RE: Span vs area
To just toss in a few things here....
The effect of the air passing by a spinning cylinder is, I believe, called the Coanda effect, named after the fellow that discovered it.
And flat bottomed airfoils are just a freak coincidence. If you search around here you'll find lot's written about the subject. Basically there are two types of airfoils, symetrical and cambered. With symetrical being just a special case of the camber being 0%.
But all cambered airfoils, be they flat bottomed, "semi symetrical" or undercambered all share the same charactaristic that they will generate lift at a 0* angle of attack. This is because the camber curve redirects the airflow and produces lift. When you start working with cambered airfoils you bring another term into the discussion, the zero lift angle. This is the negative angle at which the airfoil produces no lift.