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If a wing is at a positive angle of attack, then the vortices produced at the wingtip will generate downwash and induced drag but on the contrary, if the wing is at a negative angle of attack, then the vortices produced at wingtip will generate upwash and induced thrust so in this case ( negative angle of attack ) , are the wing tip vortices still harmful or not ?

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    $\begingroup$ Just look at that wing with positive AoA upside-down: et voilà $\endgroup$
    – sophit
    May 19, 2023 at 5:04
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    $\begingroup$ Sophit is right. The only difference the -ve AoA will make is that the vortices will rotate in the opposite direction. The wing will still produce induced drag just as it would at +ve AoA. $\endgroup$ May 19, 2023 at 5:43

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Vortices do not produce up- or downwash, they are the consequence of it. Up- and downwash are the result of pressure differences around the wing. You might also read that up- and downwash are caused by circulation (which is an abstract concept from potential theory). This is correct but less intuitive to understand.

Next, we need to agree what Angle of attack means. This could be the geometric angle between the direction of movement and a reference line on the wing (mostly the chord of the airfoil), or the difference between the actual direction of motion and the one where no lift is created. For your question the latter definition will be much more useful.

At positive angle of attack the wing creates lift, so it will deflect the oncoming air downward. To fill the void that the downward movement would leave behind, air will flow into that space from the sides, causing a rotating motion. Inertia will keep that motion going until viscosity damps it down.

If the wing has washout, the inner wing might create positive lift while the outer wing creates a downforce. Any lift on the wing, regardless of direction, will cause induced drag. Downforce at the tips will, however, lower the bending moment that the wing is subject to and allow to build the wing lighter, thus saving induced drag indirectly by lowering the requirement for lift. Note that at the tail and in the downwash of a lift-producing wing, indeed the pressure distribution which causes the downforce can also create induced thrust.

Wingtip vortices are neither beneficial nor harmful. They are only an unavoidable byproduct of lift creation with limited wingspan.

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