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In this site induced drag is often explain as downward deflection of the air streaming around the wing.

Airfoil (2D) also deflect air downward(otherwise it would not produce lift), why then airfoil dont has induced drag? I never understood that.

It is clearly visible at pictures below that both, wing and airfoil deflect air down.

Wing

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Airfoil

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One potential answer could be quote of PeterKampf:

"However, a wing of infinite span will use an infinite amount of air for lift production, so an infinitely small amount of downward acceleration already suffices to produce lift."

My question to that:

If airfoil(wing with infinity span) dont deflect any flow down because it use infinite amount of air, why then streamlines at every pictures/diagram/wind tunnel shows downward direction above and under the airfoil and behind trailing edge?

(Net momentum change imparted to the air by the airfoil is downward, this you can hear in this VIDEO, listen from 21:25 - 22:45 )

user707264
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You probably know that the vortex field created by a wing consists of three parts:

  1. The bound vortex which is responsible for lift,
  2. the two free vortices which trail behind the wing, and
  3. the starting vortex which closes the vortex system.

Now calculate the downward speed at some distance behind the wing when only the bound and the starting vortex are present and the distance between both is very large. I won't do the mathematics for you (simply use the Biot-Savart law; it's very easy to do in two dimensions only), but I will give you the results:

If no free vortices are present, the induced speed at some distance is practically zero, both ahead and behind the wing. Technically, you will have a tiny upward speed component ahead of the wing and a tiny downward speed component behind the wing, and the starting vortex will make this downward speed component larger than the upward speed component, but given enough distance from the vortex core both components are of negligible strength.

You can think of an airfoil as of a wing of infinite span where the two free vortices are infinitely away, so their influence is infinitely small. Reduce span, and the two free vortices will move closer and the downward speed component between them will start to become non-negligible. In a real wing with very limited span and at some distance behind the wing, they will add a constant downward speed which we call downwash. On the wing they do this, too, only that here the induced speeds are dominated by the bound vortex. But the downward speed induced by the free vortices does have an effect: It will rotate the resultant aerodynamic force slightly backwards (you will need to add a constant translational speed for a force to manifest itself in your calculations, though). This backward force component is called induced drag.

Remove the free vortices and you remove downwash and with it induced drag. Unfortunately, doing this is only possible in theory.

Peter Kämpf
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  • Thanks for explantion,now is clear. I misinterpreted your explanation because I was looking at downwash at airfoil, not at some distance behind.
    "Remove the free vortices and you remove downwash and with it induced drag. Unfortunately, doing this is only possible in theory." Is it possible if wing lower side is completely connected to ground, for example sliding to ice surface?     – user707264 Dec 03 '22 at 10:44
  • @JurgenM Any flow over a moving object will create overspeed and, thus, suction. Undesired lift on cars is a real problem, see the initial design of the Audi TT. This should be close enough to your airfoil on ice. – Peter Kämpf Dec 04 '22 at 04:56