Monday, October 26, 2009

Soda Springs power estimate

The Soda Springs Low-Key went rather well in most regards. As a participant,I was pleased with my finishing place. I usually train with a PowerTap, but for most races (especially hillclimbs!) I leave the powertap wheel home and instead use a carbon race-only tubular (either my Reynolds MV-32T or my Mt Washington).

On hillclimbs, though, I can generally estimate the power. The key parameters are total weight, rolling resistance coefficient, wind drag coefficient, and air density. For PowerTap-equivalent power I do not need drivetrain efficiency, since drivetrain losses aren't measured by the PowerTap, anyway. Given these, it's simple enough to calculate power from speed.

So, some numbers:
  • weight: I was 125 lb in the morning upon wakening. Given input - output, I was probably close to this at the start. Curiously, I'd been almost 3 lb lighter the last time I weighed myself two days before. A lot depends on what I've been eating and how hydrated I am. Additionally, my bike weighed out at 11 lb 6 ounces before the start. This was one ounce more than I expected, but I'd accidentally mounted the wrong tire on my front wheel. Hard to comprehend how I could have gone through an entire tire-glueing procedure without noticing this.... I only noticed it, in fact, when I was looking at a photo of myself after the race! Add in the weight of shoes, clothing, and my water bottle and I figure around 4 extra pounds is pretty close: should be within 1% of actual total weight.

The pre-climb weigh-in (Rich Hill photo)

  • Rolling Resistance: My rear tire has a value reported by Al Morrison to be 0.234%. I accidentally had a Veloflex Carbon on my front wheel, with a value of 0.312%. Given the slope, the rear wheel should be responsible for around 2/3 of the total, the front wheel around 1/3, putting the average around 0.26%. The road on the climb is rough in sections, so I'll assume an actual value of around 0.4%.
  • Air density: At Redwood Estates in the hills over Los Gatos (1690 ft elevation), air pressure was 29.98 inches of Hg, while the temperature was 67.2 F with 70% humidity at 10:32 pm, around the time of the climb. These values yield an air density of 1.13 kg/meter³.
  • Wind drag coefficient: I'll use the value I extracted from Old La Honda data, CdA = 0.36 meters².

Okay, then. I climbed 2368 feet over 5.35 miles in 32:04. For these sorts of calculations, with mixed imperial and metric units, the Unix "units" program is great, as it handles the unit conversions.
  1. Climbing power = weight × feet gained / time = 234 watts
  2. Rolling resistance power = weight × Crr × speed = 11 watts
  3. Wind resistance power = ½ ρ CdA × speed³ = 18 watts
  4. Acceleration power: I went from 0 to 10 mph over 32:04, which works out to 0.3 watts, or zero with the 1 W precision used here. I never braked during the climb, so there were no other accelerations which were not canceled by other decelerations.
  5. Total = 263 watts
If I wanted to determine SRM or Quarq Cinqo watts (or MetriGear Vector), I'd divide by an efficiency term, for example 0.97, and thereby estimate maybe 271 watts.

I was probably around 290 watts (PowerTap equivalent) when I set my Old La Honda PR in July. Sure, Soda was almost twice the duration, but that's only responsible for a few %. Specifically, assuming a critical power model where AWC = CP × 60 seconds, which generally fits my data, I'd expect a 2.7% loss in power going from OLH to SS: around 8 watts. This at least brings my effective OLH power above 270 watts PT-equivalent, not bad for the Noon Ride, but not up to competition standards.

I think it shows a difference between off-season (lifting, running, generally not pushing things too hard) and in-season fitness. The same applies for everyone in the Low-Keys, however. None of the top guys are in mid-summer fitness.

D'oh! (Rich Hill photo)

So what was the penalty of my bad tire choice? Let's use Al's numbers of 0.08% difference for the wheel, blow that up to 0.11% for the rougher road, and assume 1/3 of weight on the wheel, yielding 1.0 watts lost to propulsion out of 263. Using a formula I derived earlier, with 88% of the power mass-proportional, this yields a speed penalty of 0.30%, or 5.9 seconds. There's also a mass penalty, as the Record is slightly heavier, around 1 ounce. That penalty is an extra 0.6 seconds, bringing the total to 6.5 seconds. I was 22 seconds down on Eric, however, so this mistake didn't affect my placing.

For error analysis, a large source of uncertainty is the total climbing. For every 10 feet of error in the total climbing feet that's a difference of 1.0 watt. But the climbing feet agree with those recorded by two other riders on their barometric altimeters, each recording slightly less, not more climbing than the Garmin data I used as a reference. I'll stick with the Garmin numbers, since they're less susceptible to barometic drift due to the GPS signal used as a calibration correction to the barometric signal, the latter better for detail.

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