Gear ratio question

[Beekeeper]

This is only hypothetically speaking. I’m only interested in the maths

Assuming riding on the flat and a constant cadence at all times with a 15t Bosch chainring at the front and an 11t sprocket at the rear, what size front sprocket would you need to replace the 15t with in order to double the speed of the bike at that same cadence?

 

[Jackware]

You would need a 47.5 tooth front sprocket at least

 

[KennyB]

30.
Each revolution of the chain ring turns the sprocket 15/11 revolutions. To double your speed you need to turn the sprocket through 30/11 revolutions so you need a 30 tooth chain ring. To calculate the speed you need to do a calculation involving cadence, gear ratio and circumference (or diameter x pi (or 3.14)) but that's not necessary for your question.

 

[Beekeeper]

The problem is the Gen 2 Bosch can’t really accept a front chainring much over 20t because of the space available.
For each pedal rotation it spins x2.5 to compensate for the smaller chainring

 

[urastus]

kennyb is right.