Taking A Closer Look...
This is very important and worth a second look. Most of the documentation about AC motors tends to use the term "poles" very loosely and I think I got the wrong idea about the relationship between "phases" and "poles" at first. The main thing is to realize that it's the number of subdivisions within the total poles available that defines the motor rpm.
So the EXTREME would be to use a Single Phase motor and wind it as a 12 pole design. The motor speeds that you would expect would be:
Low Throttle:
Single Phase with 2 Poles = (120 * 10) / (2) = 600 rpm
Single Phase with 4 Poles = (120 * 10) / (4) = 300 rpm
Single Phase with 12 Poles = (120 * 10) / (12) = 100 rpm
High Throttle:
Single Phase with 2 Poles = (120 * 60) / (2) = 3600 rpm
Single Phase with 4 Poles = (120 * 60) / (4) = 1800 rpm
Single Phase with 12 Poles = (120 * 60) / (12) = 600 rpm
Low Throttle:
Three Phase with 2 Poles = (120 * 10) / (2) = 600 rpm
Three Phase with 4 Poles = (120 * 10) / (4) = 300 rpm
High Throttle:
Three Phase with 2 Poles = (120 * 60) / (2) = 3600 rpm
Three Phase with 4 Poles = (120 * 60) / (4) = 1800 rpm
...based on the gearing that an ebike needs the Three Phase with 4 Poles would be okay:
Pedal Speed - From 0 to 100 rpm
Motor Speed (11-55 sprockets) - From 60 to 360 rpm
...so the pedal power would cover the lower rpms best and then the motor kicks in strongest to take the motor above 100 rpm. Pedal power would be your "extra boost" to get things going from a standstill.
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It's just like with rewinding DC brushed motors, depending on the way you wind them you get different behavior. The behavior we want for ebikes is a motor that develops it's power at lower rpm so that the gearing can be accommodated more easily. The Single Phase motor has a problem in that it cannot guarantee to start in the right direction and the (rare) Double Phase cannot guarantee starting either. So from a practical standpoint you need to go with a Three Phase. If you could increase the number of grooves in the stator from 24 to something like 48, then you could have more options. The standard stator uses:
24 grooves
12 poles
...which can be wound as:
2 pole, 4 pole and for Single Phase only 12 pole.