Energetics and mechanics of terrestrial locomotion. IV. Total mechanical energy changes as a function of speed and body size in birds and mammals

1982 ◽  
Vol 97 (1) ◽  
pp. 57-66 ◽  
Author(s):  
N. C. Heglund ◽  
M. A. Fedak ◽  
C. R. Taylor ◽  
G. A. Cavagna
Keyword(s):  
Body Size ◽  
Kinetic Energy ◽  
Elastic Energy ◽  
Mechanical Energy ◽  
Motor Units ◽  
Metabolic Energy ◽  
Small Animals ◽  
Centre Of Mass ◽  
Terrestrial Locomotion ◽  
Total Mechanical Energy

This is the final paper in or 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, Etot/Mb, can be described by one equation: Etot/Mb = 0.478. vg 1.53 + 0.685. vg + 0.072 where Etot/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 constant-speed 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.

Energetics and mechanics of terrestrial locomotion. III. Energy changes of the centre of mass as a function of speed and body size in birds and mammals

1982 ◽  
Vol 97 (1) ◽  
pp. 41-56 ◽  
Author(s):  
N. C. Heglund ◽  
G. A. Cavagna ◽  
C. R. Taylor
Keyword(s):  
Body Size ◽  
Total Power ◽  
Small Animals ◽  
Similar Data ◽  
Centre Of Mass ◽  
Average Speed ◽  
Terrestrial Locomotion ◽  
The Third ◽  
Large Animals ◽  
Level Constant

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 (ECM, 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: ECM, tot/Mb = 0.685 vg + 0.072 where ECM, 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.

Energetics and mechanics of terrestrial locomotion. II. Kinetic energy changes of the limbs and body as a function of speed and body size in birds and mammals

1982 ◽  
Vol 97 (1) ◽  
pp. 23-40
Author(s):  
M. A. Fedak ◽  
N. C. Heglund ◽  
C. R. Taylor
Keyword(s):  
Body Size ◽  
Kinetic Energy ◽  
High Speed ◽  
Specific Power ◽  
Time Interval ◽  
Specific Rate ◽  
Centre Of Mass ◽  
X Ray ◽  
Terrestrial Locomotion ◽  
Integral Number

This is the second paper in a series examining the link between energetics and mechanics of terrestrial locomotion. In this paper, the changes in the kinetic energy of the limbs and body relative to the centre of mass of an animal (EKE, tot) are measured as functions of speed and body size. High-speed films (light or X-ray) of four species of quadrupeds and four species of bipeds running on a treadmill were analysed to determine EKE, tot. A mass-specific power term, EKE, tot/Mb was calculated by adding all of the increments in EKE during an integral number of strides and dividing by the time interval for the strides and body mass. The equations relating EKE, tot/Mb and speed were similar for all bipeds and quadrupeds regardless of size. One general equation for the rate at which muscle and tendons must supply energy to accelerate the limbs and body relative to the centre of mass seems to apply for all of the animals: E'KE, tot/Mb = 0.478 vg1.53 where E'KE, tot/Mb has the units W kg-1 and vg is ground speed in m s-1. Therefore, E'KE, tot/Mb does not change in parallel with the mass-specific rate at which animals consume energy (Emetab/Mb), either as a function of speed or as a function of body size.

scholarly journals Walking in simulated reduced gravity: mechanical energy fluctuations and exchange

1999 ◽  
Vol 86 (1) ◽  
pp. 383-390 ◽  
Author(s):  
Timothy M. Griffin ◽  
Neil A. Tolani ◽  
Rodger Kram
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Metabolic Cost ◽  
Metabolic Energy ◽  
Gravitational Potential Energy ◽  
Reduced Gravity

Walking humans conserve mechanical and, presumably, metabolic energy with an inverted pendulum-like exchange of gravitational potential energy and horizontal kinetic energy. Walking in simulated reduced gravity involves a relatively high metabolic cost, suggesting that the inverted-pendulum mechanism is disrupted because of a mismatch of potential and kinetic energy. We tested this hypothesis by measuring the fluctuations and exchange of mechanical energy of the center of mass at different combinations of velocity and simulated reduced gravity. Subjects walked with smaller fluctuations in horizontal velocity in lower gravity, such that the ratio of horizontal kinetic to gravitational potential energy fluctuations remained constant over a fourfold change in gravity. The amount of exchange, or percent recovery, at 1.00 m/s was not significantly different at 1.00, 0.75, and 0.50 G (average 64.4%), although it decreased to 48% at 0.25 G. As a result, the amount of work performed on the center of mass does not explain the relatively high metabolic cost of walking in simulated reduced gravity.

scholarly journals Elastic energy savings and active energy cost in a simple model of running

2021 ◽  
Vol 17 (11) ◽  
pp. e1009608
Author(s):  
Ryan T. Schroeder ◽  
Arthur D. Kuo
Keyword(s):  
Elastic Energy ◽  
Energy Cost ◽  
Energy Savings ◽  
Mechanical Energy ◽  
Metabolic Cost ◽  
The Body ◽  
Metabolic Energy ◽  
Energetic Cost ◽  
Mass Model ◽  
Human Running

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic “Spring-mass” computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. However, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running, whether on level ground or on a slope. Here we add explicit actuation and dissipation to the Spring-mass model, and show how they explain substantial active (and thus costly) work during human running, and much of the associated energetic cost. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m s-1) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. With both work and rapid force costs, the model reproduces the energetics of human running at a range of speeds on level ground and on slopes. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.

scholarly journals Changes in Energy Cost and Total External Work of Muscles in Elite Race Walkers Walking at Different Speeds

2014 ◽  
Vol 44 (1) ◽  
pp. 129-136 ◽  
Author(s):  
Wiesław Chwała ◽  
Andrzej Klimek ◽  
Wacław Mirek
Keyword(s):  
Kinetic Energy ◽  
Total Energy ◽  
Energy Cost ◽  
Direct Method ◽  
Mechanical Energy ◽  
Mass Movement ◽  
Average Energy ◽  
Centre Of Mass ◽  
External Work ◽  
Race Walking

Abstract The aim of the study was to assess energy cost and total external work (total energy) depending on the speed of race walking. Another objective was to determine the contribution of external work to total energy cost of walking at technical, threshold and racing speed in elite competitive race walkers. The study involved 12 competitive race walkers aged years with 6 to 20 years of experience, who achieved a national or international sports level. Their aerobic endurance was determined by means of a direct method involving an incremental exercise test on the treadmill. The participants performed three tests walking each time with one of the three speeds according to the same protocol: an 8-minute walk with at steady speed was followed by a recovery phase until the oxygen debt was repaid. To measure exercise energy cost, an indirect method based on the volume of oxygen uptake was employed. The gait of the participants was recorded using the 3D Vicon opto-electronic motion capture system. Values of changes in potential energy and total kinetic energy in a gate cycle were determined based on vertical displacements of the centre of mass. Changes in mechanical energy amounted to the value of total external work of muscles needed to accelerate and lift the centre of mass during a normalised gait cycle. The values of average energy cost and of total external work standardised to body mass and distance covered calculated for technical speed, threshold and racing speeds turned out to be statistically significant. The total energy cost ranged from 51.2 kJ.m-1 during walking at technical speed to 78.3 kJ.m-1 during walking at a racing speed. Regardless of the type of speed, the total external work of muscles accounted for around 25% of total energy cost in race walking. Total external work mainly increased because of changes in the resultant kinetic energy of the centre of mass movement.

Three-dimensional kinematics and limb kinetic energy of running cockroaches.

1997 ◽  
Vol 200 (13) ◽  
pp. 1919-1929 ◽  
Author(s):  
R Kram ◽  
B Wong ◽  
R J Full
Keyword(s):  
Kinetic Energy ◽  
High Speed ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Three Dimensional ◽  
The Body ◽  
Morphological Data ◽  
Fast Running ◽  
Total Mechanical Energy ◽  
Reaction Forces

We tested the hypothesis that fast-running hexapeds must generate high levels of kinetic energy to cycle their limbs rapidly compared with bipeds and quadrupeds. We used high-speed video analysis to determine the three-dimensional movements of the limbs and bodies of cockroaches (Blaberus discoidalis) running on a motorized treadmill at 21 cm s-1 using an alternating tripod gait. We combined these kinematic data with morphological data to calculate the mechanical energy produced to move the limbs relative to the overall center of mass and the mechanical energy generated to rotate the body (head + thorax + abdomen) about the overall center of mass. The kinetic energy involved in moving the limbs was 8 microJ stride-1 (a power output of 21 mW kg-1, which was only approximately 13% of the external mechanical energy generated to lift and accelerate the overall center of mass at this speed. Pitch, yaw and roll rotational movements of the body were modest (less than +/- 7 degrees), and the mechanical energy required for these rotations was surprisingly small (1.7 microJ stride-1 for pitch, 0.5 microJ stride-1 for yaw and 0.4 microJ stride-1 for roll) as was the power (4.2, 1.2 and 1.1 mW kg-1, respectively). Compared at the same absolute forward speed, the mass-specific kinetic energy generated by the trotting hexaped to swing its limbs was approximately half of that predicted from data on much larger two- and four-legged animals. Compared at an equivalent speed (mid-trotting speed), limb kinetic energy was a smaller fraction of total mechanical energy for cockroaches than for large bipedal runners and hoppers and for quadrupedal trotters. Cockroaches operate at relatively high stride frequencies, but distribute ground reaction forces over a greater number of relatively small legs. The relatively small leg mass and inertia of hexapeds may allow relatively high leg cycling frequencies without exceptionally high internal mechanical energy generation.

Energetics and mechanics of terrestrial locomotion. I. Metabolic energy consumption as a function of speed and body size in birds and mammals

1982 ◽  
Vol 97 (1) ◽  
pp. 1-21 ◽  
Author(s):  
C. R. Taylor ◽  
N. C. Heglund ◽  
G. M. Maloiy
Keyword(s):  
Oxygen Consumption ◽  
Energy Consumption ◽  
Body Size ◽  
Mammalian Species ◽  
Allometric Equation ◽  
Metabolic Energy ◽  
Published Data ◽  
Terrestrial Locomotion ◽  
Speed Range ◽  
Rate Of Oxygen Consumption

This series of four papers investigates the link between the energetics and the mechanics of terrestrial locomotion. Two experimental variables are used throughout the study: speed and body size. Mass-specific metabolic rates of running animals can be varied by about tenfold using either variable. This first paper considers metabolic energy consumed during terrestrial locomotion. New data relating rate of oxygen consumption and speed are reported for: eight species of wild and domestic artiodactyls; seven species of carnivores; four species of primates; and one species of rodent. These are combined with previously published data to formulate a new allometric equation relating mass-specific rates of oxygen consumed (VO2/Mb) during locomotion at a constant speed to speed and body mass (based on data from 62 avian and mammalian species): VO2/Mb = 0.533 Mb-0.316.vg + 0.300 Mb-0.303 where VO2/Mb has the units ml O2 s-1 kg-1; Mb is in kg; and vg is in m s-1. This equation can be expressed in terms of mass-specific rates of energy consumption (Emetab/Mb) using the energetic equivalent of 1 ml O2 = 20.1 J because the contribution of anaerobic glycolysis was negligible: Emetab/Mb = 10.7 Mb-0.316.vg + 6.03 Mb-0.303 where Emetab/Mb has the units watts/kg. This new relationship applies equally well to bipeds and quadrupeds and differs little from the allometric equation reported 12 years ago by Taylor, Schmid-Nielsen & Raab (1970). Ninety per cent of the values calculated from this genera equation for the diverse assortment of avian and mammalian species included in this regression fall within 25% of the observed values at the middle of the speed range where measurements were made. This agreement is impressive when one considers that mass-specific rates of oxygen consumption differed by more than 1400% over this size range of animals.

scholarly journals Does Elastic Energy Enhance Work and Efficiency in the Stretch-Shortening Cycle?

1997 ◽  
Vol 13 (4) ◽  
pp. 389-415 ◽  
Author(s):  
Gerrit Jan van Ingen Schenau ◽  
Maarten F. Bobbert ◽  
Arnold de Haan
Keyword(s):  
Elastic Energy ◽  
Mechanical Energy ◽  
Mechanical Efficiency ◽  
The Body ◽  
Metabolic Energy ◽  
Whole Body ◽  
Levels Of Organization ◽  
Cyclic Movements ◽  
Stretch Shortening Cycle ◽  
Different Levels

This target article addresses the role of storage and reutilization of elastic energy in stretch-shortening cycles. It is argued that for discrete movements such as the vertical jump, elastic energy does not explain the work enhancement due to the prestretch. This enhancement seems to occur because the prestretch allows muscles to develop a high level of active state and force before starting to shorten. For cyclic movements in which stretch-shortening cycles occur repetitively, some authors have claimed that elastic energy enhances mechanical efficiency. In the current article it is demonstrated that this claim is often based on disputable concepts such as the efficiency of positive work or absolute work, and it is argued that elastic energy cannot affect mechanical efficiency simply because this energy is not related to the conversion of metabolic energy into mechanical energy. A comparison of work and efficiency measures obtained at different levels of organization reveals that there is in fact no decisive evidence to either support or reject the claim that the stretch-shortening cycle enhances muscle efficiency. These explorations lead to the conclusion that the body of knowledge about the mechanics and energetics of the stretch-shortening cycle is in fact quite lean. A major challenge is to bridge the gap between knowledge obtained at different levels of organization, with the ultimate purpose of understanding how the intrinsic properties of muscles manifest themselves underin-vivo-like conditions and how they are exploited in whole-body activities such as running. To achieve this purpose, a close cooperation is required between muscle physiologists and human movement scientists performing inverse and forward dynamic simulation studies of whole-body exercises.

scholarly journals Locomotion Energetics of the Ghost Crab: II. Mechanics of the Centre of Mass During Walking and Running

1987 ◽  
Vol 130 (1) ◽  
pp. 155-174 ◽  
Author(s):  
REINHARD BLICKHAN ◽  
ROBERT J. FULL
Keyword(s):  
Mechanical Design ◽  
Mechanical Energy ◽  
Stride Frequency ◽  
Centre Of Mass ◽  
Unit Distance ◽  
Ghost Crab ◽  
Locomotor Apparatus ◽  
Terrestrial Locomotion ◽  
Ghost Crabs ◽  
Energy Conserving

Terrestrial locomotion involving appendages has evolved independently in vertebrates and arthropods. Differences in the mechanical design of the locomotor apparatus could impose constraints on the energetics of locomotion. The mechanical energy fluctuations of the centre of mass of an arthropod, the ghost crab Ocypode quadrata (Fabricius), were examined by integrating the ground reaction forces exerted during sideways locomotion. Crabs used a pendulum-type energy exchange mechanism during walking, analogous to an egg rolling end over end, with the same effectiveness as birds and mammals. Moreover, ghost crabs were found to have two running gaits. A switch from a slow to a fast run occurred at the same speed and stride frequency predicted for the trot-gallop transition of a quadrupedal mammal of the same body mass. In addition, the mass-specific mechanical energy developed over a unit distance was independent of speed and was within the limits measured for birds and mammals. Despite the obvious differences in mechanical design between crabs and mammals, energy-conserving mechanisms and the efficiency of locomotion were remarkably similar. These similarities may result from the fact that the muscles that generate forces during terrestrial locomotion have relatively conservative mechanical and energetic properties.

Analysis of the blast furnace operations with a volume of 5000 m3 on tuyeres of different diameters from the positions of full mechanical energies of flows of combined blow and hearth gas

2020 ◽  
Vol 76 (7) ◽  
pp. 691-699
Author(s):  
V. P. Lyalyuk
Keyword(s):  
Blast Furnace ◽  
Kinetic Energy ◽  
Gas Flow ◽  
Cooling System ◽  
Mechanical Energy ◽  
Depth Of Penetration ◽  
Short Term Result ◽  
Total Mechanical Energy ◽  
Hearth Gas ◽  
Different Diameters

In the commissioning period of the development of pulverized coal injection technology (PCI) on a blast furnace No. 9 with a volume of 5000 m3 of PJSC “ArcelorMittal Kryvyi Rih”, frequent cases of burnout of refrigerators of the cooling system of the shoulders and air tyueres appeared due to the highly developed peripheral gas flow. An attempt to limit the gas flow at the periphery by controlling the distribution of charge materials on the top produced a short-term result. Based on the prevailing ideas, that to reduce the intensity of the peripheral gas flow, it is necessary to increase the speed of the blast and, accordingly, the kinetic energy of the blast flow, flowing out of the air tuyeres of a blast furnace, it was decided to reduce their diameter. As a result of analysis of the operation of the specified blast furnace using the technology of PCI on tuyeres with a diameter of 150 and 140 mm, increased peripheral gas flow with a smaller diameter was established. Based on the results of the analysis, conclusions were made by many researchers and it was shown that with constant kinetic energy of the blast, flowing from the tuyeres of different diameters, the dimensions of the combustion zone are always larger before the tuyeres of a larger diameter. This is explained by the fact that the kinetic energy of the gas flow is only a part of their total mechanical energy. It was shown that to analyze the change in the size of the combustion zones and the depth of penetration of the hearth gas, it is necessary to use the full mechanical energy of the flows of the combined blast on the cut of the tuyere and hearth gas. It was established that the transition to PCI in a blast furnace instead of natural gas, it always causes an increase in the peripheral gas flow. The main reason for this phenomenon is associated with a decrease in the total mechanical energy of blast and hearth gas. It was recommended on a blast furnace with a volume of 5000 m3 with a hearth diameter of 14.7 m and the PCI technology to maintain the total mechanical energy of the blast flow at least 2100–2600 kJ/s, and the full mechanical energy of the hearth gas flow at least 5100–5300 kJ/s.

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