Article Figures & Tables
Figures
- Fig. 1.
Mechanical energy of the centre of mass of the body during running steps at the indicated speeds. In each panel the curves show the gravitational potential energy (Ep, blue), the kinetic energy of vertical motion (Ekv, red), the kinetic energy of forward motion (Ekf, brown), the kinetic energy of motion in the sagittal plane (Ek=Ekv+Ekf, green), and the total translational energy of the centre of mass in the sagittal plane (Ecm=Ep+Ek, black). The records were obtained as described in the Materials and methods from the signals of a force platform. In each panel, the zero line corresponds to the minimum attained by the Ep curve. Note that the maximum of Ek occurs in close proximity to the maximum of Ekv during the downward displacement, whereas it follows the maximum of Ekv during the lift (vertical dotted lines). The horizontal bars indicate the time of contact during the step (from minimum to minimum of Ep). The time of contact during which positive external work is done (increment of Ecm) is indicated in red, whereas the time of negative external work (decrement of Ecm) is indicated in blue. Subject: 72.5 kg mass, 1.79 m height, 23 years old.
- Fig. 2.
Vertical displacement during contact and amplitude of oscillation of the elastic system. The fractions of the vertical displacement of the centre of mass of the body taking place during contact, Sc/Sv (filled circles: downward displacement, open circles: upward displacement), and when the vertical force is greater than body weight, Sce/Sv (filled squares: downward displacement, open squares: upward displacement) are given as a function of the running speed. It can be seen that Sc/Sv decreases markedly with speed. Except at very low speeds when the aerial phase may be nil (Sc/Sv≈1: e.g. upper left panel in Figs 1 and 7), the downward displacement while the foot is in contact with the ground is smaller than the upward displacement during contact: the ballistic fall of the centre of mass is greater than the ballistic lift (see Fig. 7). In contrast, the amplitude of the vertical oscillation below the equilibrium point, Sce/Sv, changes less with speed and approaches one half of the vertical displacement Sv both during compression (down) and recoil (up) of the spring. The vertical bars indicate the standard deviation of the mean calculated in each velocity class; the figures near the symbols indicate the number of items of the mean. Lines represent the weighted mean of all the data (Kaleidagraph 3.6.4); their only purpose is to be a guide for the eye: they do not describe the underlying physical mechanism.
- Table 1.
Speeds at which tpush and tbrake are significantly different
Speed (km h-1) tpushvs tbrakeP 2 2.88×10-11 3 4.24×10-10 4 2.03×10-7 5 1.81×10-8 6 4.48×10-8 7 2.18×10-10 8 2.60×10-9 9 1.71×10-9 10 6.05×10-8 11 8.17×10-6 12 8.63×10-5 13 0.00 14 0.37 15 0.01 16 0.26 17 0.49 18 0.11 19 0.05 20 0.02 - Fig. 3.
The normalized ratio (see Materials and methods) between maximal downward and upward velocities attained at each step by the centre of mass of the body is plotted as a function of the running speed. The greater vertical velocity attained during the downward displacement indicates: (i) a lower vertical force exerted by the structures supporting the body at the lowest speeds when the aerial phase is nil, together with (ii) a ballistic fall greater than the ballistic lift at higher speeds (Fig. 2). Statistics as in Fig. 2.
- Fig. 4.
The peak in kinetic energy of the centre of mass, Ek=Ek,f+Ek,v, attained because of gravity in its motion forwards and downwards is greater than the peak attained because of the muscular push in its motion forwards and upwards. Note that the downward/upward asymmetry decreases with speed due to the large increase of Ek,f relative to Ek,v (Fig. 1). The difference between the two peaks attained by Ek at each step also remains positive at the highest running speeds (inset). Statistics as in Fig. 2.
- Fig. 5.
The lower support of the body during the downward displacement of the centre of mass relative to upward displacement is indicated on the ordinate by a ratio Rint,down/Rint greater than 0.5 at all running speeds (abscissa). Note that Rint is the cumulative value at the end of the step of the instantaneous Ek–Ep transduction: data show that the transduction of Ep into Ek during the downward displacement is greater than the transduction of Ek into Ep during the upward displacement [see Rint(t) curve in Fig. 7]. Statistics as in Fig. 2.
- Fig. 6.
Positive and negative external work durations. The times during which positive external work is done at each step during the push (open circles and red bars in Fig. 1) and negative external work is done during the brake (filled circles and blue bars in Fig. 1) are plotted as a function of the running speed. It can be seen that the duration of positive external work is clearly greater than the duration of negative external work up to a speed of 14 km h–1 (asterisks indicate P<0.05: see Table 1). This suggests that, with increasing speed, the work contribution by the contractile machinery is progressively substituted by elastic storage and recovery by tendons (see text). Statistics as in Fig. 2.
- Fig. 7.
The four phases of the bounce of the body during the running step. Each panel illustrates the changes in gravitational potential energy, Ep, and in kinetic energy of motion in the sagittal plane, Ek=Ekv+Ekf, of the centre of mass of the body simultaneously with the Ep–Ek energy transduction, Rint(t). The energy curves are normalized to oscillate between zero and one. Each panel begins and ends at the lowest value of the Ep curve. Same steps illustrated in Fig. 1. The different colors in the Ep curve distinguish the fractions of the step where the vertical force exerted on the ground is greater than body weight (red), and lower than body weight (blue), with lighter blue indicating the aerial phase (not present in the upper left panel). The four phases correspond to the vertical displacement during the upward acceleration Sce,up (red) and deceleration Sae,up (blue), and the downward acceleration Sae,down (blue) and deceleration Sce,down (red). The vertical dotted lines are drawn through the two peaks of Ek and encompass the fraction of the step where a transduction occurs between Ep and Ek as indicated by the increments of the Rint(t) curve below and above crossing the broken lines. Note that the transduction of Ek into Ep during the lift [lower-left increment of Rint(t)] is smaller than the transduction of Ep into Ek during the downward displacement (upper-right increment). In the horizontal tracts of the Rint(t) curve no transduction occurs between Ep and Ek and muscle–tendon units absorb simultaneously Ep and Ek (phase β) and increase simultaneously Ep and Ek (phase α). Note that whereas most of β is confined within Sce,down, α extends beyond Sce,up within a large fraction of Sae,up due to a continuing increase of Ek.
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