# How does downwash affect angle of attack?

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.

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.

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, 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.

• 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
• @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
• @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 0:32
• @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 3:02
• @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

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.

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

• … for small angles, aspect ratios > 5 and lift curve slope $c_{L\alpha}=2\pi$. – Peter Kämpf Oct 25 '20 at 10:01