Aerodynamic lift

Thanks for a very cogent article on aerodynamic lift. Among many articles on this subject, mine is on ArXiV. (In order to see the animation, download the entire .zip file and compile the .tex with pdflatex.) I humbly submit that Bernoulli’s equation is not applicable because the conditions for its applicability are not met on or around an airfoil. Your description of the cause of the Coanda effect and its accompanying pressure decrease on a surface curving away from the flow seems to me to be very clear. The pressure profile around a wing is shown in John D. Anderson’s “Introduction to Flight” and was measured independently also by Tilman Buntz for Marco Colombini for their research at the University of Genoa (see ). The greatest pressure difference is near the leading edge just downstream from the stagnation line. The upwash resulting from the interaction of the air molecules with the bottom surface of the wing adds to the flow here.

Over the surface of the wing, the pressure field is the result of the impacts of the air molecules and nothing else. Circulation, upwash, drag, lift… all are the result of the interaction of the air molecules with each other and with the surface of the wing. Newton’s third law predicts this exactly but we have no computers to keep track of so many collisions (of the order of 10^23). In order to be able to even begin to handle the problem, the fluid approximation is made. This approximation is good for a good part of the flow but it becomes invalid in the vicinity of the surface, i.e. the boundary layer. As soon as there is significant particle-particle interaction, the fluid approximation runs into trouble.

Charlie Crummer (

But what about the treadmill?

Is this the article you are commenting on? How do Airplaines Fly, really?

ccrummer: welcome to the Straight Dope Message Boards, we’re glad to have you here. Read around, we think you’ll find things to attract you.

When starting a thread, it’s helpful to others to provide a link to the column or staff report you’re commenting on. Saves lots of search time, and stops people from repeating what’s already in the article. I’m hoping that Khadaji got the right link? And you’ll know for next time.

Thanks, Khadaji, much appreciated.

So aerodave describes two explanations: one based on Newton’s third law and the other based on pressure differentials. Referring to the pressure explanation, he says

Should this be taken to mean that the two explanations are different ways of viewing the same phenomenon? Or are these two separate lift-generating mechanisms that have an additive effect, and Dave is giving us permission to only understand one of them?

They’re two different routes that arrive at the same answer. Those of us who surround ourselves with the physics day in and day out don’t even question that they are alternative but equivalent descriptions. The underpinnings of the pressure-based method still derive from Newton’s laws, just as a momentum-based approach does. With either method you’re just taking the basic governing equations (which are themselves just a couple steps removed from Newton’s Laws) and deriving the ones you want to apply to the problem. The diffference between the momentum (“Newton”) method and the pressure (“Bernoulli”) method is in the way you derive…the way you lump various terms together or split others apart. The result is a pair of distinct analytical approaches that are really the same underneath it all.

With enough information about the flow, you will reach the same answer using either analytical approach, just by a different path.

There is a very long thread in this forum where the dual nature of the Newton/Bernoulli approach is debated seemingly endlessly. It’s little more than a bunch of people talking past each other, usually in violent agreement. But if you filter the noise, you might just find some interesting points.

And, in general, I’ve got no issue with the points in ccrummer’s OP. This duality between explanations gives some people heartburn. But the more you look into it, the more you realize that any apparent discrepancy is only an illusion. The reality is that all valid explanations for lift come from the same sound physical principles, though they may appear in different disguises.