Sorry,but This is a totally wrong explanation :"In straight and level flight, both wings have the same projected surface, which is smaller than the actual surface. Under gust, the lower wing being closer from "flat" has a greater projected surface, hence generate more lift, so the lower wing goes up....That's simply how it works, and why dihedral give roll stability"

if you just rotate the wind axis, you will discover your mistake
(you can also rotate your viewing position...)


I have talked with some aerodynamic engineer at my company,
and he finally succeeded to give me a good explanation.

dihedral do not roll back the A/P !!!
it's just create a Croll_beta derivative (Rolling moment coefficient due to side-slip).
That means, It couples between yaw and roll.
Having a sudden gust, A/P sideslip and then dihedral causes
a roll moment into the turn !!!
what happens is that beta angle (sideslip) become alfa.
Dihedral actually elimnates sideslip by turning it into alfa angle,
and this is a real directional stability.
finally the A/P rolls back due to it's low C.G position,
this has nothing to do with dihedral...

This is similar to the longtitudinal axis, static stability is the ability
of the A/P to eliminate sudden increase in alfa due to gust
(negative pitch moment is created in order to drop
the nose down)

I will be happy to get some feedback, to see if my
theory-about dihedral affect is correct

B.T.W
I am an aeronautical engineer myselfe...