You may want to take a look at the
Friction Drive FAQ.
There's usually a centrifugal clutch between the engine and the roller. So, the engine has to be above a certain RPM before the clutch engages. That's normally in the 2500 to 3000 RPM range. But, for 4-strokes, the clutch engagement RPM may be lower.
When the clutch is engaged, the roller RPM is the same as the engine RPM (unless the clutch is slipping.)
As the roller (or, for that matter, any wheel) spins, a point on the outside of the roller is moving at some speed that is dependent on the distance from the center of the spinning roller, and the RPM of the roller.
That speed can be calculated as follows:
Velocity (in MPH) equals Roller Diameter (in inches) times RPM times pi times 60 divided by 5280 divided by 12
V = (60*pi*d*RPM) / (5280 * 12)
The whole thing can be simplified to
V = d * RPM * 0.002975
or
V = d * RPM / 336.14
Note - For the metric system, with wheel diameter in cm and speed in Km/Hr, the constants are different:
V = d * RPM * 0,001885
or
V = d * RPM / 530,5
So, a 1 inch roller, at 7500 RPM, could push you along at up to 22.3 mph and a 1.5 inch roller at the same RPM would 33.5 MPH. Likewise, a 7/8 inch roller would give you a 19.5 MPH max speed
Note that this calculation results in the maximum speed you could attain - it does not account for slope, rider weight, wind resistance, engine power, roller/tire resistance, tire rolling resistance, air pressure, or any other variables that could impact your final upper speed.
Here's the link to the
gearing/friction drive calculator I wrote a while back.