Originally posted by

**Evan**View Post- I am repeating myself here but the circulation is a speed profile, not a force. Only pressure gradients can make the air accelerate and bed its path.

- The air doesn't has upwash, downwash, accelerates above and slows down at the bottom BECAUSE of circulation Circulation is THE NAME THAT WE GAVE TO this distribution of speeds.

- The circulation is NOT a vortex. The circulation is the distribution of speeds around a vortex. A vortex has rotor. Around the vortex however the rotor is zero ("rotor" is a vectorial magnitude of a vectorial function (like a speed field), it can be understood as how fast would a ball rotate around its own axis if you hold it in one position (not free to move but free to rotate). Around a 2D airfoil (or around a spinning cylinder), outside of the boundary layer, the rotor is zero.

- The bound vortex is not induced by the starting vortex, they are created simultaneously because vorticity shall be conserved (like energy or momentum).

- In a 2D airfoil (that can be though as a wing of infinite wingspan) there is no starting vortex. The vortex is considered to continue infinitely along the infinite span and you never see the vortex bending back near the wingtip and joining back at the starting vortex. You can think that the wingtips and the vortex ends meet in the infinity (think that they form a circle of infinite diameter) and such a closed vortex has voticity zero (like a smoke ring) so you are not creating or destroying vorticity by increasing or reducing the lift. But you don't have "one vortex". You have a system of vortexes that add up to a finite vorticity (finite in 2D, it becomes zero if you extend it to infinity) and that can be replaced by a single vortex that will work very well to model the lift force but not to model the lift around the airfoil.

- In a 3D wing, the situation is much more complex The figure that I think you have in mind, like a long rectangle where one off the short sides is basically the wing (or the bound vortex), the other short side is the starting vortex, and the long sides get longer and linger as the wing moves forward (with the bound vortex) and the starting vortex remains still is a gross simplification, useful for some things, but not to describe in detail the flow of air around a wing.

- Both in the 2D and 3D versions, if you use the single vortex model, you can explain and measure accurately many things including lift, induced drag, induced angle of attack in the tail, ground effect... but you will have air flowing through the walls of the airfoil. Reality is more complicated than "a vortex". If you want I can go to the more complete explanation.

- In any event, vortexes don't occur in potential flow because the rotor in potential flow is always zero (but potential flow ha solutions for cortices introduced artificially in the model as singularities, and you don;t even need to establish the vortex itself, you can establish the circulation caused by it, like with the Kutta condition). In reality, all the vorticity (not the circulation) happens in regions where the viscosity cannot be neglected and hence the flow cannot be modeled as potential, like the boundary layers and the core of the vortex systems (like the core of the wingtip vortexes). That is complicated to do (it can be done, computers do it all the time) so it is useful to artificially out vortexes here and there as singularities in the potential flow model, with that vortexes having a similar effect to the vorticity that takes place in those regions.

- And now you want to deal with non-stationary aerodynamics? With an airfoil that is not moving steady in a steady stream of air but that is changing airspeed an d angle of attack? And that will make the explanation more clear?

Evan, before trying to explain the lift it terms to your satisfaction, please try to explain to me, in terms to your satisfaction, why does the tracks of the train in a curve make the exact force that they make on the train?

And by the way, even if your explanation was right, I don't see how that would satisfy neither the pilot nor the 8 years old.

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