Where did the false "equal transit-time" explanation of lift originate from?
关于升力“等时”错误解释的起源
History of Science and Mathematics
Where did the false "equal transit-time" explanation of lift originate from?
提问于 5 年前，8 个月前 修改于 昨天 浏览 1.2 万次
这个问题展示了研究的努力，它是有用且清晰的。
据称，一种“广泛流传”的错误观点是，机翼因其不对称形状而产生升力，迫使上方的空气更快地流动，以便它们在后缘与下方的空气同时汇合，并且根据 Bernoulli's equation，机翼下方的压力必然更高。
我只在它被揭穿时才遇到过这种“等时”理论，因此似乎更常见的是将其指出是错误的，而不是声称它是正确的。
这种不正确的理论是否曾经是一个常见的误解？ 这种误解是否源于特定的来源？
edited Aug 18, 2019 at 9:32
asked Aug 18, 2019 at 5:39
eugenhu
- If you've only encountered it when it's being debunked, then that is because of recent improvements in education. When I was at school this explanation was virtually always used, and every single time I wondered why the top parcel of air couldn't just travel at the same speed as the bottom one, which was never explained. – Robert Furber
- During grade school, which textbook was used in physics? Do you recall? Or even earlier, the "science" books? Examine their explanations of lifting-force. (The physics class might get it right, but all other books are typically promoting this "longer path" fallacy. – wbeaty
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This answer is useful 9 Klaus Weltner 和 Martin Ingelman-Sundberg (来自 Frankfurt 大学物理系) 在一篇最终未发表的论文 “Physics of Flight — reviewed” 中，提交给 2003 年的 European Journal of Physics，他们认为“等时”误解的最初来源，在某种程度上是不知不觉地，是空气动力学先驱 Ludwig Prandtl 大约在 1922 年。
他们的文章以 “Darstellung der Aerodynamik in Schulphysikbüchern” 的摘要开头，这是一本由 Klaus Niermann 于 1989 年出版的书：
Niermann 分析了过去一百年内出版的所有德语教科书，调查了空气动力升力的解释。 主要结果是，自 1920 年代以来，基于 Bernoulli's law 的解释占据主导地位。 他发现对当代美国和英国教科书的调查也是如此。
作者最终得出结论：
因此，路径长度推理的起源可能在于 Prandtl 在 1922 年给出的图表。
通过这张图，Prandtl 试图表明内层的空气粘附在表面上。 在一点上，这张图是不正确的。 它表明体积保持在相同的垂直位置，并且表明最初相邻的空气在翼型的末端再次相遇。 [...] 这种类型的图表可能会误导学者们得出这样的假设：相邻的空气在通过翼型后必须再次相遇。
文本说是 1922 年，这很可能指的是原始德语出版物，尽管作者引用的实际参考资料是美国国家航空咨询委员会制作的英文翻译，标题为 “Applications of Modern Hydrodynamics to Aeronautics” 并于 1923 年出版。
edited Aug 23, 2019 at 8:07
john-hen
This answer is useful 8
等时谬论的流行比从单一来源传播的错误更为复杂。 它很简单，直观上很有吸引力（经常会提到吹过翼型，以及围绕不对称机翼的流线的错误图片），并且可以快速完成工作。 就像地球与太阳之间距离变化解释季节一样，或者教科书中对历史的伪解释，例如对无理数发现的“危机”，或者 Maxwell's 为 Ampere's equation 添加额外项的“数学”原因。“真相就是有效的东西”。 Eastwell 在 Bernoulli? Perhaps, but What about Viscosity? 中列出了以下动机：
"• Simplified Bernoulli explanations are quick, sound logical, and make correct predictions. As Brusca (1986b) said with a sense of satisfaction, the prediction is “in complete agreement with what happens in practice” (p. 15). This would be fabulous if it wasn’t for the fact that these explanations are also wrong! • Statements like “as the speed of a moving fluid increases, the pressure within the fluid decreases” facilitate a misunderstanding of Bernoulli’s principle and, when used in a sweeping sense and therefore out of context, are wrong. • Viscosity, entrainment, and the Coanda effect are not to be found in lower-level literature, despite the fact that such literature deals with phenomena that rely on these concepts. • There appears to be a desire to have a single, best explanation for an observed behaviour when in fact a combination of factors may be “at play” "
这个谬论很可能是由多个教科书作者和物理老师独立重新发明的。 Norman Smith 是 1972 年第一个发出警报的人之一，他在 Bernoulli and Newton in Fluid Mechanics 中说：
"Millions of children in science classes are being... told that Bernoulli's theorem is responsible for lift on the airplane wing and for the force that makes a spinning baseball travel in a curved path. Unfortunately, the "dynamic lift" involved in each of these items is not properly explained by Bernoulli's theorem.
[...] 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 (or that the molecules must meet again) 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.
[...] The use of Bernoulli apparently began in this country some 30 years or more ago and has spread throughout school science books and popular literature to exclude virtually any mention of Newton and momentum. College-level aerodynamics textbooks generally do not use this approach, though it would not be surprising to find a few exceptions... It might be well to point out that the Bernoulli explanation is used mostly in the United States British, for example, seem to use Newton's third law in textbooks and popular literature ".
Eastwell 在 2007 年写道，情况并没有太大变化，如果不是更糟的话：
"Such a pressure difference is commonly justified, on the basis of Bernoulli's Principle, by statements such as “when air sweeps across a surface at high speed the pressure on that surface is lowered” (“Bernoulli Station,” 1989, p. 308) or “as the speed of a moving fluid increases, the pressure within the fluid decreases” (Mitchell, n.d., n. 1), or it is implied on this basis (e.g., Brusca, 1986b). This reasoning for the pressure difference, found not only in popular writings but also in specialist, peer-reviewed journals (e.g., see also Bauman & Schwaneberg, 1994; Holmes, 1996), is wrong."
现在甚至 Wikipedia 都有一个标题为 False explanation based on equal transit-time 的小节，也许潮流终于发生了转变。 并不是说使用 Bernoulli's equation 完全错误，而是它带有一些错误的附加组件。 正如 Beatty 在 Airfoil Lifting Force Misconception Widespread in K-6 Textbooks 中指出的那样：
"Air-deflection and Newton's Laws explain 100% of the lifting force. Air velocity and Bernoulli's equation also explains 100% of the lift. There is no 60% of one and 40% of the other. One of them looks at pressure forces, the other looks at F=ma accelerated mass. For the most part they're just two different ways of simplifying a single complicated subject. Much of the controversy arises because one side or the other insists that only their view is correct.
[...] Social psychology aside, there are also several serious mistakes usually associated with the "popular" explanation described above. Those who believe the "popular" explanation are wrongly insisting that any parcels of air divided by the wing's leading edge must meet again at the trailing edge. This is incorrect. Actually it doesn't even occur: experiments easily show that the air above a wing far outraces the air below, and parcels never meet again. (In fact, if a wing is adjusted so the parcels really do merge, this is always the zero-lift configuration!) The same people also believe that wings fly only because of pressure, and that wings don't need to deflect the oncoming air downwards. Also incorrect. These and several other mistakes commonly appear in elementary science texts, as well as in popular articles about aircraft physics. These mistakes change the popular "airfoil-shape" explanation into a system of misconceptions. "
edited Aug 19, 2019 at 3:28
This answer is useful 5
不对称形状（而不是其用“等时”的解释！）来自解释升力的第一个数学理论 (Chaplygin's formula，西方称为“Blasius theorem”)。 我认为“相等时间”的理论是在试图向非数学家解释 Chaplygin-Joukowski 理论时发展起来的 :-)
在某些情况下，该理论与实验非常吻合。 由于迄今为止不存在完整的数学理论，因此该主题向所有关于“是什么导致升力”的推测开放。 反对“不对称理论”的一个合理的论点是，飞机可以倒飞 :-)
answered Aug 18, 2019 at 18:54
Alexandre Eremenko
This answer is useful 4
这种解释可能已经被多次独立地“重新发现”，并且不太可能指出特定的起源。
Ackroyd 在 'Babinsky's Demonstration: The Theory of Flight and Its Historical Background' (Journal of Aeronautical History, 2015) 中说：
想象一下两个相邻的空气元素 ... A 和 B ... 即将到达翼型的前缘。 元素 A 从翼型上方通过，而元素 B 从下方通过。 最终，元素 A 到达翼型的尾部或后缘，并且根据此论点，元素 B 必须同时到达尾部，以便恢复其与元素 A 相邻的位置…… 这种有缺陷的飞行解释得以幸存，并且仍然广受欢迎，这可能是因为它具有简单性。 它的起源现在似乎消失在时间的迷雾中，尽管它在机组人员培训手册中的使用可能为它赢得了普及，并扩展到了学校教科书，甚至是偶尔的英国 A Level 考试试卷。
一些来源说，这种解释有时用于飞行训练手册中。
以上解释非常广泛。 它可以在许多教科书中找到，据我所知，它也用于 RAF 的教学手册中。
来源：Holger Babinsky (2003). How do wings work?. Phys. Educ. Vol. 38. p.498. 访问：http://www3.eng.cam.ac.uk/outreach/Project-resources/Wind-turbine/howwingswork.pdf
Ballow 在谈到他作为 Nevada Air National Guard 成员从 Air Force 训练手册中学习的经验时说：
培训涵盖了 Air Force 培训手册中概述和解释的飞行理论 [...] 升力是由空气流过机翼产生的。 由于机翼的上表面是弯曲的，而下表面是直的，因此流过机翼上表面的空气必须行进更远的距离，因此它会变薄。
来源：Tom Ballow (2005). The New Science of Flight and Movement. p.13. 访问：https://books.google.com.au/books?id=Wba1JfqHmDYC&pg=PA13
r/flying subreddit 上的讨论：
DPE used the 'equal transit time theory' of lift as the correct way to explain lift. What do?
Aviation Stack Exchange 上的帖子：
Why is the wrong explanation of “air travels a longer distance and creates a lift” so popular?
Principle of aerodynamic lift: are misconceptions also taught in flight schools?
以下是一些使用“等时”参数的具体实例。
具有攻角的叶片顶部上的距离大于转子叶片底部表面上的距离。 经过顶部的空气分子必须比经过底部的空气分子移动得更快，才能同时在后缘相遇。
来源：Federal Aviation Administration (2012). Helicopter Instructor's Handbook, Chapter 3 Aerodynamics of Flight. p.2. 访问：https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/media/FAA-H-8083-4.pdf
机翼的形状看起来像一个侧卧的细长水滴…… 通常顶部比底部弯曲更多，使得上表面比底部稍长。 由于经过顶部和底部的空气必须同时到达机翼的后部，因此经过顶部的空气不仅必须移动得更快，而且还会改变方向并向下偏转。
来源：DoD 101 - An Introduction to the Military, Aircraft for Amateurs 访问：https://fas.org/man/dod-101/sys/ac/intro.htm
以下示例来自较旧的期刊论文。
这种粒子在“形状”顶侧的加速将加快上层空气粒子朝向后缘的速度，以便使它们与其紧邻的底侧相邻，它们在引导边缘处分开。 因此，粒子对一起撞击前缘，分开，但仍然一起到达后缘 - 尽管顶部粒子必须移动得更快才能做到这一点。
来源：Norwood Russell Hanson (1965). Aristotle (And Others) on Motion through Air. The Review of Metaphysics, Vol. 19, No. 1. 链接：https://www.jstor.org/stable/20124101
如果我们考虑一个机翼穿过静止的空气，那么空气的主要影响是向下的推力。 为了近似这是唯一的净效应，通过机翼上方和下方所需的时间是相同的。 因此，上方的空气必须移动得更快（相对于机翼），才能跟上较低的流线。
来源：Robert P. Bauman and Rolf Schwaneberg (1994). Interpretation of Bernoulli’s equation. The Physics Teacher Vol. 32. p.485. 链接：https://aapt.scitation.org/doi/pdf/10.1119/1.2344087
至于为什么曾经需要调用“等时”。
我找不到任何物理上的理由，也许它的表面直观性源于与某种连续性方程/条件混淆，几乎好像在引导边缘处分离的空气包裹必须在后缘重新连接，否则会“积聚空气”在路径较长的一侧（当然，避免这种情况不需要“等时”要求）。 这个 Quora 问题似乎表明存在一些与此相关的困惑：Why continuity equation must be followed by aerofoil?
edited Aug 23, 2019 at 5:21
eugenhu
This answer is useful 4
"Hat der Körper eine gleichmäßige Geschwindigkeit in ruhender Luft, so wird auch in der den Körper umgebenden Luft eine gleichmäßige Bewegung eintreten, die im wesentlichen darin besteht, daß die Luft vor dem Körper sich auseinander thut und hinter dem Körper wieder zusammengeht."
Otto Lilienthal 1889
翻译为
"如果身体在静止的空气中具有恒定的速度，那么在围绕身体的空气中也会产生均匀的运动，这主要包括空气从身体分离并在身体后面再次汇合。"
answered May 3, 2020 at 9:53
Ortac
This answer is useful 4
在您提出这个问题大约两年后，UNSW Canberra 的航空高级讲师 Graham Wild 在 arXiv 的物理教育部分发布了一篇预印本，试图回答这个问题：[2110.00690] On the Origins and Relevance of the Equal Transit Time Fallacy to Explain Lift. 他将这种误解追溯到 1744 年的 D'Alembert，他只是 假设 等时 (ETT)。 后来的工作（1752 年）旨在从应用于流体的 Newton's laws 中推导出 ETT 属性。 欧拉在 1757 年随后（错误地）证实了这种不正确的推导，从而赋予了它权威性。 ETT 结果确实适用于潜在流，但此类流不会产生升力。 Wild 的论文（我尚未完全消化）讨论了 ETT 是否可以在帮助理解升力的起源方面发挥作用，并将其作为一个悬而未决的问题。
edited yesterday
answered Nov 3, 2021 at 6:21
