On Bicycles, and.... what else is there?

The last time I considered the constant cadence approximation as it applies to circular chainrings. Recall the principal issue is that the constant cadence approximation makes the following assumption for each pedal stroke: = × where ω is the angular velocity of the pedals, τ is the propulsive torque, and brackets signify a time-average. The error from this approximation is obviously: × − which is fairly trivially shown to equal: − ) × (ω − )> which is proportional to the correlation coefficient between torque and angular frequency, where a positive correlation results in an underestimation of power. Angular frequency is proportional to what I refer to as "instantaneous cadence": the rate at which the crank arms are revolving. So the issue comes down to whether the instantaneous cadence is correlated with applied torque, or similarly, if it's correlated with applied power (assuming applied power fluctuations are due more to torque changes than cadence c...