Does limb length predict the relative energetic cost of locomotion in mammals?

Do relatively longer limbs result in a lower energetic cost of locomotion? To determine whether or not cost is correlated with limb length in some way other than that due to their respective relationships to body mass, we have removed the effects of size by calculating the residuals of the relationship between each character and body size. We then regressed the pairs of residuals on one another. Because biological variables do not occur in a series of units that have evolved independently, the degree of divergence of two species is likely to be influenced by the length of time since they last shared a common ancestor. We therefore corrected for the phylogenetic relatedness of species. Data on the energetic cost of locomotion of a wide variety of species were taken from published sources. Data on limb lengths were taken from specimens in various museum collections which were similar in body mass (± 12%) to the specimens on which the cost measurements were made. None of the correlations between the residuals of either fore- or hindlimb length and neither of two estimates of the cost of locomotion was significant at P = 0.05. It is concluded that limb length does not importantly influence an animal's locomotor efficiency. These results do not imply the lack of a close relationship between cost and stride length.     

The effect of lower limb length on the energetic cost of locomotion: implications for fossil hominins

The consequences of the relatively short lower limbs characteristic of AL 288-1 have been widely discussed, as have the causes and consequences of the short limbs of Neanderthals. Previous studies of the effect of limb length on the energetic cost of locomotion have reported no relationship; however, limb length could have accounted for as much as 19% of the variation in cost and gone undetected (Steudel and Beattie, 1995; Steudel, 1994, 1996). Kramer (1999) and Kramer and Eck (2000) have recently used a theoretical model to predict the effect of the shorter limbs of early hominids, concluding that the shorter limbs may actually have been energetically advantageous. Here, we took an experimental approach. Twenty-one human subjects, of varying limb lengths, walked on a treadmill at 2.6, 2.8, 3.0 and 3.2m.p.h., while their expired gases were analyzed. The subjects walked for 12 minutes at each speed and their rates of oxygen consumption (VO2) over four minutes were averaged to estimate VO2. We also measured each subject's height, weight and lower limb length. Lean body mass and % fat were determined using dual-energy x-ray absorptiometry. ANCOVA with total VO2 at either speed as the dependent variable and total lean mass, % fat and lower limb length as covariates resulted in all three covariates having a significant positive effect on VO2 at p<0.01. Subjects with relatively longer lower limbs had lower locomotor costs. Thus the short lower limbs characteristic of some hominid taxa would have resulted in more costly locomotion, barring some physiological anomaly. The magnitude of this effect is substantial; Neanderthals are estimated to have had locomotor costs 30% greater than those of contemporary anatomically modern humans. By contrast the increase in lower limb length seen in H. erectus would have mitigated the increase in locomotor costs produced by the increase in body size.     

Explaining the scaling of transport costs: the role of stride frequency and stride length

The mechanisms which enable large animals to transport a unit of body mass through a unit distance at a lower metabolic cost than smaller animals have been the subject of numerous studies. Recent investigations have concluded that stride frequency is a main determinant. We examine the role of both stride frequency and stride length in determining the scaling of the cost of transport.
Slopes for regressions between stride frequency and speed and stride length and speed were determined in four species of rodents. These data were pooled with literature values for the slopes of stride frequency, stride length and cost of locomotion (all vs. speed) for a total of 17 species ranging in size from 30 g to 250 kg. Interspecific equations were calculated for each of these slopes versus body mass, and residuals from these allometric lines were calculated. Residuals were compared to see if variation in the rate of cost increase at a given size is related to variation in the rates of stride frequency and/or stride length increase.
The residual analysis revealed that the variation in transport cost is explicable only in terms of the interaction of stride frequency and stride length slopes. The product of the scaling exponents for stride frequency slope and stride length slope is not significantly different from the scaling exponent for the cost of transport. A model seeking to explain the scaling of the cost of transport must therefore consider the influence of both stride length and stride frequency.
We propose that absolutely longer limbs allow large animals to minimize the rate of increase of stride frequency and stride length with speed, and that this allows utilization of muscles with lower intrinsic rates of contraction, which in turn results in a lower mass-specific cost of transport.     

Maximum walking speed and lower limb length in hominids

In 1984, Helene (Am. J. Physics 52:656) and Alexander (Am. Scientist 72:348–354) presented equations which purported to explain how lower limb length limited maximum walking speed in humans. The equations were based on a simplified model of human walking in which the center of mass (CoM) “vaults” over the supporting leg. Increasing walking speed by increasing stride frequency or stride length would increase the upward acceleration of the CoM in the first half of stance phase, to the point that it would be greater than the downward pull of gravity, and the individual would become airborne. This constitutes running by most definitions. While these models ignored various mechanical factors, such as knee flexion during midstance, that reduce the vertical movement of the CoM, the general idea is plausible inasmuch as the CoM of the body does oscillate vertically with each step. One hypothesis tested here is whether it is indeed the interaction between the pull of gravity and the individual's own upward acceleration that determines at what speed (or cadence) he changes from walking to running. Another hypothesis considered is that increased lower limb length (L) was selected for in early hominids, because of the locomotor advantages of longer lower limbs. Results indicate, however, that while L was clearly related to maximum possible walking speed, it was not an important factor in determining maximum “comfortable” walking speed. These and other results from the recent literature suggest that increased lower limb length provided no selective advantage in locomotion, and other explanations should be sought. © 1996 Wiley-Liss, Inc.     

Energetics in Homo erectus and other early hominins: the consequences of increased lower-limb length

Previous studies of daily energy expenditure (DEE) in hominin fossils have estimated locomotor costs using a formula that was based on six species, all 18 kg or less in mass, including no primates, and that has a number of other problems when applied in an ecological context. It is well established that the energetic cost of human walking is lower than that of representative mammals, particularly for individuals with long lower limbs. The current study reevaluates the daily energy expenditures of a variety of hominin species using more appropriate approaches to estimating locomotor costs. To estimate DEE for primates, I relied on published data on body mass, day range, and the percentage of time spent in various activities. Based on those data, I calculated a value for nonlocomotor DEE. I then used a variant of a method that I have suggested elsewhere to calculate the daily cost due to locomotion (DEEL) and summed the two to calculate total DEE. The more up-to-date methods for calculating the cost of travel result in lower estimates of this aspect of the energy budget than seen in previous studies. Values obtained here for DEE in various representatives of Australopithecus are lower than reported previously by around 200 kcal/day. Taking into account the greater economy of human walking, particularly the effect of the longer lower limbs found in many later Homo species, also results in lowered estimates of DEE. Elongation of the lower limbs in H. erectus reduced relative travel costs nearly 50% in comparison to A.L. 288-1 (A. afarensis). The present method for calculating DEE indicates that female H. erectus DEE was 84% greater than that of female Australopithecus; this disparity is even larger than that suggested by previous workers.     

Limitations imposed by wearing armour on Medieval soldiers' locomotor performance

In Medieval Europe, soldiers wore steel plate armour for protection during warfare. Armour design reflected a trade-off between protection and mobility it offered the wearer. By the fifteenth century, a typical suit of field armour weighed between 30 and 50 kg and was distributed over the entire body. How much wearing armour affected Medieval soldiers' locomotor energetics and biomechanics is unknown. We investigated the mechanics and the energetic cost of locomotion in armour, and determined the effects on physical performance. We found that the net cost of locomotion (C(met)) during armoured walking and running is much more energetically expensive than unloaded locomotion. C(met) for locomotion in armour was 2.1-2.3 times higher for walking, and 1.9 times higher for running when compared with C(met) for unloaded locomotion at the same speed. An important component of the increased energy use results from the extra force that must be generated to support the additional mass. However, the energetic cost of locomotion in armour was also much higher than equivalent trunk loading. This additional cost is mostly explained by the increased energy required to swing the limbs and impaired breathing. Our findings can predict age-associated decline in Medieval soldiers' physical performance, and have potential implications in understanding the outcomes of past European military battles.     

Influences of limb proportions and body size on locomotor kinematics in terrestrial primates and fossil hominins

During locomotion, mammalian limb postures are influenced by many factors including the animal's limb length and body mass. Polk (2002) compared the gait of similar-sized cercopithecine monkeys that differed limb proportions and found that longer-limbed monkeys usually adopt more extended joint postures than shorter-limbed monkeys in order to moderate their joint moments. Studies of primates as well as non-primate mammals that vary in body mass have demonstrated that larger animals use more extended limb postures than smaller animals. Such extended postures in larger animals increase the extensor muscle mechanical advantage and allow postures to be maintained with relatively less muscular effort (Polk, 2002; Biewener 1989). The results of these previous studies are used here to address two anthropological questions. The first concerns the postural effects of body mass and limb proportion differences between australopithecines and members of the genus Homo. That is, H. erectus and later hominins all have larger body mass and longer legs than australopithecines, and these anatomical differences suggest that Homo probably used more extended postures and probably required relatively less muscular force to resist gravity than the smaller and shorter-limbed australopithecines. The second question investigates how animals with similar size but different limb proportions differ in locomotor performance. The effects of limb proportions on gait are relevant to inferring postural and locomotor differences between Neanderthals and modern Homo sapiens which differ in their crural indices and relative limb length. This study demonstrates that primates with relatively long limbs achieve higher walking speeds while using lower stride frequencies and lower angular excursions than shorter-limbed monkeys, and these kinematic differences may allow longer-limbed taxa to locomote more efficiently than shorter-limbed species of similar mass. Such differences may also have characterized the gait of Homo sapiens in comparison to Neanderthals, but more experimental data on humans that vary in limb proportions are necessary in order to evaluate this question more thoroughly.     

Running energetics of the North American river otter: do short legs necessarily reduce efficiency on land?

Semi-aquatic mammals move between two very different media (air and water), and are subject to a greater range of physical forces (gravity, buoyancy, drag) than obligate swimmers or runners. This versatility is associated with morphological compromises that often lead to elevated locomotor energetic costs when compared to fully aquatic or terrestrial species. To understand the basis of these differences in energy expenditure, this study examined the interrelationships between limb morphology, cost of transport and biomechanics of running in a semi-aquatic mammal, the North American river otter. Oxygen consumption, preferred locomotor speeds, and stride characteristics were measured for river otters (body mass=11.1 kg, appendicular/axial length=29%) trained to run on a treadmill. To assess the effects of limb length on performance parameters, kinematic measurements were also made for a terrestrial specialist of comparable stature, the Welsh corgi dog (body mass=12.0 kg, appendicular/axial length=37%). The results were compared to predicted values for long legged terrestrial specialists. As found for other semi-aquatic mammals, the net cost of transport of running river otters (6.63 J kg(-1)min(-1) at 1.43 ms(-1)) was greater than predicted for primarily terrestrial mammals. The otters also showed a marked reduction in gait transition speed and in the range of preferred running speeds in comparison to short dogs and semi-aquatic mammals. As evident from the corgi dogs, short legs did not necessarily compromise running performance. Rather, the ability to incorporate a period of suspension during high speed running was an important compensatory mechanism for short limbs in the dogs. Such an aerial period was not observed in river otters with the result that energetic costs during running were higher and gait transition speeds slower for this versatile mammal compared to locomotor specialists.     

Stride length and its determinants in humans, early hominids, primates, and mammals

Primate stride lengths during quadrupedal locomotion are very long when compared to those of nonprimate quadrupedal mammals at the speed of trot/gallop transition. These exceptional lengths are a consequence of the relatively long limbs of primates and the large angular excursions of their limbs during quadrupedalism. When quadrupedal primates employ bipedal gaits they exhibit much lower angular excursions. Consequently their bipedal stride lengths do not appear to be exceptional in length when compared to other mammals. Angular excursions of the lower limbs of modern humans are not exceptionally large. However, when running, humans exhibit relatively long periods of flight (i.e., they have low duty factors) when compared to other mammals including primates. Because of these long periods of flight and their relative long lower limbs, humans have running stride lengths that are at the lower end of the range of stride lengths of quadrupedal primates. The stride length of the Laetoli hominid trails are evaluated in this context.     

Posture, gait and the ecological relevance of locomotor costs and energy-saving mechanisms in tetrapods

A reanalysis of locomotor data from functional, energetic, mechanical and ecological perspectives reveals that limb posture has major effects on limb biomechanics, energy-saving mechanisms and the costs of locomotion. Regressions of data coded by posture (crouched vs. erect) reveal nonlinear patterns in metabolic cost, limb muscle mass, effective mechanical advantage, and stride characteristics. In small crouched animals energy savings from spring and pendular mechanisms are inconsequential and thus the metabolic cost of locomotion is driven by muscle activation costs. Stride frequency appears to be the principal functional parameter related to the decreasing cost of locomotion in crouched animals. By contrast, the shift to erect limb postures invoked a series of correlated effects on the metabolic cost of locomotion: effective mechanical advantage increases, relative muscle masses decrease, metapodial limb segments elongate dramatically (as limbs shift from digitigrade to unguligrade designs) and biological springs increase in size and effectiveness. Each of these factors leads to decreases in the metabolic cost of locomotion in erect forms resulting from real and increasing contributions of pendular savings and spring savings. Comparisons of the relative costs and ecological relevance of different gaits reveal that running is cheaper than walking in smaller animals up to the size of dogs but running is more expensive than walking in horses. Animals do not necessarily use their cheapest gaits for their predominant locomotor activity. Therefore, locomotor costs are driven more by ecological relevance than by the need to optimize locomotor economy.     

Pedestrian locomotion energetics and gait characteristics of a diving bird, the great cormorant, Phalacrocorax carbo

Great cormorants Phalacrocorax carbo are foot propelled diving birds that seem poorly suited to locomotion on land. They have relatively short legs, which are presumably adapted for the generation of high forces during the power stroke of aquatic locomotion, and walk with a pronounced "clumsy waddle". We hypothesise (1) that the speed, independent minimum cost of locomotion (C min, ml O2 m(-1)) will be high for cormorants during treadmill exercise, and (2) that cormorants will have a relatively limited speed range in comparison to more cursorial birds. We measured the rate of oxygen consumption (V02) of cormorants during pedestrian locomotion on a treadmill, and filmed them to determine duty factor (the fraction of stride period that the foot is in contact with the ground), foot contact time (tc), stride frequency (f), swing phase duration and stride length. C min was 2.1-fold higher than that predicted by their body mass and phylogenetic position, but was not significantly different from the C min of runners (Galliformes and Struthioniformes). The extrapolated gamma-intercept of the relationship between V02 and speed was 1.9-fold higher than that predicted by allometry. Again, cormorants were not significantly different from runners. Contrary to our hypothesis, we therefore conclude that cormorants do not have high pedestrian transport costs. Cormorants were observed to use a grounded gait with two double support phases at all speeds measured, and showed an apparent gait transition between 0.17 and 0.25 m s(-1). This transition occurs at a Froude number between 0.016 and 0.037, which is lower than the value of approximately 0.5 observed for many other species. However, despite the use of a limited speed range, and a gait transition at relatively low speed, we conclude that the pedestrian locomotion of these foot propelled diving birds is otherwise generally similar to that of cursorial birds at comparable relative velocities.     

The effects of body proportions on thermoregulation: an experimental assessment of Allen's rule

Numerous studies have discussed the influence of thermoregulation on hominin body shape concluding, in accordance with Allen's rule, that the presence of relatively short limbs on both extant as well as extinct hominin populations offers an advantage for survival in cold climates by reducing the limb's surface area to volume ratio. Moreover, it has been suggested that shortening the distal limb segment compared to the proximal limb segment may play a larger role in thermoregulation due to a greater relative surface area of the shank. If longer limbs result in greater heat dissipation, we should see higher resting metabolic rates (RMR) in longer-limbed individuals when temperature conditions fall, since the resting rate will need to replace the lost heat. We collected resting oxygen consumption on volunteer human subjects to assess the correlation between RMR and lower limb length in human subjects, as well as to reexamine the prediction that shortening the distal segment would have a larger effect on heat loss and, thus, RMR than the shortening of the proximal segment. Total lower limb length exhibits a statistically significant relationship with resting metabolic rate (p<0.001; R(2)=0.794). While this supports the hypothesis that as limb length increases, resting metabolic rate increases, it also appears that thigh length, rather than the length of the shank, drives this relationship. The results of the present study confirm the widely-held expectation of Allen's rule, that short limbs reduce the metabolic cost of maintaining body temperature, while long limbs result in greater heat dissipation regardless of the effect of mass. The present results suggest that the shorter limbs of Neandertals, despite being energetically disadvantageous while walking, would indeed have been advantageous for thermoregulation.     

Energetics of walking and running: insights from simulated reduced-gravity experiments.

On Earth, a person uses about one-half as much energy to walk a mile as to run a mile. On another planet with lower gravity, would walking still be more economical than running? When people carry weights while they walk or run, energetic cost increases in proportion to the added load. It would seem to follow that if gravity were reduced, energetic cost would decrease in proportion to body weight in both gaits. However, we find that under simulated reduced gravity, the rate of energy consumption decreases in proportion to body weight during running but not during walking. When gravity is reduced by 75%, the rate of energy consumption is reduced by 72% during running but only by 33% during walking. Because reducing gravity decreases the energetic cost much more for running than for walking, walking is not the cheapest way to travel a mile at low levels of gravity. These results suggest that the link between the mechanics of locomotion and energetic cost is fundamentally different for walking and for running.     

Locomotion patterns in two South American gymnophthalmid lizards: Vanzosaura rubricauda and Procellosaurinus tetradactylus

We quantified gait and stride characteristics (velocity, frequency, stride length, stance and swing duration, and duty factor) in the bursts of locomotion of two small, intermittently moving, closely related South American gymnophthalmid lizards: Vanzosaura rubricauda and Procellosaurinus tetradactylus. They occur in different environments: V. rubricauda is widely distributed in open areas with various habitats and substrates, while P. tetradactylus is endemic to dunes in the semi-arid Brazilian Caatinga. Both use trot or walking trot characterised by a lateral sequence. For various substrates in a gradient of roughness (perspex, cardboard, sand, gravel), both species have low relative velocities in comparison with those reported for larger continuously moving lizards. To generate velocity, these animals increase stride frequency but decrease relative stride length. For these parameters, P. tetradactylus showed lower values than V. rubricauda. In their relative range of velocities, no significant differences in stride length and frequency were recorded for gravel. However, the slopes of a correlation between velocity and its components were lower in P. tetradactylus on cardboard, whereas on sand this was only observed for velocity and stride length. The data showed that the difference in rhythmic parameters between both species increased with the smoothness of the substrates. Moreover, P. tetradactylus shows a highly specialised locomotor strategy involving lower stride length and frequency for generating lower velocities than in V. rubricauda. This suggests the evolution of a central motor pattern generator to control slower limb movements and to produce fewer and longer pauses in intermittent locomotion.     

Scale Effects between Body Size and Limb Design in Quadrupedal Mammals

Recently the metabolic cost of swinging the limbs has been found to be much greater than previously thought, raising the possibility that limb rotational inertia influences the energetics of locomotion. Larger mammals have a lower mass-specific cost of transport than smaller mammals. The scaling of the mass-specific cost of transport is partly explained by decreasing stride frequency with increasing body size; however, it is unknown if limb rotational inertia also influences the mass-specific cost of transport. Limb length and inertial properties – limb mass, center of mass (COM) position, moment of inertia, radius of gyration, and natural frequency – were measured in 44 species of terrestrial mammals, spanning eight taxonomic orders. Limb length increases disproportionately with body mass via positive allometry (length ∝ body mass^0.40); the positive allometry of limb length may help explain the scaling of the metabolic cost of transport. When scaled against body mass, forelimb inertial properties, apart from mass, scale with positive allometry. Fore- and hindlimb mass scale according to geometric similarity (limb mass ∝ body mass^1.0), as do the remaining hindlimb inertial properties. The positive allometry of limb length is largely the result of absolute differences in limb inertial properties between mammalian subgroups. Though likely detrimental to locomotor costs in large mammals, scale effects in limb inertial properties appear to be concomitant with scale effects in sensorimotor control and locomotor ability in terrestrial mammals. Across mammals, the forelimb''s potential for angular acceleration scales according to geometric similarity, whereas the hindlimb''s potential for angular acceleration scales with positive allometry.     

Dynamic plantar pressure distribution during terrestrial locomotion of bonobos (Pan paniscus)

We collected high-resolution plantar pressure distributions of seven bonobos during terrestrial bipedal and quadrupedal locomotion (N = 146). Functional foot length, degree of hallux abduction, and total contact time were determined, and plots, showing pressure as a function of time for six different foot regions, were generated. We also studied five adult humans for comparison (N = 13). Both locomotion types of the bonobo show a large variation in plantar pressure distributions, which could be due to the interference of instantaneous behavior with locomotion and differences in walking speed and body dimensions. The heel and the lateral midfoot typically touch down simultaneously at initial ground contact in bipedal and quadrupedal walking of bonobos, in contrast with the typical heel-strike of human bipedalism. The center of pressure follows a curved course during quadrupedalism, as a consequence of the medial weight transfer during mid-stance. Bipedal locomotion of bonobos is characterized by a more plantar positioning of the feet and by a shorter contact time than during quadrupedal walking, according to a smaller stride and step length at a higher frequency. We observed a varus position of the foot with an abducted hallux, which likely possesses an important sustaining and stabilizing function during terrestrial locomotion.     

The energetic cost of locomotion: humans and primates compared to generalized endotherms

A wide range of selective pressures have been advanced as possible causes for the adoption of bipedalism in the hominin lineage. One suggestion has been that because modern human walking is relatively efficient compared to that of a typical quadruped, the ancestral quadruped may have reaped an energetic advantage when it walked on two legs. While it has become clear that human walking is relatively efficient and human running inefficient compared to "generalized endotherms", workers differ in their opinion of how the cost of human bipedal locomotion compares to that of a generalized primate walking quadrupedally. One view is that human walking is particularly efficient in comparison to other primates. The present study addresses this by comparing the cost of human walking and running to that of the eight primate species for which data are available and by comparing cost in primates to that of a "generalized endotherm". There is no evidence that primate locomotion is more costly than that of a generalized endotherm, although more data on adult Old World monkeys and apes would be useful. Further, human locomotion does not appear to be particularly efficient relative to that of other primates.     

Limb morphology,bipedal gait,and the energetics of hominid locomotion

How viable is the argument that increased locomotor efficiency was an important agent in the origin of hominid bipedalism? This study reviews data from the literature on the cost of human bipedal walking and running and compares it to data on quadrupedal mammals including several non-human primate species. Literature data comparing the cost of bipedal and quadrupedal locomotion in trained capuchin monkeys and chimpanzees are also considered. It is concluded that increased energetic efficiency would not have accrued to early bipeds. Presumably, however, selection for improved efficiency in the bipedal stance would have occurred once the transition was made. Would such a process have included selection for increased limb length? Data on the cost of locomotion vs. limb length reveal no significant relationship between these variables in 21 species of mammals or in human walking or running. © 1996 Wiley-Liss, Inc.     

An analytical estimation of the energy cost for legged locomotion

Legged locomotion requires the determination of a number of parameters such as stride period, stride length, order of leg movements, leg trajectory, etc. How are these parameters determined? It has been reported that the locomotor patterns of many legged animals exhibit common characteristics, which suggests that there exists a basic strategy for legged locomotion. In this study we derive an equation to estimate the cost of transport for legged locomotion and examine a criterion of the minimization of the transport cost as a candidate of the strategy. The obtained optimal locomotor pattern that minimizes the cost suitably represents many characteristics of the pattern observed in legged animals. This suggests that the locomotor pattern of legged animals is well optimized with regard to the energetic cost. The result also suggests that the existence of specific gait patterns and the phase transition between them could be the result due to optimization; they are induced by the change in the distribution of ground reaction forces for each leg during locomotion.