Energetic Cost of Generating Muscular Force During Running: A Comparison of Large and Small Animals

This paper addresses the question of how muscles use energy as animals move along the ground at a constant speed. Most attempts to explain the energetics of terrestrial locomotion have assumed that the major energetic cost occurs when muscles shorten and perform mechanical work (Fenn, 1930; Hill, 1950; Cavagna, Saibene & Margaria, 1964; McMahon, 1975; Alexander, 1976; Cavagna, Heglund & Taylor, 1977). Furthermore, it is generally assumed that the muscles perform this work at close to their maximal efficiency, which is though to be nearly the same for all vertebrate striated muscle (Hill, 1950; Alexander, 1973; Alexander & Goldspink, 1977). Recent studies scaling the mechanical work performed by running animals to body size indicate that these assumptions are not justified. Mass specific energy cost of locomotion varies as a regular function of body size (Taylor, Schmidt-Nielsen & Raab, 1970; Taylor, 1977), while mass specific mechanical work of locomotion is nearly independent of body size (Heglund, 1979; Heglund et al. 1979). For example, a 30 g mouse uses approximately 15 times as much energy to move each gram of its body a given distance along the ground as a 100 kg pony, but the mechanical work per unit mass which is necessary to keep each gram of its body moving at a constant speed is the same for the mouse and the pony. Thus it appears that the energy consumed by muscles of running animals is not used primarily for performing work.

If the amount of mechanical work performed by muscles does not determine the amount of energy they use when animals run at a constant speed, what are the other activities that the muscles are involved in that require energy? It is useful to think of muscles as ‘biological machines’ for converting chemical energy into force. If they shorten while generating force, they perform mechanical work (work = force × distance). However, during level running, the muscles of an animal generate force and consume energy not only while they are shortening, but also while they are being stretched (e.g., to slow the animal’s fall and to reverse the direction of its limbs) and while their length remains constant (to stabilize the joints). Work is performed on the active muscle when it is stretched, and no work is done by the active muscle when its length does not change.

It seemed reasonable to postulate that the rate at which muscles of running animals consume energy might be related to the magnitude of the integral of force over the time during which it is developed during running. The area under the curve of muscle force v. time (the so-called tension-time integral) is commonly related to energy consumption in both isolated and in situ skeletal muscle experiments and in studies of heart muscle. The tension-time integral determines the rate of energy consumption for isometric muscular activities (Feng, 1931; Sandberg & Carlson, 1966).

We have been able to increase the force-time integral of the muscles of a running animal by known amounts while simultaneously measuring oxygen consumption. This enables us to determine the increments in energy utilization for known increments of force-time integral. We have applied this technique to animals over a nearly 3-orders of magnitude range of body mass.

Twenty six white rats (all male, average weight 274 g), two dogs (one male, average weight 27 kg and one female, average weight 23 kg), two humans (both males, average weights of 72 and 101 kg), and two horses (both females, average weights of 114 and 124 kg) were utilized in these experiments. The rats were housed in activity wheels and the other animals were exercised regularly before and during the experiments.

All subjects were trained to run on the treadmill while carrying a load equal to between 20 and 30% of their body mass. Special harnesses were constructed for the horses, dogs and rats which allowed the load to be evenly distributed along the length of the back. The human subjects wore commercially available back packs with a metal frame. Lead shot packed in foam rubber was used for adjusting the load to the desired mass. The oxygen consumption at a given speed declined as the training progressed until it reached a constant value after a period of one to three weeks. A subject was considered to be trained once this constant value was obtained. Only data from trained subjects were used in this study.

Rate of oxygen consumption was measured while subjects ran on a treadmill for 15 min without a load, followed by 15 min with a load, and another 15 min without a load. The loading conditions and the speeds used with each experimental animal under each condition are given in Table 1.

Three approaches were taken to determine whether acceleration of the animal changed when they carried loads: (1) stride frequency was measured under the same speed and loading conditions as oxygen consumption; (2) time of contact of each foot relative to the other feet was measured while horses and dogs ran at a variety of speeds with and without loads (using high speed films); and (3) vertical accelerations of horses and dogs were measured at a variety of speeds and loading conditions (using an accelerometer attached to the back of the animals).

Stride frequency was determined three times for each experimental condition where oxygen consumption was measured. The interval for 25 strides was timed with a stopwatch.

Time of contact of each foot relative to the other feet was determined from cine films taken at 200 frames/s⁻¹ with an Eclair GV-16 camera. The dogs and ponies were filmed from the side at an angle which enabled us to see their feet and the tread clearly. A clock that made 10 revolutions per second was placed in the field of view and served as a time calibration. Two dogs were filmed at three speeds (1 · 97, 2 · 54 and 3 · 91 m/s⁻¹) and four loading conditions (1·0, 1·16, 1·22 and 1·26 times body mass). One horse was filmed at two speeds (2·68 and 3·14 m/s⁻¹) and three loading conditions (1·0, 1·07, and 1·22 times body mass).

Both the vertical acceleration and its integral, the vertical velocity, were measured by mounting a linear accelerometer (Entran Model no. E6C-240-5D) on the backs of the dogs and horses just caudal to the scapula, in a position estimated to be above the centre of mass. Continuous recordings were made using a Grass Instruments polygraph (Model 5 A).

was found for trotting rats, trotting and galloping dogs, running humans, and trotting horses carrying loads ranging between 7% and 27% of their body mass (Table 1). The mean of the individual proportionality constants determined for each experimental condition was 1·01 ±s.D. 0·017.

There was no systematic change in stride frequency as a result of carrying these loads and the maximum difference between the loaded and unloaded frequency in any experiment was less than 1·5%.

The average number of feet supporting the animal over an integral number of strides decreased with increasing speed, but was not changed as a result of carrying load (Table 2). The time of contact of each foot relative to the other feet was also approximately the same when animals ran with and without a load. Fig. 2 demonstrates the absence of any effect of load on foot fall patterns under a ‘worst case’ situation in our experiments: it compares the foot fall patterns of a dog running at the heaviest loading condition and the highest speed used in our experiments with those of the dog running at the same speed without any load.

The average upward vertical acceleration during the time the feet were in contact with the ground measured using the accelerometer was approximately the same when the horses and dogs ran at the same speed with and without a load (Table 3).

The average ratio of vertical accelerations of the loaded/unloaded animal was 1·01 ± 0·01.

The evidence in support of the second assumption is not as strong. Cavagna & Kaneko (1977) and Heglund (1979) have shown that the amount of energy required to accelerate the limbs relative to the centre of mass is about half of the amount required to sustain the speed and height of the centre of mass at the running speeds used in these experiments. In our experiments, the load was not distributed over the limbs of the animals and would not have increased the energy required to accelerate and decelerate the limbs relative to the centre of mass. However, a large part of the decreases in kinetic energy as the limbs decelerate appears to be sorted elastically and recovered on reacceleration, resulting in a small metabolic cost for movement of limbs. The evidence for this elastic storage comes from direct measurements of the increases in kinetic energy of the limb relative to the trunk (Heglund, 1979; Heglund et al. 1979) and metabolic energy consumed by the limb muscles (unpublished observations from our laboratory) as a function of speed. If the metabolic cost of moving the limbs relative to the centre of mass is small, then most of the energy consumed would appear to be used to sustain the speed and height of the centre of mass.

The rate at which the unloaded or loaded human or animal expended energy increased dramatically with speed. If the force exerted by the muscles on the centre of mass is broken down into its horizontal and vertical components, only the integral of the horizontal accelerating forces with time increases with increasing speed (Cavagna et al. 1977). The integral of vertical force exerted by the muscles on the centre of mass over a stride must remain the same at all speeds and equal to the weight of the animal plus any load in order for the animal’s centre of mass to remain at the same height from stride to stride. Because the integral of vertical force with time is nearly an order of magnitude greater than the integral of accelerating horizontal force with time (Cavagna et al. 1977), the integral of the total force exerted by the muscles on the centre of mass increases only slightly with increasing speed. We must conclude, therefore, that the energetic cost of generating force over time (∫ F dt) increases with increasing speed.

Another important consequence of the direct proportionality between the increased oxygen consumption and mass of the load is that small animals use more oxygen and consume more energy to carry each gram of a load a given distance than large animals, just as they expend more energy to carry each gram of their own body mass a given distance. Thus the cost of generating muscular force at a given speed appears to increase dramatically with decreasing body size.

Our results do not distinguish between work and force, both should increase in the same proportion as a result of carrying a load. However, a plausible hypothesis can be formulated in terms of force that is consistent with our data, but not in terms of work, at least if we assume muscles are operating at close to their maximal efficiency.

The intrinsic velocity of active muscle fibres should increase both with increasing speed and with decreasing animal size at any particular speed (Hill, 1950; Close, 1972). It has been suggested (Alexander & Goldspink, 1977) that cost of generating force is is proportional to the rate at which the cross bridges between the actin and myosin cycle, and this rate increases in direct proportion to intrinsic velocity. If this is the case, it might explain the increase in energetic cost of generating force both at higher speeds and with decreasing body size. Although the experiments will be difficult, this is a testable hypothesis.

This work was supported by NIH grants no. 18140-02, -03, -04, and NSF grant no. PCM75-22684.