The following is what I have written elsewhere, bear in mind it was written specifically to address the origional forums comments:
Having worked in the controls industry since 2002 and dabbled with motors for a long time before that
I will say the only correct way that I’ve found to control shaded pole motor speed is by varying the frequency of the supply. Ignore the other person who said there are no single phase Variable Speed Drives, I’ve fitted dozens of them for small central heating pumps at 50W up to several KW.
The thing about shaded pole motors is they require their design power to work properly and reducing the speed by reducing the voltage has 2 distinct effects:
1/ the available torgue drops off very very rapidly to the point a 10% reduction of speed may easily remove it’s ability to start under any sort of load, including bathroom fans. Therefore it will require full voltage to start correctly.
2/ Running at the incorrect speed for the supply frequency will result in crazy back EMF levels and WILL result in higher current, to the point the motor WILL be running at a hotter, and very likely excessive, temperature with the resultant early failure. A number of times I’ve measured supply currents in excess of 5 time,s and even 10 times, the design current.
Resistive or triac dimmers MAY appear to do the job but caveat emptor.
I once demonstrated the effect with an extractor fan, slightly bigger than the average domestic bathroom fan and a resistor, as the series resistance went up, so did the motor current... affecting the power factor. This was a system installed by a rival company with several relays to add more resistors in parallel to progressively increase speed as the humidity increased. The fan ran 24/7 but repeatedly failed in well under a year (and fan supplier/manufacturer were refusing to keep honouring their 7 year warranty) whereas an identical fan elsewhere in the building ran at full speed 24/7 with no issues for years (as long as it was regularly cleaned). We replaced the botch with a VSD and gave a total 3 year guarantee, I believe we didn't get called in to honour it.