LeSving wrote:
Circulation is very much a physical concept,
Not really, but lets leave it at that because this is one of those “high-level” university cafeteria discussions which I have already had in the past 
Circulation is a mathematical concept: namely a line integral around a closed curve. But I digress.
I believe Kutta and Zhukovsky developed the mathematical concept, as it isn’t a concept in physics.
In the meantime the bicycle mechanics were quietly getting on with wind tunnel experimentation :)
RobertL18C wrote:
In the meantime the bicycle mechanics were quietly getting on with wind tunnel experimentation :)
“heavier-than-air flying machines are impossible”, Lord Kelvin 1895, he know maths & mechanics & thermodynamics better than anyone but he failed to see bicyle-flying mechanics by Wright Brothers & Glenn Curtiss just 10 years later
Alpha_Floor wrote:
Circulation is a mathematical concept: namely a line integral around a closed curve.
Similar to a force F. It’s an abstract mathematical concept of mass times acceleration
All math is just that, math, no more – no less. The point however is that circulation, as abstract as you want it to be, has a value around a lifting body, while it is zero when there is no lift. It’s the integral of (udx + vdy + udz) along any closed curve around the body (it can be defined in other terms, but that’s only juggling with math). This is very tangible and can be measured by simply measuring the velocities along the curve and integrate them up. This will give you an exact value of the lift, and lift is a real thing, but no more real than the velocities of the air around the foil.
At that amount of circulation, the stagnation point (or separation point if you want), happens to land on the trailing edge, as by magic. The only thing left to explain is why does the stagnation point land on the trailing edge, but this is only a straight forward fluid momentum consideration. There really isn’t much to explain. The old men Kutta, Joukowsky and others, knew exactly what was going on. The main problem for them was to be able to calculate it, to describe it in terms that could be used in practical applications. Pre CFD, or pre computer, this could only be done by rather complex and abstract mathematics, involving mind boggling transformations of airfoil shapes and flow fields, and applying the condition that separation occurs at the trailing edge.
The shortest explanation of lift is because the stagnation point is pushed back to the trailing edge on an airfoil. No more explanation than that is needed, and no more explanation is usually given. The rest is obvious, also the reason why this must be. The problem with this explanation is it doesn’t make sense for most people. IMO that problem is because most people don’t want to do what it takes to understand it, not with the explanation itself
What is not equally obvious perhaps, or intuitive, is the transient transition from non lift condition to lift condition and corresponding shedding of vortices (as explained by White). But IMO, that is also one key in understanding the whole concept of circulation by moving the stagnation point, and why this is the cause of lift. The air itself starts out in the “usual way”, but the airfoil immediately “forces” the air to move the stagnation point to an “un natural” position. You can call it the path of least resistance if you want. It’s equally natural as water always runs down hill.
