What is the mathematical limits of human speed? That question was addressed in an interesting article yesterday on The Final Sprint website.

John Einmahl, a Dutch mathematician and professor at Tilberg University in Germany, claims to have recently discovered that the world record in the 100m sprint can be lowered by another half-second. Einmahl claims that Asafa Powell’s current record of 9.77 seconds mark can be reduced to 9.29 now, and Paul Tergat’s record of 2:04:55 can only be improved by 49 seconds…

…Paula Radcliffe’s current marathon mark of 2:15.25 could drop by 8:50…

…He stated that in his field the unbelievable can be accepted; but the impossible is not recognized. Despite his results, the mathematician acknowledged that extraordinary performances may come along, contradicting his findings.

This is interesting to me. The article does not go into detail into how exactly he computed this, and the link to more information and sources was broken. Bummer to math and running geeks alike. Oh well.

Personally, I’ve always been optimistic that the men’s marathon record would be improved by several minutes still. It would seem that given enough training improvements, enough time, and enough prize incentive, that eventually someone would come along and break the 2:00:00 marathon barrier. Adeel speculates similarly on the Complete Running Network. For the record, 2-hour pace comes out to about 4:34/mile, but hey, didn’t people once say that the 4-minute mile was beyond human limits? And if a million moneys could type Hamlet over enough time, surely someone will break 2:00:00 at some point.

Okay, but let’s say for fun that John Einmahl the mathematician is correct, and that someday a runner, let’s call him “Super-Tegat” reaches the human genetic potential of running and busts out a 2:04:06 on a flat, sea-level course. End of story, he can go no faster right? Nonsense, Super-Tergat sold himself short. He should have ran the St. George Marathon. Not to speculate too much, but St. George is most likely the fastest certified course on earth, as long as you are trained for downhill and altitude. And Super-Tergat is all of that. No, St. George is not record-eligible (has a downhill gradient greater than 1%), but let’s just speculate here. The idea is no worse than the Steroid Olympics.

So let’s assume that Super-Tergat spent a good year training in Salt Lake City at elevation, running up and down the Cottonwood Canyons to calibrate his legs to the hills. He is ready to race in Utah. Weather conditions at St. George are perfect, 45 deg F at the start with no wind. My course profile calculations indicate that the course has a cumulative elevation gain of 410 feet and cumulative elevation loss of 2976 feet. Over the marathon distance (138375 feet), this equates to 0.296% uphill gradient and 2.151% downhill gradient.

Tim Noakes in the Lore of Running summarized a study that indicated that energy savings of running downhill was about half of the energy cost of running uphill at the equivalent gradient. For each 1% increase in gradient, running speed would decrease by 0.65 km/hr; for each 1% decrease in gradient, running speed would increase by about 0.35 km/hr. Given the total uphill and downhill gradients of St. George, how much faster will Super-Tergat run? The time of 2:04:06 converts to 20.4 km/hr. His net energy savings due to the given gain and loss converts to an increase in speed of 0.56 km/hr, increasing his overall speed to 20.96 km/hr. This equates to just over 4:36/mile and an overall time of about 2:00:40. Rats, just missed it! I’m assuming no effects on altitude either for the sake of this fun. Runworks.com has a great running calculator that uses the Noakes formula and comes up with results that confirm my own math (which is reassuring). Sasha’s Utah Race Predictor is based more on empirical data and observation, as I understand it, but is known to be uncannily accurate. Sasha’s calculator comes up with a time of 2:02:03, so is a bit more conservative, but may indirectly factor in the effects of altitude.

If St. George offered a huge purse to break 2:00:00, I imagine it would happen sooner rather than later, despite the fact that the course isn’t record eligible. Super-Tergat will come some day.