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Describing lift as the result of "equal transit time" on both sides of an airfoil is a fallacious theory widely found in technical books and articles for general public (see below for details about this explanation).

But such explanation is also found in aviation books, in spite being identified by NASA as an incorrect theory (NASA explains that if lift is computed from fluid laws, based on airspeed on both sides of the airfoil, the result will not be in line with what is observed in real life).

Question

Is this very popular theory also taught this way in flight schools? (please note the question is about pilot teaching, not about what is lift.)

Annex: Popular explanation of lift from equal transit time:

Supporters of this theory explain aerodynamic lift results from the differential of pressure between lower and upper sides of a wing created by Bernoulli principle. They say:

  • Air has to move a longer distance on the upper side because of the curve of the profile (not correct for all wing profiles).

  • Both sides must be traveled in an equal amount of time so that air molecules that were nearby ahead of the wing, will meet again behind it (may be right or wrong.)

    enter image description here

  • By Bernoulli's principle accelerated airflow has lower pressure. Pressure is then lower on top of the wing, and higher on bottom. Hence the wing receives a force which has a vertical component upward. This component balances the weight of the aircraft, and allows to stay aloft.

mins
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    this is well discussed over on the physics.SE: http://physics.stackexchange.com/questions/290/what-really-allows-airplanes-to-fly – ratchet freak Aug 21 '14 at 19:19
  • Very good. I'm adding this reference to the question section. Note the question is about what is taught at flying school. – mins Aug 21 '14 at 19:30
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    The See How It Flies explains physics relevant for flying aircraft, including lift and it is targeted specifically at aviators. – Jan Hudec Aug 21 '14 at 21:18
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    The "Bernoulli vs Newton" is the biggest nonsense. The actual answer is "Bernoulli and Newton" and it's actually Newton's first law (inertia of the stream is needed get stall in the picture). – Jan Hudec Aug 22 '14 at 07:48
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    @JanHudec: "Bernoulli vs Newton" retrieves more results from Google, this was the point. The 3 laws of motion seem to apply in lift generation. Air downwash is balanced by lift, according to 3rd law (see this slide for clarity). – mins Aug 22 '14 at 15:43
  • @mins: It might retrieve more results, question is whether they are more correct results. Of course the downwash is balanced by lift and vice versa by 3rd law, but it does not explain why the wing produces downwash in the first place. For that you need to consider inertia of the air flowing along the oblique surface and leaving the trailing edge (the first law) and Bernoulli's equation to calculate the pressure field. And by then the math becomes pretty complicated and has numerical solution only. – Jan Hudec Aug 22 '14 at 15:54
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    Newton's law explains why pushing the air down pushes the aircraft up. It doesn't explain why the air gets pushed down in the first place. – user253751 Apr 02 '15 at 06:27
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    Conversely, Bernoulli's law explains why the air goes down, but not why the aircraft goes up. – user253751 Apr 02 '15 at 06:28
  • @immibis : The Bernoulli explanation, at least as it is usually presented (changes in airflow speed create changes in pressure) doesn't explain why the airflow speed changes. 'Equal transit time' is an incorrect attempt to explain that. Bernoulli's law does not even explain the relationship between pressure and speed; it asserts it as a fact. Any causal explanation for that fact starts from Newtonian mechanics. – sdenham Jun 24 '15 at 13:45
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    @JanHudec : I have no problem with Bernoulli's law being included in an explanation, but the fact is that Newton explains Bernoulli, and not the other way round. As I implied in my reply to immibis, if you start from Bernoulli, you reach the point where you need to explain why the airflow velocity changes, and that has been the point of introduction of many falsehoods, including the 'equal transit time' fallacy. – sdenham Jun 24 '15 at 13:53
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    @sdenham: I agree. – Jan Hudec Jun 24 '15 at 20:22
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    Note that as stated, lift from downwash is perfectly valid and true—the laws of motion do hold there. The common fallacy is imagining the air particles reflecting of the underside of the wing like balls bouncing off a wall. Which at crude approximation works for explaining post-stall lift, but does nothing to explain why the air above the wing is also deflected. Unfortunately explaining that is rather difficult (you have to bring in inertia and viscosity and bunch of other stuff). – Jan Hudec Feb 06 '17 at 18:46
  • "are misconceptions also taught in flight school": Of course they are. It wouldn't be a flight school if it didn't teach misconceptions. – quiet flyer May 08 '19 at 22:09
  • @quietflyer: You probably didn't get the meaning of this question. I was not asking if misconceptions are mentioned and identified as such, but if they are used and identified as correct theories. – mins May 08 '19 at 22:15

4 Answers4

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I am a CFI who teaches at a large (+200 students) flight school in the United States. You might be surprised to hear this, but...

We really don't worry about how a wing works that much.

As far as I'm concerned, the technical explanation for how a wing works is a subject for the engineers who build and design such things. Private pilot applicants (at least all of the ones that I have met) are more concerned with things like "How do I get the plane into the air??" and "What do I do if it starts coming back down again in a hurry?"

In fact, Van Sickle's Modern Airmanship starts off the chapter on aerodynamics by saying (paraphrased):

Some of the concepts presented in this chapter are wrong, but they are useful illustrations.

So, to answer your question, we teach that:

  1. The alignment of the wing to the relative wind displaces air downward, which creates lift.
  2. Because of the shape of the airfoil, air on top of the wing has a lower pressure than air below the wing, which also causes lift.

And unless a student asks us for more information, we leave it at that.

If you hope to become an aircraft designer or research fluid dynamics, you'll quickly be corrected of any misconceptions you may have about Mr. Bernoulli and his asymmetric wing. Most student pilots, however, are satisfied with a pre-discussion "What we'll talk about today isn't technically correct, but you'll find it a lot easier to understand the necessary concepts this way."

Peter Kämpf made a worthwhile comment:

It is really not so hard to understand aerodynamics correctly, and you make it sound as if you prefer a short term gain over a profound basis which could help pilots to really understand what happens with their plane and to select the most appropriate action.

Which is very true - it's not difficult to understand aerodynamics correctly. I'll defend my viewpoint with an analogy: Consider a store where you are shopping with a child who doesn't yet understand decimal addition. You have two purchases, one costing $5.08 and one costing $3.99. The child adds the big numbers and tells you that the final price will be $8. You now have (at least) two choices: you could begin a discussion of significant figures and fractional multiplication (can't forget tax!), or you could praise the child for applying the skills they do have and getting an answer which is pretty close.

Is it better if the child eventually understands how to calculate tax rather than simply trusting what the cashier reads off the screen? Of course. But at the stage where most of my students are, it's much more valuable to their development as pilots to simply praise them for being close enough.

As regards JAL123, I am in 100% agreement with you. By the time you as a pilot have progressed sufficiently in your development to be flying something with a turbine pushing it, you should certainly know the principles and concepts of your machine to the highest degree of accuracy.

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Steve V.
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    It is really not so hard to understand aerodynamics correctly, and you make it sound as if you prefer a short term gain over a profound basis which could help pilots to really understand what happens with their plane and to select the most appropriate action. – Peter Kämpf Aug 22 '14 at 06:58
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    @PeterKämpf: It depends on which level of understanding you need. For pilot it's enough to know that the lift is proportional to square of indicated speed and angle of attack until some point where it decreases abruptly because stall happens. The common explanations don't help that, because they don't explain stall; I'd say just showing pictures of the streamlines should be enough. – Jan Hudec Aug 22 '14 at 07:41
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    JanHudec: Consider JAL123 - if the pilot had had a basic understanding of flight mechanics (and the influence of altitude on his brain functions), this accident could probably have been avoided. The plane was still somewhat controllable, flying on for one hour after the loss of most of its vertical tail. BTW: Stall is not the only thing a pilot needs to understand. But if he/she doesn't even have a basic grasp of aerodynamics, he/she is just a glorified bus driver. – Peter Kämpf Aug 22 '14 at 08:50
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    @PeterKämpf even though no-one in sim was able to do better than the crew[1]? – ratchet freak Aug 22 '14 at 10:21
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    @ratchet freak: A B-52H could be brought down safely in 1964 after losing its vertical tail. But the pilots used a different strategy, knowing that flying low improves directional stability. The Japanese crew was totally overwhelmed, and I think the other crews in the simulator were at the same level of education. Japanese education prefers rote learning, but if there is no procedure, they have no means of developing a new, successful strategy. – Peter Kämpf Aug 22 '14 at 11:54
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    @PeterKämpf that B52 still have aileron+elevator control; while JAL123 didn't (only engine diff-thrust) – ratchet freak Aug 22 '14 at 12:01
  • @ratchetfreak: ... and elevator trim. How else could they compensate for the missing mass of the vertical? Admitted, the plane was marginally flyable, but at the chosen altitude less than at lower altitude. That is my main point - the pilots did not know how to help themselves. – Peter Kämpf Aug 22 '14 at 13:54
  • @PeterKämpf - I've expanded my answer to take into account your excellent comments. Thanks very much! – Steve V. Aug 22 '14 at 13:55
  • @SteveV. Are you sure 2nd and 3rd links are correct? How do I get the plane into the air?? is linked to Money; and What do I do if it starts coming back down again in a hurry? is to Control.Unload Event. – Farhan Aug 22 '14 at 14:06
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    @Farhan - Those are the intended link targets. "What makes an airplane fly? Money." is a well known joke among aviators in the USA, and "Unload for control" is a method of upset recovery. – Steve V. Aug 22 '14 at 14:09
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    @SteveV. Got it. I heard about the money relation with airplane flying but wasn't too sure if many pilots are .NET programmers in their free time. – Farhan Aug 22 '14 at 14:27
  • B-52H link by @Peter Kämpf went bad, I found good link here: B52-H landed with no tail – Peter M. - stands for Monica Oct 13 '15 at 16:45
  • @ratchetfreak In case you're interested, I notice that on 2 June 2017, for some reason, someone saw fit to delete the story about the simulations from the Wikipedia page you linked: https://en.wikipedia.org/w/index.php?title=Japan_Airlines_Flight_123&type=revision&diff=783502803&oldid=783497475 – David K Dec 25 '17 at 23:30
  • Something is bad with you links - e. g. your 2nd link "How do I get the plane into the air??" points to Money in Wikipedia, and your 3rd link, What do I do if it starts coming back down again in a hurry? points to Microsoft .NET Framework function :-( – MarianD May 08 '19 at 20:21
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I can only speak on behalf of the Australian Syllabus as put out by CASA (Civil Aviation Safety Authority - Australia), but we are expected to teach both Bernoulli's Theorem, and the Theorem of Air Deflection (I believe this is the second theory you are talking about in regards to Newton's Laws).

BUT, we are also expected to teach these items as theories, not laws, as there is no law on the creation of lift. So to a degree, you could say we do teach misconceptions, but also at the same time we openly acknowledge those misconceptions to those we are teaching.

The other part we openly admit is that both theories have merit to at least help understand certain important characteristics of Aerodynamics in-flight, great example is a stall. We have the Centre of Pressure that moves further forward along the Wing Chord as the Angle of Attack is increased, due to the "peak" of dynamic air pressure being more forward along the wing chord. At the "Critical Angle" in is at its most forward position. As soon as we exceed the Critical Angle, the wing is stalled and instantaneously, the Centre of Pressure moves aft along the chord line to a position approximately half way along the chord due to Bernoulli's theorem no longer having the principle effect on our wing. Now the theorem of air deflection takes over, and we look at using the "hand out the window of a moving car" analogy.

James Ham
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    Could you make it clearer what you're referring to when you say Bernoulli's Theorem and teach these items as theories, not laws? Bernoulli's Principle (an increase in fluid speed means a decrease in fluid pressure) simply describes a physical reality; it's not really a theory. – Steve V. Aug 22 '14 at 03:41
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    @SteveV. - The theorem is how this applies to an aircraft Aerofoil, as there is not a physical venturie. The principle is solid, and at no stage in doubt, but how this applies to a wing, and the overall production of Lift is still only a Theorem. As for your answer below, this may be the case with the FAA syllabus, but other countries, such as Australia, it is a requirement that all PPL applicants have a basic understanding of how Lift is generated, and for CPL applicants, there must be a good understanding of how Lift is generated (at least the Theorems associated). – James Ham Aug 22 '14 at 05:07
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    You seem to misunderstand what a theorem is (it's a proven result of mathematics) and what a scientific theory is (it's an experimentally verified explanation of how the world works). A scientific "law" is just a scientific theory that is so old and famous that it has a fancier name. To say "we teach these as theories not laws" is a huge misunderstanding of what science is. – David Richerby Aug 22 '14 at 07:13
  • And a "law" doesn't even mean it's more complete or accurate than a "theory." Consider the law of gravity, which has been superseded by the theory of relativity. – yshavit Oct 07 '15 at 15:41
  • By "Bernoulli's Theorem", do you mean equal transit time or something else (because Bernoulli's theorem obviously holds around the wing; it just leaves too many free variables and fixing them by assuming equal transit time is the error)? And by "Theorem of Air Deflection" do you mean the reflecting bullets or something else (because air is deflected downwards; it is just the idea that it is because the particles hit the underside and reflect like balls bouncing off a wall that is wrong)? If you mean these, how do you explain stall? If you don't, please clarify what you mean. – Jan Hudec Feb 06 '17 at 18:37
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I was taught at Civil Air Patrol flight school in 1958 that the Bernoulli effect was the only way that a wing generates lift. I don't remember what our textbook was except that it was also used by the USAF. Our instructors obviously felt that this fact was not vital, and it appeared on no exams. As Steve V. says, we really didn't worry about how a wing works.

A model airplane builder in our town flew a craft that was nothing more than a flat metal disk plus an engine, rudder, and elevons. It had a very long takeoff roll and was a beast to fly, but it was clearly flying the wing and not just hanging on its prop. It was, in fact, a 25" enameled steel Texaco Gas sign. No Bernoulli effect was possible.

Also, we had seen many technical drawings of early Wright, Santos-Dumont, and Curtis aircraft, all with flat or curved wings of constant thickness over practically the whole chord. Clearly these aircraft did not generate a Bernoulli differential. We had lots of evidence that Bernoulli was not necessary for heavier-than-air flight.

So I would say that this misconception was taught in some flight schools in 1958, but it did little actual harm. Students who wanted to just fly ignored it and got on with just flying. Students who were interested in aeronautical science already knew not to accept any such simple explanation where fluid dynamics is concerned.

A. I. Breveleri
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  • The whole 1990s controversy started because Dr. Klaus Weltner tried to get the "transit time" stuff removed from European cert. exams. Also I note that thin flat "barn doors" fly entirely by Bernoulli Effect. See JS Denker's physics page, showing that the air flows much faster over the top than the bottom. http://www.av8n.com/how/htm/airfoils.html#sec-circulation (And, "Bernoulli Explanation" is not about camber, or about thick wings. The Wright Flyer had canvas wings where the upper and lower paths were the same, yet still the air flowed much faster over the top.) – wbeaty Nov 03 '23 at 07:35
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I would like to add my $.02 to this question. Lift is defined (in the aerodynamic texts) as the upward component of the force that the air exerts on the wing. The force is composed of the tangential (sheer) forces that tend to contribute mostly to drag, as well as the pressure (normal) forces that tend to contribute to lift. As for designing the most efficient wing, the answer is trial and error. Hundreds of different mathematically-defined airfoils are put into a wind tunnel and their lift and drag coefficients are measured. They are then published in a book like this one for future aerospace engineers to decide which airfoil best suits their purpose. The question as to why the pressure happens to be lower on the top compared to the bottom of the wing is not really that important. Heaps of empirical data show that it is the observed phenomena, and we work with it from there, as unsatisfying as that may be.

Greg
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    I beg to differ! Empirical work is needed in fields like medicine where we understand too little to make logical conclusions, but aerodynamics is really well understood so deductive reasoning gets you to the best result more quickly. Also, you fail to answer the original question, which is whether wrong concepts are still taught in flight school. Maybe you want to add to your answer in order to improve it. – Peter Kämpf Aug 23 '14 at 10:23
  • I agree that aerodynamics is well understood, but just because it is well understood does not mean that you do not benefit immensely from empirical data. As for the original question, the way I learned it is that air flows faster over the top, leading to less pressure, leading to an upward 'pull' on the wing. The curvature of the wing allows for this to happen. As for Bernoulli/Newton, etc, they dont seem to describe this relationship between wing shape and lift, which is why it is unsatisfying for me. OTOH the lift coeff, which seems to relate the 2, is found mainly through empirical tests. – Greg Aug 23 '14 at 11:19
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    I agree that having looked at a lot of empirical data will give you an intuitive "feel" for what is right. But not understanding the underlying physics behind it robs you of the capability to extend this knowledge to new situations. Then you are in a similar position to a pilot trained in Japan: You are excellent at performing well-trained procedures, but if something happens which you did not train in advance, you are helpless. – Peter Kämpf Aug 23 '14 at 11:25
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    The actual question is "Is it taught this way in flight schools". This answer doesn't seem to address the question. – Steve V. Aug 23 '14 at 13:06