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Many aerodynamics textbooks, as well as many answers on here and similar websites claim that the downwash downstream of a wing induces a net angle of attack that is lower than just looking at flow direction and chord orientation would have you believe. They then often go on to say that lift is perpendicular to this "induced flow direction", explaining that the component parallel to the originally perceived flow direction is induced drag. I struggle with this idea, because my current understanding of lift dictates that downwash itself is a product of lift generation and therefore a product of angle of attack.

Also, when looking at visualisations of flow fields around a wing, we can see both upwash ahead of the wing and downwash behind it. Intuitively, I'm inclined to think that the downwash, being downstream of the wing, can't really affect the flow dynamics around the wing anymore. Conversely, the upwash, being upstream of the wing, should affect the flow around it, increasing angle of attack and therefore lift produced.

enter image description here

The only explanation I've come up with is this, though I'm not sure if it's correct:

Since any wing producing lift must introduce a net downwash on the surrounding air, the average air movement over the whole wing must also be negative. I guess my problem with this explanation is that I've always thought of angle of attack as a function of just chord orientation and flow direction. Is it correct to assume that, looking at the flow field closely around a wing, "traditional angle of attack" doesn't matter as much since the large induced flow velocities in front of the wing will make actual "aerodynamical" angle of attack, i.e. the angle at which the oncoming air actually hits the wing (as opposed to the angle between freestream flow direction and chordline) differ significantly?

I apologise if my question isn't very comprehensible, I had quite a hard time formulating it. In any case, I'd be glad for an answer, and I'll try my best to clarify what's unclear.

Moritz Heppler
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Is it correct to assume that, looking at the flow field closely around a wing, "traditional angle of attack" doesn't matter as much since the large induced flow velocities in front of the wing will make actual "aerodynamical" angle of attack, i.e. the angle at which the oncoming air actually hits the wing (as opposed to the angle between freestream flow direction and chordline) differ significantly?

Yes. Just witness the angle at which slats are pointing down: They are oriented to the local direction of flow which is strongly up at the leading edge when the coefficient of lift is high.

Typical landing configuration of an airliner wing

Typical landing configuration of an airliner wing, from an article by A. M. O. Smith, McDonnell-Douglas, in Journal of Aircraft, Vol 12 No 6, 1975. As always: Converging streamlines indicate accelerating flow and falling pressure while diverging streamlines show decelerating flow and rising pressure.

Note that the double slotted flap here is instrumental in inducing this steep local flow angle: Without it, the wing would not produce nearly as much lift and the suction on the upper side would be much weaker, causing less local bending of the direction of flow.

Note as well that the angle of attack of the airfoil is 0° while the streamlines entering the drawing on the left already have a marked upwash angle. The same happens in reverse at the right side where the flow shows a distinct downwash. This is a 2D simulation and at infinite distance to the airfoil the direction of flow is strictly horizontal. On both sides, because this airfoil does not produce induced drag in 2D flow (an effect also known as d'Alembert's paradox).

On a real wing, however, the tip effects reduce the lift curve slope so the local wing section will show a lower lift coefficient at the same geometrical angle of attack. Now suction and upwash are reduced (but still exist) and the air flowing off the wing leaves it with an added downward speed component. The far-field flow pattern now does not any more have the symmetry of equal up- and downwash. Instead, the downwash angle is increased to twice the magnitude of the reduced upwash angle because the influence of the free vortices in the wake must be added. The result is a backward tilt of the sum of all pressure forces acting on the wing which we call induced drag.

Peter Kämpf
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  • I'm struggling a bit with the last part of your answer. What exactly do you mean by "tip effects"? Also, if lift coefficient, and in turn suction and upwash are reduced, wouldn't the downwash be reduced too, since it is proportional to downwash angle/lift generated? – Moritz Heppler Oct 24 '20 at 16:24
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    @MoritzHeppler "Tip effects" is the reduction of lift due to pressure equalisation at the wing tips. Yes, downwash would be reduced without the additional effect of the free vortices which are shed precisely because circulation goes to zero at the tip. So the tip effects increase the downwash behind the wing (more precise: In the inner $\pi/4$) and add an upwash left and right of it. – Peter Kämpf Oct 24 '20 at 18:50
  • So the increase in downwash on a 3d wing compared to a 2d (or rather, the presence of a net downwash at all) occurs only due to the wake rolling up in itself? If that's the case, I have another question: the wake only starts rolling up when it has left the wing, so how can it still induce a downwards flow in the air still affecting a wing? Or is the point that the apparent downwash you'd see on a field of streamlines isn't entirely due to the pure lift produced by a wing, but rather a combination of it and the wake vortices further "blowing" the air aft of the wing downwards? – Moritz Heppler Oct 24 '20 at 19:22
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    @MoritzHeppler No, wake rollup is only the consequence of lift and drag. The free vortices (which will form the wake) induce that downwash on the whole flow field around the wing, so it is tilted compared to the 2D case. I shouldn't have said "behind the wing" but "on and behind the wing". – Peter Kämpf Oct 25 '20 at 00:32
  • I think I'm having some trouble with wording. Would it be correct to say that, because of the tip effects (i.e. pressure changing towards ambient/freestream pressure the closer you get to the tip) and following spanwise flow, the wake is made up of vortices, which is why it rolls up in itself? – Moritz Heppler Oct 25 '20 at 22:36
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    @MoritzHeppler: That is exactly right. Most authors call the local flow around the wing tip the tip effect. But this is too narrow. When you include the gradual decrease of lift from the wing's middle towards the tips in that definition, it becomes correct. – Peter Kämpf Oct 26 '20 at 03:02
  • How does that tie in to the benefits of a high aspect ratio? Say wing area is kept the same, but there is a span extension. Obviously you turn more air to a lesser extent rather than less air more strongly, so AoA and pressure differential between upper and lower surface is smaller, i.e. average pressure on both surfaces is closer to freestream pressure. Therefore, the pressure change along span is less pronounced, meaning less spanwise flow -> weaker wake vortices -> less downwash induced -> less induced drag? – Moritz Heppler Oct 26 '20 at 18:29
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    @MoritzHeppler: This has been answered here. Generally, the tip effects have relatively less influence and a weaker vortex strength suffices for the same lift because more air is affected by it. The pressures on the wing are the same, but extend over a smaller chord. – Peter Kämpf Oct 26 '20 at 19:29
  • After reading that answer and some others linked there, I'm a bit uncertain about the conclusions I've drawn again. I'm thinking that, if, say, pressure stayed the same along the whole span (without thinking how you'd facilitate such a distribution), the downwash aft of the wing would equal the upwash in front of it. However, this means that no net downwards deflection has occurred, ergo no lift produced. part 1/2 – Moritz Heppler Oct 26 '20 at 20:46
  • But if the wing is finite, and pressure does move towards ambient as span increases, you would expect the downwash to increase with span too, because it is induced by increased vorticity resulting from the increasing spanwise flow as you move closer to the tip. Could you explain if and where I'm making a mistake in my thinking process? Also I apologise for my difficulty in comprehending the subject, I'm really not sure why I have so much trouble with it. part 2/2 – Moritz Heppler Oct 26 '20 at 20:47
  • @MoritzHeppler The combination of high vorticity and a small spanwise vorticity gradient near the center produces the same downwash as a low vorticity with a high spanwise vorticity gradient near the tip. Downwash is evenly distributed over span. – Peter Kämpf Oct 26 '20 at 21:47
  • In that case I have some reading up to do, because I thought vorticity was solely a byproduct of tip effects, and therefore would increase as you move along span. Again, I'd just like to say thank you for your very detailed answers. – Moritz Heppler Oct 26 '20 at 21:57
  • @MoritzHeppler: No, vorticity is highest at the center and decreases towards the tips. Try this answer. – Peter Kämpf Oct 26 '20 at 22:01
  • Let us continue this discussion in chat. – Moritz Heppler Oct 26 '20 at 22:14
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downwash downstream of a wing induces a net angle of attack that is lower...

So add in a horizontal stabilizer to your picture and raise and lower your AOA (you can drop flaps too).

What is interesting is that, since the horizontal stabilizer is generally configured to produce negative lift (down force), the down wash will increase its negative AOA.

When dropping flaps in a 172, the nose up pitch is very noticable.

Robert DiGiovanni
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Angle of attack AoA, aspect ratio A, and downwash deflection angle E, are linked by:

sin E = 4 sin AoA/(2+A)

Derivation here: Chris Waltham, Flight without Bernoulli https://booksc.org/book/45382205/a4710b

xxavier
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