Research ArticleAPPLIED SCIENCES AND ENGINEERING

How to run 50% faster without external energy

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Science Advances  25 Mar 2020:
Vol. 6, no. 13, eaay1950
DOI: 10.1126/sciadv.aay1950
  • Fig. 1 Augmented running.

    The augmentation device is a robotic exoskeleton represented by a variable stiffness spring. (A) Swing. The leg is coupled to the spring. As the leg extends, the spring is compressed and the stiffness of the spring is increased. The latter can be achieved by a variable stiffness mechanism, which increases stiffness by decreasing the effective length of the spring [see (28, 3032), Materials and Methods, and movie S1]. The exoskeleton provides mechanical advantage to the human such that large leg extension, small leg force, and small leg stiffness provide small spring compression, large spring force, and large spring stiffness. (B) Ground contact. The leg is decoupled from the spring and the mechanism that changes stiffness is locked. As the leg flexes, the spring extends while the stiffness of the spring stays constant. (C) Spring-mass model of augmented running.

  • Fig. 2 Top speeds of human-powered locomotion.

    World records in natural running (12.3 m/s) (1), running with a spring blade prosthesis (11 m/s) (13), ice-skating (15 m/s) (52), and cycling (21.4 m/s) (fig. S7) (2) and the top speed predicted for augmented running (20.9 m/s). There is a linear empirical relation vmax ∝ ΔtE/T between the world record speeds and the relative time available for each leg to supply energy in running, ice-skating, and cycling. The air resistance limit is given by a cube-root relation vmax ∝ (ΔtE/T)1/3 (see Materials and Methods). This relation is calculated assuming that the energy supply rate of each leg is 18 W/kg (25), which is near to what has been measured for world-class cyclists (26).

  • Fig. 3 Augmented running.

    (A) Running speed. (B) Swing and stance times. (C) Ground reaction force at touchdown. (D) Spring stiffness during ground contact. The top speed predicted by the model (20.9 m/s, black) is approximately 96% of the air resistance limit (21.9 m/s, blue). The average acceleration of the body is within safely tolerable accelerations (fig. S3). The parameters used to obtain these predictions are taken from the current world record holder sprinter Usain Bolt (table S1).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/13/eaay1950/DC1

    Fig. S1. Spring-mass model of augmented running.

    Fig. S2. Stable augmented running.

    Fig. S3. Acceleration and ground contact time.

    Fig. S4. Approximate spring force.

    Fig. S5. Stability of augmented running.

    Fig. S6. Motion of the body in augmented running.

    Fig. S7. Average world record speed.

    Table S1. Estimated physical parameters of the 100-m world record holder sprinter Usain Bolt.

    Movie S1. Augmented running.

    References (5053)

  • Supplementary Materials

    The PDF file includes:

    • Fig. S1. Spring-mass model of augmented running.
    • Fig. S2. Stable augmented running.
    • Fig. S3. Acceleration and ground contact time.
    • Fig. S4. Approximate spring force.
    • Fig. S5. Stability of augmented running.
    • Fig. S6. Motion of the body in augmented running.
    • Fig. S7. Average world record speed.
    • Table S1. Estimated physical parameters of the 100-m world record holder sprinter Usain Bolt.
    • Legend for movie S1
    • References (5053)

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Augmented running.

    Files in this Data Supplement:

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