Saturday, April 24, 2010

predicting Old La Honda running time

Here's the model I described, fitting an equation to Minetti's data:

revised fit to combined run/walk dataRevised fit to combined run/walk data from Minetti

I should in theory be able to predict my time running up Old La Honda Road, assuming I am equally adapted to running as I was at cycling when I set my Old La Honda cycling PR last year.

From that ride I calculated this was around 299 watts as would be measured by an SRM, Quarq, or Metrigear Vector, or 5.31 W/kg. So what if
I could sustain that for the somewhat longer time I'd need to run up the hill?

First, I calculate the energy needed to run up Old La Honda. The simple way would be to take the average grade and use that, but instead I divided the climb into segments using iBike data and calculated the work required for each segment.

This work neglects wind resistance (it's from treadmill data) so I need to add that. Given a height of 1.69 meters, a width of 40 cm, and a CD = 0.8 with ρ = 1.15 kg/m³, I can calculate wind resistance as a function of speed: Pw = ½ ρ CD A v³, where A is my cross-sectional area (0.68 m²) and v is my speed. Since wind resistance power affects speed, and speed determines wind resistance power, the solution needs to be done self-consistently. I assume I weigh what I did when I did the Old La La Honda PR, and I added 3 lb for shoes and clothes. I used a Perl script for the calculation.

The result: it predicts I could run up Old La Honda in 23:38, a pace of 4:23 per km. Now I can state with 100% certainty I couldn't run that now. I view a prediction like that what a proto me, not having taken up cycling but running instead, could have done. Or maybe not even: maybe the same individual, similarly trained, can't produce as much power running as cycling.

In contrast, Gary Gellin ran a 24:29 during the first year of the Low-Key Hillclimbs. Gary's always been a bit faster than me riding uphill, and is a much better runner. So this reinforces the optimism of the calculation.

One possibility is running on a real road surface is less efficient than running on the treadmill used by Minetti. Another possibility is riding about allows for more work production (either greater metabolic exertion or a higher efficiency of conversion of metabolic exertion to mechanical work). At least the first issue should be evident in examining additional studies, as the issue of the energy cost of running has been investigated before: Minetti's work was unique in the range of road grades used.

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