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


6. New Model Parameters for Modern World Records

The parameters (5) are more than likely out of date, as they were calculated by fitting records almost 25 years old [1]. Also, these were fitted for a model which does not accurately model the velocity curves of sprinters. For example, a 100 m runner's velocity is not strictly increasing, but rather peaks between 40 and 60 m. Table 1 lists the sprint WRs as of March 1997, from 50 m to 400 m [4],[5].

Table 1: Men's Sprint World Records as of March 1997. Wind speed of `i' indicates indoor performance; `A' indicates performance at altitude.
Event t (s) vw (m/s) Athlete Location Date
50 m 5.56 i Donovan Bailey (CAN) Reno, NV 9 Feb 1996
55 m 5.99 i, A Obadele Thompson (BAR) Colorado Springs, CO 22 Feb 1997
60 m 6.41 i Andre Cason (USA) Madrid, ESP 14 Feb 1992
100 m 9.84 +0.7 Donovan Bailey (CAN) Atlanta, GA 27 Jul 1996
200 m 19.92 i Frank Fredericks (NAM) Lievin, FR 18 Feb 1996
19.32 +0.4 Michael Johnson (USA) Atlanta, GA 1 Aug 1996
300 m 32.19 i Robson daSilva (BRA) Karlsruhe 24 Feb 1989
400 m 44.63 i Michael Johnson (USA) Atlanta, GA 4 Mar 1995
43.29 Harry Reynolds (USA) Zurich 17 Aug 1988

New parameters (f,) and (f,,c) have been obtained (by a similar method to that of Keller [1]) from the four straight-track sprint WRs (50 m, 55 m, 60 m, and 100 m), and are listed in (13, 14). These reproduce the short sprint times quite well (Table 2). The equations in 4 were fit by a nonlinear least-squares method, using the Statistical Analysis Software (SAS) package. In all cases considered here, appropriate convergence criteria were met after several iterations (using the Gauss-Newton method). The upper and lower asymptotic 95% confidence levels for each fit herein are given.

with (lower, upper) asymptotic 95% confidence levels of f=(10.060,10.399), =(1.124, 1.170), and

with (lower, upper) asymptotic 95% confidence levels of f=(8.290, 10.901), =(0.981,1.567), c=( -0.065, 0.180).

Table 1a: World records by lane for 200 m (from [11]).
Lane Athlete t200 Location Date
1 John Carlos USA 20.12A Mexico City 16 Oct 68
Daniel Effiong NIG 20.15 Zurich 04 Aug 93
2 Robson da Silva BRA 20.00 Barcelona 10 Sep 89
3 Michael Johnson USA 19.32 Atlanta 01 Aug 96
4 Pietro Mennea ITA 19.72A Mexico City 12 Sep 79
Michael Johnson USA 19.79 Goteborg 11 Aug 95
5 Michael Johnson USA 19.66 Atlanta 23 Jun 96
6 Joe DeLoach USA 19.75 Seoul 28 Sep 88
7 Carl Lewis USA 19.80 Los Angeles 08 Aug 84
8 Michael Johnson USA 19.79 New Orleans 28 Jun 92

Aside from the 100 m WR (where the reaction time is known, treac = +0.174 s [9]), a (perhaps liberal) reaction time of +0.16 s has been assumed. By using the indoor races to calculate parameters, one is inherently removing the possibility of wind-assisted times. This has not been done in the case of the 100 m WR (where the wind-reading was +0.7 m/s [9]), which may provide some source of error.

In light of the discussions of Tibshirani's extension with relation to observed velocity curves, the parameters (13) are cited only for comparison with older values (although predictions using (13) are offered in Table 2, as a comparison to Keller's results). Otherwise, this work will use only the parameters of (14).

Table 2: Model predictions of Men's Sprint WRs; traw = trace - treac where treac = 0.16 s for all races except 100 m (where it has a known value of 0.17 s).
Event trace traw tfit
(Keller)
tfit
(Tibs.-Keller)
50 m 5.56 5.40 5.40 5.40
55 m 5.99 5.83 5.83 5.83
60 m 6.41 6.25 6.26 6.25
100 m 9.84 9.67 9.67 9.67

Section index
5. 200m Races: Adjusting for the Curve
7. Predicting the 200m World Record
Curve Model
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