G. A. Cavagna

Mechanical work and efficiency in level walking and running

1. The mechanical power spent to accelerate the limbs relative to the trunk in level walking and running, Ẇint, has been measured at various ‘constant’ speeds (3‐33 km/hr) with the cinematographic procedure used by Fenn (1930a) at high speeds of running.

The determinants of the step frequency in running, trotting and hopping in man and other vertebrates.

1. During each step of running, trotting or hopping part of the gravitational and kinetic energy of the body is absorbed and successively restored by the muscles as in an elastic rebound. In this study we analysed the vertical motion of the centre of gravity of the body during this rebound and defined the relationship between the apparent natural frequency of the bouncing system and the step frequency at the different speeds. 2. The step period and the vertical oscillation of the centre of gravity during the step were divided into two parts: a part taking place when the vertical force exerted on the ground is greater than body weight (lower part of the oscillation) and a part taking place when this force is smaller than body weight (upper part of the oscillation). This analysis was made on running humans and birds; trotting dogs, monkeys and rams; and hopping kangaroos and springhares. 3. During trotting and low‐speed running the rebound is symmetric, i.e. the duration and the amplitude of the lower part of the vertical oscillation of the centre of gravity are about equal to those of the upper part. In this case, the step frequency equals the frequency of the bouncing system. 4. At high speeds of running and in hopping the rebound is asymmetric, i.e. the duration and the amplitude of the upper part of the oscillation are greater than those of the lower part, and the step frequency is lower than the frequency of the system. 5. The asymmetry is due to a relative increase in the vertical push. At a given speed, the asymmetric bounce requires a greater power to maintain the motion of the centre of gravity of the body, Wext, than the symmetric bounce. A reduction of the push would decrease Wext but the resulting greater step frequency would increase the power required to accelerate the limbs relative to the centre of gravity, Wint. It is concluded that the asymmetric rebound is adopted in order to minimize the total power, Wext + Wint.

The mechanics of sprint running

1. The effect of the velocity of shortening on the power developed by the muscles in sprint running was studied by measuring the mechanical work done to accelerate the body forward from the start to about 34 km/hr.

The determinants of the step frequency in walking in humans.

The mechanical power spent during walking in lifting and accelerating the centre of mass, Wext, has been measured at three given speeds maintained at different step frequencies: at any given speed, Wext is smaller the greater the step frequency used. The mechanical power spent in accelerating the limbs relative to the centre of mass during walking at a given speed, but with different step frequencies, Wint, was calculated from previous data obtained during free walking (Cavagna & Kaneko, 1977). At a given walking speed, Wint increases with the step frequency. The total power, Wtot = Wext + Wint, reaches a minimum at a step frequency which is 20‐30% less than the step frequency freely chosen at the same period. The step frequency at which Wtot is minimum increases with speed in a similar way to the natural step frequency during free walking.

The role of gravity in human walking: pendular energy exchange, external work and optimal speed

1 During walking on Earth, at 1.0 g of gravity, the work done by the muscles to maintain the motion of the centre of mass of the body (Wext) is reduced by a pendulum‐like exchange between gravitational potential energy and kinetic energy. The weight‐specific Wext per unit distance attains a minimum of 0.3 J kg−1 m−1 at about 4.5 km h−1 in adults. 2 The effect of a gravity change has been studied during walking on a force platform fixed to the floor of an aircraft undergoing flight profiles which resulted in a simulated gravity of 0.4 and 1.5 times that on Earth. 3 At 0.4 g, such as on Mars, the minimum Wext was 0.15 J kg−1 m−1, half that on Earth and occurred at a slower speed, about 2.5 km h−1. The range of walking speeds is about half that on Earth. 4 At 1.5 g, the lowest value of Wext was 0.60 J kg−1 m−1, twice that on Earth; it was nearly constant up to about 4.3 km h−1 and then increased with speed. The range of walking speeds is probably greater than that on Earth. 5 A model is presented in which the speed for an optimum exchange between potential and kinetic energy, the ‘optimal speed’, is predicted by the balance between the forward deceleration due to the lift of the body against gravity and the forward deceleration due to the impact against the ground. 6 In conclusion, over the range studied, gravity increases the work required to walk, but it also increases the range of walking speeds.

The two power limits conditioning step frequency in human running.

1. At high running speeds, the step frequency becomes lower than the apparent natural frequency of the bodys bouncing system. This is due to a relative increase of the vertical component of the muscular push and requires a greater power to maintain the motion of the centre of gravity, Wext. However, the reduction of the step frequency leads to a decrease of the power to accelerate the limbs relatively to the centre of gravity, Wint, and, possibly, of the total power Wtot = Wext + Wint. 2. In this study we measured Wext using a force platform, Wint by motion picture analysis, and calculated Wtot during human running at six given speeds (from 5 to 21 km h‐1) maintained with different step frequencies dictated by a metronome. The power was calculated by dividing the positive work done at each step by the duration of the step (step‐average power) and by the duration of the positive work phase (push‐average power). 3. Also in running, as in walking, a change of the step frequency at a given speed has opposite effects on Wext, which decreases with increasing step frequency, and Wint, which increases with frequency; in addition, a step frequency exists at which Wtot reaches a minimum. However, the frequency for a minimum of Wtot decreases with speed in running, whereas it increases with speed in walking. This is true for both the step‐average and the push‐average powers. 4. The frequency minimizing the step‐average power equals the freely chosen step frequency at about 13 km h‐1: it is higher at lower speeds and lower at higher speeds. The frequency minimizing the push‐average power approaches the freely chosen step frequency at high speeds (around 22 km h‐1 for our subjects). 5. It is concluded that the increase of the vertical push does reduce the step‐average power, but that a limit is set by the increase of the push‐average power. Between 13 and 22 km h‐1 the freely chosen step frequency is intermediate between a frequency minimizing the step‐average power, eventually limited by the maximum oxygen intake (aerobic power), and a frequency minimizing the push‐average power, set free by the muscle immediately during contraction (anaerobic power). The first need prevails at the lower speed, the second at the higher speed.

The mechanics of running in children.

1 The effect of age and body size on the bouncing mechanism of running was studied in children aged 2‐16 years. 2 The natural frequency of the bouncing system (fs) and the external work required to move the centre of mass of the body were measured using a force platform. 3 At all ages, during running below ≈11 km h−1, the freely chosen step frequency (f) is about equal to fs (symmetric rebound), independent of speed, although it decreases with age from 4 Hz at 2 years to 2.5 Hz above 12 years. 4 The decrease of step frequency with age is associated with a decrease in the mass‐specific vertical stiffness of the bouncing system (k/m) due to an increase of the body mass (m) with a constant stiffness (k).Above 12 years, k/mand fremain approximately constant due to a parallel increase in both kand mwith age. 5 Above the critical speed of ≈11 km h−1, independent of age, the rebound becomes asymmetric, i.e. f< fs. 6 The maximum running speed (Vf,max) increases with age while the step frequency at remains constant (≈4 Hz), independent of age. 7 At a given speed, the higher step frequency in preteens results in a mass‐specific power against gravity less than that in adults. The external power required to move the centre of mass of the body is correspondingly reduced.

The resonant step frequency in human running

Abstract At running speeds less than about 13 km h–1 the freely chosen step frequency (ffree) is lower than the frequency at which the mechanical power is minimized (fmin). This dissociation between ffree and fmin was investigated by measuring mechanical power, metabolic energy expenditure and apparent natural frequency of the body’s bouncing system (fsist) during running at three given speeds with different step frequencies. The ffree requires a mechanical power greater than that at fmin mainly due to a larger vertical oscillation of the body at each step. Energy expenditure is minimal and the mechanical efficiency is maximal at ffree. At a given speed, an increase in step frequency above ffree results in an increase in energy expenditure despite a decrease in mechanical power. On the other hand, a decrease in step frequency below ffree results in a larger increase in energy expenditure associated with an increase in mechanical power. When the step frequency is forced to values above or below ffree, fsist is forced to change similarly by adjusting the stiffness of the bouncing system. However the best match between fsist and step frequency takes place only in proximity of ffree (2.6–2.8 Hz). It is concluded that during running at speeds less than 13 km h–1 energy is saved by tuning step frequency to fsist, even if this requires a mechanical power larger than necessary.

The landing–take-off asymmetry in human running

SUMMARY In the elastic-like bounce of the body at each running step the muscle–tendon units are stretched after landing and recoil before take-off. For convenience, both the velocity of the centre of mass of the body at landing and take-off, and the characteristics of the muscle–tendon units during stretching and recoil, are usually assumed to be the same. The deviation from this symmetrical model has been determined here by measuring the mechanical energy changes of the centre of mass of the body within the running step using a force platform. During the aerial phase the fall is greater than the lift, and also in the absence of an aerial phase the transduction between gravitational potential energy and kinetic energy is greater during the downward displacement than during the lift. The peak of kinetic energy in the sagittal plane is attained thanks to gravity just prior to when the body starts to decelerate downwards during the negative work phase. In contrast, a lower peak of kinetic energy is attained, during the positive work phase, due to the muscular push continuing to accelerate the body forwards after the end of the acceleration upwards. Up to a speed of 14 km h–1 the positive external work duration is greater than the negative external work duration, suggesting a contribution of muscle fibres to the length change of the muscle–tendon units. Above this speed, the two durations (<0.1 s) are similar, suggesting that the length change is almost totally due to stretch–recoil of the tendons with nearly isometrically contracting fibres.

Old men running: mechanical work and elastic bounce

It is known that muscular force is reduced in old age. We investigate what are the effects of this phenomenon on the mechanics of running. We hypothesized that the deficit in force would result in a lower push, causing reduced amplitude of the vertical oscillation, with smaller elastic energy storage and increased step frequency. To test this hypothesis, we measured the mechanical energy of the centre of mass of the body during running in old and young subjects. The amplitude of the oscillation is indeed reduced in the old subjects, resulting in an approximately 20% smaller elastic recovery and a greater step frequency (3.7 versus 2.8 Hz, p=1.9×10−5, at 15–17 km h−1). Interestingly, the greater step frequency is due to a lower aerial time, and not to a greater natural frequency of the system, which is similar in old and young subjects (3.6 versus 3.4 Hz, p=0.2). Moreover, we find that in the old subjects, the step frequency is always similar to the natural frequency, even at the highest speeds. This is at variance with young subjects who adopt a step frequency lower than the natural frequency at high speeds, to contain the aerobic energy expenditure. Finally, the external work to maintain the motion of the centre of mass is reduced in the old subjects (0.9 versus 1.2 J kg−1 m−1, p=5.1×10−6) due to the lower work done against gravity, but the higher step frequency involves a greater internal work to reset the limbs at each step. The net result is that the total work increases with speed more steeply in the old subjects than in young subjects.