- body mass: around 1 lb
- equipment mass: let's say 1 lb
- rolling resistance coefficient: 20% seems reasonable. This was really seat-of-the-pants.
- wind drag coefficient: 10% seems about right
- distance 0.1 miles. Exact starting location, the placement of the finish, and line through the corners are all factors
- altitude gained: 15 feet sees consistent with individual reports
- wind speed: Zero was assumed. Given variable winds reported at Redwood Estates, a conservative estimate of error of this estimate is probably 1 mph
- transmission coefficient: based on differences in chainline, I'll say 1%. This doesn't affect the derived Powertap-equivalend power, but it does affect the significance of comparisons in power from one ride to the next.
- time: 2 seconds seems good: 1 second with recording the finish time, and 1 second for a delay in starting from when the horn was honked
- acceleration: I may have crossed the finish as fast as 15 mph
- body mass & equipment mass: I'm assuming each affects power the same. These affect climbing power, rolling resistance power, and acceleration power. The resulting changes are:
- climbing power: ΔP = 1.7 W
- rolling resistance watts: ΔP = 0.08 W
- acceleration power: ΔP = 0.02 W.
- rolling resistance coefficient: changes rolling resistance power in proportion to error: ΔP = 2.2 W.
- wind resistance coefficient: changes wind resistance power in proportion to error: ΔP = 1.8 W
- distance: this affects wind resistance, rolling resistance, and acceleration power. First, a 0.1 mile difference out of 5.35 miles is a 1.87% difference in speed. From this:
- Wind resistance increases by approximately 3 × 1.87%, +5.71%: ΔP = 1.0 W.
- rolling resistance increases by 1.87%: ΔP = 0.21 W.
- Acceleration power increases by approximately 2 × 1.87%, ΔP = 0.01 W
- altitude gained: weight × height / time: ΔP = 1.5 W
- wind speed: wind resistance changed proportional to twice the ratio of wind speed error to bike speed: ΔP = 3.6 W.
- transmission coefficient: error in power = error in transmission coefficient × total power: ΔP = 2.6 W
- time: the time error was 0.10%. This affects climbing and rolling resistance power by the same fraction. Wind resistance power is affected by 3 times this proportion. Acceleration power is affected by twice this proportion (an insignificant contribution). In total: ΔP = 0.31 W
- acceleration: changes acceleration power by up to +125%: ΔP = 0.4 W
Okay.... drum roll....
So my estimate of 263 W could in effect be anywhere from 257 W up to 269 W. Given the 8 W difference from OLH distance to Soda Springs distance, that would be an effective OLH power of as high as 277 W powertap-equivalent. Were I to have extracted that value, given my present fitness, I'd not be concerned, especially since there's similar error bars on that 290 W estimate from my Old La Honda climb this summer.
So the end result is: don't place too much importance in these sorts of physics-based power estimates. There's too many variables, too many sources of error, even for something as straightforward as a steep hillclimb.
Perhaps surprising in the strong influence of wind resistance on the error estimate: that term alone increased the uncertainty by 1.2 W. And we made a seemingly trivial estimate of the uncertainty in the wind speed: only 1 mph, essentially impossible to detect without instruments.
So don't sell that power meter yet.