The top speed of human running, 12.3 m/s (1), is near half the top speed of cycling, 21.4 m/s (2), despite both motions being human powered. The lower speed of running suggests that humans have untapped energy-supplying capability, which can be used in cycling but cannot be used for faster running. Cycling is faster than running partly because (i) the rolling motion of the wheels prevents collisional energy losses from stepping (3) but also because (ii) wheels can support the weight of the body in place of the legs (4, 5), while (iii) pedals enable the human to supply energy continuously in the air (5) instead of intermittently when the leg is on the ground (6). These three features enable the bicycle to double the top speed of running, despite supplying no external energy and adding weight to the human. The same features may lead to novel augmentation devices that could increase the running speed using untapped human power, without wheels or external energy.
Humans have attempted to surpass their natural running capability using springs for at least a century (7, 8). Springs cannot provide external energy but have been shown to reduce the energy cost of walking by 7.2 ± 2.6% (9), running by 4% (10) to 8 ± 1.5% (11), and jumping by 24% (12). However, the current top speed of augmented running, 11 m/s, achieved using a spring prosthesis in series with the legs (13), is 10% below the top speed of natural running. A spring in series with the legs can mitigate collisional energy losses but requires the legs to provide a large force to support the body, unlike the wheel of a bicycle (10, 13, 14). A spring in parallel with the legs can support the body and therefore enable the human to use all the leg force to push against the ground and accelerate (15, 16). However, regardless of whether a spring is used in series or in parallel with the legs, the ground contact time is reduced to 0.1 s at the top speed of natural running (1), which severely limits the amount of energy the legs can supply in high-speed running (6, 17–20). This fundamental limitation necessitates a different use of springs to bypass the top speed of natural running.
We conceive an unconventional means of running, which could allow the human to maximize top running speed by supplying energy in the air instead of on the ground (Fig. 1). This may be achieved by augmenting the human with variable stiffness springs attached to the limbs. In the air, the limbs supply energy by simultaneously compressing and increasing the stiffness of the springs (Fig. 1A). Upon touchdown, the stiff springs redirect the vertical motion of the human instead of the legs, while the energy stored in the springs is released to increase the horizontal running speed (Fig. 1B). In the proposed augmented running, (i) the energy supplied by the limbs is no longer limited by the short ground contact time, (ii) the springs support the body instead of the limbs, and (iii) the springs mitigate collision energy losses like the wheel of a bicycle. Therefore, the proposed means of augmented running confers defining features of cycling, which may enable humans to go beyond the top speed of natural running (movie S1).
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).
Figure 3 provides a detailed account of augmented running predicted by the model (solid lines) compared to the estimated and measured data from natural running and cycling (dashed lines) (fig. S7) (1, 2, 17). According to these predictions, the augmented running may reach the top speed of natural running
m/s in 10 steps and may require 150 steps to reach vmax ≈ 20.9 m/s. At the top speed, the time available to supply energy in the air Δts ≈ 533 ms is six times longer than the ground contact time in natural running
ms and 1.5 times longer than the swing time in natural running
ms, while the ground contact time in augmented running Δtg ≈ 19.3 ms is more than four times shorter than the ground contact time in natural running (Fig. 3B). On the ground, the spring exerts a maximum force of F ≈ 21 kN, which is six times the maximum force exerted by the human FN ≈ 3.6 kN (Fig. 3C), while the stiffness of the spring k ≈ 234 kN/m is 11 times the stiffness of a human leg at the top speed of natural running kN ≈ 21 kN/m (Fig. 3D). The physical requirements in augmented running are beyond the capability of a biological limb but may be achieved using a robotic variable stiffness spring exoskeleton.