The 200 m World Record: 19.32 s

Excerpt from : Mureika, J. R., Canadian Journal of Physics 81 (7), 895-910 (2003)

These splits are the results of a simulation using the model presented in the journal referenced above. The simulation results are presented in the first Table, and are compared to the reported results in the second Table. The difference between the two tends to average around 0.04 s, with the noted exception at 146.42 m. This mismatch is most likely due to a clerical error, a methodological error, or combination of both.

d (m)	Split (s)	v (ms$^{-1}$)	$\Delta_{10}$
10	1.766	8.426	1.766
20	2.852	9.872	1.086
30	3.823	10.673	0.971
40	4.738	11.138	0.915
50	5.625	11.402	0.887
60	6.496	11.535	0.871
70	7.361	11.581	0.865
80	8.225	11.566	0.864
90	9.091	11.506	0.866
100	9.964	11.416	0.873
110	10.844	11.301	0.880
120	11.733	11.222	0.889
130	12.626	11.172	0.893
140	13.524	11.084	0.898
150	14.431	10.969	0.907
160	15.348	10.834	0.917
170	16.277	10.684	0.929
180	17.220	10.523	0.943
190	18.178	10.354	0.958
200	19.152	10.180	0.974

At sea-level in 0-wind conditions, the time would translate to $19.219 + 0.161 = 19.380~$s (always assuming a 0.161 s reaction). Had it been run in Mexico City, the model suggests a 19.172 s in still wind, and 19.099 s with a straight +2 ms$^{-1}$ tail-wind. Furthermore, letting $\xi \rightarrow 0$, at sea-level the ``straight track'' equivalent of his 10.13 s split would theoretically be 9.909 s, with a straight 200 m clocking of 18.950 s (note that the world record for a straight 200 m is reported as 19.5 s, wind 1.84 ms$^{-1}$, for American sprinter Tommie Smith in San Jose, 7 May 1966).

The second table contains the corresponding theoretical 50 and 100 m interval analysis. Note the incredible split of 8.786 s between 40-140 m. Although such ``running-start'' performances are rarely clocked, track-lore has it that Carl Lewis marked an 8.86 s leg in the 4x100m relay [ATFS 2001 Annual, Peter Matthews (ed.)]. If this simulation is accurate, this constitutes one of the fastest 100 m intervals run by any athlete in history! The corresponding simulated 150 m split would be 14.592 s, officially reported as 14.60 s.

Table: Comparison with recorded data from Drut, G., Revue des entraineurs francais d'athlétisme (Spécial) 143 (July/August 1996). Rounding procedure is IAAF standard.

d (m)	Recorded (s)	Model (s)	Rounded	Difference
90	9.29	9.253	9.26	-0.03
100	10.13	10.125	13.13	0.00
110	11.00	11.005	11.01	+0.01
131.14	12.93	12.889	12.89	-0.04
140.28	13.75	13.710	13.71	-0.04
146.42	14.57	14.266	14.27	-0.30
158.56	15.42	15.376	15.38	-0.06
167.70	16.27	16.224	16.23	-0.04
176.84	17.12	17.082	17.09	-0.03
185.98	17.97	17.953	17.96	-0.01
200	19.32	19.313	19.32	0.00

Table: Raw 50 m and 100 m interval analysis of Michael Johnson's 200 m World Record.

50 m		100 m
Interval (m)	Split (s)	Interval	Split
0 - 50	5.625	0 - 100	9.964
50 - 100	4.339	40 - 140	8.786
100 - 150	4.467	50 - 150	8.806
150 - 200	4.721	100 - 200	9.188