of the flow are greatest close to the airfoil and decrease gradually far above and below. All of these features of the velocity field also appear in theoretical models for lifting flows.<ref name="Clancy 1975, Section 4.5">Clancy (1975), Section 4.5</ref><ref> Milne-Thomson (1966.), Section 5.31</ref> |
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The pressure is also affected over a wide area, in a pattern of non-uniform pressure called a ''pressure field''. When an airfoil produces lift, there is always a diffuse region of low pressure above the airfoil, and there is usually a diffuse region of high pressure below, as illustrated by the isobars (curves of constant pressure) in the drawing. The pressure difference that acts on the surface is just part of this pressure field.<ref name="McLean 2012, Section 7.3.3.7"/> |
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===Mutual interaction of pressure differences and changes in flow velocity=== |
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The non-uniform pressure exerts forces on the air in the direction from higher pressure to lower pressure. The direction of the force is different at different locations around the airfoil, as indicated by the block arrows in the ''pressure distribution with isobars'' figure. Air above the airfoil is pushed toward the center of the low-pressure region, and air below the airfoil is pushed outward from the center of the high-pressure region. |
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According to ''Newton's second law'', a force causes air to accelerate in the direction of the force. Thus the vertical arrows in the ''pressure distribution with isobars'' figure indicate that air above and below the airfoil is accelerated, or turned downward, and that the non-uniform pressure is thus the cause of the downward deflection of the flow visible in the flow animation. To produce this downward turning, the airfoil must have a positive angle of attack or have its rear portion curved downward as on an airfoil with camber. Note that the downward turning of the flow over the upper surface is the result of the air being pushed downward by higher pressure above it than below it. Some explanations that refer to the "Coandă effect" suggest that viscosity plays a key role in the downward turning, but this is false. (see below under "[[#Controversy regarding the Coandă effect|Controversy regarding the Coandă effect]]"). |
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The arrows ahead of the airfoil indicate that the flow ahead of the airfoil is deflected upward, and the arrows behind the airfoil indicate that the flow behind is deflected upward again, after being deflected downward over the airfoil. These deflections are also visible in the flow animation. |
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The arrows ahead of the airfoil and behind also indicate that air passing through the low-pressure region above the airfoil is sped up as it enters, and slowed back down as it leaves. Air passing through the high-pressure region below the airfoil sees the opposite: It is slowed down and then sped back up. Thus the non-uniform pressure is also the cause of the changes in flow speed visible in the flow animation. The changes in flow speed are consistent with ''Bernoulli's principle'', which states that in a steady flow without [[viscosity]], lower pressure means higher speed, and higher pressure means lower speed. |
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Thus changes in flow direction and speed are directly caused by the non-uniform pressure. But this cause-and-effect relationship is not just one-way; it works in both directions simultaneously. The air's motion is affected by the pressure differences, but the existence of the pressure differences depends on the air's motion. The relationship is thus a mutual, or reciprocal, interaction: Air flow changes speed or direction in response to pressure differences, and the pressure differences are sustained by the air's resistance to changing speed or direction.<ref> McLean (2012), Section 3.5 </ref> A pressure difference can exist only if something is there for it to push against. In the case of an aerodynamic flow, what a pressure difference pushes against is the inertia of the air, as the air is accelerated by the pressure difference.<ref name="McLean 2012, Section 7.3.3.9"/> And this is why the mass of the air is important, and why lift depends on air density. |
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In summary, sustaining the pressure difference that exerts the lift force on the airfoil surfaces requires sustaining a pattern of non-uniform pressure spread over a wide area around the airfoil. This requires maintaining pressure differences in both the vertical and horizontal directions, and thus requires both downward turning of the flow and changes in flow speed according to Bernoulli's principle. The pressure differences and the changes in flow direction and speed sustain each other in a mutual interaction. The pressure differences follow naturally from Newton's second law and from the fact that the flow along the surface naturally follows the predominantly downward-sloping contours of the airfoil. And the fact that the air has mass is crucial to the interaction.<ref name="McLean 2012, Section 7.3.3.9"/> |
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===How simpler explanations fall short=== |
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Producing a lift force requires both downward turning of the flow and changes in flow speed consistent with Bernoulli's principle. Each of the simplified explanations given above in [[#Simplified_physical_explanations_of_lift_on_an_airfoil|Simplified physical explanations of lift on an airfoil]] falls short by trying to explain lift in terms of only one or the other, thus explaining only part of the phenomenon and leaving other parts unexplained. <ref> McLean 2012, Section 7.3.3.12 </ref> |
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==Quantifying lift== |
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===Pressure integration=== |
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When the pressure distribution on the airfoil surface is known, determining the total lift requires adding up the contributions to the pressure force from local elements of the surface, each with its own local value of pressure. The total lift is thus the [[integral]] of the pressure, in the direction perpendicular to the farfield flow, over the entire surface of the airfoil or wing.<ref>Anderson (2008), Section 5.7</ref> |
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<math>L = \oint p\mathbf{n} \cdot\mathbf{k} \; \mathrm{d}S, </math> |
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where: {{clarify|date=November 2017|reason=Is S the same planform area as above or the total surface area all over?}} |
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* '''n''' is the normal unit vector pointing into the wing, and |
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* '''k''' is the vertical unit vector, normal to the freestream direction. |
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The above lift equation neglects the [[skin friction]] forces, which typically have a negligible contribution to the lift compared to the pressure forces. |
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By using the streamwise vector '''i''' parallel to the freestream in place of '''k''' in the integral, we obtain an expression for the [[pressure drag]] ''D<sub>p</sub>'' (which includes the pressure portion of the profile drag and, if the wing is three-dimensional, the [[lift-induced drag|induced drag]]). If we use the spanwise vector '''j''', we obtain the side force ''Y''. |
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:<math> |
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\begin{align} |
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D_p &= \oint p\mathbf{n} \cdot\mathbf{i} \; \mathrm{d}S, |
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\\[1.2ex] |
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Y &= \oint p\mathbf{n} \cdot\mathbf{j} \; \mathrm{d}S. |
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\end{align}</math> |
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The validity of this integration generally requires the airfoil shape to be a closed curve that is piecewise smooth. |
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===Lift coefficient=== |
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{{Main article|lift coefficient}} |
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Lift depends on the size of the wing, being approximately proportional to the wing area. It is often convenient to quantify the lift of a given airfoil by its ''lift coefficient'' <math>C_L</math>, which defines its overall lift in terms of a unit area of the wing. |
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If the value of <math>C_L</math> for a wing at a specified angle of attack is given, then the lift produced for specific flow conditions can be determined using the following equation:<ref>{{citation |last=Anderson |first=John D. |year=2004 |title=Introduction to Flight |edition=5th |publisher=McGraw-Hill |isbn=0-07-282569-3 |pages=257–261}}</ref> |
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:<math> |
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L = \tfrac12\rho v^2 S C_L |
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</math> |
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where |
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* <math>L</math> is the lift force, |
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* <math>\rho</math> is the [[air density]], |
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* <math>v</math> is the velocity or [[true airspeed]], |
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* <math>S</math> is the wing area, and |
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* <math>C_L</math> is the lift coefficient at the desired angle of attack, [[Mach number]], and [[Reynolds number]]<ref> |
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{{citation| |
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last=Yoon| |
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first=Joe| |
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title=Mach Number & Similarity Parameters| |
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publisher=Aerospaceweb.org| |
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url=http://www.aerospaceweb.org/question/aerodynamics/q0156.shtml| |
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date=2003-12-28| |
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accessdate=2009-02-11 |
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}} |
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</ref> |
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==Mathematical theories of lift== |
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Mathematical theories of lift are based on continuum fluid mechanics, assuming that air flows as if it were a continuous fluid.<ref>Batchelor (1967), Section 1.2</ref><ref>Thwaites (1958), Section I.2</ref><ref>von Mises (1959), Section I.1</ref> Lift is generated in accordance with the fundamental principles of [[physics]], the most relevant being the following three principles:<ref>"Analysis of fluid flow is typically presented to engineering students in terms of three fundamental principles: conservation of mass, conservation of momentum, and conservation of energy." 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/papers_phys/fluids/Bernoulli_Newton_lift.pdf |title=Archived copy |accessdate=2009-09-10 |deadurl=no |archiveurl=https://web.archive.org/web/20090411055333/http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/Bernoulli_Newton_lift.pdf |archivedate=April 11, 2009 |df=mdy-all }}</ref> |
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* [[Conservation of momentum]], which is a consequence of [[Newton's laws of motion]], especially Newton's second law which relates the net [[force]] on an element of air to its rate of [[momentum]] change, |
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* [[Continuity equation#Fluid dynamics|Conservation of Mass]], including the assumption that the airfoil's surface is impermeable for the air flowing around, and |
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* [[Conservation of energy]], which says that energy is neither created nor destroyed. |
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Because an airfoil affects the flow in a wide area around it, the conservation laws of mechanics are embodied in the form of [[Partial differential equations|partial-differential equations]] combined with a set of [[boundary condition]] requirements which the flow has to satisfy at the airfoil surface and far away from the airfoil.<ref>White(1991), Chapter 1</ref> |
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To predict lift requires solving the equations for a particular airfoil shape and flow condition, which generally requires calculations that are so voluminous that they are practical only on a computer, through the methods of [[computational fluid dynamics]] (CFD). Determining the net aerodynamic force from a CFD solution requires "adding up" ([[integration (mathematics)|integrating]]) the forces due to pressure and shear determined by the CFD over every surface element of the airfoil as described under "[[#Pressure_integration|Pressure integration]]". |
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The [[Navier-Stokes equations]] (NS) provide the potentially most accurate theory of lift, but in practice, capturing the effects of turbulence in the boundary layer on the airfoil surface requires sacrificing some accuracy and using the [[Reynolds-averaged Navier–Stokes equations|Reynolds-Averaged Navier-Stokes equations]] (RANS). Simpler but less accurate theories have also been developed. |
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===Navier-Stokes (NS) equations=== |
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These equations represent conservation of mass, Newton's second law (conservation of momentum), conservation of energy, the [[Viscosity#Newtonian and non-Newtonian fluids|Newtonian law for the action of viscosity]], the [[Fourier heat conduction equation#Fourier.27s law|Fourier heat conduction law]], an [[equation of state]] relating density, temperature, and pressure, and formulas for the viscosity and thermal conductivity of the fluid.<ref> Batchelor (1967), Chapter 3 </ref> |
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<ref> Aris (1989) </ref> |
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In principle, the NS equations, combined with boundary conditions of no through-flow and [[No-slip condition|no slip]] at the airfoil surface, could be used to predict lift in any situation in ordinary atmospheric flight with high accuracy. However, lifting flows in practical situations always involve turbulence in the boundary layer next to the airfoil surface, at least over the aft portion of the airfoil. Predicting lift by solving the NS equations in their raw form would require the calculations to resolve the details of the turbulence, down to the smallest eddy. This is not yet possible, even on the most powerful current computer.<ref name="Spalart 2000">Spalart(2000) Amsterdam, The Netherlands. Elsevier Science Publishers.</ref> So in principle the NS equations provide a complete and very accurate theory of lift, but practical prediction of lift requires that the effects of turbulence be modeled in the RANS equations rather than computed directly. |
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===Reynolds-Averaged Navier-Stokes (RANS) equations=== |
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These are the NS equations with the turbulence motions averaged over time, and the effects of the turbulence on the time-averaged flow represented by [[turbulence modeling]] (an additional set of equations based on a combination of [[dimensional analysis]] and empirical information on how turbulence affects a boundary layer in a time-averaged average sense).<ref> White(1991), Section 6-2 </ref><ref> Schlichting(1979), Chapter XVIII </ref> A RANS solution consists of the time-averaged velocity vector, pressure, density, and temperature defined at a dense grid of points surrounding the airfoil. |
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The amount of computation required is a minuscule fraction (billionths)<ref name="Spalart 2000"/> of what would be required to resolve all of the turbulence motions in a raw NS calculation, and with large computers available it is now practical to carry out RANS calculations for complete airplanes in three dimensions. Because turbulence models are not perfect, the accuracy of RANS calculations is imperfect, but it is good enough to be very helpful to airplane designers. Lift predicted by RANS is usually within a few percent of the actual lift. |
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===Inviscid-flow equations (Euler or potential)=== |
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The [[Euler equations (fluid dynamics)|Euler equations]] are the NS equations without the viscosity, heat conduction, and turbulence effects.<ref> Anderson (1995) </ref> As with a RANS solution, an Euler solution consists of the velocity vector, pressure, density, and temperature defined at a dense grid of points surrounding the airfoil. While the Euler equations are simpler than the NS equations, they still do not lend themselves to exact analytic solutions. |
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Further simplification is available through [[potential flow]] theory, which reduces the number of unknowns that must be solved for and makes analytic solutions possible in some cases, as described below. |
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Either Euler or potential-flow calculations predict the pressure distribution on the airfoil surfaces roughly correctly for angles of attack below stall, where they might miss the total lift by as much as 10-20%. At angles of attack above stall, inviscid calculations do not predict that stall has happened, and as a result they grossly overestimate the lift. |
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In potential-flow theory, the flow is assumed to be [[irrotational]], i.e. that small fluid parcels have no net rate of rotation. Mathematically, this is expressed by the statement that the [[Curl (mathematics)|curl]] of the velocity vector field is everywhere equal to zero. Irrotational flows have the convenient property that the velocity can be expressed as the [[gradient]] of a scalar function called a [[potential]]. A flow represented in this way is called [[potential flow]].<ref>"...whenever the velocity field is irrotational, it can be expressed as the gradient of a scalar function we |
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call a velocity potential φ: V = ∇φ. The existence of a velocity potential can greatly simplify the analysis of inviscid flows by way of potential-flow theory..." Doug McLean ''Understanding Aerodynamics: Arguing from the Real Physics'' p 26 Wiley {{cite book |url=http://onlinelibrary.wiley.com/doi/10.1002/9781118454190.ch3/pdf |title=Archived copy |accessdate=2013-02-04 |deadurl=no |archiveurl=https://web.archive.org/web/20131208001834/http://onlinelibrary.wiley.com/doi/10.1002/9781118454190.ch3/pdf |archivedate=December 8, 2013 |df=mdy-all |doi=10.1002/9781118454190.ch3 |year=2012 |work=Understanding Aerodynamics |pages=13–77}}</ref><ref>Elements of Potential Flow California State University Los Angeles {{cite web |url=http://instructional1.calstatela.edu/cwu/me408/Slides/PotentialFlow/PotentialFlow.htm |title=Archived copy |accessdate=2012-07-26 |deadurl=no |archiveurl=https://web.archive.org/web/20121111220110/http://instructional1.calstatela.edu/cwu/me408/Slides/PotentialFlow/PotentialFlow.htm |archivedate=November 11, 2012 |df=mdy-all }}</ref><ref> Batchelor(1967), Section 2.7 </ref><ref> Milne-Thomson(1966), Section 3.31 </ref> |
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In potential-flow theory, the flow is usually further assumed to be incompressible. Incompressible potential-flow theory has the advantage that the equation ([[Laplace's equation]]) to be solved for the potential is [[Linear#Physics|linear]], which allows solutions to be constructed by [[Superposition principle|superposition]] of other known solutions. The incompressible-potential-flow equation can also be solved by [[conformal mapping]], a method based on the theory of functions of a complex variable. In the early 20th century, before computers were available, conformal mapping was used to generate solutions to the incompressible potential-flow equation for a class of idealized airfoil shapes, providing some of the first practical theoretical predictions of the pressure distribution on a lifting airfoil. |
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A solution of the potential equation directly determines only the velocity field. The pressure field is deduced from the velocity field through Bernoulli's equation. |
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[[Image:Airfoil Kutta condition.jpg|thumb|right|400px|Comparison of a non-lifting flow pattern around an airfoil and a lifting flow pattern consistent with the Kutta condition, in which the flow leaves the trailing edge smoothly.]] |
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Applying potential-flow theory to a lifting flow requires special treatment and an additional assumption. The problem arises because lift on an airfoil in inviscid flow requires [[Circulation (fluid dynamics)|circulation]] in the flow around the airfoil (See "[[#Circulation_and_the_Kutta-Joukowski_theorem|Circulation and the Kutta-Joukowski theorem]]" below), but a single potential function that is continuous throughout the domain around the airfoil cannot represent a flow with nonzero circulation. The solution to this problem is to introduce a [[branch cut]], a curve or line from some point on the airfoil surface out to infinite distance, and to allow a jump in the value of the potential across the cut. The jump in the potential imposes circulation in the flow equal to the potential jump and thus allows nonzero circulation to be represented. However, the potential jump is a free parameter that is not determined by the potential equation or the other boundary conditions, and the solution is thus indeterminate. A potential-flow solution exists for any value of the circulation and any value of the lift. One way to resolve this indeterminacy is to impose the [[Kutta condition]],<ref> Clancy (1975), Section 4.8</ref><ref> Anderson(1991), Section 4.5</ref> which is that, of all the possible solutions, the physically reasonable solution is the one in which the flow leaves the trailing edge smoothly. The streamline sketches illustrate one flow pattern with zero lift, in which the flow goes around the trailing edge and leaves the upper surface ahead of the trailing edge, and another flow pattern with positive lift, in which the flow leaves smoothly at the trailing edge in accordance with the Kutta condition. |
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===Linearized potential flow=== |
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This is potential-flow theory with the further assumptions that the airfoil is very thin and the angle of attack is small.<ref> Clancy(1975), Sections 8.1-8 </ref> The linearized theory predicts the general character of the airfoil pressure distribution and how it is influenced by airfoil shape and angle of attack, but is not accurate enough for design work. For a 2D airfoil, such calculations can be done in a fraction of a second in a spreadsheet on a PC. |
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===Circulation and Kutta-Joukowski=== |
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[[Image:Circulation-around-aerofoil.svg|thumb|right|300px|Circulation component of the flow around a moving airfoil.]] |
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When an airfoil generates lift, several components of the overall velocity field contribute to a net circulation of air around it: the upward flow ahead of the airfoil, the accelerated flow above, the decelerated flow below, and the downward flow behind. |
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The circulation can be understood as the total amount of "spinning" (or [[vorticity]]) of air around the airfoil. |
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The [[Kutta–Joukowski theorem]] relates the lift on an airfoil to this [[Circulation (fluid dynamics)|circulation]] component of the flow.<ref name="Clancy 1975, Section 4.5"/><ref name="von Mises 1959, Section VIII.2">von Mises (1959), Section VIII.2</ref><ref name="Anderson1991, Section 3.15">Anderson(1991), Section 3.15</ref> In particular, it requires the [[Kutta condition]] to be met, in which the rear stagnation point moves to the airfoil trailing edge and attaches there for the duration of flight. |
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The Kutta-Joukowski theorem is a key element in an explanation of lift that follows the development of the flow around an airfoil as the airfoil starts its motion from rest and a starting vortex is formed and left behind, leading to the formation of circulation around the airfoil.<ref>Prandtl and Tietjens (1934)</ref><ref>Batchelor (1967), Section 6.7</ref><ref>Gentry (2006)</ref> Lift is then inferred from the Kutta-Joukowski theorem. This explanation is largely mathematical, and its general progression is based on logical inference, not physical cause-and-effect.<ref>McLean (2012), Section 7.2.1</ref> |
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The Kutta-Joukowski model does not predict how much circulation or lift a given airfoil will produce. Calculating the lift from Kutta-Joukowski requires a known value for the circulation. |
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The circulation around a conventional airfoil, and hence the lift it generates, is dictated by both its design and the flight conditions, such as forward velocity and angle of attack. Lift can be increased by artificially increasing the circulation, for example by boundary-layer blowing or the use of [[blown flap]]s. In the [[Flettner rotor]] the entire airfoil is circular and spins about a spanwise axis to create the circulation. |
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==Three-dimensional flow== |
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[[Image:Wing isobars.jpg|thumb|right|300px|Cross-section of an airplane wing-body combination showing the isobars of the three-dimensional lifting flow.]] |
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[[Image:Wing velocity vectors.jpg|thumb|right|300px|Cross-section of an airplane wing-body combination showing velocity vectors of the three-dimensional lifting flow.]] |
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The flow around a real three-dimensional wing involves significant additional issues, especially relating to the wing tips. For a wing of low aspect ratio, such as a typical [[delta wing]], two-dimensional thories may provide a poor model and three-dimensional flow effects can dominate.<ref>Milne-Thomson (1966), Section 12.3</ref> Even for wings of high aspect ratio, the three-dimensional effects associated with finite span can affect the whole span, not just close to the tips. |
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===Wing tips and spanwise distribution=== |
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The vertical pressure gradient at the wing tips causes air to flow sideways, out from under the wing then up and back over the upper surface. This reduces the pressure gradient at the wing tip, therefore also reducing lift. The lift tends to decrease in the spanwise direction from root to tip, and the pressure distributions around the airfoil sections change accordingly in the spanwise direction. Pressure distributions in planes perpendicular to the flight direction tend to look like the illustration at right.<ref> McLean (2012), Section 8.1.3 </ref> This spanwise-varying pressure distribution is sustained by a mutual interaction with the velocity field. Flow below the wing is accelerated outboard, flow outboard of the tips is accelerated upward, and flow above the wing is accelerated inboard, which results in the flow pattern illustrated at right.<ref>McLean (2012), Section 8.1.1</ref> |
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There is more downward turning of the flow than there would be in a two-dimensional flow with the same airfoil shape and sectional lift, and a higher sectional angle of attack is required to achieve the same lift compared to a two-dimensional flow.<ref>Hurt, H. H. (1965) ''Aerodynamics for Naval Aviators'', Figure 1.30, NAVWEPS 00-80T-80</ref> The wing is effectively flying in a downdraft of its own making, as if the freestream flow were tilted downward, with the result that the total aerodynamic force vector is tilted backward slightly compared to what it would be in two dimensions. The additional backward component of the force vector is called [[lift-induced drag]]. |
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[[Image:Tip vortex rollup.png|thumb|300px|Euler computation of a tip vortex rolling up from the trailed vorticity sheet.]] |
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The difference in the spanwise component of velocity above and below the wing (between being in the inboard direction above and in the outboard direction below) persists at the trailing edge and into the wake downstream. After the flow leaves the trailing edge, this difference in velocity takes place across a relatively thin shear layer called a vortex sheet. |
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===Horseshoe vortex system=== |
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[[Image:Wing horseshoe vortex.jpg|thumb|right|300px|Planview of a wing showing the horseshoe vortex system.]] |
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The wing tip flow passing behind the wing creates a tip vortex. As the main vortex sheet passes downstream from the trailing edge, it rolls up at its outer edges, merging with the tip vortices. The combination of the wingtip vortices and the vortex sheets feeding them is called the vortex wake. |
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In addition to the vorticity in the trailing vortex wake there is vorticity in the wing's boundary layer, which is often called the bound vorticity and which connects the trailing sheets from the two sides of the wing into a vortex system in the general form of a horseshoe. The horseshoe form of the vortex system was recognized by the British aeronautical pioneer Lanchester in 1907.<ref>Lanchester (1907)</ref> |
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Given the distribution of bound vorticity and the vorticity in the wake, the [[Biot-Savart law]] (a vector-calculus relation) can be used to calculate the velocity perturbation anywhere in the field, caused by the lift on the wing. Approximate theories for the lift distribution and lift-induced drag of three-dimensional wings are based on such analysis applied to the wing's horseshoe vortex system.<ref>Milne-Thomson (1966), Section 10.1</ref><ref>Clancy (1975), Section 8.9</ref> In these theories, the bound vorticity is usually idealized and assumed to reside at the camber surface inside the wing. |
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Because the velocity is deduced from the vorticity in such theories, there is a tendency for some authors to describe the situation in terms that imply that the vorticity is the cause of the velocity perturbations, using terms such as "the velocity induced by the vortex," for example.<ref>Anderson (1991), Section 5.2</ref> But attributing mechanical cause-and-effect between the vorticity and the velocity in this way is not consistent with the physics. <ref>Batchelor (1967), Section 2.4</ref><ref>Milne-Thomson (1966), Section 9.3</ref><ref>Durand (1932), Section III.2</ref> The velocity perturbations in the flow around a wing are really caused by the pressure field.<ref>McLean (2012), Section 8.1</ref> |
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==Manifestations of lift in the farfield== |
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===Integrated force/momentum balance in lifting flows=== |
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[[File:Airfoil control volumes.jpg|thumb|400px|right|Control volumes of different shapes that have been used in analyzing the momentum balance in the 2D flow around a lifting airfoil. The airfoil is assumed to exert a downward force -L' per unit span on the air, and the proportions in which that force is manifested as momentum fluxes and pressure differences at the outer boundary are indicated for each different shape of control volume]] |
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The flow around a lifting airfoil must satisfy Newton's second law, or conservation of momentum, both locally at every point in the flow field, and in an integrated sense over any extended region of the flow. For an extended region, Newton's second law takes the form of the ''momentum theorem for a control volume'', where a [[control volume]] can be any region of the flow chosen for analysis. The momentum theorem states that the integrated force exerted at the boundaries of the control volume (a surface integral), is equal to the integrated time rate of change ([[material derivative]]) of the momentum of fluid parcels passing through the interior of the control volume. For a steady flow, this can be expressed in the form of the net surface integral of the flux of momentum through the boundary.<ref>Shapiro (1953), Section 1.5, equation 1.15</ref> |
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The lifting flow around a 2D airfoil is usually analyzed in a control volume that completely surrounds the airfoil, so that the inner boundary of the control volume is the airfoil surface, where the downward force per unit span <math>-L'</math> is exerted on the fluid by the airfoil. The outer boundary is usually either a large circle or a large rectangle. At this outer boundary distant from the airfoil, the velocity and pressure are well represented by the velocity and pressure associated with a uniform flow plus a vortex, and viscous stress is negligible, so that the only force that must be integrated over the outer boundary is the pressure.<ref name="Lissaman 1996">Lissaman (1996), Section titled "Lift in thin slices: the two dimensional case"</ref><ref name="Durand 1932">Durand (1932), Sections B. V. 6 and B. V. 7</ref><ref name="Batchelor 1967 p. 407">Batchelor (1967), Section 6.4, p. 407</ref> The free-stream velocity is usually assumed to be horizontal, with lift vertically upward, so that the vertical momentum is the component of interest. |
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For the free-air case (no ground plane), it is found that the force <math>-L'</math> exerted by the airfoil on the fluid is manifested partly as momentum fluxes and partly as pressure differences at the outer boundary, in proportions that depend on the shape of the outer boundary, as shown in the diagram at right. For a flat horizontal rectangle that is much longer than it is tall, the fluxes of vertical momentum through the front and back are negligible, and the lift is accounted for entirely by the integrated pressure differences on the top and bottom.<ref name="Lissaman 1996"/> For a square or circle, the momentum fluxes and pressure differences account for half the lift each.<ref name="Lissaman 1996"/><ref name="Durand 1932"/><ref name="Batchelor 1967 p. 407"/> For a vertical rectangle that is much taller than it is wide, the unbalanced pressure forces on the top and bottom are negligible, and lift is accounted for entirely by momentum fluxes, with a flux of upward momentum that enters the control volume through the front accounting for half the lift, and a flux of downward momentum that exits the control volume through the back accounting for the other half.<ref name="Lissaman 1996"/> |
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The results of all of the control-volume analyses described above are consistent with the Kutta-Joukowski theorem described above. Both the tall rectangle and circle control volumes have been used in derivations of the theorem.<ref name="Durand 1932"/><ref name="Batchelor 1967 p. 407"/> |
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===Lift reacted by overpressure on the ground under an airplane=== |
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[[File:Pressure footprint isometric b.jpg|thumb|400px|right|Illustration of the distribution of higher-than-ambient pressure on the ground under an airplane in flight]] |
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A lifting wing (or airfoil) always produces a pressure field in the surrounding air, as explained under "[[#The wider flow around the airfoil|The wider flow around the airfoil]]". The pressure differences associated with this field die off gradually with increasing distance from the wing, becoming very small at large distances, but never disappearing altogether. Below the airplane, the pressure field persists as a positive pressure disturbance that reaches all the way to the ground, forming a pattern of slightly-higher-than-ambient pressure on the ground, as shown on the right<ref>Prandtl and Tietjens (1934), Figure 150</ref>. Although the pressure differences are very small far below the airplane, they are spread over a wide area and add up to a substantial force. For steady, level flight, the integrated force due to the pressure differences is equal to the total aerodynamic lift of the airplane and to the airplane's weight. According to Newton's third law, this pressure force exerted on the ground by the air is matched by an equal-and-opposite upward force exerted on the air by the ground, which offsets all of the downward force exerted on the air by the airplane. The net force due to the lift, acting on the atmosphere as a whole, is therefore zero, and thus there is no integrated accumulation of vertical momentum in the atmosphere, as was noted by Lanchester early in the development of modern aerodynamics.<ref>Lanchester (1907), Sections 5 and 112</ref> |
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==See also== |
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{{div col|4}} |
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* [[Bilgeboard]] |
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* [[Boomerang]] |
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* [[Centerboard]] |
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* [[Circulation control wing]] |
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* [[Diving plane]] |
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* [[Downforce]] |
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* [[Drag coefficient]] |
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* [[Drag (physics)]] |
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* [[Fin]] |
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* [[Flipper (anatomy)]] |
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* [[Flow separation]] |
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* [[Fluid]] |
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* [[Fluid dynamics]] |
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* [[Foil (fluid mechanics)]] |
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* [[Formula One car]] |
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* [[Glider (aircraft)|Glider]] |
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* [[Hydrofoil]] |
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* [[Keel]] (hydrodynamic) |
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* [[Küssner effect]] |
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* [[Lift coefficient]] |
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* [[Lift-induced drag]] |
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* [[Lift-to-drag ratio]] |
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* [[Lifting-line theory]] |
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* [[Newton's laws of motion#Newton's third law|Newton's third law]] |
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* [[Propeller]] |
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* [[Sail]] (aerodynamics) |
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* [[Skeg]] |
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* [[Spoiler (automotive)]] |
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* [[Stall (fluid mechanics)]] |
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* ''[[Stick and Rudder]]'' |
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* [[Surfboard fin]] |
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* [[Wingtip vortices]] |
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{{div col end}} |
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==Footnotes== |
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{{reflist|30em}} |
{{reflist|30em}} |
||
== |
==External links== |
||
*[http://www.idintos.eu/ Seaplane based on the closed-system concept] |
|||
*{{Citation |last1=Abbott |first1=I. H. |last2=von Doenhoff |first2=A. E. |year=1958 |title=Theory of Wing Sections |publisher=Dover Publications}} |
|||
*[https://www.facebook.com/pages/PrandtlPlane/119452018086122 Facebook page on PrandtlPlane and Idintos (both closed-system concepts)] |
|||
*{{Citation |last1=Anderson |first1=D. F. |last2=Eberhardt |first2=S. |year=2001 |title=Understanding Flight |publisher=McGraw-Hill.}} |
|||
*[https://web.archive.org/web/20071113234733/http://aerodyn.org/Wings/noplane.html The aerodynamics of non-planar wing systems] |
|||
*{{Citation |last=Anderson |first=J. D. |year=1991 |title= Fundamentals of Aerodynamics, 2nd edition |publisher=McGraw-Hill}} |
|||
*[http://www.advanced-ac.de/ Student hosted research project at FH Aachen University of Applied Sciences] |
|||
*{{Citation |last=Anderson |first=J. D. |year=1995 |title=Computational Fluid Dynamics, The Basics With Applications |isbn=0-07-113210-4}} |
|||
*{{Citation |last=Anderson |first=J. D. |year=1997 |title=A History of Aerodynamics |publisher=Cambridge University Press}} |
|||
*{{Citation |last=Anderson |first=John D. |year=2004 |title=Introduction to Flight |edition=5th |publisher=McGraw-Hill |isbn=0-07-282569-3 |pages=352–361, §5.19}} |
|||
*{{Citation |last=Anderson |first=J. D. |year=2008 |title=Introduction to Flight, 6th edition |publisher=McGraw Hill}} |
|||
*{{Citation |last=Aris |first=R. |year=1989 |title=Vectors, Tensors, and the basic Equations of Fluid Mechanics |publisher=Dover Publications}} |
|||
*{{Citation |last=Auerbach |first=D. |year=2000 |title=Why Aircraft Fly |journal=Eur. J. Phys. |volume=21 |issue=4 |pages=289–296 |doi=10.1088/0143-0807/21/4/302 |bibcode=2000EJPh...21..289A}} |
|||
*{{Citation |last=Babinsky |first=H. |year=2003 |title=How do wings work? |journal=Phys. Educ. |volume=38 |page=497 |doi=10.1088/0031-9120/38/6/001|bibcode=2003PhyEd..38..497B }} |
|||
*{{Citation |last=Batchelor |first=G. K. |year=1967 |title=An Introduction to Fluid Dynamics |publisher=Cambridge University Press}} |
|||
*{{Citation |last=Clancy |first=L. J. |year=1975 |title=Aerodynamics |publisher=Longman Scientific and Technical}} |
|||
*{{Citation |last=Craig |first=G. M. |year=1997 |title=Stop Abusing Bernoulli |publisher=Anderson, Indiana: Regenerative Press}} |
|||
*{{Citation |last=Durand |first=W. F., ed. |year=1932 |title=Aerodynamic Theory, vol. 1 |publisher=Dover Publications}} |
|||
*{{Citation |last=Eastlake |first=C. N. |year=2002 |title=An Aerodynamicist’s View of Lift, Bernoulli, and Newton |journal=The Physics Teacher |volume=40 |doi=10.1119/1.1466553 |pages=166–173}} |
|||
*{{Citation |last=Jeans |first=J. |year=1967 |title=An Introduction to the Kinetic theory of Gasses |publisher=Cambridge University Press}} |
|||
*{{Citation |last=Kulfan |first=B. M. |year=2010 |title=Paleoaerodynamic Explorations Part I: Evolution of Biological and Technical Flight |publisher=AIAA 2010-154.}} |
|||
*{{Citation |last=Lanchester |first=F. W. |year=1907 |title=Aerodynamics |publisher=A. Constable and Company}} |
|||
*{{Citation |last=Langewiesche |first=W. |year=1944 |title= Stick and Rudder - An Explanation of the Art of Flying |publisher=McGraw-Hill}} |
|||
*{{Citation |last=Lissaman |first=P. B. S. |year=1996 |title=The facts of lift |publisher=AIAA 1996-161}} |
|||
*{{Citation |last=Marchai |first=C. A. |year=1985 |title=Sailing Theory and Practice |publisher=Putnam}} |
|||
*{{Citation |last=McBeath |first=S. |year=2006 |title=Competition Car Aerodynamics |publisher=Sparkford, Haynes}} |
|||
*{{Citation |last=McLean |first=D. |year=2012 |title=Understanding Aerodynamics - Arguing from the Real Physics |publisher=Wiley}} |
|||
*{{Citation |last=Milne-Thomson |first=L. M. |year=1966 |title=Theoretical Aerodynamics, 4th edition. |publisher=Dover Publications}} |
|||
*{{Citation |last1=Prandtl |first1=L. |last2=Tietjens |first2=O. G. |year=1934 |title=Applied Hydro- and Aeromechanics |publisher=Dover Publications}} |
|||
*{{Citation |last=Raskin |first=J. |year=1994 |title=Coanda Effect: Understanding Why Wings Work |url=http://jef.raskincenter.org/published/coanda_effect.html |archiveurl=https://web.archive.org/web/20070928072421/http://jef.raskincenter.org/published/coanda_effect.html |archivedate=September 28, 2007}} |
|||
*{{Citation |last=Schlichting |first=H. |year=1979 |title=Boundary-Layer Theory, Seventh Edition |publisher=McGraw-Hill}} |
|||
*{{Citation |last=Shapiro |first=A. H. |year=1953 |title=The Dynamics and Thermodynamics of Compressible Fluid Flow |publisher=Ronald Press Company}} |
|||
*{{Citation |last=Smith |first=N. 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 }} |
|||
*{{Citation |last=Spalart |first=P. R. |year=2000 |title=Strategies for turbulence modeling and simulations |publisher=International Journal of Heat and Fluid Flow |volume=21 |issue=3 |page=252}} |
|||
*{{Citation |last1=Sumer |first1=B. |last2=Mutlu; Fredsøe, Jørgen |first2=|year=2006 |title=Hydrodynamics around cylindrical structures (revised ed.) |publisher=}} |
|||
*{{Citation |last=Thwaites |first=B., ed. |year=1958 |title=Incompressible Aerodynamics |publisher=Dover Publications}} |
|||
*{{Citation |last=Tritton |first=D. J. |year=1980 |title=Physical Fluid Dynamics |publisher=Van Nostrand Reinhold}} |
|||
*{{Citation |last=Van Dyke |first=M. |year=1969 |title=Higher-Order Boundary-Layer Theory |journal=Annual Review of Fluid Mechanics |doi=10.1146/annurev.fl.01.010169.001405 |volume=1 |pages=265–292}} |
|||
*{{Citation |last=von Mises |first=R. |year=1959 |title=Theory of Flight |publisher=Dover Publications}} |
|||
*{{Citation |last=Waltham |first=C. |year=1998 |title=Flight without Bernoulli |journal=The Physics Teacher |volume=36 |doi=10.1119/1.879927 |pages=457–462}} |
|||
*{{Citation |last=Weltner |first=K. |year=1987 |title=A comparison of explanations of the aerodynamic lifting force |journal=Am. J. Phys. |volume=55 |page=53 |doi=10.1119/1.14960}} |
|||
*{{Citation |last=White |first=F. M. |year=1991 |title=. Viscous Fluid Flow, 2nd edition |publisher=McGraw-Hill}} |
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*{{Citation |last1=Wille |first1=R |last2=Fernholz |first2=H. |year=1965 |title=Report on the first European Mechanics Colloquium, on the Coanda effect |journal=J. Fluid Mech. |volume=23 |issue=4 |pages=801–819 |doi=10.1017/s0022112065001702 |bibcode=1965JFM....23..801W}} |
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*{{Citation |last1=Williamson |first1=C. H. K. |last2=Govardhan |first2=R |year=2004 |title=Vortex-induced vibrations |journal=Annual Review of Fluid Mechanics |volume=36 |pages=413–455 |bibcode=2004AnRFM..36..413W |doi=10.1146/annurev.fluid.36.050802.122128}} |
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*{{Citation |last=Zdravkovich |first=M. M. |year=2003 |title=Flow around circular cylinders 2 |publisher=Oxford University Press |pages=850–855 |isbn=0-19-856561-5}} |
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=== External media === |
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==Further reading== |
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*[https://web.archive.org/web/20071029132401/http://www.strange-mecha.com/aircraft/VTOL/model49aafss.jpg Convair Model 49 image] |
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{{refbegin|2}} |
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*[https://www.youtube.com/watch?v=Tg38zF4B-Lo#t=0m58s Amateur wind tunnel testing of planar and annular wings]—[[YouTube]] video |
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*''Introduction to Flight'', John D. Anderson, Jr., McGraw-Hill, {{ISBN|0-07-299071-6}} – The author is the Curator of Aerodynamics at the Smithsonian Institution's National Air & Space Museum and Professor Emeritus at the University of Maryland. |
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*''Understanding Flight'', by David Anderson and Scott Eberhardt, McGraw-Hill, {{ISBN|0-07-136377-7}} – The authors are a physicist and an aeronautical engineer. They explain flight in non-technical terms and specifically address the equal-transit-time myth. Turning of the flow around the wing is attributed to the Coanda effect, which is quite controversial. |
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* ''Aerodynamics'', Clancy, L. J. (1975), Section 4.8, Pitman Publishing Limited, London {{ISBN|0-273-01120-0}}. |
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* ''Aerodynamics, Aeronautics, and Flight Mechanics'', McCormick, Barnes W., (1979), Chapter 3, John Wiley & Sons, Inc., New York {{ISBN|0-471-03032-5}}. |
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*''Fundamentals of Flight'', Richard S. Shevell, Prentice-Hall International Editions, {{ISBN|0-13-332917-8}} – This book is primarily intended as a text for a one semester undergraduate course in mechanical or aeronautical engineering, although its sections on theory of flight are understandable with a passing knowledge of calculus and physics. |
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*"Observation of Perfect Potential Flow in Superfluid", Paul P. Craig and John R. Pellam (1957) ''Physical Review'' '''108'''(5), pp. 1109–1112, {{doi|10.1103/PhysRev.108.1109}} – Experiments under [[superfluidity]] conditions, resulting in the vanishing of lift in inviscid flow since the [[Kutta condition]] no longer is satisfied. |
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*"Aerodynamics at the Particle Level", Charles A. Crummer (2005, revised 2012) – A treatment of aerodynamics emphasizing the particle nature of air, as opposed to the fluid approximation commonly used. https://arxiv.org/pdf/nlin/0507032.pdf |
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*"Flight without Bernoulli" Chris Waltham Vol. 36, Nov. 1998 THE PHYSICS TEACHER – using a physical model relying only on Newton’s second law, the author presents a rigorous fluid dynamical treatment of flight. http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/fluids/fly_no_bernoulli.pdf |
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*''Bernoulli, Newton, and Dynamic Lift'' Norman F. Smith School Science and Mathematics vol 73 Part I: http://onlinelibrary.wiley.com/doi/10.1111/j.1949-8594.1973.tb09040.x/pdf Part II http://onlinelibrary.wiley.com/doi/10.1111/j.1949-8594.1973.tb08998.x/pdf |
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{{refend}} |
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==External links== |
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{{Wiktionary|lift}} |
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* [http://www.grc.nasa.gov/WWW/K-12/airplane/bernnew.html Discussion of the apparent "conflict" between the various explanations of lift] |
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* [http://www.grc.nasa.gov/WWW/K-12/airplane/lift1.html NASA tutorial, with animation, describing lift] |
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* [http://www.grc.nasa.gov/WWW/k-12/airplane/foil2.html NASA FoilSim II 1.5 beta. Lift simulator.] |
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* [http://www.diam.unige.it/~irro/ Explanation of Lift with animation of fluid flow around an airfoil] |
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* [http://www.av8n.com/how/ A treatment of why and how wings generate lift that focuses on pressure.] |
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* [http://user.uni-frankfurt.de/~weltner/ Physics of Flight – reviewed. Online paper by Prof. Dr. Klaus Weltner.] |
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* [http://www.iop.org/EJ/article/0031-9120/38/6/001/pe3_6_001.pdf How do Wings Work? – Holger Babinsky] |
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* [http://www.planeandpilotmag.com/component/zine/article/289.html Plane and Pilot Magazine Bernoulli Or Newton: Who's Right About Lift?] |
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* [https://www.youtube.com/watch?v=aFO4PBolwFg One Minute Physics How Does a Wing actually work? You Tube video] |
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* [https://www.zhaw.ch/de/forschung/personen-publikationen-projekte/detailansicht-publikation/publikation/212513/ From Summit to Seafloor - Lifted Weight as a Function of Altitude and Depth by Rolf Steinegger] |
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[[Category:Wing configurations]] |
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{{Use mdy dates|date=October 2011}} |
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[[Category:Aircraft wing design]] |
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Revision as of 23:52, 11 August 2018
A closed wing is a wing that effectively has two main planes which merge at their ends so that there are no conventional wing tips. Closed wing designs include the annular wing (commonly known as the cylindrical or ring wing), the joined wing, the box wing and spiroid tip devices.[1]
Like many wingtip devices, the closed wing aims to reduce the wasteful effects of wingtip vortices which occur at the tips of conventional wings. However such benefits are difficult to realize. Many closed wing designs do offer structural advantages over a conventional cantilever monoplane.
Characteristics
Wingtip vortices form a major component of wake turbulence and are associated with induced drag, which is a significant contributor to total drag in most regimes. A closed wing avoids the need for wingtips and thus might be expected to reduce wingtip drag effects.
In addition to potential structural advantages over open cantilevered wings, closed wing surfaces have some unique aerodynamic properties:
1) For a lifting system constrained to fit within a rectangular box of fixed horizontal (spanwise) and vertical dimensions as viewed in the freestream flow direction, the configuration that provides the absolute minimum induced drag for a given total vertical lift is a closed system, i.e. a rectangular boxplane with lifting surfaces fully occupying all four boundaries of the allowed rectangular area.[2] However, the induced-drag performance of the ideal closed boxplane can be approached very closely by open configurations such as the C-wing discussed below.[1]
2) For any lifting system (or portion of a lifting system) that forms a closed loop as viewed in the freestream flow direction, the optimum lift (or circulation) distribution that yields the minimum induced drag for a given total vertical lift is not unique on the closed-loop portion, but is defined only to within a constant. This is because, regardless of what the circulation distribution is to start with, a constant circulation can be added to the closed-loop portion without changing the total lift of the system or the induced drag.[1] This is the key to explaining how the C-wing produces nearly the same induced-drag reduction as the corresponding fully closed system, as discussed below.
The upshot is that although closed systems can produce large induced-drag reductions relative to a conventional planar wing, there is no significant aerodynamic advantage that uniquely accrues to their being closed rather than open.[1]
Configurations
Various types of closed wing have been described:
- Box wing
- Rhomboidal wing
- Flat annular wing
- Concentric wing and fuselage
History
Pioneer years
An early example of the closed wing was on the Blériot III aircraft, built in 1906 by Louis Blériot and Gabriel Voisin. The lifting surfaces comprised two annular wings mounted in tandem. The later Blériot IV replaced the forward annular wing with a biplane and added a canard foreplane to make it a three-surface aircraft. It was able to leave the ground in small hops before being damaged beyond repair.
Based on the work of G.J.A. Kitchen, Cedric Lee and G. Tilghman Richards built and flew several annular-wing aeroplanes in which the fore and aft segments were on the same level. The first was a biplane. It was followed by a series of monoplanes, the last of the line remaining in use until 1914.[3]
World War II
In 1944, the German designer Ernst Heinkel began working on an annular-wing VTOL multirole single-seater called the Lerche, but the project was soon abandoned.[citation needed]
Postwar
During the 1950s, the French company SNECMA developed the Coléoptère, a single-person VTOL annular wing aircraft. The aircraft proved dangerously unstable despite the development and testing of several prototypes, and the design was abandoned. Later proposals for closed-wing designs included the Convair Model 49 Advanced Aerial Fire Support System (AAFSS) and the 1980s Lockheed "Flying Bog Seat" concept.[citation needed]
Dr. Julian Wolkovitch continued to develop the idea in the 1980s, claiming it was an efficient structural arrangement in which the horizontal tail provided structural support for the wing as well as acting as a stabilizing surface.[4][5]
The Spiroid winglet, a design currently under development by Aviation Partners, is a closed wing surface mounted at the end of a conventional wing. The company announced that the winglets fitted to a Gulfstream II reduced fuel consumption in the cruise phase by over 10%.[6][7]
The Finnish company FlyNano flew a prototype of a closed wing ultralight aircraft, the FlyNano Nano on 11 June 2012.[8][9]
An aircraft was also designed and constructed with a closed wing in Belarus.[10]
Miscellaneous modern examples include:
- Stanford study[11]
- Lockheed Ringwing
Closed wings remain mostly confined to the realms of studies and conceptual designs, as the engineering challenges of developing a strong, self-supporting closed wing for use in the large airliners which would benefit most from increases in efficiency have yet to be overcome.
The closed wing is also used in water, for surfboard fins of the type also known as the tunnel fin.
Lockheed Martin Environmentally Responsible Aviation Project
During 2011, the Environmentally Responsible Aviation Project at NASA's Aeronautics Research Mission Directorate invited study proposals towards meeting NASA's goal of reducing future aircraft fuel consumption by 50% compared to 1998. Lockheed Martin proposed a box wing design along with other advanced technologies.[12][13]
Prandtl Box Wing
In 1924 the German aerodynamicist Ludwig Prandtl suggested that a box wing, under certain conditions, might provide the minimum induced drag for a given lift and wingspan.[14] In his design two offset horizontal wings have vertical wings connecting their tips and shaped to provide a linear distribution of side forces. The configuration is said to offer improved efficiency for a range of aircraft.
In the 1980s, the Ligeti Stratos used this approach.[15][16] The name "PrandtlPlane" was coined in the 1990s in research by Aldo Frediani et. al. of the University of Pisa.[17] It is currently also used in some ultralight aircraft,[18]
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IDINTOS[18] (IDrovolante INnovativo TOScano) is a research project, co-funded by the regional government of Tuscany (Italy) in 2011 in order to design and manufacture an amphibious ultralight PrandtlPlane. The research project has been carried out by a consortium of Tuscan public and private partners, led by the Aerospace Section of the Civil and Industrial Engineering Department of Pisa University, and has resulted in the manufacturing of a 2-seater VLA prototype.[19]
The configuration is also claimed to be theoretically efficient for wide-body jet airliners. The largest commercial airliner, the Airbus A380, must make efficiency trade-offs to keep the wingspan below the 80-meter limit at most airports, but a closed wing with optimal wingspan could be shorter than that of conventional designs, potentially allowing even larger aircraft to use the current infrastructure.[20]
C-wing
The C-wing is a theoretical configuration in which much of the upper centre section of a box wing is removed, creating a wing that folds up and over at the tips but does not rejoin in the centre. A C-wing can achieve very nearly the same induced-drag performance as a corresponding as a box wing, as shown by the calculations illustrated below.[21]
Each of the first three rows in the illustration shows a different C-wing configuration as it is taken through a sequence of theoretical induced-drag calculations in which the wingtips are brought closer together, culminating in the limiting case on the right, where the gap has been taken to zero and the configuration has become a closed box wing (referred to as the "Quasi-closed C-wing" because the calculations were carried out in the limit as the gap went to zero).
The parameter ε is the optimal aerodynamic efficiency ratio[citation needed] and represents the ratio between the aerodynamic efficiency of a given non-planar wing and the corresponding efficiency of a reference classical cantilevered wing with the same wing span and total lift. Both efficiencies are evaluated under their respective optimal conditions. Values of ε greater than 1 indicate lower induced drag than that of a classical cantilevered wing for which ε = 1.[citation needed]
Note that all of the C-wing configurations have ε greater then 1 and that there is little difference (no difference to the two decimal places shown in two of the cases) between a configuration with a substantial gap (the second entry in each row) and the corresponding closed configuration (the third entry in each row). This is because the optimum lift loading calculated for the quasi-closed cases is very small over the upper centre section, and that part of the wing can be removed with little change in lift or drag.
The lift distributions shown here for the quasi-closed cases look different from those typically shown for box wings in the classical literature (see Durand, figure 81, for example).[2] The classical solution in Durand was obtained by a conformal-mapping analysis that happened to be formulated in a way that led to equal upward loadings on the horizontal panels of the box. But the optimum loading is not unique.[1] A constant inward loading (corresponding to a constant circulation) can be added to a classical loading like that shown by Durand to obtain a loading like those in the quasi-closed cases below. The two methods of analysis give different-looking versions of the optimum loading that are not fundamentally different. Except for small differences due to the numerical method used for the quasi-closed cases, the two kinds of loading are in principle just shifted versions of each other.
References
- ^ a b c d e Kroo, I. (2005), "Nonplanar Wing Concepts For Increased Aircraft Efficiency", VKI lecture series on Innovative Configurations and Advanced Concepts for Future Civil Aircraft June 6–10, 2005
- ^ a b Durand, W. F., ed., "Aerodynamic Theory", Volume II, Julius Springer, 1935. Also New York, Dover Publications
- ^ Lewis, P.; British Aircraft 1809-1914, Putnam, 1962, pages 340-343,
- ^ "Future Technology and Aircraft Types". Adg.stanford.edu. Retrieved 2012-07-04.
- ^ Wolkovitch, Julian, The Joined Wing: An Overview[permanent dead link], AC A Industries, Inc., Torrance, California, 1985
- ^ "Blended Winglets and Spiroid Technology". aviationpartners.com. Retrieved 2009-09-25.
- ^ Gratzer 1999.
- ^ Grady, Mary (12 June 2012). "FlyNano Goes Electric, Starts "Airborne Test Flights"". AVweb. Retrieved 7 July 2012.
- ^ FlyNano (12 June 2012). "Airborne". Retrieved 7 July 2012.
- ^ "Planes with ellipse wings, creative oddity of the past". gizmowatch.com. Archived from the original on 2013-01-24. Retrieved 2010-01-06.
{{cite web}}: Unknown parameter|deadurl=ignored (|url-status=suggested) (help) - ^ "Nonplanar Wings: Closed Systems". Aero.stanford.edu. Retrieved 2012-07-04.
- ^ Barnstorff, Kathy (2012-01-27). "New Ideas Sharpen Focus for Greener Aircraft". www.nasa.gov website. NASA Langley Research Center. Retrieved December 17, 2012.
- ^ Rosenblum, Andrew; Pastore, Rose (2012-05-01). "The Jets of the Future". Popular Science magazine. Retrieved December 17, 2012.
- ^ Prandtl, L. "Induced Drag of Multiplanes", National Advisory Committee for Aeronautics, Technical note No. 182, from Technishe Berichte, Volume III, No. 7, 1924, pp. 309-315
- ^ Ligeti Stratos History (archived)
- ^ Ligeti Stratos joined wing aircraft (in French language)
- ^ Frediani A., "The Prandtl wing". VKI lecture series: Innovative Configurations and Advanced Concepts for Future Civil transport Aircraft, June 06–10, 2005
- ^ a b http://www.idintos.eu/
- ^ V. Cipolla, A. Frediani, F. Oliviero, M. Pinucci, E. Rizzo, R. Rossi . "Ultralight amphibious PrandtlPlane: the final design", Proceedings of Italian Association of Aeronautics and Astronautics XXII Conference, Naples (Italy), 2013.
- ^ Frediani A., Cipolla V., Rizzo E., "The PrandtlPlane Configuration: Overview on Possible Applications to Civil Aviation", Variational Analysis and Aerospace Engineering: Mathematical Challenges for Aerospace Design, Springer US, 2012, 66, 179-210
- ^ Demasi Luciano, Dipace Antonio, Monegato Giovanni, and Cavallaro Rauno; "An Invariant Formulation for the Minimum Induced Drag Conditions of Non-planar Wing Systems", AIAA Journal (2014), in press
External links
- Seaplane based on the closed-system concept
- Facebook page on PrandtlPlane and Idintos (both closed-system concepts)
- The aerodynamics of non-planar wing systems
- Student hosted research project at FH Aachen University of Applied Sciences
