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?
In: 7
Wind turbines is a more precise term for the ones that generate electricity. (Windmill is traditionally the ones that grind grain but enough people use it that it’s said to be acceptable.)
Wind turbines convert wind energy into rotational energy. Airplane props, helicopter blades, and ceiling fans are *driven* with shaft power.
Generally longer blades are more efficient for turbines: https://www.energy.gov/eere/articles/wind-turbines-bigger-better So fewer works better.
Propellers and helicopter rotors, you don’t want the tip to exceed the speed of sound, and to not strike other structures. They also need to be manageable to apply power to. Helicopters and larger propellers can, like wind turbine blades, change pitch: see https://en.wikipedia.org/wiki/Propeller_(aeronautics) under variable pitch. (Fixed-pitch propellers are for ones where the simplicity outweighs the efficiency benefits.)
Ceiling fans don’t have to design for maximum conversion of turning power to aerodynamics, so can go for quietness and aesthetics at higher priorities.
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