Contribution of wing vertical location to roll stability
An aeroplane in a pure co-ordinated turn has a deflection of both the ailerons and the rudder. This is cumbersome however, much easier to only deflect the wheel, tilt the lift vector, and let the aircraft sway into the turn. The vertical tail will then experience a slip angle, which will point the nose into the direction of the turn at the expense of a small sway velocity: sideways.

So now the question is: how does the aeroplane react to a sideways incoming airstream. What we want is that if the pilot deflected the wheel to the right, he has to keep the wheel to the right to maintain the right hand turn. So upon an un-coordinated turn, without touching the pedals, we want the aircraft to try to level itself again upon an incoming sideways velocity.



If we look at what happens to a low wing aircraft first, we see that the incoming sideways stream sees little resistance when streaming over the fuselage top, but gets caught in the wing/fuselage intersection and builds up pressure there. So the sideways velocity introduces a rolling moment in the direction of the turn, which the pilot has to compensate for by turning the wheel the other way. This is not the behaviour that we want.



In order to correct for that, we can introduce wing dihedral: now the incoming sideways air stream wants to level the aeroplane again, and the pilot needs to keep the wheel deflected into the turn, which is what we want.

And of course, with a high-wing aeroplane the above is valid vice-versa: the sideways stream wants to level the aircraft, so the roll behaviour is naturally how we want it to be already. Depending on the wing/fusleage shape and many other factors, the aeroplane can be too stable and we'll need to implement anhedral, wings pointing down.