Hrmph.
The real issue is the exact proper motion, not the dispersion about the mean.
Although I suppose outliers can be interesting, even in small N groups.
This is very clever.
I award it a clear: "damn, I wish I had thought of that...!"
"Velocity dispersions in a cluster of stars: How fast could Usain Bolt have run?
H. K. Eriksen, J. R. Kristiansen, O. Langangen, I. K. Wehus
(Submitted on 1 Sep 2008 (v1), last revised 2 Sep 2008 (this version, v2))
Since that very memorable day at the Beijing 2008 Olympics, a big question on every sports commentator's mind has been "What would the 100 meter dash world record have been, had Usain Bolt not celebrated at the end of his race?" [...] We revisit this question by measuring Bolt's position as a function of time using footage of the run, and then extrapolate into the last two seconds based on two different assumptions[...] In these two cases, we find that the new world record would have been 9.61 +/- 0.04 and 9.55 +/- 0.04 seconds, respectively, where the uncertainties denote 95% statistical errors."
Am. J. Phys. (submitted)
Figure from paper, showing the author's estimated extrapolated position of Bolt if had maintained his acceleration to the end of the race rather than pull up.
The second figure is Bolt's actual position close to the end of the race, as he started pulling up and reduced his acceleration, the lead figure is a photoshopped estimate of how much further Bolt would have got at the time at which he would have been extrapolated to have crossed the finish line, if he has sustained his acceleration.
They predict that if Bolt can maintain his acceleration after 8 seconds through to the end of the race, and if he has some tailwind, but within the limits permitted for a record run to be recorded, then he could just break 9.5 secs for the 100m.
Very impressive.
Steve Hsu at Information processing had some strong opinions on Bolt's perfomance: Phelps, Shmelps - Bolt is the man and Bolt is the greatest of all time
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