A Simple Model...: 9. A Practical Application: Donovan Bailey

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

9. A Practical Application: Donovan Bailey

On Saturday, July 27th 1996, at 21:00 EST, Donovan Bailey (DB) of Canada crossed the 100 m finish line in a new WR time of 9.84 s (+0.7 m/s wind). Thanks to excellent documentation of data from this race, it is possible to find an "exact" solution to the equations 6, and hence solve them for the parameters (f,

,c). The relevant data are given in [9],

Since the system equations used are different than Keller's, the maximum velocity will not be simply v_max = f. The maximum value of v(t) is found to be

with dv(t_max)/dt = 0. The values (f,

,c) = (7.96,1.72,0.156) are thus obtained. These can be compared with those obtained in [2] by a least-square fit to the official splits listed in Table 7: (f,

,c) = (6.41, 2.39, 0.20). Note that the higher value of f and lower values of

, c are likely a manifestation of solution method and accounting for reaction time.

It is emphasized that, while it is possible to obtain an exact set of values for the parameters, these are not DB's parameters, since the model does not account for wind assistance and drag.

Table 7: Predicted splits (s) and speed (m/s) compared with official for Bailey's 100 m final in Atlanta. Reaction time is rounded to +0.17 s.
Split	10 m	20 m	30 m	40 m	50 m	60 m	70 m	80 m	90 m	100 m
Speed (s)	9.32	10.95	11.67	11.99	12.10	12.10	11.99	11.85	11.67	11.47
Raw	1.89	2.90	3.79	4.64	5.47	6.29	7.12	7.96	8.81	9. 67
+reaction	2.06	3.07	3.96	4.81	5.64	6.46	7.29	8.13	8.98	9.84
Official	1.9	3.1	4.1	4.9	5.6	6.5	7.2	8.1	9.0	9.84

9.1 Predicting DB's 200 m times

Using the parameters obtained in Section 9, and the model framework established in Section 5, 200 m times will be obtained for DB as run on both indoor and outdoor tracks. Resulting split times are "raw" ( i.e. without reaction time), but the final time will be given both with and without reaction time (roughly 0.15 s, which is faster than his 1996 Olympic 100 m final reaction time of 0.174 s).

Table 8 shows calculated times and velocities for DB running in lane 4 (p=4) for varying values of ². Since the actual value of this parameter is unknown, in order to determine its possible value predicted times will be matched with DB's past 200 m performances. While no conclusive value of ² could be determined from Section 7.2, perhaps DB's performances can help shed light. The IAAF lists [4] his best 200 m clocking as 20.76 s, with a 20.39 s wind-assisted performance, in 1994. Assuming that his time will be lower in 1997 (but most likely not world class, or sub-20s, due to his training as a 100 m specialist), it wil be assumed that DB is currently capable of running roughly 20.20 to 20.30 s. This would tend to favor a value of ² between 0.50 and 0.70. Predicted indoor performances are listed in Table 9.

Table 8: Bailey's predicted outdoor 200 m times, as run in lane 4.
² t₅₀ v₅₀ t₁₀₀ v₁₀₀ t₁₅₀ t₂₀₀ t₂₀₀ +0.16
0.25 5.53 11.74 9.89 11.03 14.56 19.81 19.97
0.36 5.55 11.60 9.98 10.85 14.69 19.96 20.12
0.50 5.59 11.43 10.09 10.65 14.84 20.13 20.29
0.60 5.61 11.31 10.16 10.51 14.93 20.24 20.40
0.70 5.63 11.20 10.24 10.39 15.09 20.43 20.59

For indoor 200 m, Bailey's performance seems to greatly suffer for large , which further supports the claim of smaller values for indoor tracks. A 200 m clocking above 21 s is hardly expected by a world class sprinter! In fact, even the 21 s times (² = 0.40, 0.50) seem somewhat slow for the 100 m WR holder. These could suggest that the indoor be quite low (² < 0.4).

Analogous to Table 5, segment times and velocities for DB have been calculated, and are listed in Table 10.

Table 9: Bailey's predicted indoor 200 m times, as run in lane 4.
² t₅₀ t₁₀₀ t₁₅₀ t₂₀₀ t₂₀₀+0.16
0.20 5.62 9.91 14.88 20.32 20.48
0.30 5.68 10.01 15.17 20.71 20.87
0.40 5.75 10.13 15.43 21.05 21.21
0.50 5.81 10.22 15.67 21.37 21.53
0.60 5.88 10.32 15.91 21.68 21.84
0.70 5.94 10.42 16.13 21.97 22.13
0.80 5.99 10.50 16.33 22.23 22.39

Table 10: Bailey parameter times and velocities for curve (c1=40.58 m, c2=59.42 m), and straight (s1 = 50 m) race segments for indoor 200 m.
² t_c1 v t_s1 v t_c2 v
0.20 4.79 11.20 9.07 11.58 14.88 9.40
0.30 4.84 10.90 9.17 11.53 15.17 9.06
0.40 4.89 10.62 9.26 11.49 15.43 8.80
0.50 4.94 10.38 9.34 11.46 15.67 8.56
0.60 4.99 10.15 9.43 11.42 15.91 8.35

Section index

8. Is the 300m Now a Short Sprint?

10. Discussion and General Conclusions

Curve Model

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Table 8: Bailey's predicted outdoor 200 m times, as run in lane 4.
²	t₅₀	v₅₀	t₁₀₀	v₁₀₀	t₁₅₀	t₂₀₀	t₂₀₀ +0.16
0.25	5.53	11.74	9.89	11.03	14.56	19.81	19.97
0.36	5.55	11.60	9.98	10.85	14.69	19.96	20.12
0.50	5.59	11.43	10.09	10.65	14.84	20.13	20.29
0.60	5.61	11.31	10.16	10.51	14.93	20.24	20.40
0.70	5.63	11.20	10.24	10.39	15.09	20.43	20.59

Table 10: Bailey parameter times and velocities for curve (c1=40.58 m, c2=59.42 m), and straight (s1 = 50 m) race segments for indoor 200 m.
²	t_c1	v	t_s1	v	t_c2	v
0.20	4.79	11.20	9.07	11.58	14.88	9.40
0.30	4.84	10.90	9.17	11.53	15.17	9.06
0.40	4.89	10.62	9.26	11.49	15.43	8.80
0.50	4.94	10.38	9.34	11.46	15.67	8.56
0.60	4.99	10.15	9.43	11.42	15.91	8.35

Section index	8. Is the 300m Now a Short Sprint?	10. Discussion and General Conclusions
Curve Model	Main home page