The Root Problem
As the number of blades increases, the hub centre becomes very cluttered with metal, and not so much air. Also the pitch at the root of the blade needs to be much coarser than at the tip, which is not very efficient at low speeds.
Beyond 80 blades, as in a turbine, the whole root is solid metal, with the blades just occupying a few inches on the outer perimeter. This requires some elaborate ducting and nose cone design to get the air to the right place. Maybe more blades is the way to go, as ultimately in a single engine airplane, the air needs to be moved outwards to the diameter of the fuselage anyway.
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