Can cycle power predict sprint running performance?

  • Gerrit Jan van Ingen Schenau
  • Ron Jacobs
  • Jos J. de Koning


A major criticism of present models of the energetics and mechanics of sprint running concerns the application of estimates of parameters which seem to be adapted from measurements of running during actual competitions. This study presents a model which does not perpetuate this solecism. Using data obtained during supra-maximal cycle ergometer tests of highly trained athletes, the kinetics of the anaerobic and aerobic pathways were modelled. Internal power wasted in the acceleration and deceleration of body limbs and the power necessary to overcome air friction was calculated from data in the literature. Assuming a mechanical efficiency as found during submaximal cycling, a power equation was constructed which also included the power necessary to accelerate the body at the start of movement. The differential equation thus obtained was solved through simulation. The model appeared to predict realistic times at 100 m (10.47 s), 200 m (19.63 s) and 400 m (42.99 s) distances. By comparison with other methods it is argued that power equations of locomotion should include the concept of mechanical efficiency.

Key words

Anaerobic power Efficiency Mechanical power 


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  1. Aleshinsky SY (1986) An energy “sources” and “fractions” approach to the mechanical energy expenditure problem I–V. J Biomech 19:287–315Google Scholar
  2. Behncke H (1987) Optimization models for the force and energy in competitive sports. Math Methods Appl Sci 9:298–311Google Scholar
  3. Boileau RA, Maghew JL, Riner WF, Lussier L (1982) Physiological characteristics of elite middle and long distance runners. Can J Appl Sport Sci 7:167–172Google Scholar
  4. Dapena J, Feltner ME (1987) Effects of wind and altitude on the times of 100 meter sprint races. I.J.S.B. 3:6–39Google Scholar
  5. Davies CTM (1980) Effects of wind assistance and resistance on the forward motion of a runner. J Appl Physiol 48:702–709Google Scholar
  6. Di Prampero PE (1981) Energetics of muscular exercise. Rev Physiol Biochem Pharmacol 89:143–222Google Scholar
  7. Fenn WO (1930) Frictional and kinetic factors in the work of sprint running. Am J Physiol 92:583–611Google Scholar
  8. Fukanaga T, Matsuo A (1981) Mechanical energy output and joint movements in sprint running. Ergonomics 24:765–772Google Scholar
  9. Furusawa K, Hill AV, Parkinson JL (1927) The dynamics of sprint running. Proc R Soc 102 B:713–720Google Scholar
  10. Haan A de, van Ingen Schenau GJ, Ettema GJ, Huijing PA, Lodder MAN (1989) Efficiency of rat medial gastrocnemius muscles in contractions with and without an active prestretch. J Exp Biol 141:327–341Google Scholar
  11. Henry FM (1954) Time-velocity equations and oxygen requirements of “all-out” and “steady-pace” running. Res Q 25:164–177Google Scholar
  12. Henry FM (1955) Prediction of world records in running sixty yards to twenty-six miles. Res Q 26:147–158Google Scholar
  13. Henry FM, Trafton IR (1951) The velocity curve in sprint running. Res Q 22:409–422Google Scholar
  14. Hill AV (1927) Muscular movement in man: the factors governing speed and recovery from fatigue. McGraw-Hill, New YorkGoogle Scholar
  15. Ikai M (1968) Biomechanics of sprint running with respect to the speed curve. Biomechanics I. Karger, Basle, pp 282–290Google Scholar
  16. Ingen Schenau GJ van (1982) The influence of air friction in speed skating. J Biomech 15:449–458Google Scholar
  17. Ingen Schenau GJ van, Cavanagh PR (1990) Power equations in endurance sports (survey). J Biomech 23:865–881Google Scholar
  18. Ingen Schenau GJ van, Hollander AP (1987) Comment on ‘A mathematical theory of running’ and the application of this theory. J Biomech 20:91–95Google Scholar
  19. Ingen Schenau GJ van, Boer RW de, Geysel JSM, de Groot G (1988) Supra-maximal tests in evaluating physical condition of male and female athletes. Eur J Physiol 57:6–9Google Scholar
  20. Ingen Schenau GJ van, Koning JJ de, de Groot G (1990) A simulation of speed skating performances based on an equation of power production and power dissipation. Med Sci Sports Exerc 22:718–728Google Scholar
  21. Katch VL (1973) Kinetics of oxygen uptake and recovery for supra maximal work of short duration. Int Z Angew Physiol 31:197–201Google Scholar
  22. Keller JB (1973) A theory of competitive running. Physics Today 26:43–47Google Scholar
  23. Kyle CR (1979) Reduction of wind resistance and power output of racing cyclists and runners traveling in groups. Ergonomics 22:387–397Google Scholar
  24. Kyle CR, Caiozzo VJ (1986) The effect of athletic clothing aerodynamics upon running speed. Med Sci Sports Exerc 18:509–515Google Scholar
  25. Kyle CF, Wapert RA (1989) The wind resistance of the human figure in sports. Proceedings First IOC World Congress on Sport Sciences, US Olympic Committee, Colorado Springs, p 287Google Scholar
  26. Lloyd BB (1966) The energetics of running: an analysis of world records. Adv Sci 22:515–530Google Scholar
  27. Lloyd BB, Zacks RM (1972) The mechanical efficiency of treadmill running against a horizontal impeding force. J Physiol 223:355–363Google Scholar
  28. Mader A, Heck H, Liesen H, Hollmann W (1983) Simulative Berechnungen der dynamischen Änderungen von Phosphorylierungspotential, Laktatbildung und Laktatverteilung beim Sprint. Dtsch Z Sportmed 1:14–22Google Scholar
  29. Margaria R (1976) Biomechanics and energetics of muscular exercise. Clarendon Press, OxfordGoogle Scholar
  30. Morton RH (1985) Mathematical representation of the velocity curve of sprint running. Can J Appl Sport Sci 10:166–170Google Scholar
  31. Peronnet F, Thibault G (1989) Mathematical analysis of running performance and world running records. J Appl Physiol 67:453–465Google Scholar
  32. Pugh LGCE (1976) Air resistance in sport. Medicine sport vol. 9. Advances in exercise physiology. Karger, Basle, pp 149–164Google Scholar
  33. Vaughan CL, Matravers DR (1977) A biomechanical model of the sprinter. J Human Mov Stud 3:207–213Google Scholar
  34. Volkov NI, Lapin VI (1979) Analysis of the velocity curve in sprint running. Med Sci Sports 11:332–337Google Scholar
  35. Ward-Smith AJ (1985) A mathematical theory of running, based on the first law of thermodynamics, and its application to the performance of world class athletes. J Biomech 18:337–349Google Scholar
  36. Williams KR, Cavanagh PR (1983) A model for the calculation of mechanical power during distance running. J Biomech 16:115–128Google Scholar
  37. Zacks RM (1973) The mechanical efficiencies of running and bicycling against a horizontal impeding force. Int Z Angew Physiol 31:249–258Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Gerrit Jan van Ingen Schenau
    • 1
  • Ron Jacobs
    • 1
  • Jos J. de Koning
    • 1
  1. 1.Faculty of Human Movement SciencesFree UniversityAmsterdamThe Netherlands
  2. 2.Department of Functional AnatomyAmsterdamThe Netherlands

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