CJ/Usain revisited

I just read Pinoy's take on an imaginary Usain v CJ race. Awesome idea but there is literally a math error every sentence. I thought this idea was cool enough to warrant putting some effort into. Here is my take on the race from the perspective of an engineer. ( and it ends better than I expected =] )

First, my beef with Pinoy's method is that he uses a single equation the entire way through: distance * velocity = time. The equation is actually time * velocity = distance. Anyone that does not believe me should take dozens of hours to drive to the grocery store. In Pinoy's case, he uses the bad equation to calculate that Usain is running at .106 yards a second. That's 3.816 inches a second. Then he uses the same equation to extrapolate a bunch more times. In some cases two math wrongs make a right. In this case it's just really, really wrong.

The way I went about it was using a trend line onto Usain Bolt's 10, 20, 30, 40+ meter split times during his 100m dash.


x-axis is meters and y-axis is time

------------math warning--------------

These distances are in meters. 36.58m is the equivalent of 40yds. Therefore, we need to find where the line hits 36.58m. To do this, I used the regression tool at, which spit out this equation:

y = -2.558333333·10-6 x4 + 2.641666667·10-4 x3 - 9.904166667·10-3 x2 + 2.495833333·10-1 x + 0.146

which fits perfectly. Plug in 36.58 for x,

------------end math warning-------------

and we get a 40yd time of..... 4.3726s. Compare to CJ's 4.24s.

BUT WAIT. People say, what about the fact that Usain had to react to a starting gun? Included in Usain's data is a .146s reaction time to the gun. Subtract that from his time and he has a theoretical time of 4.23s. Which means he beats our CJ by a fingertip. However, think about how much time those dreadlocks add to CJ's time LOL. That's an easy tenth right there. Then think about how perfectly efficient Usain's body is for sprinting at this point. CJ could easily gain another tenth by losing some Cuervo pounds (Lendale is a bad influence) along with some more specialized working out.

Conclusion: not a perfect model, but I have Usain winning by just over a hundredth of a second. However, like I said, I think CJ EASILY makes this time up. Usain has to have been told this as well. This is the probably the reason why he is not accepting a race. Think of how much endorsement money he stands to lose.

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