Unfortunately, found exactly that yesterday, when I did 15 mi of mostly flat neighborhood laps watching the power ratio S on my SL 1's display:
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S is the top field here. In principle, it should have been pretty constant for constant E at Pr values along the pre-saturation ramp in the plot of mechanical motor power Pm vs Pr.
Provided the ramp's actually a straight line.
Manipulated assist ease E via the SL 1's E = M MicroTune. (In principle, the varying M should have had no effect on S.) Tried to keep Pr below any reasonable saturation value Prs.
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Kept cadence at 70-100 rpm, a range where Px (max motor power available at M = 100) and motor efficiency are reasonably flat. Official data here.
The only findings I'm prepared to share at this time:
1. Not clear how to interpret much of the variation seen in S. So yes, maybe not as valuable a tool as I'd hoped.
2. Sometimes S was constant over a range of Pr values likely to be under Prs, sometimes not. Will try again.
3. S is
very nonlinear in E — in fact, roughly quadratic, meaning that doubling E generally
quadrupled S! The S vs. E curve from the official SL 2 Prs data is more exponential than quadratic. No idea what's going on here.
Cadence only enters the picture via Px and efficiency. Keeping cadence at 70-100 rpm as I did pretty much eliminates that confounding factor. In which case, cadence and the gear you're in become irrelevant.
Power is power, and on the SL 1, rider power Pr is a
measured quantity.