Here are the 2 plausible reasons why a stages pm drift from a trainer at different cadence's:
(1) higher torque creates more slip (for those with tire-on trainer)
(2) higher torque reveals more left-right imbalance from rider ...which is picked up only by the 1-sided stages
And since bike computers only display cadence, and cyclists only talk of cadence, no need to remind everyone of grade school physics. Because the practical real world results means a stages PM might show different variance to a trainer at differences cadences and different loads, which is masked when comparing avg values across a complete ride, and becomes misleading when one assumes they "match" perfectly while turbo-training in different conditions
youngs_modulus wrote:I have no doubt you’ve seen one meter read higher than another, but cadence isn’t the reason. It can’t be.
I’m about to explain why, but I should warn you that I design scientific instruments for a living, so I think about this subject way too much.
TL;DR: Cadence can’t explain different readings because of the way power is calculated from what these meters actually measure (torque). While there are a lot of reasons one meter might read higher than another in the short term, if the two readings converge over the course of a ride, the meters are effectively reading the same torque, and that’s what matters.
Ok; on to the gritty details:
Power is torque times angular velocity (omega). In other words, P = T ω. Omega is conventionally in units of radians per second, but that’s a straight unit conversion from RPM. (E.g., 100 RPM = 10.472 rad/s).
For two meters on the same bike, ω (cadence) is the same, because angular velocity is trivial to measure and doesn’t drift. So if the meters are giving substantially different readings, they’re necessarily measuring different torque values.
All meters do some signal processing to turn their strain gage readings into torque measurements, and the details of how they do that are part of what cause different meters to read differently at any given moment. For example, one meter may have a different thermal compensation algorithm than another, causing readings to diverge with temperature. Smoothing is a big deal in signal processing, and discretization error can affect the power displayed on your bike computer (though not as much at the meter) for short periods of time.
But the fact that two meters have measured a very similar amount of work done over the course of a ride (kiloJoules, which is essentially average power) means that they agree about torque (and they necessarily agree about cadence).
Going back to the formula that all power meters use to convert strain measurements to power: power is torque times cadence. If, at a given cadence, two meters disagree, that’s because they’re measuring a different torque. And if they’re measuring different torques beyond a certain margin of error, one or both is miscalibrated.
A power meter with a miscalibrated slope would be off by the same amount (proportionally) regardless of cadence, so you wouldn’t see of a difference there due to cadence. A power meter with a miscalibrated offset could read high at low torque and low at high torque or vice versa. But the error is torque-dependent, not cadence-dependent.
Keep in mind that most powermeters change their offset (their “zero”) multiple times over the course of a ride. Thermal compensation demands this. Meters try to do this when you’re not pedaling, ideally when stopped at a light. But many people load up their drivetrain slightly at lights. If you were stopped at a light with your left foot on the ground and your right leg resting on the pedal at 90 degrees to TDC, a Stages meter would get an accurate offset at that stop while a Qarq would get a slightly erroneous one due to the weight of your leg on the right crank. This would cause the two meters to give slightly different readings until the next zero.
The point is, there are many, many reasons why one meter would disagree with another, but cadence isn’t one of them. And if two meters agree over the course of a ride, they basically agree on torque, and since that’s what they’re measuring, you can’t really ask for more than that.
I bet you’re sorry you asked.