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In frog muscle fibres, tetanically stimulated at a sarcomere length of about 2 pm, stretched at a velocity of 1 length s-1 and released against a force equal to the maximum isometric, P0, a phase of rapid isotonic shortening takes place after release. As the amplitude of the stretch is increased from 1 · 5 to 9 % of the initial length: (1) the amount of rapid isotonic shortening increases up to 9–10 nm per half sarcomere and (2) the stiffness of the fibre (an indication of the number of bridges attached) decreases to a value about equal to that measured during an isometric contraction. If a 5-10 ms delay is left between the end of stretch and release, the amount of rapid isotonic shortening increases to about 12nmhs-1. A 300-500 ms delay, however, results in a decrease in rapid isotonic shortening to about 5nmhs-1 and also results in velocity transients against P0 that are similar to those described during release from a state of isometric contraction. It is concluded that the force attained after large, fast stretches is due to a greater force developed by each bridge and not to a greater number of bridges. After the elastic recoil (when the force is suddenly reduced to P0), these strained bridges are able to shorten by about 12nmhs-1, suggesting that, during and immediately after stretching, they are charged to levels of potential energy greater than those attained in an isometric contraction.

The work done at each step during level walking and running to lift the centre of mass of the body, Wv, and to increase its forward speed, Wf, and the total mechanical energy involved (potential + kinetic) Wext, have been measured at various 'constant' speeds (2‐32 km/hr) with the technique described by Cavagna (1975). 2. At intermediate speeds of walking (about 4 km/hr) Wv = Wf and Wext/km is at a minimum, as is the energy cost. At lower speeds Wv greater than Wf whereas at higher speeds Wf greather than Wv: in both cases Wext/km increases. 3. The recovery of mechanical energy, through the pendular motion characteristic of walking, was measured as (/Wv/ + /Wf/ ‐ Wext)/(/Wv/ + /Wf/): it attains a maximum (about 65%) at intermediate speeds. 4. A simple model, assuming that in walking the body rotates as an inverted pendulum over the foot in contact with the ground, fits the experimental data better at intermediate speeds but is no longer tenable above 7 km/hr. 5. In running the recovery defined above is minimal (0‐4% independent of speed), i.e. Wext congruent to /Wv/ + /Wf/: potential and kinetic energy of the body do not interchange but are simultaneously taken up and released by the muscles with a rate increasing markedly with the speed (from about 1 to 4 h.p.). 6. Wext increases linearly with the running speed Vf from a positive y intercept owing to the fact that Wv is practically constant independent of Vf. On the contrary, Wf = aVf2/(1 + bVf), where b is the ratio between the time spent in the air and the forward distance covered while on the ground during each step.

1. The work done at each step to lift and accelerate the centre of mass of the body has been measured in competition walkers during locomotion from 2 to 20 km/hr. 2. Three distinct phases characterize the mechanics of walking. From 2 to 6 km/hr the vertical displacement during each step, Sv, increases to a maximum (3.5 vs. 6 cm in normal walking) due to an increase in the amplitude of the rotation over the supporting leg. 3. The transfer, R, between potential energy of vertical displacement and kinetic energy of forward motion during this rotation, reaches a maximum at 4‐5 km/hr (R = 65%). From 6 to 10 km/hr R decreases more steeply than in normal walking, indicating a smaller utilization of the pendulum‐like mechanism characteristic of walking. 4. Above 10 km/hr potential and kinetic energies vary during each step because both are simultaneously taken up and released by the muscles with almost no transfer between them (R = 2‐10%). Above 13‐14 km/hr an aerial phase (25‐60 msec) takes place during the step. 5. Speeds considerably greater than in normal walking are attained thanks to a greater efficiency of doing positive work. This is made possible by a mechanism of locomotion allowing an important storage and recovery of mechanical energy by the muscles.

The work done at each step, during level walking at a constant average speed, to lift the centre of mass of the body, to accelerate it forward, and to increase the sum of both gravitational potential and kinetic energies, has been measured at various speeds on children of 2‐12 years of age, with the same technique used previously for adults (Cavagna, 1975; Cavagna, Thys & Zamboni, 1976). The pendulum‐like transfer between potential and kinetic energies (Cavagna et al. 1976) reaches a maximum at the speed at which the weight‐specific work to move the centre of mass a given distance is at a minimum ('optimal’ speed). This speed is about 2 X 8 km/hr at 2 years of age and increases progressively with age up to 5 km/hr at 12 years of age and in adults. The speed freely chosen during steady walking at the different ages is similar to this ‘optimal’ speed. At the ‘optimal’ speed, the time of single contact (time of swing) is in good agreement with that predicted, for the same stature, by a ballistic walking model assuming a minimum of muscular work (Mochon & McMahon, 1980). Above the ‘optimal’ speed, the recovery of mechanical energy through the potential‐kinetic energy transfer decreases. This decrease is greater the younger the subject. A reduction of this recovery implies a greater amount of work to be supplied by muscles: at 4 X 5 km/hr the weight‐specific muscular power necessary to move the centre of mass is 2 X 3 times greater in a 2‐year‐old child than in an adult.

We have examined the efficiency of vertebrate striated muscle at two different organizational levels: whole animals and isolated muscles. Terrestrial locomotion is used as a model of ‘normal’ muscular contraction; animal size and running speed are used as independent variables in order to change either the metabolic requirements of the muscles or the mechanical power production by the muscles over a wide range of values. The weight-specific metabolic power input to an animal increases nearly linearly with speed and increases with decreasing body size, while the weight-specific mechanical power output increases curvilinearly with speed and is independent of size. Consequently, the efficiency of the muscles in producing positive work increases with speed and the peak efficiency increases with increasing body size, attaining values of over 70 % in large animals, but only 7 % in small ones. The isolated muscle experiments were performed on frog muscle, and rat ‘fast’ and ‘slow’ muscles. We measured the work done, the oxygen consumed during recovery from the stimulation, and calculated the efficiency and the ‘economy’ (the cost of maintaining tension). The muscles were made to: (i) emulate the contractions seen during locomotion, i.e. shorten after a pre-stretch; or (ii) shorten at the same velocity and from the same muscle length as in (i), but without the pre-stretch. It was found that in mammalian muscles the peak efficiency with a pre-stretch attained high values, approaching the peak efficiencies in large animals. The maximum efficiency (attained at 1 length s−1 in fast muscle and at 0 · 5 lengths s−1 in slow muscle) did not differ much in the two muscles, whereas economy was greater in the slow muscle than in the fast muscle.

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 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.

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.

This is the third in a series of four papers examining the link between the energetics and mechanics of terrestrial locomotion. It reports measurements of the mechanical work required (ECM,tot) to lift and reaccelerate an animal’s centre of mass within each step as a function of speed and body size during level, constant average speed locomotion. A force platform was used in this study to measure ECM,tot for small bipeds, quadrupeds and hoppers. We have already published similar data from large animals. The total power required to lift and reaccelerate the centre of mass (ĖCM,tot) increased nearly linearly with speed for all the animals. Expressed in mass-specific terms, it was independent of body size and could be expressed by a simple equation : where ĖCM,tot/Mb has the units of W kg−1 and vg is speed in m s−1. Walking involves the same pendulum-like mechanism in small animals as has been described in humans and large animals. Also, running, trotting and hopping produce similar curves of ECM,tot as a function of time during a stride for both the small and large animals. Galloping, however, appears to be different in small and large animals. In small animals the front legs are used mainly for braking, while the back legs are used to reaccelerate the Centre of mass within a stride. In large animals the front and hind legs serve to both brake and reaccelerate the animal; this difference in mechanics is significant in that it does not allow the utilization of elastic energy in the legs of small animals, but does in the legs of large animals.

This is the nal paper in our series examining the link between the energetics and mechanics of terrestrial locomotion. In this paper the kinetic energy of the limbs and body relative to the centre of mass (EKE,tot of paper two) is combined with the potential plus kinetic energy of the centre of mass (ECM,tot of paper three) to obtain the total mechanical energy (excluding elastic energy) of an animal during constant average-speed locomotion. The minimum mass-specific power required of the muscles and tendons to maintain the observed oscillations in total energy, Ėtot/Mb, can be described by one equation : where Ėtot/Mb is in W kg−1 and vg is in m s−1. This equation is independent of body size, applying equally as well to a chipmunk or a quail as to a horse or an ostrich. In marked contrast, the metabolic energy consumed by each gram of an animal as it moves along the ground at a constant speed increases linearly with speed and is proportional to Mb−0·3. Thus, we have found that each gram of tissue of a 30 g quail or chipmunk running at 3 m s−1 consumes metabolic energy at a rate about 15 times that of a 100 kg ostrich, horse or human running at the same speed while their muscles are performing work at the same rate. Our measurements demonstrate the importance of storage and recovery of elastic energy in larger animals, but they cannot confirm or exclude the possibility of elastic storage of energy in small animals. It seems clear that the rate at which animals consume energy during locomotion cannot be explained by assuming a constant efficiency between the energy consumed and the mechanical work performed by the muscles. It is suggested that the intrinsic velocity of shortening of the active muscle motor units (which is related to the rate of cycling of the cross bridges between actin and myosin) and the rate at which the muscles are turned on and off are the most important factors in determining the metabolic cost of constantspeed locomotion. Faster motor units are recruited as animals increase speed, and equivalent muscles of small animals have faster fibres than those of larger animals. Also, the muscles are turned on and off more quickly as an animal increases speed, and at the same speed a small animal will be turning muscles on and off at a much higher rate. These suggestions are testable, and future studies should determine if they are correct.