升力本文重定向自 升力

机翼升力的简化物理解释

简化解释的限制

• 质量守恒的解释建立于上表面流管会变窄，但这并不能解释为什么流管会改变尺寸。要知道为什么空气会这样流动需要更复杂的分析。
• 有时，人们会提出一个几何参数来说明为什么流管的尺寸会发生变化：有人断言，与底部相比，顶部“阻碍”或“压缩”空气的程度更大，因此流管更窄。对于底部平、顶部弯的传统机翼情形，这感觉是直观的。但它并没有解释平板、对称机翼、帆船帆布或倒飞的传统机翼是如何产生升力的，基于收缩量计算升力的尝试也无法预测实验结果。
• 常见的等过境时间版本是错误的，解释见下文。

量化升力

压力积分

${\displaystyle L=\oint p\mathbf {n} \cdot \mathbf {k} d\mathbf {S} }$

• S是机翼的投影（平面形状）区域，测量值与平均气流垂直;
• n是指向机翼的正常单位矢量;
• k是垂直单位向量、垂直于自由流方向。

升力系数

${\displaystyle L={\frac {1}{2}}\rho v^{2}SC_{L}}$

• L是升力
• ρ是空气密度
• v是速度或真实空速
• S是翼面俯视面积
• ${\displaystyle C_{L}}$是所需迎角、马赫数和雷诺数的升力系数

升力的数学理论

• 动量守恒，这是牛顿运动定律的结果，尤其是牛顿第二定律，将空气中的合力和动量时变率联系起来。
• 质量守恒，包括机翼表面不被周围流动的空气所渗透的假设。
• 能量守恒，也就是说能量既不会被创造也不会被破坏。

• 爬升英语Climb

参考资料

1. ^ What is Lift?. NASA Glenn Research Center. [2009-03-04]. （原始内容存档于2009-03-09）.
2. ^ ,谢础，贾玉红，黄俊，吴永康. 航空航天技术概论（第2版）. 北京航空航天大学出版社. 2008: 3. ISBN 978-7-81124-428-1.
3. ^ Forces in a Climb. NASA. [2015-02-06]. （原始内容存档于2015-02-16） （英语）.
4. ^ Clancy, L. J., Aerodynamics, Section 5.2
5. ^ "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 Archived copy. [2012-04-20]. （原始内容存档于2014-04-27）.
6. ^ "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 [1]页面存档备份，存于互联网档案馆
7. ^ "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 Archived copy (PDF). [2011-07-12]. （原始内容 (PDF)存档于2011-07-07）.
8. ^ "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
9. ^ "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 Archived copy - Tom Benson Interview. [2012-07-26]. （原始内容存档于2012-04-27）.
10. ^ "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 Archived copy (PDF). [2009-09-10]. （原始内容存档 (PDF)于2009-04-11）.
11. ^ Ison, David, Bernoulli Or Newton: Who's Right About Lift?, Plane & Pilot, [2011-01-14], （原始内容存档于2015-09-24）
12. ^ "...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, Fundamentals of Physics 3rd Ed., John Wiley & Sons: 378
13. ^ Anderson and Eberhardt (2001)
14. ^ Langewiesche (1944)
15. ^ "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, Sailing Aerodynamics, Adlard Coles Limited: 17
16. ^ "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." Lift from Flow Turning. NASA Glenn Research Center. [2009-07-07]. （原始内容存档于2011-07-05）.
17. ^ "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 [2]
18. ^ "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
19. ^ "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 Archived copy (PDF). [2011-08-04]. （原始内容存档 (PDF)于2011-09-28）.
20. ^ 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."
21. ^ "...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. Bernoulli and Newton in Fluid Mechanics. The Physics Teacher. 1972, 10 (8): 451. Bibcode:1972PhTea..10..451S. doi:10.1119/1.2352317.
22. ^ Smith, Norman F. Bernoulli, Newton and Dynamic Lift Part I. School Science and Mathematics. 1973, 73 (3): 181. doi:10.1111/j.1949-8594.1973.tb08998.x.
23. Anderson (2004) - Section 5.19.
24. ^ "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 Archived copy (PDF). [2009-09-10]. （原始内容存档 (PDF)于2009-04-11）.
25. ^ McLean 2012, Section 7.3.3.12
26. ^ "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
27. ^ "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 Archived copy (PDF). [2012-07-26]. （原始内容 (PDF)存档于2013-12-07）.
28. ^ "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 Archived copy. [2016-01-26]. （原始内容存档于2016-01-26）.
29. ^ "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 Archived copy. [2012-07-26]. （原始内容存档于2012-07-17）.
30. ^ "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 Archived copy (PDF). [2012-07-26]. （原始内容 (PDF)存档于2013-12-07）.
31. ^ "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 Archived copy (PDF). [2009-09-10]. （原始内容存档 (PDF)于2009-04-11）.
32. ^ "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. [3][永久失效链接]
33. ^ McLean 2012, Section 7.3.3.12
34. ^ "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 [4][永久失效链接]
35. ^ "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 Archived copy. [2011-08-04]. （原始内容存档于2012-03-17）.
36. ^ Anderson, David, Understanding Flight, 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.
37. ^ Anderson, John. Introduction to Flight. 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
38. ^ Archived copy. [2012-06-10]. （原始内容存档于2012-06-30）. Cambridge scientist debunks flying myth UK Telegraph 24 January 2012
39. ^ Flow Visualization. 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.
40. ^ "...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，存于互联网档案馆
41. ^ "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. Incorrect Lift Theory. NASA. 2006-03-15 [2010-08-12]. （原始内容存档于2014-04-27）.
42. ^ "...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. Bernoulli, Newton, and Dynamic Lift, Part I. Bernoulli's Theorem: Paradox or Physical Law?. School Science and Mathematics. 1972-11-30 [2015-01-19]. （原始内容存档于2015-01-19）.
43. ^ 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".Fixed-wing aircraft facts and how aircraft fly. [2009-07-07]. （原始内容存档于2009-06-03）.
44. ^ ...it leaves the impression that Professor Bernoulli is somehow to blame for the "equal transit time" fallacy... John S. Denker. Critique of "How Airplanes Fly". 1999 [2009-07-07]. （原始内容存档于2009-11-20）.
45. ^ 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. Physical principles of winged flight. [2009-07-07]. （原始内容存档于2009-08-02）.
46. ^ Fallacy 1: Air takes the same time to move across the top of an aerofoil as across the bottom. Peter Eastwell, Bernoulli? Perhaps, but What About Viscosity? (PDF), The Science Education Review, 2007, 6 (1) [2009-07-14], （原始内容存档 (PDF)于2009-11-28）
47. ^ "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
48. Anderson, David; Eberhart, Scott, How Airplanes Fly: A Physical Description of Lift, 1999 [2008-06-04], （原始内容存档于2016-01-26）
49. Raskin, Jef, Coanda Effect: Understanding Why Wings Work, 1994 [2019-08-25], （原始内容存档于2007-09-28）
50. Auerbach, David, Why Aircraft Fly, Eur. J. Phys., 2000, 21 (4): 289, Bibcode:2000EJPh...21..289A, doi:10.1088/0143-0807/21/4/302
51. ^ Denker, JS, Fallacious Model of Lift Production, [2008-08-18], （原始内容存档于2009-03-02）
52. ^ Wille, R.; Fernholz, H., Report on the first European Mechanics Colloquium, on the Coanda effect, J. Fluid Mech., 1965, 23 (4): 801, Bibcode:1965JFM....23..801W, doi:10.1017/S0022112065001702
53. ^ Auerbach (2000)
54. ^ Denker (1996)
55. ^ Wille and Fernholz(1965)
56. ^ White, Frank M., Fluid Mechanics 5th, McGraw Hill, 2002
57. ^ McLean (2012), Section 7.3.3
58. ^ Langewiesche (1944)
59. Milne-Thomson (1966), Section 1.41
60. ^ Jeans (1967), Section 33.
61. ^ McLean 2012, Section 7.3.3.7
62. ^ Clancy (1975), Section 4.5
63. ^ Milne-Thomson (1966.), Section 5.31
64. ^ McLean (2012), Section 3.5
65. ^ McLean 2012, Section 7.3.3.9"
66. ^ McLean 2012, Section 7.3.3.9
67. ^ McLean 2012, Section 7.3.3.12
68. ^ Anderson (2008), Section 5.7
69. ^ Anderson, John D., Introduction to Flight 5th, McGraw-Hill: 257, 2004, ISBN 978-0-07-282569-5
70. ^ Batchelor (1967), Section 1.2
71. ^ Thwaites (1958), Section I.2
72. ^ von Mises (1959), Section I.1
73. ^ "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 Archived copy (PDF). [2009-09-10]. （原始内容存档 (PDF)于2009-04-11）.
74. ^ White (1991), Chapter 1
75. ^ Milne-Thomson (1966), Section 12.3