the optimal number of blades on a windmill is 3. Airplane props, helicopter blades, and ceiling fans can all have any number of blades. Why?
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You can have any number of blades on a wind turbine including 1, you do need a counterweight if you have 1 blade.
One problem is momentum on the tower when the wind changes direction, the rotor change direction too. With two blades the momentum is diffrent when the blades are horizontal or vertical but with three they will even out and be constant. I guess that any odd number will work the same way but am not sure.
More blades will be less efficient because of the drag increase. The most cost-efficient in regards just to power is a single blade but because of vibration and the forces when it changes direction three blade is a more cost-efficient overall system.
What you really like to improve efficiency is longer blades, wind turbines get taller and taller with larger and larger rotor diameters.
Airplanes and helicopters have practical limitations on how large you can have the rotor so adding more blades is the cheapest way to get out more power. You get more drag but can also output more power. The rotors on a helicopter and propellers on an airplane is not on top of a tall tower and the direction of their do not change relative to the vehicles so you do not have the same problem as a wind turbine with two blades.
Ceiling fans are stationary so two blades is a simple way to make them without a counterweight, you can add more blades to get more air moving with the same diameter. Another important factor is how they look even when they are stationary. It is not efficient you exactly care most about but looks size, and the amount of air they can move. Add to that sound is also very important.
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