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Lift does not affect a helicopter or gyro-copter because the force "propels the flying machine in the direction of motion." That is defined as thrust, so helicopters use vertical thrust, though it is generated due to the same principle that generates lift on an airplane wing.

Spinning helicopter rotors create faster moving air above them, just like airplane wings. The Bernoulli principle describes how the faster moving air creates lower pressure above the rotors or wings. The higher air pressure below will push the rotor or wing up. That's how helicopters or gyrocopters can fly!