E-Bike Drive System Question

[BrianG]

I was just thinking, is there any reason why a smaller drive system isn't used on the rim where the brake calipers sit? I would think it would be a whole lot easier than using an elaborate sprocket system or the use of special hub motors.

For example: The diameter of a 26" bike wheel at the rim is probably closer to 24". If a 2" rubber wheel drives the rim and is directly coupled to a motor spinning at 20k rpm, this would equate to a speed of around 40mph.

Just thinking out loud here...