# Equal transit time fallacy and Newton's laws of motion

I've seen the equal transit time theory being used to explain aerodynamic lift [basis is Bernoulli's principle] several times. However recently I've been told that there is NO physical compulsion for air above an aerofoil to have to travel across it at the same time as the air below the aerofoil.

There're quite a few questions on this site that deal with the fallacy but none [as far as I've seen] specifically mention WHAT PROBLEMS WOULD ONE ENCOUNTER BY ACCEPTING THE EQUAL TRANSIT THEORY.

I mean sure, plenty of sources bring up the concept of air parcels having been proved [by computer simulation] to travel FASTER above the aerofoil than below it, but I haven't come across any specific contradiction the equal transit theory would throw up.

Though I vaguely recall coming across some article that stated the equal transit time would violate Newton's laws of motion. If this is correct then WHICH law of motion would it violate and HOW would the law be violated?

If there's anything else [apart from the laws of motion] which contradict the equal transit theory, I'd love to hear it.

• Equal transit time is the worst explanation for lift ever... Sorry you had to encounter it! – tpg2114 Jun 30 '16 at 15:02
• Any explanation of lift that is not based on momentum conservation is simply false. That includes a naive use of Bernoulli which pretends that there is such a thing as "suction above the wing" while completely ignoring the really essential part of the flow under and behind the wing. – CuriousOne Jun 30 '16 at 15:55
• ^ I don't think Bernoulli's theorem disavows momentum conservation, though it doesn't specifically dwell on it.....also how does it "pretend" there's suction above the wing? As for flow BEHIND the wing, I've never really put much though into it, but I guess it does deserve some attention, thanks for pointing that out............ @CuriousOne – user122395 Jun 30 '16 at 16:04
• Bernoulli's Principle is an expression of energy conservation. Energy is not conserved in this case, to begin with and energy and momentum conservation are two completely different laws based on different spacetime symmetries. If you never put any thought into what happens behind the wing, then you never understood where lift comes from, I am afraid, and neither have the innumerable textbook authors who have been applying Bernoulli wrong for a century. – CuriousOne Jun 30 '16 at 16:10
• @AaronAbraham To head off the next possible question about "How can lift be generated in an inviscid fluid without violating conservation of energy," check out my answer here. Always remember -- any "model" for lift (Bernoulli, equal transit, bound vortex, etc etc) is a simplification for making the mathematics easier. They all neglect something, or many things, and they only stick around because they "work" within the limitations. – tpg2114 Jun 30 '16 at 17:29

Equal transit time would violate Newton's laws of motion in the sense that the computer simulations that are based on Newton's laws of motion show that equal transit time is false. I don't think you can show that using a simple heuristic argument or a simple equation, but the computer simulations do count as a valid proof, albeit perhaps not one you find satisfying. (Provided, of course, you've been careful to show that the error bars are small enough to rule out the possibility of equal transit time.)

In fact, I don't think that equal transit time does violate any of Newton's laws of motion in general, because if you make the airplane wing perfectly up-down symmetric then presumably it would be true. So it isn't physically impossible in general, it just happens to not be true in the vast majority of cases.

• Yes, but I'm really curious to know WHICH law of motion is violated and HOW. Thank you all the same though....... – user122395 Jun 30 '16 at 16:13
• @AaronAbraham I don't think there's a simple analytic answer to that. – tparker Jun 30 '16 at 16:24
• ^ Ouch.......thanks anyway though.... – user122395 Jun 30 '16 at 16:25
• @AaronAbraham I expanded on my answer – tparker Jun 30 '16 at 16:28
• "if you make the airplane wing perfectly up-down symmetric then presumably it would be true"- not so. Again - lift doesn't occur without circulation, and circulation is nothing more than top air getting to the trailing edge before bottom air. – Mike Dunlavey Jun 30 '16 at 16:35

As always, read John Denker's wonderful ebook.

To quickly answer the question, the equal-time argument is a wrong application of Bernoulli. Bernoulli is right. Bernoulli plus the Kutta condition (air can't flow up over the trailing edge) is what makes flight possible.

If one accepted the equal-time argument

• it would not explain how airplanes can fly inverted, or use symmetrical airfoils, as aerobatic aircraft do.

• @AaronAbraham: Bernoulli is nothing more than $F=ma$ (conservation of momentum) in a fluid. If there is lift, then there is higher pressure below and lower pressure above. Therefore airspeed is lower below and higher above, so the air above gets to the trailing edge first (even if the path above is longer). To a first approximation, the shape doesn't matter, as long as the trailing edge is sharp (so the air can't flow around to the top). The shape affects things like stall speed, drag, etc. If the air on top doesn't get to the back edge first - no circulation, no downwash, no lift. – Mike Dunlavey Jun 30 '16 at 20:55