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Originally Posted by DrMemory
The only way to have a continuous (wide range) variable speed AC motor (not the 2 to 4 speed version) is to use a VFD (Variable FREQUENCY Drive). This can be done electronically by converting AC voltage to DC, and then converting the DC back to AC at different frequencies (at the motors rated AC voltage) to drive the AC motor.
You can also convert the AC to DC and use a DC motor. This is what variable speed AC hand drills do.
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VFD's are not the only way to have a variable speed motor. You can also do the job with varying the AC voltage on a shaded pole motor. The drawback is the efficiency and torque of the motor decrease as the rate of slip increases (rotation rate vs the line frequency). However in the case of fans and pumps the load also decreases with rpm and this is not a problem. The drop in efficiency means there is more self heating in the motor, but this is cancelled out by the fact that as the voltage drops, so does the total power into the motor. The method is not usually used in industry because of cost reasons or the need to maximize efficiency.
I suggest you go get a cheap variable transformer and plug a fan into it. You'll find that you can smoothly control rpm from 0 all the way up to max speed. The motor doesn't overheat nor are their any other problems with using this method.