万维百科

升力本文重定向自 升力

波音747正在利用空气产生的升力着陆。

升力英语:Lift)。当流体流经一个物体的表面时会对其产生一个表面力,而则这个力垂直于流体流向的分力即为升力,与之相对的则是平行于流体流向的阻力。如果流体是空气时,它产生的升力便叫做空气动力航空器要想升到空中,必须能产生能克服自身重力的升力。

升力主要是靠机翼对空气取得,飞机的机翼断面形状有很多种类,依照每种形状适用于不同功用的飞机,飞机的机翼从断面来看,通常机翼上半部曲面及下半部曲面不一样,通常为上半部曲面弧长较长,空气流经飞机机翼截面,因空气流过机翼表面时被一分为二,经过机翼上表面的空气是沿着曲线运动的(因为机翼上表面是弯曲的),所以会产生负压(负压提供空气沿曲线运动所需的向心力),而经过机翼下面的空气是沿着比较平缓的表面运动的(机翼下表面相对平直),所以不会产生负压(参见简化的物理解释),机翼下部压力高,上部压力小,压力高的地方会往压力低的部分移动,这就是升力的由来。

解释

升力取决于空气的密度,速度的平方,空气的黏性以及空气的可压缩性,空气流经物体的表面积,物体的形状,以及物体与气流的夹角。一般来说,升力与物体外形,气流夹角,空气的黏性,以及空气的可压缩性这几项的关联是非常复杂的。

升力,就是向上的力。从机翼流线谱中看出:相对气流稳定而连续地流过机翼时,上下表面的流线情况不同。上表面流线是弯曲的,其气会产生负压、因此压力小;而下表面流线较平直的,其气流不会产生负压,压力较大。因此,产生了上下压力差。这个压力差就是空气动力(R),它垂直流速方向的分力就是升力(Y)。流过各个剖面升力总合就是机翼的升力。升力维持飞机在空中飞行。

机翼升力的简化物理解释

机翼的横截面决定了机翼的形状。

机翼是流线型的,能够产生比阻力大得多的升力。平板可以产生升力,但其升力不如流线型机翼来得大,阻力也略高。

有几种方法可以解释机翼如何产生升力。某些方法较为严格复杂,有些则是错的。例如,基于牛顿运动定律的解释和基于伯努利原理的解释皆可以解释升力。

当机翼造成空气向下偏转,由于牛顿第三定律,空气必须对机翼施加相等的向上反作用力。

流体偏转及牛顿定律

气流经过机翼时,机翼会对空气施加向下的力,根据牛顿第三定律,空气必须对机翼施加大小相等、方向相反的反作用力,也就是方向朝上的升力。

气流在经过机翼时改变方向,沿着向下弯曲的路径流动。根据牛顿第二定律,这种流动方向的改变,需要机翼对空气施加向下的力。牛顿第三定律则要求空气对机翼施加向上的力; 因此产生了与方向变化相反的反作用力——升力。

气流之所以向下偏转,并非仅仅由机翼的下表面造成,机翼上方的气流也占了很大的因素。


流速增加及伯努利原理

伯努利原理指出,流体的压力和速度之间存在着直接的数学关系,因此,如果知道气流中每一点的速度,就可以计算出压力,反之亦然。对于任何产生升力的机翼,必然存在压力不平衡,即顶部的平均气压低于底部。伯努利原理指出,这种压力差必须伴随着速度差。

围绕机翼产生升力的流线和流管。注意上面较窄的流管和下面较宽的流管。

质量守恒

由理论和实验中观察到的流动型态,上表面流速增加的原因,可以用流管夹紧和质量守恒来解释。

对于不可压缩流,质量不会被创造或破坏,所以当流管变窄时,为了保持流量恒定,在每个流管内,体积流率(例如每分钟的体积单位)必须保持恒定,变窄区域内会增加流速,以满足质量守恒原理。

在机翼的情形,因为向上流动和围绕机翼,所以上部流管收缩。由于质量守恒,流速必须随着流管面积的减小而增大。同样,下部流管会膨胀,导致流速变慢。

根据伯努利原理,上表面流速较快,因此上表面压力小于流速较慢的下表面压力。这种压力差产生了向上的净空气动力。

简化解释的限制

产生升力需要维持垂直和水平方向上的压力差,故同时需要“气流的向下偏转”以及“符合伯努利原理的流速变化”。因此上述的简化解释不够完整,因为它们只根据其中一项来定义升力。根据细节,简化的解释还有其他缺陷。

基于流体偏转和牛顿定律的解释是正确的,但仍不完整。它并没有解释,机翼如何使比它实际碰触部分还远得多的流体也能产生偏转。此外,它也没有解释水平方向上的压力差是如何维持的。也就是说,它忽略了相互作用中“伯努利原理所影响的部分”。

而伯努利原理的解释,建立在上表面有更高的流速,但未能正确解释是什么导致了流速加快:

  • 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。

只考虑伯努利的解释意味着,速度差是由压力差以外的原因所引起,且根据伯努利原理,速度差会再导致压力差,但是这种隐含的单向因果关系是一种误解,压力和速度之间真正的因果关系是相互的。最后,只有伯努利的解释不能解释垂直方向上的压力差是如何维持的。也就是说,它们忽略了相互作用中向下偏转气流的部分。

替代解释、误解和争议

对于机翼升力的产生,人们提出了许多不同的解释,大多数是为了向大众解释升力现象。虽然这些解释可能与上述解释有共通点,但可能会引入额外的假设和简化。有一些解释引入了被证明是错误的假设,如“相同过境时间假设”。一些则是使用了有争议的术语,如“康达效应”。

基于相同过境时间的错误解释

在基础或常见的资料中,“等过境时间”理论经常用于描述升力,该理论错误地认为,在机翼前缘分离的气团必须在后缘重新汇合,迫使沿较长上表面飞行的空气速度更快。然后引用伯努利原理得出结论,沿着机翼底部移动的气流速度较慢,气压一定会更高,从而推动机翼上升。

然而,没有物理原理要求等过境时间这个条件成立,实验结果则表明该假设是错误的。事实上,机翼上方产生升力的空气运动速度比等过境理论预测的要快得多。此外,这个理论也违反了牛顿第三运动定律,因为它描述了作用在机翼上的力,却没有伴随着反作用力。

空气必须同时到达后缘的论断有时被称为“等时间谬论”。

机翼升力的错误解释,相同过境时间之插图。


康达效应之争议

起初,康达效应指的是,流体射流(jet)会维持“附着在偏离流体的相邻弯曲表面”的趋势,由此将环境空气卷入英语Entrainment (hydrodynamics)流体。 这种效应命名自罗马尼亚的空气动力学家康达(HenriCoandă),他在多项专利中充分应用了该效应。

更广泛地说,一些人认为,这种效应包括了任何“流体边界层会去附着在曲面上”的趋势,而不只是专用于流体射流的边界层。在这个更广泛的意义上,某些人用康达效应解释为何气流会维持在机翼上的附着状态。例如,Jef Raskin描述了一个简单的演示,用一根吸管吹气,使气流通过机翼的上表面,机翼因此向上偏转,从而证明康达效应能够产生升力。这个演示以流体喷射(吸管所排放的气流)紧临曲面(翼面),正确展示了康达效应。然而,上表面的气流是一个复杂的、充满涡流的混合层,而与此同时,下表面的气流却是静止的。因此,这个演示的物理性质与一般在机翼上的气流有很大的不同。这种用法在一些流行的空气动力学参考文献中也曾出现过,而这是对“康达效应”充满争议的用法。更公认的空气动力学领域观点是,康达效应被定义在比上述更受限的意义上,沿着上表面的气流只是反映出“缺乏了边界层的分离”; 因此它不是康达效应的一个例子。

基本的升力因素

压力差

攻角(迎角)

机翼形状

流况

边界层及机翼阻力

失速

钝体(阻流体)

更全面的物理解释

在“机翼升力的简化物理解释”中,有两种主要解释:一种是基于气流向下偏转(牛顿定律),另一种是基于压力差而伴随流速变化(伯努利原理)。这两种现像中的任何一种,都在一定程度上辨识了升力的面貌,但未解释其他重要部分。更全面的解释包括向下偏转和压力差(包括与压力差相关的流速变化),以及对气流更详细地研究。

机翼表面的升力

机翼形状和攻角共同作用,使机翼在气流经过时对空气施加向下的力。根据牛顿第三定律,空气必须对机翼施加一个大小相等、方向相反(向上)的力,也就是升力。

当机翼表面出现压力差,空气会对机翼表面施加净力。流体中的压力在绝对意义上总是正的,因此,必须把压力看作是推,而不是拉。因此,在机翼的任何地方,无论上表面或下表面,机翼会被压力往内推挤。为了对机翼的存在作出反应,气流通过时,会降低上表面压力以及增加下表面压力。因为向上推的下表面压力比向下推的上表面的压力来得大,最终的结果就是向上的升力。

压力差直接造成作用于机翼表面的升力; 然而,要理解压力差是如何产生的,就需要理解气流在更大范围内的作用。

机翼周围的更宽流动

围绕机翼的流动:圆点随着气流移动。黑点在时间片上,时间片在前缘分成上下两部分。动画中,上表面流线和下表面流线之间的速度差异最为明显,上表面流线早于下表面流线到达后缘。圆点的颜色表示流线。

机翼在大范围内影响气流的速度和方向,产生一种称为速度场的模式。当机翼产生升力,机翼前面的流体向上偏转,而机翼上方和下方气流向下偏转,机翼后方的气流则再次向上偏转,远抛在后的气流与迎面而来的气流处于相同的状态。机翼上方的气流加快,而机翼下方的气流减慢。加上前面空气向上偏转和后面空气向下偏转,这就构成了气流的净循环成分。向下偏转及流速变化明显,并延伸到一个很广的区域,正如右边的气流动画。气流方向和速度上的差异在靠近机翼处最大,在远高于和低于机翼的地方逐渐减小。速度场的所有这些特征也出现在升力气流的理论模型中。

压力也受到大面积的影响,形成一种称为压力场的非均匀压力模式。当机翼产生升力时,机翼上方有一个低压扩散区,机翼下方通常有一个高压扩散区,如图中的等压线(恒压曲线)所示。作用于表面的压力差只是这个压力场的一部分。

带有等压线之上升机翼周围的压力分布图。 正号表示压力高于环境压力,负号表示压力低于环境压力(不是绝对意义上负压)。 在流场的不同地方,方框箭头表示作用在流体粒子的净力方向。

压力差与流速变化的相互作用

不均匀的压力,在压力由高到低的方向上,对空气施力。 在机翼周围的不同位置,如在等压线图中箭头方向所示,力的方向是不同的。 机翼上方的空气被推向低压区域中心,机翼下方的空气则被从高压区域中心向外推送。

根据牛顿第二定律,空气朝受力方向加速。因此,在等压线图中,垂直箭头指出,机翼上下方的空气被加速或向下偏转,因此,在气流动画中,非均匀压力可能是可见气流向下偏转的原因。为了产生这种向下转弯,机翼必须有一个正攻角,或是其后部向下弯曲,就像带有拱形的机翼。注意,上表面的气流向下翻转,是由于上面压力大于下面压力而将空气向下推的结果。有些解释(请参阅“康达效应”)表明,对于向下偏转,粘度将起到关键的作用,不过这是错误的解释。(请参阅“康达效应之争议”)。

机翼前方的箭头,表示前方的气流向上偏转;后方的箭头则表示,机翼后方的气流会在向下偏转后,再次向上偏转。这些偏移可以在气流动画中看到。

机翼前方和后方的箭头也表明,当空气通过机翼上方的低压区,会在进入时加速,离开时减速。空气通过机翼下方的高压区时,则是相反的情况——它先是减速,然后加速。因此,非均匀压力也是气流动画中流速变化的原因。而流速变化与伯努利原理一致,伯努利原理认为在无粘性的稳定流动中,低压力意味着高速度,而高压力意味着低速度。

因此,流动方向和速度的变化是由非均匀压力直接引起的。但这种因果关系不仅是单向的,而是在两个方向上同时奏效。空气的运动受压力差的影响,但压力差的存在取决于空气的运动。因此,这种关系是一种互惠的相互作用:气流根据压差改变速度或方向,而压差是由空气对速度或方向变化的阻力维持的。只有当有东西可以推动时,压力差才会存在。在空气动力流动中,当空气因为压力差而加速时,压力差会推动空气的惯性。这就是为什么空气质量是计算的一部分,以及为什么升力取决于空气密度。

为了维持机翼表面升力所需的压力差,需要在机翼周遭的大范围内维持不均匀的压力模式。这就要求维持垂直和水平方向的压力差,既需要气流的向下偏转,也需要根据伯努利原理造成的流速变化。压力差与气流的方向和速度变化相互作用,相互支撑。压力差理所当然来自于牛顿第二定律,也来自于流体沿着机翼主要向下倾斜的轮廓流动这一事实。而空气具有质量这点,对相互作用也至关重要。

简化解释之不足

产生升力既需要流体向下偏转,又需要与伯努利原理一致的流速变化。上述简化物理解释中给出的任一解释,只用其中一种方式来解释升力,因此只能解释现象的一部分,而未解释剩下的部分。

量化升力

压力积分

当机翼表面上的压力分布已知时,确定总升力需要将表面局部元素对压力的贡献累加,每个元素具有其自身的局部压力值。因此,总升力是在垂直于远场流动的方向上在机翼表面上的压力的积分。

  • 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

升力取决于机翼的大小,大致与机翼面积成比例。通过量化升力系数给定机翼的升力通常很方便 ,它定义了机翼单位面积的整体升力。

对于特定迎角的机翼,特定流量条件下产生的升力:

  • 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
  • 是所需迎角、马赫数和雷诺数的升力系数

升力的数学理论

升力的数学理论建立在连续流体力学的基础上,该理论假设空气作为连续流体流动。升力的成因是根据物理学的基本原理,其中最相关的有以下三条原理:

  • 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。

因为机翼影响其周围广阔区域的流动,力学守恒定律以偏微分方程的形式体现,并结合一组边界条件,必须满足在机翼表面和远离机翼之条件。

要预测升力,需要通过计算流体动力学(CFD)的方法,求解特定机翼形状和流动条件的方程,这通常需要大量的计算,只有在计算机上才有办法实现。当CFD要决定净空气动力时,会由CFD决定出在所有表面元素的压力及剪切力,并对其导致的力作"压力积分"。

纳维-斯托克斯方程(NS)提供了可能最精确的升力理论,但实际上,在机翼表面边界层,捕捉湍流的影响需要牺牲一定的精度,并且需要使用雷诺平均纳维-斯托克斯方程(RANS)。此外,也发展了其他更简单但不太准确的理论。

纳维-斯托克斯方程

雷诺平均纳维-斯托克斯方程

无黏性流方程(欧拉或势)

线性化势流

循环与库塔-儒可夫斯基定理

三维流程

围绕三维机翼的流动还涉及其他重要问题,尤其是与翼尖有关的问题。对于低展弦比的机翼,如典型的三角翼,二维理论的模型可能较差,三维流动效应占了主导地位。即使对于高展弦比的机翼,有限翼展的三维效应也会影响整个翼展,而不会只靠近翼尖。

翼尖和翼展分布

马蹄形涡旋系统

相关

  • 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. ^ 23.0 23.1 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. ^ 48.0 48.1 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. ^ 49.0 49.1 Raskin, Jef, Coanda Effect: Understanding Why Wings Work, 1994 [2019-08-25], (原始内容存档于2007-09-28)
  50. ^ 50.0 50.1 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. ^ 59.0 59.1 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

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