Yesterday’s post on applying intro physics concepts to the question of how fast and how long football players might accelerate generated a bunch of comments, several of them claiming that the model I used didn’t match real data in the form of race clips and the like. One comment in particular linked to a PDF file including 10m “splits” for two Usain Bolt races, including a complicated model showing that he was still accelerating at 70m into the race. How does this affect my argument from yesterday?
Well, that document is really a guide to fancy fitting routines on some sort of graphing calculator or something. Which is fine as far as it goes, but I think it attributes too high a degree of reality to those unofficial split times, which are obtained from some unidentified web site. They proceed to fit a bunch of complicated functions to the data, but I think they’re overthinking it.
Let’s look at the actual data, graphed in more or less the way you would expect to see it in an intro physics class: as a plot of position vs. time:
The black circles represent the times from a race in 2008, the white circles times from a race in 2009. They’re practically right on top of each other, because in absolute terms, the difference in times is pretty tiny.
Their first step is to fit a straight line to the data, which works remarkably well, even though it can’t possibly be right. Looking at the graph, though, it does look awfully linear, particularly if you threw out the first point or two. That seems pretty consistent with the “accelerate to a maximum speed and stay there” model I assumed in the previous post, especially given that we don’t know anything, really, about how these numbers were obtained.
Of course, the real test is to look at the speed as a function of time: