Speed control on a ceiling fan induction motor
I came across the following circuit diagram, is this method advisable? Won't this cause a lot of humming in the motor?


A light dimmer type of controller will work, but it will likely cause a noticeable humming or buzzing sound and may shorten the life of the motor. Reducing the voltage of an induction (asynchronous) motor will only reduce the speed slightly and then cause the motor to stall if the load requires a substantial amount of torque to operate below full speed. The torque required to operate a fan or centrifugal pump drops off drastically at reduced speed. That allows more speed reduction as illustrated below. The red curve shows the torque vs. speed requirement for a fan load. The blue curves show the motor torque vs. speed capability for various voltages. Stable operating points are points where the load requirement curve crosses the motor capability curve an near a right angle. The bottom operating point in the illustration might not be stable.

Reducing voltage is speed control by weakening the motor and allowing the load to slow it down. Changing the capacitor value or connecting to a different point on a winding produces a similar effect.

Note that the air flow of a fan is proportional to the square of speed. A speed of 90% gives 81% air flow, 80% speed give 64% air flow and 70% speed gives 49% air flow. Power is speed X flow 72% power at 90% speed and 81% flow.