升力
参考资料

↑  . NASA Glenn Research Center.   [2009-03-04]. （原始内容存档于2009-03-09）.
↑  ,谢础，贾玉红，黄俊，吴永康. . 北京航空航天大学出版社. 2008: 3. ISBN 978-7-81124-428-1.
↑  . NASA.   [2015-02-06]. （原始内容存档于2015-02-16） （英语）.
↑  Clancy, L. J., Aerodynamics, Section 5.2
↑  "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 .   [2012-04-20]. （原始内容存档于2014-04-27）.
↑  "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 p. 300  （页面存档备份，存于）
↑  "One explanation of how a wing . . 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  (PDF).   [2011-07-12]. （原始内容 (PDF)存档于2011-07-07）.
↑  "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 January 1, 1987
↑  "The lift on the body is simple...it's the reaction 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 .   [2012-07-26]. （原始内容存档于2012-04-27）.
↑  "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  (PDF).   [2009-09-10]. （原始内容存档 (PDF)于2009-04-11）.
↑  Ison, David, , Plane & Pilot,   [2011-01-14], （原始内容存档于2015-09-24）
↑  "...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: Halliday, David; Resnick, Robert, , John Wiley & Sons: 378
↑  Anderson and Eberhardt (2001)
↑  Langewiesche (1944)
↑  "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: Morwood, John, , Adlard Coles Limited: 17
↑  "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." . NASA Glenn Research Center.   [2009-07-07]. （原始内容存档于2011-07-05）.
↑  "Essentially, due to the presence of the wing (its shape and inclination to the incoming flow, the so-called angle of attack), the flow is given a downward deflection. It is Newton’s third law at work here, with the flow then exerting a reaction force on the wing in an upward direction, thus generating lift." Vassilis Spathopoulos - Flight Physics for Beginners: Simple Examples of Applying Newton’s Laws The Physics Teacher Vol. 49, September 2011 p. 373
↑  "The main fact of all heavier-than-air flight is this: the wing keeps the airplane up by pushing the air down." In: Langewiesche - Stick and Rudder, p. 6
↑  "Birds and aircraft fly because they are constantly pushing air downwards: L = Δp/Δt where L= lift force, and Δp/Δt is the rate at which downward momentum is imparted to the airflow." Flight without Bernoulli Chris Waltham THE PHYSICS TEACHER Vol. 36, Nov. 1998  (PDF).   [2011-08-04]. （原始内容存档 (PDF)于2011-09-28）.
↑  Clancy, L. J.; Aerodynamics, Pitman 1975, p. 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."
↑  "...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: Flift = m∆v/∆t = ∆(mv)/∆t. The lift force is equal to the time rate of change of momentum of the air." Smith, Norman F. . The Physics Teacher. 1972, 10 (8): 451. Bibcode:1972PhTea..10..451S. doi:10.1119/1.2352317.
↑  Smith, Norman F. . School Science and Mathematics. 1973, 73 (3): 181. doi:10.1111/j.1949-8594.1973.tb08998.x.
1 2  Anderson (2004) - Section 5.19.
↑  "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  (PDF).   [2009-09-10]. （原始内容存档 (PDF)于2009-04-11）.
↑  McLean 2012, Section 7.3.3.12
↑  "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 p. 378
↑  "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 p. 3  (PDF).   [2012-07-26]. （原始内容 (PDF)存档于2013-12-07）.
↑  "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 .   [2016-01-26]. （原始内容存档于2016-01-26）.
↑  "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 .   [2012-07-26]. （原始内容存档于2012-07-17）.
↑  "A concept...uses a symmetrical convergent-divergent channel, like a longitudinal section of a Venturi tube, as the starting point . . when such a device is put in a flow, the static pressure in the tube decreases. When the upper half of the tube is removed, a geometry resembling the airfoil is left, and suction is still maintained on top of it. Of course, this explanation is flawed too, because the geometry change affects the whole flowfield and there is no physics involved in the description." Jaakko Hoffren Quest for an Improved Explanation of Lift Section 4.3 American Institute of Aeronautics and Astronautics 2001  (PDF).   [2012-07-26]. （原始内容 (PDF)存档于2013-12-07）.
↑  "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  (PDF).   [2009-09-10]. （原始内容存档 (PDF)于2009-04-11）.
↑  "This classic explanation is based on the difference of streaming velocities caused by the airfoil. There remains, however, a question: How does the airfoil cause the difference in streaming velocities? Some books don't give any answer, while others just stress the picture of the streamlines, saying the airfoil reduces the separations of the streamlines at the upper side. They do not say how the airfoil manages to do this. Thus this is not a sufficient answer." Klaus Weltner Bernoulli's Law and Aerodynamic Lifting Force The Physics Teacher February 1990 p. 84.  [永久]
↑  McLean 2012, Section 7.3.3.12
↑  "The airfoil of the airplane wing, according to the textbook explanation that is more or less standard in the United States, has a special shape with more curvature on top than on the bottom; consequently, the air must travel farther over the top surface than over the bottom surface. Because the air must make the trip over the top and bottom surfaces in the same elapsed time ..., the velocity over the top surface will be greater than over the bottom. According to Bernoulli's theorem, this velocity difference produces a pressure difference which is lift." Bernoulli and Newton in Fluid Mechanics Norman F. Smith The Physics Teacher November 1972 Volume 10, Issue 8, p. 451  [永久]
↑  "Unfortunately, this explanation [fails] on three counts. First, an airfoil need not have more curvature on its top than on its bottom. Airplanes can and do fly with perfectly symmetrical airfoils; that is with airfoils that have the same curvature top and bottom. Second, even if a humped-up (cambered) shape is used, the claim that the air must traverse the curved top surface in the same time as it does the flat bottom surface...is fictional. We can quote no physical law that tells us this. Third—and this is the most serious—the common textbook explanation, and the diagrams that accompany it, describe a force on the wing with no net disturbance to the airstream. This constitutes a violation of Newton's third law." Bernoulli and Newton in Fluid Mechanics Norman F. Smith The Physics Teacher November 1972 Volume 10, Issue 8, p. 451 .   [2011-08-04]. （原始内容存档于2012-03-17）.
↑  Anderson, David, , New York: McGraw-Hill: 15, 2001, ISBN 978-0-07-136377-8, The first thing that is wrong is that the principle of equal transit times is not true for a wing with lift.
↑  Anderson, John. . Boston: McGraw-Hill Higher Education. 2005: 355. ISBN 978-0072825695. 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
↑  .   [2012-06-10]. （原始内容存档于2012-06-30）.  Cambridge scientist debunks flying myth UK Telegraph 24 January 2012
↑  . National Committee for Fluid Mechanics Films/Educational Development Center.   [2009-01-21]. （原始内容存档于2016-10-21）.  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.
↑  "...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 PDF （页面存档备份，存于）
↑  "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." Glenn Research Center. . NASA. 2006-03-15  [2010-08-12]. （原始内容存档于2014-04-27）.
↑  "...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, March 1973 Smith, Norman F. . School Science and Mathematics. 1972-11-30  [2015-01-19]. （原始内容存档于2015-01-19）.
↑  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. It has recently been dubbed the "Equal transit-time fallacy"..   [2009-07-07]. （原始内容存档于2009-06-03）.
↑  ...it leaves the impression that Professor Bernoulli is somehow to blame for the "equal transit time" fallacy... John S. Denker. . 1999  [2009-07-07]. （原始内容存档于2009-11-20）.
↑  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. Gale M. Craig. .   [2009-07-07]. （原始内容存档于2009-08-02）.
↑  Fallacy 1: Air takes the same time to move across the top of an aerofoil as across the bottom. Peter Eastwell,  (PDF), The Science Education Review, 2007, 6 (1)  [2009-07-14], （原始内容存档 (PDF)于2009-11-28）
↑  "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
1 2  Anderson, David; Eberhart, Scott, , 1999  [2008-06-04], （原始内容存档于2016-01-26）
1 2  Raskin, Jef, , 1994  [2019-08-25], （原始内容存档于2007-09-28）
1 2  Auerbach, David, , Eur. J. Phys., 2000, 21 (4): 289, Bibcode:2000EJPh...21..289A, doi:10.1088/0143-0807/21/4/302
↑  Denker, JS, ,   [2008-08-18], （原始内容存档于2009-03-02）
↑  Wille, R.; Fernholz, H., , J. Fluid Mech., 1965, 23 (4): 801, Bibcode:1965JFM....23..801W, doi:10.1017/S0022112065001702
↑  Auerbach (2000)
↑  Denker (1996)
↑  Wille and Fernholz(1965)
↑  White, Frank M.,  5th, McGraw Hill, 2002
↑  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: Batchelor, G.K., , Cambridge University Press: 14–15, 1967, ISBN 978-0-521-66396-0
↑  "...if a streamline is curved, there must be a pressure gradient across the streamline..."Babinsky, Holger, , Physics Education, November 2003, 38 (6): 497, Bibcode:2003PhyEd..38..497B, S2CID 1657792, doi:10.1088/0031-9120/38/6/001
↑  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, p. 53  （页面存档备份，存于）
↑  "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 Dept. of Physics and Astronomy .   [26 July 2012]. （原始内容存档于October 14, 2012）.
↑  "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 p. 52
↑  "The decrease[d lift] 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 p. 52
↑  Clancy (1975), Section 5.2
↑  Abbott, and von Doenhoff (1958), Section 4.2
↑  "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
↑  "...the important thing about an aerofoil . . 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
↑  "It requires adjustment of the angle of attack, but as clearly demonstrated in almost every air show, it can be done." Hyperphysics GSU Dept. of Physics and Astronomy  的存檔，存档日期July 8, 2012，.
↑  White (1991), Section 1-4
↑  White (1991), Section 1-2
↑  Anderson (1991), Chapter 17
↑  Anderson (1991), Chapter 17
↑  Abbott and von Doenhoff (1958), Chapter 5
↑  Abbott and von Doenhoff (1958), Chapter 5
↑  Schlichting (1979), Chapter XXIV
↑  Abbott and Doenhoff (1958), Chapter 8
↑  Williamson, C. H. K.; Govardhan, R., , Annual Review of Fluid Mechanics, 2004, 36: 413–455, Bibcode:2004AnRFM..36..413W, S2CID 58937745, doi:10.1146/annurev.fluid.36.050802.122128
↑  Sumer, B. Mutlu; Fredsøe, Jørgen,  revised, World Scientific: 6–13, 42–45 & 50–52, 2006, ISBN 978-981-270-039-1
↑  Zdravkovich, M.M.,  2, Oxford University Press: 850–855, 2003, ISBN 978-0-19-856561-1
↑  Williamson, C. H. K.; Govardhan, R., , Annual Review of Fluid Mechanics, 2004, 36: 413–455, Bibcode:2004AnRFM..36..413W, S2CID 58937745, doi:10.1146/annurev.fluid.36.050802.122128
↑  Clancy, L. J., Aerodynamics, Sections 4.5, 4.6
↑  McLean (2012), Section 7.3.3
↑  Langewiesche (1944)
1 2  Milne-Thomson (1966), Section 1.41
↑  Jeans (1967), Section 33.
↑  McLean 2012, Section 7.3.3.7
↑  Clancy (1975), Section 4.5
↑  Milne-Thomson (1966.), Section 5.31
↑  McLean (2012), Section 3.5
↑  McLean 2012, Section 7.3.3.9"
↑  McLean 2012, Section 7.3.3.9
↑  McLean 2012, Section 7.3.3.12
↑  Anderson (2008), Section 5.7
↑  Anderson, John D.,  5th, McGraw-Hill: 257, 2004, ISBN 978-0-07-282569-5
↑  Batchelor (1967), Section 1.2
↑  Thwaites (1958), Section I.2
↑  von Mises (1959), Section I.1
↑  "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  (PDF).   [2009-09-10]. （原始内容存档 (PDF)于2009-04-11）.
↑  White (1991), Chapter 1
↑  Batchelor (1967), Chapter 3
1 2  Aris (1989)
↑  Spalart (2000) Amsterdam, The Netherlands. Elsevier Science Publishers.
↑  White (1991), Section 6-2
↑  Schlichting(1979), Chapter XVIII
↑  Anderson (1995)
↑  "...whenever the velocity field is irrotational, it can be expressed as the gradient of a scalar function we 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 . . 2012: 13. ISBN 9781118454190. doi:10.1002/9781118454190.ch3.
↑  Elements of Potential Flow California State University Los Angeles .   [26 July 2012]. （原始内容存档于November 11, 2012）.
↑  Batchelor(1967), Section 2.7
↑  Milne-Thomson(1966), Section 3.31
↑  Clancy (1975), Section 4.8
↑  Anderson(1991), Section 4.5
↑  Clancy(1975), Sections 8.1–8
↑  Clancy (1975), Section 4.5
↑  von Mises (1959), Section VIII.2
↑  Anderson(1991), Section 3.15
↑  Prandtl and Tietjens (1934)
↑  Batchelor (1967), Section 6.7
↑  Gentry (2006)
↑  McLean (2012), Section 7.2.1
↑  Milne-Thomson (1966), Section 12.3
↑  McLean (2012), Section 8.1.3
↑  McLean (2012), Section 8.1.1
↑  Hurt, H. H. (1965) Aerodynamics for Naval Aviators, Figure 1.30, NAVWEPS 00-80T-80
↑  Lanchester (1907)
↑  Milne-Thomson (1966), Section 10.1
↑  Clancy (1975), Section 8.9
↑  Anderson (1991), Section 5.2
↑  Batchelor (1967), Section 2.4
↑  Milne-Thomson (1966), Section 9.3
↑  Durand (1932), Section III.2
↑  McLean (2012), Section 8.1
翼形的橫截面決定了翼形的形狀。
當翼形造成空氣向下偏轉，由於牛頓第三定律，空氣必須對翼形施加相等的向上反作用力。
圍繞翼形產生升力的流線和流管。注意上面較窄的流管和下面較寬的流管。
翼形升力的錯誤解釋，相同過境時間之插圖。
翼型的攻角
對稱翼型與有弧度翼形之比較
大攻角情形，氣流從機翼分離
圍繞翼形的流動:圓點隨著氣流移動。黑點在時間片上，時間片在前緣分成上下兩部分。動畫中，上表面流線和下表面流線之間的速度差異最為明顯，上表面流線早於下表面流線到達後緣。圓點的顏色表示流線。
帶有等壓線之上升翼形周圍的壓力分佈圖。 正號表示壓力高於環境壓力，負號表示壓力低於環境壓力（不是絕對意義上負壓）。 在流場的不同地方，方框箭頭表示作用在流體粒子的淨力方向。
圍繞機翼的無升力流型；以及符合庫塔條件的有升力流型之比較，後者氣流平穩地離開後緣
翼型周圍流動的環量
飛機機翼-機身組合的橫截面，顯示三維升力流的等壓線
飛機機翼-機身組合的橫截面，顯示三維升力流的速度向量
以歐拉法計算尾部渦流面捲起所形成的翼尖渦流
顯示馬蹄形渦流系統的機翼平面圖