# Why does the vortex created by wing affects its own angle of attack?

According to potential flow theory, we know that the lift generated by the wings is due to the vortex it creates. In case of a 3D finite wing, there is also a span wise flow due to tip leakage from bottom to upper surface. So if suppose the wing is moving towards left, then the direction of vortex should be clockwise, which in turn should produce an upwash rather than downwash. This should cause an increase in angle of attack rather than decrease.

So the downwash generated should be valid for a wing travelling behind the original wing, but we say that there is downwash on the original wing.

So where is it that I am making a mistake, vortex direction. If yes, what is the correct explanation. Please explain.

The wingtip vortices create both upwash and downwash; The downwash lies within the wingspan and affects the wing angle of attack while the upwash region lies outside the wingspan and can be utilized by another aircraft (or bird) flying behind and above the wing.

The flow induced by the downwash reduces the effective angle of attack of the (finite) wing and causes the induced drag.

See if this image clarifies your doubt.

Source: aerospaceweb.org

Consider the upwash before the wing and downwash after the wing (section).

Source: theairlinepilots.com

As it can be seen, the airflow in front of the wing is slightly directed upwards by the upwash. Now, the angle the wing makes with the horizontal datum (i.e. relative airflow) is the same.

However, the airflow is slightly turned upwards and the wing sees the air coming at it at a different angle compared to the relative airflow. As a result, the effective angle of attack (defined as the angle of attack that lies between the chord of an airfoil and the effective airflow) is reduced, so that the relative and effective airflow looks something like this:

Source: theairlinepilots.com

This difference between the relative and effective airflows is what that causes the induced drag.

Source: theairlinepilots.com

• Perhaps you could also mentiond that the same also happens in front and after the wing. Directly in front of the wing upwash occurs, wheras behind the wing downwahs occurs, see encrypted-tbn3.gstatic.com/… – ROIMaison Oct 9 '15 at 12:18
• @aeroalias Thanks for this very relevant image. But that exactly is my point, if all the induced flow effects are prevalent behind the wings, how is it so that the angle of attack which depends on flow ahead of the wing is getting altered? – Manish Oct 9 '15 at 14:23
• @ROIMaison if upwash occurs ahead of wing, then shouldn't AoA increase? – Manish Oct 9 '15 at 14:24
• @Manish See the edited answer. – aeroalias Oct 9 '15 at 18:24
• How is the angle of attack reduced if the flow is pushed up. The angle of attack would increase. – Crafterguy Jun 25 '17 at 13:52

Near the wing the bound circulation due to lift leads to an up-wash ahead of the wing and downwash behind the wing similar to the flow produced by a two-dimensional lifting wing of infinite span.

A very important effect is generated by the flow due to the vortex pair that comprises the wake (at wing tips). The semi-infinite sheet of vorticity distributed in the wake produces a downward velocity component in the free-stream ahead of the wing, at the wing and far downstream as illustrated in Figure.

The downwash by the wake leads to a reduction in the angle-of-attack of the wing relative to the free stream, reducing the lift. In addition the downwash rotates the oncoming flow vector at the wing leading to a component of drag as shown. The change in angle of attack due to the downwash generated by the wake is tg(a) = (Uz/U∞)

Source:

STANFORD UNIVERSITY, Department of Aeronautics and Astronautics, AA 200A Applied Aerodynamics, Instructor: Brian Cantwell, cantwell@stanford.edu

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