In most jurisdictions, e-bikes must not provide assistance above a certain speed. One way to achieve this is by using a freewheel mechanism and configuring the controller to never exceed the motor's max RPM.
In the EU the max assisted speed is 25 km/h, which is about 7 m/s.
A typical hybrid bike might have a 700c rim with a 1.5" tyre, giving an overall diameter of about 700mm, so a circumference of 2.2m.
This means your target wheel speed is 3.18 Hz (revs per second).
7104 rpm = 118.4 Hz
Your ideal ratio would be 118.3/3.18 = 37.2327/1
There is no way you're using a 555 tooth wheel gear. (37 x 15 = 555)
At this point you have two options and may need to use both:
- Use a planetary gearset to implement a 2-stage reduction, a 9:1 gearbox would allow you to hit 37.2 overall with a 62 tooth gear at the wheel (9 x 62/15 = 37.2). If you're using a standard size RC or powertool motor (e.g 700 series), you can probably buy off-the-shelf gearboxes that just bolt on.
- Use a different motor with a lower Kv.
The calculations above assume you want the lowest possible gearing for maximum assistance at low speeds. This is most helpful in an e-bike. I haven't made any consideration of the motor's torque curve or efficiency curve.
Most commercially sold e-bikes use a mid-drive arrangement: the motor is connected to the crank, so the motor gets the same gear reduction as the rider. This is beneficial because the motor would only need to be efficient across a narrower range of speeds, e.g 50-100rpm vs 5-25km/h. With a brushless motor your controller can apply field weakening to continue delivering max power beyond the motor's base speed.