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Determining optimal pacing strategy for the track cycling individual pursuit event with a fixed energy mathematical model

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Abstract

Competitive track cycling races are won by milliseconds, and the regulation of an athlete’s power output is an important factor in performance. The aim of this study was to use a mathematical model to predict finishing times for different pacing strategies for the individual pursuit (IP), to identify the optimal strategy in terms of fastest finishing time. Power profiles were generated for a number of common pacing strategies used in cycling, which were based on actual SRM power data for an elite, male, IP cyclist for whom the average power, maximum power, total work done and actual finishing time were known. The total work output was the same for all strategies and the finishing time was predicted using a mathematical model developed previously. The results showed that, of the strategies tested, an initial “all-out” high power acceleration phase followed by a lower constant power output produced the fastest finishing time for a 4,000 m IP event, and that the time spent in the initial high power acceleration phase had a significant effect on performance.

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Acknowledgments

The authors would like to thank BikeNZ and SPARC for use of the athlete SRM power data for this study.

Ethical standard

Ethical approval was not required for this study as no testing was carried out on live subjects and only anonymised data was used.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand

    L. Underwood & M. Jermy

Authors
  1. L. Underwood
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  2. M. Jermy
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Corresponding author

Correspondence to M. Jermy.

Appendices

Appendix 1

See Figs. 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15.

Fig. 6
figure 6

Positive pacing strategy

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Fig. 7
figure 7

Negative pacing strategy

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figure 8

All-out pacing strategy

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Fig. 9
figure 9

All-out and even pacing strategy

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Fig. 10
figure 10

Even pacing strategy

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Fig. 11
figure 11

U shaped pacing strategy

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Fig. 12
figure 12

J shaped pacing strategy

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Fig. 13
figure 13

Reverse J shaped pacing strategy

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Fig. 14
figure 14

Variable pacing strategy

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Fig. 15
figure 15

Variable pacing strategy

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Appendix 2

Athlete 1

Athlete 2

Athlete 3

Pacing strategy

Time (s)

Pacing strategy

Time (s)

Pacing strategy

Time (s)

SRM

222.063

SRM

220.228

All-out 14 s and even

272.182

All-out 14 s and variable (higher bends)

221.795

All-out 12 s and variable (higher bends)

221.131

All-out 12 s and even

272.464

All-out 14 s and even

221.958

All-out 16 s and variable (higher bends)

221.215

SRM

277.263

All-out 12 s and even

222.033

All-out 14 s and variable (higher bends)

221.342

All-out 16 s and variable (higher bends)

282.171

All-out 10 s and variable (higher bends)

222.163

All-out 10 s and variable (higher bends)

221.457

All-out 12 s and variable (higher bends)

282.201

All-out 10 s and even

222.171

All-out 10 s and even

221.630

All-out 14 s and variable (higher bends)

282.205

All-out 16 s and even

222.281

All-out 12 s and variable (higher straights)

221.739

All-out 14 s and variable (higher straights)

282.355

All-out 12 s and variable (higher bends)

222.356

All-out and linear decline (decline at 125 m)

221.791

All-out 12 s and variable (higher straights)

282.37

All-out 12 s and variable (higher straights)

222.445

All-out 12 s and even

221.815

All-out 16 s and variable (higher straights)

282.401

All-out 16 s and variable (higher bends)

222.494

All-out 16 s and variable (higher straights)

222.025

All-out 10 s and variable (higher straights)

282.433

All-out 10 s and variable (higher straights)

222.555

All-out 16 s and even

222.125

All-out 16 s and even

282.647

All-out 14 s and variable (higher straights)

222.671

All-out 14 s and variable (higher straights)

222.285

All-out 10 s and variable (higher bends)

282.749

All-out 16 s and variable (higher straights)

222.791

All-out 14 s and even

222.309

All-out 10 s and even

282.77

All-out and linear decline (decline at 125 m)

223.641

All-out 10 s and variable (higher straights)

222.454

Reverse J shaped

285.193

Reverse J shaped

223.713

Reverse J shaped

223.174

Positive

285.414

Positive

224.24

Positive

223.719

Even

285.478

Variable higher bends

224.531

Even

224.468

Variable higher bends

285.899

Variable higher straights

224.582

Variable higher bends

225.009

Variable higher straights

285.993

Even

225.09

Variable higher straights

225.043

Negative (increase at 3,500 m)

286.483

U shaped

225.354

Negative (increase at 3,500 m)

226.243

All-out and linear decline (decline at 125 m)

287.409

Negative (increase at 3,500 m)

226.099

U shaped

226.434

U shaped

287.487

J shaped

227.306

J shaped

227.446

J shaped

288.897

Athlete 4

Athlete 5

Athlete 6

Pacing strategy

Time (s)

Pacing strategy

Time (s)

Pacing strategy

Time (s)

All-out 16 s and variable (higher bends)

262.935

All-out 16 s and variable (higher straights)

273.065

SRM

268.476

All-out 12 s and even

263.44

All-out 14 s and variable (higher bends)

273.226

All-out 14 s and variable (higher bends)

276.175

All-out 14 s and variable (higher bends)

263.44

All-out 12 s and variable (higher bends)

273.314

All-out 12 s and variable (higher bends)

276.204

All-out 14 s and even

263.498

All-out 14 s and variable (higher straights)

273.36

All-out 12 s and even

276.292

All-out 12 s and variable (higher straights)

263.536

All-out 14 s and even

273.372

All-out 16 s and variable (higher bends)

276.331

All-out 16 s and even

263.543

All-out 16 s and variable (higher bends)

273.374

All-out 16 s and even

276.42

All-out 16 s and variable (higher straights)

263.665

All-out 12 s and even

273.4

All-out 14 s and variable (higher straights)

276.454

All-out 14 s and variable (higher straights)

263.672

All-out 10 s and variable (higher bends)

273.415

All-out 16 s and variable (higher straights)

276.518

SRM

267.612

All-out 10 s and even

273.419

All-out 14 s and even

276.636

All-out 10 s and even

263.996

All-out 16 s and even

273.469

All-out 12 s and variable (higher straights)

276.889

All-out 12 s and variable (higher bends)

264.05

All-out 12 s and variable (higher straights)

273.499

All-out 10 s and variable (higher bends)

276.959

All-out 10 s and variable (higher bends)

264.063

SRM

269.747

All-out 10 s and even

276.964

All-out 10 s and variable (higher straights)

264.078

All-out 10 s and variable (higher straights)

273.789

All-out 10 s and variable (higher straights)

276.985

Reverse J shaped

264.556

Reverse J shaped

274.822

Reverse J shaped

278.162

Positive

265.371

Positive

275.129

Positive

278.44

Even

266.189

Variable higher bends

276.04

All-out and linear decline (decline at 125 m)

278.978

Variable higher bends

266.231

Negative (increase at 3500 m)

277.006

Variable higher bends

279.224

U shaped

266.314

Variable higher straights

277.148

Variable higher straights

279.317

Variable higher straights

266.504

U shaped

277.159

Even

279.828

Negative (increase at 3,500 m)

266.659

Even

277.512

Negative (increase at 3,500 m)

279.828

J shaped

268.074

All-out and linear decline (decline at 125 m)

280.624

J shaped

281.741

All-out and linear decline (decline at 125 m)

271.236

J shaped

280.954

U shaped

297.709

Athlete 7

Pacing strategy

Time (s)

SRM

264.887

All-out 12 s and even

265.336

All-out 12 s and variable (higher bends)

265.358

All-out 10 s and variable (higher bends)

265.406

All-out 14 s and variable (higher bends)

265.406

All-out 10 s and even

265.421

All-out 14 s and even

265.46

All-out 12 s and variable (higher straights)

265.464

All-out 14 s and variable (higher straights)

265.481

All-out 10 s and variable (higher straights)

265.516

All-out 16 s and even

265.582

All-out 16 s and variable (higher bends)

265.606

All-out 16 s and variable (higher straights)

265.642

All-out and linear decline (decline at 125 m)

265.75

Reverse J shaped

266.697

Positive

267.731

Variable higher straights

268.037

Even

268.889

Variable higher bends

269.807

Negative (increase at 3,500 m)

270.627

J shaped

270.767

U shaped

271.929

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Underwood, L., Jermy, M. Determining optimal pacing strategy for the track cycling individual pursuit event with a fixed energy mathematical model. Sports Eng 17, 183–196 (2014). https://doi.org/10.1007/s12283-014-0153-3

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