# Why will the max lift point not be at the center of a swept but constant chord wing?

(In this question when I say "swept wing" it means the blue wing seen at the bottom. So no fuselage or anything) If you look at this graph from this answer, you'll see the max lift point of this wing is not in the center. This wing is a swept but not tapered wing:

I studied this answer and also this one for an afternoon and I can't seem to understand this. I think this is because I don't really understand the horseshoe vortex system / the bound vortex.

Consequently, I don't understand how a swept wing with no taper will have its lift fairly dramatically drop off right in the center of the wing, while the whole wing is essentially symmetrical. (This isn't considering spanwise flow)

It's hard to see how the bound vortex system translates to actual flow over a wing, if that makes sense. So the question is, why does this lift dip in the center of the swept but non tapered wing happen?

Unless it's because of this: An airfoil will create low pressure. Higher pressure freestream air will tend to be attracted to this air. As explained in the 3rd paragraph of this answer. Knowing that, air in front of a wing will bend towards the leading edge. If the wing is at an angle, this air will bend to where it's in line (mostly) with the LE, as seen in the picture below.

Because the left side of the swept wing will bend the air inwards, and so will the right side, the air on both sides of the swept wing will intersect where the red lines intersect. When this happens, it could make some turbulence or interference that could cause the dip of the graph seen in the first picture

This is the only reason I can seem to think of, although it might not be correct.

• This question is in a way asking if there is a way to explain this without using bound vortices, as I’m having some trouble understanding that. Commented Jun 15 at 3:44

## 1 Answer

It's the Mitteneffekt.

Remember that air gets sucked into the region with lowest pressure, so the streamlines get bent towards the center on the upper surface of a swept wing. This will hit an obstacle near the center: Here, streamlines converge and "fill up" the low pressure area, resulting in a higher pressure at the wing center. This explains the rise in the pressure coefficient at the center of the wing in your first plot.

If you now look at the distribution of horseshoe vortices, their intensity is proportional to the local lift coefficient. A drop in the middle is caused by pairs of horseshoe vortices which extend only over parts of the inner wing, with the free vortices trailing off not near the tips, but one near the center and the other at the outer wing. In a very crude plot this looks like this:

Horseshoe vortices on a swept wing, own work. Note the direction of rotation: The innermost free vortices indicate a drop in circulation strength at the center of the wing.