Speed, stride frequency and energy cost per stride: how do they change with body size and gait?

1988 ◽  
Vol 138 (1) ◽  
pp. 301-318 ◽  
Author(s):  
N. C. Heglund ◽  
C. R. Taylor
Keyword(s):  
Body Size ◽  
Body Mass ◽  
Energy Cost ◽  
Reaction Force ◽  
Stride Frequency ◽  
Energetic Cost ◽  
Published Data ◽  
Frequency Change ◽  
Cost Of Locomotion ◽  
The Cost

In this study we investigate how speed and stride frequency change with body size. We use this information to define ‘equivalent speeds’ for animals of different size and to explore the factors underlying the six-fold difference in mass-specific energy cost of locomotion between mouse- and horse-sized animals at these speeds. Speeds and stride frequencies within a trot and a gallop were measured on a treadmill in 16 species of wild and domestic quadrupeds, ranging in body size from 30 g mice to 200 kg horses. We found that the minimum, preferred and maximum sustained speeds within a trot and a gallop all change in the same rather dramatic manner with body size, differing by nine-fold between mice and horses (i.e. all three speeds scale with about the 0.2 power of body mass). Although the absolute speeds differ greatly, the maximum sustainable speed was about 2.6-fold greater than the minimum within a trot, and 2.1-fold greater within a gallop. The frequencies used to sustain the equivalent speeds (with the exception of the minimum trotting speed) scale with about the same factor, the −0.15 power of body mass. Combining this speed and frequency data with previously published data on the energetic cost of locomotion, we find that the mass-specific energetic cost of locomotion is almost directly proportional to the stride frequency used to sustain a constant speed at all the equivalent speeds within a trot and a gallop, except for the minimum trotting speed (where it changes by a factor of two over the size range of animals studied). Thus the energy cost per kilogram per stride at five of the six equivalent speeds is about the same for all animals, independent of body size, but increases with speed: 5.0 J kg-1 stride-1 at the preferred trotting speed; 5.3 J kg-1 stride-1 at the trot-gallop transition speed; 7.5 J kg-1 stride-1 at the preferred galloping speed; and 9.4 J kg-1 stride-1 at the maximum sustained galloping speed. The cost of locomotion is determined primarily by the cost of activating muscles and of generating a unit of force for a unit of time. Our data show that both these costs increase directly with the stride frequency used at equivalent speeds by different-sized animals. The increase in cost per stride with muscles (necessitating higher muscle forces for the same ground reaction force) as stride length increases both in the trot and in the gallop.

Energetic cost of locomotion in the tammar wallaby

1992 ◽  
Vol 262 (5) ◽  
pp. R771-R778 ◽  
Author(s):  
R. V. Baudinette ◽  
G. K. Snyder ◽  
P. B. Frappell
Keyword(s):  
Oxygen Consumption ◽  
Blood Lactate ◽  
Body Mass ◽  
Energy Cost ◽  
Physiological Adaptation ◽  
Energetic Cost ◽  
Cost Of Locomotion ◽  
Lactate Levels ◽  
Energy Cost Of Locomotion ◽  
Blood Lactate Levels

Rates of oxygen consumption and blood lactate levels were measured in tammar wallabies (Macropus eugenii) trained to hop on a treadmill. In addition, the work required to overcome wind resistance during forward locomotion was measured in a wind tunnel. Up to approximately 2.0 m/s, rates of oxygen consumption increased linearly with speed and were not significantly different from rates of oxygen consumption for a quadruped of similar body mass. Between 2.0 and 9.4 m/s, rates of oxygen consumption were independent of hopping speed, and between 3.9 and 7.9 m/s, the range over which samples were obtained, blood lactate levels were low (0.83 +/- 0.13 mmol.min-1.kg-1) and did not increase with hopping speed. The work necessary to overcome drag increased exponentially with speed but increased the energy cost of locomotion by only 10% at the average speed attained by our fast hoppers. Thus, during hopping, the energy cost of locomotion is effectively independent of speed. At rates of travel observed in the field, the estimated energy cost of transport in large macropods is less than one-third the cost for a quadruped of equivalent body mass. The energetic savings associated with this unique form of locomotion may have been an important physiological adaptation, enabling large macropods to efficiently cover the distances necessary to forage in the semiarid landscapes of Australia.

scholarly journals Animal galloping and human hopping: an energetics and biomechanics laboratory exercise

2013 ◽  
Vol 37 (4) ◽  
pp. 377-383 ◽  
Author(s):  
Stan L. Lindstedt ◽  
Patrick M. Mineo ◽  
Paul J. Schaeffer
Keyword(s):  
Body Size ◽  
Metabolic Cost ◽  
Mechanical Efficiency ◽  
Lessons Learned ◽  
Stride Frequency ◽  
Energetic Cost ◽  
Elastic Recoil ◽  
Laboratory Exercise ◽  
The Cost ◽  
Work Done

This laboratory exercise demonstrates fundamental principles of mammalian locomotion. It provides opportunities to interrogate aspects of locomotion from biomechanics to energetics to body size scaling. It has the added benefit of having results with robust signal to noise so that students will have success even if not “meticulous” in attention to detail. First, using respirometry, students measure the energetic cost of hopping at a “preferred” hop frequency. This is followed by hopping at an imposed frequency half of the preferred. By measuring the O2 uptake and work done with each hop, students calculate mechanical efficiency. Lessons learned from this laboratory include 1) that the metabolic cost per hop at half of the preferred frequency is nearly double the cost at the preferred frequency; 2) that when a person is forced to hop at half of their preferred frequency, the mechanical efficiency is nearly that predicted for muscle but is much higher at the preferred frequency; 3) that the preferred hop frequency is strongly body size dependent; and 4) that the hop frequency of a human is nearly identical to the galloping frequency predicted for a quadruped of our size. Together, these exercises demonstrate that humans store and recover elastic recoil potential energy when hopping but that energetic savings are highly frequency dependent. This stride frequency is dependent on body size such that frequency is likely chosen to maximize this function. Finally, by requiring students to make quantitative solutions using appropriate units and dimensions of the physical variables, these exercises sharpen analytic and quantitative skills.

Energetic Cost of Running with different Muscle Temperatures in Savannah MOnitor Lizards

1982 ◽  
Vol 99 (1) ◽  
pp. 269-277
Author(s):  
LAWRENCE C. ROME
Keyword(s):  
Isometric Force ◽  
Stride Frequency ◽  
Energetic Cost ◽  
Muscle Temperature ◽  
Apparent Difference ◽  
Muscle Energetics ◽  
Cost Of Locomotion ◽  
Monitor Lizards ◽  
The Cost

The purpose of this study was to determine whether the energetic cost of locomotion was independent of muscle temperature, or if it tripled with a 10 °C increase in temperature, like the cost of generating isometric force in isolated muscle preparations. For a given running speed of Savannah Monitor lizards, the energetic cost of locomotion (the difference between running and resting metabolism) was the same when muscle temperature was 28.5 °C as when it was 38 °C. It was also found that stride frequency and posture did not change with temperature, indicating that the average force exerted by the lizards' muscles during locomotion at the two temperatures was the same. This suggests that the cost of generating force in vivo is independent of temperature. Several possible explanations of the apparent difference between in vivo and in vitro muscle energetics are discussed.

Energetics of ascent: insects on inclines

1990 ◽  
Vol 149 (1) ◽  
pp. 307-317 ◽  
Author(s):  
R. J. Full ◽  
A. Tullis
Keyword(s):  
Oxygen Consumption ◽  
Minimum Cost ◽  
Metabolic Cost ◽  
Metabolic Energy ◽  
Stride Frequency ◽  
Energetic Cost ◽  
Incline Angle ◽  
Small Animals ◽  
Cost Of Locomotion ◽  
The Cost

Small animals use more metabolic energy per unit mass than large animals to run on a level surface. If the cost to lift one gram of mass one vertical meter is constant, small animals should require proportionally smaller increases in metabolic cost to run uphill. To test this hypothesis on very small animals possessing an exceptional capacity for ascending steep gradients, we measured the metabolic cost of locomotion in the cockroach, Periplaneta americana, running at angles of 0, 45 and 90 degrees to the horizontal. Resting oxygen consumption (VO2rest) was not affected by incline angle. Steady-state oxygen consumption (VO2ss) increased linearly with speed at all angles of ascent. The minimum cost of locomotion (the slope of the VO2ss versus speed function) increased with increasing angle of ascent. The minimum cost of locomotion on 45 and 90 degrees inclines was two and three times greater, respectively, than the cost during horizontal running. The cockroach's metabolic cost of ascent greatly exceeds that predicted from the hypothesis of a constant efficiency for vertical work. Variations in stride frequency and contact time cannot account for the high metabolic cost, because they were independent of incline angle. An increase in the metabolic cost or amount of force production may best explain the increase in metabolic cost. Small animals, such as P. americana, can easily scale vertical surfaces, but the energetic cost is considerable.

scholarly journals Scaling of muscle fibres and locomotion

1992 ◽  
Vol 168 (1) ◽  
pp. 243-252 ◽  
Author(s):  
L. C. Rome
Keyword(s):  
Muscle Fibre ◽  
Body Mass ◽  
Fibre Type ◽  
Fibre Types ◽  
Energetic Cost ◽  
Muscle Fibres ◽  
Small Animals ◽  
Running Speed ◽  
Cost Of Locomotion ◽  
The Cost

To reconcile the scaling of the mechanics and energetics of locomotion to recent data on the scaling of the mechanics of muscle fibres, I have extended the theory of Taylor and colleagues that the energetic cost of locomotion is determined by the cost of generating force by the fibres. By assuming (1) that the cost of generating force in a fibre is proportional to V(max) (maximum velocity of shortening) and (2) that, at physiologically equivalent speeds, animals of different body sizes recruit the same fibre types, this extension quantitatively predicts the scaling of the energetics of locomotion, as well as other observations, from the scaling of V(max) of the muscle fibres. First, the energetic cost of locomotion at physiologically equivalent speeds scales with Mb-0.16, where Mb is body mass, as does V(max) of a given fibre type. However, the energetic cost at absolute speeds (cost of transport) scales with Mb-0.30, because small animals must compress their recruitment order into a narrower speed range and, hence, recruit faster muscle fibre types at a given running speed. Thus, it costs more for small animals to move 1 kg of their body mass 1 km not only because a given muscle fibre type from a small animal costs more to generate force than from a large one, but also because small animals recruit faster fibre types at a given absolute running speed. In addition, this analysis provides evidence that V(max) scales similarly to 1/tc (where tc is foot contact time) and muscle shortening velocity (V), in agreement with recent models. Finally, this extension predicts that, at physiologically equivalent speeds, the weight-specific energetic cost per step is independent of body size, as has been found empirically.

Moving cheaply: energetics of walking in the African elephant.

1995 ◽  
Vol 198 (3) ◽  
pp. 629-632 ◽  
Author(s):  
V A Langman ◽  
T J Roberts ◽  
J Black ◽  
G M Maloiy ◽  
N C Heglund ◽  
...  
Keyword(s):  
Fuel Economy ◽  
African Elephant ◽  
Metabolic Energy ◽  
Energetic Cost ◽  
Allometric Relationships ◽  
Cost Of Locomotion ◽  
Biological Laws ◽  
Large Animals ◽  
The Cost

Large animals have a much better fuel economy than small ones, both when they rest and when they run. At rest, each gram of tissue of the largest land animal, the African elephant, consumes metabolic energy at 1/20 the rate of a mouse; using existing allometric relationships, we calculate that it should be able to carry 1 g of its tissue (or a load) for 1 km at 1/40 the cost for a mouse. These relationships between energetics and size are so consistent that they have been characterized as biological laws. The elephant has massive legs and lumbers along awkwardly, suggesting that it might expend more energy to move about than other animals. We find, however, that its energetic cost of locomotion is predicted remarkably well by the allometric relationships and is the lowest recorded for any living land animal.

Dynamics of photoconversion processes: the energetic cost of lifetime gain in photosynthetic and photovoltaic systems

2021 ◽  
Author(s):  
Robert Godin ◽  
James R. Durrant
Keyword(s):  
Kinetic Model ◽  
Solar Energy ◽  
Energy Conversion ◽  
Energy Cost ◽  
Energetic Cost ◽  
Photovoltaic Systems ◽  
Simple Kinetic Model ◽  
Energy Conversion Systems ◽  
Order Of Magnitude ◽  
The Cost

The energy cost of lifetime gain in solar energy conversion systems is determined from a breadth of technologies. The cost of 87 meV per order of magnitude lifetime improvement is strikingly close to the 59 meV determined from a simple kinetic model.

Efficiency of uphill locomotion in nocturnal and diurnal lizards

1996 ◽  
Vol 199 (3) ◽  
pp. 587-592 ◽  
Author(s):  
C Farley ◽  
M Emshwiller
Keyword(s):  
Body Mass ◽  
Low Cost ◽  
Minimum Cost ◽  
Mechanical Work ◽  
Energetic Cost ◽  
Cost Of Transport ◽  
Unit Distance ◽  
Cost Of Locomotion ◽  
Average Body Mass ◽  
Average Body

Nocturnal geckos can walk on level ground more economically than diurnal lizards. One hypothesis for why nocturnal geckos have a low cost of locomotion is that they can perform mechanical work during locomotion more efficiently than other lizards. To test this hypothesis, we compared the efficiency of the nocturnal gecko Coleonyx variegatus (average body mass 4.2 g) and the diurnal skink Eumeces skiltonianus (average body mass 4.8 g) when they performed vertical work during uphill locomotion. We measured the rate of oxygen consumption when each species walked on the level and up a 50 slope over a range of speeds. For Coleonyx variegatus, the energetic cost of traveling a unit distance (the minimum cost of transport, Cmin) increased from 1.5 to 2.7 ml O2 kg-1 m-1 between level and uphill locomotion. For Eumeces skiltonianus, Cmin increased from 2.5 to 4.7 ml O2 kg-1 m-1 between level and uphill locomotion. By taking the difference between Cmin for level and uphill locomotion, we found that the efficiency of performing vertical work during locomotion was 37 % for Coleonyx variegatus and 19 % for Eumeces skiltonianus. The similarity between the 1.9-fold difference in vertical efficiency and the 1.7-fold difference in the cost of transport on level ground is consistent with the hypothesis that nocturnal geckos have a lower cost of locomotion than other lizards because they can perform mechanical work during locomotion more efficiently.

Effect of Body Size on Treadmill Economy in Female Adolescents and Adults

2005 ◽  
Vol 17 (3) ◽  
pp. 301-310
Author(s):  
Colleen M. Grossner ◽  
Emily M. Johnson ◽  
Marco E. Cabrera
Keyword(s):  
Body Size ◽  
Oxygen Uptake ◽  
Body Mass ◽  
Female Adolescents ◽  
Stride Frequency ◽  
Oxygen Cost ◽  
Adolescents And Adults ◽  
Cost Differences ◽  
Main Factor

Differences in oxygen uptake (VO2) relative to body mass between children and adults walking or running at a given speed might be the result of body size differences. In order to determine whether body size is the main factor affecting these differences in VO2 per kg, we investigated treadmill economy in 10 female adolescents (girls) and 10 women who were matched for body size. There were no significant differences between groups in anthropometrics, stride frequency, or VO2peak. Mean mass-specific VO2 was not significantly different during walking (girls: 12.3 ± 1.7 ml·kg-1·min-1; women: 10.9 ± 1.4 ml·kg-1·min-1) or running (girls: 30.5 ± 3.5 ml·kg-1·min-1; women: 29.0 ± 2.0 ml·kg-1·min-1). Body size appears to have the largest effect on oxygen cost differences usually seen between girls and women during locomotion.

scholarly journals Energetic cost of locomotion as a function of ambient temperature and during growth in the marsupial Potorous tridactylus.

1993 ◽  
Vol 174 (1) ◽  
pp. 81-95
Author(s):  
R V Baudinette ◽  
E A Halpern ◽  
D S Hinds
Keyword(s):  
Oxygen Consumption ◽  
Ambient Temperature ◽  
Multiple Regression ◽  
Stride Length ◽  
Energy Use ◽  
Linear Increase ◽  
Stride Frequency ◽  
Energetic Cost ◽  
Cost Of Transport ◽  
Cost Of Locomotion

In the marsupial, the potoroo, multiple regression analysis shows that ambient temperature makes a minor (2%) contribution towards variation in oxygen consumption with speed. This suggests that the heat generated during running is substituted for heat which would otherwise have to be generated for temperature regulation. Maximum levels of oxygen consumption are also temperature-independent over the range 5-25 degrees C, but plasma lactate concentrations at the conclusion of exercise significantly increase with ambient temperature. Adult potoroos show a linear increase in oxygen consumption with speed, and multiple regression indicates that the most significant factor affecting energy use during running is stride length. Juvenile potoroos have an incremental cost of locomotion about 40% lower than that predicted on the basis of body mass. The smaller animals meet the demands of increasing speed by increasing stride length rather than stride frequency, as would be expected in a smaller species. Our results show that juvenile potoroos diverge significantly from models based only on adult animals in incremental changes in stride frequency, length and the cost of transport, suggesting that they are not simply scaled-down adults.

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