In electric axes you need to gear down a lot to allow the motor to actually reach a desired speed quickly. This is why the few drill powered axes around appear to hit fairly hard. Jamie's, for example, I believe has a 5:1 reduction from the drill to the weapon. That puts the total reduction to a huge 180:1 if it's a standard drill gearbox. Allowing for load, some 100rpm on the axe shaft.

People never seem to gear very low with axes. Unless you have a dynamic ratio built into the transmission and a stonking powerhouse motor, I don't think you'd be able to accelerate to much more than, say, 250rpm on the axe. I'm sure all of this can be calculated and that's a wild guess.

If the scooter motor above is running nominal voltage I believe they typically spin around 2500rpm. With the 4.2:1 ratio that means the axe is in theory able to reach 600rpm. I'd be very surprised if it were to come close to that speed inside 180 degrees of swing. I think it's safe to say that to an extent you gain speed if you gear for less speed. If I were to ever build an axe without an accelerating mechanism I'd aim for around 250-300rpm tops, as you're getting the most out of your motor for greatest efficiency. Which is why the drill axes seem to work so well. The entirety of the useful energy put out by the tiny motor is used and so the axe comes round hard, despite the at first ridiculously high sounding gear reduction.

I... I t-think. :P