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An airfoil has a rounded leading edge and a wedge shaped trailing edge to reduce drag. The airflow is separated at the “stagnation point” on the rounded leading edge and closes again at the thin end of the trailing wedge. Strictly speaking, the air is "cut" by the rounded leading edge, not the sharp trailing edge. That is opposite to a knife blade.
The profile of a wind generator blade is an airfoil. There is a twist in the blade that keeps the angle of attack of the airfoil section similar at different radii. That is needed because the airspeed at the airfoil is the vector sum of blade rotation velocity and the wind velocity.
Helicopters mostly have symmetrical blades without twist, so depending on their RPM, they will generate lift somewhere along their length, usually different on each side due to helicopter airspeed.
The old style windmills operated on the same principle. They do not have a nice aerodynamic profile but their blade does have an angle of attack and generate lift somewhere along the blade's length. The canvas cover or “sail” that is not normally seen today takes the profile of the blade frame and behaves in a very similar way to the curved sail on a boat. “Patent” sails that have mechanically operated slats have a slight twist along the blade to increase their efficiency. The canvas sails are furled, or the patent slats opened, to reduce power in strong winds.
Most old wooden windmills on hills have long since burned down during wind storms. Without canvas on the blades their "bare poles" are still driven by the strong wind and cannot be kept side on to the wind. As the wind storm continues, the miller processes all the corn he can to slow the mill, until all has been processed. The wooden brake blocks on the wind-wheel slip and need cooling water to prevent fire, the miller then tires and collapses from exhaustion carrying water from the nearest available source to the top of the tower.