Are there variable pitch propellers, where pitch is set so that the blades constantly are at their maximum lift to drag ratio AoA, whatever the incoming relative wind speed & direction?
Such a variable pitch propeller would be powered by some electric engine, able to equally produce torque for clockwise and anti-clockwise operation.
Such a variable pitch propeller would be free on its pitch axis, able to rotate 360°, each blade being mounted on two ball bearings, inside propeller's hub. This way maximum aerodynamic efficiency could be reached whatever the needs:
take off at low relative pitch, cruise at some higher pitch, ability to produce efficient reverse thrust after landing. Each of these at maximum lift to drag ratio AoA.
Each blade is balanced about this pitch axis, so that it is statically stable, and aerodynamically always trying to pitch up by its own aerodynamic configuration, towards its best lift/drag ratio angle of attack.
Each blade becomes an individual glider/flying wing, trying to pitch up.
For the sake of understanding, imagine a propeller with trailing edge tabs set at an angle allowing only thrust generation, regardless of the direction of rotation of the propeller.
This tab is not a viable way to build such a blade, it may instead look like some conventional blade, having some negative incidence blade tip combined with swept back tip, or some standard geometry, with a reflex airfoil, or both, or something else.
The idea here could be to have an automated variable pitch prop with the least amount of moving parts, where pitch is set by aerodynamic forces at its optimal angle. Instead of going for constant rpm, this one goes towards constant maximum lift.
For instance, cutting power off would induce some reverse windmilling, adding power in windmilling direction will generate reverse thrust.
During forward flight, pitch would adjust on resultant airplane's velocity + blade's rotational velocity.
Question is : Are there propellers of this kind? If not what are the drawbacks I don't see?