| 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.
=(1.124, 1.170), and
=(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 |
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