I would like to run a standard multi-speed desk fan at a lower speed than its minimum setting. On Amazon, one reviewer recommended a variac for fan control, saying that it could adjust the fan from barely-on up to full speed, without introducing the hum that sometimes occurs with triac-based controls. As I understand it, variacs are simply adjustable transformers, which reduce the voltage fed to the fan (and triacs working in phase-controlled manner have a similar effect).
However, most fans are induction motors, and I always thought these had a weak response to voltage. For example, Figure 27 here shows that peak torque occurs around 70% of synchronous speed regardless of the applied voltage. I believe the operating speed must always be somewhere above this speed. If this is true, then the only effect you could get by adjusting the voltage would be to reduce the operating speed from ~90% of synchronous speed to ~70% of synchronous speed, at which point the fan would stall. This doesn't sound like enough variation to be useful (and is at odds with the variac reviews on Amazon).
Does this sound correct? If this is the case, then it sounds like my best option is to find a fan speed controller that uses a triac to cut the voltage for whole AC cycles, along the lines described in an earlier question. But that is a challenge, since most fan controllers that I've found don't include descriptions of their mode of operation.