comparing Powertap to Speed-Power model

I typically use my Powertap on training rides, but when racing, I've not done so since I placed third Ross's Epic Hillclimb up Pine Flat Road in Sonoma back around 2008 or so, At the climb, I'd decided the added weight of my Powertap wheel was worth it for the pacing advantage of power. Unfortunately, my battery died on the start line, so I carried the substantial extra mass of the Powertap up the hill for no advantage. Despite the lack of power, though, I had arguably the best climb of my life, staying with a critical surge I might well have not gone with had I been pacing off the meter. That surge led into a flat/slightly descending part where being with the group was a critical advantage. When the climbing began again, steeply, I felt as if I was going to crack, but then most of the others cracked more. Without the weight of that wheel I may well have been one place better.

But power is also useful for post-ride analysis. But for that, I rely on the standard power model. For climbs it requires reasonable estimates of rolling resistance coefficient, total mass, wind resistance coefficient, and air density. Air density is predictable from altitude, or if you look at nearby meterological data (which I rarely do), adding in barometric pressure and maybe, if especially fanatical, relative humidity. For modeling power meters which work ahead of the drivetrain you also need drivetrain efficiency, but not for Powertap data, which measures downstream of the drivetrain.

I decided to compare the model to my Powertap data from Old La Honda this past week. For CdA I used 0.45 m² which is likely suitable given I climb on the hoods or tops (Tour magazine measured 0.32 m² for a dummy in the wind tunnel, and this number has been found to work well for pro cyclists when analyzing race data). For air density I used 1.226 kg/m³ but then adjusted it for measured altitude, exponentially with a reference altitude of 8150 meters (this has relatively small but observable effect on Old La Honda). The rolling resistance coefficient I set to 0.4% which would apply to inflated tires on smooth pavement. This may be optimistic for parts of Old La Honda but the pavement is presently in very good condition by historical standards, as it has been for several years. For mass I used an estimate of my own (58 kg) with additional estimates of my bike (8 kg) and of "other stuff" (2 kg). This estimate is likely slightly low, in particular the "other stuff" which includes clothing, helmet, tool bag, Garmin, bell, pump, and water bottle (around half-full).

Anyway, without any specific calibration, the model fits fairly well. Here's the result:

Any conclusions I might gain from the power meter data would also be gained by the model, with the possible exception of that anomalous spike in modeled power at 2.2 km. There's also a significant underestimate in measured power from 3.2 km to 3.8 km.

So what causes that spike? To answer that I set the inertial mass to zero in the model, and presto, the spike was gone. Of course inertia is an important part of cycling kinetics. Acceleration requires power, and decelleration returns it. But the issue with inertia is it amplifies errors in bike speed. In this case I was calculating speed from GPS position, and GPS position is subject to noise.

But the Garmin reports speed directly as well as position. It gets speed from the Powertap wheel, which measures it directly. So I used this speed instead of calculating it. That solved the problem.

Here's the result:

So the model works quite well. Sometimes power appears a bit shifted relative to the Powertap, but the overall trend is clear: I was running out of gas. Had this been a record attempt, having left my Powertap wheel at the bottom, I likely would have had a valid analysis of my effort.