Chaos
Feedback | Help | Exit
Chaos
Search:
   
 
 
 
Previous Article
Neuromechanical tuning of nonlinear postural control dynamics
Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinea...
Next Article
Gait dynamics in Parkinson's disease: Common and distinct behavior among stride length, gait variability, and fractal-like scaling
Parkinson's disease (PD) is a common, debilitating neurodegenerative disease. Gait disturbances are a frequent cause of disability and impairment for patients with PD. This article provides a brief in...

Optimal speeds for walking and running, and walking on a moving walkway

Chaos 19, 026112 (2009); doi:10.1063/1.3141428

Published 29 June 2009

You are not logged in to this journal. Log in

Manoj Srinivasan
Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
Many aspects of steady human locomotion are thought to be constrained by a tendency to minimize the expenditure of metabolic cost. This paper has three parts related to the theme of energetic optimality: (1) a brief review of energetic optimality in legged locomotion, (2) an examination of the notion of optimal locomotion speed, and (3) an analysis of walking on moving walkways, such as those found in some airports. First, I describe two possible connotations of the term “optimal locomotion speed:” that which minimizes the total metabolic cost per unit distance and that which minimizes the net cost per unit distance (total minus resting cost). Minimizing the total cost per distance gives the maximum range speed and is a much better predictor of the speeds at which people and horses prefer to walk naturally. Minimizing the net cost per distance is equivalent to minimizing the total daily energy intake given an idealized modern lifestyle that requires one to walk a given distance every day—but it is not a good predictor of animals' walking speeds. Next, I critique the notion that there is no energy-optimal speed for running, making use of some recent experiments and a review of past literature. Finally, I consider the problem of predicting the speeds at which people walk on moving walkways—such as those found in some airports. I present two substantially different theories to make predictions. The first theory, minimizing total energy per distance, predicts that for a range of low walkway speeds, the optimal absolute speed of travel will be greater—but the speed relative to the walkway smaller—than the optimal walking speed on stationary ground. At higher walkway speeds, this theory predicts that the person will stand still. The second theory is based on the assumption that the human optimally reconciles the sensory conflict between the forward speed that the eye sees and the walking speed that the legs feel and tries to equate the best estimate of the forward speed to the naturally preferred speed. This sensory conflict theory also predicts that people would walk slower than usual relative to the walkway yet move faster than usual relative to the ground. These predictions agree qualitatively with available experimental observations, but there are quantitative differences. ©2009 American Institute of Physics
History: Received 1 April 2009; accepted 3 May 2009; published 29 June 2009
Permalink: http://link.aip.org/link/?CHAOEH/19/026112/1
BUY THIS ARTICLE   (US$24)
Download PDF (194 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 87.85.G-
    Biomechanics (biomedical engineering)
  • YEAR: 2009

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (62)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. J. A. Borelli, On the Movement of Animals (De Motu Animalium, Pars prima) (Springer-Verlag, Berlin, 1680), p. 152 (translated by P. Maquet, 1989).
  2. R. McN. Alexander, Principles of Animal Locomotion (Princeton University Press, Princeton, 2003).
  3. T. M. Kubow and R. J. Full, “The role of the mechanical system in control: A hypothesis of self-stabilization in hexapedal runners,” Philos. Trans. R. Soc. London, Ser. B 354, 849 (1999).
  4. G. A. Brooks, T. D. Fahey, T. P. White, and K. M. Baldwin, Exercise Physiology: Human Bioenergetics and Its Applications (Mayfield, Mountain View, CA, 2000).
  5. J. E. A. Bertram and A. Ruina, “Multiple walking speed-frequency relations are predicted by constrained optimization,” J. Theor. Biol. 209, 445 (2001).
  6. P. R. Cavanagh and K. R. Williams, “The effect of stride length variation on oxygen uptake during distance running,” Med. Sci. Sports Exercise 14, 30 (1982).
  7. P. Högberg, “How do stride length and stride frequency influence the energy-output during running?” Arbeitsphysiologie 14, 437 (1952).
  8. A. D. Kuo, “A simple model predicts the step length-speed relationship in human walking,” J. Biomech. Eng. 123, 264 (2001).
  9. J. M. Donelan, R. Kram, and A. D. Kuo, “Mechanical and metabolic determinants of the preferred step width in human walking,” Philos. Trans. R. Soc. London, Ser. B 268, 1985 (2001).
  10. A. Hreljac, “Preferred and energetically optimal gait transition speeds in human locomotion,” Med. Sci. Sports Exercise 25, 1158 (1993).
  11. R. Margaria, Biomechanics and Energetics of Muscular Exercise (Clarendon, Oxford, UK, 1976).
  12. A. E. Minetti and R. McN. Alexander, “A theory of metabolic costs for bipedal gaits,” J. Theor. Biol. 186, 467 (1997).
  13. A. Thorstensson and H. Robertson, “Adaptations to changing speed in human locomotion: Speed of transition between walking and running,” Acta Physiol. Scand. 131, 211 (1987).
  14. C. T. Farley and C. R. Taylor, “A mechanical trigger for the trot-gallop transition in horses,” Science 253, 306 (1991).
  15. S. J. Wickler, D. F. Hoyt, E. A. Cogger, and G. Myers, “The energetics of the trot-gallop transition,” J. Exp. Biol. 206, 1557 (2003).
  16. A. D. Kuo, J. M. Donelan, and A. Ruina, “Energetic consequences of walking like an inverted pendulum: Step-to-step transitions,” Exerc. Sport Sci. Rev. 33, 88 (2005).
  17. M. Srinivasan and A. Ruina, “Computer optimization of a minimal biped model discovers walking and running,” Nature (London) 439, 72 (2006).
  18. F. Massaad, T. M. Lejeune, and C. Detrembleur, “The up and down bobbing of human walking: A compromise between muscle work and efficiency,” J. Physiol. (London) 582, 789 (2007).
  19. J. D. Ortega and C. T. Farley, “Minimizing center of mass vertical movement increases metabolic cost in walking,” J. Appl. Physiol. 99, 2099 (2005).
  20. R. McN. Alexander, “Optimum walking techniques for quadrupeds and bipeds,” J. Zool. 192, 97 (1980).
  21. R. McN. Alexander, “A model of bipedal locomotion on compliant legs,” Philos. Trans. R. Soc. London, Ser. B 338, 189 (1992).
  22. F. C. Anderson and M. G. Pandy, “Dynamic optimization of human walking,” J. Biomech. Eng. 123, 381 (2001).
  23. A. Ruina, J. E. Bertram, and M. Srinivasan, “A collisional model of the energetic cost of support work qualitatively explains leg-sequencing in walking and galloping, pseudo-elastic leg behavior in running and the walk-to-run transition,” J. Theor. Biol. 237, 170 (2005).
  24. M. Srinivasan and A. Ruina, “Idealized walking and running gaits minimize work,” Proc. R. Soc. London, Ser. A 463, 2429 (2007).
  25. M. Srinivasan, “Why walk and run: Energetic costs and energetic optimality in simple mechanics-based models of a bipedal animal,” Ph.D. thesis, Cornell University, 2006.
  26. H. J. Ralston, “Energy-speed relation and optimal speed during level walking,” Eur. J. Appl. Physiol. 17, 277 (1958).
  27. G. J. Bastien, P. A. Willems, B. Schepens, and N. C. Heglund, “Effect of load and speed on the energetic cost of human walking,” Eur. J. Appl. Physiol. 94, 76 (2005).
  28. H. J. Ralston, “Energetics of human walking,” in Neural Control of Locomotion, edited by R. M. Herman, S. Grillner, P. S. G. Stein, and D. G. Stuart (Plenum, New York, 1976).
  29. C. J. Pennycuick, “On the running of the gnu (Connochaetes Taurinus) and other animals,” J. Exp. Biol. 63, 775 (1975).
  30. D. F. Hoyt and C. R. Taylor, “Gait and the energetics of locomotion in horses,” Nature (London) 292, 239 (1981).
  31. A. C. Bobbert, “Energy expenditure in level and grade walking,” J. Appl. Physiol. 15, 1015 (1960).
  32. S. J. Wickler, D. F. Hoyt, E. A. Cogger, and M. H. Hirschbein, “Preferred speed and cost of transport: The effect of incline,” J. Exp. Biol. 203, 2195 (2000).
  33. A. E. Minetti, L. P. Ardigo, and F. Saibene, “The transition between walking and running in humans: Metabolic and mechanical aspects at different gradients,” Acta Physiol. Scand. 150, 315 (1994).
  34. R. McN. Alexander, “Optimization and gaits in the locomotion of vertebrates,” Physiol. Rev. 69, 1199 (1989).
  35. R. A. Norberg, “Optimal flight speed in birds when feeding young,” J. Anim. Ecol. 50, 473 (1981).
  36. V. Radhakrishnan, “Locomotion: Dealing with friction,” Proc. Natl. Acad. Sci. U.S.A. 95, 5448 (1998).
  37. A. Hedenstrom and T. Alerstam, “Optimal flight speed of birds,” Philos. Trans. R. Soc. London, Ser. B 348, 471 (1995).
  38. R. Margaria, P. Cerretelli, P. Aghemo, and G. Sassi, “Energy cost of running,” J. Appl. Physiol. 18, 367 (1963).
  39. K. L. Steudel-Numbers and C. M. Wall-Scheffler, “Optimal running speed and the evolution of hominin hunting strategies,” J. Hum. Evol. 56, 355 (2009).
  40. D. R. Carrier, “The energetic paradox of human running and hominid evolution,” Curr. Anthropol. 25, 483 (1984).
  41. J. M. Tough and C. A. O'Flaherty, Passenger Conveyors (Taylor & Francis, New York, 1971).
  42. B. J. Mohler, W. B. Thompson, S. H. Creem-Regehr, H. L. Pick, Jr., and W. H. Warren, Jr., “Visual flow influences gait transition speed and preferred walking speed,” Exp. Brain Res. 181, 221 (2007).
  43. J. R. Lishman and D. N. Lee, “The autonomy of visual kinaesthesis,” Perception 2, 287 (1973).
  44. J. Pailhous, A. Ferrandez, M. Fltlckiger, and B. Baumberger, “Unintentional modulations of human gait by optical flow,” Behav. Brain Res. 38, 275 (1990).
  45. J. Aldrich, “R. A. Fisher and the making of maximum likelihood,” Stat. Sci. 12, 162 (1997).
  46. F. Rieke, D. Warland, R. de Ruyter van Steveninck, and W. Bialek, Spikes: Exploring the Neural Code (MIT Press, Cambridge, 1997).
  47. S. B. Young, “Assessing the benefits of automated pedestrian movement systems in airport terminals,” Ph.D. thesis, University of California, Berkeley, 1998.
  48. S. B. Young, “Evaluation of pedestrian walking speeds in airport terminals,” Transp. Res. Rec. 1674, 21 (1999) (No. 99-0824).
  49. S. B. Young (personal communication).
  50. M. H. Bornstein and H. G. Bornstein, “The pace of life,” Nature (London) 259, 557 (1976).
  51. R. V. Levine and A. Norenzayan, “The pace of life in 31 countries,” J. Cross Cult. Psychol. 30, 178 (1999).
  52. J. Cardinal, S. Collette, F. Hurtado, S. Langerman, and B. Palop, “Optimal location of transportation devices,” Comput. Geom. 41, 219 (2008).
  53. D. Braess, “Ber ein paradoxon aus der verkehrsplanung,” Unternehmensforschung 12, 258 (1968)
  54. [“On a paradox of traffic planning,” Transp. Sci. 39, 446 (2005)].
  55. Y. A. Korilis, A. A. Lazar, and A. Orda, “Avoiding the Braess paradox in non-cooperative networks,” J. Appl. Probab. 36, 211 (1999).
  56. P. Guerin and B. G. Bardy, “Optical modulation of locomotion and energy expenditure at preferred transition speed,” Exp. Brain Res. 189, 393 (2008).
  57. T. Prokop, M. Schubert, and W. Berger, “Visual influence on human locomotion: Modulation to changes in optic flow,” Exp. Brain Res. 114, 63 (1997).
  58. E. Varraine, M. Bonnard, and J. Pailhous, “Interaction between different sensory cues in the control of human gait,” Exp. Brain Res. 142, 374 (2002).
  59. W. J. Davis and J. L. Ayers, “Locomotion: Control by positive feedback optokinetic responses,” Science 177, 183 (1972).
  60. I. Rock and D. Smith, “The optomotor response and induced motion of the self,” Perception 15, 497 (1986).
  61. M. V. Srinivasan, S. W. Zhang, M. Lehrer, and T. S. Collet, “Honeybee navigation en route to the goal: Visual flight control and odometry,” J. Exp. Biol. 199, 237 (1996).
  62. A. E. Patla, “Understanding the roles of vision in the control of human locomotion,” Gait and Posture 5, 54 (1997).
  63. A. Mahboobin, P. J. Loughlin, M. S. Redfern, and P. J. Sparto, “Sensory re-weighting in human postural control during moving-scene perturbations,” Exp. Brain Res. 167, 260 (2005).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics