Why local(section) lift coefficient(CLL) is higher near the wing tips compared to the root on untwisted tapered wings and untwisted swept(aft) wings?

Question

Why local(section) lift coefficient(CLL) is higher near the wing tips compared to the root on untwisted tapered wings and untwisted swept(aft) wings?

I know that in an elliptical wing(untwisted) the absolute angle of attack is the same in all the wing span so, the reduction in lift is 'proportional' to the reduction in area/chord of the section and then the CLL is equal in all the wing span. I also know that in a retangular wing(untwisted), the effective angle of attack(due to the tip vortex) causes a reduction in the CLL in the tips compared to the wing root.

Even that I understand the flow pattern over swept wings(Attachment line/Spanwise airflow and it's effects on lift and in the boundary layer, adverse pressure gradient and tip stall)I just can't figure out, intuitively, the relation between this flow pattern and the increase in the CLL in the direction of the wing tips.

[ CL = L / S.q ] Seems to be too simplistic to analise this particular case.

Answer 1

For the swept wing, as you go out along the wing, each section of the wing is effectively flying in the upwash of the tip vortex of the section immediately next to, and inboard of it. So, each section has its angle of attack increased by all of the sections inboard of it. The root section, of course, does not have anything inboard of it, and the tip section is affected (to at least some extent) by all the sections inboard (and ahead) of it.

Birds fly in V-formations to take advantage of this effect. Each bird is flying in the upwash of the tip vortex of the bird ahead and toward the center of the V, and is thus "flying downhill" aerodynamically.

But, that upwash increases the angle of attack, and the effects add up as you move outboard, until they reach a peak effect near the tip.

You can really see this on hang glider wings: if you stand next to one as it's about to take off, you can see the tips appear to be at a negative incidence relative to the wind, and yet they are lifting, because the wing sweep increases their local AoA.

Answer 2

Section lift coefficient depends on angle of attack. A greater angle of attack means higher lift coefficient.

A wing producing lift "pushes" air from below around the front and over the top. This is called circulation. When the leading edge is swept, whether from taper or wing sweep, some of that air is "pushed" toward the tip and then over the top. This happens all along the wing, so that when you get all the way to the tip there is a lot of more air going over the top than there was in the center of the wing. Think of it like this snowplow with an angled blade:

The additional airflow going over the wing the farther out you get increases local angle of attack and therefore the local section lift coefficient.

Answer 3

It’s because, on a tapered or a swept wing, the tips are so small that they cannot hold the vortices that are being formed, because of which the vortices are formed inboard. Therefore there is no reduction in the effective angle of attack at the tips whereas there is a reduction in the effective angle of attack inboards and hence, the local lift coefficient is higher closer to the tips as compared to the root.