A Simple Model for Predicting Sprint Race Times Accounting for Energy Loss on the Curve --- J. R. Mureika

8. Is the 300 m Now a Short Sprint?

Keller determined that the maximum distance over which an athlete could run using the strategy f(t) = f was dcrit = 291 m [1]. Likewise, physiologists have suggested that a human cannot run at full speed for longer that 30 s (see [6] and references therein). While the latter study is just over 10 years old, one wonders whether or not dcrit has dropped. Alternatively, if a sprinter can run a sub-30 s 300 m, would this entail that the different strategy used for races longer than 291 m no longer applies?

As with the 200 m, Table 5 outlines possible 300 m record times, as run in lane 4 of a standard indoor track. Since the actual (if there is one) value of 2 is unknown, a range of 0.30 to 0.50 is chosen in light of the 200 m results. In the case of lane 4, the race is made up of the segments (in meters)

The estimated time for the first two choices of 2 are under the 30 s barrier by more than half a second, while 2 = 0.5 yields a value of 29.72 s (with reaction). Comparison to the current WR of 32.19 s (Table 1) give time differentials of approximately 2.49 to 3.06 s! The 300 m times may be a product of a decaying fit to the data. However, the time differentials cited appear far too large to be manifestations of statistical error alone, which would suggest that there is an additional mechanism (perhaps physiological in origin) at work over this distance. This approach would suggest that the 300 m is still not a sprint, by the definition of Keller [1].

Table 6: Predicted indoor 300 m World Records, as run in lane 4.
2t50t100t150t200t250t300t300+0.16
0.305.52 9.87 14.55 19.13 24.08 28.99 29.15
0.405.55 9.93 14.69 19.29 24.33 29.27 29.43
0.505.59 10.00 14.85 19.47 24.59 29.56 29.72

Section index
7. Predicting the 200m World Record
9. A Practical Example: Donovan Bailey
Curve Model
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