J. exp. Bid. (198a), 97, 1-a 1

^Vith a figures

Printed in Great Britain

ENERGETICS AND MECHANICS OF TERRESTRIALLOCOMOTION

I. METABOLIC ENERGY CONSUMPTION AS A FUNCTION OF SPEEDAND BODY SIZE IN BIRDS AND MAMMALS

BY C. R. TAYLOR, N. C. HEGLUND AND G. M. O. MALOIY

Museum of Comparative Zoology, Harvard University,Old Causeway Road, Bedford, MA 01730

and Department of Animal Physiology, University of Nairobi,P.O. Box 29053, Nairobi, Kenya

(Received 28 May 1981) *

SUMMARY

This series of four papers investigates the link between the energetics andthe mechanics of terrestrial locomotion. Two experimental variables are usedthroughout the study: speed and body size. Mass-specific metabolic rates ofrunning animals can be varied by about tenfold using either variable.

This first paper considers metabolic energy consumed during terrestriallocomotion. New data relating rate of oxygen consumption and speed arereported for: eight species of wild and domestic artiodactyls; seven speciesof carnivores; four species of primates; and one species of rodent. These arecombined with previously published data to formulate a new allometricequation relating mass-specific rates of oxygen consumed (^o,/Af(,) duringlocomotion at a constant speed to speed and body mass (based on data from62 avian and mammalian species):

V0JMh = 0-533 Mb-°-*u.va+0-300 M6-o-»oa

where fy)t/Mb has the units ml Ot s-1 kg"1; Mb is in kg; and v is in m s"1.

This equation can be expressed in terms of mass-specific rates of energy con-sumption (j^metab/^ft) using the energetic equivalent of 1 ml 0 8 = 20-1 Jbecause the contribution of anaerobic glycolysis was negligible:

^metab/M. = IO7 M6-°-»«.»a + 6-O3 Mft-»-»»»

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 calculatedfrom this general equation for the diverse assortment of avian and mammalianspecies included in this regression fall within 25 % of the observed values atthe middle of the speed range where measurements were made. This agree-ment is impressive when one considers that mass-specific rates of oxygenconsumption differed by more than 1400% over this size range of animals.

2 C. R. TAYLOR, N. C. HEGLUND AND G. M. O. MALOIY

INTRODUCTION

In this series of four papers we investigate the link between the energetics and themechanics of terrestrial locomotion by measuring both the metabolic energy con-sumed and the mechanical energy changes that occur as birds and mammals movealong the ground. We use two experimental variables throughout the study: speedand body size.

It is generally assumed that most of the energy consumed by the muscles of runninganimals is used in the transformation of chemical energy into mechanical energy(Hill, 1950; McMahon, 1975; Cavagna, Thys& Zamboni, 1976; Cavagna, Heglund &Taylor, 1977; Alexander, 1977; Alexander, 1980; Alexander, Jayes & Ker, 1980).A. V. Hill (1950) used dimensional analysis to predict how a variety of locomotoryparameters, including rates at which muscles work and consume metabolic energy,change with body size. He limited his consideration to the peak performance of ananimal moving at its top speed. He assumed that three properties were common to allvertebrate striated muscle, regardless of size: the maximal force developed per cross-sectional area; the maximum work performed by each gram of muscle during acontraction; and the maximum efficiency with which muscles convert chemicalenergy into mechanical work. His analysis predicted that large and small animalswould reach the same top speed, and at that speed the muscles of small animalswould be working and consuming energy at much higher rates. A simple way ofsummarizing Hill's logic is that each gram of muscle performs the same amount ofwork and consumes the same amount of energy during a step, but the small animalshave to take many more steps to cover the same distance because of their shorter legs.Therefore when running at the same speed small animals should have higher stridefrequencies and consume energy at higher rates.

Both of our experimental variables provide the potential for large changes in therate of energy consumption. Aerobic metabolism of a running animal can be increasedby about tenfold over resting rates. Also, mass-specific metabolic rates of animalsrunning at the same speed vary by 10 to 15-fold over the size range of animals used inthis study (Taylor, 1977). Tenfold differences in mass-specific metabolic rates shouldbe large enough to overcome the uncertainties inherent in mechanical energy measure-ments and enable us to establish the link, if any, between metabolic and mechanicalenergy.

This first paper considers the metabolic energy consumed during terrestriallocomotion. More than 10 years ago, Taylor et al. (1970) developed a simple, empiric-ally based equation that predicted the metabolic energy consumption by runningmammals from two simple and easily measured parameters: speed and body mass.They found that metabolic cost of running increased linearly with speed over a widerange of speeds; and that this relationship between metabolism and speed varied as aregular function of body mass. Measurements were made on six species of mammalsranging from 21 g to 18 kg. The results of this study have been substantiated by manymeasurements on a variety of mammalian species (Taylor, 1977). Recently, Fedak &Seeherman (1979) have reported that the energy cost of locomotion is the same forbipeds and quadrupeds regardless of size. However, an important gap in the litis a lack of measurements from large wild animals.

Energy consumption during locomotion 3

In this paper, we extend the data on energetic cost of locomotion to include:(1) a greater diversity of animals; (2) a greater range of running speeds from individualanimals; and (3) a greater size range of animals. Then we calculate a revised allometricequation for energy cost of locomotion. We compare the metabolic rates calculatedusing the revised equation with the observed rates at the middle of the speed rangeobtained for each animal. Additionally, we formulate allometric equations for taxo-nomically related groups of animals (where the data base is sufficient) and comparethese equations with the general equation for birds and mammals. This analysisshould enable us to find out whether costs vary from group to group. The equationsare used in the subsequent papers for comparison with similar equations describingmechanical energy changes within an animal.

MATERIALS AND METHODS

Experimented approach

Energy consumption as a function of treadspeedTo obtain a reproducible relationship between rate of energy consumption and

speed for animals running on a treadmill, we have: (1) used 'trained' animals; (2)made the measurements at each speed over a long enough interval to be certain that asteady-state oxygen consumption was achieved; and (3) ascertained that the energywas being derived primarily from aerobic metabolism over the entire range of speeds.

Training animals to run on the treadmill required a period of weeks to months,depending on the species and the individual animal. Two factors seemed important inthe training. First, the animals were frightened when first introduced to the treadmilland did not run with normal gaits or stride frequencies at a given speed. Trainedanimals had the same gait and stride frequency for a given speed on the treadmill andon the ground. Second, the oxygen-consumption experiments required far greaterendurance than would normally be required in nature. We have found that when ahuman or animal begins to tire, its oxygen consumption increases. As the trainingprogressed, animals were able to run much longer without tiring, and oxygen con-sumption remained constant during the run. Rate of oxygen consumption (POt) wasmeasured while the animals were being trained. We considered that the animalswere trained once we were able to obtain reproducible values for V'Ot at any speed.

To achieve a steady-state J^, we measured t[,t of the trained animals for 15-30 minat each speed. Frequently, J^ was higher during the first 2-3 min of a run. We didnot include these higher values, but used an average over the remainder of the run.We assumed these higher values were either the result of repayment of an anaerobic' start-up cost' or due to an abnormal gait as the animal adjusted to the tread speedat the beginning of a run.

To ensure that all of the energy was being provided aerobicaJly, R values (f^0JPOt) were determined during the run, and blood lactate values were determined atthe beginning and end of the runs at the highest speeds. We selected our top speeds sothat R values were less than 1 -o and less than 1 % of the total energy consumed couldie attributed to anaerobic glycolysis on the basis of the energy derived from the lacticid that accumulated during the run (Seeherman et al. 1981).

4 C. R. TAYLOR, N. C. HEGLUND AND G. M. O. MALOIY

Energetic cost of locomotion as a function of body size

We used the equations relating energy consumption and speed for individualanimals to develop allometric equations. Allometry is the study of how structuresand/or functions vary with body mass. One calculates the power function whichdescribes how a parameter, Y, changes with body mass, Mb:

Y = a.M6b (i)

where the exponent b is called the scaling factor. It is convenient to use the logarithmictransformation

logy = loga + b.logM6 (2)

in order to calculate regression coefficients and confidence intervals.In order for allometry to yield meaningful results, both the range of body mass and

the number of animals must be great enough to yield small 95 % confidence limits.

Animals

A review of existing data (Taylor, 1977) indicates that the principal gaps on energeticcost of locomotion are for large wild mammals. Therefore, we decided to take advantageof the diversity of large wild mammals living in Africa and carried out a major part ofthis work in Kenya. We obtained eight species of wild and domestic artiodactyls andthree species of carnivores by capture or purchase. The wild artiodactyls in order ofincreasing body mass were: 2 suni (Nesotragus moschatus, av. body mass 3-50 kg);2 dik-diks (Madoqua kirkii, av. body mass 435 kg); 2 wildebeest (Connochaetestaurinus, av. body mass 92-0 kg); 2 waterbucks (Kobus defassa, av. body mass 114 kg);and 2 elands (Taurotragus oryx, av. body mass 213 kg). The domestic artiodactyls inorder of increasing body mass were: 2 African goats {Capra hircus, av. body mass20-0 kg); 2 African sheep (Ovis aries, av. body mass 23-0 kg); 2 zebu cattle (Bos indicus,av. body mass 254 kg). We also obtained three species of the small carnivores. Inorder of increasing body mass they were: 3 dwarf mongooses (Helogale pervula, av.body mass 0-583 kg); 2 banded mongooses (Mungos mungo, av. body mass 1-15 kg);2 genet cats (Genetta tigrina, av. body mass 1-46 kg). The bovids were housed infacilities provided by the East African Veterinary Research Organization at Muguga.Muguga is in the Kenya highlands and a little over 2000 m above sea level. The averagebarometric pressure at Muguga during these experiments was 787 mbar (590 Torr).The viverrids were housed at the University of Nairobi, in Nairobi. This is also in theKenyan highlands and a little less than 2000 m above sea level. The average barometricpressure during these experiments was 835 mbar (626 Torr).

At our laboratory in the United States, we purchased four species of primates, onespecies of rodent, and four species of carnivores. The primates in order of increasingmass were: 3 tree shrews (Tupaia glis, av. body mass o-124 kg); 3 bush babies (Galagosenegalensis, av. body mass 0-240 kg); 3 stump-tailed macaques (Macaca speciosa,av. body mass 5-10 kg); and 2 hamadryas baboons (Papio hatnadryas, av. body mass850 kg). The rodent was the flying squirrel (3 individuals, Glaucomys volans, av.body mass 0063 kg). The carnivores in order of increasing size were: 1 ferret (Mustelanigripes, av. body mass 0-542 kg); 2 domestic cats (Felis catus, av. body mass 3 90 ^

Energy consumption during locomotion 5

h. domestic dogs (Canis famUaris, av. body mass 436 kg); and 2 wolves (Canis lupus,av. body mass 23-1 kg).

Methods

Rates of oxygen consumption and carbon dioxide production were measuredsimultaneously using an open-circuit system. The system has been described anddiagrammed schematically in Seeherman et al. (1981). The mongooses, genet cats,tree shrews, bush babies, flying squirrel and domestic cats ran in plexiglass (perspex)boxes that slid on the surface of the tread (analogous to a mask enclosing the entireanimal). The other animals wore lightweight masks for measurements of gas exchange.Air was metered through the boxes or masks at rates between o-io and i-oo 1 s"1 (STP)for the small animals and 1 and 40 1 s - 1 (STP) for the larger animals. Xr

Ot was calculatedusing eq. 7,:

V°> 0-9581

(modified from Tucker (1968)), where J^t is the oxygen consumption in 1 s-1, jagkis the air flow rate through the mask or box in 1 s~x, Fj is the mole fraction of oxygenentering the box or mask and FE is the mole fraction leaving the box or mask, and0-9581 is a constant assuming the R value is o-8, Fj is 0-2094 and FMtO is zero. R values(^x>i/^ot) were measured in a number of experiments. They fell between 07 and0-9 over the speed ranges for which data are reported.

Flow meters were calibrated daily by 'replacing the animal' in the box or maskwith a tube into which N4 was metered with a precision flowmeter at a known rate,^Nr ^ « w a s s e ' e c t e d s o that ^ Ssve a change in Oa concentration that was similar tothat caused by the P^ of the animal. The flow leaving the mask, 1 ^ ^ , was the sameduring the calibration and during the experiment. The N2 flowing into the maskdecreased the amount of room air that was being drawn into the mask. The room airhad a fractional concentration of O2 of 02094, therefore each litre of Ng displaced209-4 m^ °f Og. The fractional concentration of oxygen leaving the mask when N2 wasadded (FE) equalled:

Solving this equation for J^,aBk yields:

_ 0-2094 ?N, , ,~ c-2094-iV ^5;

The accuracy of the entire system was found to be better than ± 3 % .The face mask system gave 95% response in 1 min for a step reduction in the

oxygen content of the air from 20-94 to 19-94%. The enclosed treadmill system gave a95% time response in less than 2 min for the same step change in the oxygen contentof the air.

Systems which utilize loose-fitting face masks require large flow rates in order toensure that all expired air is collected. Increasing the flow should decrease the magni-tude of any leak, and decreasing the flow should increase the magnitude of any leak,

found no difference in the rate of oxygen consumption when the flow rate was

C. R. TAYLOR, N. C. HEGLUND AND G. M. 0 . MALOIY

(A) Artiodactyla

oi

aE

2-5

20

1-5

10

0-5

0

2-5

20

1-5

10

Suni(N. moschatus)3-50 kg

Dik-dik(M. kirkli)4-35 kg

a, o-5

African goat(C. hlrcus)200 kg

Fat-tailed sheep (••)(O. aries)2 3 0 kg

Wildebeest ( • )

(C. taurtnus)920 kg

2-5

2 0

1-5

10

0-5

0Waterbuck (• )(AT. defassa)114 kg

Eland (•)(7". oryx)213kg

Zebu cattle(B. tndicus)254 kg

0 2 4 6 8 0 2 4 6 8

Speed (m s"1)

Fig. i. For legend sec page 8.

changed by 25% and were therefore confident that we were recovering all of theexpired air.

Net rates of energy derived from anaerobic glycolysis (of the whole animal) werecalculated from rates of change in lactate concentration in the blood during the runsby assuming a P/lactate ratio of 1-5 (Seeherman et al. 1981). Blood samples wereobtained by cardiac puncture in the small animals and through catheters that had beenchronically implanted in the external jugular vein in the larger animals. The lactateconcentrations of blood samples were analysed using Boehringer Mannheim Lactate

if

o

I8

iXo

Energy consumption during locomotion

(B) Carnivore

2-5

2-0

1-5

1-0

0-5

0

Ferret.(M. ntgripes)

0-542kg

/

'- 2-5

O

I

Banded mongooseOW. mungo)115 kg

20

Domeitic cat ( • )(F. calus)3-90 kg

Dog(-)(C. famillaris)4-36 kg

Dwarf mongoose{H. parvula)

. 0-583 kg

Genet cat(G. tigrtna)I-45 kg

8 0Wolf(C. lupus)

. 231 kg

8 0 2 4 6 8

Speed ( m f )Fig. i. For legend see page 8.

Test Combinations and a Beckman u.v. Spectrophotometer (model 24). Fifty filsamples of blood were used for the analysis with small animals and | ml samples forthe larger animals.

RESULTS

Oxygen consumption as a Junction of speed

Steady-state oxygen consumption of the 20 species investigated in this studyincreased linearly with tread speed over a wide range of speeds (Fig. 1A-C). We foundit convenient to use mass-specific oxygen consumption (rate of oxygen consumption

C. R. TAYLOR, N. C. HEGLUND AND G. M. O. MALOIY

(C) Primates

2-0

1-5

10

OS

0

Tree shrew

(7"0-

7

glis)124 kg

Bushbaby(C. senegalensis)0-240 kg

2-5

20

0 8 0Stumped-tailed macaque(M speciosa)510kg

Hamadryas baboon(P. hamadryas)8-50 kg

8 0

Rodentia

2-5

2-0

1-5

10

0-5

0

Flying squirrel(G. volans)0-063 kg

Speed (m s"1)Fig. i. Maas-specific oxygen consumption (&otfMt) plotted as a function of speed for 8 speciesof artiodactyls (Fig. i A), 7 species of carnivores (Fig. 1 B), 4 species of primates and 1 species ofrodent (Fig. 1 C). VOl/Mt increased nearly linearly with speed. The contribution to energyconsumption by anaerobic glycolysis was negligible over the speed ranges reported in thisfigure. The least-squares regression of the functions relating l o,/-M& an^ speed are given foreach of these species in Table 1.

divided by body mass) for comparing animals of difFeient size because this enabled usto plot the data for the entire size range on the same co-ordinates.

The linear increase in oxygen consumption with speed makes it possible to expressthe relationship between oxygen consumption and speed for each animal by a linear,equation of the form

Vot/Mb = slope. 8peed+ Y intercept. (6)

Energy consumption during locomotion 9

In Table 1 we have included the values for the Y intercept and slope (calculated usingthe method of least squares) and the coefficient of determination for the linear re-gression (r2). Table 1 groups the animals taxonomically, and includes data from 42species taken from the literature in addition to the 20 species studied here.

Oxygen consumption accounted for the major part of the metabolic energy con-sumption over the range of speeds used in this study. At the maximum speeds reportedin Table 1, R values were less than i-o and the rate of accumulation of lactate duringthe run accounted for less than 1 % of the energy available from the oxygen con-sumption.

Energetic cost of locomotion as a function of body size

There are two components to the energetic cost of locomotion (measured asP0JMb): an extrapolated zero speed cost (the Y intercept) and an incremental cost(the slope) (see equation 6). Both are constant for an individual animal because therelationship between energy consumption and speed is linear. However, both changewith body size. Fig. i(A-C) are organized in terms of increasing body mass forprimates, carnivores, and artiodactyls. It is obvious from looking at these graphs thatboth the Y intercept and the slope decrease with increasing body size. This decreaseis very general, being found among all the taxonomic groups of mammals and birds(Table 1).

Fig. 2 plots the Y intercept (top) and the slope (bottom) of the equations relatingVvJMb and speed against body mass on logarithmic co-ordinates. The solid pointsrepresent new data and the open points previously published data. Both visualcomparison of the open and closed points, and linear regression analysis show there isno significant difference between the new data presented in this paper and the datain the literature. However, the new data reduces the 95 % confidence intervals for theconstants and the scaling factors. Therefore, we will limit our discussion of theallometric equations to those for the combined data.

The allometric equation for the Y intercept for all birds and mammals (except lion,red kangaroo and waddlers) was found to be

Y intercept = 0-300 Mb-°zm (7)

where Y intercept has the units ml 0 , s"1 kg-1 and Mb is in kg. The 95 % confidenceintervals for both the constant and the scaling factor were small (0-268-0-335 for theconstant and —0-261 to —0-346 for the scaling factor).

The allometric equation for the slope for all birds and mammals combined (exceptlion, red kangaroo, and waddlers) was found to be

slope = 0-533 Mb~<>™ (8)

where the slope has the units ml Oj m- 1 kg-1 and Mb is in kg. The 95 % confidenceintervals for both the constant and the scaling factor were small (0-502-0-566 for theconstant and —0-293 to —0-339 ^or the scaling factor).

The lion, red kangaroo and the waddlers (ducks, geese and penguins) were notincluded in our allometric equations because either their energy consumption did notincrease linearly with speed over a wide range of speeds (lion and big red kangaroo :£hassin et al. 1976; Dawson & Taylor, 1973) or there was a large additional component*o the energetics that was unique (waddlers: Pinshow, Fedak & Schmidt-Nielsen,

Tab

le I

. E

wge

tic

cost

of

loco

mot

ion f

or mammals a

nd b

irh

D

ata

from

th

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are

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bine

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ith

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dat

a fo

r zo

spe

cies

rep

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d in

th

is papa t

o c

alcu

late

a n

ew a

llom

etri

c eq

uati

on o

f th

e fo

rm

VoS

/Mb =

Y in

terc

ept+

slop

e.v,

, (w

here

Vo,

is

rat

e of

oxy

gen

cons

umpt

ion

in m

l Oa

s-',

Mb

is b

od

y m

ass

in k

g, a

nd

v,

is s

pee

d i

n m

s-I

).

Th

e p

erce

ntag

e di

ffer

ence

(% d

iff)

bet

wee

n ob

serv

ed r

ates

of

oxyg

en c

onsu

mpt

ion

and

the

rate

cal

cula

ted

usin

g th

is n

ew e

qu

atio

n (

equa

tion

g

in te

xt)

are

give

n fo

r a

spee

d at

the

mid

dle

of t

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. v,

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1978

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(197

5)

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o sa

pien

s (H

um

an)

0.87

-2

7.3

New

dat

a

0.89

25

.3

New

dat

a

0.71

- 24

.9

Par

sons

& T

aylo

r (1

977)

0.

85

2.04

P

arso

ns &

Tay

lor

(197

7)

0.81

10

.6

Tay

lor

& R

ownt

ree

(197

3)

0.79

10

.3

Par

sons

& T

aylo

r (1

977)

0.97

8.

03

New

dat

a

0'79

14

.5

New

dat

a

0.59

- 10

.9

Mah

oney

(19

80)

0.92

35

.6

Tay

lor &

Row

ntre

e (I

973

)

-

43.4

M

arga

ria

et a

l. (1

963)

CL

AS

S

OR

DW

F

amil

y G

enus

spec

ies

(Com

mon

nam

e)

For

equat

ion :

V~

,/M

~

= Y

inte

rcep

t+ s

lope

.v,

I 3

Mb

Y in

terc

ept,

S

lope

, r a

D

iff.

(k

g)

ml O

ds

kg

ml O

h

kg

(%I

Ref

eren

ce

ED

EN

TA

TA

D

asyp

odid

ae

Dos

ysus

mve

mci

nctu

s (A

rmad

illo

)

RO

DE

NT

IA

Sci

uri

dae

G

lauc

omys

vola

ns

(Fly

ing s

quir

rel)

T

amia

sciu

rus h

udto

nicu

s (R

ed s

quir

rel)

T

amia

s st

riat

us

(Chip

munk)

0.97

-6

.69

New

dat

a

0.48

20

.5

Wunder

& M

orr

ison (

1974

)

0.93

-

-22.

3 S

eeher

man

et a

l. (1

981)

3.

60

Wunder

(19

70)

0.91

- I 5

.3

Fed

ak &

See

her

man

(I 97

9)

-

-23-5

T

aylo

r et

al.

(197

0)

-

34.0

Y

ouse

f et

al.

(197

3)

Sper

mop

hilu

s tr

idec

emlin

eatu

s (I

3-li

ned

grou

nd s

quir

rel)

Sp

enno

phil

us t

eret

icau

dus

(Rou

nd-t

aile

d gro

und s

quir

rel

Am

mos

perm

ophi

lus

harr

isii

(A

ntel

ope

gro

und s

quir

rel)

H

eter

om

yid

ae

Dip

odom

ys m

erri

ami

(Mer

riam

's k

anga

roo

rat)

- 16

.6

Tay

lor

et a

l. (1

970)

0.

50

- 14

.3

Thom

pso

n e

t al.

(198

0)

-

81.4

Y

ouse

f et

al.

(I 97

0)

-

- 10

.3

Tay

lor

et a

l. (

1970

)

0.85

- 8.

83

Thom

pso

n e

t a1

(198

0)

Dip

odom

ys s

pect

abili

s (K

anga

roo

rat)

D

ipod

omys

des

erti

(Des

ert k

anga

roo

rat)

P

edet

idae

P

edet

es c

apen

sis

(Spri

ng h

are)

C

aice

tida

e B

aiom

ys t

aylo

ri'

(PY

FY

mou

se)

Muri

dae

M

us m

uscu

lus

(Whit

e m

ouse

)

0.67

26-9

T

hom

pso

n e

t al.

(198

0)

0.97

- 20

.0

See

her

man

et a

l. (1

981)

-

10.2

T

aylo

r et

al.

(19

70)

0.81

- 2

.q

Tay

lor

et a

l. (

1972

) 0.

66

12.5

O

ron e

t 01.

(198

1)

&UlU

MN

*

(Whi

te r

at)

I -0

9 -

Tay

lor

et a

l. (1

970)

0.

97

egg

::J

See

herm

an c

t al.

(198

1)

Not

omys

ale

xis

(Aus

tral

ian

hopp

ing

mou

se)

Not

omys

cer

oin

w

(Faw

n ho

ppin

g m

ouse

)

I '9

6 -

7.13

B

audi

nett

e et

al.

(197

6 6

)

0.69

0.

95

- 25.

4 D

awso

n (1

976)

CA

RN

IVO

RA

C

anid

ae

Can

is fa

mili

aris

(D

omes

tic

dog)

0'

34

-

- 12.

5 T

aylo

r et

al.

(197

0)

0.19

0.

99

-33.

2 N

ew d

ata

0.17

-

- 2-8

7 T

aylo

r et

al.

(I 9

70)

0.22

0.

95

2.77

S

eehe

rman

, H. J

. (p

ers.

com

m.)

0.1

0

-

-2.9

9 C

erre

tell

i et a

l. (1

964)

0.33

0.

98

22.8

T

aylo

r et

al.

(197

1 b)

0'23

0.

80

15-9

N

ew d

ata

Lyc

aon

pict

us

(Afr

ican

hun

ting

dog

) C

anis

lupu

s (W

olf)

M

uste

lida

e M

uste

lo n

igri

pes

(Fer

ret)

M

arte

s pen

nunt

i (F

ishe

r)

Viv

erri

dae

Hel

ogal

e pa

rvul

a (D

war

f m

ongo

ose)

M

ungo

s m

ungo

(B

ande

d m

ongo

ose)

G

enet

to ti

grin

a (G

enet

cat

) F

elid

ae

Fel

is c

atus

(D

omes

tic

cat)

L

eo l

eo

(Lio

n),

0.52

0.

75

7.85

N

ew d

ata

0.40

0.

96

6.01

P

owel

l, R

. (p

en.

co

w.)

0.

3 I

0.92

10

.8

Pow

ell, R. (p

ers.

com

m.)

0.67

0.

80

4.28

N

ew d

ata

0.42

0.

89

-4.5

1 N

ew d

ata

0.64

0.

86

35-9

N

ew d

ata

0.40

0-

88

-22.

6 N

ew d

ata

0.30

0.

92

54.4

S

eeh

enn

an e

t al.

(198

1)

0.36

0.

96

69.0

C

hass

in e

t al.

(197

6)

Aci

nuny

x ju

batu

s (C

heet

ah)

0.14

0.

93

2.67

T

aylo

r et

al.

(197

4)

CL

AS

S

OR

DE

R

Fam

ily

Gen

us s

peci

es

(Com

mon

nam

e)

Fo

r eq

uati

on :

vo'o

,/~

b =

Y-i

nter

cept

+ slo

pe. u

, 7

, M

b

Y i

nter

cept

, S

lope

, r a

D

iff.

(k

g)

ml

O,/s

kg

m

l Oh

kg

(%

)

PE

RI~

~OD

AC

TY

LA

E

quid

ae

Equ

us c

abal

lus

(Hor

se)

107

0.03

9 0.

15

0.96

15

.3

Fed

ak &

See

herm

an (

1979

)

AR

TIO

DA

CT

YL

A

Sui

dae

Sus

scro

fa

(Min

iatu

re p

ig)

Bov

idae

N

esot

ragu

s m

osch

atus

(S

uni)

M

adoq

ua k

irki

i (D

ik-d

ik)

Gaz

ella

gaz

ella

(D

eser

t ga

zell

e)

Con

nodm

etes

tour

inus

(W

ilde

bees

t)

Ko

h de

fass

a (W

ater

buck

) T

auro

trag

us o

ryx

(Ela

nd)

Cap

ra h

ircu

s (A

fric

an d

omes

tic

goat

) (U

S. d

omes

tic

goat

)

32.3

S

eeh

erm

an e

t al.

(198

1)

26.8

N

ew d

ata

-9.5

8 N

ew d

ata

.- 12.0

T

aylo

r et

al.

(197

4)

-24.

6 N

ew d

ata

2.37

N

ew d

ata

- 9.1

2

New

dat

a

19.6

N

ew d

ata

- 7.

25

Tay

lor

et a

l. (

I 974

)

8.34

N

ew d

ata

- 7.

58

New

dat

a

Ovi

s ar

ies

(Fat

-tai

led

shee

p)

Bos

indi

cus

(Zeb

u ca

ttle

)

AV

ES

ST

RUT

HI O

N IF

OR

ME^

S

tmth

ion

idae

St

ruth

io

(Ost

rich

) 0.1

I

0.93

- 5.

18

Fed

ak &

See

herm

an (

1979

)

0.34

-

51.8

T

aylo

r et

al.

(197

1 a)

RH

EIF

OR

MP

~ R

heid

ae

Rhe

a am

eric

ona

(Rhe

a)

ANSB

RIm

RM

E)

Ana

tida

e A

nser

am

er

(Gre

ylag

goo

se).

TINAMIFORME

Tin

amid

ae

Not

hopr

octo

pen

tland

i (T

inam

ou)

SPHWI~CIPORM~~

Sph

enio

cida

e A

pten

odyt

es fo

tste

ri

20.8

0.

13

(Em

pero

r pe

ngui

n)+

P

ygos

celis

a&

liae

3.89

0.

26

(Ade

lie

peng

uin)

. E

udyp

tula

alb

osi

g~

ta

1.15

0.

34

(Whi

te-f

3ipp

ered

pen

guin

)*

CALLIFORME

Pha

sian

idae

E

xcal

fact

oria

chi

nens

is

(Pai

nted

qua

il)

Col

inus

virg

inia

mu

(Bob

whi

te q

uail

) A

lect

oris

grn

eca

(Chu

kar

part

ridg

e)

Num

idid

ae

Num

ida

mel

eagn

gns

(Gui

nea

fow

l)

Mel

eagr

idid

ae

Mel

eagr

is g

allo

pavo

(T

urke

y)

CHARADRIIFORME)

Cha

radi

idae

C

hara

driu

s wih

ia

(Wil

son'

s pl

over

)

CU~~LIPORME~

Cuc

ulli

dae

Geo

cocc

yx ca

lifm

ian

us

(Roa

d ru

nn

er)

46.8

F

edak

et a

l. (1

974)

1'20

-

- 7.9

8 F

edak

et

al. (

1974

)

0.43

0.

66

52.3

P

insh

ow e

t al.

(197

7)

0.76

0.

88

77.4

P

insh

ow e

t al.

(197

7)

1.1

1

0.90

61

.3

Pin

show

et a

l. (1

977)

1'20

-

- 18

.5

Fed

ak e

t al.

(197

4)

0.90

-

-I 1.

6 F

edak

et

al. (

1974

)

0.69

-

6.25

F

edak

et a

l. (

I 974

)

0.47

7-

18

Fed

ak e

t al.

(197

4)

0.41

-

12.7

F

edak

et a

l. (1

974)

0.01

8 0.

67

1.85

-

- 23

.7

Fed

ak &

See

herm

an (1

979)

0.29

0.

61

0.59

0.

73

4.06

F

edak

& S

eehe

rman

(197

9)

+ D

ata

excl

uded

fro

m a

llom

etri

c eq

uati

ons,

see

tex

t.

16 C. R. TAYLOR, N. C. HEGLUND AND G. M. 0 . MALOIY

1000

0001 0-01 01 1 10 100 1000

Body mass (kg)

1000

0-001 0-01 01 1Body mass (kg)

10 1000

W * » J m**«*iv \ n O /

Fig. 2. The two components of energetic cost of locomotion are plotted as a function of bodymass on logarithmic co-ordinates: Y intercept (top) and slopes (bottom) of the relationship:

V0JMt = Y intercept + slope, u,

(where ^o,/A^» w the mass-specific oxygen consumption of an animal running at speed v,).The Y intercept is proportional to the —0-303 power of body mass and the slope proportionalto —0-316 power. See equations (7) and (8) of the text for the allometric equations repre-senting Y intercept and slope calculated by linear regression analysis from the data presentedhere. Open symbols represent data from the literature; closed symbols represent new data fromthis paper; circles represent data from wild species; and triangles represent laboratory/domestic species.

Energy consumption during locomotion 17

DISCUSSION

Oxygen consumption as a function of speed

The nearly linear increase in oxygen consumption as a function of speed observedin this study is in agreement with the findings of previous studies (Taylor et al. 1970;Taylor, 1977; Taylor, 1980). One of the reasons for initiating this series of studies wasto find out whether the linear increase could be explained by the mechanical energychanges that occur within an animal. We will therefore defer the discussion of thelinear increase to the subsequent papers where both metabolic and mechanicalenergies can be compared.

Energetics of locomotion as a function of size

The allometric functions for the Y intercepts (equation 7) and the slope (equation 8)can be combined into a single equation (see equation 6) for predicting $o,/Mb fromspeed and body mass:

V0JMb = 0-533 Mb-*™.v0 + 0-300 M6-°-303 (9)

where V0JMb has the units ml Ot s"1 kg"1, Mb is in kg, and va is speed in m s ~x.This equation is very general. Table 2 compares the constants and scaling factors

for both terms of the general equation for birds and mammals with various groupingsof species: all mammals, all birds, all wild animals, all domestic animals, Marsupials,Insectivores, Artiodactyla, Carnivora, Rodentia, and Primates. None of the groupsdiffered from the general equation at the 95 % level of confidence. The major differenceis wider confidence intervals of the smaller groups because both the number of speciesand range in body mass are smaller.

How well does the general equation estimate the oxygen consumption observed forindividual animals ? For each of the species included in the regression analysis, wepresent the percentage deviation between the values calculated from the generalequation and the observed value for the middle of the speed range for which oxygenconsumption data were available. At the mid-speed, 90 % of the calculations for speciesincluded in the regression fall within 25 % of the observed value. This agreement isimpressive when one considers that mass-specific oxygen consumption changes bymore than 1400% over this size range of animals.

It is convenient to express eq. 9 in terms of mass-specific rates of energy consump-tion (Emeiah/Mb) for comparison with rates of mechanical energy changes in thesubsequent papers of this series. This conversion can be made using the energeticequivalent of 1 ml O, equals 20-1 J, because the contribution of anaerobic glycolysiswas shown to be negligible:

= 107 M6-°-»".w,, + 6-o3 M6-o-"O3 ( IO)

where £metab/M6 has the units watts kg"1.

Energy consumption per step at equivalent speeds

A. V. Hill's dimensional arguments outlined in the introduction of this paperPredicted that, in mass-specific terms, muscles of small animals would be working^ consuming energy at much highei rates than those of large animals.

C. R. TAYLOR, N. C. HEGLUND AND G. M. 0. MALOIY

h hh hhhhhhhh $5 xmi%f:; 0 0 0 b 0 0 0 0 0 0 b I 1 1 1 1 1 1 1 1 1 1

I I I I I I I I & L LL V V V V W Y V U

u - 2 z'2' E::R::$% * 2 g * * " " f " * N 0 0 0 0 0 0 0 0 0 I I 1 I I I I I I I I

; 4 6 dI;, I ; ,w-Gdn-6 Cg \O 3 ; N r n N N * l - \ O I N " ? ? ? ? a B 0 0 0 0 0 0 0 0 0 0

u I I I I I I I I I I I u\D m o m m b b 3 Z % w m w m r o w m v r 2 2; N * N ! " ? N ? ? 0 0 0 0 0 0 0 0

I I I I I I I I I I I

Energy consumption during locomotion

Table 3. Energy consumed during a stride by each gram of body mass for quadrupeds ofdifferent size moving at a 'physiologically equivalent speed' {trot-gallop transition speed)

Speed and stride frequency at the trot-gallop transition are calculated from the allometric equationsgiven by Heglund, Taylor & McMahon (1974), and the rate of energy consumption at this speed wascalculated using equation 10 in the text.

Body mass(kg)

o-oii-o

100

Speed at trot-gallop transition

(m s-1)

0-511-53461

Stride frequency at Metab. energytrot-gallop transition consumed per kg per stride

(strides s"1) (J stride"1 kg"1)

8-54448

559500

5 5 3

The findings of this paper are in general agreement with Hill's predictions for howrates of energy consumption should change with size. Hill's analysis, however, waslimited to top speed, which he used as an equivalent speed for comparing animals ofdifferent body size. Measurements of energy consumption at top speed are not avail-able, but comparisons can be made for quadrupeds at the speed where they changegaits from a trot to a gallop. Heglund, Taylor & McMahon (1974) have proposed thatthis is a ' physiologically similar speed' for quadrupeds of different size. Both the speedat which quadrupeds change from a trot to a gallop, and the stride frequency at thisspeed, change in a regular manner with body mass and can be estimated using allo-metric equations given by Heglund et al. (1974). Table 3 gives the trot-galloptransition speed and the stride frequency at this speed calculated for a 10 g, 1 kg, and100 kg animal using these equations. The amount of energy consumed at this speedwas calculated using eq. 10, and cost per stride was obtained by dividing the rate ofenergy consumption by stride frequency. This analysis reveals that the amount ofmetabolic energy consumed per stride by each gram of muscle at this speed remainsalmost constant (5 J stride"1 kg"1) over a change in Mb of 4 orders of magnitude.

The finding that energy cost per stride by each gram of muscle at an equivalentspeed is almost the same for large and small animals seems to indicate that HuTs logicis correct, i.e. the work performed per stride and the efficiency with which musclesperform this work are constant. We will return to this matter in the fourth and finalpaper of this series where it is possible to compare these assumptions with measure-ments of the rate at which mechanical work is performed by an animal's muscles as itruns at a constant average speed.

The essential part of this work depended on a field study on wild animals in Kenya.It would not have been possible without the support of various Kenyan authorities.We thank particularly the Kenyan Minister of Wildlife and Tourism for providingpermits and for helping to obtain animals; Dr Walter Masiga, Director, East AfricanVeterinary Research Organization, Muguga, Kenya, for making the excellent largeanimal facilities of his organization available to us for these studies. This study wouldnot have been feasible without the most generous support of the School of VeterinaryMedicine at the University of Nairobi; we thank the authorities of the University ofNairobi for all the encouragement and material help received during planning andIxecution of the study.

20 C. R. TAYLOR, N. C. HEGLUND AND G. M. 0 . MALOIY

We thank Garth Ballantyne, Russ Baudinette, Daphne Cooke, Vaughn Langman,Timothy Lay, Victoria Rowntree, Emmett Schmidt, Howard Seeherman and TomShatten who all helped acquire the new data reported here.

We also gratefully acknowledge the excellent technical assistance received fromMs Gayle Kaufman and Ms Margaret McCutchin.

We finally acknowledge the financial support received for this study through thefollowing grants: U.S. National Science Foundation (PCM75-22684 & PCM78-23319to C. R. Taylor); National Institutes of Health (AM 18140 & AM 18123 to C. R.Taylor); National Geographic Society grant to C. R. Taylor; Guggenheim Foundationgrant to C. R. Taylor; Nuffield Foundation grant to G. M. O. Maloiy; WellcomeTrust grant to G. M. O. Maloiy.

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