Just realized I found myself a new favorite quote 
:
The elephant is the circulation.
Paul Bevilaqua, former chief engineer at Lockheed Martin Skunk Works.
I still believe this is the way it works:
Alpha_Floor wrote:
Relevant to this thread:
Outdated and irrelevant 
This is relevant, a complete explanation in fact
https://aerospaceamerica.aiaa.org/departments/so-you-think-you-know-lift-better-read-this/
Relevant to this thread:
https://www.scientificamerican.com/article/no-one-can-explain-why-planes-stay-in-the-air/
LeSving wrote:
You can dive into the philosophy of mathematics vs reality of course, but that’s a rabbit hole with no ending, or start for that matter. It leads nowhere.
Well we seem to agree on that!
Alpha_Floor wrote:
Well sorry to say but this is not correct :)
You can believe whatever you want, and that issue has been debated for a long time, so it’s not a clear cut thing. Today there is no debate over it however, other than by students at universities perhaps. The issue has settled.
Alpha_Floor wrote:
Circulation is defined as a line integral around a closed loop. It doesn’t get more mathematical than that…
Well, that’s the mathematical definition of circulation, and is used to calculate it for any given flow field with known velocity vectors. Force is defined as acceleration times mass, it’s equally mathematical. Everything in physics are mathematical concepts. You can dive into the philosophy of mathematics vs reality of course, but that’s a rabbit hole with no ending, or start for that matter. It leads nowhere.
Now please, explain those vortices by Prandtl please, preferably in a non-circulation way
Peter wrote:
It is 100% Newtonian mechanics
Is it? Bose Einstein Condensate is 100% a quantum state, yet it can be described by Navier Stokes equations Think about that for a minute or two.
It’s a bit appalling that intelligent aviators self restrict their understanding of matter to Newtons laws for rigid bodies. Anyone with an IQ of 30+ understands that air is not a rigid body.
But you are correct of course, it’s 100% Newtonian mechanics. You only have to specify: Newtonian mechanics of a fluid, also known as fluid mechanics
LeSving wrote:
Lift has very little to do with viscosity. Nothing in fact.
Well sorry to say but this is not correct :)
LeSving wrote:
Circulation is not a mathematical concept
Circulation is defined as a line integral around a closed loop. It doesn’t get more mathematical than that…
Alpha_Floor wrote:
Circulation is a result of viscosity, and that is a physical idea. So I’d rather say lift has a lot to do with viscosity and without viscosity there would be no lift rather than speaking about circulation which is a line integral around a closed loop which is correct but doesn’t help in understanding anything.
Sorry to say, but every thing in those sentence are wrong Circulation is not a “physical idea”, it’s real. It’s what tornadoes are made from. It’s what a tornado IS. But I guess some people “don’t believe” in tornadoes as well Just a mathematical curiosity? The same goes for wingtip vortices. Circulation is weird and often counter intuitive, it creates strange effects and has some peculiar properties, particularly in 3D, which is perhaps the reason it is down played in all layman’s explanations of lift. But, the fact remains. There is absolutely no way to understand lift without understanding circulation. It will all be just bits and pieces with no coherence.
Lift has very little to do with viscosity. Nothing in fact. There have been lots of speculation of what exactly causes the Kutta condition, which seems to be some kind of odd ad hoc law of nature. Is it viscosity? is it the Coanda effect? Is it momentum effects. This has been solved (see further “up” in this thread) by variational principles, which is in essence the same principle underlying F = m*a for instance, or conservation of mass. That video by Prandtl is a fundamental key. Why these vortices when the airfoil starts and stops? What happens in between? Are those vortices not circulation? If you understand those vortices, you understand lift.
Prandtl is considered the father of modern fluid dynamics. He was probably the first person on the face of the earth that understood lift. Not just foils, but full 3D, induced drag, wing tip vortices, planforms. The optimum planform for a wing is an elliptical shape. Why? The Spitfire is the direct result of Prandtl’s work, and the only reason for this elliptic shape is minimizing induced drag by optimizing circulation over the entire wing.
Circulation doesn’t so much explain lift, as it is more correct to say that circulation IS lift. So what is circulation? Just a mathematical concept? The whole Navier Stokes equations are nothing but a mathematical concept, but so is also F=m*a (Newton), which is implicit in the Navier Stokes equations. Circulation is the ability of a fluid to swirl around itself. Where a rigid body has translational and rotational motion only, which can be described by F = m*a (Newton), a fluid is much more, well fluid. It can do translational and rotational motion, but it also sheer and bend, squeez and stretch. Circulation is a combination of rotation, often translation, and sheer, squeez and stretch if you want.
Circulation is not a mathematical concept, it is a natural way of motion for a fluid. It’s as natural for a fluid as translation and rotation is for a rigid body. Mathematics can be used to describe it of course, in the same manner as mathematics can be used to describe the motion of a rigid body.
It is 100% Newtonian mechanics
The only thing above (or below) NM is quantum effects, relativity, etc
