Preposterous extrapolations: climate change and marathon runners

Burning fossil fuels has increased atmospheric levels of carbon dioxide. Yet an inevitable corollary of this fact remains widely unappreciated. Combustion theorists have long noted that fire, whether it occurs in a coal power plant, an internal combustion engine, a gas turbine, both fuel and oxygen. Both are consumed by the fire.

So stoichiometry tells us that oxygen levels in the atmosphere must be going down. Have they? Yes, they have: Andrew Manning and Ralph Keeling of the Scripps Institute of Oceanography have measured the decrease in atmospheric oxygen arising (mostly) from combusion of fossil fuels. From 1990 to 2000, oxygen in the air decreased by about 0.0031% 0.015%.

I find that fact to be amazing in and of itself. “But how will having less oxygen in the air change your life,” you might say. “Where’s the news I can use?” If you’re a runner, well, here we go…the atmosphere is thinner at altitude, and as a result, runners go slower. Conveniently for preposterous extrapolaters, some intrepid physiologists have developed a semi-theoretical (does that sound better or worse than semi-empirical?) estimate for the effect that altitude has on running. At sea level oxygen partial pressure is about 160 mmHg, but air up at an elevation of 520 meters has an oxygen partial pressure of 150 mmHg or so. And the physiologists’ semi-theory says that marathon world record equivalent times at 520 m are about 128 seconds slower.

Combining the atmospheric and phsyiological data, we see that world-record equivalent marathon times in the year 2000 might be 0.067 0.32 seconds slower than in 1990, due to the depletion of atmospheric oxygen by fossil fuel combustion. And, since the decline in running performance at altitude is somewhat offset by decreased wind resistance in the thinner air, decreasing oxygen at a constant pressure might be twice as worse as just thinning out the air.

For men between 18 and 34, the qualifying time for the Boston Marathon is 31:10:59. That’s about 51% slower than world record pace, meaning that slower runners huff, puff, and struggle for oxygen for a longer time. So I think it’s reasonable to assume that fossil-fuel-driven depletion of oxygen from the atmosphere lowers finishing times by a corresponding lower amount.

The end result? If you’re a runner, and you miss qualifying for the Boston Marathon by 0.2 1 second or less, you can use climate change as an excuse.

(The exercise of calculating the most probable number of people who have missed qualifying for Boston due to climate change is left to the reader.)

UPDATE: I was off by five-fold! The change in atmospheric oxygen from 1990 to 2000 was not 0.0031%; it is closer to 0.015% (as should have been clear to had I read the caption to Table 2 in this paper more carefully.) That means that world-record equivalent marathon times may have gone up by between 0.3 and 0.6 seconds due to oxygen depletion in the atmosphere. Times for male would-be Boston qualifiers have gone up from 3:10:59 by a full second. Thanks to Ralph Keeling for the correction, and also be sure to check out his new web site on atmospheric oxygen research.

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