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.
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
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 :)
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.
LeSving wrote:
Circulation is very much a physical concept
For sure it’s an obscure maths where you throw everything under the rug
It’s like talking in electromagntics about field formulations vs potentiel formulations, you need the latter to unify maths of electromagnatics but the fomer to integrate forces
Some will tell you potentiel formulations are the real thing but they are not unique which is puzzling if one gets deep in physics, even gravity is not a physical force, I would disagree when my SEP engine stops in general relativity, it’s just complex time-space maths, in quantum physics it’s just holographic representation of quantum field equations on space boundary under AdS/CFT duality…
Ted wrote:
Except the air moves well before the wing gets there.
Yes, it’s part of the circulation. It is really hard to explain in words, and must be seen. However this effect is small compared with the acceleration above the wing. This in turn is caused by the difference of sucking and blowing (see below).
Alpha_Floor wrote:
The Kutta condition doesn’t explain anything either, it is more of an empirical observation. Why does there have to be a stagnation point at the trailing edge?
It explains everything, if you let yourself be explained It’s all about fluid momentum. Fluid momentum is NOT like the momentum of a solid body. A fundamental concept of fluid momentum is sucking and blowing are two very different things. This is easy to see using a vacuum cleaner. Put a nozzle on the exhaust and it will blow at least across the room. The same nozzle on the suction end, and you have to be really close to feel the sucking flow. Yet, the momentum at both ends are the same.
In essence, the accelerated flow above the wing (blowing), will blow the initial stagnation point at the top of the wing back to the trailing edge. It will do this because aft part on top of the wing cannot suck the air from the underside to the top, and the blowing direction on the underside is parallel to the underside pointing aft and down. However, a prerequisite for this to happen is that the flow on the top side does not separate. It has to stick to the surface. This is helped by viscosity.
LeSving wrote:
Then you will actually see of the air moves. It starts with zero velocity, the wing comes, and you will see the main movement is circulation and acceleration.
Except the air moves well before the wing gets there.
LeSving wrote:
it makes no difference if the air is moving, or the wing is moving.
There is a big difference when you consider momentum the aircraft moves as whole, so you have to consider the momentum of the aircraft as a whole. The air isn’t a single object so each part of it can have different “momentum”, each molecule has it own momentum, of course it is much more complex and at some point newtons laws do break down.
Alpha_Floor wrote:
I am of the opinion that circulation does not explain anything. Circulation is a mathematical concept, not a physical one.
The Kutta condition doesn’t explain anything either, it is more of an empirical observation. Why does there have to be a stagnation point at the trailing edge? And why is circulation such as to move this stagnation point to the trailing edge? It’s not at all trivial.
Circulation is very much a physical concept, just like the rotation of the propeller or wheels. Just think about it for a minute. You are flying in dead still air. How does the air move when an airplane comes flying by? Well, the wing is like a flying vortex of air. We are used to looking at lift animations and videos from wind tunnels where the air is moving, not the wing. This isn’t at all what is happening. In real life, the wing is moving through the air. The air itself has zero velocity.
From a physics or mathematical point of view, it makes no difference if the air is moving, or the wing is moving. It’s the relative velocity that is important. But, I assure you, from a human cognitive perspective, it makes a huge difference. Then you will actually see of the air moves. It starts with zero velocity, the wing comes, and you will see the main movement is circulation and acceleration. I’m sure someone can dig up a YouTube video showing this.
I am of the opinion that circulation does not explain anything. Circulation is a mathematical concept, not a physical one.
The Kutta condition doesn’t explain anything either, it is more of an empirical observation. Why does there have to be a stagnation point at the trailing edge? And why is circulation such as to move this stagnation point to the trailing edge? It’s not at all trivial.
Viscosity plays a huge role here. Without viscosity, there would be no lift.
Silvaire wrote:
In regard to knowledge applicable to light aircraft design what has been forgotten since the late ‘50s is probably a more extensive list than what may have been learned
Very well put. Also remember that the book is meant for aviators. It’s not an engineering book. It’s not a science paper in cutting edge aerodynamics research, and it’s not a “popular science” book. Also important, it’s a rock solid reference for anyone creating courses and similar.
What is almost always missed on “popular explanations” of lift is the transient phases. What happens when a wing starts from zero velocity and all of a sudden starts to create lift when moving. Well, it doesn’t happen “all of a sudden”. This transition helps to get a mental picture of lift, and in particular circulation.
This is from Fluid Mechanics by Frank M White. One of the most used books about general fluid mechanics at universities, typically second and third year courses (lots of math is needed first).
Clearly four things are involved (at least): Fluid momentum – causing circulation due to the sharp trailing edge for which the fluid simply cannot follow around from bottom to top. Then there is viscosity and the conservation of momentum. It’s this one little detail about shedding of starting and stopping vortices that often is omitted. Conservation of momentum of a wing (or any moving object for that matter) is not fulfilled until the object has come to a full stop and all the starting vortices have been “cancelled” by stopping vortices.
That little starting vortex is what puts everything in motion regarding lift – the circulation. Whenever the lift is increased, vortices are shed, and whenever lift is decreases, stopping vortices are shed. It’s a direct cause-effect relationship with increased/decreased circulation, hence lift. You could say that lift IS circulation, and nothing else. All the “Bernoulli and Newton” arguments are simple effects caused by this circulation. This is not the same as wing tip vortices on finite wings, but related, since both are circulation.
