**A project in correcting power data for altitude to gauge aerobic stress.**

The aerobic stress of a cycling effort is gauged “fairly” by using power (assuming the power meter is calibrated. c.f. Brailsford’s Bullshit) only when the relative aerobic effort stays fair across the measurement. In the case of going to altitude, the blood-delivery demands on the heart, blood, and lungs increases because the amount of oxygen being drawn into the lungs with each breath is reduced. The effect is a physiological state of “I am breathing like I am doing 330 watts, but I’m only getting 270 watts out of my legs”.

Below is my power data from the Mt.Evans Hill climb (July 25, 2015). I rode in the Pro-1-2 field and placed right near the back of the pack. I dispatched myself out the rear of the peloton at 9.7 kms (end of the blue datapoints) and rode solo (green datapoints) the remaining 33.9 kms. We had just surged for a minute at around 4.4 Watts/kg and I was going to find myself in serious trouble in short order if I kept with the pack. The result here is 280.0 Watts which amounts to around 3.22 Watts/kg. The duration of my effort was 140.6 minutes. My bike weighed an additional 17.5 lbs and I started with 3.3 lbs of fluids which I consumed by halfway where I took on another 3.3 lbs of fluids which I drank by the top.

power data vs time with splined trendlines

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The power data is exponentially weighted by the altitude that it was produced at (i.e. weighted by oxygen content of air at that altitude) and then corrected by the time-weighted altitude of the effort. The correction is linear and amounts to ensuring that the mean-power calculation matches the corrected and uncorrected data. (This finds that relative to sea-level [exp(0)=1] this power has a mean discount of 67.15% or equivalently the ride occurred at an average of 3185 m elevation). The formula is at right and the predicted trend for power is shown below in blue. Note that this trend is not itself exponential as the rate of ascent was not linear.

power data vs time with trend expected by altitude

Shows distinct difference between riding with the peloton and riding solo.

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Performance relative to the expected trendline is also calculated (i.e. flatten the blue line above to determine when I was going hard and when I was going easy in terms of oxygen delivery). The trend below matches to a much greater degree the perceived exertion during the race, the fact that I felt like I was absolutely lighting it up towards the finish is clear on this plot, and not clear at all from the power data alone. Following the short descent to Summit Lake around 6700 seconds I get onto the final switchbacks where I push myself 5% rising to 15% above the average “aerobic power” for the effort. Consider that Coggans power-zones are all about 15% of FTP wide I managed to lift myself almost an entire zone towards the finish. This was not a case of holding things in reserve to spend at the finish. It was the case of getting in serious anaerobic debt during the final 20 minutes of the effort.

Power trend relative to the expected flat-line based on altitude-weighted average.

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Finally a few extrapolations that show that the model is imperfect. It suggests that if done at sea level I should/would have been able to do 417 Watts. If done in Edmonton I should have been able to do 383 Watts. Some TT-like efforts in the 140 minute range that I have at much lower elevations are my two races at Oliver in the 93km TT where I managed 284 and 298 watts. Neither of those efforts in Oliver was O2 constrained. The model works well to predict fade as I move from where I am acclimatized (arguably ~1500 m) to where I am not (4200 m) because it accounts correctly for the rate-limiting feature of cycling ergogenesis in those conditions. Going from Ft.Collins down, the rate-limiting feature of my performance over a 2+hr effort would not be oxygen delivery and so the gains in performance would not be seen.

Sea level watts!

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