RPM versus power

[Gerhard]

I have done some power check at 80rpm and marked the wattage (@80rpm) for 100 to 500 watts on the flywheel case, to help me switch the setting during a structured workout.

The data fetishist in me needed to check these damper settings at 50, 60, 70, 90 and 100 rpm as well and I think I ‘discovered’ a structural relation between power and RPM - more than I expected (though it does make sense..)

50rpm - 25% of power @80rpm
60rpm - 42% of power @80rpm
70rpm - 67% of power @80rpm
90rmp - 140% of power @80rpm
100rpm - 190% of power @80rpm

These are my personal estimates. Is there any official calculation to get actual percentages? I guess the power calculations are sort of open source, but dont know where to find them..

[Nomath]

The general relation between power and rotation speed for an air-braked flywheel is : P = C * ω³ + ω * J * dω/dt
Here ω is the angular velocity of the flywheel, which for a BikeErg will be proportional to the RPM's of the pedals. C is the drag coefficient.
For a BikeErg the variations in the angular velocity over a pedal turn are very small, so the second term is negligible. Hence P = C * ω³.
So you can expect a cubic relation between power and RPM.
If you take 80 rpm as the point of reference (100%), the formula predicts :
- 50 rpm : P = (50/80)³ x 100% = 24%
- 60 rpm : P = (60/80)³ x 100% = 42%
- 70 rpm : P = (70/80)³ x 100% = 67%
- 90 rpm : P = (90/80)³ x 100% = 142%
- 100 rpm : P = (100/80)³ x 100% = 195%
Your estimates are remarkably close to these theoretically predicted values.

The nice thing is that the formula also accounts for the effect of the drag factor: it is linear. So if you change the drag factor from 125 to 100, the power goes down by 20%.

[Gerhard]

Thx Nomath!