Monday, October 28, 2013

Chicago Marathon Winner and His Apparent Lack of Work

The Chicago Marathon was run on October 13, the first major marathon in the United States since the Boston Marathon.  Its male winner was Dennis Kimetto, and he finished the marathon in 2 hours, 3 minutes, and 45 seconds, beating the record of 2:04:38 set last year.  He was just a farmer a few years ago, and now is setting records in international marathons.

I wanted to calculate his average speed as well as his total work (just for the marathon not training) and see how much energy he had to expend to run the marathon in record time.  To calculate his average speed (assuming a flat course) I found the total amount of time he was running (7425 seconds) and divided the total distance (26.1 miles or 42155.8 m) and found his average velocity to be 5.6 m/s.  Assuming he accelerated to this speed in the first 10 meters of the race, I found his acceleration by using vf=vo+2ax.  I found his acceleration to his top speed to be 0.28 m/s^2.  And then assumed his acceleration for the remainder of the race to be 0 m/s^2, assuming he held a constant speed for the remaining 42145.8 m.  So his average acceleration would be 6.64x10^-5 m/s^2.  I also assumed his mass to be approximately 50 kg, and calculated his total work by using W=Fd, finding his total work to be 140J.

This seems absurdly low compared to the amount of energy expended by Usain Bolt in his record setting run (28500 J), and even the energy expended (1968 J) by the world high jump record holder (Javier Sotomayor) in his world record jump of 2.45m.  This comparison is because our current work equations do not take into account the force necessary to maintain one's speed over a period of time, merely looking at the amount of acceleration.  Though Kimetto was assumed to be running at a constant speed for over two hours, his acceleration was almost 0, meaning that with our current equations, this seems as if he was inputting very little work for his two hours of running at record setting pace.  Obviously, Kimetto was putting a lot of work into his running, but by our numbers, it was much easier for him to run 26.1 miles in two hours than for Usain Bolt to run 100m in 9.58s.


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