A Simple Model...: 7. Predicting the 200 m World Record

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

7. Predicting the 200 m World Record

By a straight application of the model as described above, it is possible to obtain predicted WR times for the 200 m sprint. In addition, it seems logical to obtain predictions for indoor 200 m races, as well, where the dynamics of curve sprinting should be more apparent. For outdoor performances, d_c = 100 m in (11), and d_s = 100 m, and this is the same for all eight lane choices (p= 1-8). Recall that d_c is not the curve length for all lanes, only the distance run on the curve. For indoor races, the total distance is calculated by

where d_c1,2 depend on the lane choice. Since standard indoor tracks are 200 m in lane 1, it follows that d_c1 = d_c2= d_s = 50 m. The radius obviously increases for subsequent lanes, and using (8), one obtains d_c1 = 40.58 m and d_c2 = 59.42 m. The latter value is the total length of the curved portion of lane 4, while the former is the distance run after the stagger.

For all tables, unless otherwise indicated the times listed will be raw (i.e. minus reaction time). Only the final race times include reaction, as indicated in the column headings.

7.1 Outdoor 200 m

Calculations using various values of increasing

(

²) are detailed in Table 3 and Table 4. For outdoor races (Table 3), a

² range of 0.50 to 0.80 has been used. Before the 1996 Olympic Games, the estimated times given would have been considered almost unbelievable. However, in light of the current 200 m WR (at the time of writing), the times are not so far fetched. The 19 s barrier is on the verge of being broken for

² = 0.50, while for higher

², the current WR is approached. It is interesting to note that, for

² = 1.00, the model predicts a time of 19.30 s, quite close to Michael Johnson's 19.32 s. These predictions are ideally for zero-wind readings, while the 19.32 s was assisted with a wind of +0.4 m/s. Barring serious injury, It is possible that Johnson will again lower his 200 m WR mark this coming summer (1997), so we could very well see times in the range predicted in Table 3.

Table 3: TK parameter (f=9.596,=1.274, c=0.058) predicted outdoor 200 m World Records for various values of , assuming race is run in lane 4. v₁₀₀ is the velocity for the given split.
² v₁₀₀ t₁₀₀ t₂₀₀ t₂₀₀+0.16
0.50 11.14 9.92 18.86 19.02
0.60 11.06 9.97 18.92 19.08
0.70 10.98 10.02 18.98 19.14
0.80 10.91 10.06 19.03 19.19

As a comparison to Keller's prediction of 19.25 s [1], which can be considered a straight-track 200 m (² = 0), this model yields t₂₀₀ = 18.54 + 0.16 = 18.70 s, with a split of 9.67 s (which is just the prediction for the 100 m WR).

7.2 Indoor 200 m

Indoor tracks have much shorter radii of curvature than do outdoor tracks. The centrifugal forces acting on a sprinter will be much higher for large v_c, so it makes sense that the value of

assigned to subsequent calculations should be lower than for outdoor ones. This is physically realized by banked turns on indoor tracks, which are generally 2 to 4 feet at maximum height. How much lower a value of

one should choose probably depends on the height of the particular bank, so again no accurate estimate can be made. Due to the R^-1 force dependence, then a

(

²) ratio in the range of 2:1 (4:1) might be expected for an outdoor:indoor ratio (under the assumption that the average maximal velocity about the curve is the same). Accurate time and velocity measurements at the end of each race segment (curves and straights) have been calculated, and accurate measurement of these quantities can help determine validity of the model (see Table 5).

Table 4: Predicted indoor 200 m World Records for various values of , assuming race is run in lane 4.
² t₅₀ t₁₀₀ t₁₅₀ t₂₀₀ t₂₀₀+0.16
0.20 5.50 9.82 14.40 18.98 19.14
0.30 5.55 9.88 14.56 19.17 19.33
0.40 5.60 9.95 14.72 19.35 19.51
0.50 5.64 10.01 14.86 19.52 19.68
0.60 5.69 10.08 15.00 19.68 19.84

Table 5: TK 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 4.67 11.16 8.99 11.63 14.40 10.70
0.30 4.71 10.95 9.05 11.62 14.56 10.47
0.40 4.75 10.76 9.11 11.61 14.72 10.27
0.50 4.78 10.59 9.16 11.60 14.86 10.09
0.60 4.82 10.43 9.22 11.59 15.00 9.92

Frank Fredericks of Namibia broke the 20 s barrier indoors in 1996 (see Table 1), setting a new 200 m indoor WR of 19.92 s. This can be used to estimate possible values of that could be used. Clearly, any value under ² = 0.60 is quite reasonable, and in fact the 19.51 s prediction for ² = 0.40 is attractive, as it does not seem beyond the realm of possibility. This does not follow the 4:1 ratio outlined above, however there is no real reason to believe that it should. The only real stipulation is that indoor values of should be smaller than outdoor ones.

7.3 Can the 19 s barrier be broken?

Suppose that a value of

² = 0.60 holds for outdoor performances (this assumption is based on results of Section 9.1). The predicted 200 m record is 19.08 s, assuming a reaction of +0.16 s (Table 5). The minimum possible time allowed without a false start being called would be 19.02 s (this, of course, assumes no wind speed, for which the predictions have been made; if there is a sufficient legal tail wind, the mark would certainly fall). How should this athlete train in order to break the 19 s barrier?

A 0.4% increase in the value of f would give a raw time of 18.85 s, with a 100 m split of 9.94 s
(v₁₀₀ = 11.10 m/s). Whereas, a larger decrease of 9% in c (greater "endurance") would yield a raw time of 18.83 s, with a marginally slower split of t₁₀₀ = 9.95 s, but a slightly faster v₁₀₀ = 11.11 m/s. This is an extreme case, but does show how the model parameters might be useful to athletes and coaches as a training gauge.

Various articles [9], [10] have made attempts to predict the future trends of WR performances, and the former states that a sub-19s 200 m could be realized by 2040 (although it also predicts a 100 m time of 9.49 s to match). The authors of [10] are more optimistic, predicting a WR of 18.97 s being set as early as 2004. While their prediction of 19.52 s for 1977 is off, it might be retroactively made consistent by Michael Johnson's 19.32 s WR from the 1996 Olympic Games. If the predicted times of Table 5 are near accurate, and considering the simple argument above, then the 2004 projection may not be far off the mark.

Section index

6. New Model Parameters for Modern World Records

8. Is the 300m Now a Short Sprint?

Curve Model

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Table 3: TK parameter (f=9.596,=1.274, c=0.058) predicted outdoor 200 m World Records for various values of , assuming race is run in lane 4. v₁₀₀ is the velocity for the given split.
²	v₁₀₀	t₁₀₀	t₂₀₀	t₂₀₀+0.16
0.50	11.14	9.92	18.86	19.02
0.60	11.06	9.97	18.92	19.08
0.70	10.98	10.02	18.98	19.14
0.80	10.91	10.06	19.03	19.19

Table 4: Predicted indoor 200 m World Records for various values of , assuming race is run in lane 4.
²	t₅₀	t₁₀₀	t₁₅₀	t₂₀₀	t₂₀₀+0.16
0.20	5.50	9.82	14.40	18.98	19.14
0.30	5.55	9.88	14.56	19.17	19.33
0.40	5.60	9.95	14.72	19.35	19.51
0.50	5.64	10.01	14.86	19.52	19.68
0.60	5.69	10.08	15.00	19.68	19.84

Table 5: TK 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	4.67	11.16	8.99	11.63	14.40	10.70
0.30	4.71	10.95	9.05	11.62	14.56	10.47
0.40	4.75	10.76	9.11	11.61	14.72	10.27
0.50	4.78	10.59	9.16	11.60	14.86	10.09
0.60	4.82	10.43	9.22	11.59	15.00	9.92

Section index	6. New Model Parameters for Modern World Records	8. Is the 300m Now a Short Sprint?
Curve Model	Main home page