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Q:

How does change in propeller speed affect thrust efficiency?

A:

Spinning a fixed-pitch propeller faster lowers its efficiency. Just like wings, propellers generate force using differences in air pressure and angle of attack. But, unlike wings, propellers have different angles of attack along their blades. Because of this, spinning a propeller too fast can cause it to generate more drag than lift. So, more sophisticated planes have variable-pitch propellers to better control the angle of attack of the propellers.