Animal Locomotion

Animal Locomotion

Second Edition

Andrew A. Biewener
Charles P. Lyman Professor of Biology
Director, Concord Field Station, Harvard University

Sheila N. Patek
Associate Professor of Biology, Duke University

1
1
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Table of Contents

Preface ix
List of Variables xi

1 Physical and Biological Properties and Principles: Related to Animal Locomotion 1

1.1 Environmental media 1

1.2 Physics and energetics of movement 2
1.3 Biomechanics of locomotor support 3
1.4 Scaling: the importance of size 7
1.5 Dimensions and units 9
1.6 Summary 11

2 Muscles and Skeletons: The Building Blocks of Animal Movement 12

2.1 Muscles 12
2.2 Molecular organization: mechanism of force generation and shortening 12
2.3 Levels of force generation and the isometric force-length relationship 14
2.4 Power, efficiency and the isotonic force-velocity relationship 16
2.5 “Work loops”: time varying force-length behavior of muscles 18
2.6 Excitation–contraction coupling and motor units 20
2.7 Muscle fiber types 22
2.8 Fiber architecture and its effects on muscle volume and energy use 25
2.9 Skeletons 27
2.10 The connection between muscle and skeleton 27
2.11 Vertebrate endoskeletons 28
2.12 Invertebrate exoskeletons 30
2.13 Hydrostatic skeletons 30
2.14 Skeletons as jointed lever systems 31
2.15 Summary 33

3 Energetics of Locomotion 34

3.1 Linking cellular metabolism to locomotor energetics 34

3.2 Sources and time course of energy usage during exercise 35
3.3 Endurance and fatigue 40
3.4 Energy costs across terrestrial locomotor speeds 40
3.5 Energy cost relative to body size 47
3.6 Energy cost of incline running 52
vi TA B L E O F C O N T E N T S

3.7 Cost of swimming 53

3.8 Cost of flight 54
3.9 Locomotion costs compared 56
3.10 Intermittent exercise 58
3.11 Other adaptations for increased aerobic capacity 59
3.12 Summary 59

4 Movement on Land 61

4.1 Biological wheels: why so few? 61

4.2 Limbs as propulsors: support and swing phases 62
4.3 Limb mechanical advantage and joint torques: interaction
of limb posture and ground reaction force 64
4.4 Locomotor gaits 67
4.5 Stride frequency and stride length relative to speed and size 69
4.6 Spring-mass properties of running 71
4.7 Maneuverability versus stability 73
4.8 Froude number and dynamic similarity 76
4.9 Inferring gait and speed of fossil animals 77
4.10 Mechanical work: potential and kinetic energy changes
during terrestrial locomotion 77
4.11 Collisional mechanics of legged locomotion 80
4.12 Legged robotics 82
4.13 Limbless locomotion 82
4.14 Muscle work versus force economy 84
4.15 Tendon springs and muscle dampers 85
4.16 Summary 88

5 Movement in Water 90

5.1 Thrust and drag 90

5.2 Inertia, viscosity and Reynolds number 91
5.3 Steady flow: drag and streamlines 93
5.4 Swimming fish, mammals and cephalopods: movement at high Re 95
5.5 Jet-based fluid propulsion 103
5.6 Movement at low Re: the reversibility of flow 104
5.7 Movement at intermediate Re: switching between paddles and rakes 108
5.8 Air-water interface: surface swimming, striding and sailing 108
5.9 Biological robotics in and on water 112
5.10 Summary 112

6 Movement in Air 114

6.1 Flight forces: lift, drag and thrust 115

6.2 Power requirements for steady flight 119
6.3 Gliding flight 121
6.4 Flapping flight 125
6.5 Flight motors and wing anatomy 132
6.6 Flight maneuvering and stability 139
 TA B L E O F C O N T E N T S vii

6.7 Unsteady aerodynamic mechanisms 143

6.8 Summary 146

7 Jumping, Climbing and Suspensory Locomotion 147

7.1 Jumping 147

7.2 Jump take-offs and trajectories 148
7.3 Scaling of jumps 149
7.4 Power enhancements to jump performance 152
7.5 Interactions with the substrate during jumping 156
7.6 Climbing and attachment mechanisms 158
7.7 Suspensory locomotion 162
7.8 Inspiration for synthetic systems 163
7.9 Summary 163

8 Neuromuscular Control of Movement 165

8.1 Sensory elements 165

8.2 Sensorimotor integration via local reflex pathways 169
8.3 Muscle recruitment in relation to functional demand:
force, speed and endurance 174
8.4 Reciprocal inhibition: a basic feature of sensorimotor neural circuits 182
8.5 Distributed control: the role of central pattern generators 183
8.6 Case examples of motor control 185
8.7 Summary 187

9 Evolution of Locomotion 190

9.1 Large-scale trends in animal locomotion 190

9.2 From genes to locomotion 197
9.3 Comparative methods and animal locomotion 198
9.4 The relevance of evolution to robotics and bio-inspired design 200
9.5 Summary 202

References205
Index219
 Preface

The goal of this book is to provide a synthesis of the ment, we can understand the common principles that
physical, physiological, evolutionary, and biomech- underlie each mode of locomotion. A second is that
anical principles that underlie animal locomotion. size matters. One of the most amazing aspects of biol-
An understanding and full appreciation of animal ogy is the enormous spatial and temporal scale over
locomotion requires the integration of these prin- which organisms and biological processes operate.
ciples. Throughout this book, we present, as broadly Within each mode of locomotion, animals have evolved
as possible and within a reasonable amount of space, designs and mechanisms that effectively contend with
a discussion of animal locomotion that is accessible the physical properties and forces imposed on them
to undergraduates, yet also of value to more advanced by their environment. Understanding the con­straints
graduate students and professionals. Toward this of scale that underlie locomotor mechanisms is
end, we provide the necessary introductory founda- essential to appreciating how these mechanisms have
tion that will allow a more in-depth understanding evolved and how they operate. A third theme is the
of the physical biology and physiology of animal importance of taking an integrative and compara-
movement. In so doing, we hope that this book will tive evolutionary approach in the study of biology.
illuminate the fundamentals and breadth of these Organisms share much in common. Much of their
systems, while inspiring our readers to look more molecular and cellular machinery is the same. They
deeply into the scientific literature and investigate also must navigate similar physical properties of their
new features of animal movement. environment. Consequently, an integrative approach
Animal locomotion is so rich and diverse that it is to organismal function that spans multiple levels of
daunting to try to write an introductory book, even biological organization provides a strong under-
at an upper-level undergraduate or graduate level. standing of animal locomotion. By comparing across
The scales of locomoting animals range from micro- species, common principles of design emerge. Such
scopic to house-sized and the habitats extend from comparisons also highlight how certain organisms
the moist surface of delicate leaves to the depths of may differ and point to strategies that have evolved
the open ocean. The study of animal locomotion itself for movement in diverse environments. Finally,
extends back thousands of years as humans have per- because convergence upon common designs and
formed observational and experimental studies of the generation of new designs result from historical
animal capabilities, whether due to simple fascination processes governed by natural selection, it is also
or with the desire to emulate nature’s capabilities. This important that we ask how and why these systems
is a big, historic field offering a wealth of inspiration, have evolved.
yet the field is grounded in a set of physical rules When we decided to write the second edition of
that unites much of the diversity and allows us to this book, which was first published more than a dec-
write a concise book about the core principles of ade ago, our goal was to bring the first edition up to
animal locomotion. date, increase the diversity of animals covered in the
Several themes run through this book. The first is book, and to address the burgeoning fields of evolu-
that by comparing the modes and mechanisms by tionary analysis of locomotion and the application of
which animals have evolved the capacity for move- animal locomotor mechanisms to the development
x P R E FA C E

of novel engineering devices. Naturally, the funda- are central to the dynamic nature of complex loco-
mental rules of physics have not changed, yet the motor systems. We wrap up the book with a chapter
depth of knowledge and development of impressive on the evolution of locomotion that examines the
technical approaches to the study of these systems broad trends in the evolution of locomotion, as well
have moved quickly in particular areas. Some areas as the methods and levels of analysis for examining
covered in the first edition could be written in the locomotor diversity. It is clear that between the first
span of a few paragraphs, and now an entire chapter and second edition of this book, there has been
of new discoveries could be devoted to the topic. exceptional growth in the comparative biomechanics
Without a doubt, the biggest challenge of writing and physiology of animal locomotion.
and synthesizing this new edition was keeping the We have many people to thank for helping with
book straightforward and focused on guiding, fun- both the first and second editions of this book. We
damental principles, while trying to figure out how are grateful to our students and colleagues with
to navigate all of the fabulous discoveries that we whom we have shared the fascination and love of
simply could not fit in this short volume. As in the animal movement, physiology and biomechanics.
first edition, our foremost goal was to capture the These interactions that have come from our work
fundamentals underling the study of animal loco- and discussions are the best part of science. For
motion, even if it meant leaving out much of the their insights on the first edition of the book, we
research and history of this vibrant field. thank George Lauder, Bob Shadwick, Gary Gillis,
We have re-organized the book in multiple ways, Ty Hedrick, Jim Usherwood, Bob Full, Tom Roberts,
both in terms of the coverage of the chapters and the and Peter Weyand. Michael Dickinson and Bret
topics of the chapters. The book begins with a chap- Tobalske provided feedback on both editions. We
ter on the fundamentals of motion, and quickly thank Walter Federle for his assistance with synthe-
moves to a chapter focused on muscles, a source of sizing the field of adhesion in this second edition.
motion unique to animals, and how muscles interact We thank the students of Duke University’s “How
with animal skeletons to transmit force for move- Organisms Move” course and Brown University’s
ment and support. We next consider the energetics “Animal Locomotion” course taught by Sharon
of locomotion, focusing on how the metabolic cost Swartz for their feedback on the second edition, espe-
of terrestrial movement varies with animal size and cially Sarah Beaverson, Aakash Jain and Suzanne
speed, and compares with the cost of flying and Ou. We are grateful to Rachel Crane and Grace Farley
swimming. We then examine the principles of loco- for their editorial assistance. We thank our editors
motion through a series of chapters that explore for their assistance with the process of writing the
three major habitats - land, water, and air. The sev- first and second editions. Most of all, we are grate-
enth chapter probes a suite of locomotor modes ful to our families for their support and patience.
that transcend particular habitats and these modes This book is dedicated to Dick Taylor, Beth Brainerd,
include jumping, suspensory locomotion and adhe- Farish Jenkins, Jr. and Karel Liem, whose unbounded
sion. The eighth chapter examines the neuromuscu- enthusiasm for comparative physiology and love of
lar control of movement, providing an overview of animal locomotion are an inspiration to so many
sensory-motor pathways and motor recruitment that students and scientists.
 List of Variables

A area, m2 EMA effective mechanical advantage or lever arm

A wavelength amplitude, m ratio, dimensionless
Am muscle cross-sectional area, or ‘physiological’ ε strain, dimensionless
cross-sectional area (PCSA) of a pinnate ε0 maximum operating strain, dimensionless
muscle, m2
Af fiber cross-sectional area, m2 F force, N
AR aspect ratio, dimensionless F0 isometric muscle force, N
a acceleration, m s−2 Fadd adductor force, N
α incline slope or angle of support (o, degree) Far acceleration reaction force, N
Ffrict static frictional grip, N
b (wing) span, m and scaling exponent, Flat laterally directed force, N
dimensionless Fm force of muscle fibers, N
β duty factor, dimensionless Fr Froude number, dimensionless
BL body length, m f frequency, Hz
BM body mass, kg fnat natural frequency, Hz
BW body weight, N fs stride frequency, s−1 or Hz
Ft tendon force, N
Ca added mass coefficient, dimensionless Ftan tangent force, N
Cd coefficient of drag, dimensionless
Cl lift coefficient, dimensionless G ground reaction force, N
CM center of mass, kg GH horizontal fore-aft ground reaction force, N
Cnet net cost of transport, J m−1 GML medio-lateral ground reaction force, N
Ctot total cost of transport, J m−1 g acceleration due to gravity, m s−2
c cost coefficient, J N−1 GV vertical ground reaction force, N
c' (wing) chord, m Γ circulation (line integral of velocity flow), m2 s−1
cs slipping coefficient, dimensionless
h height, m
D diameter, m η coefficient of friction, dimensionless
D drag, N η’ wave efficiency, dimensionless
d local drag, N
dL limb displacement, m I' moment of inertia, kg m2
ΔL muscle shortening, m
ds muscle shortening, m k spring stiffness, N m−1
d(θ) change in joint angle, rad or deg KE kinetic energy, J
kleg leg spring stiffness, N m−1
E Young’s modulus or elastic modulus, Pa
E* total energy, J l or L length, m
Ėmetab metabolic energy rate, J s−1 L lift force, N
Eff energetic efficiency, % (dimensionless) Lc step length, m
xii L I S T O F VA R I A B L E S

LCM distance that center of mass is accelerated, m T thrust, N

lf muscle fiber length, m T' torque, N m
Ll limb length traveled during landing, m Ts stride duration or time, s
Lpect lift force produced by pectoral fins, N t time, s
Ls sarcomere length or stride length, m tair time airborne during a jump, s
Lt limb length traveled during takeoff, m tc time of limb ground contact or time required
Ltot maximum jump length, m to take off, s
λ wavelength (body undulation), m θ various angles (joint, limb, heading, glide,
grip), rad or deg
m, M mass, kg
μ viscosity, Pa s U* amount of strain energy absorbed per unit
volume of material, J m−3
P power, W or J s−1
P* mass-specific power output, W kg−1 V̇O2max rate of oxygen consumption, ml O2 s−1
PE potential energy, J V volume of accelerated fluid, m3
PPE potential energy power, W or J s−1 v velocity, m s-1
ϕ collision angle, rad or deg vflap velocity of flapping wing, m s−1
vg glide velocity, m s−1
r and R moment arm, m vh horizontal velocity or component of take-off
R resultant propulsive force, N velocity, m s−1
Re Reynolds number, dimensionless vmax maximum velocity, m s−1
ρ density of fluid, kg m−3 vr resultant velocity (of a wing), m s−1
RQ respiratory quotient, dimensionless vs sinking speed (of a glider), m s−1
vt take-off velocity, m s−1
S surface area, m2 vv vertical component of take-off velocity, m s-1
S strength or maximum stress, N m−2 vw water velocity, m s−1
s position of moving object or v* muscle’s intrinsic shortening velocity,
projectile, m lengths s−1
σ force per unit area or stress, N m−2
σ0 maximum operating stress, N m−2 W work, J
σf failure stress, N m−2 Wf work of fracture, J m−2
 C H A PT ER 1

Physical and Biological Properties

and Principles
Related to Animal Locomotion

Observations of the beauty, grace and sheer athleti- and the fundamentals of loading and forces in ani-
cism of locomoting animals inspire human fascination mal mechanics. We offer a quick review of scaling
with movement. Which aspects of flight do darting analyses as well as the key dimensions and units
hummingbirds and bumblebees share in common? used in this book.
How do they differ from a soaring petrel? Which
principles of design are shared by a racing antelope,
1.1 Environmental media
a scurrying lizard or a running cockroach, and in
what ways do they differ? The grand scale of bio- Land, air and water constitute the physical world of
logical sizes and evolutionary diversity yields an organisms. To a large extent, the properties of these
impressive range of locomotor mechanisms. Yet, media dictate the locomotor mechanisms that ani-
underlying this amazing diversity are fundamen- mals have evolved. For animals that move on land
tal principles of biological organization that can and fly, the properties of the air and gravity dominate
explain most of these locomotor systems. Studies of their physical world. For most aquatic animals,
animal locomotion depend on an understanding of however, gravity is of little concern. In addition, air
the physical principles that govern how animals and water play an important role as respiratory
move and properties of the media through which media and therefore affect locomotor design in
they move. These studies, in turn, explain why cer- terms of how energy is supplied for powering
tain biological devices, such as a wing or a fin, share and sustaining movement. The capacity to move
features that have evolved for movement within between physical environments is also important to
their particular fluid environments. many animals. This is the case for flying animals
This book is about how animals move. It addresses that must also be capable of movement on land or
basic physical principles and properties of the through water, as well as for terrestrial animals that
media in which animals move, seeking to explain live near the shore where locomotion in air and
the mechanical design and locomotor function of water are both required.
animals within these media. It also attempts to
capture the amazing diversity of animal design
1.1.1 Physical properties of media
and movement. Much of this diversity arises from
the enormous range of sizes—from microscopic A few, key physical properties of air and water
swimmers to the largest whales (1015 orders of mag- impact nearly any animal movement and locomotor
nitude in mass)—and the breadth of environments mechanism (Table 1.1). Air and water are both ­fluids:
that animals inhabit. In this first chapter, we lay the fluid movement past the body of organisms is fun-
groundwork for the more focused subsequent damental to nearly all forms of animal locomo-
chapters. We examine the role of the environment tion—even burrowing. Recent studies of burrowing

Animal Locomotion. Second Edition. Andrew A. Biewener & Sheila N. Patek, Oxford University Press (2018).
© Andrew A. Biewener & Sheila N. Patek 2018. DOI: 10.1093/oso/9780198743156.001.0001
2 A N I M A L L O C O M OT I O N

Table 1.1 The physical properties of air and water that influence the mechanisms of locomotion.

Physical property Air Water Proportional difference

Density (g/cm3) @ 25°C 0.0012 1.000 830

1.02 (seawater)
Dynamic viscosity 18 x 10−6 1 x 10−3 55
(Pa s = Ns/m) @ 20oC
Oxygen content (ml O2/L) 209 7 30
Heat capacity (cal/L°C) 0.31 1000 3200

in granular media, such as sand, demonstrate an weight, in addition to aerodynamic thrust to over-
intriguing mix of fluid and solid properties and come drag associated with moving in a forward dir-
associated locomotor strategies. Of all the fluid ection. Aquatic animals, on the other hand, need
properties, however, density varies the most: water not worry much about supporting their weight,
density exceeds that of air by more than 800-fold. because the density of their bodies nearly matches
The difference in viscosity, though smaller in mag- that of water. Most aquatic animals therefore are
nitude, also has an important influence on how neutrally, or slightly negatively, buoyant in water.
fluid moves past an organism in motion. The higher density and viscosity of water, however,
Even though aerial flight and aquatic locomo- means that drag poses a formidable obstacle to their
tion depend on the same fluid dynamic principles, movement. Consequently, drag reduction is crit-
the difference in density of these two media has ical, particularly at moderate to large size.
significant implications for respiratory design and Differences in the oxygen content and heat capacity
the capacity for flight, swimming and terrestrial of the two media also affect the activity levels and
locomotion of land animals. Oxygen content and locomotor strategies of animals. The greater oxygen
the heat capacity of air versus water indirectly content of air generally affords higher levels and
influence locomotor systems by affecting their broader strategies of activity for flying and running
thermal and respiratory function. As we will see, animals versus swimming animals. The higher heat
the locomotor capacity and strategy of animals capacity of water further constrains the locomotor
depends on the delivery of oxygen to their tissues, capacities of swimming animals by making it more
especially the muscles, in order to generate meta- difficult for them to maintain a warmer body
bolic energy in the form of adenosine triphosphate ­temperature than their surrounding environment.
(ATP). Temperature and the availability of oxygen However, there are many exceptions to these g ­ eneral
supply from the environment are critical to loco- rules. Aquatic and cold-acclimated animals have
motor design. evolved, and can adaptively express, metabolic
en­zymes that work well at low temperatures, enab­
ling them to compensate for a colder environment.
1.1.2 Impact of physical media on locomotor In addition, differing metabolic pathways for energy
function production afford animals varied locomotor strat-
egies for daily activity that enable equally success-
Because of its much lower density and viscosity, ful performance compared with that achieved by
air imposes proportionately smaller resistive (drag) warmer animals.
forces for flying and terrestrial animals than for
aquatic animals. The main problem for terrestrial
­animals therefore lies in overcoming mass-related
1.2 Physics and energetics of movement
gravi­tational forces as they move. The low density
of air also means that flying animals must generate Animals move by exerting forces (F, measured in S.I.1
sufficient aerodynamic force (lift) to support their units of Newtons, N) on their external environment,
 P H YS I C A L A N D B I O L O G I C A L P R O P E RT I E S A N D P R I N C I P L E S 3

whether it is a solid substrate, air, or water. By within the mitochondria by electron transport and
Newton’s First Law: oxidative phosphorylation).
F = ma (1.1)
1.3 Biomechanics of locomotor support
where m is the mass (in kilograms, kg) of the body The forces required for locomotion are typically gen-
moved and a is its acceleration (m/sec2). Therefore, erated by the motor proteins within muscles, which
an animal’s weight is a force produced by the accel- are transmitted to the external environment by means
eration of Earth’s gravity acting on its mass (m g). of a skeleton. These forces cause deformations in the
To move its body, an animal must do work (W): structures that transmit them. The ability of a struc-
W = Fd (1.2) ture to resist deformation when subjected to a given
force is a measure of its stiffness and is the slope of a
where d is the distance (in meters, m) that the ani- structure’s force-length relationship (Fig. 1.1a). Linearly
mal’s body moves as a result of the net force acting elastic structures are defined as having a linear force-
on it, in reaction to the forces that the animal trans- length relationship, typical of a simple spring that
mits to the environment. Work (in Joules, J) repre- is stretched. Although linear elasticity is easier to
sents the mechanical energy required to move the analyze, many biological structures exhibit non-
­
animal’s body. The amount of mechanical energy linear elasticity. Because larger structures can support
required to move per unit time, larger forces, engineers commonly normalize for dif-
ferences in the size of structures by dividing the force
= =
P W /t Fd/t = Fv (1.3)
acting on a structure by the structure’s cross-sec-
represents the mechanical power (P, in Watts) of tional area (A, Fig. 1.1b). When normalized in this
locomotion, and thus can be related to the forces way, a force is defined as a stress (Greek sigma, σ):
that an animal exerts as it moves a given distance σ = F/A (1.6)
per unit time, or the velocity (v) of its movement.
The energetic efficiency (Eff) of an animal’s move- Common units of stress relevant to the musculo-
ment can be calculated by comparing the metabolic skeletal systems of animals during locomotion are
energy consumed (energy input) to the mechanical =
N/mm 2
=
( 10 6
N/m 2 1 MN/m 2 , or 1 MPa), or
work (energy output) performed over a given N/cm ( = 10 kN/m 2 , or 10 kPa). Because these
2

period of time: units of stress may be new to many readers, and also
counterintuitive, a useful example is that the weight
Eff = Energy Out / Energy In (1.4) of an apple (about 1 N, certainly an apropos ­definition
= Work/Metabolic Energy of a Newton!) balanced on the end of a toothpick (of
(1.5)
1 mm2 cross-sectional area) exerts a stress of 1 MPa.
or equivalently, the mechanical power output ver- Whereas forces act on structures, stresses can be
sus the metabolic power input (Pout / Pin ) . Typically, thought of as being transmitted through the struc-
locomotor efficiencies are determined by compar- ture. Large structures also undergo larger deform­
ing the oxygen consumption of an animal with the ations than smaller structures. Once again, in order
mechanical work performed over an integral num- to account for differences in size, deformations or
ber of strides. Because all animals must ultimately changes in length are normalized by dividing by
balance their energy needs by means of aerobic the structure’s resting (unloaded) length (Fig. 1.1b,c),
(oxygen-dependent) metabolism, measurements of and are defined as a strain (Greek epsilon, ε):
oxygen consumption are commonly used to assess
ε = ∆L / L (1.7)
the energy supply of ATP needed for sustainable
locomotor activity. Typically, a value of 20.1 kJ/liter As engineering terms, therefore, stress and strain
O2 is used. This value assumes that ATP is produced have quite distinct meanings. However, whereas strain
by means of aerobic glycolysis (the breakdown of represents the real physical deformation of a struc-
glycogen into glucose and its transformation via ture in response to being loaded, the stress acting
glycolysis and the Kreb’s cycle into ATP production within the material represents a conceptualization
4 A N I M A L L O C O M OT I O N

(a) Structural properties (b)

F F
Linear spring F
4F A A
F A
k L

Force
= L 4A
Slope ΔL ΔL
ΔL 4L
=k
F
F F
x
Deformation (ΔL) 4F 4 × ΔL

Material properties
F
(c) F Force and length change not equivalent
σ Stress and strain equivalent
Stress (F/A)

Slope
=E

Strain (ΔL/L)
ε

Figure 1.1 The mechanical properties of structures can be defined by how they deform in relation to different applied loads. (a) When a force (F)
is applied to a structure with cross-sectional area (A), it deforms a given length (∆L). In linearly elastic structures, such as this spring which is
lengthened linearly with the application of a force, the slope of force versus deformation represents the spring stiffness (k). (b) The response of a
structure to a load varies in relation to its size. Size can be measured in terms of length or cross-sectional area. Structural properties, such as
stiffness, k, in (a), do not account for size and thus vary across these examples. In contrast, material properties account for size by incorporating
relative length or cross-sectional area; these examples are equivalent in terms of stress and strain. (c) Stress and strain are normalized for
differences in size and thus reflect the material properties of a structure. The slope of stress versus strain represents the elastic modulus (E) of a
material.

of the intensity of force transmission. Finally, by ball or an elastic band) and may be used to do
considering the size-independent properties of a work. Elastic structures exist within animals that
material, stress and strain have an equivalent rela- can be used to store and recover elastic strain energy
tionship to that of force and length (Fig. 1.1c), in and thus reduce the work and metabolic cost of
which the stiffness of the material is the slope of the locomotion.
stress-strain relation, and is defined as the elastic The elastic modulus and the energy absorbed
modulus (also known as “Young’s modulus,” E): before failure defines whether a material is “rigid”
or “compliant” and “brittle” versus “tough.” Rigid
E = σ /ε (1.8)
materials deform little when loaded and have a
The force that causes a structure to break (Fig. 1.1a) high elastic modulus, whereas compliant materials
corresponds to the strength, or maximum stress undergo considerable strain for a given load and
(Fig. 1.1c) that a structure can bear before failing. have a low modulus. Tough materials absorb
This also defines the strain at failure. The area under considerable elastic strain energy before failing,
the force-length curve represents the amount of whereas brittle materials, such as glass, absorb very
energy ( 1/2 F × d , for linearly elastic elements) that little (Fig. 1.2c). Generally, tough materials are not
is absorbed by a structure when it is loaded (Fig. 1.2a). as rigid—i.e. they have a lower elastic modulus—as
Similarly, the area under the stress-strain curve rep- brittle materials. On the other hand, although brittle
resents the amount of strain energy absorbed per materials may have a high failure strength and elas-
unit volume of material ( U* = 1/2σ ε ; Fig. 1.2b). If a tic modulus, they often fail relatively easily, especially
structure is unloaded before breaking, this energy when subjected to impact loads. Consequently, the
can be recovered elastically (much like a rubber amount of energy absorbed to failure is a measure
 P H YS I C A L A N D B I O L O G I C A L P R O P E RT I E S A N D P R I N C I P L E S 5

(a) (b)

Ff σf

Stress
Force
Lf
σo U*

εo εf
Deformation Strain

(c) ‘Brittle’ ‘Rigid’

‘Tough’
U*1
U*2 U*2 >> U*1
Stress

‘Compliant’

Strain

Figure 1.2 The response of materials and structures to force and deformation yields information about stored energy, failure, and overall
behavior during loading. (a) The energy absorbed by a structure when loaded is equal to the area under its force-deformation curve (for linearly
elastic structures this is 1 / 2F × ∆1). The structure will break if force (Ff ) or deformation (Lf ) reach the threshold for failure. (b) The area under a
material’s stress-strain curve also represents the energy absorbed per unit volume (U*; hatched area represents energy absorbed to failure and gray
area represents energy absorbed at a maximum operating stress (σo) and strain (εo)). Typically, σo and εo of a material are much less than its
failure stress (σf) and failure strain (εf). The ratio of a material’s failure stress relative to its operating stress (σf /σo) is often used to define the
safety factor of a material or a structure. (c) The slopes of stress-strain curves can be used to compare the response of a material to loading. When
stress increases rapidly with a small amount of strain, the material is “brittle”. In contrast, slow accumulation of stress with increasing strain
indicates a compliant material. Tough materials store a much larger amount of energy (U*2) compared to brittle materials (U1* ).

of the material’s “toughness.” Because biological that shortens the structure along a given axis. When
structures are often subjected to dynamic loads, subjected to bending, both tensile and compressive
their ability to absorb strain energy is often the crit- stresses act within a structure (Fig. 1.3b). Compression
ical factor determining whether they break. In gen- occurs on the concave surface and tension on the
eral, most biomaterials have evolved designs that convex surface, with the greatest stress acting at the
enable them to be tough, so that they can absorb a surfaces in the plane of bending. Consequently, there
considerable amount of energy before breaking. As a is a gradient of stress (and strain) from ­maximum
result, rigid biomaterials, such as bone or insect c­ uticle, compression on one surface to maximum tension
exhibit a stress-strain relationship intermediate to on the opposite surface (Fig. 1.3c). This means that
brittle and compliant materials (Fig. 1.2c). midway through the structure’s cross-section a neu-
tral plane exists where stress and strain are zero. If a
structure is subjected to bending and axial compres-
1.3.1 Modes of loading
sion or tension, this will cause a shift in the neutral
The mechanical loading of support structures con- plane, displacing it from the midpoint of the sec-
sists of four types of loads: 1) axial tension, 2) axial tion. Unlike axial compression or tension, stresses
compression, 3) bending, and 4) torsion (Fig. 1.3). due to bending depend on the shape of the cross-
When subjected to axial loads, the stress developed section as well as its size. This is because material
depends only on the structure’s cross-sectional area located near the neutral plane of bending experi-
relative to the magnitude of the applied load. ences lower stresses.
Tension is defined as an axial load that elongates a Beam-like elements with hollow, rather than solid,
structure, whereas compression is defined as a load cross-sections therefore provide much better resistance
6 A N I M A L L O C O M OT I O N

(a) such as the long bones of a vertebrate limb, are more

+ΔL L
F likely to experience large bending-induced stresses
F Tension
than short elements, such as the vertebrae.
−ΔL A
In addition to axial loading and bending, struc-
−F −F Compression
tures may also be loaded in torsion, which involves
a rotational moment applied about the long axis of
(b) Bending a beam-like structure (Fig. 1.3d). As with bending,
−M +M cross-sectional shape also influences how well tor-
L /2 sion is resisted. In this case, shape depends on the
distribution of material away from the neutral axis
Cantilever bending
L
of torsion (for a circular beam this is the midpoint of
−M the cross-section). In general, biological structures
that effectively resist bending also provide effective
resistance to torsional loads. Strong twisting of the
(c) body about a structural member is not common in
Compression −ε the natural movements of most animals, but there
Strain
Tension ε=0 +ε are contexts when enabling twisting can reduce fail-
ure, such as in coral arms that twist in response to
(d)
flow, or accommodate failure, such as in long insect
Torsion legs that twist slightly or buckle when launching
rapidly (Bayley et al., 2012; Etnier, 2003; Vogel, 2007).
When twisting happens suddenly and without mech-
Figure 1.3 Biological (and synthetic) structures are subjected to a anisms to reduce stresses, such as when a ski’s bind-
variety of loading modes. Whereas (a) long-axis (axial) tension and ing fails to release in response to a twisting motion
compression result in uniform stress or strain distributions across the
of the skier’s body, unfortunate consequences often
cross-section of a beam, (b) bending and torsion produce non-uniform
gradients of stress and strain. (c) In the case of bending, maximum result!
tension and compression occur on opposing surfaces with a plane of
zero strain across the beam’s midsection (neutral plane of bending).
(d) In torsion, the location of zero strain is an axis running through the 1.3.2 Safety factors
center of the beam. Typically, bending and torsion produce much
Like human-engineered devices, biological struc-
greater strains, with the possibility of failure, than when a structure is
loaded in tension or compression. tures are designed (by means of natural selection) to
have a “factor of safety” in order to reduce their risk
to bending for a given weight (Fig. 1.3c). This is why of failure. Safety factors are often defined in terms of
bicycle frames and many other structures (tent the ratio of a structure’s strength relative to the max-
poles) are constructed with a tubular design. For the imum stress that it is likely to experience over its
more ambitious reader, the mechanical basis of this lifetime of use ( σ f / σ o , Fig. 1.2b). Engineered struc-
shape factor, termed the second moment of area, tures are typically built to have safety factors as high
is provided in engineering texts (e.g. Beer and as ten. This means that the maximum anticipated
Johnston, 1981; Wainwright et al., 1976). A symmet- load would not exceed one-tenth of the structure’s
ric tubular shape is favored when a range of bending maximum load capacity. With a safety factor of ten,
loads in various directions are likely to act on the the chance of failure is quite low; a comforting fact
structure. Finally, the stresses developed in bending when using an elevator to move up several floors of
depend not only on the magnitude of the bending a tall building! With more stringent performance
force (Fb), but the bending moment ( Fb × L / 2 , in the requirements (such as aircraft, which must minimize
case of bending stresses developed at a midpoint of weight) or a lower cost for failure, the safety of a
a beam, Fig. 1.3b left; and Fb × L , in the case of stresses structure may be less. Safety factors might also be
at the base of a beam subjected to cantilever bend- defined in terms of toughness and strain energy.
ing, Fig. 1.3b right). This means that longer beams, However, because these are often much more diffi-
 P H YS I C A L A N D B I O L O G I C A L P R O P E RT I E S A N D P R I N C I P L E S 7

cult to measure, stress is most often used to define a 1.4 Scaling: the importance of size
structure’s safety factor.
Biological safety factors are generally less than Size is arguably one of the most important variables
the safety factors of engineered buildings and affecting the function and form of organisms. This
mechanical devices; more often ranging between is because changes in size during growth and over
two and eight. For example, in order for the tibia of evolutionary time impose changes in the relative
a gazelle, which has failure strength of 200 MPa, to dimensions of organisms that have important func-
maintain a safety factor of four during fast gallop- tional consequences. Many physiological processes
ing or jumping, the size of its tibia and its manner and mechanical properties depend on key struc-
of loading must ensure that the maximal stresses tural dimensions, such as surface area or thickness,
developed within the bone do not exceed 50 MPa which change dramatically with changes in size.
during these activities. The lower safety factors of When differently sized structures retain the same
biological structures are likely due, in part, to the shape, they are considered to scale isometrically,
fact that animals must also pay a price for main- or to be “geometrically similar.” For geometrically
taining and transporting the mass of their tissues similar structures (Fig. 1.4), all linear dimensions scale
when they move. This cost is likely balanced against in proportion to one another. That is, Lengths (L) are
the benefit of a reduced risk of failure (Alexander, proportional to diameters (D); areas (A) are propor-
1981). Finally, it is likely that the failure of struc- tional to L2 or D2, and to volume (V)2/3.
tures that would most reduce an animal’s fitness, As a result, area-dependent processes change at
such as a primary limb bone versus a distal phal­ a different rate with respect to processes that are lin-
anx or a feather shaft, would favor a higher safety ear- or volume-dependent. This is important for
factor. The relative incidence of bone fracture both the physiological and mechanical functions of
within thoroughbred race-horses appears to pro- organisms. For example, the capacity of animals to
vide evidence of this: fracture is highest in the dis- sustain activity depends on their ability to transport
tal limb bones, lower in the proximal femur and oxygen and fuel substrates to the mitochondria inside
humerus, and lowest in the vertebral column and their muscle fibers. Ultimately, this depends on the
skull (Currey, 1981). rate of diffusion across cellular and mitochondrial

l
a d

l∝L∝d∝D
a ∝ l 2∝ d 2
a∝A

Figure 1.4 Geometric scaling strongly influences the relative dimensions of differently sized animals. For example, while length dimensions scale
linearly across different animals, area (A) scales with the square of length.
8 A N I M A L L O C O M OT I O N

membranes, which in turn depends on the surface- A similar area versus volume constraint operates
area of exchange surfaces. However, if the energy with respect to mechanical support. This is because
demand or work required to move the animal stress depends on force per unit area, which means
depends on its mass (or volume), this poses a scale- that stresses are likely to increase with size (again,
dependent constraint of energy supply relative to for a 100-fold increase in mass, weight-related stresses
energy demand that is proportional to A/V or can be expected to increase nearly five-fold). Unless
V −1/3 (equivalent to M −1/3 ) for geometrically simi- the tissue strength of the skeleton increases in a
lar animals. In other words, a 100-fold increase in similar fashion, the risk of failure may become
size can be expected to impose nearly a five-fold exceedingly high. For animals built of similar
reduction in an animal’s capacity to fuel its activity. mater­ials, this means that they must either evolve
This would mean that an animal’s mass-specific mechanisms for reducing the weight-related forces
metabolism, defined as the amount of energy that gen­erated within their musculoskeletal systems or
each gram of its tissue requires to meet its metabolic drastically restrict their performance.
needs, would decrease five-fold due to the decrease To a certain extent, animals may deviate from
in surface area relative to volume at a larger size. geometric similarity, in order to compensate for
The effect of size on energy metabolism associated the scale effects of size. When this happens distor-
with fueling locomotor activity is discussed at length tions of shape, or allometric changes in structural and
in Chapter 3. functional properties, occur with size. Allometric

(a) 14

12

10 area vs volume0.75

8
Area

(b) 3.5
6 3 isometric
isometric 2.5
Length

4 2
1.5
2 1 length vs volume0.25
0.5
0 0
0 10 20 30 0 10 20 30
Volume Volume
(c) (d)
Positive
allometry
Log Y

Log area
Negative
Log length allometry a

Log volume (or log mass) Log X

Figure 1.5 Scaling of morphological and physiological features can be compared on arithmetic or logarithmic coordinates. The shape and
variation in scaling relationships are illustrated in terms of (a) area versus volume and (b) length versus volume on arithmetic coordinates and (c)
on logarithmic coordinates. The isometric scaling pattern is depicted as a grey line in each graph and the allometric relationship is shown as dark
line. Scaling of area vs volume is positively allometric and length vs volume is negatively allometric. (d) Given the typical scatter of biological data,
a least-squares linear regression fit of the logarithmically-transformed data is used to determine the scaling exponent (slope, b) and coefficient
(y-intercept, a) of the exponential relationship: Y = aX b.
 P H YS I C A L A N D B I O L O G I C A L P R O P E RT I E S A N D P R I N C I P L E S 9

scaling might reflect, for example, either a relative where b is termed the “scaling exponent” and a is
shortening or lengthening of an element or its rela- the “scaling coefficient” relating changes in variable
tive thickening or thinning for a given mass or Y to changes in variable X. This equation can be lin-
area. When the scaling change is greater than that earized by means of logarithmic transformation:
expected for isometry, it is defined as positive
log Y = log a + b log X (1.10)
allometry; when less than the isometric expectation,
it is defined as negative allometry. Even m ­ oderate in which case, the scaling exponent becomes the
allometric scaling requires substantial distortions slope, b, and log a is the Y-intercept of the line relat-
in shape when size changes over ­several orders of ing log Y to log X (Fig. 1.5d). Frequently, base-10
magnitude (Fig. 1.5). A good example of positive logarithms are used to linearize the exponential
allometry is the scaling of mammalian lung sur- relationships describing the structural and physio-
face area (Fig. 1.6a), in which lung surface area logical scaling of organisms (as in Fig. 1.6a).
was found to scale with a slope of 0.92 when plot- However, natural logarithms (ln, base e) are some-
ted on logarithmic axes. This indicates that the times also used (as in Fig. 1.6b). The linear relation-
lungs of larger mammals are much more finely ship described by Eq. 1.10 has the benefit of allowing
partitioned than would be expected if geometric- data to be graphed over several orders of magni-
ally similar to the lungs of small mammals. The tude and the use of regression methods for statistical
observed scaling of lung surface area also suggests evaluation of empirically determined relationships
a greater aerobic capacity for locomotion than if between two variables. Such “bivariate plots” com-
the lungs of larger animals remained isometric in monly have scatter around the predicted scaling
design (see Chapter 3). In a more recent re-analysis line, which provides a measure of how strongly cor-
of morphometric data for respiratory surface area related the two variables are with respect to each
of both ectothermic and endothermic air and water other. Deviations from the observed scaling pattern
breathers that incorporated phylogenetic effects may also provide important insight into how a par-
(Gillooly et al., 2016), similar positive allometric ticular species has evolved a distinctive functional
scaling was found for endothermic respiratory design. Chapter 9 (Evolution) discusses in greater
surface area ( slope = 0.89 ) , which exceeded the detail how scaling analyses are performed across
scaling of respiratory surface area in ectotherms the phylogenetic relationships of animals.
( slope = 0.78 ; Fig. 1.6b). This provides an example
in which the scaling of a key structural feature of
1.5 Dimensions and units
the lungs, important to diffusive gas exchange, can
be related to the metabolic demand for gas It is important (and of practical use) to distinguish
exchange. If, on the other hand, differently sized between dimensions and units in describing and
animals retain a similar shape (i.e. scale close to analyzing the design of organisms. Dimensions rep-
geometric similarity) alternative mechanisms must resent the fundamental physical features of a variable.
evolve to compensate for functional constraints of Variables such as force (F) are defined in terms of
size. We will see how size affects locomotor mech- mass (M) and the mass’ acceleration (a). Similarly,
anisms. Indeed, much of the locomotor diversity velocity is defined in terms of the dimensions length
of animals reflects this fundamental aspect of their (L) per unit time (T). The quantitative measure of
biology. dimensions is expressed in terms of units. Conse­
quently, depending on the set of units used to meas-
ure them, variables will have different values. Units
1.4.1 Allometric equation
for force may be a dyne, a Newton, or pound. Units
Geometric or allometric scaling of physiological of length may be inches, centimeters, or meters. The
functions and structural dimensions can be related Standard International (SI) system of units has been
to changes in size by the exponential equation, adopted throughout the scientific community and
is the system that will be used in this book. Because
Y = a Xb (1.9) it is a metric system, forces are measured in Newtons,
10 A N I M A L L O C O M OT I O N

(a)
1000
Giraffe
Slope = 0.92 Eland
Wildebeest Camel
(isometry predicts 0.67) Zebu cattle
Alveolar surface area (m2) 100
Gazelle
Sheep
Goat

Dik-dik
10 Suni

Genet cat

1 Dwart mongoose

0.1 1 10 100 1000

Body mass (kg)

(b)

15
ln(respiratory surface area)

Slope = 0.89

10

Slope = 0.78

0 4 8 12
In(Body Mass)
Ectotherms Endotherms

Figure 1.6 The scaling of respiratory surface area with body mass in vertebrates exhibits positively allometric slopes, indicating strong selection
for pulmonary diffusion capacity so that oxygen uptake meets the increased metabolic demand for oxygen delivery at larger size. (a) For terrestrial
mammals, lung alveolar surface area scales with as slope of 0.92. Adapted from Gehr et al. (1981). (b) When accounting for phylogeny and considered
more broadly across endothermic birds and mammals, respiratory surface area scales similarly to the non-phylogenetic analysis shown in (a). The
slope for endotherms (0.89) exceeds the slope for ectothermic vertebrates (0.78). Isometric or geometrically similar scaling would predict a slope
of 2/3 (or 0.67). Adapted from Gillooly et al. (2016).
 P H YS I C A L A N D B I O L O G I C A L P R O P E RT I E S A N D P R I N C I P L E S 11

lengths in meters, and ­velocities in meters per sec- The contrast in density between water and air has
ond (m/s). major consequences for the large drag forces that
All biological and physical variables can be defined must be overcome in water, as well as for heat
in terms of three fundamental dimensions: length, transfer and oxygen access. In order to generate
mass and time. Several variables with their com- forces, animal structures must resist and accom-
monly used dimensions and fundamental dimen- modate loads. The characterization of load on bio-
sions are shown in Table 1.2. These dimensions logical structures therefore revolves around force,
provide a means for ensuring that equations are length changes, cross-sectional area and the mode
dimensionally correct (which is of equal, if not greater, of loading, such as bending. In addition, biological
importance than being quantitatively c­orrect; as structures and materials must accommodate energy
quantitative accuracy depends on dimensional without failure, which is measured in terms of
accuracy). This, in turn, can often help to identify a compliance, toughness, rigidity and ­brittleness, and
key variable that may be missing from the equa- also in terms of safety factors, which represent the
tion, if the equation is found to be dimensionally factor above normal loads that an animal can with-
incorrect. stand without breaking. Scaling is fundamental to
locomotion—not just in terms of the size and forces
of locomotion, but also the access to oxygen across
1.6 Summary
sizes given the substantial differences in the way
In this first, foundational chapter of Animal Loco­ that surface area and volume scale relative to length.
motion, we launched a series of key ideas that will These basic principles will appear throughout the
reappear throughout the book. The media in which book as we explore the media through which ani-
animals locomote are important not only to the gen- mals locomote as well as the scaling, biomechanics
eration of locomotor forces, but also to the ability and energetics that accompany the diversity of loco-
to acquire enough oxygen to power the motion. motor mechanisms and environments.

Table 1.2 The dimensions of key biological variables used for

dimensional analysis.
Additional reading
Variable Common dimensions Fundamental dimensions Alexander, R. M. (1983). Animal Mechanics, 2nd ed. London:
Blackwell Scientific.
Force Mass and acceleration MLT −2
Vogel, S. (2013). Comparative Biomechanics: Life’s Physical
Velocity Distance and time LT−1 (equivalent in this case) World. Princeton, Princeton University Press.
Work Force and distance ML2T−2 Wainwright, S. A., Biggs, W. D., Currey, J. D. and Gosline,
J. M. (1976). Mechanical Design in Organisms London:
Stress Force and area ML−1T−2
Arnold.
 CH A PT ER 2

Muscles and Skeletons

The Building Blocks of
Animal Movement

Animal locomotion depends on the organization, (W = F∆L) , which is measured in terms of joules
physiology and biomechanical properties of mus- ( N m ) . Muscles most commonly change length
cles and skeletons. Musculoskeletal systems encom- over distances of millimeters, so that the work they
pass the mechanical interactions of muscles and perform is given in millijoules (mJ). Work per unit
skeletal elements that ultimately transmit force for time, in turn, equals the power ( P = F∆L / ∆t ,
movement and support. Muscles not only perform 1 Watt = 1 J/s ) produced by a muscle. By definition,
work by contracting and shortening to generate muscles produce positive power when they shorten
force, they can also operate as brakes to slow the (decreases in length are defined as being positive).
whole body or a single appendage. Muscles can However, as we will see, muscles can also function
also function as struts (rod-like) to maintain the to generate force with little or no change in length,
position of a joint and facilitate elastic energy in which case the contraction is referred to as isomet-
storage and recovery. Skeletal muscles share a
­ ric. Ideal isometric contractions result in zero work
basic organization and all rely on the same protein and power. Muscles can also maintain a constant
machinery for generating force and movement. force while changing length (isotonic contraction).
Variation in muscle function, therefore, depends Other muscles may lengthen as they generate force
on the underlying mechanical and energetic com- (e.g. lowering a barbell during a biceps workout),
ponents, enzymatic properties and activation by the thereby absorbing energy and doing negative work
nervous system. Muscles require an internal, exter- (ΔL is defined as negative in this case).
nal or hydrostatic skeletal system to transmit force
for movement and support. In the vertebrates and
2.2 Molecular organization: mechanism
arthropods, muscle force transmission occurs through
jointed skeletal segments and levers. The variation of force generation and shortening
and mechanics of musculoskeletal systems enable In skeletal muscles, overlapping sets of actin and
animals to support themselves and move through myosin filaments are arranged in repeating units
their diverse environments. called sarcomeres along a muscle fiber’s length
(Fig. 2.1). Each sarcomere is comprised of two sets
of actin filaments extending from either end (z-disc)
2.1 Muscles
of the sarcomere. The actin filaments overlap by
In order to function as biological motors, muscles interdigitating with the myosin filaments that extend
generate movement by doing work. Muscles do this from the sarcomere midline. The sarcomeres are
by exerting force (F) while shortening (change in organized in series (joined together at neighboring
length, ΔL). Hence, the term “muscle contraction.” z-discs) and form a myofibril that runs end to end
The product of force and length change equals work within the muscle fiber. This regular patterning and

Animal Locomotion. Second Edition. Andrew A. Biewener & Sheila N. Patek, Oxford University Press (2018).
© Andrew A. Biewener & Sheila N. Patek 2018. DOI: 10.1093/oso/9780198743156.001.0001
 M U S C L E S A N D S K E L E TO N S 13

(a) (b) (c)

Filament
t
Mitochondria

Z-disk mc

I-band Transverse M
tubules
sr
Sarcoplasmic
Sarcomere

reticulum
A-band
d
(d) (e)
Motorneuron
Z-disk

Sarcolemma

Fibrils

Figure 2.1 Cross-striated and obliquely-striated muscles are formed by hierarchical structuring and organization of actin and myosin filaments
into sarcomeres. (a) Striated muscle is made of muscle fibrils within which the filaments [thin (actin) and thick (myosin)] form sarcomeres. The actin
thin filaments connect to the Z-disks and form a characteristic banding pattern with the lighter I band around each Z-disk, where the actin
filaments attach, and the darker A band which extends the length of the myosin filaments. Muscles are powered by ATP produced by the mitochon-
dria that are spread throughout muscle cells. The transverse tubules (T-tubules) conduct an arriving stimulus from a motorneuron to stimulate Ca2+
ion release from the sarcoplasmic reticulum and trigger cross-bridge cycling and muscle contraction. Reprinted from Loeb and Gans (1986) with
permission from Elsevier. (b) In these transmission electron micrographs (TEM) of squid (Loligo pealei) the tentacle fibers exhibit a cross-striated
appearance (right image) whereas the arm muscles have obliquely-striated fiber arrangements (left image). Scale bar 1 μm. Image from Kier and
Curtin (2002) with permission of the Company of Biologists Ltd. (c–e) The hexagonal organization of myosin and actin filaments can be seen in
cross-section with insets (d–e) showing higher magnification images of the myofilament arrays. Synchronous insect flight muscle, large scale
bar = 1 μm, small scale bar = 0.1 μm; reproduced from Josephson et al. (2000) with permission of the Company of Biologists Ltd. Abbreviations: SR,
sarcoplasmic reticulum; M, myofilaments; t, tracheole; d, dyad (connection between SR and t-tubule).

organization of sarcomeres within the ­ myofibrils site and re-attach to another binding site along the
creates a striped appearance when viewed under a actin filament. The actin filaments are comprised of
microscope. Therefore, these skeletal muscles are actin monomers organized into an extended double
often referred to as striated muscle (in contrast to helical chain. A recent study indicates that the num-
smooth muscles found in arteries, the gut and else- ber of myosin heads binding during contraction can
where, which lack sarcomeric organization). In add- be modulated based on the load; high loads stretch
ition to the cross-striated vertebrate and invertebrate the thick filament increasing the number of add­
muscles, obliquely striated muscles are found in itional myosin heads that may form cross-bridges
annelids and cephalopods. (Linari et al., 2015).
During a muscle contraction, myosin cyclically Each cross-bridge cycle involves the hydrolysis
attaches to and detaches from actin (cross-bridge (splitting) of one ATP molecule. Chemical energy
cycling) so that the actin and myosin filaments move released from ATP is converted into the force and
past each other in opposite directions. The flexible rotational movement of the myosin head. As a
heads of the myosin molecules, projecting from the result, myosin is both a machine that transforms
myosin filament, form the cross-bridges that attach chemical energy into mechanical work and an
and detach in a cyclical fashion at binding sites enzyme (myosin-ATPase) that hydrolyzes ATP. ATP
along the actin filaments. Myosin filaments are made hydrolysis occurs at the final step of the cross-
of a polymeric chain of myosin protein ­elements, bridge cycle when the myosin head detaches from
each consisting of a heavy chain and two light chains actin and is then free to seek another binding site.
that form a pair of globular domains at the myosin’s ATP binding energizes the actin-myosin complex,
“head” end. Each myosin head is flexible and cap- enabling the subsequent conformational rotation of
able of undergoing conformational rotation in the the myosin head. Rates of cross-bridge cycling (and
presence of ATP. ATP binds to each cross-bridge and ATP hydrolysis) that underlie the speed of muscle
allows the myosin to release from the actin binding shortening and force development, therefore, can
14 A N I M A L L O C O M OT I O N

be assayed based on the myosin-ATPase activity of populate. This section examines force generation
a muscle’s fibers. Across muscle systems and spe- ranging from the level of myofilament overlap up
cies, myosin occurs in different isoforms that yield a to the number of cross-bridges formed during a
large array of outputs in terms of myosin head rota- muscle contraction. Whereas skeletal muscle force
tion rate, release, force and stroke distance. per unit area of activated fibers is fairly constant
Cross-bridge cycling begins when Ca 2+ is released across vertebrates, ranging from 18–30 N/cm2; as a
into the muscle cell and stops when Ca 2+ is removed. result of differing actin-myosin filament lengths,
Motorneurons transmit action potentials to the invertebrate muscles can generate specific forces as
­muscle fiber, causing a depolarization that spreads to high as 200 N/cm2 (Taylor, 2000).
the sarcoplasmic reticulum (SR), which then releases The force of an actively contracting sarcomere
Ca 2+ from the SR into the ­muscle cell. The presence depends on the changing amount of overlap be­tween
of Ca 2+ allows myosin heads to bind to actin and ini- the actin and myosin filaments during a contraction.
tiates cross-bridge cycling. When the muscle con- Within an actively contracting sarcomere, the chan-
traction ends, Ca 2+ is actively pumped back into ging effect of force development across varying
the SR and the myosin heads can no longer bind to amounts of actin-myosin filament overlap is called
actin. Release of Ca 2+ depends on the number of the force-length relationship (Fig. 2.2a) and constitutes
motor-endplate potentials transmitted to the muscle one of the fundamental properties of striated skel-
cell’s SR: with increasing ­depolarization frequency etal muscle. To examine the force-length relation-
of the muscle’s fiber, more Ca 2+ is released. An ship, the force generated by a muscle at a sequence
increase in the number of Ca 2+ ions allows muscles of fixed lengths (isometric contractions) is meas-
to generate force over shorter time periods. For ured experimentally. The initial discovery of the
most muscles, the energetic cost of Ca 2+ release and force-length relationship was based on X-ray dif-
uptake by the SR is ~25 percent of the cost associ- fraction images of myofilament overlap in sarcomeres,
ated with force generation. combined with force measurements of isomet­ric con-
Force is generated only during one direction of tractions in which the muscle was held at these dif-
the rotational movement of the myosin head: the ferent amounts of myofilament overlap (Gordon
bending of the myosin head toward the sarcomere et al., 1966).
midline. Consequently, as force develops, the sarco­ This classic study revealed that as actin and
mere becomes shorter, resulting in an increased ­myosin filaments increasingly overlap in shortened
overlap between the thick and thin filaments. When sarcomeres, active force increases, but only up to a
the contraction is completed, large elastic protein maximal level of force. Once maximal force is achieved,
molecules (titin) that extend from the thick fila- the force plateaus and then decreases as actin and
ments to the z-discs, restore the sarcomere back to myosin filaments overlap further in shortened
its resting position while also mediating the overall sarcomeres. Excessive overlap of the actin filaments
stiffness of the sarcomere. The multiple cycles of causes disrupted spacing within the myofilament
myosin attachment, force generation and shorten- lattice. With increasing overlap, the actin filaments
ing, detachment, and subsequent re-attachment are increasingly interfere with one another, block effect-
summed across the sarcomere and along the length ive myosin cross-bridge binding, and ultimately
of the myofibrils, yielding an overall shortening of reduce contraction force. At extremely short sarco-
the muscle fiber and, ultimately, force generated at mere lengths, the myosin filaments push against the
the ends of the muscle. z-discs. Force-length relationships suggest that
muscle fibers (and by implication, muscles) should
2.3 Levels of force generation and the operate at an ­ intermediate range of sarcomere
lengths (typically ±5 percent to ±15 percent of the
isometric force-length relationship
optimal s­ arcomere length) to enable maximal force
The force generated by a muscle arises at multiple development. The dependence of force on the
structural scales and results from the activation length of the contracting sarcomere is further influ-
dynamics of sarcomeres and the muscle fibers they enced by the change in position and orientation of
 M U S C L E S A N D S K E L E TO N S 15

(a)

Isometric force
40% 100% 160%
Percent resting length of sarcomere

(b) Ls
Rest 10 Ls Net
–20% 8 Ls 2 Ls

Rest 5 Ls Net
–20% 4 Ls 1 Ls

Figure 2.2 Muscle force can be modified at several levels of organization of a sarcomere. (a) The amount of overlap between thin (actin) and
thick (myosin) filaments defines the isometric force-length curve for striated muscle exposed to a series of isometric contractions at different
lengths. Maximum isometric force occurs when thick and thin filaments overlap such that the maximum number of cross-bridges can be formed
(Gordon et al., 1966). To the right along the force-length curve, force is lower when the sarcomere length (Ls) is long and the thick and thin
filaments have reduced overlap. On the left-hand side of the curve, force is lower because the excess overlap disrupts the actin-myosin spacing.
(b) The number of sarcomeres in series determines how the fractional shortening of individual sarcomeres sums to determine changes in fiber (and
whole muscle) length. As the number of sarcomeres increases, their summed change in length increases. Invertebrates can vary the length of the
sarcomere (Ls) in addition to varying the number of sarcomeres in series (not shown here). A longer sarcomere increases the amount of force
produced by the sarcomere, due to the increased number of cross bridges formed at a given instant, but decreases the speed of fiber shortening.

the myosin heads relative to actin filaments: in and actin filaments, which means that more cross-
order to maintain a constant volume in the muscle bridges can be formed with neighboring actin fila-
fiber, the fibers bulge radially during contraction, ments. As a result, longer sarcomeres are able to
increasing the spacing between myosin and actin fila- generate greater force than shorter sarcomeres.
ments. This change in spacing steepens the slope of Differences in sarcomere length also affect the speed
the ascending and descending limbs of the force- of shortening of a fiber, with longer sarcomeres gen-
length relationship for insect flight muscle (Williams erally contracting at slower speeds.
et al., 2013). The number of sarcomeres within a fiber affects
Moving up in scale from the changing overlap the absolute change in length for a given fractional
of actin and myosin that primarily defines a shortening of individual sarcomeres. Longer fibers
­sarcomere’s force-length relationship, the force gen- allow a muscle to achieve a greater overall length
erated by a muscle fiber is also determined by the change for a given fractional length change of its
total number of possible actin-myosin cross-bridges sarcomeres (Fig. 2.2b); muscles that undergo greater
within a sarcomere. The number of possible cross- length change (i.e. produce greater displacement)
bridges is proportional to a sarcomere's length. The are likely to have longer fibers (with more s­ arcomeres
sarcomere lengths of vertebrate skeletal muscles in series) than muscles that function over shorter
are surprisingly uniform, typically falling in the displacements. Both vertebrates and invertebrates
range of 2.0 to 2.8 μm, whereas invertebrate skel- vary the number of sarcomeres within a fiber to
etal muscles exhibit a great diversity of sarcomere adjust fiber length relative to the muscle’s func-
lengths, 1.9 to 17.8 μm among arthropods and up tional range of operating length.
to 40 μm in annelid worms (Smith et al., 1973; The elastic properties of muscular systems—from
Taylor, 2000). Longer ­sarcomeres have longer myosin sarcomeres up to musculoskeletal attachment—
16 A N I M A L L O C O M OT I O N

(a) Inactive muscle passive elastic properties due largely to connective

tissue elements within the muscle. When an inactive
muscle is stretched from its resting length, it will
passively resist the imposed stretch by developing
Passive
force (Fig. 2.3a). Consequently, the force-length
Force

properties of skeletal muscles result from a combin-

ation of their active and passive components (Fig.
2.3b). While the force-length properties are critical
to understanding the molecular basis of muscle
force development and shortening, the passive
40% 100% 160%
elastic properties of muscles are important to their
behavior under in vivo conditions and cannot be
(b) Contracting pinnate muscle
overlooked. The passive elastic properties of mus-
cles depend on their fiber architecture and the
Passive + active
amount of connective tissue to which the fibers
attach within the muscle. Muscles with short fibers
Force

and more extensive connective tissue (see discus-

Active
sion of pinnate versus parallel fibered muscles in
Passive
Section 2.8) exhibit a steeper rise in their passive
resistance to stretch compared with longer fibered
muscles that have less connective tissue investing
40% 100% 160% the fibers (Fig. 2.3c).

(c) Contracting parallel-fibered muscle

2.4 Power, efficiency and the isotonic
Passive + active force-velocity relationship
In addition to the force-length relationship described
Force

Active in the previous section, the force-velocity (F–v) rela-

tionship represents a second fundamental property
Passive
of skeletal muscle (Fig. 2.4). The velocity of fiber
shortening (and lengthening) affects the amount of
40% 100% 160%
force that a muscle can develop. Starting from an
Percent resting length isometric contraction (zero velocity; peak force, P0),
Figure 2.3 Muscles exhibit both active and passive force-length the velocity of shortening (v) increases and force
properties. (a) When a resting muscle (i.e., not actively contracting) is hyperbolically decreases until the muscle reaches
stretched from its resting length (100% length), connective tissue within maximum shortening velocity (vmax) while approach-
the muscle resists stretching and generates a J-shaped force-displacement ing zero force. The hyperbolic nature of the force-
curve typical of compliant materials. (b) In a contracting pinnate muscle
velocity relationship was first described by A. V.
with considerable connective tissue, active force generation builds from
~40% resting length starting point and then sums with its passive Hill in 1938, having previously won a Nobel Prize
connective tissue components once the muscle is stretched beyond its in 1922 for his work on the energy and efficiency of
resting length (100%). When stretched past resting length, the active muscle contraction. As the speed of filament sliding
force declines and the stretch-resistance of the passive components increases, fewer unbound myosin cross-bridge heads
gradually increases. (c) In parallel-fibered muscles that have less are able to successfully bind to actin sites. Because
connective tissue, the passive component is much smaller than for a
pinnate muscle, (b) and there is a larger drop in tension at longer lengths.
fewer cross-bridges form as a muscle shortens at a
higher velocity, the force developed by the muscle’s
mediate the force developed across varying amounts fiber is reduced, thus resulting in an inverse rela-
of myofilament overlap (Fig. 2.3). In ­addition to tionship between fiber shortening velocity and
their active force-length properties, muscles possess force development.
 M U S C L E S A N D S K E L E TO N S 17

(a) (b)

Muscle efficiency (work out/energy in)

0.25
efficiency 100% power

Percent maximum power

Po

Force

0.3 0.5 1 0.3 0.5 1

Lengthening Shortening v/vmax
v/vmax

Figure 2.4 The Hill isotonic force–velocity curve explains tradeoffs between force generation and contraction velocity while also revealing the
combination of force and velocity that allows a muscle to generate peak power output. (a) The Hill isotonic force–velocity curve for skeletal muscle
during muscle shortening and lengthening. When compared to peak isometric force (P0), muscle lengthening (x-axis negative values) can yield
much greater forces over short distances than occurs during muscle shortening (x-axis positive values). The x-axis variable (ratio of shortening
velocity (v) relative to maximum velocity (vmax)) is typically used, because it allows for comparisons across muscle sizes and speeds. (b) Maximum
muscle power (work per unit time) occurs at higher v/vmax on the force–velocity curve (~0.4 v/vmax) than maximum muscle efficiency (mechanical
work output/metabolic energy input) which occurs at 0.3 v/vmax on this graph. Efficiency and power both converge at zero when muscles contract
isometrically (zero velocity; v /v max = 0 ) and at maximal velocity (zero force; v /v max = 1 ). Therefore, muscle contraction rates are likely to vary
according to whether an animal is maximizing efficiency versus power or velocity output.

In addition to the examples of force development the cross-bridge is lost. Indeed, excessive muscle
during fiber shortening, muscles also generate force stretch may be a leading contributor to m ­ uscle
when lengthening and, indeed, can briefly generate injury. Active muscle lengthening and the enhance-
much higher forces during lengthening than are ment of force that it facilitates is thought to occur in
achieved during isometric contractions (Fig. 2.4a). the locomotion of many animals, but it normally
If a muscle contracts when loaded by a force that happens over brief instances in time and short
exceeds its maximal isometric force, it will be length changes.
actively lengthened. This can occur, for instance, Given that force times velocity is equal to power,
when a person lands from a jump. Upon landing, peak-power output of a muscle can be predicted by
the knee extensor muscles contract to prevent the plotting the product of force and velocity from the
legs from collapsing, are lengthened as the knee ini- empirically-determined force-velocity relationship
tially flexes and then are re-extended to absorb (Fig. 2.4b). For most skeletal muscles, maximum
the energy of the falling body. Active lengthening of power is developed at about 0.4v / vmax. Therefore,
the extensor muscle occurs, because the weight of the muscles that function to generate mechanical power
body exceeds the isometric (P0) contractile force of (e.g. flight muscles of insects and birds, axial mus-
the muscles’ fibers. With an increase in the rate of cles of fish, mantle muscles that power the jetting
lengthening, the force developed by a muscle rises of squid) operate with shortening velocities in the
sharply. The additional force that the muscle gener- range that yields maximal power output. One inter-
ates while being actively lengthened is provided by esting consequence of peak power occurring at a
a rapid stretch of the myosin cross-bridges attached particular combination of muscle force and velocity
to the actin filaments. This heightened level of force is that animals of larger body size or that are push-
(up to 1.8 times peak isometric force) can only occur, ing against large loads may be constrained to oper-
therefore, over very short lengthening distances ate at a different point on the force-velocity curve,
and short time periods. At greater distances of fiber thus leading to sub-maximal power output. For
lengthening, or longer time periods, the cross-bridges example, large animals that support substantial
detach and the additional elastic restoring force of body weight must operate their locomotor muscles
18 A N I M A L L O C O M OT I O N

with greater force and lower velocity, thereby decreas- and physiological properties of muscles are likely
ing their power output and speed compared to to differ from the classical description of their
smaller animals. Even in aquatic systems with ani- ­force-length and force-velocity properties, which
mals of varying body size, the dynamic effects of are based on idealized isometric and isotonic
size on drag forces cause frogs of different sizes ­contractile states.
to operate at different points on the F–v curve The muscle work loop is a contractile method
(Clemente and Richards, 2013) and thus fail to oper- (Josephson, 1985) for calculating net muscle work
ate at optimal power output. by variably activating a muscle during imposed
Also, key to a muscle’s performance is its effi- sinus­oidal changes in length and force. For many
ciency, yet peak efficiency occurs at a different muscles that propel an undulating body or recipro-
point on the force-velocity curve than peak power cating limbs, the length changes of the muscle may
(Fig. 2.4b). Muscle efficiency is defined as the be approximated by a sinusoidal pattern of length
amount of work (force times distance) that a ­muscle change. The particular timing of muscle activation
performs divided by the chemical energy (ATP) relative to its shortening and lengthening is critical
that it consumes during a contraction. Because dir- to the net work that the muscle performs during a
ect measurements of ATP use are difficult to make, contraction cycle. The work loop technique varies
extremely sensitive thermal measurements of the the length and activation of a muscle to examine
heat released by a contracting muscle (energy lost), how these factors affect the force generated and dis-
relative to the amount of work performed, have tance of contraction—in other words, the varying
provided a reliable alternative approach for meas- work output (∆F × ∆L) of the muscle.
uring muscle efficiency  = Work / ( Work + Heat )  . Force development is examined during muscle
These measurements have shown that the effi- shortening and lengthening—in the example shown
ciency of skeletal muscle is maximal at a lower (Fig. 2.5), a sinusoidal length pattern is imposed.
shortening velocity ( 0.3 v / vmax , Fig. 2.4b) than Work loop experiments measure the force that the
the velocities that m ­ aximize mechanical power. muscle develops when it is activated at varying pre-
Consequently, when locomotor efficiency is more set lengths. When activated so that the force devel-
important than power output, muscles can be oped by a muscle is greatest during shortening,
expected to contract more slowly than in circum- counter-clockwise vectors of force development cir-
stances when maximum power is required (e.g. cumscribe an elliptical region representing positive
during a high-power escape response). work. In the small region of muscle-lengthening,
“negative” work is generated as the muscle is
stretched. Although somewhat nonsensical in the
2.5 “Work loops”: time varying force- context of physics, the term negative work is simply
a convention among muscle physiologists to dis-
length behavior of muscles
tinguish between shortening, positive work and
While the isometric force-length and isotonic lengthening, negative work performed by muscles.
force-velocity relationships described have proven Negative work represents the energy absorbed by a
extremely useful for understanding the design and muscle. When the work loop experiment is run
properties of different muscles, neither provides an such that a muscle generates more force during
accurate description of how muscles function under lengthening than shortening, the vectors change
dynamic conditions. The force-velocity relationship direction to circumscribe an elliptical region in the
is determined by stimulating the muscle and allow- clockwise direction, thereby generating mostly
ing it to shorten against a fixed load over a very ­negative work.
short range of length (<5 percent); however, in liv- A muscle’s work performance is primarily deter-
ing animals, muscles develop force and change mined by the timing and duration of muscle activa-
length under dynamic conditions, in which both tion relative to the muscle’s changing length (Fig.
force and length change at different rates during the 2.5) in relation to the magnitude of force developed.
period of a contraction. Consequently, the mechanical When a muscle is activated, it generates force, but
 M U S C L E S A N D S K E L E TO N S 19

1 2 3 4
(a)
2

3 Force

Force
1
Net +

4
Length
Length
Activation
(b)
2

3
1
Force

Net – Length

4
Activation
Length
Time

Figure 2.5 Muscle work loops allow experimental examination of time-varying patterns of muscle force, activation patterns and length change
that are common to the in vivo locomotor behavior of many muscles. Work loops generated from sinusoidal oscillations of muscle force and length
yield positive (a, counter-clockwise) and negative (b, clockwise) work loops depending on whether the muscle is activated and force is generated
during muscle shortening (a) or lengthening (b). (a) In a positive work loop, the area in the center of the loop is the net work that the muscle
performs over the contraction cycle. The hatched area at lower right is the negative work (energy absorbed) by the muscle while being lengthened
during this phase of the cycle. The negative work is subsequently recovered when the muscle shortens, yielding the net work within the loop. The
muscle activity in a positive work loop occurs during muscle shortening. The zero phase of muscle activity is defined by the length of the muscle
and in this example, it occurs at point 1, when the muscle begins to shorten. (b) A clockwise “negative work loop” results from a delay in the
phase of muscle shortening and associated muscle activation. This causes the muscle to do little work while it is shortening (hatched region: Force
is low or zero) and absorb energy by developing greater force while being lengthened.

length changes can occur at varying time points activation of the muscle occurs later, when the
after force development begins. We can define ­muscle is nearly finished shortening, and the acti-
phase zero as the moment at which a muscle begins vation lasts into a substantial period of lengthening,
to shorten. Activation of a muscle immediately the muscle’s force-length behavior will result in a
before the onset of shortening (negative phase: –0.1 clockwise (negative) work loop (Fig. 2.5b). Finally,
to 0) and with a duration lasting midway through if a muscle’s activation is limited to when it under-
shortening (relative phase: 0.25) is most favorable goes little, or no length change, it will develop force
for effective force development and subsequent isometrically and do little work (not shown).
positive work during shortening (Fig. 2.5a). This Work loop experiments have provided insights
is because the initial period of muscle activation into the muscle properties underlying the dynam-
occurs while the muscle is briefly being stretched ics of muscle length change and force develop-
or develops force under near-isometric conditions. ment, which are thought to operate during in vivo
From the force–velocity relationship (Fig. 2.4), we locomotor activity. Muscles that function to do
know that muscles develop greater force under work and generate power (equal to the work per
these conditions. If activation of the muscle is contraction times the contraction frequency), such
delayed until after it begins to shorten (relative as the leg muscles that power locust and frog
phase: 0 to 0.5), its ability to develop force and do jumping, and the flight muscles of birds, character-
work during shortening will likely be reduced. If istically have broad counter-clockwise work loops
20 A N I M A L L O C O M OT I O N

(Fig. 2.5a). Fish axial body muscles have been by the nervous system (see Chapter 8). Inverte­
studied extensively using the work loop tech- brate and vertebrate skeletal muscle fi ­ bers can be
nique. These studies have examined the effects of distinguished most generally as being either twitch
swimming speed in relation to cycle frequency, or tonic. When twitch fibers are activated, they
length change, timing of activation, and tempera- develop force, and when their ­stimulation ceases,
ture on the muscles’ ability to generate mechanical they relax. In contrast, slow tonic fibers can maintain
power. During swimming, the axial musculature their tension for long periods of time by maintain-
on the convex side of the body’s bend is activated ing cross-bridge attachment and limiting cross-
to generate force just before shortening, during the bridge cycling, well after their neural activation
time when the fibers finish being stretched. This has ended. As a result, slow tonic muscle fi ­ bers
allows the fibers to develop force rapidly, as they provide a means for adjusting and maintaining ten-
subsequently shorten and the animal’s body to sion at low energy cost for long time periods. We
bend in the opposite direction (becoming concave). primarily focus on the properties of twitch-type
This local force is either transmitted posteriorly skeletal muscle fibers, and the faster contracting
down the length of the animal’s body to the tail or non-twitch fibers of invertebrates, in relation to
is transmitted directly to the fluid adjacent to the how they are recruited for adjustments in muscle
body surface for propulsion. Thus, muscle work is force, speed and endurance.
transformed into hydrodynamic work. Traveling In the vertebrates, skeletal muscle fibers respond
waves of bending and fluid propulsion are driven in an all-or-nothing fashion as the depolarization
down the animal’s body in this way, by means of a of the fiber spreads rapidly along the fiber’s length
transmitted wave of electrical activation by the from the motor endplate. As a result, they are
nervous system to the muscles along the body ­considered “twitch” type fibers. The firing rate of
axis. action potentials transmitted to the motor end-
In contrast to the counter-clockwise positive work plates influences the magnitude and time course of
loop of fish swimming, muscles that operate as force that the muscle develops by regulating the
brakes to absorb energy, such as when overcoming amount of calcium that is released from the SR.
the inertia of a moving limb or decelerating the Nearly all vertebrate skeletal muscles that power
body’s motion, can be expected to generate clock- locomotion are comprised of “twitch” fibers, which
wise negative work loops (Fig. 2.5b). Finally, as develop a characteristic pattern of force (Fig. 2.6)
we’ll see in Chapter 4, muscles may also function to in response to an endplate depolarization. Multiple
contract economically by developing force with lit- stimuli at slow to moderate frequencies result in
tle or no change in length, so that they do little net an “unfused tetanus” that yields an elevated, but
work. When this occurs, the force-length behavior rippled force pattern (Fig. 2.6b). With an increase
of these muscles results in little or no area contained in stimulation frequency, the magnitude of force
within the loop. Indeed, in this case the term “work increases further (a property termed “summation”)
loop” is a misnomer, and the overall pattern of and achieves a smooth force plateau, or “fused
force-length behavior is actually much more similar tetanus” (Fig. 2.6c). The stimulation frequency
to that of a spring (see Fig. 4.12). required to elicit a fused tetanus is greater in faster
contracting muscle fibers. Faster contracting m ­ uscles
2.6 Excitation–contraction coupling develop force more rapidly than slower contracting
muscles, but fatigue more quickly. In most instances,
and motor units
vertebrate skeletal muscles generate fused tetanic
In addition to the levels and dynamics of force gen- contractions during locomotion. For very fast ­muscles,
eration described in the previous sections, the amount such as rattlesnake shaker muscle or humming-
of force developed by a muscle is also influenced by bird flight muscle, this is the case even if the muscle
the number of cross-bridges formed in parallel across is activated with relatively few stimulating spikes
the myofilament lattice, which is ultimately deter- (Altshuler et al., 2010; Rome and Lindstedt, 1998;
mined by the number of muscle fi ­ bers stimulated Tobalske et al., 2010).
 M U S C L E S A N D S K E L E TO N S 21

(a) Twitch

Relative force
Nerve stimulus

(b) Unfused tetanus

Relative force

Nerve stimulus
Fused tetanus

(c)
Relative force

Nerve stimulus

Time

Figure 2.6 Muscle force response to varying frequencies of stimulation in (a) a single twitch stimulus, (b) unfused tetanus, and (c) fused tetanus.
These patterns are for twitch-type muscle fibers. A fused tetanus is achieved when the stimulation frequency is high enough to produce a smooth
(and elevated) plateau in muscle force.

In the case of invertebrate muscles, a majority Most skeletal muscles are activated directly by
of the fibers typically do not respond in an all- motorneurons that innervate a subpopulation of
or-nothing fashion. Instead, these fibers respond to fibers within a muscle (except for the asynchronous
nerve stimulation by developing graded patterns of flight muscles of insects; see Chapter 6). A motor unit
­depolarization produced by multiple motorneuron consists of the motorneuron and the set of muscle
terminals that are distributed along the length of fibers that it innervates. In nearly all mammalian,
the muscle fiber. Local motor junction potentials avian and reptilian muscles, adult muscle fibers are
sum over the length of the fiber to produce a net innervated by a single motorneuron; however, in
depolarization in the fiber, as a whole. In addition, some fish and amphibian muscles, as well as those
invertebrate skeletal muscle fibers may also receive of various invertebrates, a muscle fiber may be
inhibitory input from their motorneurons, in con- innervated by more than one motorneuron (poly-
trast to vertebrates whose motorneurons act solely neuronal innervation). In animals lacking polyneu-
in an excitatory fashion. The graded activation of ronal innervation, the fibers innervated by the
invertebrate muscle fibers, therefore provides a motorneuron (i.e. those comprising the motor unit)
fundamentally different mechanism compared to share similar contractile properties. This may result,
the vertebrates for controlling the force output of a in part, from a trophic influence of the motorneuron
muscle. on the fibers. In other words, the activation frequency
22 A N I M A L L O C O M OT I O N

from the motorneuron affects the biochemical and logical and ecological significance when comparing
contractile properties of the fiber(s). multiple species. The characteristics and properties
Modulation of force output by twitch-type s­ keletal of twitch muscle fiber types have been most thor-
muscles is therefore achieved by the ­nervous sys- oughly studied in mammals; the classification
tem’s recruitment of motor units within a muscle scheme used here is largely based on these studies.
(covered in detail in Chapter 8). The number of Although this classification reflects the bias of
­fibers innervated by a motorneuron can vary. For twitch mammalian fiber types, it provides a concep-
example, finer control of force can be achieved by tual scheme that can be usefully extended to the
having a larger number of small motor units. The broader diversity of skeletal muscle fibers found in
steering muscles of flying insects can be innervated other animal groups. Characteristics of non-twitch
by a single motorneuron. In this case, force is modu- invertebrate muscle fibers will be discussed in Chapter
lated by varying the number and frequency of nerve 8, when we consider the neural control of motor
stimuli as well as the time-course of d­ epolarization function.
(Tu and Dickinson, 1994). Three main types of twitch muscle fibers are gen-
erally recognized within mammals, birds and rep-
tiles: slow-oxidative (SO), fast-oxidative-glycolytic
2.7 Muscle fiber types
(FOG) and fast-glycolytic (FG). Table 2.1 lists sev-
Both vertebrate and invertebrate skeletal muscles eral key contractile, metabolic and cytological fea-
commonly have twitch fiber populations that pos- tures of these three types of fibers. Myosin isoforms
sess differing contractile and metabolic characteris- are determined by protein immunohistochemistry.
tics. Distinguishing among these features has led to Qualitative descriptions of contractile and meta-
a series of descriptive classifications of muscle fiber bolic properties determine whether fibers are classi-
types. Although these classification schemes sug- fied as SO (also termed type I fibers), FOG (also
gest discrete types of muscle fibers, in fact variation referred to as IIa and IIx) and FG fibers (also termed
can exist within a population of fibers of a given type IIb). Myosin with a fast ATPase rate (i.e. fast
type. Consequently, differences between fiber types cross-bridge cycling rate) is characteristic of fibers
are often qualitative, yielding more of a continuum that contract rapidly. More oxidative fibers have
of properties across the spectrum of muscle fiber slower myosin ATPase rates, which means that they
types. Nevertheless, differences in motor recruit- develop force and shorten more slowly. A slower
ment and function can be usefully ascribed to dif- rate of shortening is also associated with their reli-
ferences in fiber type within and between muscles ance on aerobic synthesis of ATP via mitochondrial
within a species and can often have profound physio­ oxidative phosphorylation. Hence, slow-oxidative

Table 2.1 Twitch (phasic) skeletal muscle fiber types (based largely on mammalian patterns).

Property/feature Slow-oxidative (SO) Fast-oxidative- Fast-glycolytic

glycolytic (FOG) (FG)
Alternative slow twitch fast-twitch red fast-twitch white
classifications type I type IIa type IIb

Myosin isoform slow cross-bridge cycling rapid cross-bridge cycling rapid cross-bridge cycling
2+
SR Ca ATPase
2+
slow SR Ca uptake
2+
fast SR Ca uptake fast SR Ca2+ uptake
Contraction speed slow fast fast
Krebs cycle enzymes high intermediate low
# mitochondria and capillaries high intermediate low
Contraction endurance high intermediate low
 M U S C L E S A N D S K E L E TO N S 23

fibers show a high quantity of oxidative enzymes, small- to moderate-sized birds. For example, up to
such as succinate dehydrogenase or citrate syn- 85 percent of a pigeon’s primary flight muscle con-
thase. In contrast, fast-glycolytic fibers store large sists of FOG fibers. Clear differences exist among
amounts of glycogen and have a high quantity of mammals as well. Whereas canids (dogs, coyotes,
glycolytic enzymes, such as glycerol diphosphatase, wolves) have high proportions of oxidative fibers
enabling them to generate ATP rapidly via anaerobic allowing them to hunt and forage actively for long
metabolism. FG fibers fatigue quickly (due to meta- periods, felids (cats, lions) have relatively few oxi-
bolic acidosis), whereas SO fibers can contract for dative fibers, relying on stealth and burst pursuit to
long periods without becoming fatigued. As their catch their prey. Such differences clearly distinguish
name suggests, fast-oxidative-glycolytic (FOG) ­fibers the temperaments and personalities of our most
possess intermediate properties. popular pets!
Associated with their metabolic reliance on In most fish, two distinct populations of fibers
­aerobic ATP synthesis, SO fibers are also more richly occur within the axial musculature: the red fibers
supplied with capillaries and myoglobin (reflecting are slow-oxidative, whereas the white fibers are
a high capacity for vascular supply of O2), and con- fast-glycolytic (Fig. 2.7). Typically, the red fibers
tain many more mitochondria than FG fibers. FG constitute a relatively small portion of the myotome
fibers, on the other hand, have a more extensive, and are found in a longitudinal band either near the
well-developed sarcoplasmic reticulum, associated body surface (most fish) or closer to the backbone,
with the need for rapid Ca2+ activation and uptake within the larger white component, in certain spe-
for fast contraction speed. Recruitment among fiber cialized “regionally endothermic” fish (tunas, bill
populations with these differing metabolic and con- fish, mackerel and lamnid sharks). These fish are
tractile properties allows animals to use particular capable of maintaining their deeper red muscle at a
sets of muscles or muscle fibers for particular tasks. warmer temperature than the surrounding water. At
Rapid burst activity, as during escape or prey cap- slow swimming speeds, only the red slow-oxidative
ture, is best powered by FG fibers, whereas slower fibers are activated to produce a slow traveling
movements and control of posture favors recruit- wave of propulsion. As swimming speed increases,
ment of SO fibers. Finally, it is worth emphasizing white muscle fibers are also recruited to power
again that slow twitch-oxidative fibers are distinct swimming, providing faster and stronger waves of
from and not to be confused with the slow-tonic propulsion. Because the white (FG) fibers are less
­fibers found in certain muscles of invertebrates and oxidative than the red (SO) fibers, however, endur-
vertebrates. ance is progressively reduced at faster swimming
Fiber type features vary within and across clades. speeds. The locomotor performance of most fish
As ectotherms, most reptilian species rely on burst (which are ectotherms) is strongly affected by water
activity rather than sustained locomotion in order temperature. Interestingly, at low temperatures,
to obtain food and avoid predation. The leg muscles several fish begin to recruit faster contracting white
of lizards, not surprisingly, have a predominance of fibers at slower swimming speeds in order to com-
FG fibers that are well suited to burst anaerobic pensate for reduced muscle power output at these
activity. On the other hand, mammals and birds are low temperatures (see Fig. 8.10, Rome et al., 1984).
able to sustain locomotor activity that is fueled In regionally endothermic fish, such as tunas and
by aerobic metabolism for much longer periods. bill fish, countercurrent heat exchangers maintain
Consequently, their muscles have much higher pro- internal red muscle temperatures as much as 10°C
portions of oxidative (SO and FOG) fibers. Most greater than the surrounding water. By keeping
spectacularly, the high wing beat frequency of hum- their red musculature warm, the fish are able to
mingbirds (45–60 Hz) requires that nearly 50 p ­ ercent achieve greater endurance and faster swimming
of flight muscle volume is occupied by mitochon- speeds in colder waters.
dria (the other half consists of myofilaments and By alternately shortening and lengthening to bend
sarcoplasmic reticulum). Nearly all their flight ­muscle the fish’s body and tail back and forth, the axial
is comprised of FOG fibers. This is also true of many ­musculature of swimming fish does mechanical work
24 A N I M A L L O C O M OT I O N

5 cm

Red
muscle

(a) (b)

Figure 2.7 Red and white axial muscle organization is evident in cross-sections of (a) mackerel and (b) tuna (two scombrid fish). In most fish,
such as the mackerel, the red muscle represents a limited portion of the myotomal muscle and is located just beneath the skin lateral to the white
muscle. In tuna and other fish which warm their red muscle, the red muscle is more extensive and lies medially to much of the white muscle.
Counter-current heat exchange keeps the red muscle warmer than the water and the rest of the fish (some fish also maintain elevated brain and
eye temperatures). Reproduced from Westneat and Wainwright (2001) with permission from Elsevier.

during the shortening phase of its length cycle as it shortening (Fig. 2.5). This allows the muscles at
contracts to develop force. Studies of the neural acti- any one location on the animal’s body to do work
vation of muscle segments at different sites along the ( force × shortening distance ) . This work is transmit-
length of swimming fish show that the muscles are ted posteriorly along the animal’s body, to its tail, and
typically activated just as they finish being pas- used to produce the hydrodynamic thrust necessary
sively lengthened, so that they develop force while to propel the animal forward. Studies of both the
 M U S C L E S A N D S K E L E TO N S 25

slow-oxidative red and fast-glycolytic white muscle parallel-fibered and pinnate-fibered ­muscles (Fig.
fibers from fish indicate that they shorten at a vel­ 2.8). Parallel-fibered muscles have fi ­ bers that run
ocity that is close to their optimum (0.3 to 0.4 v / vmax ; end-to-end within the muscle in a direction parallel
Fig. 2.4) for doing work efficiently and generating to the muscle’s axis of force transmission. Typically,
power (work/time). Hence, fish typically cruise at a parallel-fibered muscles have relatively long fibers
steady uniform speed using their red muscle to maxi- and attach directly to the skeleton with little or no
mize their swimming efficiency and reduce their external tendon. In contrast, pinnate-fibered mus-
cost of movement. When they accelerate or swim cles are built with shorter fibers attached at an angle
quickly, they use their white muscle to maximize to the muscle’s principal axis of force transmission.
power output for escaping predation or to catch prey. Pinnate muscles often attach via an external tendon
to the animal’s skeleton.
Pinnate muscles can be architecturally quite com-
2.8 Fiber architecture and its effects on
plex. Uni-pinnate muscles have fibers that are all
muscle volume and energy use oriented at similar angles in a single plane and
In addition to a muscle’s intrinsic force-length and attach to the distal tendon. Bi-pinnate muscles have
force-velocity properties and its fiber type character- two sets of fibers at roughly mirror-image angles,
istics, the arrangement and orientation of a m­ uscle’s which attach to a central distal tendon. Multi-pinnate
fibers (fiber architecture) also affect its contractile muscles have more complex fiber architectures with
function. Muscles are traditionally divided into two varying planes of angled fibers. In general, muscles
fundamental classes based on their architecture: that are more pinnate also have shorter fibers.
Due to differences in fiber length, parallel-fibered
muscles of equal mass (and volume) have a smaller
Parallel Unipinnate Bipinnate fiber cross-sectional area compared with pinnate
Ft
muscles (Figs 2.8 and 2.9). As previously noted,
because all striated muscles depend on the same
α
myofilament interaction for force generation, the
If
Fm force developed by a muscle generally varies in
direct proportion to its fiber cross-sectional area. In
other words, the maximum isometric stress (force/
fiber area) that striated muscles can develop is
largely constant across a broad diversity of inverte-
α brate and vertebrate animals (although, certain
(Aponeurosis)
invertebrate muscles with long sarcomeres, such as
crab pincers, are able to generate unusually high
stresses). Consequently, because of their shorter
fibered architecture, pinnate muscles of equal mass
are capable of generating greater forces than paral-
(External tendon) lel-fibered muscles. Although pinnate muscles suf-
Ft = Fm cosα fer some loss of force transmission due to the angle
of their fibers, this is more than offset by their
greater fiber area.
Figure 2.8 In contrast to parallel-fibered muscle, the fibers of The cross-sectional area of a parallel-fibered
pinnate muscles exert force at an angle to the muscle and tendon muscle (Am) can be determined from its mass and
long-axis. The effective force is a product of the cosine of the muscle mean fiber length (lf), given a known density (1060
fibers’ pinnation angle (α). Ft, tendon force; Fm, muscle fiber force; lF, kg m–3 is a typical value for striated muscles), as
muscle fiber length. However, because the number of fibers and their
cross-sectional area (for a given muscle volume) is much greater,
follows:
pinnate muscles commonly generate much larger forces compared
with parallel-fibered muscles. Am = m / ρ m lf (2.1)
26 A N I M A L L O C O M OT I O N

The effective “physiological” cross-sectional area of muscle). In terms of muscle work, the increase in
a pinnate muscle (*Am, also referred to as PCSA) can force achieved by a pinnate architecture is coun-
be calculated by accounting for the muscle fibers’ tered by the decreased shortening capacity of its
pinnation angle (α, Fig. 2.8) as, ­fibers. Consequently, all muscles have generally the
same capacity for doing work on a per unit mass
*Am = Am cos α (2.2)
basis, irrespective of their fiber architecture.
These equations enable the following simple A muscle’s fiber architecture also affects its rate
comparison between a parallel-fibered and pinnate of energy use based on the volume of muscle that
muscle. If we assume the two muscles have equal must be activated to generate a given force. Longer
mass, set the parallel fibers equal to ten times the parallel-fibered muscles require more energy to
length of the pinnate fibers, and set the pinnation generate a given force than short, pinnate-fibered
angle to 20° in the pinnate muscle, the parallel- muscles, because longer fibers require the forma-
fibered muscle will have a fiber area that is only tion of more cross-bridges to transmit force along
1 / 9.4 [= (1 / 10 × cos (20°)] or 0.106 times that of the their length than short fibers (Biewener and Roberts,
pinnate muscle. Correspondingly, the effective 2000; Roberts et al., 1997). Consequently, the ATP
force that the pinnate muscle transmits to its tendon cost per force generated, a measure of a muscle’s
(Ft) equals the force developed by the muscle’s force economy, increases with muscle fiber length.
­fibers ( Fm ) × cos α , which in this case is 9.4 times For example, two muscles of equal volume, but
greater than the parallel fibered muscle. An important with fiber lengths that differ by threefold will also
advantage of a parallel fiber architecture is that it differ in their fiber cross-sectional areas (Af) by
provides a greater range of shortening (in the previ- threefold (Fig. 2.9). To generate a given force, both
ous example, the parallel-fibered muscle would muscles must recruit the same Af; however, the
contract ~ tenfold greater distance than the pinnate longer fibered muscle has three times the volume

Vactive Af
Muscle A
Muscle A
parallel-fibered

lf = 3
Muscle B

lf = 1
Af
Muscle B
pinnate-fibered

Vactive

Figure 2.9 Muscle pinnation, fiber length and recruitment of fibers influence force generation and energetic costs. In this drawing of a wallaby
leg, the hamstrings are parallel-fibered with long fiber lengths (lf) and the gastrocnemius and plantaris (calf muscles) are pinnate with short fiber
lengths. Long-fibered muscles (Muscle A; from a parallel-fibered muscle) require a greater activated volume (Vactive) than short-fibered muscles
(Muscle B; from a pinnate muscle), given the same cross-sectional area of recruited fibers (Af). In the example shown, because Muscle A has fiber
lengths (lf) that are three times longer than Muscle B, Muscle A requires a three-fold greater active volume and cost for the same cross-sectional
area of fiber activation as in Muscle B. Thus, muscles with shorter fibers can achieve greater force economy.
 M U S C L E S A N D S K E L E TO N S 27

and three times the number of cross-bridges. Con­ such as tendons, apodemes and ligaments, help to
sequently, given that both muscles contract under stabilize the joints and link muscles to the skeleton.
similar conditions, the cost to generate a given force In this section, we consider the three major c­ ategories
will be three times as great in the longer fibered of skeletons and the role of muscle attachment for
muscle. As we’ll see, this simple effect of muscle varying locomotor output.
geometry on ATP utilization can have profound
effects on the energy use of a muscle and its role in
locomotor function. 2.10 The connection between muscle
Pinnate fiber architecture offers an additional
and skeleton
level of control because pinnation angles may change
during a contraction affecting the force and short- To transmit forces, muscles must connect to the
ening velocity of the muscle as a whole (Azizi skeleton. Vertebrates and arthropods use tendons
et al., 2008). For example, in turkey gastrocnemius and apodemes, respectively, to transmit muscle forces
muscles that are activated to achieve high velocity to the skeleton. Tendons not only attach m ­ uscle and
muscle contractions at the fiber level, the muscle skeletons, they also serve as an ­important part of
changes shape to increase overall muscle velocity energy storage and release. Tendons and apodemes
rather than muscle force. Specifically, as the muscle can function as highly ­resilient springs (Fig. 2.10),
contracts, its pinnation angle increases which simul- returning up to 93 percent of the energy that is stored
taneously reduces force transmission, but enhances when stretched. The slight loss of energy (7 percent),
the overall velocity output of the muscle. By con- reflected by the “hysteresis” in the loading versus
trast, at high forces, the pinnation angle decreases unloading behavior of tendon is not uncommon for
such that the fiber’s force vector is directed more in many tissues and reflects the fact that tendons dis-
line with the muscle’s action, increasing overall play both viscous (energy lost) and elastic (energy
muscle force output, but at the expense of overall recovered) properties.
muscle velocity. This phenomenon is referred to as In addition to losing some energy when unloaded,
“variable gearing,” and demonstrates that muscles tendon also exhibits “non-linear” stress-strain behav-
can enhance or offset the underlying force-velocity ior, having a characteristic “J”-shaped curve. At
tradeoffs of their fibers at the myofibril level by low stresses, the “toe” region of the curve has a
shifting the force vectors arising from the dynamic- low slope. As stress increases, the slope increases
ally changing pinnate muscle fiber angles. until it becomes relatively constant at moderate to
higher stresses (and strains). The change from low
to higher stiffness (or modulus) results from the
sliding and re-alignment of collagen fibrils within
2.9 Skeletons
the tendon at low stresses, which are then pulled on
Locomotion requires effective transmission of directly when the tendon’s stiffness increases. The
­internal muscle forces to the external environment. toe region is fairly small; above a strain of about
In unicellular and multicellular animals, this is two to three percent, the slope of the tendon’s
accomplished by having a combination of rigid stress–strain curve can be considered nearly con-
compression-resistant and flexible tension-resistant stant. Over this linear range of behavior, tendon has
elements. Multicellular animals possess three types an elastic modulus of about 1.2 GPa. Tendon rup-
of skeletons: endoskeletons, exoskeletons and hydro- tures at stresses in the range of 100–120 MPa, indi-
static skeletons. Endoskeletons and e­ xoskeletons cating a failure strain of about 10 percent. Based on
transmit force using rigid materials that deform measurements of tendon stresses in running verte-
minimally. Hydrostatic skeletons use liquid as an brates, maximal tendon strain ranges from ~5 to 6
incompressible skeletal component and, less-com- percent.
monly, pneumo-hydrostatic skeletons use a com- The non-linear and slightly viscoelastic behavior
bination of liquid and gas (found in terrestrial of the tendon contrasts with the linearly elastic
crabs) (Taylor and Kier, 2006). Tensile ­elements, behavior that was used to provide a simple overview
28 A N I M A L L O C O M OT I O N

100

Tendon

Stress (MPa) 50 Loading

Energy lost
(∼7%)
Unloading

4 8
Strain (%)

Figure 2.10 The stress-strain curve of vertebrate tendon illustrates the hysteresis that occurs between loading and unloading. The area within
the hysteresis loop (white) reflects the energy that is lost as heat due to the viscous properties of the tendon. For vertebrate tendons, hysteresis is
as low as 7%. The remaining area (shaded) represents the energy that is recovered elastically (93% of energy used to stretch the tendon) and that
can be used to offset muscle work. Although tendon is less stiff at lower stresses, its overall properties are well-suited to function as an effective
spring for energy recovery. Most tendons operate at strains up to about 5–6%.

and comparison of the properties of various bio- allowing the shark to transmit force p ­ osteriorly
logical materials introduced in Chapter 1. Never­ with a large mechanical advantage to bend its body
theless, the tendon is stiff (1.2 GPa) and highly and ultimately its tail (Wainwright et al., 1978). In
resilient (93 percent) over much of its functional tunas, well-developed lateral tendons emanate from
range, making it an excellent material for storing the axial muscles to attach to the tail. The presence of
and recovering elastic strain energy. This cycling of these large tendons is strong evidence that they
elastic strain energy reduces the mechanical work transmit significant forces and ­corresponds with the
and the metabolic cost of locomotion. A reasonable dominant use of caudal fin propulsion. Recordings
estimate for the strain energy recovery of vertebrate of forces from these tendons confirm their role in
tendons is: 0.5 F∆L × 0.93 , or 0.465 F ΔL (where F is powering oscillation of the tail (Knower et al., 1999).
the maximum force transmitted by the tendon and The complex arrangement of fish axial muscles and
ΔL is its total change in length). Variation in tendon the many connective tissue and skeletal components
and apodeme stiffness allows tuning to the dur- to which they attach makes their study a fascinating
ation of muscle force development during elastic and ongoing challenge.
energy storage, as has been demonstrated in grass-
hoppers and bullfrogs that store elastic energy in
2.11 Vertebrate endoskeletons
their springs over short and long durations, respect­
ively (Rosario et al., 2016). Internal bony elements comprise the skeletons of
The consequences of muscle-skeleton connections vertebrates. Except for certain elements of the skull,
have also been intensively studied in fish. Forces the skeleton first develops and grows as cartilaginous
developed by the axial muscles (myomeres) of fish elements that later ossify by means of calcification
are anchored by or transmitted to the vertebral col- of the cartilage and subsequent mineralization of
umn and to the tail. In sharks, a cross-fibered array collagen (a process known as “endochondral ossifi-
of collagen fibers beneath the skin is also used as an cation”). The bones of mature animals are compos-
“external body tendon” to which the muscles attach, ites—consisting of two or more materials—generally
 M U S C L E S A N D S K E L E TO N S 29

(a) (b)
E

Bone
Bone mechanical properties

Wf S

Shell Cuticle

Stress
Cartilage

62 67 72 Strain
Percentage mineralization

Figure 2.11 Mineralization and stress-strain curves vary across skeletal materials. (a) Bone properties (S, strength, or maximum stress; E, elastic
modulus, or stiffness; and W f , work of fracture) vary as a function of bone mineralization (modified from Currey, 1984). (b) The stress-strain
behavior of various skeletal tissues varies dramatically and matches the mechanical function of the skeletal tissue in support and energy flow.

two-thirds mineral (hydroxyapatite) and one-third ials, such as cartilage, absorb energy by undergoing
type I collagen. The mineral phase of bone is a considerable deformation (Fig. 2.11b). However, as
hydrated calcium phosphate salt secreted by bone a consequence, they are not rigid enough to func-
cells, which crystallizes and grows on the type I col- tion effectively for force transmission as a lever or
lagen fibers that these cells also deposit into the over long distances. Consequently, bone appears
extracellular matrix. As the collagen becomes min- to have evolved a level of mineralization that
eralized, the bone’s stiffness (ratio of load versus ­enables it to meet these competing requirements.
deformation, see Chapter 1) increases. One interesting exception is the calcified cartilage
Increased mineralization of a bone increases its that secondarily evolved within elasmobranchs
stiffness and makes it stronger, but this diminishes (sharks and rays), and provides an alternative solu-
its ability to absorb the energy of impact loads tion for a rigid vertebrate endoskeleton. As a rela-
(making it more brittle). Mineralization levels for tively thin tissue layer at the articular end of a bone,
a diversity of limb bones occupy a fairly narrow cartilage functions well to absorb energy and distrib-
range (63–70 percent), suggesting that this tradeoff ute loads transmitted across a joint. The c­ artilage
between stiffness, strength and energy absorption is found in synovial joints (which represent most of
important (Currey, 1984; Fig. 2.11a). Consequently, the mobile joints of the vertebrate body) also pro-
bone is a rigid supportive material providing stiff- vides excellent lubrication through the synovial
ness to transmit forces effectively, yet is capable of fluid that is secreted into the joint cavity, taken up
deforming sufficiently (<1 percent) so that it can by the cartilage, and squeezed into a low-friction film
absorb a substantial amount of energy before failing between the load-bearing surfaces of the articular
(Fig. 2.11b). Interestingly, distal wing bones of bats ends of the bones.
have mineralization as low as 60 percent, suggest- While bone fracture and tendon rupture do occur,
ing a potential role of wing flexibility in flight they are relatively rare events. Failure of important
(Papadimitriou et al., 1996; Swartz and Konow, skeletal elements likely poses a significant biological
2015). In contrast, highly brittle materials like glass cost to an animal’s fitness. This cost is successfully
are often strong, but easily break: they have a high avoided by the evolution of material and structural
failure stress, but absorb little energy due to their properties that are sufficient for a skeleton to bear the
extremely high modulus. More compliant mater- loads normally applied during an animal’s lifetime.
30 A N I M A L L O C O M OT I O N

As a result, skeletons operate with safety margins— failing (Fig. 2.11b). Joints within the exoskeleton are
strengths that exceed their maximum likely loads achieved by hinged articulations between adjacent
by as much as three to fivefold, or even greater. In rigid cuticle elements with flexible (untanned) c­ uticle
addition to the large size range of growth that they lying over the joint to allow movement.
allow, a distinct advantage of bony endoskeletons is The calcium carbonate shells of bivalve mollusks,
their ability to be repaired, so that fracture need not due to their absence of a significant organic compo-
incur a permanent and likely fatal cost (Currey, nent, are extremely stiff and fairly brittle (Fig. 2.11b).
1984). The extremely hard skeletal surface conferred by
calcium carbonate enhances the resistance to damage
by boring organisms common in aquatic environ-
2.12 Invertebrate exoskeletons
ments. However, mollusks still must resist impact
The invertebrate exoskeleton necessitates internal and crushing loads from predators and intense
attachment of muscles and apodemes. By contain- wave-action in intertidal habitats. When the shells
ing the soft tissues inside, exoskeletons have the are used for locomotion, as in scallops, the shells
advantage of providing good protection and, in the articulate by a simple hinge joint at their base allow-
case of terrestrial animals, resistance to desiccation. ing them to be clapped together to expel water out
On the other hand, exoskeletons severely limit the of the animal’s mantle cavity (see Chapter 5).
animal’s growth and are susceptible to damage
on their exterior surface. Wounded arthropods can
perform minimal repairs to the exoskeleton; major
2.13 Hydrostatic skeletons
fractures necessitate molting (shedding) of the old
exoskeleton and growth of new exoskeleton. To per- Hydrostatic skeletons are the most widely distrib-
mit growth, arthropod exoskeletons must be shed uted types of skeleton in the animal kingdom (espe-
at regular intervals. The calcium carbonate shells of cially prevalent in cnidarians, worms, spiders and
bivalve molluscs and brachiopods grow by accre- mollusks) and form important components within
tion at the border of the shell. Growth in size of the endo- and exoskeletons of other animals as well.
­molluscan soft parts is facilitated by shells with For example, hydrostatic compressive support is
geometries (cone, hemi-ellipsoid) that allow an im­portant to single-celled organisms, against which
increase in size while maintaining a similar shape arrays of actin filaments and microtubules can act to
(isometry). transmit tensile forces. In vertebrates, the articular
The cuticle of arthropod exoskeletons, like bone, discs present between the vertebrae represent hydro-
is also a composite material. Most arthropod exo- static components that are effective in resisting com-
skeletons contain approximately 15–20 percent stiff pressive loads transmitted between the vertebrae.
polysaccharide chitin fibers (similar in structure Most commonly, a hydrostatic skeleton is formed
to cellulose) embedded in a protein matrix. Within by a pressurized fluid-filled body cavity that is
crustaceans, additional stiffness is achieved by the surrounded by a tension-resisting, fiber-reinforced
incorporation of calcium carbonate. The cuticle of skin, or wall. In the case of vertebrate articular discs,
most exoskeletons, however, is stiffened mainly the annulus of the disc has collagen fibers arranged
by “tanning” (sclerotization), a process in which in layers that resist the gel-like nucleus pulposus
the cuticle matrix proteins become cross-linked by contained inside. The hydrostatic ­skeletons of cnidar-
­quinones and dehydrated to provide stiff reinforce­ ians, worms and other animals that must rely on
ment of the chitin fibers. The chitin fibers are bonded their skeleton for movement as well as support. The
to each other in cross-ply layers, much like ply- walls of these hydrostatic skeletons are typically made
wood. In apodemes, the chitin fibers lie parallel to of fiber-reinforced layers and two sets of antagonis-
each other similar to the organization of collagen tic muscles (e.g. circular and longitudinal).
fibers in vertebrate tendons. Tanned cuticle has Because liquid is incompressible, hydrostatic
approximately half the stiffness and strength of skeletons transmit the forces developed by the ani-
bone, but, as a result, absorbs more energy before mal’s muscles to enable changes of body shape and
 M U S C L E S A N D S K E L E TO N S 31

(a) (b) (c)

Knee extensor
agonists

Knee flexor
antagonist

Ankle extensor
agonists F
F r = G R = T’
Ankle flexor
antagonist ds ds = r dθ
r
G r
Ankle joint R R
dθ
dL

(d) (e) (f)

ds ds
r/ G/ r/ R r
2 R 2 2
dθ dθ
dL /
2
dL

Figure 2.12 Muscle attachment location influences skeletal output. (a) Organization of muscle agonists and muscle antagonists within a
vertebrate limb. (b) Schematic diagram showing the torque (T ´, or moment) balance of an extensor muscle force (F ) relative to the ground reaction
force (G) at the ankle joint, which depends on the mechanical advantage, or moment arms (r and R), of each force vector. This torque balance
ignores torques due to segment inertia and weight, which are quite small in relation to the torque produced by the ground reaction force (G)
during limb support. (c) The mechanical advantage, or “in-lever”, of a muscle affects joint motion and limb displacement (dL). Angular motion (dθ)
of a distal segment (in this case, the foot) depends on muscle shortening (ds) in relation to its moment arm (r). (d) The torque that a muscle (ankle
extensor) can produce is reduced in half when its moment arm is reduced by 50% (i.e., the muscle acts closer to the joint). (e) However, by acting
more closely to the joint, or with a shorter “in-lever” (moment arm = r/2), shortening of the muscle (ds) produces twice the range of motion (and a
twofold increase in joint velocity). (f) With a shorter “out-lever” (defined as the length of the distal segment, or foot, in this case), the range of
motion is reduced for a given joint angle displacement compared with (c) above. These differences in muscle mechanical advantage reflect a
fundamental tradeoff between force (or torque) and velocity of movement, as well as the range of motion that a muscle can produce. This affects
locomotor performance and how muscles are arranged with respect to the skeletons of animals.

locomotor movement. Consequently, animals that 2.14 Skeletons as jointed lever systems
have hydrostatic skeletons do not depend on the
rigid mechanics of force transmission that are char- In animals with rigid skeletons, muscles produce
acterized by animals with endo- and exoskeletons. movement and transmit force by developing tor-
In most instances, locomotion is slow and non-­ ques (or moments) at specific joints. Because mus-
dramatic. However, spiders use a hydraulic system cles can only generate tensile (pulling) forces,
to rapidly move their legs. Similarly, high ­performance reciprocal movements of appendages (e.g. flexion
jetting locomotion has evolved within certain ceph- and extension of a joint) require the action of oppos-
alopod molluscs (squid) that use hydrostatic pres- ing, or antagonistic sets of muscles (Fig. 2.12a). As
sure developed within their mantle cavity to move already noted, this is also true for animals with
at high speeds (see Chapter 5). hydrostatic skeletons. In some animals, a single
muscle may power locomotion, but the muscle is
32 A N I M A L L O C O M OT I O N

always associated with a passive elastic element (in While these geometric force-displacement rela-
the case of scallops, an abductin pad) that acts as the tionships offer an excellent starting point for
muscle’s antagonist by storing elastic strain energy ­interpreting musculoskeletal dynamics, these rela-
when the muscle contracts and restoring this energy tionships can shift dramatically when the loading
when the muscle relaxes to produce the reciprocal regime changes either in terms of muscle dynamics
motion of the skeleton. or environmental forces acting back onto the skeleton.
The joint torque (T´, or moment) developed by a When realistic environmental loads are imposed on
muscle (Fig. 2.12b) depends on its force (F) and its these systems, the force-displacement relationships
mechanical advantage, or moment arm (r): are less clear-cut. For example, in a spring-loaded
locust jump, when spring-mass dynamics are
T ′ = Fr (2.3) included, the leg velocity is actually independent of
the system’s mechanical advantage. Similarly, in the
Correspondingly, muscle shortening (ds) can be
rapidly rotating mantis shrimp’s appendage with
related to joint displacement (Fig. 2.12d) by the fol-
mechanical advantage geared for speed, the drag
lowing relationship:
forces impose such a large cost that the long out-
ds = r dθ (2.4) lever actually reduces the output velocity (McHenry
et al., 2012).
or, The fiber architecture of muscles is often related
ds / dt = r dθ / dt (2.5) to their mechanical advantage and organization
within a limb. Muscles that attach further from a
for velocity, where dθ is the change in joint angle joint’s rotational axis typically have longer fibers.
measured in radians (1 radian = 180 / π ) . Equations This enables them to maintain a fractional shorten-
2.4 and 2.5 are approximations, but they hold well ing range similar to that of muscles with shorter
for small angles (<0.5 rad). Attachment further ­fibers that act closer to the joint. This is advanta-
from the joint’s center of rotation increases a mus- geous due to the force-length property of striated
cle’s mechanical advantage, but increases the dis- muscle fibers (Fig. 2.3). An animal can achieve
tance that a muscle must shorten to produce a given ­muscle gearing, much like the transmission of an
angular displacement of the joint. Consequently, the automobile, through muscle action at different loca-
torque that a muscle can develop varies inversely with tions relative to a joint. A close attachment to the
the range of joint motion that it can produce. joint provides a high gear for fast, but less forceful
The mechanical advantage of the limb shown in movements (Fig. 2.12d and e). Action further away
Figure 2.12b is twice that of the limb in Figure 2.12c, from the joint offers a low gear for slower, more
allowing it to develop twice the force against the forceful movement (Fig. 2.12b and c). Muscles that
ground (G) for a given extensor muscle force. However, act in concert to produce a similar joint movement
the angular excursion of the foot is 50 percent less are termed “agonists” or “synergists” and are opposed
(Fig. 2.12d versus 2.12e). The length of the s­keletal by an antagonist muscle or muscle group.
segment to which a muscle or its tendon attaches also The range of motion at a joint is largely dictated
affects its relative mechanical and displacement by the shape of the joint. Many exoskeletal and
advantage for generating force and movement at the some endoskeletal joints are hinged, single degree
end of the segment. The longer the distal skeletal seg- of freedom joints, which means that rotation can
ment (Fig. 2.12d versus 2.12f), the greater the range of occur only about a single axis (these joints have two
movement achieved for a given angular displace- sets of muscle antagonists: flexors and extensors).
ment of the joint or range of muscle shortening. Thus, However, there is a considerable diversity of joints
as will become evident in subsequent chapters, the beyond this most simple arrangement. Exoskeletal
mechanical organization of muscles in relation to an and vertebrate endoskeletal joints range from hinged,
animal’s skeleton greatly influences how animals single degree of freedom joints to ball-and-socket
adjust to the effects of size, their locomotor kine- joints in which rotation can occur about three inde-
matics, and their ability to accelerate and maneuver. pendent axes. With a greater range of motion, the
 M U S C L E S A N D S K E L E TO N S 33

number of antagonist muscle pairs required to tral e­ xperimental technique for calculating the posi-
produce and control reciprocal joint motion is often tive and negative work that can be generated by a
increased. Invertebrate joint diversity is found in muscle as it undergoes time-varying patterns of
­
mouthparts, antennae and locomotor appendages. length and force in relation to activation, and this
In the vertebrates, multi-axial joint motion is char- has led to a recent focus on the incorporation of
acteristic of more proximal joints (the shoulder and realistic ­environmental forces when determining
hip joints), whereas distal limb joints are more the work, power and efficiency of a muscle in more
restrictive (1° and 2° of freedom) in their potential natural contexts. Additional control of motor output
range of motion. Perhaps these joint restrictions is achieved through innerv­ation of single or mul-
allow distal segments to be lighter (fewer sets of tiple muscle fibers, called motor units. Their pattern
antagonistic muscles are required to control joint of recruitment strongly influences the mechanical
motion) and more easily controlled by the nervous output of the muscle as well as its aerobic and
system (Chapter 8). anaerobic capacity. Fiber architecture affects the
force, velocity and work of locomoting animals.
Hydrostatic s­ keletons, exoskeletons and endoskel-
2.15 Summary
etons interface with muscles to achieve a great
Starting with the fundamental molecules of muscle diversity of locomotor systems. Forces are trans-
contraction and building up to the arrangements of mitted through liquid, as well as stiffer materials,
muscle attachments on a diversity of skeletons, it is such as bone, chitin and the ceramic shells of
clear that muscles influence locomotor output at molluscs. Any analysis of the remarkable loco-
­
many scales and contexts. Velocity, force, length, motor capabilities of animals necessarily returns to
work, and power dominated this discussion of the these fundamental building blocks of muscles and
role of muscle in locomotor systems, and each of skeletons.
these aspects emerge at multiple levels of organiza-
tion. Actin and myosin arrangements, numbers and
activation determine force and velocity output at Additional reading
the molecular scale. The size, number and arrange- Ahn, A. N. (2012). How muscles function—the work loop
ment of sarcomeres within muscle fibers determine technique. J. Exp. Biol. 215(7), 1051–2.
the distance and force of contractions. By serially Azizi, E., Brainerd, E. L. and Roberts, T. J. (2008). Variable
adjusting the length of a muscle during a sequence gearing in pennate muscles. Proc. Natl. Acad. Sci. USA
of isometric contractions, the canonical force-length 105(5), 1745–50.
Gordon, A. M., Huxley, A. F. and Julian, F. J. (1966). The
curve of muscle output is determined. Similarly, by
­variation in isometric tension with sarcomere length in
serially adjusting the force of a muscle during a
vertebrate muscle fibres. J. Physiol. 184, 170–92.
sequence of isotonic contractions, the canonical force- Kier, W. M. (2012). The diversity of hydrostatic skeletons.
velocity curve emerges that informs the potential J. Exp. Biol. 215(8), 1247–57.
peak-power output of a muscle. Combining these Vincent, J. (2012). Structural Biomaterials: 3rd Edition.
two approaches, muscle work loops serve as a cen- Princeton, NJ: Princeton University Press.
 CH A PT ER 3

Energetics of Locomotion

Locomotion represents one of the most important against gravity dominates the cost of moving on land
components of the energy budget of most animals. and through air, overcoming resistive forces of drag
Whether movement is rapid and brief, as when a strongly affects the energy cost of movement through
lizard escapes from a predator into its burrow, or water and air. Physical differences of land, water and
more prolonged, as when a bird or an African ante- air also affect how energy use changes with the speed
lope migrates hundreds of kilometers, the energetic of movement. Finally, we will consider locomotor
cost of movement strongly influences survival strategies and mechanisms by which animals may
and reproduction. In this chapter, we focus on how avoid fatigue to achieve increased endurance capacity.
energy metabolism and the cost of locomotion vary
in terms of speed and body size; these two variables
3.1 Linking cellular metabolism to
exert the strongest influence on how much energy
an animal uses to move. locomotor energetics
The energetic cost of terrestrial locomotion, which All animals produce ATP by means of either anaerobic
has been best studied, will be examined in detail (absence of O2) or aerobic metabolic pathways. ATP is
first and related to the fuel sources that animals rely the ultimate currency for converting chemical energy
on to generate adenosine triphosphate (ATP). These (7.3 kcal/mole) into mechanical work (whether for
fuel sources influence patterns of energy use over muscle contraction or for membrane transport of
time and, in part, determine an animal’s capacity for ions and other compounds). Enzymes that catalyze
sustainable aerobic metabolism. Animals that sus- the splitting of ATP are “ATPases.” In muscle cells,
tain high levels of aerobic metabolism have great myosin (-ATPase) catalyzes the splitting of ATP to
endurance capacity, and can maintain warm body convert chemical energy for force generation and
temperatures while operating over a broad range of length change at the level of individual cross-bridges.
thermal niches. We will see that patterns of energy As discussed in Chapter 2, fast-twitch fibers that gen-
use and an animal’s aerobic capacity are closely erate force rapidly have high myosin-ATPase rates,
linked to its thermoregulatory strategy. Patterns of whereas slow-twitch fibers have slow rates.
energy use across terrestrial gaits, sloped substrates Aerobic metabolism allows animals to sustain
and level ground will also be considered, together activity (repeated muscle contractions) over longer
with models that have been proposed to explain the periods of time without becoming fatigued. Although
basis for observed scaling patterns of energy use anaerobic metabolism provides a rapid supply of
with body size and speed. ATP to initiate activity or to facilitate rapid move-
The energetic cost of terrestrial locomotion will then ments, the generation of lactate as an end-product
be compared with the energetics of swimming and of anaerobic metabolism inevitably leads to meta-
flight. Whereas the support of an animal’s weight bolic acidosis (reduced pH of the cells and interstitial

Animal Locomotion. Second Edition. Andrew A. Biewener & Sheila N. Patek, Oxford University Press (2018).
© Andrew A. Biewener & Sheila N. Patek 2018. DOI: 10.1093/oso/ 9780198743156.001.0001
 E N E R G E T I C S O F L O C O M OT I O N 35

fluids) and fatigue. Consequently, activities that that it consumes per unit time (defined as its rate of
.
rely on anaerobic metabolism are “non-sustainable.” oxygen consumption, or Vo2 ). Alternatively, the
Ulti­mately, anaerobic products must be re-converted amount of carbon dioxide that an animal produces
or broken down by aerobic pathways, requiring a can be measured. Both methods assume a 1:1
“recovery period,” during which an animal is largely molar equivalence of O2 consumption and CO2
inactive. ATP production by both anaerobic and aer- production, which is expected for carbohydrate
obic pathways is therefore important and influen­ces ­metabolism. Under these conditions, the animal’s
how animals regulate their activity over time. respiratory quotient (RQ), defined as the ratio
. .
Because an animal’s net energy and pH balance Vco2 / Vo2 is expected to be one. When fat or pro-
­ultimately depends on the use of oxygen to support tein metabolism occurs, the RQ is decreased (RQ for
aerobic metabolism, measuring an animal’s oxygen fat = 0.71 and for protein = 0.81 ). Consequently,
consumption represents a key method for studying the relative importance of fat versus carbohydrate
the time-course and magnitude of energy use for oxidation can be inferred by the degree to which RQ
differing activities. falls below one (under most circumstances protein
The principal fuel sources of most animals are oxidation for energy can be assumed to be zero),
­carbohydrates (sugars and starches) and fats. Whereas although certain migrating birds may metabolize
the energy yield per weight of carbohydrate (4.2 kcal significant muscle protein to fuel the end-stages of
g−1) is ~45% that of fat (9.4 kcal g−1), both provide their flight (Schwilch et al., 2002). Because 4.7–5.0
similar energy relative to the amount of oxygen kcal are produced for each liter of oxygen that is
required for their oxidation (carbohydrate: 5.0 kcal/L consumed to burn carbohydrate or fat as a fuel, and
O2 and fat: 4.7 kcal/L O2). Importantly, because fat given 1 kcal = 4.184 kJ , 20.1 kJ of ATP are produced
yields more energy per weight, it provides the most for each liter of oxygen consumed (or 20.1 J/ml O2).
efficient storage for long-term energy needs. Hence, Measurements of oxygen consumption or carbon
fat is commonly stored and used for activities such dioxide production depend on an animal being
as migration and hibernation. Its disadvantage, com- at “steady-state,” which requires no change in
pared with carbohydrate, is that fat is slower to ­metabolic status and activity intensity. Although the
­mobilize from adipose storage sites within the body. time-lags between the onset of activity and cellular
It can be mobilized more quickly when stored as lipid metabolism required to meet the demand for energy
droplets within the cell itself. Birds and other animals (a few seconds) and between cellular metabolism
have relatively high levels of lipid within their muscle and the elevation of respiratory and cardiovascular
cells, reflecting their ability to burn fat more readily gas transport processes (a few more seconds) are
than the muscles of other animals, such as humans. In short, the lag between the animal’s gas exchange sta-
general, carbohydrate is utilized first by most animals tus and the time when a stable O2 or CO2 content can
to initiate the production of ATP (following the initial be reliably measured by a gas analyzer is ­considerably
use of high-energy phosphate stores in muscle cells, longer (many seconds to minutes). Consequently,
such as creatine phosphate). Animals that specialize respirometry measurements of animal metabolism
in the economical use of fat for long-term energy sup- require a certain period of steady activity by the
ply, such as migratory birds, have evolved special- animal in order to obtain reliable measurements of
ized proteins (adipose binding proteins) to facilitate steady-state energy use. This time lag can be decreased
the breakdown and transport of fatty acids from adi- by reducing the length and size of tubing connecting
pose storage sites for fatty acid oxidation in the liver. the chamber or mask to the gas analyzer or by increas-
ing the flow rate of sampled gas.

3.1.1 Quantifying energy use: respirometry

measurements of oxygen consumption or 3.2 Sources and time course of energy
carbon dioxide production usage during exercise
The steady-state metabolism of an animal can be When an animal begins to move or alters its activity
measured by quantifying the amount of oxygen level, a lag exists between changes in the immediate
36 A N I M A L L O C O M OT I O N

Immediate demand

ATP
(Steady state)
PCr
Oxidative
Glycolysis
phosphorylation

Energy

Time

Figure 3.1 The energetic demand in muscle cells (gray dashed line) is supplied by different compounds, depending on the duration of the
activity. When an animal begins to exercise, ATP and phosphocreatine (PCr) provide energy. Subsequently, increased anaerobic ATP synthesis is
generated by glycolysis. Increased aerobic ATP synthesis then occurs via oxidative phosphorylation until a steady state of aerobic metabolism is
reached as exercise continues.

demand for ATP by its muscles and the time required can be thought of as representing an “oxygen deficit,”
to supply ATP by cellular metabolism (Fig. 3.1). To during which some lactate is produced. As the
meet the immediate demand for ATP, a high-energy ­animal’s total demand for energy is increasingly
phosphate pool resides within skeletal (and cardiac) met by aerobic synthesis, ATP supply by anaerobic
muscle cells. In most animals, this is creatine phos- glycolysis diminishes. As long as the energy demand
phate, or phosphocreatine (PCr), which supplies for a given level of exercise is within the aerobic
high-energy Pi to rapidly convert ADP into ATP, limit of the animal, subsequent ATP production is
allowing time for the activation of glycolysis to achieved by aerobic ­metabolism. At this point, the
anaerobically generate additional ATP. Many inver- animal can be considered to be in steady state aerobic
tebrates also store arginine phosphate in their mus- metabolism, during which its aerobic metabolic rate
cles to supplement PCr. Anaerobic production of can be reliably measured.
ATP continues until oxygen delivery and aerobic Once the animal ceases activity and returns to a
ATP synthesis in the mitochondria can be increased resting state, it begins to “pay back” this deficit
to meet the total demand for energy. Oxygen trans- (Fig. 3.2a). As with the onset of ATP demand when
port to mitochondria depends on a multi-step pro- exercise commences, ATP demand immediately
cess that is initiated with increased oxygen uptake by declines to a resting level once the exercise bout
the respiratory system. In vertebrates, this is linked ends. Nevertheless, an animal’s metabolic rate
in series with bulk transport of oxygen by the cardio- re­mains elevated for some period of time after
vascular system to the muscle cells and other tissues, activity ends, gradually declining to a resting level.
and subsequent diffusion to the mitochondria. The This elevated post-exercise oxygen metabolism, or
capacity for oxygen delivery at each of these steps is “oxygen debt,” reflects the need for ­aerobic syn-
functionally linked to an animal’s aerobic capacity thesis of ATP to regenerate the PCr pool that was
(Weibel et al., 1981). In insects, a tracheal system depleted at the onset of activity, as well as the need
allows oxygen to diffuse directly to metabolizing to convert lactate back to pyruvate. Lactate can be
cells, which may be assisted by ventilation. converted back to pyruvate when sufficient oxy-
gen is available, which is then oxidized by means
of the Krebs cycle and oxidative phosphorylation.
3.2.1 Oxygen deficit, post-exercise oxygen
It also allows other metabolic intermediates to be
recovery, and steady state metabolism
re-established to their pre-exercise levels. This pat-
The initial supply of ATP from PCr and anaerobic tern of metabolism and energy use is simple to
glycolysis resulting from the lag in aerobic m
­ etabolism verify. After taking a jog, a person’s heart rate
 E N E R G E T I C S O F L O C O M OT I O N 37

(a)
VO2 steady state oxygen
O2 deficit

Energy demand
consumption

O2 debt

Rest
Start End
Time
(b) (c)
Non-sustained burst exercise
Endurance exercise (endotherms)
Energy demand

Energy demand
(ectotherms)

O2 debt O2 debt
small large/prolonged
Rest Rest
Start End Start End
Time Time

Figure 3.2 The capacity for aerobic versus anaerobic energy supply during exercise varies with exercise intensity and thermoregulatory
strategy. (a) The delay in aerobic energy supply relative to energy demand at the start of exercise results in an “O2-deficit” at the onset of
exercise (denoted by gray shading), which ends once the animal reaches a steady state level of aerobic metabolism (V̇o2). This is “paid back” as
the “O2-debt” at the end of exercise. This elevated post-exercise oxygen consumption reflects the need to re-metabolize the lactate produced by
early glycolysis to meet the more immediate demand for energy, as well as to re-establish resting levels of other metabolites, including
phosphocreatine (see Fig. 3.1). (b) By sustaining higher levels of aerobic metabolism, endothermic animals are capable of endurance exercise
over longer periods of time, compared with (c) ectothermic species that generally have limited aerobic capacity for sustainable exercise. Gray
lines in each graph denote the energy demand for exercise versus time. Whereas the oxygen deficit incurred by more aerobic (and typically
endothermic) species is small, ectothermic animals that rely heavily on anaerobic ATP supply incur a large oxygen deficit, limiting their
endurance. Consequently, ectotherms are typified by brief bursts of activity interposed with longer periods of recovery metabolism.

and breathing rate remain elevated for a noticeable ing a balanced resting metabolic state is referred
period of time (often referred to as “catching one’s to as “excess post-exercise oxygen consumption”
breath”). This reflects the metabolic need for con- (EPOC) (Gaesser and Brooks, 1984). For the pur-
tinued oxygen delivery to the mitochondria to fuel poses of broader comparisons of energy supply
continued aerobic production of ATP associated ­relative to exercise intensity across animals with
with “payment” of the oxygen debt after the end differing metabolic strategies, as well as when com-
of exercise. paring more athletic versus less athletic species, it
Due to differences in the metabolic pathways is reasonable to assume that the excess amount of
used to oxidize glucose to meet the initial demand oxygen consumed during post-exercise recovery,
for energy supply and the subsequent recovery although not causal, approximately represents the
phase of metabolism to re-establish resting pools deficit in aerobic energy supply incurred at the start
of intermediate metabolites (regeneration of PCr, of exercise (Fig. 3.2a).
breakdown of lactic acid, re-synthesis of glycogen, For endothermic (birds, mammals, and flying
etc.), the areas under the curves representing the insects) and a few regionally endothermic (tuna)
“oxygen deficit” and “oxygen debt” are not neces- animals with intermediate to high aerobic capacities
sarily equal. Because of this, the period of elevated that allow for sustained activity over more ­prolonged
oxygen consumption associated with re-establish- periods of time, the oxygen deficit incurred at the
38 A N I M A L L O C O M OT I O N

onset of activity is typically a small fraction of the the post-exercise oxygen metabolism of ectothermic
total amount of energy expended over the course of species is generally much more prolonged than for
an exercise bout (Fig. 3.2b). For ectothermic species endothermic species (Fig. 3.2c). Consequently, ecto-
that depend considerably more on anaerobic energy thermic species t­ ypically utilize short bouts of exer-
supply, the oxygen deficit represents a much greater cise for foraging, escape or mating, followed by
fraction of their total energy expenditure. As a result, longer intervals of rest and recovery metabolism.

(a)
Sprint
O2 deficit

VO2max
Vo2
Energy demand

O 2 debt

Rest
Start End
Time
(b)

Endo
Aerobic energy supply

VO2max

Recovery
Ecto

Endo
Rest
Ecto
Start End
Time

Figure 3.3 An animal’s capacity for aerobic energy supply relative to energy demand determines how much of an anaerobic oxygen deficit it
incurs and how prolonged is its recovery metabolism. These patterns differ considerably for ectotherms and endotherms. (a) When exercise
intensity (energy demand) exceeds an animal’s maximum aerobic capacity, or V̇o2max , a large O2 deficit is incurred over the course of exercise that
requires a long period of recovery metabolism after exercise has ended. The ratio of V̇o2max to resting metabolic rate (rest) defines an animal’s
“factorial aerobic scope”. (b) The time-course of aerobic energy supply during exercise in an endotherm (“endo”; black line) versus a similarly-
sized ectotherm (“ecto”; gray line) parallels the difference in their resting metabolic rate (rest; when adjusted for body temperature). Although
ectotherms have a much lower maximal aerobic capacity than endotherms, both groups of animals can have similar factorial aerobic scopes,
indicating a similar capacity for elevating aerobic metabolism relative to resting rates. However, considerable variation in aerobic scope exists
within both kinds of animals.
 E N E R G E T I C S O F L O C O M OT I O N 39

3.2.2 Sustainable activity, maximum aerobic resting metabolic rate). Measurements of rheas (a
metabolism, and metabolic scope flightless bird) indicate factorial aerobic scopes
similar to dogs (Bundle et al., 1999). In general, fly-
An animal’s ability to sustain a given level of activ- ing birds have factorial aerobic scopes of about
ity requires that its metabolic demand for ATP be 10–20. Consequently, the high aerobic scope of the
met by a steady state supply of oxygen for mito- ground-dwelling rhea might, in part, reflect its evo-
chondrial oxidation. An animal’s maximum rate of
. lutionary ancestry as a flying bird.
oxygen consumption (Vo2 max ) or maximum aerobic Large aerobic scopes require high rates of respira-
capacity, therefore, sets a limit to sustainable aerobic tory gas exchange (ventilation and diffusion), cardiac
activity (Fig. 3.3a). Technically, if an animal’s demand output and mitochondrial oxidative metabolism.
for energy does not exceed its maximum aerobic Athletic humans typically have factorial aerobic scopes
capacity, it should be able to sustain that level of ranging from 20–30, but less-active humans have fac-
exercise indefinitely—at least until its primary fuel torial scopes of 15 or less. Generally, across a diverse
stores (glycogen and fat) are depleted. In practice, range of vertebrate taxa, factorial metabolic scopes in
however, an animal’s maximum s­ ustainable perform­ the range of 6–20 are observed. In a broad sense,
ance is generally achieved at about 80–85% of
. therefore, humans are a fairly aerobic species, and
its Vo2 max (this practical limit is based largely on the endurance running capacity of hominids has
data for human athletes and a few mammalian quad- been argued as a key driver of the evolution of our
rupeds). This likely reflects a number of factors that striding bipedal gait (Bramble and Lieberman, 2004).
contribute to physiological fatigue. In studies of The large number of well-trained human marathon
human runners, training not only enhances a run-
. runners attests to our species’ running ability (des-
ner’s Vo2 max , but also increases their ability to exploit
. pite an alarming number who may alternatively pre-
a greater range of their Vo2 max . This results from fer sedentary daily behaviors).
physiological adaptations of a person’s cardio- .
Even though the Vo2 max and absolute metabolic
respiratory system that enhance oxygen uptake and scope of ectothermic vertebrates are considerably
delivery to their tissues, as well as improved bio- less than those of endothermic vertebrates, ecto-
chemical oxidative capacity within their muscles for therms generally have similar factorial metabolic
ATP supply. Lowering the oxygen deficit incurred at scopes compared to endotherms (5–15) due to their
the start of exercise and limiting lactate accumula- lower resting metabolic rates. On average, resting
tion likely contributes to improved aerobic capacity.
. rates of ectotherms are roughly 3.5- to 4-fold less
As an animal approaches its Vo2 max , there is also than similarly sized endotherms when compared at
likely to be a progressive increase in anaerobic ATP the same body temperature (Fig. 3.3b). This means
synthesis in active muscle fibers causing a gradual that their maximum aerobic capacity is similarly
build-up of lactate and eventual fatigue, even though
. less. When characterizing an ectothermic animal’s
the animal may not be exercising at its Vo2 max .
. metabolism in relation to temperature effects (as may
.The ratio of an animal’s Vo2max to its resting result from migration or climate change), absolute
( Vo2 rest , or basal) metabolic rate represents an ani- metabolic scope has been argued to be a better
mal’s factorial metabolic scope; whereas, the absolute
. . measure of an ectotherm’s capacity for movement
difference between Vo2 max and Vo2 rest is an animal’s (Clark et al., 2013).
absolute metabolic scope. Aerobic species generally Perhaps not surprisingly, lungless salamanders
have evolved greater metabolic scopes than spe- that breathe through their skin have lower factorial
cies that rely more heavily upon anaerobic energy scopes (1.6- to 3.5-fold) than lunged salamanders
supply. Some of the highest factorial aerobic scopes (3.5- to 7-fold) (Full et al., 1988), indicating that
have been measured in quadrupedal mammals. cutaneous gas exchange is more limiting than lung
Dogs have factorial metabolic scopes of about 30, ventilation. Invertebrates (e.g. ants, beetles, ghost
while horses and pronghorn antelope reach 50–60
. crabs and cockroaches) also have similar factorial
(i.e. their Vo2 max is 50–60 times greater than their scopes as vertebrates (ranging from 6- to 18-fold)
40 A N I M A L L O C O M OT I O N

when compared during running. However, for insects ences in aerobic capacity do not translate into differ-
such as beetles that also fly (Rogowitz and Chappell, ences in top speed. The burst speeds of ectotherms and
2000), factorial aerobic scopes can exceed 100! Dif­ endotherms are generally similar when compared
ferences in the factorial capacity among species to at similar body temperatures and body size. This
elevate aerobic metabolism from resting rates likely reflects the fact that the capacity of skeletal muscle to
relates to differences in mitochondrial density within generate mechanical force and power is generally simi-
cells and oxygen delivery capacity. lar across diverse vertebrate and invertebrate taxa
when operating under similar conditions. With suf-
ficient ATP, the contractile capacities of endother-
3.3 Endurance and fatigue mic and ectothermic muscles for work and force are
When an animal’s demand for ATP exceeds its ­aerobic broadly similar. Hence, it is the time-course and
capacity, it must rely increasingly on anaerobic energy underlying metabolic pathways of ATP supply that
supply (Fig. 3.3a). This leads to metabolic fatigue ­determine the capacity for sustaining the muscles’
due to lactate production and decreased pH. As a operation at a given level of locomotor intensity.
result, an animal’s endurance strongly depends on Endurance and maximum sustainable activity are
its aerobic capacity. Highly aerobic species have the features that vary most in relation to thermo-
greater endurance at a given level of exercise com- regulatory strategy and aerobic capacity.
pared with less-aerobic species. This is particularly
the case when comparing endothermic birds, mam- 3.4 Energy costs across terrestrial
mals and flying insects with most ectothermic inver-
locomotor speeds
tebrates, fish, amphibians and reptiles. The evolution
of a heightened aerobic capacity afforded by endo- To run faster, animals move their limbs more rap-
thermy was likely important to the exploitation of idly and reduce the time that their feet remain in
wider thermal niches, favoring broader daily and contact with the ground (see Chapter 4, Fig. 4.2).
seasonal activity strategies, as well as the successful Because of this, an animal’s muscles must generate
invasion of more diverse terrestrial climates. On the greater forces, contract more quickly and work at
other hand, reduced rates of metabolism enable greater rates when moving at faster speeds. All of
ectotherms to achieve more economical metabolic these processes require a greater rate of metabolic
strategies. By reducing their longer-term energy energy supply. Somewhat surprisingly, the rate of
requirements, ectotherms may improve their ability energy expenditure (measured via the animal’s O2
to survive challenging environmental conditions. consumption, or CO2 production) increases linearly
Notably, winter moths have the remarkable ability with increasing speed in a diverse range of terres-
to fly at low metabolic cost with extremely low trial vertebrates and invertebrates (Fig. 3.4). This
­thoracic temperatures, which allows them to exploit also generally holds across changes of gait. The lin-
a thermal niche that is otherwise unavailable to ear increase in energy expenditure with speed is
most ectotherms (Heinrich and Mommsen, 1985). surprising, because increases in cost associated
Differences in thermoregulatory strategy thus with the kinetic energy of swinging the limbs back
strongly influence the profile of energy metabol- and forth would suggest an exponential increase
ism during exercise. Most endothermic species are with speed (∝ v2). The cost due to drag resulting
­capable of prolonged periods of sustained activity, from air resistance on the body would also be
with brief periods of recovery metabolism (Fig. 3.3b). expected to increase ∝ v2 (it is because of drag that
In contrast, most ectothermic species usually exceed automobiles suffer large increases in fuel cost at
their aerobic capacity for all but very slow speeds of higher speeds). Except when there is a stiff wind,
movement, requiring much longer periods of recov- most animals move so slowly or are sufficiently
ery. Consequently, most ectotherms generally rely on large that air resistance is generally not a significant
.
brief bouts of activity when foraging, or burst activ- factor. The linear increase in Vo2 (equivalent to
.
ity to catch prey or avoid predators. energy metabolism, Emetab ) relative to speed observed
Although endurance and movement distance are for a wide variety of legged animals indicates that
strongly affected by an animal’s aerobic capacity, differ- limb kinetic energy and drag are not as important
 E N E R G E T I C S O F L O C O M OT I O N 41

as the cost associated with the magnitude and rate of As an animal runs faster, its rate of oxygen con-
muscle force generation, and the cost of turning sumption eventually levels off, reaching a maximal
. .
muscles on and off. level (Vo2 max ). The speed at which Vo2 max is attained
The slope of the line relating energy use to running defines an animal’s maximum aerobic speed (MAS).
speed (J/s divided by m/s = J/m ) represents the Theoretically, this sets the limit for an animal’s sus-
incremental or “net” cost of transport (Cnet). Cnet is the tainable activity. Above this speed, the additional
amount of energy an animal expends to move a given energy required to move at faster speeds must be
.
distance (Cnet = [Emetab – y-intercept cost ]/ speed) , met by anaerobic ATP supply. Because anaerobic
which is the inverse of a vehicle’s fuel cost (km/liter metabolism results in the accumulation of lactate (or
of fuel). Because of the linear increase in energy cost other anaerobic end-products in the case of inverte-
with speed, the net cost of transport for a running ani- brate runners), movement that exceeds an animal’s
mal is the same at any speed. This is a rather remark- MAS results in metabolic acidosis and fatigue. As
able result. It means that the incremental amount of noted, sprint or intensive exercise of this nature requires
energy that an animal uses to run a kilometer is nearly subsequent inactivity to allow recovery from accu-
the same whether it runs at a fast or leisurely pace. mulated lactate, as well as the need for an animal to
We will explore the basis for this observation in replenish fuel reserves and re-establish resting levels
Section 3.5.1. of intermediate metabolites. Because of this, sustain-
When an animal’s oxygen consumption relative able running speeds are typically 80–85% of an indi-
to running speed is extrapolated to zero velocity, the vidual’s MAS. An increase in blood lactate levels and
y-intercept of the line is typically about 70% greater a leveling off in oxygen consumption signal that an
.
than the animal’s actual resting oxygen consumption. animal has reached its Vo2 max .
This y-intercept may be considered a “start-up” cost,
but its basis remains unclear. The total cost of trans-
. 3.4.1 Ectothermic versus endothermic
port (Ctot = Emetab / speed) reflects the “start-up” cost
and slope-related energy cost. Because of this, an
energy patterns
animal’s total cost of transport is greater at slower In Section 3.2. we discussed how an animal’s
speeds (resulting from a greater y-intercept fraction ­thermoregulatory strategy affects the time course
of total energy cost) than at higher speeds. and relative importance of aerobic versus anaerobic

Anaerobic
supply
Metabolic rate Emetab (J/s)

VO max
2

Aerobic
scope

Lactate production
BMR (equivalent energy units)
max. aerobic
Speed
speed

.
Figure 3.4 An animal’s metabolic rate (E metab , or rate of aerobic energy supply) obtained from steady state oxygen consumption (V̇o2 ) measure-
ments increases linearly with respect to locomotor speed in nearly all terrestrial species. Metabolic rate increases up to a maximal level (V̇o2max)
that determines the maximum aerobic capacity of an animal. At greater speeds, the additional demand for energy must be supplied by anaerobic
glycolysis, which leads to fatigue. The intercept of the line formed by metabolic rate (V̇o2 ) versus speed exceeds the basal metabolic rate (BMR) of
the animal.
42 A N I M A L L O C O M OT I O N

sources of energy supply to its exercising muscles. this reflects the limited aerobic capacity for sustain-
What effect does this have on ectothermic compared able exercise of most ectothermic species. Studies of
to endothermic locomotor energetics? If the loco­ salamanders, toads and other lizards (Bennett, 1978)
motor energetics of a mammal and a reptile of similar suggest a similar pattern of energy use relative to
size are compared, three things stand out (Fig. 3.5). sustainable speed as that observed for monitor liz-
First, at a comparable body temperature (37°C), a ards (Varanus spp.). These lizards were the first ani-
reptile expends less energy than a mammal at any mals used to compare reptilian locomotor energetics
given speed. Second, the speed range over which a with those of mammals. Nevertheless, there is a
reptile can sustain activity and meet its energy need to expand studies of ectothermic vertebrate
demands by aerobic metabolism is extremely limited and invertebrate taxa to test how patterns of limb
compared with a mammal. Third, the rate of increase contact time, stride length, stride frequency and
in energy metabolism with speed (slope) is the same muscle force relate to energy use in a broader range
for endotherms and ectotherms. Because an ecto- of terrestrial animals. A recent comparative study of
therm has a four-fold lower intercept, its cost of lacertid lizards showed that different species use
transport is less than a similarly sized mammal at varying patterns of stride length and stride fre-
any given speed. The lower metabolic rate, cost of quency to increase speed and that maximal sprint
transport and lower maximum aerobic speed of speed depends on microhabitat use, with more
ectotherms reflect the evolution of a more economical arboreal lizards relying on increases in stride fre-
strategy. However, it comes at the price of a more quency to increase speed (Vanhooydonck et al., 2002).
limited capacity for sustainable activity. Interestingly, However, no corresponding comparisons were made
the slope of the line relating metabolic energy of locomotor energy costs or muscle force require-
expenditure to speed is the same for similarly sized ments across these taxa. In general, most studies of
reptiles and mammals. This suggests that similar lizard locomotion have focused on maximum sprint
mechanisms underlie the change in metabolic rate speed in relation to stride length and stride fre-
relative to speed for these two groups of animals. quency, with widespread patterns observed, but
In comparison to the many studies of birds and generally have not tested these patterns against
mammals, fewer studies have been carried out on measurements of aerobic and ­anaerobic metabolic
steady exercise in amphibians and reptiles. Partly, capacity.

Endotherm
Maximum
Metabolic rate Emetab

Aerobic
Anaerobic (ecto)

Aerobic Ectotherm
Maximum

Anaerobic (endo)
MASecto Speed MASendo

Figure 3.5 A comparison of the rate of energy use (V̇o2 ) relative to running speed of a lizard (ectotherm, gray lines) and a mammal (endotherm,
black lines) of similar sizes. Both animals exhibit the same increase in (V̇o2 ) with speed, but the aerobic capacity (V̇o2 max) of the ectothermic lizard
is much more limited than the endothermic mammal. This greatly limits its maximum aerobic speed (MAS). Consequently, lizards and most other
ectotherms rely on short bursts of activity fueled by anaerobic glycolysis. This requires a long period of recovery metabolism and rest between
exercise bouts. At any given aerobic speed, the rate of energy use by the lizard is less than that of the mammal.
 E N E R G E T I C S O F L O C O M OT I O N 43

3.4.2 Kangaroo and wallaby hopping: a ity to hop at variable speeds with little change in
remarkable relationship between energy cost metabolic energy expenditure reflects the effective
and speed recovery of elastic energy in leg tendons (discussed
in Chapter 4). The energy cost associated with pro-
In contrast to the linear increase of aerobic energy ducing greater muscle force and faster contractions
use rate relative to speed that nearly all terrestrial to move at faster speeds is offset by the increase in
­animals exhibit, wallabies and kangaroos are two tendon elastic energy recovery. Wallabies and kan-
groups of moderate to large marsupials whose rate garoos hop faster by increasing their stride length
of energy use levels off when they hop and, dis- rather than their hopping frequency. A constant
tinctly from all other studied animals, does not hopping frequency also likely slows the rate of force
increase at faster speeds (Fig. 3.6a). The increase at development at faster speeds, favoring a more uni-
slow speeds reflects their pentapedal walking gait, form metabolic rate (see Section 3.5.1). The econom-
which involves the sequential use of the tail in com- ical hopping ability of kangaroos likely reflects their
bination with fore and hind limbs. Recent work need to forage over wide areas to exploit sparse
(O’Connor et al., 2014) shows that the tail provides food resources that characterize much of their arid
substantial propulsive work during walking. Al­though habitat, in addition to reducing the cost for females
pentapedal walking works well for f­oraging, hop- carrying pouch young (Baudinette and Biewener,
ping is used to move over longer distances. The abil- 1998). In contrast, the rate of energy use in smaller

(a)
Metabolic rate Emetab (J/s)

Typical mammal
Elastic
energy
savings

Kangaroos and wallabies

Twofold savings at 6 m/s

Speed

(b)

Walk Run
Cnet (J/m)

1 2 3 4 5 6
Speed (m/s)

Figure 3.6 Locomotor energy costs can be offset by the recovery of elastic energy from leg tendons in some hopping animals, whereas in other animals,
energy costs are tied to locomotor mode and gait. (a) Once a kangaroo or wallaby begins to hop, its metabolic rate does not increase at faster speeds, in
contrast to the increase observed in other terrestrial animals. This difference likely reflects their ability to store and recover substantial elastic energy in their
long leg tendons. The steep increase at low speeds reflects their less economical pentapedal walking gait. (b) The net energy cost of transport (Cnet, J/m)
versus speed is curvilinear when humans walk, with a minimum cost at an intermediate walking speed of about 1.3 m/s. The net cost of running is about
50% greater than during the minimum cost of walking, but remains fairly constant across running speeds.
44 A N I M A L L O C O M OT I O N

hopping animals (including both marsupials and cost. Third, more CM work is performed per dis-
rodents) increases with hopping speed similar to tance during running than during walking (Cavagna
other terrestrial animals of their size. This reflects, and Kaneko, 1977). However, CM work does not
in part, the inability of these smaller animals to sharply increase with a change of gait and, in con-
achieve significant energy savings due to their rela- trast to metabolic cost, CM work per unit distance
tively thick tendons (see Chapter 4). does not level off at faster running speeds.
Careful measurements of oxygen consumption
obtained from horses trained to extend their gaits
beyond normal speed ranges (Hoyt and Taylor, 1981)
3.4.3 Energy costs in the context of gait
also show that the increase in energy cost with
For most animals studied thus far, little evidence speed is not a simple linear trend across gaits
exists for a change in metabolic cost as a function (Fig. 3.8a). Instead, metabolic rate increases when a
of speed and across changes of gait. Four notable horse extends its speed beyond its normal gait
exceptions are humans, horses, kangaroo and wal- range (as, for example, when a horse trots at a
labies (the anomalies of the latter two were slower speed than it would normally walk, or when
described in the previous section). For humans it walks at a faster speed than it would normally
(Fig. 3.6b), the net metabolic cost of running is as trot). Consequently, the metabolic cost of transport
much as 50% greater than walking and does not in horses exhibits a curvilinear pattern within gaits.
change appre­ciably over a range of aerobic run- Within both a walk and a trot, a clear minimum cost
ning speeds (Margaria, 1976). On the other hand, of transport is observed (Fig. 3.8b). By changing
the cost of transport for walking varies with speed gait, horses are able to reduce their cost of transport
and has a minimum at about 1.3 m s−1, indicating so that it is maintained consistently over a broad
an optimal speed for minimizing energy use. This range of speeds. The linear increase in metabolic
minimum cost of walking speed likely derives rate with running speed observed generally for
from the use of a step length and stride frequency other animals (Fig. 3.4), and the resulting uniform
combination that reduces step-to-step energy tran- net cost of transport, suggest that gait changes in
sitions balanced against the cost of swinging the other species may serve a similar role as they do in
limbs [see Chapter 4; (Donelan et al., 2002a)]. More horses. However, because of the difficulty in docu-
.
effective body center-of-mass (CM), KE, and PE menting curvilinear relationships between Vo2 and
exchange may also contribute. speed, this has not yet been confirmed.
The reason for the increase in cost of transport When animals are allowed to select the speed at
from walking to running is less certain; however, which they move, they commonly move at an inter-
three factors are likely important. First, when chan­ mediate speed within a gait. In the case of horses
ging gait from a walk to a run, limb contact time with (Fig. 3.8c) and walking humans, this is closely asso-
the ground (tc) drops, requiring limb muscles to gen- ciated with their minimum cost speed and is often
erate force at faster rates. This can only be achieved referred to as an animal’s “preferred speed” within
by recruiting faster muscle fibers, which consume a gait. The basis for the minimum cost at preferred
energy at faster rates (increased 1/tc, Fig. 3.7a). speed observed within a particular gait for horses
Second, human limb mechanical advantage (discussed has yet to be identified. Nevertheless, there is evi-
further in Chapter 4) decreases from walking to dence that migratory animals prefer to use a rela-
running (Fig. 3.7b), due mainly to a change in knee tively narrow range of speeds within a gait when
posture during running. Whereas the knee is rela- moving long distances (Pennycuick, 1975). Studies
tively extended during walking, it is more flexed of rodents and other small animals also indicate
during running. Although this helps to absorb the that animals may select preferred speeds within
impact of the body during each footfall, it requires gaits when moving over short distances. These
increased knee extensor (quadriceps) muscle force, observations suggest that changes in gait can have
which likely contributes to an increased metabolic important energetic consequences, in addition to
 E N E R G E T I C S O F L O C O M OT I O N 45

(a) Walk Human Run

1/tc
2

0 1 2 3 4 5 6 7

(b) 1.2
Hip
EMA (r/R)

0.8

0.4

F
(c) 2.0
Knee
R
1.6
r
EMA (r/R)

1.2

0.8

0.4

G
(d) 0.8
Ankle
EMA (r/R)

0.4

0 1 2 3 4 5 6 7
Speed (m/s)

Figure 3.7 Across locomotor speeds, gait shifts are accompanied by shifts in the period of limb contact time and mechanical advantage of the
limb. (a) As in other animals, limb ground contact time (tc) decreases as humans move at faster speeds and when switching gaits (vertical gray bar),
such that 1/tc increases across the transition from a walk to a run. (b–d) The effective mechanical advantage of human limb extensors (EMA = r / R,
see Chapter 4) remains fairly uniform at different speeds within a gait, but decreases about three-fold at the knee (c) when humans change gait
from a walk to a run. The decrease in knee extensor EMA (which results from a more flexed running posture at the knee) and the corresponding
increase in 1/tc likely contribute to the increase in the energy cost of running versus walking (Fig. 3.6b).
46 A N I M A L L O C O M OT I O N

100 (a)
Walk Trot Gallop

VO2 (ml O2/s)

50

0 1 2 3 4 5 6 7

28
(b)

24

20
Cost of transport (ml O2/m)

16

(c)
Walk Trot Gallop
12 12
Number of trials

8 8

4 4

0 1 2 3 4 5 6 7
Speed (m/s)

Figure 3.8 Horses were trained to locomote at a wide range of speeds within each gait category on a treadmill to test how the costs of
transport changed across each gait. V̇o2 measurements demonstrated that (a) metabolic rate exhibits a curvilinear relationship versus speed
within a gait, and, (b) the cost of transport in horses (left y-axis) has a minimum at a particular speed within each gait because of the curvilinear
increase in energy use with speed. (c) The minimum costs of transport speeds are those that horses prefer to use when they move at self-selected
speeds over-ground, using each gait (number of trials shown on right y-axis). (Adapted from Hoyt and Taylor, 1981; with permission MacMillan
Magazines, Ltd.)
 E N E R G E T I C S O F L O C O M OT I O N 47

allowing animals to run faster. Future work evalu- (a)

ating the energetic and mechanistic basis of gait

Mass-specific metabolic cost

changes in terrestrial locomotion is needed. Mouse
Squirrel
Agouti Dog
3.5 Energy cost relative to body size

(VO2/kg)
Goat
Because of their size, larger animals expend more
energy to move than small animals. But does the Man
energetic cost of locomotion vary in proportion to Horse
an animal’s body mass? To answer this question
and compare animals of different size, the meta-
bolic cost of locomotion can be normalized by body Speed
mass to yield the animal’s mass-specific rate of oxy- (b)
gen consumption (e.g. ml O2 s−1 kg−1). This can be

cost of transport (log(VO2/kg/m))

converted to J s−1 kg−1 or W kg−1, assuming a value

(Net) Mass-specific
of 20.1 J ml−1 O2 of oxygen consumed. Doing so
reveals that smaller animals exhibit higher mass-
specific costs of transport compared with large slope = −0.32
­animals. This means that the slopes of the linear
mass-specific rate of energy use relative to running x
speed vary inversely with body size (Fig. 3.9a). For
example, it costs a mouse 20 times more energy to
move a gram of its body a given distance compared
with a dog and 30 times more energy than a horse. log (body mass)
When compared over a range of size, the scaling of
Figure 3.9 Smaller animals require a greater increase in mass-
mass-specific net cost of transport (Cnet), determined specific metabolic rate with increased speed and, as a result, have
as the slope of metabolic rate relative to running greater (mass-specific) net cost of transport than larger animals. (a)
speed in terrestrial animals, follows a general rela- Mass-specific metabolic rate (V̇o2 kg−1 increases more quickly relative
tionship (Fig. 3.9b). Cnet is proportional to BM−0.32 and to speed in small animals compared to large animals. (b) The net
mass-specific cost of transport (V̇o2 kg−1m−1) for terrestrial locomotion
appears to apply equally well to endothermic and
scales inversely (slope = –0.32) and linearly with body mass when
ectothermic vertebrate runners (Taylor et al., 1982), plotted on logarithmic coordinates (net cost kg-1 ∝ BM–0.32). The net
as well as invertebrate runners (Full, 1991). cost of transport for human runners (“X”) is slightly higher than a
A more recent analysis, however, argues that mammalian quadruped of similar size (but see Rubenson et al., 2007).
differences in locomotor limb posture must be
­
considered when analyzing how metabolic cost
­
varies with size (Reilly et al., 2007). Whereas small speed) in small-crouched versus large-erect animals
animals typically have crouched limb postures, parallel those observed for metabolic cost (Fig.
larger animals move with more erect limbs. When 3.10b). Changes in stride frequency also parallel
mass-specific metabolic data are examined more those of metabolic cost, suggesting that rates of
closely, animals smaller than 1 kg body mass with muscle force development and muscle activation-
crouched limbs show a steep (arithmetic) decrease relaxation influence how the rate of energy use
in cost relative to size, but larger (>1 kg) more erect varies with speed and size. This is explored in the
animals show a much smaller change (Fig. 3.10a). Section 3.5.1.
Although differences in muscle mechanical advan- Another re-analysis of the scaling of locomotion cost
tage and force (as discussed in Chapter 4) appear in terrestrial vertebrates shows that when the cost of
not to explain the differing metabolic cost scaling running is distinguished from the cost of walking, dif-
patterns, arithmetic differences in the scaling of ferent scaling relationships emerge (Rubenson et al.,
relative stride frequency (normalized to running 2007). When “non-locomotor” resting metabolic rates
48 A N I M A L L O C O M OT I O N

(a) Mouse
60
Crouched limbs Erect limbs
Mouse
50
Cost of locomotion (J/kg/m)

40
Squirrel
Dog Deer Horse
30

20

Genet
10 Tenrec
Horse
Total external energy of the CM (~1.1)
0
0.01 0.1 1 10 100 1000
Body mass (kg)
Stride frequency (str s–1)
Mouse

nk
Sku

(b)
g
Do

8
Mouse

Eland
6
St
Stride length (m str –1)

rid Speed
ef
re
que
nc
Slope

4 ys
lop
e
Skunk

2
Dog
Speed

Stride length slope

0
0.01 0.1 1 10 100 Eland 1000
Body mass (kg)

Figure 3.10 Size-related differences in limb posture (crouched, triangles; erect, squares) are associated with different arithmetic patterns of cost
of locomotion, as well as the slopes of stride parameters versus speed in terrestrial mammals, when compared on semi-logarithmic coordinates. (a)
Whereas the mass-specific cost of locomotion decreases arithmetically with a steep slope in crouched animals <1 kg, it changes very little in
animals >1 kg body mass. (b) Arithmetic differences in the regression slopes of stride frequency (open symbols) versus speed relationships for
small crouched (triangles) and large erect (squares) animals plotted on semi-log coordinates exhibit parallel patterns to cost of locomotion,
whereas the pattern for slopes of stride length (closed symbols) versus speed do not. (Adapted from Reilly et al., 2007; reproduced with
permission Elsevier).
 E N E R G E T I C S O F L O C O M OT I O N 49

are subtracted from the gross metabolic cost of locomotion. This largely depends on changes in
walking or running at a particular speed, the mass- stride frequency and step length across animal sizes
specific cost of walking (Cwalk ∝ BM − 0.45 ) scales with as they move at different speeds (Heglund and
a steeper negative slope than the cost of running Taylor, 1988). To increase speed, animals move their
(Crun ∝ BM − 0.34 ) . Using this “subtraction” method to limbs more rapidly, increasing their stride frequency
calculate cost of locomotion also results in slightly (as well as their stride length; Chapter 4), which
different overall scaling patterns for the earlier requires their limb muscles to contract at faster
reported scaling of net cost of locomotion (Cnet), as rates and to be turned on and off more frequently.
previously defined. This a­ nalysis re-assessed the For a given animal size, however, the time-averaged
notion that the cost of human running is substan- force that the muscles must generate to support the
tially greater (>50%) than predicted for a quadruped animal’s body weight remains constant, irrespect­
of similar size, suggesting that humans are “uneco- ive of the speed at which it runs. This reflects the
nomical” runners (see Fig. 3.9b). However, analysis fact that an increase in force magnitude is offset by
of a broader sample of human running data and use a reduction in limb support time. Consequently,
of the subtraction method indicates that human run- the increased energy cost to move at faster speeds
ning costs only exceed the predicted allometric cost likely results from the increased rate of force devel-
by ~17%. Because other species (including horses opment and the need to activate the muscles at
and antelope) also exhibit greater than predicted higher rates. Faster rates require increased Ca 2+
running costs—that equal or exceed human run- pumping for muscle activation-relaxation and more
ners—it may be that human running is not as uneco- costly myosin-ATP turnover within the muscle’s cells
nomical as previously argued. Nor is human walking (see Chapter 2).
unusually cheap compared with the cost of walking Modeling the rate of muscle force development as
of other animals, which may well reflect the differing the inverse of limb contact time (1/tc) with the ground
scaling relationships for Cwalk compared to Crun (for revealed that the weight-specific rate of ­metabolic
which Cwalk is higher than Crun in small animals, but energy expenditure (Watts N−1, or J s−1 kg−1) varied
lower in large animals). Nevertheless, to move a inversely with ground contact time, or directly with
given distance, walking is still less expensive than 1/tc in different sized mammals (Fig. 3.11a,b; (Kram
running for humans. and Taylor, 1990). This suggests that there is a con-
stant relationship between the amount of energy
3.5.1 Modeling rates of muscle force expended to support a given fraction of body weight
(J N-1) by the limb (Fig. 3.11c), which Kram and Taylor
development, activation-relaxation, and limb
(1990) termed a “cost coefficient” (c):
swing to estimate metabolic energy cost
.
Emetab / BW = c(1 / tc ) (3.1)
The differences in size- and speed-related energy
costs were originally thought to arise from the Equation 3.1 indicates that animals consume the
amount of work an animal’s muscles perform to same amount of energy per unit weight for each
transport its weight and move its limbs. However, step that they take, suggesting that faster contract-
several studies showed that different-sized animals ing muscle fibers underlies much of the observed
perform the same mass-specific work to move their increase in metabolic energy expenditure with
body and limbs (Heglund et al., 1982). The rate of increasing speed.
work performed (mechanical power) also did not Because larger animals have longer limbs and use
increase with speed, in contrast to the increase in lower stride frequencies, they cover a greater dis-
metabolic rate with speed. tance during each step (Lc) compared with small
Instead, increases in energy cost with speed animals, with an animal’s running velocity (v)
(Fig. 3.9a) and the inverse scaling of mass-specific quantified as step length divided by limb contact
energy cost relative to size (Fig. 3.9b) appear to be time:
determined largely by differences in the rate and fre-
quency of muscle force generation during terrestrial v = Lc / tc (3.2)
50 A N I M A L L O C O M OT I O N

(a) 5
Kangaroo rat

Emetab /weight (W/N)

4 Dog
Ground squirrel
3
Spring hare
2 Pony

(b) 30
Kangaroo rat

20 Ground squirrel
1/tc (s–1)

Dog
Spring hare
10 Pony

(c) 1.0
ground force (J/N)
Cost c per unit

0.6

0.2

0 1 2 3 4 5 6 7 8
Speed (m/s)

Figure 3.11 A comparison of animals moving at different speeds yields consistent increases in weight-specific metabolic rate and 1/ground
̇ / BW) parallels (b) the
contact time, such that energy use relative to ground contact force remains constant. (a) Weight-specific metabolic rate (Emetab
increase in ground contact time (1/tc) as a function of speed for different sized running and hopping animals. (c) When energy use is normalized to
̇ / G, J N−1), the different animals are found to consume a similar amount of energy per unit ground
the force (G) an animal exerts on the ground (Emetab
force, irrespective of the speed that they run. This cost coefficient “c” is about 0.2 J N–1. Open symbols are for trotting and closed symbols are for
galloping. The ‘x’ and ‘+’ symbols represent hopping. (Adapted from Kram and Taylor, 1990; with permission MacMillan Magazines, Ltd.)

This allows the weight-specific metabolic cost of is important to note that Kram and Taylor’s “force-
.
transport (C tot = Emetab BW −1v −1 ) to be defined as, hypothesis” focuses on vertical ground forces needed
to support body weight. Assuming that the hori-
Ctot = c(1 / Lc ) (3.3)
zontal forces that must be generated and the iner-
Regardless of their size, animals use the same tial cost of swinging the limbs are negligible
amount of weight-specific energy during each step. fractions of total locomotion cost, how reasonable
Therefore, larger animals can move a greater dis- are these assumptions?
tance for a given amount of energy (Fig. 3.12). The Using blood flow measurements to estimate
longer step (and stride) lengths of larger animals pro- muscle energy use, Marsh et al. (2004) subse-
vide a simple explanation for their lower mass- (or quently showed that limb swing muscles consti-
weight-) specific cost of transport (Pontzer, 2007a). It tute ~25% (stance muscles constitute the other ~ 75%)
 E N E R G E T I C S O F L O C O M OT I O N 51

Step length
1.0

0.8
Pony

Step length (m)

0.6
Dog

0.4
Spring hare

0.2
Ground squirrel
Kangaroo rat
0 1 2 3 4 5 6 7 8
Speed (m/s)

Figure 3.12 Animals generally increase their step length (the distance traveled while the limb is in contact with the ground) at faster speeds. The
lower cost of transport of larger animals is explained by the fact that they move a greater distance during the time that their limbs are in contact
with the ground (greater step length), but consume proportionally the same amount of energy to support their weight (constant “c”, Fig. 3.11c).
Open symbols are for trotting and closed symbols are for galloping. The ‘x’ and ‘+’ symbols represent hopping. (Adapted from Kram and
Taylor, 1990; with permission MacMillan Magazines, Ltd.)

of the total metabolic cost of guinea fowl during The model of weight-support cost based on time
walking and running. Such measurements are dif- of contact (Kram and Taylor, 1990) also assumes that
ficult to carry out, and thus hard to generalize to the muscles operate over similar regions of their
other animals. But it seems likely that limb swing force-velocity curve regardless of body size and
costs may be a substantial component of overall perform proportionately similar work at e­ quivalent
metabolic cost, in addition to those linked to muscle running speeds (Heglund et al., 1982; Taylor, 1994).
force generation during stance. To address this, While this may be a reasonable hypothesis, the sim-
Pontzer (2005) modeled how limb length may plicity of Equation 3.1 ignores the additional costs
affect swing costs, as well as horizontal and verti- associated with turning muscles on and off, and the
cal ground force costs. The costs of generating hori­ work that muscles perform. The energy cost associ-
zontal ground forces and swinging the limb may ated with muscle activation and relaxation is gener-
contribute as much as 40% to the total cost of loco- ally ~25–40% of the total cost for generating force
motion. When tested against oxygen consumption (Woledge et al., 1985). However, because differences
data, Pontzer’s (2007b) model more accurately pre- in the costs associated with activation-relaxation and
dicted changes in locomotion cost with speed for cross-bridge cycling co-vary with the speed of muscle
humans, dogs and goats than those based on Kram contraction, separating these costs is challenging.
and Taylor’s (1990) vertical force cost coefficient, If muscle shortening work increases with speed,
or those based on a Froude number (see Chapter 4). part of the increase in energy cost may also reflect
Though lower, Pontzer’s estimates of limb swing increased muscle recruitment at faster speeds due
cost for humans, dogs and goats, also match fairly to force-velocity effects (discussed in Chapter 2).
well those measured by Marsh et al. (2004). While Future attempts to quantify changes in the cost of
the cost of supporting body weight clearly is an muscle activation-relaxation and muscle work should
­important determinant of metabolic cost, the costs aim to better delineate how much of the change
of swinging the limbs and producing horizontal in energy cost with speed and body size can, in
forces to move over ground also contribute. fact, be linked to cross-bridge related costs of force
52 A N I M A L L O C O M OT I O N

development. A recent modeling analysis (Pontzer, sum of horizontal running (Chor) and the metabolic
2016) suggests that the cost of muscle activation-relax- cost of raising the body’s center of mass (CPE).
ation may be much higher than previously thought If one assumes that the efficiency of doing work is
and, together with estimates of cross-bridge cycling the same for the muscles of both small and large
costs, could better explain the cost of running and animals, the mass-specific metabolic cost of doing
climbing. However, the very high (~ 140%) activation- potential energy work should also be the same. This
relaxation versus cross-bridge cycling costs extrapo- cost has been estimated as the cost when running at
lated by Pontzer’s ­analysis substantially exceeds costs an incline minus the cost when running at the same
previously measured (Woledge et al., 1985) and draws speed on level ground:
attention to the need for further study.
Cincl – Chor = CPE sin α (3.5)

CPE mass-specific values range from 16 to 27 J kg−1

m−1 across animals. Therefore, the metabolic cost of
3.6 Energy cost of incline running
incline running should be greater at a given incline
Many animals regularly scale rocks, trees and vari- for a large animal because it has a lower mass-­specific
able slopes in their environment. These inclines metabolic cost for horizontal running than a small
likely affect the metabolic cost of movement because animal (Fig. 3.9a). That is, the cost of raising the
additional energy must be expended in raising (and body’s center of mass when running up an incline
lowering) the animal’s center of mass. The rate of can be expected to be a greater fraction of total meta-
mechanical work associated with increasing the bolic cost in larger animals. Is this the case?
body’s potential energy (PPE) is, Consistent with the extra cost of potential energy
work, the metabolic cost of incline running is greater
PPE = m g v sin α (3.4)
than for level locomotion. Figure 3.13a shows the pat-
where m is the animal’s body mass, g is gravitational terns of oxygen consumption measured for cock-
acceleration, v is the animal’s velocity and α is the roaches running on a horizontal track, and, 45° and 90°
angle of ascent. Equation 3.4 also applies to descent, inclines. Cockroaches and other insects not only scale
in which the rate of PE loss depends on running vertical walls, but can also run upside down! Many
speed and angle of descent. Most past work has lizards also scale vertical walls, seemingly with
focused on the energy cost of uphill running. The ease. When cockroaches run up 45° and 90° inclines,
total cost of incline running can be considered the their metabolic cost increases two- and three-fold

(a) 8 (b) 0.4 24°

Dogs
Cockroaches 90°
6 0.3 0°
VO2 (ml O2/g/h)

VO2 (ml O2/g/h)

45°
4 0.2
9°
0° Humans
0.1 0°
2

0.2 0.4 0.6 0.8 2 4 6

Speed (m/s) Speed (m/s)

Figure 3.13 The metabolic cost of incline running by (a) cockroaches and (b) dogs and humans increases with the slope of the ground (shown
here in degrees) and is greater than during horizontal running (0°). However, the extra cost cannot be explained by differences in the rate of
potential energy work to move uphill.
 E N E R G E T I C S O F L O C O M OT I O N 53

compared with running on a level surface. Even for This allows for the recruitment of fewer fibers to
these small animals, incline running incurs a signifi- generate a given level of force (Chapter 2) and likely
cant cost. When humans and dogs run up an incline contributes to the reduced locomotor cost. However,
(Fig. 3.13b), their cost also increases (50% at 9° incline the extent to which muscles can contract eccentric-
and 79% at 24° incline, respectively). However, no ally and avoid damage is limited, and this may con-
regular pattern for energy cost of incline running is tribute to the increased cost of locomotion at very
observed across animal sizes (Full and Tullis, 1990). steep descent angles. Changes in stride frequency
If a given value for the metabolic cost of raising the (lower when running downhill versus uphill) sug-
body’s center of mass is used (assuming constant gest that some of the decreased cost may also reflect
muscle efficiency), the predicted cost of incline a slower rate of force development and reduced
­running is typically much greater, and in several muscle activation-relaxation costs associated with
instances, less than the observed cost. Research on taking longer strides.
ghost crabs (Tullis and Andrus, 2011) has also A study of leaf-cutting ants (Holt and Askew, 2012)
found incline running costs to be much higher than revealed that ants adjust their speed to maintain a
those predicted by a constant muscle efficiency constant rate of metabolic energy use across differ-
hypothesis. ent incline and decline gradients, moving more
Consequently, it seems likely that, across animal quickly on a level versus incline or decline gradi-
sizes, muscles do not operate with similar efficiency. ents. Nevertheless, the cost of transport increased
Or, perhaps, other factors influence the energy cost with both incline and decline gradients, which is
of incline running. Because changes in stride fre- consistent with the increased cost observed for
quency and ground contact time (tc) are not signifi- cockroaches, ghost crabs and horses on incline gra-
cantly affected by incline, the cost of incline running dients, and humans on steep decline gradients.
does not appear to be affected by the rates of muscle These results suggest that ants vary speed in rela-
force development and activation-relaxation, as is tion to gradient as they move, to reduce their verti-
the case when running on a level surface (Fig. 3.11). cal journey time and vertical cost of transport. The
Another possibility is that postural changes associ- manner in which energy cost changes with ­variable
ated with incline running may affect limb mechan­ grade in other terrestrial animals deserves greater
ical advantage in such a way that the magnitude of scrutiny before broader generalizations of locomo-
­muscle force required to elevate the body when tion biomechanics can be established with respect
running uphill is greater than when running on to incline and decline movement energetics. Loco­
level ground. Changes in muscle force require- motion over variable terrain with an array of terrain
ments, as discussed previously, would likely affect angles represents more natural requirements of
the amount of energy required to move uphill. This movement for many terrestrial animals. The meta-
remains to be investigated. bolic cost to move over irregular surfaces has largely
In contrast to uphill running, the energetics of been ignored. However, a recent study (Voloshina
downhill running has been much less studied. Except et al., 2013) shows that humans expend 28% more
for studies of humans running on different inclines energy walking on a variable treadmill terrain sur-
and declines (Margaria, 1976; Minetti et al., 1994), face (±2.5 cm) that required increased hip and knee
the question of energy cost during downhill loco- work together with increased muscle co-activation
motion has not been well studied. When humans compared to a smooth treadmill ­surface.
run and walk downhill, their metabolic cost decreases
with a steeper angle of descent, but only up to −10°
(Minetti et al., 1994). At −10°, the cost is 35% less
3.7 Cost of swimming
than when running on a level. At steeper descent
angles, the energy cost of locomotion begins to The metabolic energy cost of swimming has been
increase. During downhill running, the limb mus- measured in a diversity of vertebrates, including
cles must increase the degree to which they contract fish, marine mammals, humans, muskrats, platy-
eccentrically (active lengthening) to absorb energy. pus, ducks, penguins, turtles and marine iguanas.
54 A N I M A L L O C O M OT I O N

In contrast, few invertebrate taxa have been studied 1000

with respirometry aside from shrimp and squid
(see Videler, 1993 for review) and more recently a
Tuna
nudibranch mollusk that swims and crawls (Caldwell
750
and Donovan, 2003). These measurements are based

VO2 (ml O2/kg/h)

on respirometry studies of oxygen consumption ∝v 1.4
made in a closed-flow tank for gill breathers (e.g.
Brett, 1965) or with the use of a breathing chamber 500
positioned at the water’s surface for aerial breathers. Salmon
In contrast to terrestrial locomotion, these data
show that the metabolic cost of swimming increases 250
∝v 2
exponentially with speed (Dewar and Graham, 1994;
Fig. 3.14). This reflects the increased drag that swim-
ming animals experience at higher speeds (Chapter 5),
which increases ∝ v2. The data for swimming sal­ 0.5 1.0 1.5
mon fit this more closely than those more recently Speed (m/s)
reported for tuna, in which the exponent is closer to
1.5. Similar to terrestrial animals, the mass-specific Figure 3.14 The rate of energy use (V̇o2 ) by salmon and tuna
increases in an exponential fashion with increased swimming
cost of transport of swimming decreases with
speed (v). This reflects the increasing effect of drag (∝ v2) that must
increasing size in fish (∝ BM−0.30, Fig. 3.16). However, be overcome at a higher speed. The exponent for salmon fits this
surface swimmers incur a three- to five-fold greater fairly well, but tuna do not follow the expected scaling based
cost than underwater swimmers. As is discussed solely on drag (∝ v1.4; data from Brett (1965) and Dewar and
in Chapter 5, this likely results from the additional Graham, 1994).
cost of wave-drag. Human swimmers have a
­particularly high cost of transport for their size. the metabolic rates of flying birds, bats and insects
Consequently, despite the fact that elite swimmers are expected to increase exponentially with speed,
appear to be near their theoretical limit in terms of particularly at faster speeds. However, the high
performance, it comes at a high price. Clearly our ­aerodynamically induced power cost to support
terrestrial locomotion c­apacity greatly outstrips their weight in air (see Chapter 6) means that meta-
our swimming abilities in water. In lion nudi- bolic power also rises steeply at slow speeds, reach-
branchs, the cost of swimming is six-fold higher ing a maximum during hovering. Consequently, in
compared with crawling, though the cost of trans- contrast to swimming and running, flying animals
port is similar. Compared with other underwater incur a high cost to move at slow speeds and when
swimmers, the jetting of squid also incurs a five- hovering. The decrease in induced power relative to
fold greater cost. It is likely that this heightened the increase in parasite and profile power (which
cost has limited the evolution of jetting as a more both result from drag) predicts a “U-shaped” power
common means of aquatic movement. Finally, curve (see Fig. 6.4). Energy curves of this shape
there is evidence that fish have the lowest cost of ­suggest that there is a minimum cost speed (at which
transport for their size, with shrimp, aquatic rep- ­metabolic energy expenditure is at a minimum dur-
tiles and cetaceans having higher mass-specific ing flight) and a minimum cost of transport speed—
transport costs (see Section 3.9). also referred to as the maximum-range speed (Fig. 6.4).
Maximum-range speed is determined by the tan-
gent to the curve that gives the lowest slope
(energy rate/speed = transport cost). Birds likely
3.8 Cost of flight
use this speed when flying longer distances, such as
As in the case of swimming animals, the increased when migrating (Alerstam and Hedenström, 1998;
power required to overcome drag (∝ v2) means that Pennycuick, 1989).
 E N E R G E T I C S O F L O C O M OT I O N 55

Although the “U-shaped” power curve fits the pat- quency and amplitude. Changes in forward flight
tern of energy use for fixed-wing aircraft, the evi- speed arise mainly from changes in the animal’s
dence for U-shaped metabolic power curves in flying body pitch and associated wing stroke angle, which
animals has yielded mixed results. Measurements of alter the relative amount of thrust that the wings
the metabolic rates of bumblebees (Ellington, Machin, produce in relation to lift for weight support. In
and Casey, 1990) and hummingbirds (Berger, 1985; order to fly faster, both species tilt their body head-
Clark and Dudley, 2010) during forward flight down—shifting their wings’ angle of attack to prod-
show flat or minimally curved power relationships uce greater thrust. As a result, their metabolic rate
over a range of slow to moderate speeds (Fig. 3.15a). during moderate and slow flight speeds remains
The metabolic cost of hovering for these species is similar. At faster speeds, the metabolic rate of hum-
also similar. However, when measured during mingbirds is elevated, but (as for other birds) this
feeding (Clark and Dudley, 2010), the power require- in part may reflect the added drag when an animal
ment for hovering hummingbirds is slightly ele- wears a mask (Berger, 1985) versus when oxygen
vated. A relatively flat power relationship, in part consumption measurements are made at a feeder
reflects the fact that bumblebees and humming- (Clark and Dudley, 2010).
birds flap their wings (and underlying energy Measurements of metabolic rate during flight in
demands of their flight muscles) at a uniform fre- certain birds and bats have also yielded results that

(a) 400 Bumblebee

60

VO2 (ml O2 g−1 h−1)

Hovering
300
VO2 (W/kg)

200 Hummingbird 30

100

4 8
(b) 200

150 Budgerigar

Starling
VO2 (W/kg)

100
Pigeon

50 Bat

4 8 12 16 20
Speed (m/s)

Figure 3.15 Whereas the rate of energy used by (a) bumblebees and hummingbirds is fairly constant with speed, (b) birds and bats exhibit a
more “U”-shaped pattern with flight speed (as might be expected for steady state aerodynamics—see Chapter 6). These measurements are based
on the oxygen consumption of animals trained to fly in wind tunnels. (Adapted from Ellington, 1991).
56 A N I M A L L O C O M OT I O N

100

Mass-specific cost of transport (J/kg/m)

10 Running
∝M −0.30

Flying
∝M −0.23
1
Swimming
∝M −0.30

0.01 0.1 1 10 100 1000 10000

Body mass (kg)

Figure 3.16 The mass-specific cost of transport decreases with increasing body mass in running mammals, flying insects and birds, and
swimming fish, but is highest for running and lowest for swimming at a given body mass. (Adapted from Schmidt-Nielsen, 1972).

suggest a flatter power curve than predicted by 3.9 Locomotion costs compared
­classical aerodynamic theory (Fig. 3.15b). However,
measurements for budgerigars (Tucker, 1968) and Compared with other forms of locomotion, swim-
more recently, cockatiels (Bundle and Dial, 2003; ming is likely the least expensive means of move-
Morris et al., 2010) found pronounced U-shaped ment (Fig. 3.16). Flying has an intermediate trans­port
power curves over sustainable flight speeds, consist- cost, and running is most expensive. The low cost of
ent with ­aerodynamic theory (Chapter 6). One chal- swimming may seem counterintuitive because of
. drag, but the buoyancy of aquatic animals reduces
lenge to metabolic studies is that Vo2 data are
difficult to obtain at more demanding flight speeds. their need to expend energy for weight support.
Except for only a few bats and birds—most notably In addition, most swimmers travel at low speeds
hummingbirds—the power costs d ­ uring hovering (e.g. fish: 0.3 to 3 m s−1) compared with flying ani-
are generally non-sustainable. Similarly, very fast mals (5 to 25 m s−1), which greatly reduces drag and,
flight speeds also likely require significant anaerobic hence, their swimming cost. Moving slowly, but
energy supply. Consequently, flying animals sus- being buoyant, has its advantages.
tain movement over a narrower fraction of their speed The differences in cost of transport depicted in
range than running animals. Another complication Figure 3.16 are based on a comparison of animals
is that when scientists make respirometry measure- that are specialized for each mode of locomotion
ments, birds often alter their flight behavior and represent diverse phylogenetic groups. When
(Bundle and Dial, 2003; Morris et al., 2010) and more closely related animals are compared, do ­similar
avoid intermittent flapping-gliding or flapping- differences in transport cost emerge? Mammals rep-
bounding phases characteristic of free flight, which resent one such group of animals that exhibits spe-
may result in a higher power cost for flight. Finally, cialized terrestrial, aquatic and flying forms. Their
changes in flight muscle efficiency resulting from relatively “recent” re-invasion of the oceans 60 mil-
changes in shortening ­velocity (see Chapter 2 and lion years ago, reflects key differences in swimming
Section 6.5.) may also influence metabolic energy cost specialization relative to fish. When marine mam-
with changes in flight speed. mal swimming specialists (dolphins, seals and
whales) are compared with semi-aquatic mammals
 E N E R G E T I C S O F L O C O M OT I O N 57

(a) 100

Mass-specific cost of transport (J/kg/m)

Semi-aquatic mammals
∝M −0.18
10 Tuna at
38°C

Marine mammals
∝M −0.29
1 Fish
∝M −0.30

0.01 0.1 1 10 100 1000 10000

(b) 100
Mass-specific cost of transport (J/kg/m)

10 Running mammals

Flying bats
All ∝M −0.31

1
Marine mammals

0.01 0.1 1 10 100 1000 10000

Body mass (kg)

Figure 3.17 Mass-specific cost of transport differs across different clades of swimmers, but converges regardless of locomotor mode when only
mammals are compared. (a) Mass-specific cost of transport is higher for semi-aquatic mammals relative to marine mammals. Tuna swimming at
a body temperature of 38°C match closely what would be extrapolated for marine mammal swimming specialists (ectothermic fish exhibit lower
swimming costs). (b) When the swimming transport costs of marine mammals are compared with those for mammalian runners and flyers (bats),
similar scaling patterns for all groups are observed. (Adapted from Williams, 1999).

(including humans), their transport costs are much mals likely required an initially high locomotor
lower, but still greater than for fish (Fig. 3.17a). energy cost that was subsequently reduced with the
When marine mammals are compared with running evolution of a more specialized swimming capabil-
mammals, the scaling regressions depicting changes ity (Williams, 1999).
in cost of transport relative to body size are closely The higher transport costs of specialized marine
overlapping (Fig. 3.17b) (Williams, 1999). The trans- mammals compared with fish likely reflect a higher
port costs for flying bats also fall close to those for maintenance metabolic cost in marine mammals pri-
swimming and running specialists of similar size. marily due to being endothermic. Because water pro-
Hence, the re-invasion of an aquatic habitat by mam- motes a much higher rate of heat loss than air,
58 A N I M A L L O C O M OT I O N

ectothermic fish experience reduced heat loss (or cycling). Sprinters and middle-to-long distance
compared with endothermic aquatic mammals, runners often train by running a number of short
which lowers their cost for temperature regulation. bouts of intensive high-speed sprints interspersed
Consistent with this, the resting metabolic rates of by p­ eriods of moderate exercise or brief periods of
aquatic mammals, despite greater insulation, are rest, rather than running at high speed for a single,
1.7- to 2.4-fold greater than those predicted for ter- longer-fatiguing bout of exercise. This enables
restrial mammals of similar size (Williams, 1999). runners to achieve a longer period of higher-speed
Interestingly, tuna have a similar transport cost for exercise, improving their endurance capacity by
their size as marine mammal swimming specialists. improving cardiopulmonary and skeletal muscle
This likely reflects the higher-metabolic cost associ- aerobic fitness.
ated with using warm internal red muscle for sus- However, if excess post-exercise oxygen con-
tained active swimming (Chapter 5). sumption (EPOC) differs from the metabolic cost
required to begin exercise, then total metabolic cost
will be altered and may be of special significance for
3.10 Intermittent exercise
intermittent patterns of activity. In contrast to stud-
Metabolic responses to exercise are nearly always ies indicating increased endurance with intermit-
studied under steady conditions (while an animal tent exercise noted already, studies of mice (Baker
moves at a constant speed on a treadmill, swims at and Gleeson, 1999) have shown that short, intensive
a constant speed in a flow tank or flies at a constant bouts of exercise can elevate overall transport costs,
speed in a wind tunnel). However, most animals with post-exercise recovery metabolism reaching up
naturally exhibit intermittent patterns of activity of to 90% of the energy consumed during one minute of
varying intensity. Although less common, studies of intense exercise. In humans, post-exercise recovery
intermittent exercise in both invertebrate and verte- metabolism also increases with both exercise inten-
brate runners indicate that intermittent activity sity and duration. However, if the post-exercise cost
­patterns can substantially enhance endurance, or an of ­metabolism is equivalent or close to the anaer-
animal’s capacity for moving over longer distances. obic costs incurred at the start of exercise (as shown
That is, the time-averaged speed and distance over in Fig. 3.2), the measurement of a steady-state cost
which an animal can move without fatiguing is should be consistent with intermittent patterns of
increased by interspersing periods of rest and recov- locomotion. Edwards and Gleeson (2001) confirmed
ery metabolism between bouts of activity. this expectation and demonstrated that repeated
By moving at faster speeds over shorter periods bouts of exercise at frequent intervals resulted in
of time, with intervening rest periods, animals may transport costs similar to steady movement over the
be able to travel a greater distance without tiring. same distance.
Periods of intervening rest allow animals to avoid Intermittent swimming has also been observed
fatigue and thereby cover a larger distance than if via video cameras mounted on diving Weddell and
they moved at a steady but slower speed. In ghost elephant seals, as well as bottlenose dolphins and
crabs, intermittent patterns of activity and brief blue whales (Williams et al., 2000). These marine
pauses have been shown to increase the distance mammals must dive without breathing. They
that the animals can travel two- to five-fold, and in increase their aerobic capacity and, as a result, the
lizards (frog-eyed gecko) a 1.7-fold increase in distance and depth of their dives by gliding during
distance capacity has been observed (Weinstein
­ the descent of a dive. Intermittent periods of gliding
and Full, 2000). Intermittent patterns of activity are have also been observed during ascent. The ability
hypothesized to be more important for enhancing to glide while descending appears to result from
endurance in ectothermic species that have a low their collapsed lungs, which allow them to achieve
aerobic scope. However, even for endothermic negative buoyancy. Similarly, small birds exhibit
species, such as humans, intermittent exercise can intermittent flap-bounding and flap-gliding pat-
enhance endurance capacity. Indeed, this is the basis terns of flight (Tobalske, 2001) that are argued to
for high-intensity interval training in track and field reduce their metabolic and aerodynamic power
 E N E R G E T I C S O F L O C O M OT I O N 59

requirements (Rayner et al., 2001; discussed fur- to operate at temperatures that may be up to 15°C
ther in Chapter 6). greater than the surrounding water. In other fish,
The ability to increase endurance by means of metabolic heat produced by their swimming mus-
intermittent patterns of exercise likely involves the cles is lost when the warmed venous blood is car-
regular replenishment of intermediate fuel sub- ried to the gills for gas exchange. Because of the
strates, before products of anaerobic glycolysis red muscle’s elevated temperature, tuna and other
build up to disruptive and fatiguing levels. By “warm-muscle” fish can operate with increased
maintaining anaerobic products at modest levels, aerobic capacity in much cooler waters than other
the rate of recovery may be increased, readying an large fish. In addition to their swimming muscles,
animal for a subsequent bout of exercise. After 14 tunas and billfish also keep their viscera, brain and
years, since the first edition of this book, it remains eyes warm (Block, 1986; Block, 1994), improving
the case that more studies are needed to assess their visual and mental capacity as large predators
whether recovery metabolism differs substantially in open cooler waters.
from start-up costs and what the biochemical basis Another adaptation for increased endurance is
is when they differ, as well as whether intermittent found in diving mammals that must carry their
activity patterns significantly impact an animal’s oxygen stores on board when they dive to depth for
daily energy budget for movement. Available evi- long periods. In addition to other physiological
dence suggests that contrary to a favorite child’s adaptations, elephant seals, Weddell seals and other
tale of the tortoise and the hare, slow and steady diving mammals possess unusually large amounts
doesn’t always win the race! of myoglobin within their muscles, which allows
them to store much more oxygen within their body
3.11 Other adaptations for increased than terrestrial mammals of similar size (Kooyman
and Ponganis, 1998). The ability to store oxygen
aerobic capacity
and to avoid excessive lactate production and
In addition to intermittent exercise, various animals ensuing metabolic acidosis is clearly critical to
show specialized adaptations for increased endur- their ability to dive for long periods before resur-
ance. One of the more remarkable is the capacity of facing to breathe.
tunas and lamnid sharks (makos and great whites)
to maintain regionally-elevated swimming muscle
temperatures (Carey, 1973). In contrast to most fish
3.12 Summary
that have a narrow band of red muscle located near Patterns of energy use during terrestrial locomotion
the body surface (Chapter 5), these heterothermic exhibit generally similar relationships with speed
fish possess an enlarged region of warm red muscle and body size, despite considerable diversity in the
located deep within the myotome. Associated with number of limbs used to move, the type of skeleton
this novel anatomic location, the red muscle is sup- used for support, and the thermoregulatory strat-
plied by a vascular network, or rete, of arteries that egy employed. The consistency of these patterns
passes from the outer body surface inward to the reflects the biochemical conservatism of the meta-
muscle. As the colder oxygenated blood carried by bolic pathways within cells, as well as the organiza-
the arteries from the gills moves inward, it is heated tion and contractile properties of the skeletal muscles
by warm venous blood that passes in the opposite that power movement.
direction from the exercising red muscle. By the Differences in patterns of energy use are most
time the venous blood reaches the body surface extreme in terms of aerobic capacity and endurance.
before returning to the heart, it loses nearly all of its Variation in energy use also emerges when compar-
heat to the inward-flowing arterial blood. This vas- ing locomotion on land versus in water or air.
cular network forms a countercurrent heat exchanger Tradeoffs incurred by greater or lower energy cost
that traps the metabolic heat produced by the active are likely balanced by the benefits that arise from
red muscle, preventing it from being lost to the sur- the exploitation of the habitats that these locomotor
rounding cooler water. This allows the red muscle modes afford. The tight link between energy use
60 A N I M A L L O C O M OT I O N

and locomotor performance reflects the central aquatic ectotherms are likely to maximize their fitness
importance of how locomotor energy costs fit into at temperatures that also maximize their ­aerobic
an animal’s overall energy budget. While minimiz- scope, thereby providing them with greater capacity
ing energy use may be of considerable selective for growth and reproduction (Pörtner and Farrell,
value, it is not the only aspect of performance that 2008; Pörtner and Knust, 2007). Temperature increases
must be weighed in terms of understanding the due to climate change might therefore result in
locomotor design and capacity of an animal. Burst reduced aerobic scope and reduced ­survivorship.
speed, maneuverability and strength, among ­others, Others argue caution when interpreting this evi-
are traits that must also be considered important to dence, given that studies of some fish show reduced
an animal’s locomotor performance. Future field growth and reproduction at temperatures that maxi-
research will illuminate how intermittent patterns of mize their aerobic scope (Clark et al., 2013). Clearly,
activity affect energy use and performance. Finally, additional careful study is needed in order to under-
as exemplified by the comparison among swimming, stand how temperature influences aerobic scope in
flying and running mammals, it is also clear that evo- relation to the capacity for activity, growth and repro-
lutionary ancestry can have an important bearing duction.
on the energetics of locomotor performance, which
prior scaling analyses have largely not considered.
Finally, with the growing recognition of how cli-
mate change impacts biodiversity, studies of ther- Additional reading
mal effects on energy use and other physiological
Alexander, R. McN. (1999). Energy for Animal Life. Oxford:
traits have exploded in recent years. In this context,
Oxford University Press.
considerable attention is being focused on how the Bennett, A. F. (1994). Exercise performance of reptiles. Adv.
aerobic scope of aquatic ectotherms changes with Vet. Sci. & Comp. Med. 38B, 113–38.
temperature and what this may forecast for the suc- Taylor, C. R. (1994). Relating mechanics and energetics dur-
cess and survival of today’s species. Some argue that ing exercise. Adv. Vet. Sci. & Comp. Med. 38A, 181–215.
 C H A PT ER 4

Movement on Land

Animals must support their weight when moving explored in relation to size scaling and gait use,
over land, while also accommodating changes in allowing the gaits and speeds of dinosaurs to be
terrain and the conditions of the ground underfoot. inferred. Next, we discuss how the mechanical
Most terrestrial animals accomplish this by using energy cost of terrestrial locomotion may be con-
limbs to exert forces on the ground. Some groups of served, comparing pendular motion of the body
animals have lost their limbs (snakes) or never during walking, the spring-mass mechanics of run-
evolved them in the first place (worms), relying ning, and the collisional mechanics of limb-ground
instead on contractions of body muscles to trans- contact across different gaits. Such approaches have
mit force between their body axis and the ground. been central to the design of biologically-inspired
Undulatory modes of terrestrial locomotion are legged robots. We review recent work on limbless,
frequently associated with a burrowing existence. undulatory terrestrial locomotion. The chapter con-
In other animals (salamanders and lizards), some cludes with a section about energy conservation and
combination of body undulation and limb propul- the use of elastic energy mechanisms.
sion moves the body forward. In this chapter we
focus on the mechanisms and strategies for legged
4.1 Biological wheels: why so few?
locomotion on land. Recent studies have examined
how animals maneuver and accelerate, as well as Humanity’s device for efficient land transport—the
how they stabilize body movements when running. wheel—has rarely evolved in biology as a means of
A large body of work on terrestrial locomotion has terrestrial locomotion. Other than for a few animals
also yielded inspiration for a new generation of (e.g. somersaulting mantis shrimp and rolling lar-
legged robots that can move more nimbly over
­ val insects), wheels have not proven a viable solu-
irregular terrain than previous robot designs. tion for animal transport (LaBarbera, 1983). Partly
In this chapter, we first consider fundamental fea- this reflects the difficulty of evolving a biological
tures associated with using limbs to move over rotary engine, at least beyond the scale of a rotary
ground. We explore the biomechanical implications molecular motor (Chapter 5 explores bacterial fla-
of legged locomotion in relation to terrestrial gaits gellar locomotion as a system in which rotary pro-
and how running speed varies in relation to stride pulsion has evolved). However, a basic reason for
length and stride frequency. Next, we examine the their biological absence is that wheels are simply
spring-mass properties of walking and running (i.e. not well-designed for movement over uneven ter-
modeling the mass of the body and its motion as rain. (Over the course of human history, wheel-based
supported by a spring-like limb) in the context of transport has required substantial infrastructure costs
maneuverability and stability during terrestrial loco- associated with building and maintaining level roads,
motion. The concept of dynamic similarity will be and the often-encountered pot hole attests to the

Animal Locomotion. Second Edition. Andrew A. Biewener & Sheila N. Patek, Oxford University Press (2018).
© Andrew A. Biewener & Sheila N. Patek 2018. DOI: 10.1093/oso/9780198743156.001.0001
62 A N I M A L L O C O M OT I O N

poor performance of a wheel when negotiating body weight (BW). The integral of time-varying
an uneven surface.) Instead, natural selection has GV is defined mathematically as: ∫ Gvdt = BW . As
favored the evolution of limbs within arthropods shown in Figure 4.2 for a quadruped, this requires
and vertebrates to negotiate variable terrain. The that the shaded areas during which Gv < 0.5BW
ability of animals to maneuver around obstacles (assuming that each limb supports half the animal’s
and over uneven surfaces is unparalleled by any weight, or 1.0 BW by one biped limb) are matched
vehicle. Because of this, recent robotics research has by the summed hatched areas during which
turned to the design of animal limbs and legged Gv > 0.5 BW. At rest, the force acting on a limb is
transport as a means for inspiring and designing approximately equal to BW/n, where n is the number
robots capable of traversing the challenging terrains of limbs that support the animal’s weight (e.g. n = 2
found in nature (Full and Koditschek, 1999; Raibert, for a biped; n = 4 for a quadruped). The exact distri-
1986; Altendorfer et al., 2002; Collins et al., 2005; bution of weight support depends on the location
Spenko et al., 2008). of the animal’s center of mass (CM) relative to its
limbs—in most vertebrate quadrupeds (many pri-
4.2 Limbs as propulsors: support mates are exceptions) the CM is shifted toward the
forelimbs, so that the forelimbs support more of the
and swing phases
animal’s weight. When an animal moves, the forces
When an animal’s limb contacts and pushes against exerted by the limbs on the ground rise and fall dur-
the ground, it experiences a ‘ground reaction force’. ing limb support, and are zero whenever no limbs
The vertical component (Gv) of the ground reaction are on the ground (defined as the “aerial phase” of a
force serves to support the animal’s weight, while stride). As a result, the maximum force exerted by
the horizontal fore-aft (GH) and mediolateral (GML) a single limb on the ground is always higher than
components allow the animal to accelerate or decel- when an animal is standing at rest. When the limbs
erate, and to maneuver and balance (Fig. 4.1). Over remain in contact with the ground for a longer
a series of strides the average vertical force exerted period of time, smaller forces are required (Fig. 4.2a),
on the ground by the limbs must equal an animal’s but this limits speed of movement. To increase speed,

(a) Ground reaction forces (b) (c)

Vertical GV

G
Horizontal GH
(fore–aft)

GV
G
GV
Mediolateral

(at T1)
GH
GML

GML
T1
Time

Figure 4.1 A running quadruped experiences ground reaction forces on each foot during a stride. (a) Vertical (GV), horizontal fore-aft (GH), and
mediolateral (GML) components of the ground reaction force are exerted on a limb during the support phase of the stride (represented ­schematically).
(b) At T1 of hind limb support in (a), the vectors (GV and GH) visible in lateral view sum to the net vector (G) in that plane. (c) The vectors GV and
GML acting on the hind limb are idealized on a photo of a running cheetah, summing to the resultant of the ground force vector G in the frontal
plane.
 MOVEMENT ON LAND 63

animals must move their limbs more rapidly, redu- The locomotor cycle, or stride, can be divided
cing the time of limb ground contact and increasing into support and swing phases of each limb, with
the magnitude of force that a limb must exert against the stride period equal to the time required to com-
the ground (Fig. 4.2b,c). Consequently, ground reac- plete one cycle of limb movement (see Fig. 4.2c).
tion forces on individual limbs increase as animals These are also referred to as the propulsive and
move faster, whereas peak ground forces acting on an recovery phases of the limb. The relative fraction of
individual limb are t­ ypically less than body weight the stride period (Ts) represented by a limb’s sup-
when an animal moves slowly; they can be much port or ground contact phase (tc, sec) is defined as
greater than an animal’s body weight at faster speeds. the limb’s duty cycle (β = tc/Ts). Hence, as animals
The maximum force required by a single limb can move faster, the duty factor of their limbs decreases
also be reduced by using more limbs to support an (Fig. 4.2d), requiring an increase in the maximum
animal’s weight (e.g. a hexaped versus a quadruped). force limbs exert against the ground. Animals move

Walk Trot or run

(a) (b)
Vertical ground

L R

Vertical ground
force GV

L R

0.5BW force GV 0.5BW

(β = 0.65) (β = 0.50)
Horizontal ground

Horizontal ground
force GH

force GH

Time
Time

(c) Stride Period, Ts (d)

Gallop Walk Run, trot and gallop
Vertical ground

F H
force GV

Duty factor β (=tc / Ts )

0.5BW 0.5

tc (β = 0.35)
Horizontal ground

Speed
force GH

Time

Figure 4.2 Vertical and horizontal fore-aft ground reaction forces (shown for a quadruped) vary in magnitude and duration as a function of speed
and gait: (a–c) For any gait, 0.5 BW is the level of force required by a limb to support the body weight (BW) of a quadruped through time (for a biped
it would be 1.0 BW). The ground force must rise above this level for a period of time (hatched regions) to offset the time during which Gv < 0.5 BW
(shaded regions) for a quadruped (or <1.0 BW for a biped). Duty factor (β) is the ratio of limb contact time (tc) divided by the stride period (Ts), shown
in (c) for a gallop (F, forelimb, H, hind limb). (d) The duration of limb support and duty factor both decrease with increasing speed, requiring greater
ground reaction forces to support the body and more quickly moving limbs. When duty factor decreases below 0.5, animals typically switch to a
running or trotting gait.
64 A N I M A L L O C O M OT I O N

faster by increasing either their stride frequency done by obtaining high-speed video of limb kine-
or their stride length (the distance traveled over matics synchronized to recordings of ground reac-
one stride cycle), or by doing both. The relative tion force components by means of a force platform.
importance of the two depends on the type of gait For humans and large animals, but also more
employed by the animal. Even when an animal recently for much smaller animals, it is possible to
moves at a steady speed, its limbs exert decelerat- attach reflective markers that infrared video cam-
ing and accelerating horizontal forces in the direc- eras can track automatically to collect the coordin-
tion of travel during each phase of limb support ate data for analysis. Figure 4.3 shows an animal’s
(Fig. 4.2). The relative magnitude of acceleration limb position (in lateral view) and the ground reac-
versus deceleration differs according to which limb tion force acting on the limb, derived from the verti-
(i.e. fore, middle or hind limb) is in contact with the cal and fore-aft horizontal components (GV and GH),
ground, and may vary according to the animal’s for three video frames, for which joint torques devel-
size, speed and gait. For example, forelimbs exert a oped in the plane of the animal’s forward motion
decelerating bias and hindlimbs exert an accelerat- can be determined. For more complex, three-dimen-
ing bias in fore-aft GH. Further, the net horizontal sional motion and joint torques, it is necessary to
accelerating force exerted by an animal’s limbs is obtain one or more additional views of the limb
positive when the animal accelerates to increase to determine 3D joint coordinates (Hedrick, 2008,
speed, is negative when it slows down, and is zero ­provides a useful MATLAB script for this) and to
when it moves at a steady speed. Animals also exert incorporate the mediolateral ground reaction force
medio-lateral forces with their limbs (Fig. 4.1), par- component (GML).
ticularly when changing direction (see Section 4.7), Because the torque acting at a joint must be bal-
but these are typically much smaller in magnitude anced by muscle force (Fm), when the foot is on the
than forces exerted in the vertical and horizontal ground the magnitude of this force is mainly deter-
fore-aft directions during forward movement. mined by the muscle’s (or muscle group’s) moment
arm (r) relative to the moment arm (R) of the ground
reaction force (G, Fig. 4.4a), or: Fm × r = G × R (tor-
4.3 Limb mechanical advantage and joint ques are the cross-product of the force and moment
torques: interaction of limb posture and arm vectors). By defining “r” and “R” as the per-
pendicular distance to the joint center and then
ground reaction force
rearranging the equation, we obtain the following
The ground reaction force relative to the limb’s pos- relationship between mechanical advantage and
ture during support largely determines the torques force: r / R = G / Fm . These moment arm and force
(T´), or moments, acting about the joints of the limb. ratios provide a measure of the “effective mechanical
In addition to these “external” joint torques, the advantage” of limb muscles (EMA). Over the entire
inertia and weight of individual limb segments also period of support this can be calculated as,
contribute to the net joint torque. Inverse dynamics
EMA = ∫ Gdt / ∫ Fmdt (4.1)
is the method by which these joint torque compo-
nents are determined. Although important during Defined in this way, the effective mechanical advan-
the swing phase of the limb, inertial and gravita- tage of a limb represents a measure of the magni-
tional torques resulting from limb segment motion tude of time-integrated muscle force that must be
are generally small relative to the external torques developed for a given time-integrated ground force
produced by the ground reaction force during the during the support phase of the stride; in other
stance phase of the stride (Alexander, 1983; Winter, words, EMA is the ratio of ground impulse to muscle
1990). By tracking the movements (or kinematics) of impulse. By aligning the joints more closely in the
an animal’s limb and the position of its joints with direction of the ground reaction force, the magni-
respect to the time-course of ground reaction force, tude of joint torques and, hence, muscle forces can be
the external torques developed during limb sup- reduced (Biewener, 1989 & 2005). This has important
port can be determined (Fig. 4.3). This is commonly implications for both the mechanical design of
 MOVEMENT ON LAND 65

(a)

T1 T2 T3

(b) Ground reaction forces (c)

T1 T2 T3 T1 T2 T3
Joint torque (N cm) 300
Knee
200
Vertical GV

100
Hip
0
6 13 23
–100
Frame number (time)
Horizontal GH

time

Figure 4.3 Limb configuration and ground reaction force can be used for calculating external joint torques. (a) At times T1, T2, and T3 and their
corresponding limb configurations, (b) the ground reaction forces are illustrated as well as the (c) changes in ground reaction torques acting at the
hip and knee. G exerts a flexor torque at the knee throughout most of limb support (requiring knee muscle extensor force to counter this). G also
exerts a flexor torque at the hip (requiring hip extensor force) during the first 60% of limb support but, as G passes behind the hip joint, it exerts
an extensor torque during the latter 40% of limb support (which must be balanced by hip flexor activity).

a­ nimal limbs and the energetic cost of locomotion affects muscle contraction speed and force require-
(discussed in Chapter 3). ments in relation to joint rotation and ground reac-
The inverse of limb EMA (R/r) defines “muscle tion force. Their study revealed that human ankle
gearing” at a joint. Similar to bicycle gears, a high- extensors operate with a low-gear ratio (high EMA)
gear ratio favors greater rotational joint motion for early in stance, enhancing muscle stretch during
a given amount of muscle shortening (and a greater force development, followed by an increase in gear
speed of rotation for a given muscle shortening ratio later in stance, favoring muscle shortening
velocity) with low torque (or moment) production. that powers ankle extension and more rapid foot
In contrast, a low-gear ratio favors greater torque, rotation for limb propulsion.
but a slower range and rate of movement. In a study Changes in limb mechanical advantage, or ­muscle
of muscle gearing at the human ankle joint, Carrier gearing, are important for enabling differently-
et al. (1994) quantified changes in gearing over the sized mammals to maintain similar peak muscle and
course of limb support to evaluate how gearing bone stresses, and thus, similar safety factors in
66 A N I M A L L O C O M OT I O N

(a) (b)
Fm Postures shift

EMA ∝ BW 0.26

EMA = r/R = ʃG/ʃFm

1.0
walk
r /R = G /F m human
run

G macropods
r 0.1
R

0.01 0.1 1.0 10 100 1000

Body mass (kg)

Figure 4.4 Animals adjust their limb muscles’ effective mechanical advantage across body mass and gait by changing their posture. (a) Effective
limb mechanical advantage (EMA) is defined as the ratio of the moment arms of the ground reaction force or as the ratio of the ground reaction
force to extensor muscle force. During limb support EMA = ∫ G / ∫ Fm . (b) Because of changes in locomotor limb posture, EMA generally increases
with size for terrestrial mammals, scaling ∝ BW 0.26 (Biewener, 1989). This allows larger mammals to support their weight while running, without
exceeding their muscle force capacity and limb bone strength. In contrast, macropods (gray line) exhibit no significant change in EMA with size. As
a result, large hopping macropods develop high tendon stresses during hopping, allowing them to store and recover substantial elastic energy.
Human EMA values (open circles) are shown for walking and running, relative to hind limb EMA values (closed circles) for other mammals.

relation to locomotive movement. As noted in bone forces scale ∝ BW 0.74 rather than ∝ BW 1.0. By
Chapter 2, the relative scaling of muscle and bone matching the scaling of muscle fiber area and bone
area to body weight (i.e. volume) poses a significant area (∝ BW 0.75), muscle and bone stress are main-
design problem for achieving comparable mechanical tained at nearly constant magnitudes across a wide
support over a broad range of sizes in animals built size range within terrestrial mammals.
of similar tissues. In mammals and birds (and other While important to maintaining similar skeletal
vertebrates), the capacities of skeletal muscle to gen- safety factors, a size-related shift in posture likely
erate force per unit area (muscle stress) and for limb represents a tradeoff in maneuverability at larger
bones to transmit mechanical load per unit area sizes. Changes in mechanical advantage within ter-
(bone stress) are very similar. Consequently, if ­limits restrial mammals achieved through shifts in limb
to locomotive performance are to be avoided, peak posture are also likely limited for species with body
muscle and bone forces must scale proportionally sizes greater than 300 to 500 kg (Biewener, 1990).
to changes in muscle fiber area and bone area, and Consequently, very large land animals have more
not in proportion to body mass. limited locomotor performance with respect to
Differently-sized mammals achieve a mass-specific speed. Interestingly, for the quadrupedal species
reduction in peak musculoskeletal forces by adopt- that have been studied, limb mechanical advantage
ing different locomotor postures, which change the does not seem to change substantially as a function
mechanical advantage of their limbs (Biewener, 1989; of speed and gait, reflecting the consistent patterns
2005; Fig. 4.4b). Compared with the crouched pos- of limb kinematics in relation to an animal’s limb
tures and low mechanical advantage of small mam- musculoskeletal organization.
mals, larger mammals run with more upright postures. Studies of felids (Day and Jayne, 2007) and hop-
This aligns their joints more closely with the ground ping macropods (wallabies and kangaroos: Bennett
reaction force, enabling them to operate with a high and Taylor, 1995; McGowan et al., 2008) suggest
mechanical advantage, which reduces the forces that limb EMA changes less across body size when
that their muscles and bones must support relative more closely related taxa are compared. The study
to their weight (BW). Because of this, muscle and of felids was limited to kinematic assessment of
 MOVEMENT ON LAND 67

walking captive felids and an inferred vertically- mechanical advantage within more closely related
oriented ground reaction force at mid-support. groups. The near constancy of limb EMA within
With little change in limb EMA at faster speeds, felids and macropods may, therefore, reflect phylo-
larger felids would need to withstand 8-fold greater genetic effects rather than the biomechanics of
forces for their weight or suffer substantial limits on scaling.
performance. Small cats may well have greater leap-
ing ability for their size than large cats; however,
4.4 Locomotor gaits
further study of felid postural limb mechanics over
a broader range of performance is needed to answer Locomotor gaits are generally defined by the rela-
this question. The generally limited scaling and tive timing of limb support during the stride. Changes
low limb EMA observed across macropod sizes in gait are associated with movement at different
may underlie the substantial elastic energy savings speeds and typically involve a ­discontinuous change
that larger hoppers achieve by operating with high in limb kinematics and/or support mechanics.
­muscle and tendon stresses (Chapter 3). However, Three general classes of gaits have been defined:
operating with large tendon strains during steady- walking, running or trotting (and hopping), and
speed hopping likely limits their ability to acceler- galloping. Detailed kinematics descriptions and
ate (Biewener and Bertram, 1991). comparisons for vertebrate animals are presented
The relative constancy of limb EMA across macro- elsewhere (Gambaryan, 1974; Hildebrand, 1988).
pod sizes may reflect an evolutionary increase in size
favored by improved energetic savings to reduce for-
4.4.1 Walking
aging costs. Historically, macropods evolved to larger
sizes after large predators had gone extinct and were Walking gaits involve overlapping periods of sup-
absent in Australia, arguably reducing selection on port among the limbs (duty cycles, β > 0.5; Fig. 4.2a).
the ability to accelerate and maneuver for predator For quadrupedal vertebrates, hexapedal insects,
avoidance. Further study of limb mechanical advan- decapodal crustaceans, and octapedal ­spiders this
tage, or muscle gearing, in other animal groups is means that walking incorporates ­ periods during
needed to explore the extent to which changes in which three or more limbs are in contact with the
limb posture play a role in determining muscle forces ground, providing a stable base of support. Static
required for movement on land. Certainly, limb pos- stability is achieved because the body’s center of
ture affects how animals maneuver and achieve gravity falls within the area of support represented
­balance and stability, in addition to how it affects by the limbs (analogous to the way a table achieves
musculoskeletal loading. stability with only three or four legs). However, static
Interestingly, human EMA during walking matches stability is only achieved at low speeds. Bipedal walk-
that predicted for quadrupedal mammals of similar ing (by humans and ground birds) also involves over-
size (Fig. 4.4b), but is significantly lower during run- lapping periods of limb support, but static equilibrium
ning (Biewener et al., 2004). As discussed in Chapter 3 is limited (although certain birds, such as flamin-
(Fig. 3.7), the decrease in EMA during running is goes, clearly achieve this while standing and sleep-
largely due to the flexed knee posture of the human ing on one leg!). To move at faster speeds, animals
lower limb during running compared with walking, rely on dynamic balancing mechanisms. Dynamic
which substantially increases the force requirements balance requires time-varying control of an animal’s
of the knee extensors (quadriceps muscles) and cor- center of mass energy state (discussed in Section 4.4.2).
relates with an increased cost of transport of human Animals can change speed within a gait, but to
running versus walking (Fig. 3.6). move over a greater range of speed they must change
Finally, as we will discuss in Chapter 9, differ- gait. When an animal increases speed and changes
ences in the scaling of limb EMA across mammalian gait from a walk to a trot or a run, not only is its
taxa may reflect a bias for not controlling for phylo- stride period reduced owing to the increase in stride
genetic effects, which are less likely to have an frequency, but the relative fraction of limb support (duty
impact when comparing postural effects on muscle factor) also decreases (and swing phase increases).
68 A N I M A L L O C O M OT I O N

4.4.2 Trotting, running and hopping considered in Chapter 7.) During hopping, the two
hindlimbs move in phase rather than in an alternat-
Trotting and running gaits are typically characterized
ing fashion as for bipedal runners. Pacing involves
by limb duty cycles ≤ 0.5. Consequently, no overlap-
the use of in-phase limb support by the ipsilateral
ping support periods occur between alternating
fore and hind limb of quadrupeds, rather than the
phases of limb support. In a quadrupedal trot, for
contralateral diagonal fore and hind limb of trotting
example, the diagonal forelimb and hindlimb move
animals. Although horses can be trained to pace for
in unison (i.e. are “in phase”), contacting the ground
racing competition, pacing is an unnatural gait. Few
at the same time and leaving the ground to begin
quadrupeds pace under normal circumstances because
their swing phase before the contralateral forelimb
pacing is less stable owing to the ipsilateral pattern of
and hindlimb contact the ground to begin their
limb support, which results in greater side-to-side
respective support phases (Fig. 4.2b). Bipedal human
rocking body motion compared with trotting. However,
running similarly involves the absence of an overlap
camels and giraffes are notable exceptions, likely due
between the support phases of the two limbs. The gait
to their long legs, in which ipsilateral limbs might inter-
transition from walking to running in avian bipeds is
fere as they move in opposing directions during a
less distinct. Avian bipeds run with an overlapping
traditional trotting gait.
support phase between their two limbs over much of
All of these gaits are similar in that they involve a
their speed range (referred to as “grounded run-
bouncing, spring-like motion of the body on the
ning”) (Gatesy and Biewener, 1991; Rubenson et al.,
supporting limbs (see Fig. 4.9 and Section 4.10.2).
2004). Only at their fastest running speeds do birds
Whereas bipedal runners typically increase running
have non-overlapping support. Their relatively
speed by increasing both stride frequency and
longer feet may account for some of this difference,
stride length, quadrupedal trotters generally favor
but other factors also likely play a role.
an increase in speed by increasing stride frequency
Hexapedal insect running (Full et al., 1991; Full
and bipedal ­ hoppers by increasing stride length
and Tu, 1991) involves a similar gait pattern as that
(see Fig. 4.6). In all cases, the duty cycle of the limb
observed in vertebrates, in which three limbs (fore
decreases at faster speeds, requiring an increase in
and hind limb of one side, and the contralateral
musculoskeletal forces.
middle limb) are used in alternating “in-phase” tri-
pods of limb support, equivalent to the diagonal
fore and hind limb of a quadrupedal trotting mam-
4.4.3 Galloping
mal or the alternating hind limbs of a bipedal run-
ner. Sideways running crustraceans (Blickhan and In addition to walking and trotting, quadrupedal
Full, 1987) also appear to adopt a similar strategy. In mammals evolved the gallop (sometimes referred to
the case of ghost crabs, pairs of the four leading as a canter when used at lower speeds) to achieve
limbs (limbs two and four and limbs three and five) their fastest speeds. The transition from trot to gallop
are used in combination with alternating pairs of its involves a relative shift in the support phases of the
trailing limbs to achieve patterns of limb support that fore and hind limbs, such that the two forelimbs
produce forces and motions of the body (see Section move more or less in phase, followed by the two hind
4.10.2) characteristic of a bipedal running gait. limbs. By shifting the phase of limb support to allow
Two other gaits similar to running and trotting the fore and hind limbs to act together as pairs, gal-
deserve mention: these are hopping and pacing. loping animals are able to increase their stride length
Hopping is used by several marsupial (kangaroos, to a greater extent than is possible by limb movement
wallabies, rat kangaroos) and rodent (kangaroo rats, alone. This is achieved by flexion and extension of the
jerboas, spring hares) species, as well as by toads. spinal column and rotation of the shoulder girdle and
(Hopping in anurans often involves forelimb contact pelvis, which can substantially increase stride length.
and is typically not as continuous or steady as the This is most dramatic in the pursuit gallop of a chee-
hopping gait of mammals, which is often described tah, and cats in general, in which spinal flexion and
as “richochetal.” Anuran hopping and jumping are extension may provide up to a 20% increase in the
 MOVEMENT ON LAND 69

v∝BW 0.24

log speed
fs∝BW –0.14

log stride frequency

and stride length

Ls∝BW 0.38

log body weight (BW )

Figure 4.5 Maximum running speed (v) increases with body weight (BW) up to a given size, beyond which maximum speed declines (gray curve)
owing to mechanical limitations of large size. Although stride frequency (fs) decreases with size in birds and mammals, stride length (Ls) increases
substantially, resulting in the overall increase in speed with size (speed = fs Ls ). Scaling patterns are plotted on logarithmic coordinates, such that
scaling exponents represent the slopes.

animal’s stride length. Spinal flexion and extension f­orelimbs and hind limbs each move together in
also occurs in smaller rodents and other carnivores, phase, the gait is considered a “full-bound.” Bounding
but is modest or absent in larger ungulates (horses, gaits are typical of smaller rodents and carnivores,
antelope, wildebeest etc.) due to scale constraints of as well as hares and rabbits. Indeed, smaller quadru-
size. A rigid backbone in large ungulates is necessary peds seldom trot, commonly changing gait directly
to support the trunk, which is suspended between from a walk to a half-bound or bound, even at low
the hip and shoulder joints, and to transfer load to moderate speeds. Because of a reduced limb duty
between the fore and hind limbs during a gallop. This cycle, galloping involves aerial phases that may
results from the asymmetric timing of fore and hind intervene between one or both sets of limb support
limb support phases, in addition to the asymmetric phase. These aerial phases are a necessary conse-
pattern of deceleration (by the fore limbs) and accel- quence of the increased stride length that the ani-
eration (by the hind limbs) that each set of limbs mals achieve to increase their speed at a gallop.
exerts on the ground. Typically, increases in speed at
a gallop mainly involve increases in stride length 4.5 Stride frequency and stride length
with little increase in stride frequency (Fig. 4.6).
relative to speed and size
At a slow gallop (or canter), one forelimb lands
slightly ahead of the other forelimb, followed by a Size influences many general features of animal
similar pattern of support from the two hind limbs. locomotion, in addition to maneuverability and sta-
Most often, the phase difference is greater between bility. Classical arguments of isometric scaling (made
the forelimbs than between the hind limbs. At faster by A. V. Hill, a Nobel laureate who received recog-
galloping speeds, the two forelimbs and two hind nition for his work on muscle energetics (Hill, 1950))
limbs progressively land more in phase with one suggest that small and large animals should achieve
another and limb duty cycles decrease (to as low as similar top speeds. This is based on the notion that
0.2). When the two hind limbs move fully in phase, length scales inversely with frequency (l ∝ f-1 ∝
the gait is defined as a “half-bound.” When the BW 0.33, see Chapter 1). Small animals with short
70 A N I M A L L O C O M OT I O N

limbs swing their limbs at high frequencies, whereas suggests remarkable muscle performance operating
larger animals with longer limbs move them at lower at such high frequencies and contractile shortening
frequencies. Consequently, these arguments sug- velocities (due to force-velocity effects; Chapter 2).
gest that the maximum velocity ( v = Ls f s , where Ls In contrast to mites, the few other invertebrates
and fs are stride length and stride frequency) of simi- that have been studied (Fig. 4.6) increase speed by
larly constructed animals should be constant and increased frequency and stride length at slower
independent of size. speeds, but mainly increase stride length at faster
When compared across a large size range, how- running speeds (Ting et al., 1994). Several ant species
ever, terrestrial birds and mammals exhibit a scal- have recently been shown to increase running speed
ing of stride frequency ∝ BW−0.14 and a scaling of with body temperature and size, exhibiting scaling
stride length ∝ BW 0.38 at equivalent points of gait patterns similar to those of terrestrial vertebrates
(e.g. each species’ preferred trotting speed or trot- (Hurlbert et al., 2008). However, no comprehensive
gallop transition speed; Heglund and Taylor, 1988; dataset yet describes their patterns of stride fre-
Fig. 4.5). As size increases, stride length increases quency and stride length relative to speed.
more rapidly than the decreases in stride frequency, Increases in locomotor speed within and between
such that larger animals generally move faster at gaits in vertebrates also show differing taxonomic
these gaits and, by extension, are able to attain and size-related patterns relative to changes in
greater top speeds. Certainly, two of the fastest land stride frequency and stride length. Avian and
animals, the cheetah (maximum sprint speed: 100 human bipeds increase their speed by increases in
km/hr) and the pronghorn antelope (maximum sus- stride frequency and stride length at both a walk
tainable speed: 65 km/hr) are at the large end of the and a run, whereas hopping bipeds increase their
size spectrum of terrestrial animals. At very large speed almost entirely by increasing stride length,
sizes (>500 kg), however, locomotor p ­ erformance with stride frequency held nearly constant (Fig.
of terrestrial mammals is constrained due to the 4.6). Small and large mammalian quadrupeds also
effects of mechanical stress on musculoskeletal design differ in the pattern of increases in speed due to
(see Section 4.3), and variables such as speed and stride length and frequency versus gait. Small
maneuverability decline. It is unlikely that similar mammals (e.g. squirrels) increase speed mainly by
constraints of size affect performance in the largest increasing speed at a gallop. Increases at a walk and
terrestrial invertebrates because their size is limited a trot are more restricted, involving both increases
more by mechanical (local buckling) and growth in stride length and stride frequency. At a gallop,
constraints of their exoskeletons. increased speed is mainly achieved by an increase
Comparatively fewer data for changes in stride in stride length, similar to the pattern observed in
frequency and stride length relative to running hopping bipeds. In larger quadrupeds, a greater
speed exist for invertebrate runners; however, Wu fraction of the animal’s speed range is achieved
et al. (2013) found that two North American eryth- within a trot, with increases in both stride frequency
racarid mites use stride frequencies up to 80–100 Hz and stride length contributing to speed increase.
at 45–50°C, corresponding to absolute running Once the animal changes gait to a gallop, increases
velocities up to 0.13 m s–1 and relative velocities up in stride length contribute most of the increase in
to 129–133 body lengths per second (BL s–1)! Extremely speed.
high relative velocities (~170 BL s–1) have also been Non-mammalian quadrupeds (i.e. salamanders,
reported for Australian tiger beetles, exceeding lizards and alligators) generally increase speed by
the fastest relative running velocity (50 BL s–1) and comparable increases in stride frequency and stride
stride frequency (27 Hz) of the American cockroach length. This pattern of speed increase is generally
(Periplaneta americana) at 26°C—perhaps the most- characteristic of both walking and trotting gaits.
studied running insect (Full and Tu, 1991). Changes However, as these animals approach their fastest
in mite running speed (0.02–0.13 m s–1) were driven speeds, speed increases appear to be achieved by
entirely by changes in stride frequency, with little increases in stride length more than by stride
change in stride length. As Wu et al. (2013) note, this ­frequency.
 MOVEMENT ON LAND 71

Walk Run Walk Trot Gallop

Ls fs
fs Ls

Human Ls Ground
squirrel
Bipeds fs
fs
Bird Ls Ls

Dog

fs Quadrupeds
Kangaroo fs
Ls
Wildebeest
Ls
fs
Cockroach fs

Hexaped Ls
and fs
octaped Ls
Ghost cr ab Lizard

Relative speed 100% Relative speed 100%

Figure 4.6 Depending on the number of limbs used for locomotion, terrestrial animals use varying patterns of stride frequency (fs) and stride
length (Ls) to increase relative speed (for comparison of representative patterns for bipeds, quadrupeds, and invertebrate hexapeds and octapeds).
Black lines (solid and dashed) show walking and galloping gaits, whereas gray lines depict trotting or running gaits.

4.6 Spring-mass properties of running The notion that running, hopping or galloping
gaits involve spring-like function of the limb in sup-
The fairly uniform stride frequency maintained port of the animal’s body mass led workers to
during bipedal hopping and quadrupedal galloping model the limb and body as a simple spring-mass
led scientists to speculate that animals favor mov- system (McMahon et al., 1987; Blickhan, 1989;
ing at their body’s resonant frequency (fnat), which McMahon and Cheng, 1990; Fig. 4.7a). In many ter-
depends on their mass (m) and overall leg spring restrial mammals, birds and insects, mechanical
stiffness ( kleg = GV / ∆L , Fig. 4.7a). action and kinematics are predicted effectively by
( )
0.5
f nat = kleg / m (4.2) the properties of a leg-spring supporting the mass
of the body. A simple spring-mass model, such as
For a given spring stiffness, larger masses vibrate at that shown in Figure 4.7a, also predicts the scaling
lower resonant frequencies, which is consistent with of increased leg spring stiffness (kleg) with size (Farley
the scaling decrease in stride frequency (∝ BW − 0.14 ) et al., 1993). Part of the change in leg stiffness can be
noted previously for terrestrial mammals and birds. explained by the more upright l­ocomotor posture
This would indicate f nat ∝ BW −0.14 (given constant that larger mammals adopt in order to increase
density, weight is equivalent to mass), and predicts their limb mechanical advantage for weight sup-
that animal limb stiffness scales ∝BW 0.72 ( f nat 2 BW ) . port (Section 4.3 and Fig. 4.4). Indeed, the reduced
Thus, larger vertebrates move with stiffer limbs (and limb spring stiffness of a “Groucho running” human
trunks) than small vertebrates, which is consistent using flexed knees inspired McMahon et al. (1987)
with reduced flexion of the vertebral column at a to develop the concept of spring-mass running
gallop. By galloping or hopping at their body’s nat- mechanics.
ural frequency, animals are believed to reduce their The neural control of muscle activation during
energy expenditure (Heglund and Taylor, 1988). running may also be linked to the control of muscle
72 A N I M A L L O C O M OT I O N

(a) v is reduced (Ferris et al., 1998; Kerdok et al., 2002).

m
For a two-fold change in surface stiffness, Ferris
∆L
et al. (1998) found that human runners automatically
adjusted kleg by up to 68%.
Studies of running guinea fowl subjected to unantici­
pated drop perturbations (Daley and Biewener, 2006)
similarly show that spring-mass mechanics help to
kleg = GV /∆L stabilize the bird’s running dynamics. Following a
r
perturbation, variation in limb contact angle helps
to maintain a characteristic kleg. This parallels a
spring-mass model of human running that stabil-
izes through the adjustment of limb contact angle
(Seyfarth et al., 2003), rather than adjusting kleg per
se. By contrast, when substrate compliance changes,
(b) v
kleg adjustments stabilize a runner (Ferris et al. 1998).
Central to this stabilizing response is the role of
intrinsic muscle force-length and force-velocity
ma
properties (see Chapter 2), described as “preflexes”
(Loeb et al., 1999), that rapidly change muscle stiff-
ness and enhance subsequent reflex feedback (see
Gv
Chapter 8) to contribute to rapid adjustment of leg
stiffness.
Future work on spring-mass running and hop-
ping mechanics can address the extent to which the
spring-like properties of a runner’s leg are the result
Figure 4.7 Multiple spring-mass and pendulum models have been of intrinsic limb elasticity versus alternating contri-
applied successfully to terrestrial locomotion. (a) The mechanical
butions of negative muscle work (energy absorp-
energy changes of an animal’s center-of-mass (CM) during running,
trotting and hopping gaits are described well by a simple spring-mass tion) during the first half of limb support followed
model, in which the change in height, or limb length, (ΔL) of the by positive muscle work during the second half.
body’s mass (m) are determined by the spring stiffness of the leg (kleg) Either, or both, will yield the spring-like properties
relative to the magnitude of ground force (as shown at that characterize steady running mechanics as well
midstance = Gv), opposing the acceleration (a) of the animal’s mass.
as running with external perturbations.
(b) Spring-mass mechanics operating as a “spring-loaded inverted
pendulum” (SLIP), also explains the force and CM dynamics of
walking (Geyer et al., 2006). Rotational motion of the body over the
supporting limb (the horizontal tangential velocity, v, of the CM, is
shown) allows exchange of potential and kinetic energy, conserving 4.6.1 Joint work in relation to steady versus
mechanical energy of the body’s motion (see Fig. 4.9). non-steady movement
Muscles do work by causing joints to extend or flex
stiffness and its effect on the spring-like behavior of (or abduct versus adduct). Joint work is the product
the limb as a whole (see Chapter 8). Studies of of joint torque (T´) times the joint’s angular motion
humans hopping in place and running over unex- (θ, in radians): T´θ. When a joint flexes against an
pected variably compliant and damped surfaces opposing (flexor) torque (as in Fig. 4.3), the joint
(Ferris et al., 1998; Moritz and Farley, 2003) suggest absorbs energy (i.e. T´θ is defined as being negative).
that adjustment of kleg is a control strategy for stable When this occurs, the muscle that extends the joint is
running. When human runners land on a more stretched and absorbs energy, or does “negative
compliant surface, limb stiffness is increased, result- work.” When a joint extends against an opposing
ing in nearly identical CM motion and stride param- flexor torque, T´θ is positive, and the extensor
eters as when they land on a stiffer surface and kleg ­muscle shortens and does positive work. During
 MOVEMENT ON LAND 73

steady speed locomotion, certain joints (e.g. the vous system. Nevertheless, a considerable degree of
ankle joint of guinea fowl, dog and horse hindlimbs) dynamic stability appears to have evolved in the
flex and then extend while resisting an external underlying mechanics of animals and their limbs.
flexor moment, and behave in a spring-like fashion. Disturbances in balance or support when animals
Other joints either flex and absorb energy (e.g. the move over uneven and less predictable terrain can
knee joint), or extend and produce energy (e.g. the be accommodated by energy absorption at particu-
hip joint; Daley et al., 2007). When animals acceler- lar joints of a supporting limb, compensated by
ate or jump (see Chapter 7), limb joints commonly energy production at other limb joints, and ultim-
extend and do positive work (as do the muscles that ately yielding dynamic stabilization of the body.
extend the joints). During jumping, extensor mus- While several of the underlying principles and mech-
cles may initially shorten or remain isometric, allow- anisms of dynamic stabilization are only now being
ing their tendons to be stretched and then recoil recognized, they are key to understanding how mech-
rapidly so that elastic energy can be stored and anical design can simplify the seemingly complex task
released quickly, amplifying the rate at which work of control by the ­nervous system (see Chapter 8).
(i.e. power output) is performed. In contrast, when Size-related tradeoffs between maneuverability
animals decelerate or land from jumps, the limb and stability also occur. To make a turn, an animal
joints typically flex against flexor torques, thereby must generate laterally-directed forces with their
absorbing energy. Future work needs to investigate limbs that are resisted by medially-directed ground
how different limb joints contribute to limb spring- reaction forces (GML). Fig. 4.8a depicts a simple model
like properties during steady locomotion and com- for this, which assumes that the inside and outside
pare them to joints that do p
­ ositive work to accelerate limbs produce similar leg extension forces against
the animal’s CM (and limb joint) or perform nega- the ground that act through the animal’s center of
tive work to decelerate the animal’s CM and limb mass. In doing so, an animal must avoid toppling
joint. Relating muscle-tendon anatomy to the roles over (laterally). In simple terms, this is determined
that joints play in producing energy (positive work) by the angle of the animal’s limb with respect to the
or absorbing energy (negative work) across a range ground (θ) and the magnitude of the toppling torque
of locomotor behaviors will also be key to inter- (T´top = GML L sinθ) generated during a turn relative to
preting how evolution has shaped musculoskeletal the animal’s weight (Fig. 4.8a), where L is the dis-
design in relation to performance. tance from the animal’s CM to the base of its support-
ing limb. To avoid toppling over, the animal must
satisfy the following condition:
4.7 Maneuverability versus stability
GML L sinθ ≤ BW L cosθ (4.3)
As previously noted, by providing a tripod of sup-
port, walking gaits provide static stability. However, Eq. 4.3 simplifies to
walking gaits do not allow rapid movement and
GML ≤ BW cotθ (4.4)
often limit an animal’s maneuverability (the ability
to change movement direction within a given time or or
distance). Maneuverability at faster speed requires
BW ≤ GML tan θ (4.5)
dynamic stability. Even tortoises, upon which the
virtues of slow and steady walking have been the By bringing their CM closer to the ground and
fancy of children’s tales, depend on dynamic stabil- ­lowering θ, animals can make sharper turns. This is
ity during particular time periods when they walk. reflected by the more flexed limb posture that ani-
Much like learning to ride a bicycle, forward momen- mals adopt when making a turn. In general, small
tum and dynamic exchanges in kinetic and poten- animals can make sharper turns than large animals,
tial energy of the body (see Section 4.10.2) provide because small animals run with shorter, more flexed
mechanisms for stabilization of the body at faster limbs and take more frequent steps, thereby allow-
speeds. Such stabilizing mechanisms also depend ing them to turn more rapidly and potentially
on the control of movement achieved by the ner- escape larger-sized predators. A more flexed limb
74 A N I M A L L O C O M OT I O N

(a)

Topple condition:
GML L sinθ < BW L cosθ
GML < BW cotθ
–GML

BW

G
L
GV
Slip condition:
θ GML < G V η

+GML

(b)

GML

GML < G V η
r

Figure 4.8 Turning animals must resist slipping and toppling over. (a) The threshold for toppling and slipping can be measured by tracking the
location of the animal’s CM (gray circle), the forces on the inner limb that touches the ground on the inside of the curve, and the coefficient of
friction, η, that the foot (or hoof) achieves interacting with the ground. Toppling torque is defined as GML L sinθ (where L, white dashed line, is
the distance from the CM to the point of ground force application). (b) The magnitude of mediolateral ground force, GML, which critically affects
toppling and slipping, varies in relation to turning radius (r) and speed (v).

also increases the limb’s mechanical advantage

GML ≤ G V η (4.6)
for producing horizontal forces relative to vertical
forces, which can contribute to establishing a new where η represents the coefficient of friction between
movement direction (Walter, 2003). the animal’s foot and the ground. An animal’s turn-
In addition to toppling, animals must also avoid ing radius (r) depends on its velocity relative to its
slipping when making a turn. This requires that a ability to avoid slipping (Fig. 4.8a). For a given turn-
second condition be met: ing radius, the medial component of ground force
 MOVEMENT ON LAND 75

needed to provide centripetal acceleration to change change the body’s momentum vector for turning,
the body’s momentum vector is given by, this reduces GV as well as G, thereby limiting a run-
ner’s speed when making tighter turns. In compari-
GML = mv 2/r (4.7)
son to bipeds, quadrupeds have the additional
which, in order to avoid slipping, requires that, flexibility of using their forelimbs differently from
their hindlimbs when turning. In a study of racing
η ≥ cs v 2/gr (4.8)
greyhounds, Usherwood and Wilson (2005) showed
where v is the animal’s tangential velocity, g is that, in contrast to human sprinters, greyhounds are
the gravitational acceleration constant, and cs is not force limited and can use their hindlimbs to
a ­constant relating the magnitude of the vertical maintain their bend running speed similar to run-
ground reaction force to an animal’s weight ning straight sections of the track. Likewise, mice
=
( GV c= s BW cs mg ; recall from Section 4.2 that GV making 90° turns do not slow down when making
may be greater or less than an animal’s weight, tighter turns (Walter, 2003). As noted by Chang and
depending on the animal’s speed and gait). In add- Kram (2007), how the limbs generate ground
ition to the surface properties of the foot and ground, forces when an animal turns is a complex three-
η will depend on the relative contact area of the foot. dimensional task bounded by several interacting
Given that smaller animals generally have propor- ­biomechanical constraints. These include the need
tionately larger feet (i.e. greater surface area of con- to generate lateral force for centripetal acceleration
tact) for their weight, η will tend to vary inversely and to produce fore-aft breaking and propulsion
with body size. Although not yet investigated, this forces (GH) that help to control body rotations in the
suggests that smaller animals are less likely to
­ transverse plane. Jindrich et al. (2006) define a “limb
slip. To improve their grip, many animals have effectiveness number” ε´ = θp/θd to evaluate how
evolved claws and hooves that grip the surface to well turns produced by exerting a lateral force
improve turning performance when running and ­perpendicularly to the subject’s movement direction
climbing. A recent study based on GPS tracking achieve changes in body orientation (θp) relative to
combined with inertial measurement of body the new movement direction (θd)—a value of one
accelerations, showed the importance of turning indicates an ideal match. In studies of ostriches,
performance by cheetah during predatory hunts Jindrich et al. (2007) found that for both side-steps
(Wilson et al., 2013). In order to hunt successfully, and cross-over turning steps, ostriches operate with
cheetah slowed down to improve their turning ε´ = 0.9–1.2, whereas humans operate with ε´ = 2.0–
performance when closing in and chasing down 2.5. Humans, therefore, produce rotational yaw tor-
smaller, fleet-footed prey. The greater maneuver­ ques about their body’s vertical axis that must be
ability and stability of smaller animals is apparent countered by decelerating force in their direction
to anyone who has watched a larger animal chase of travel, which slows turning speed. In contrast,
its smaller intended prey (as, for example, when ostriches are able to turn with minimal breaking or
Fido chases a squirrel to the nearest available tree). accelerating forces, allowing them to turn without
In such instances, maneuverability often compen- slowing.
sates for the slower speed of the smaller animal, Another requirement for stability when maneu-
enabling it to escape its pursuer. vering and turning is to control the ground reaction
The model depicted in Fig. 4.8 is clearly an over- forces exerted about the body’s CM, specifically in
simplification of how animals turn. In reality, inside terms of roll (rotation about the fore-aft horizontal
legs and outside legs produce different ground reac- axis), pitch (rotation about the medio-lateral axis)
tion force components and magnitudes, as Chang and yaw torques (rotation about the vertical axis)
and Kram (2007) showed for flat curve running by that ground reaction forces exert about the body’s
humans. In their study, the inside leg produced CM. Simplified models (Fig. 4.8a) assume that G
lower ground reaction forces than the outside leg. acts through the CM, so that these torques are zero.
Because a fraction of leg force must be directed lat- However, this is rarely the case, as revealed by
erally to provide the centripetal force needed to ­analysis of breaking/propulsion forces relative to
76 A N I M A L L O C O M OT I O N

lateral forces of humans and ostriches (Jindrich while maintaining stability and establishing a new
et al. 2006; 2007). Measuring roll, pitch and yaw tor- heading direction.
ques is challenged by identifying the location of the
animal’s CM in relation to the time-varying ground
reaction force and where net G acts based on indi- 4.8 Froude number and dynamic
vidual limb forces—the location of the net ground
similarity
reaction force acting on the body is called the
center of pressure. Future understanding of the Measurements of the mechanics and kinematics of
­mechanisms and constraints that operate on maneu- limb support have also allowed gaits to be defined
vering and turning animals, particularly those with by a dimensionless factor known as the Froude
four or more limbs, will benefit from measurements number (Alexander and Jayes, 1983):
of individual limb forces and the resulting CM tor- Fr = v 2/gl (4.10)
ques that they produce, which must be balanced
over time to maintain stability. in which v is the animal’s velocity, g is the gravita-
Animals must change their heading in addition to tional acceleration constant and l is a characteristic
rotating their body (to their new heading direction) length (e.g. hip height) of the animal. The Froude
when turning. In their study of turning cockroaches, number normalizes the forward velocity of a mov-
Jindrich and Full (1999) defined the insect’s ability to ing animal to its limb length and gravitational accel-
redirect its heading in terms of a non-dimensional eration. These parameters represent fundamental
linear maneuverability number (LMN), defined as force interactions of stepping locomotion, in which
the ratio of lateral impulse to forward momentum: the centripetal force ( F = mv 2 / r ) acting on the body’s
mass, as it rotates over a supporting limb, balances
LMN = ∫ GML dt / mv (4.9)
the ground reaction force acting on the limb from
where v is the animal’s forward velocity prior to below (Fig. 4.7a). At the same Froude number, geo-
making a turn. Cockroaches were found to achieve metrically similar animals move in a dynamically
LMN = 0.75 , indicating a lateral impulse = 75% similar fashion, defined by constant ratios of veloci-
of their forward momentum to change heading. ties, lengths and forces of locomotion when com-
Animals that can turn more rapidly (producing pared across size. For example, two pendula of
greater yaw torque about their CM) have larger different lengths, swinging through the same angle,
LMNs. While a useful metric to compare across ani- move in a dynamically similar fashion. The Froude
mals of differing size and limb configurations, LMN number also represents the ratio of a moving body’s
characterizes the 2D requirements of turning and kinetic energy (1/2 mv2) relative to its potential energy
not those involving body lean and roll or pitch, (mgL). Equal Froude numbers, therefore imply equal
which occur out of the horizontal plane of motion ratios of kinetic to potential energy when an animal
and are linked to stability and toppling, as previ- moves. Animal gaits (studied mainly in mammals)
ously discussed. Larger animals, or those with more are fairly well-defined by Froude number, with ani-
upright limbs, likely face more severe constraints to mals generally changing gait from a walk to a trot at
turning that are unaccounted for by LMN per se. a Fr = 0.3–0.5 and from a trot to a gallop at Fr = 2–3
Additionally, Walter (2003) notes that mice rotate (Alexander and Jayes, 1983). Consequently, quadru-
their body in advance of changes in heading when pedal mammals change gait from a walk to a run
turning, enabling them to use ground reaction forces when the ratio of kinetic to potential energy is about
parallel, rather than perpendicularly, to their body 0.2 and from a trot to a gallop when the ratio is
axis to initiate a new heading direction. Further bio- about 1.25. As we’ll see in Section 4.10, this reflects
mechanics research on turning and maneuvering is the fact that kinetic energy fluctuations of an ani-
clearly needed given its relevance to natural behav- mal’s body become increasingly important at faster
iors. Few animals have been studied in which LMNs speeds. Although the Froude number and the con-
can be compared and fewer still in terms of the cept of dynamic similarity appear to work well at
underlying biomechanics needed to rotate the body, Earth’s gravity and by ignoring inertial forces that
 MOVEMENT ON LAND 77

are also important in locomotion, they don’t appear than would otherwise be possible based on skeletal
to hold as well when gravity is altered (Kram, 1997). morphology alone.

4.9 Inferring gait and speed 4.10 Mechanical work: potential

of fossil animals and kinetic energy changes during
Fossil trackways provide an historical record of the terrestrial locomotion
stride length and footfall pattern of animals. If the In addition to generating forces against the ground
foot impression on the trackway is distinct enough to support their weight, terrestrial animals must
to determine the species that made the track and also exert forces—performing mechanical work—to
reliable reconstruction of its limb skeleton is available maintain oscillations of the potential energy (PE)
from fossil material, it is possible, using an estimate and kinetic energy (KE) of their center of mass (CM)
of Fr based on stride length and the animal’s limb and limbs (Fig. 4.9). Fluctuations in PE and KE arise
height, to estimate the speed and gait used by the from periodic support of their body by their limbs.
animal at the time it made the track. Analyses such Although wheels avoid these fluctuations, the use
as these have been carried out for fossil trackways of of legs enables animals to move effectively over
human ancestors and fossil dinosaurs (Alexander uneven terrain. Consequently, CM energy fluctuations
1976; 1984). In the case of fossil hominid trackways are inherent to all forms of legged transport and
at Laetoli (Tanzania), hominids were estimated to exhibit surprisingly conservative patterns for dif-
walk at speeds of 0.5–0.75 m s–1 3 million years ago. fering locomotor gaits and modes of vertebrates
This is lower than the preferred walking speed (~1.3 (Cavagna et al., 1977), including six- and ­eight-­legged
m s–1) of modern humans. The difference likely reflects running arthropods (Blickhan and Full, 1993). There­
our early ancestors’ 33% shorter stature, rather than fore, changes in CM energy can be used to define an
limitations of their bipedal gait. animal’s gait.
In the case of dinosaurs, estimates from trackways Because an animal’s CM rises as it moves over a
located in Texas (USA) suggest that larger quadru- supporting limb (or group of supporting limbs) and
pedal sauropod dinosaurs walked rather slowly at falls as weight is transferred to the opposite limb(s),
1 m s–1. Moderately-sized bipedal theropod dino- potential energy must be supplied by an animal’s
saurs walked at speeds close to 2.2 m s–1, but ran at muscles to raise its body’s CM during every step.
speeds as high as 12 m s–1. This would certainly be a Animals also slow down and speed up during each
competitive speed for an Olympic 100 m race, over step, as reflected by the decelerating and accelerat-
which human sprinters average 10 m s–1! However, ing fore-aft ground reaction forces ( –GH & + GH ,
it is likely that the very large carnivorous theropod Figs. 4.1 and 4.2), requiring changes in kinetic energy
dinosaurs, such as Tyrannosaurus, were too large to of their CM (Fig. 4.9) and limbs relative to their
run. Biomechanical analysis (Hutchinson and Garcia, CM (not shown). This occurs even when an animal
2002) based on musculoskeletal modeling of the moves at a constant average speed: small fluctuations
extensor muscle mass needed to support their body in forward and vertical speed reflect changes in
weight, compared with the amount of muscle that kinetic energy of the animal’s body that muscles
modern running birds and cursorial mammals pos- must generate by doing work (positive work by
sess, indicate that very large theropods (ca. 6000 kg) shortening, or negative work by being stretched;
were likely poor runners and did not exceed speeds see Chapter 2). Alternatively, some of this energy
of 8–10 m s–1. Information about the width of an can be recovered from elastic sources (Alexander,
animal’s stance and length of its step, the use of 1988). Changes in vertical kinetic energy also occur
mechanical parameters such as the Froude number during each step due to the vertical component of
and biomechanical estimates of muscle capacity, ground reaction force which decelerates the ani-
which can be obtained from extant animals and mal’s “fall” when it first lands and re-accelerates
applied to fossil ones, enable a more informed its CM upward to regain potential energy. Kinetic
analysis of skeletal form and locomotor function energy changes of limb motion, as the limbs are
78 A N I M A L L O C O M OT I O N

(a)
KE
Walk

PE

A B

(b)

KE

Run

PE

Uε

A B

Figure 4.9 An animal’s CM exhibits potential energy (PE) and kinetic energy (KE) fluctuations as a function of time that vary in timing during (a)
walking and (b) running gaits. During walking, PE and KE fluctuate out-of-phase, allowing an exchange from PE → KE during time period “A” and
an exchange from KE → PE during time period “B”. During running, PE and KE fluctuate in-phase, preventing an exchange between each form of
energy as during walking. Consequently, during running, KE and PE are converted to elastic energy (Uε) in spring elements of the limb during time
period “A” and converted back to PE and KE during time period “B”. These energy exchange mechanisms reduce the amount of work that the
muscles must perform, lowering the energy cost of terrestrial locomotion.

accelerated and decelerated during both stance and cussed in Chapter 3 indicate that the energy cost of
swing phases, are greatest at faster speeds of move- terrestrial locomotion is determined more by the
ment (Fedak et al., 1982) and can incur a significant magnitude and rate of m­ uscle force generation, than
energetic cost (Marsh et al., 2004). by the amount of work that muscles perform. Hence,
Losses in potential and kinetic energy require mechanisms to reduce the mechanical energy fluc-
­muscle work to sustain the forward speed and tuations of the body and reduce the work of mus-
energy of an animal’s body, and hence, incur a cles are important for achieving an economical gait.
metabolic cost for the work that the muscles must
perform (in ­addition to supporting body weight). In
general, ­animals have evolved generally efficient
4.10.1 Walking: body and limb movement
and smooth modes of legged transport that minim-
as “inverted pendula”
ize the oscillations in PE and KE of the body’s CM,
thereby ­reducing the metabolic cost of muscular work Walking gaits allow an exchange of potential and
needed to maintain the body’s energy state at a given kinetic energy of the body’s center of mass because
speed. In ­ addition, animals have independently fluctuations in PE and KE occur out of phase
evolved similar mechanisms for reducing the work (Fig. 4.9a). PE is maximal at mid-support when an
of locomotion by means of efficient exchange of PE animal moves over its supporting limb(s) and falls
and KE, or by elastic energy storage and recovery. as the animal shifts weight support to the next
Indeed, the patterns of metabolic energy use dis- ­supporting limb(s). As the animal “falls” forward
 MOVEMENT ON LAND 79

during this shift in limb support, its KE increases. limb support, is the major determinant of the energy
Consequently, decreases in PE at this time (time cost of walking.
period “A” in Fig. 4.9a) can be converted to KE,
reducing the amount of muscle work required to
4.10.2 Running, trotting, hopping
increase the body’s KE. Similarly, as the animal’s
weight shifts over the next supporting limb(s),
and galloping: bouncing gaits
its KE decreases at the same time that its PE In contrast to walking, PE and KE of the body’s CM
rises, ­enabling an opposite exchange of KE to PE fluctuate in phase with each other during running,
(time period “B”). The ongoing exchange between trotting, hopping and galloping gaits (Fig. 4.9a).
potential and kinetic energy of the body’s CM dur- For these gaits, PE and KE decline during the first
ing walking gaits of bipeds, quadrupeds and hexa- half of limb support and increase during the second
peds occurs in a similar fashion, with an exchange half, precluding energy conservation by means of
of up to 70% estimated during walking. Often this PE and KE exchange. Does this mean that decreases
represents the animal’s preferred walking speed in PE and KE during the first half of a step are lost
and coincides with its ability to minimize its meta- and must be re-supplied by an animal’s muscles, or
bolic energy cost of transport; see Section 3.4. is there another means for conserving mechanical
The exchange of PE and KE during walking is and metabolic energy? Rather than losing center-of-
­analogous to an “inverted pendulum,” based on mass PE and KE when landing on the ground, ver-
the similar functional exchange of energy of the tebrate runners store this energy in elastic elements
pendulum of a spring-wound clock that requires of the body, primarily the tendons and ligaments of
only a small amount of spring energy per tick to the limbs (time-period “A,” Fig. 4.9b). The elastic
keep the clock running. In the case of walking ani- strain energy stored in these elements (Fig. 4.13) is
mals, this energy is supplied by the muscles dur- subsequently returned to increase the animal’s PE
ing each step and is decreased by the effectiveness and KE (time-period “B”) as it rebounds off the
with which PE and KE of the body’s CM can be ground during the latter half of limb support, help-
exchanged. ing to provide the spring-like properties of limbs
Ideal pendular motion suggests movement of the when animals run, trot or hop at faster speeds
body’s CM along an arc, during which mechanical (Fig. 4.7). The exchange between PE and KE of the
energy is conserved by exchanging PE and KE. No body’s CM and elastic strain energy provides a sec-
work should be required. However, work is required ond mechanism for reducing the amount of work
to overcome collisional energy losses when the muscles must perform when animals move at a
limbs strike the ground, in addition to an incom- steady speed. Whereas limb tendons, aponeuroses
plete exchange of PE and KE. Passive-dynamic (muscle connective tissue sheaths) and ligaments
walking robots demonstrate these ­principles of eco- are the main sites of energy savings for vertebrate
nomical gait (Collins et al., 2005; Collins et al., 2001; bipedal running and quadrupedal trotting gaits,
McGeer, 1990). Although some energy is lost due to significant savings may also be provided by liga-
limb collisions with the ground, such robots are ments and aponeuroses located in the trunks of
able to walk stably down very slight declines (~3°; quadrupeds when they gallop (Alexander, 1988).
the small rate of PE decrease providing the power The relative importance of energy savings by trunk
for walking). During walking, animals must also versus limb elastic structures, however, is not well
transition from one supporting limb to another. known and merits further study.
Such step-to-step transitions involve collisions of Although there is evidence from whole body
the leading limb that require work to r­edirect the mechanics that hexapedal (insect) and octapedal
velocity of the CM from one pendular arc to the next (crab) running also involves a bouncing gait (Full,
(Donelan et al., 2002a; Kuo et al., 2005). Studies of 1989), the sites and amount of elastic energy storage
humans walking (Donelan et al., 2002a) indicate that occur in invertebrate runners remain under-
that the work of step-to-step transitions, rather than studied and not well known. One problem is that
deviations from pendular motion during single arthropod limb muscles transmit force via apodemes
80 A N I M A L L O C O M OT I O N

or directly to their exoskeleton, which are made of the negative work of the lead limb that decreases
chitin. However, measurements of the dynamic CM velocity), which must be compensated for by
properties of whole cockroach legs indicate that positive work (W ( + ) = 1/2mv(CM +) 2
) of the trailing
they achieve resiliencies comparable to the limbs of limb to regenerate CM velocity. Limb work is there-
running mammals and birds (Dudek and Full, fore proportional to the square of the mass-
2006). Because chitin is stiffer than vertebrate ten- normalized time-integrated ground reaction forces,
don, the amount of strain energy that can be devel- or impulses, acting through the limbs on the CM (so
oped for a given force is less (see Chapter 2). that W = 1/2m(1/m ∫ Gdt 2 ), given vCM = 1/m ∫ Gdt 2 ;
Nevertheless, as we’ll see in Chapter 7, numerous or W ∝ ∫ Gdt 2 ), as depicted in Fig. 4.10a for steady-
invertebrates have evolved specialized catapult speed level walking, with positive work by the trail-
mechanisms for storing strain energy in their ing limb shown in the open square and negative
apodeme and cuticle, which allow them to achieve work by the lead colliding limb in the shaded square.
impressive jump distances for their size. Not only do limbs collide with the ground dur-
ing walking, collisions also occur in trotting, run-
ning, hopping and galloping gaits (Ruina et al.,
4.10.3 “SLIP” limb mechanics
2005). New studies adopting a collisional approach
In reality, the limbs of walking and running animals focus on how limb movements and ground reac-
flex and extend during limb support, operating as tion forces act to alter the trajectory of an animal’s
“spring-loaded inverted pendula” (“SLIP”), rather CM velocity vector, as an alternative to quantifying
than the stiff-legged motion suggested by pendular fluctuations of center of mass PE and KE, and the
movement. The degree of limb flexion depends on work required to maintain CM energy state. Such
the limb’s spring stiffness (kleg) relative to body weight an approach was key to demonstrating that lead
loading (see Section 4.6). In fact, Geyer et al. (2006) and trailing limbs of a walking biped (e.g. human)
show that a spring-mass model incorporating limb work against each other during step-to-step transi-
compliance more faithfully describes the dynamics of tions (Donelan et al., 2002b).
walking (as well as running) compared to a classical Collisional energy losses are zero when vCM is
stiff-legged inverted pendulum model (Fig. 4.7b). perpendicular to the ground reaction force, as in a
Step-to-step transitions between limbs (such as the rolling wheel (e.g. a bike on smooth level ground;
double support phase of human walking), which in which no fluctuations in PE and KE occur), but
involves opposing limb forces and the redirection increase when vCM is directed more in line with G
of CM arc-like motion (Donelan et al. 2002a), are (Fig. 4.10b). This can be quantified by the collision
also captured by a spring-mass model of walking. angle ϕ: the angle between vCM and G (shifted by
π/2 to quantify angle changes from G |vCM|). The
collision angle ϕ also equals the sum of angle λ (vCM
4.11 Collisional mechanics of legged ­ orizontal) and angle θ (G to the vertical), or
to the h
ϕ = λ + θ (Lee et al., 2011). Fig. 4.10b shows two
locomotion
ideal cases: when ϕ = 0 (λ and θ are equal and of
As we have noted, the opposing limb forces exerted opposite sign), collisional energy loss is 0, as for a
during step-to-step transitions of walking involve wheel; and when λ and θ are of similar sign (con-
CM energy loss when the lead limb collides with the sistent with compliant SLIP mechanics), collision
ground (Fig. 4.10a). In this context, limb ground con- angle ϕ increases and energy losses are greater.
tact is modeled as an inelastic collision. Collisional Impor­tantly, because vCM is directed mainly in the
energy lost by the lead limb requires that the trailing forward path of movement, changes in collision
limb(s) supply positive work to redirect CM velocity angle (and therefore collision losses) are influenced
(vCM) in an upward direction during the next step. more by fluctuations in G during limb support rela-
The work (W) performed by the limbs on the CM is tive to fluctuations in vCM.
equal to the change in KE of the CM when the lead Simple walking and running models assume that
limb collides with the ground ( W ( − ) = 1 / 2mvCM
( − ) 2 is
the direction of the ground reaction force (G) acts in
 MOVEMENT ON LAND 81

(a) (b) ϕ=λ+θ ϕ=|λ–θ|

+
v⃑CM collision fraction = ϕ / λ + θ
W (–) 1 0
F̂lead vCM
ϕ λ ϕ
F̂ trail
W (+) F θ
v⃑ –CM
ϕ

trailing leading Double

leg leg
Support
compliant SLIP zero-collision case

(c) potential
collision
0.28
actual
0.21 collision
Angle (rad)

0.14
λ

0.07
θ ϕ
0
walk run

Figure 4.10 The mechanics of terrestrial locomotion can be modeled in terms of “inelastic” collisions by the limb with the ground (Kuo et al., 2005).
(a) This approach helps to explain energy losses that occur during step-to-step transitions in walking, in which the trailing leg must do work
(W (+ ) ) to compensate for the energy lost (W ( − ) ) due to the collision of the leading leg with the ground (proportional to collision angle ϕ). The
amount of work by each limb depends on their time integrated force, F̂, and CM velocity, vCM, which affect the CM trajectory. (b) A collisional
analysis can be applied to the spring-mass or compliant “spring-loaded inverted pendulum” (SLIP) models of running and walking in which more
energy is lost (and more work must be performed) with greater ϕ. For a wheel, or limb in which vCM is perpendicular to the ground reaction force, ϕ
is zero (no collisional energy loss). (c) Collision angle (ϕ, dark gray bar) increases markedly from walking to running (and trotting), indicating much
greater actual collisional losses during running (and trotting) compared with walking and galloping. The potential for collisional energy loss
(absolute sum of λ + θ ) is also much greater for running, and matches more closely the actual collisional energy loss (= λ − θ ) compared with
walking. Walking results in a reduced actual collisional energy loss (Lee et al., 2011).

line with the limb’s direction (Fig. 4.10a). Even during walking and galloping gaits, compared
though actual limb kinematic patterns are more with little evidence of collision reduction during
complex (e.g. see Fig. 4.3), this assumption is rea- trotting, running or hopping gaits (Fig. 4.10c). The
sonably accurate. Using a collisional approach, relative magnitude of collisional energy loss was
the dot product of G and vCM (=GvCMsinϕ), which quantified as the “collision fraction”: ϕ/(λ + θ); the
equals the power generated by the limbs on the CM, ratio of the realized collision energy loss to the
can be integrated over the period of a step to deter- maximum possible energy loss of the limb with the
mine the net work the limbs perform on CM motion ground. Collision reduction leads to smaller collision
(Donelan et al., 2002b). A smaller collision angle ϕ fractions (1 → 0; Fig. 4.10b). Whereas walking and
corresponds to reduced power and, thus, reduced galloping gaits distribute limb support over mul-
limb work over the period of limb support. tiple support phases of a stride, thereby reducing
Recent analyses of collisional energy losses across collisional energy losses, the biphasic nature of limb
animal sizes, speeds and gaits (Lee et al., 2011; Lee support in quadrupedal trotting, bipedal running
et al., 2013) found evidence of collision reduction and hopping results in large collisional losses that
82 A N I M A L L O C O M OT I O N

must be recovered by either elastic energy return edu/RHex/Home) was developed based on the
or muscle work. SLIP-like mechanics of running cockroaches (Kodi­
tschek et al., 2004). RHexTM makes use of the intrin-
sic stability of compliant rotating limbs to achieve
4.12 Legged robotics
robust movement over uneven terrain, minimizing
The inverted pendular nature of center of mass PE the need for centralized control. Other legged robots
and KE exchange during walking has inspired a that stick to surfaces and climb are discussed in
variety of passive and minimally-actuated walking Chapter 7.
robots (McGeer, 1990; Collins et al., 2005—see: Both BigDogTM and RHexTM have rigid bodies,
http://ruina.tam.cornell.edu/research/topics/ unlike quadrupedal vertebrates and hexapedal
robots/index.php). These walking robots achieve arthropods that use trunk flexibility to enhance
dynamics that require minimal energy input (powered their running performance and stability. Incor­
either by a slight slope or a hip or ankle motor) to porating trunk flexibility is one area that will be key
maintain stable walking. One goal is to demonstrate for the advancement of legged robots to achieve
principles of economical walking that require min- more ­realistic animal movement and performance.
imal energy input. Such designs and strategies can, The development of quiet electric motors to power
in turn, be implemented to achieve improved pros- actuation of the robot is also key. Whereas hydraulic
thetics for amputees (e.g. Endo and Herr, 2009). actuation depends on noisy engines, recent devel-
Another area of research is to design exoskeletal opment of a cheetah-like robot (see: http://video.
devices that can assist human movements, either to mit.edu/watch/mit-robotic-cheetah-28824/)
reduce muscle work and energy costs or to enhance demonstrates a significant advance in using high-
performance beyond the range that muscles can pro- power/weight electric motors (Seok et al., 2013),
vide (e.g. Collins et al., 2015; Sawicki et al., 2009). yielding a weight-specific cost of transport [mech-
The recent work based on an unpowered exoskeletal anical energy/(weight x distance)] similar to
device to assist ankle extension was able to reduce mammals of similar size and much less than that
the metabolic cost of human walking by 7%. Such achieved by comparably sized BigDogTM. Even
devices are also helping to improve the design of though the cheetah robot is currently the fastest
active orthotics (e.g. Gordon et al., 2006). running robot, its top speed (4.2 m s–1) is still far
The spring-mass nature of a compliant SLIP model less than the speeds (16.7–25 m s–1) real cheetahs
of running, trotting and hopping gaits has simi- achieve in pursuing prey (Wilson et al., 2013).
larly inspired a variety of bipedal and quadrupedal Finally, visual guidance of movement will ultimately
robots. Beginning with a single bouncing monopod require the integration of reasonably high-speed,
and subsequently a bouncing biped, Raibert (1986) high-fidelity video cameras that can integrate visual
showed how steady running and hopping gaits cues in real time to guide the robot’s movements: a
could be achieved using simple control laws. Since major hurdle for achieving truly autonomous robots
then, Raibert and colleagues at Boston Dynamics (as well as self-driving cars).
have developed a variety of actuated robots that
achieve an impressive range of autonomous per-
4.13 Limbless locomotion
formance (see: http://www.bostondynamics.com/
index.html), including recovering from slips and Although the large majority of terrestrial animals
moving over uneven terrain. BigDogTM was inspired, move using limbs, certain invertebrates (e.g. nema-
in part, by the locomotion of goats and dogs (Lee todes and earthworms) and vertebrates (e.g. snakes
et al., 2011) with engineering design development and sand lizards) have evolved surface and subter-
based on prior robotics expertise utilizing servo- ranean locomotion by means of undulatory loco-
hydraulics for limb actuation, in relation to limb motion of their body axis, without the use of limbs.
spring elasticity, and limb support timing based on Burrowing and subterranean locomotion enables
fairly simple control laws. Similarly, a small hexa- these animals to escape from high daytime temperat-
pedal robot RHexTM (see: http://kodlab.seas.upenn. ures in desert environments, as well as from predators,
(a) (d)

Cam 2 & 3

Cam 1 Cam 4

1 cm

Above surface

2 cm

(e)
Horizontal wave
Below surface

(b) (c)

η' = 1 η' = 0.5

1
A 2 –90°
vx /λ (s–1)

λ
0.5 Head Tail
1
LP CP LP CP

0 0 Vertical wave
A/L λ/L 0 2 4
f (Hz)

Figure 4.11 Legged reptiles “swim” through and limbless reptiles undulate over granular substrates. (a) Sandfish lizards “swiming” were filmed burrowing and foraging for food while undulating
through their sandy substrate. X-ray recordings reveal limb movements relative to the body, from which (b) the amplitude (A) and wavelength (λ) of body undulations can be measured and
normalized with respect to body length (L), along with (c) the animal’s forward velocity (vx ) normalized to wave speed (LP, loosely packed media - black triangles; CP, closely packed media - gray
circles). Sandfish lizards increase speed by increasing undulatory frequency not wavelength. As a result, swimming velocity is a constant fraction (0.5) of wave velocity (η’ = wave efficiency); (d)
Similarly, fluidized beds have been used for analyzing the sidewinding motion of sidewinder rattlesnakes. (e) Sidewinding uses large horizontal waves propagating from the head to tail to push
against the substrate and move the body “sideways”. Adapted from Maladen et al. (2009) Fig. 1 (a,b,c and e), with permission The American Association for the Advancement of Science and Astley
et al. (2015) Fig. 1 and Fig. 2 (b,c), with permission The National Academy of Science.
84 A N I M A L L O C O M OT I O N

or to forage for food within the ground. Through the moving over loose sandy substates, serpentine undu-
use of a fluidized bed (Fig. 4.11d) that can alter the lation does not enable effective movement. In these
packing density of granular media, Goldman and cases, snakes typically adopt a sidewinding or con-
colleagues (Astley et al., 2015a; Maladen et al., 2009; certina kinematic pattern of movement (Gans, 1974;
Marvi et al., 2014) have discovered novel mechanisms Jayne, 1986).
and developed new theory to describe the move- Sidewinding snakes translate over loose sandy
ment of sand-fish lizards burrowing and swimming substrates by means of lifting certain body segments
through granular substrates, and how sidewind- while others remain in static ground contact (Fig.
ing snakes and biomimetic snake robots maneuver 4.11e). Positions of contact move from head to tail,
and effectively move over the surface of loose sandy leaving pairs of parallel lines on the ground. This
substrates of varying gradients. minimizes shear forces at contact. In studies of desert
Sand-fish lizards effectively burrow into and swim sidewinder rattlesnakes, Marvi et al. (2014) show
through sand (or glass beads used to model differ­ent that as the substrate incline increases, the length of
granular media) by means of large amplitude ­traveling body contact with the sand increases. This allows the
waves of body undulations, with their limbs retracted snake to reduce the contact stresses that it applies to
against their body (Fig. 4.11a; Maladen et al., 2009). the granular substate, which is critical for moving up
Increases in swimming speed are achieved by a steeper gradient because the substrate yield stress
increased undulatory frequency (f) and not by changes (when granular flow occurs) decreases with steeper
in the wavelength (λ) of the traveling wave (Fig. angles. Sidewinding can also be described by the
4.11b,c). Surprisingly, the relationship between f and λ superposition of horizontal and vertical body waves
was found to be independent of the packing volume with a ± 90° relative phase. In a recent study, Astley
of the granular media (loose packed (LP) versus close et al. (2015a) show that the exceptional maneuverab­i­
packed (CP)). Further, lizards swam at velocities lity of sidewinder rattlesnakes is achieved by adjust-
that were a constant fraction (~0.5) of their wavespeed, ing the relative phase of their body waves (Fig. 4.11e),
indicating that they do not trace a continuous path yielding two turning mechanisms: (1) differential
through the substrate, but must progress by d ­ eforming turning, achieved by increasing the amplitude of the
the medium, pushing particles behind them as they horizontal wave that creates a change in direction
move forward. Using “resistive force theory,” Maladen proportional to its normalized body displacement,
et al. (2009) show that sand-fish lizards must o­ vercome and (2) reversal turning, achieved by a 180° phase
frictional drag between moving particles by means shift in the vertical wave that causes the snake to
of granular thrust to swim through the substrate. reverse its movement direction. Importantly, in the
Inertial forces are negligible, similar to low Reynolds two studies of sidewinding gradient ascent over
number aquatic swimming described in Chapter 5. loose sand (Marvi et al., 2014) and turning (Astley
Many snakes move over ground by means of an et al., 2015a), the investigators were able to demon-
undulatory traveling wave that produces frictional strate improved performance of a snake robotic
reaction forces against the ground perpendicularly model that utilized the biomimetic principles that
to discrete regions of their body axis that are in con- emerged from their work on real snakes.
tact with the ground (Gans, 1974; Gray, 1946; Jayne,
1986). Generally, by exerting anteromedial forces
4.14 Muscle work versus force economy
and by having an axial frictional resistance to move-
ment less than their transverse frictional resistance, Because work must be done to swing the limbs back
serpentine undulatory waves propel the snake for- and forth, raise the animal’s CM height, and over-
ward. Ideally, when no slip occurs between the come collisional losses during every step, it was
snake and its points of ground contact, the snake’s long thought that the main function of muscles in
forward velocity matches the velocity of its traveling terrestrial locomotion was to perform the work
wave, and it follows a continuous path. However, necessary for these movements. Positive mechan-
when the substrate does not provide a­ dequate antero­ ical work is done by a muscle when it shortens as it
medial irregularities for resistive forces or when develops force. “Negative work” is done when it is
 MOVEMENT ON LAND 85

stretched (Chapter 2). These functions are certainly (Biewener et al., 1998b). In these muscles, force is
important when energy is required as an animal developed rapidly under nearly isometric condi-
pushes off from the ground during running or jump- tions when the animal’s limb lands on the ground
ing, and when energy must be absorbed when land- (Fig. 4.12). In some instances, a brief initial stretch
ing. However, as discussed in Chapter 3, the amount of the muscle’s fibers may allow the muscle to gen-
of work performed by animals of different sizes erate 1.5–1.8 times greater force than when isomet-
to run at different speeds does not correlate well ric, providing an additional 50–80% energy savings
with the metabolic energy cost of terrestrial loco- in terms of force economy. In the distal leg muscles
motion (Heglund et al., 1982). Instead, it appears of running turkeys and hopping wallabies, the mus-
that metabolic energy cost is determined by the rate cles do little work. Instead, tendon elastic energy
and magnitude of force that muscles must gener- savings represents 60–96% of the total work per-
ate to support an animal while it runs (Kram and formed by the muscle-tendon unit as a whole.
Taylor, 1990). Interestingly, a recent study by Holt et al. (2014)
One reason why muscle work may not correlate found no difference in the cost of force production by
well with metabolic energy expenditure during a muscle (mouse iliofibularis) undergoing a stretch-
steady-level locomotion is that much of the energy shorten contraction cycle (negative followed by posi-
that might otherwise be lost is recovered by efficient tive work, simulating the amount of energy that
potential and kinetic energy exchange during walk- could be stored and recovered within a tendon) com-
ing, or by elastic energy return in tendons and liga- pared with when the muscle contracted isometrically.
ments (see Section 4.15). In addition, many limb In addition to demonstrating that muscles consume
muscles may contract with little length change and less energy when they are stretched versus when they
hence do little or no net work. These muscles may contract isometrically or when they shorten, Holt
instead undergo a brief period of stretch or isomet- et al. (2014) argue that tendon elastic energy savings
ric force development that facilitates more econom- need not reduce the metabolic cost of force produc-
ical force development than when a muscle shortens tion. Instead, long tendons may have evolved to
as it develops force. This is due to the fact that a reduce limb inertia swing costs, as well as the cost
muscle generates less force when it shortens more of muscle force generation primarily by favoring
rapidly (Section 2.4) and also consumes more shorter fibers that decrease the volume of muscle
energy than when it is stretched or contracts iso- that must be activated to produce a given force.
metrically. When muscles contract isometrically, or
when they are briefly lengthened, they can generate
greater force and consume less metabolic energy.
4.15 Tendon springs and muscle dampers
Under these conditions, a smaller fraction of the
muscle’s fibers must be activated to generate a Biological springs play diverse roles in locomotion
given force. This increases a muscle’s “force econ- (Roberts and Azizi, 2011) – from storing and releas-
omy” by decreasing the amount of energy (ATP) ing elastic energy in tendons and muscle aponeuroses
that must be expended per unit force produced. (as well as within muscle fibers themselves) to allow-
As discussed in Chapter 2 (Section 2.8, Fig. 2.8), ing muscles to operate beyond their intrinsic limits,
the architecture of a muscle is also important in such as when powering jumping (see Chapter 7).
determining its force economy. Shorter pinnate- Tendon springs may also serve to protect muscles
fibered muscles are more economical for generating from potentially damaging eccentric contractions
force than longer parallel-fibered muscles. In add- by stretching before the muscle does, allowing the
ition, short-fibered muscles also often attach to long muscle fibers to be stretched more slowly (Konow
tendons that favor increased elastic energy savings. et al., 2012). Given that tendons return ~93% of the
The importance of force economy was first demon- energy stored when they are loaded (Chapter 2),
strated in the lateral gastrocnemius of running the dissipation of energy by muscle-tendon units
­turkeys by Roberts et al. (1997) and has also been must ultimately result from stretch of the muscle’s
shown in the leg muscles of hopping wallabies fibers; doing so at a slower rate can prevent injury.
86 A N I M A L L O C O M OT I O N

(a) Wallaby hopping

Stance
300

Force (N)
200

100

Plantaris
0
18

Length (mm)
17
16
15
14
EMG

0.1 s

(b) Turkey gastrocnemius (running) Wallaby plantaris (hopping)

Net work: Net work:

–6 mJ –12 mJ

Force
(50 N) Force
(100 N)

0 0.2 0.4 –0.1 0 0.1

Strain (ΔL/L0)

Figure 4.12 Distal muscles of running and hopping animals often do little net work and instead favor force economy and tendon elastic energy
savings. (a) In vivo recordings from the plantaris hind leg muscle of a hopping wallaby during a single hop reveal that the muscle undergoes a
stretch-shorten contractile pattern following activation that generates maximal force with little net length change. (b) The in vivo work pattern of
fractional length change (strain) of the gastrocnemius of a running turkey relative to force is very similar to the force-strain behavior of the
plantaris muscle of a hopping wallaby. The area within each loop represents the work that the muscle performs (which is small and negative in
each case). The thicker lines in each work loop denote the time during which the muscle is activated based on its EMG (adapted from Roberts
et al., 1997 and Biewener et al., 1998b).

The long tendons and foot ligaments of many ani- substantial enough that when these animals hop,
mals (Fig. 4.13), including humans, provide the their metabolic cost of locomotion does not increase
opportunity for significant elastic energy recovery, at faster speeds (Chapter 3; Fig. 3.5). This remarkable
reducing the work that muscles must perform to observation is in contrast to all other terrestrial ani-
move the animal’s body, in addition to reducing limb mals that have been studied, even those with highly
swing inertial costs by reducing distal limb mass. In specialized tendons, such as horses and antelope. It
wallabies and kangaroos, elastic energy recovery is has been estimated that tammar wallabies hopping
 MOVEMENT ON LAND 87

Springs in animal limbs

(a) Ungulates (b) Wallabies and kangaroos

Forelimb Hindlimb
Hindlimb

G LG, MG and PL
SDF
PL
DDF
DDF
FDL

Susp-Lig Susp-Lig

Figure 4.13 The principal muscle-tendon units in ungulates, kangaroos and wallabies have architectures that favor economical force generation
and elastic energy savings. Muscles in the distal limbs of (a) horses and other ungulates (SDF, superficial digital flexor; DDF, deep digital flexor; PL,
plantaris; G, gastrocnemius; S-Lig, suspensory ligament) and (b) kangaroos and wallabies (FDL, flexor digitorum longus; MG, medial gastrocnemius;
LG, lateral gastrocnemius) are pinnate and short fibered. Each muscle attaches to a long tendon (thick black and gray lines) that allows for
substantial elastic energy recovery.

at 6 m s–1 reduce their metabolic energy expenditure Instead, their relatively thick leg tendons appear to
by 50% through elastic energy recovery in their leg be more effective for jumping and predator escape
tendons alone (Biewener and Baudinette, 1995). (Biewener and Blickhan, 1988). The inability of small
Additionally, female tammar wallabies can carry hopping rodents to store significant tendon elastic
pouch young weighing up to 15% of their own energy may result from their size. If scaled up (iso-
weight without incurring an additional cost by metrically) to the size of a much larger wallaby or
increased elastic energy savings in the mother’s leg kangaroo, kangaroo rats would be well-suited for
tendons (Baudinette and Biewener, 1998). The ability effective elastic energy savings. However, recent scal-
to carry loads for “free” is another unique feature of ing analysis (Bullimore and Burn, 2005) suggests that,
wallaby hopping compared with other vertebrate due to lower EMA (Fig. 4.4) and higher muscle-­
runners that have been studied. tendon forces, elastic energy recovery relative to the
However, effective elastic energy savings is not amount of muscle work performed may not be more
universal. Small heteromyid and dipodid rodents limited in smaller animals. Further work to explore
appear to have tendons that are too thick to enable how size affects elastic energy recovery is clearly
them to develop sufficient levels of strain energy for needed. Nevertheless, the independent evolution of
the forces that are required during steady-speed a bipedal hopping and jumping gait in kangaroo
hopping (Biewener et al., 1981; Moore et al., 2015). rats and jerboas with low tendon energy recovery
88 A N I M A L L O C O M OT I O N

indicates that factors other than phylogenetic ancestry, Many of the muscles that attach to the distal leg ten-
such as less predictable movement patterns (Moore dons of these animals have extremely short fibers.
et al., 2015), likely selected for the muscle-tendon In some muscles, the fibers are as short as 5–7 mm
architecture and locomotor behavior of these animals. and attach to tendons that are nearly one meter in
Although other terrestrial vertebrates may not length. Until recently, the role of these short-fibered
achieve comparable metabolic energy savings as muscles had been a mystery: their contraction can-
wallabies and kangaroos, tendon energy recovery is not provide effective control of length because ten-
clearly important to their ability to conserve energy don stretch (at 3% strain = ~ 30 mm) greatly exceeds
that their muscles would otherwise have to perform the muscle’s fiber length. Rather than being an evo-
as mechanical work (but see Holt et al., 2014). In lutionary vestige from earlier, less cursorial ungulates,
humans, elastic energy savings in the Achilles ten- Wilson et al. (2001) show that these short-fibered mus-
don and ligaments of the foot is estimated to reduce cles effectively damp the mechanical vibrations pro-
muscle work by up to 50% in a human runner (Ker duced by the impact of a horse limb with the ground.
et al., 1987); in horses, elastic energy savings is esti- Indeed, damping is more effective when the muscles
mated to reduce muscle work by up to 40% at a are actively stimulated than when they are passive.
trot and a gallop (Biewener, 1998). Measurements in Such vibrations might otherwise have damaging
running turkeys (Roberts et al., 1997) indicate that effects on the animal’s joints over a long period of use.
elastic energy storage can be quite significant, and The importance of short-fibered muscles as shock
indirect estimates also point toward the importance absorbers explains their retention in modern ungu-
of tendon elastic energy savings in dogs and other lates and likely their role in other animals as well.
trotting animals (Cavagna et al., 1977). Elastic energy Finally, tendons can also amplify the power output
recovery has also been shown to power forelimb of muscles to which they attach. When an animal
protraction in horses (Wilson et al., 2002). accelerates, as occurs during jumping, the work that
For muscle-tendon units, elastic energy savings are the muscles perform when they contract is limited by
not free. Metabolic energy must be consumed by the their rate of shortening (Roberts and Azizi, 2011). By
muscles to generate the force needed to operate ten- storing energy elastically as the tendon is stretched
don springs, but as we have previously discussed, this by the contracting muscle, energy can then be released
can be accomplished at lower cost when a muscle con- from the tendon much more rapidly than the rate
tracts isometrically or is briefly stretched. Importantly, of work performed by muscle shortening, thereby
energy cost is further reduced by muscles that have increas­ing power output (energy/time). It is
shorter and typically more pinnate fibers, since this important to note that work per se is unchanged:
reduces the volume of muscle that must be recruited the tendon doesn’t add energy but instead allows the
to generate a given force (Section 2.8). This raises the energy to be released at a faster rate. An important
question – why have a muscle that consumes energy component of such mechanisms is a “catch” that
at all? Although tendon elastic energy savings may be keeps the muscle-tendon unit at a constant length, so
important, muscles must also control movement that energy stored in the tendon can be released rap-
(Chapter 8). Without an active force-generating idly to power movement. These fascinating catapult
­muscle attached via a tendon to the skeleton, the mechanisms for powering jumping and acceleration
control of length change and limb segment displace- are discussed in detail in Chapter 7.
ment becomes entirely passive. Consequently, mus-
cles are key to controlling overall muscle-tendon
4.16 Summary
length changes and associated limb segment motion.
In addition to controlling length, one other role Terrestrial locomotion encompasses an amazing array
appears to be important for retaining energy-­ of legged animals and yet, basic principles of loco-
consuming muscles that transmit force to passive motor mechanics and energetics still emerge across
­tendons. Some of the most highly specialized muscle-­ this diversity. Animals of differing sizes and construc-
tendon systems for elastic savings are found in the tion all contend with weight support and movement
legs of horses and other ungulates (Fig. 4.13). over varying terrain. Walking gaits involve pendular
 MOVEMENT ON LAND 89

exchange of the body’s potential and kinetic energy to engineering and biology. Such robots embrace the
reduce muscle work and energy cost. Running gaits intrinsic stabilizing properties of spring-mass mech­
involve an elastic bounce of the body over the support- anics which allow the robots to operate with rela-
ing limb, allowing for elastic energy recoil of spring tively simple control principles. These insights have
elements in the limb to reduce muscle work. In hop- inspired a new class of prosthetics and exoskeletal
ping kangaroos and wallabies, this energy recovery robotics. ­Passive-dynamic walkers demonstrate the
can be quite remarkable, and in humans can provide elegance of ­minimally-actuated movement, ­helping to
50% of the work that leg muscles would otherwise guide simplification of prosthetic and orthotic devices.
have to perform. Recent studies demonstrate that a Slithering robots inspired by snakes and sand liz-
compliant spring-loaded inverted pendulum based on ards show how burrowing and movement over
spring-mass mechanics explains both walking and granular substrates can be achieved without legs.
running dynamics. Furthermore, animals expend Despite the common principles that underlie
mechanical energy to overcome collisional interactions ­legged locomotion and the many recent studies that
of their limbs with the ground. Distributed footfall pat- have added to our understanding of how animals
terns of walking and galloping gaits reduce collisional move with grace, speed and stability when maneu-
losses. Reduced energy cost is also favored by muscles vering over complex terrain, there is still much to be
that generate force economically. This is best achieved studied and understood. How important is muscle
by having short-fibered muscles that generate force work relative to muscle force and activation in deter-
under isometric or stretch-shorten conditions. In add­ mining the energy cost of locomotion? What are the
ition to having an important effect on length control key innovations by which animal locomotor traits
and energy use, muscle-tendon architecture also plays have evolved within different groups of animals?
an important role in the damping of unwanted Comparative phylogenetic studies are needed to
­vibrations of the limb. These patterns of whole body answer this latter question. Improved understanding
energy exchange, and the roles of muscles and ten- of maneuvering and non-steady locomotion will be
dons underlying them, apply to two-legged, four-­ critical to assessing animal movement under natural
legged, six-legged runners and even eight-legged conditions. New remote-sensing tools enable animal
runners that run sideways! Legged locomotion has movement to be quantified and more accurately
the distinct advantage of providing an effective means assessed in an ecological context. Understanding the
of transport over uneven and unpredictable terrain. interplay between intrinsic muscle-tendon proper-
Animals change gait and reduce the time that ties and the need for reflex-mediated nervous control
their limbs remain in contact with the ground to of movement, along with testing design principles
move faster, requiring them to be dynamically stable. that are implemented in legged robots and powered
Basic mechanical properties of limbs and joints orthotics, will advance their use for gait assistance
(stiffness, energy absorption, spring energy recov- and remote assessment of challenging environments.
ery and work output) provide dynamic stabilization We next dive into swimming and then come up
and help to simplify the motor control task of the for air to discuss flight, which both involve move-
nervous system. Running faster also requires effect­ ment through fluids. While gravity remains of con-
ive support of greater forces. In animals of very dif- cern for flying animals, it can largely be ignored by
ferent size, but built of similar materials, adjustments those that swim.
in the organization and posture of the limb are import­
ant for regulating the level of force and stress that
must be transmitted. Adjustments of limb posture Additional reading
and body size are also important influences on the
Biewener, A. A. (1990). Biomechanics of mammalian ter-
ability of an animal to maneuver and turn.
restrial locomotion. Science 250, 1097–103.
The mechanical and energetic principles of legged Hildebrand, M. B. (1988). Analysis of Vertebrate Structure,
locomotion have stimulated the fabrication of a broad 3rd. ed. New York: Wiley and Sons.
array of two- four- and six-legged robots. Legged Winter, D. A. (1990). Biomechanics and Motor Control of
robotics is a fast-growing field at the interface of Human Movement. New York: Wiley and Sons.
 CH A PT ER 5

Movement in Water

Swimming animals span an enormous range of of as the mass of water that is accelerated by the
sizes and shapes. The largest living organisms on animal’s body to a given average velocity. The rate
Earth, the whales, are 1010 greater in mass than at which the animal transfers momentum to the water
swimming bacteria, yet both must contend with a (i.e. mass × acceleration) determines the amount of
fluid environment. In spanning such a broad size thrust that it generates:
range, aquatic organisms have evolved a variety of T = mv / t (5.1)
propulsive mechanisms to move through the water.
These mechanisms include oscillatory movements (where v is the velocity of fluid of mass m moved
that range from bacterial flagella to the fins of fish per unit time). Thus, one way for a fish to generate
and flukes of whales. They also include the jetting more thrust and swim faster is to beat its tail at a
of squid and the rowing of cilia. In this chapter, we higher frequency (increasing v/t). Thrust is defined
will identify common principles that underlie these here as the force exerted by the fluid on the animal’s
various propulsive ­mechanisms and consider the body in reaction to the fluid being accelerated by the
consequences of size. Size plays an important animal’s body (Fig. 5.1). Thrust acts in the direction
role in dictating which physical properties of the of an animal’s motion through the fluid. Due to the
medium are most important to particular propulsive oscillatory motion of many aquatic propulsors, a
mechanisms, such that distinct propulsive mech­ lateral component of force (Flat) is also exerted,
anisms are evident across the size array of swimmers. which generally cancels out over successive tail
Some of these principles and scales are emerging in beat cycles.
the vibrant field of biorobotic swimmers. At the same time that an animal must generate
thrust to move forward, it is resisted by the move­
ment of the fluid past its own body. The resistive
force exerted by the fluid on its body is termed
5.1 Thrust and drag
drag. Drag acts opposite to an animal’s forward
As in all other environments, locomotion in water motion and hence, opposes thrust (Fig. 5.1). As a
involves the use of body appendages or body sur­ resistive force, drag represents the rate at which
faces to generate propulsion, or thrust, by pushing momentum is lost by the animal to the fluid mov­
against the surrounding medium. In the aquatic ing past its body. Effective swimming therefore
environment, this involves the active transfer of requires propulsive mechanisms that enhance thrust
momentum from moving portions of an animal’s and reduce drag. Before discussing these mech­
body to the water surrounding it. The momentum anisms, we need to consider the underlying hydro­
(mass x velocity) that is transferred can be thought dynamic basis of drag.

Animal Locomotion. Second Edition. Andrew A. Biewener & Sheila N. Patek, Oxford University Press (2018).
© Andrew A. Biewener & Sheila N. Patek 2018. DOI: 10.1093/oso/9780198743156.001.0001
 M O V E M E N T I N W AT E R 91

(a)

T D

Shed fluid mass (m)

Thrust = mv/t

(b)

R
Flat

Figure 5.1 Fish can generate thrust (T) through caudal fin oscillations which are balanced by drag (D) forces on the moving fish. (a) Thrust and
drag forces of a swimming fish (lateral view). Caudal fin oscillation generates the velocity (v) of the shed fluid mass (m) which transfers momentum
(mv) to the surrounding fluid. The rate of momentum transfer equals thrust (mv/t). (b) The fish’s tail generates a net propulsive force, R, with an
anterior component of thrust and a lateral component (Flat) that cancel out over successive tail beats. The shed vortices of the water are depicted
for both right and left movements of the tail.

5.2 Inertia, viscosity and Reynolds number of shear. As was introduced in Chapter 1, shear rep­
resents the relative deformation or sliding of paral­
When a swimming animal moves through the lel layers of a fluid (or a solid) with respect to one
water, its motion is enhanced by its own inertia and another. The more the fluid resists being sheared,
is resisted by the fluid. The inertial forces required the greater its viscosity. Because viscosity depends
to keep an animal’s body moving depend on its on the ratio of shear stress to shear rate, it has units
mass and changes in its forward velocity. Drag of stress x time (Pa s). Mineral oil (glycerin) has a
forces arise from the resistive forces due to fluid viscosity of 1.49 Pa s at 20°C, which is 1.49 × 10 3
movement past the animal’s body. Drag forces times greater than the viscosity of fresh water (0.001
depend on the viscosity of the fluid (friction drag) Pa s, at 20°C). Understanding the differences in the
and the pressure exerted by the fluid on the organ­ viscosity of these and other fluids is useful when
ism (pressure drag). The relative importance of constructing mechanical models of organisms in
friction and pressure drag depends on the size order to study their hydrodynamic performance
and speed of the animal. Pressure drag is most under simulated biological conditions. However,
important for large animals that swim at fast
­ the viscosity of the aquatic environments inhabited
speeds, whereas friction drag is most critical at by biological organisms can be considered to be
small size and slow speeds. As will be explained, essentially the same (sea water has a viscosity that
pressure drag results from the pressure gradient is generally only about seven percent greater than
developed from the front to the back of the swim­ fresh water).
ming organism due to flow separation. Because it is The relative importance of inertial forces to vis­
not a hydrostatic pressure, it does not change with cous forces during locomotion through a fluid is
swimming depth. defined by the Reynolds number (Re), a dimen­
Viscosity (μ) is a measure of the resistance of a sionless parameter that is central to the dynamics
fluid to being sheared, or more precisely, to its rate of flow:
92 A N I M A L L O C O M OT I O N

ρ lv of swimming and flight, as both depend on the

Re = (5.2) same fluid dynamic principles. Consequently,
µ
we will return to Re when discussing flight in
where ρ is the density of the fluid, l is a characteris­ Chapter 6.
tic length (body length, fin length, or wing length in At high Re (>100) inertial forces dominate, but at
the case of a flying animal), v is the organism’s for­ low Re (« 1) viscous forces reign. This has important
ward velocity relative to the fluid, and μ is the flu­ consequences for the propulsive mechanisms used
id’s viscosity. Although not derived here, Re is at high versus low Re. The Reynolds numbers at
the ratio of inertial (ρSv2) to viscous (μSv/l) forces which various aquatic and flying organisms oper­
­experienced by an organism (where S is some meas­ ate are given in Table 5.1. In contrast to a 3 m tuna
ure of the organism’s surface area exposed to the that glides several body lengths through the water
flow). Vogel (1994) gives a readable and entertain­ when it stops swimming due to its own inertia, a
ing discussion of the physical basis for Re and its 200 μm ciliate almost immediately stops once it
­importance to biological fluid mechanics. ceases to swim. Berg (1983) provides a dramatic
The Reynolds number is a key metric in studies example of the absence of inertia at very low
of animal locomotion, because it provides a quanti­ Reynolds numbers, calculating that a bacterium
tative approach for judging the relative importance coasts 0.1 angstroms, or the diameter of a hydrogen
of inertial to viscous forces, which fundamentally atom, once its flagellum stops beating! At these low
affect the organism’s movement through a fluid Reynolds numbers (typically at extremely small
medium. At equal Reynolds numbers, flow charac­ body sizes), aquatic locomotion becomes counterin­
teristics are the same. This allows one to model tuitive with respect to our own experience as large-
flow conditions at different scales (e.g. build a bodied swimmers (humans operate at a Re of about
small model of a very large organism, or vice versa) 106). As we will discuss in Section 5.7, the intermediate
while keeping Re the same. It is central to the study range of Re, between about 0.1 and 100, both ­inertial

Table 5.1 Reynolds Number for various flyers and swimmers.

Animal or aircraft Speed Reynolds number

Concorde jet Flying at 600 m s–1 30,000,000,000

Humpback whale Swimming at 5 m s–1 150,000,000
Mini-light aircraft Flying at 50 m s–1 10,000,000
Tuna Swimming at 10 m s –1
10,000,000
Human Swimming at 1 m s–1 2,000,000
Duck Flying at 20 m s –1
300,000
Hummingbird Flying at 10 m s–1 40,000
Large dragonfly Flying at 5 m s–1
5,000
Trout fry Escape swimming at 0.2 m s–1 3,000
Copepod Escape swimming at 0.2 m s –1
300
Fruit fly Flying at 2 m s–1 30
Sea urchin larva Swimming at 1 mm s–1 0.3
Spermatazoan Swimming at 0.2 mm s –1
0.03
Bacterium Swimming at 0.01 mm s–1 0.00001

Modified from Vogel (1994).

 M O V E M E N T I N W AT E R 93

and viscous forces operate and change as a function vidual fluid particles at different locations within
of Re. a field of flow. In practice, streamlines can be visual­
One means of assessing the effects of Re is to ized (within a flow tank; Fig. 5.7c) by adding dyes
measure drag force directly on an organism, or a to the fluid at discrete locations or by mixing small,
model of an organism, in a flow tank (see Fig. 5.7) neutrally buoyant particles to the fluid and observ­
and relate this to its shape and velocity, in order to ing their motion. An important principle under­
calculate a drag coefficient (Cd). The drag coefficient lying fluid mechanics is the “continuity of flow,”
represents an experimental measure of the ratio of which requires that the volume flow rate of fluid
measured drag force (D) to the theoretically pre­ moving past an organism is constant. In other
dicted drag force: words, all fluid must be accounted for—akin to the
­conservation of energy principle: fluid can neither
Cd = 2D /( ρ Sv 2 ) (5.3)
be created nor lost. In an idealized fluid (zero vis­
Or, cosity, Fig. 5.2a) the streamlines move symmetrically
past the long cylindrical object. Symmetrical and
D = (Cd ρ Sv 2 ) / 2 (5.4)
parallel streamlines are called laminar flow. In laminar
Consequently, the drag force experienced by an flow, flow is greatest lateral to the object and has
organism, associated with both pressure and fric­ local zero velocity regions, or stagnation points, at
tion drag, depends on the drag coefficient (meas­ the front and rear of the object. Because of the sym­
ured for a given Re), the density of the fluid (ρ) some metry of flow, the pressures exerted on the object
measure of the surface area of the organism (S) (for balance out and suggest that the drag on an object
swimming animals this is most often the frontal should be zero.
area projected to the oncoming flow), and the square However, in practice (i.e. in real fluids), stream­
of the animal’s forward velocity. As we know from lines never actually flow symmetrically around an
riding a bike and the concerns of automobile fuel object. First, real fluids have viscosity, so that all
economy, drag forces depend heavily on velocity water in contact with the surface of the organism is,
(drag is proportional to v2). At low Re, the drag by definition, stationary and therefore has a local
coefficient is large, reflecting the importance of vis­ zero velocity. This is often referred to as the “no-slip
cous forces. At higher Re, the drag coefficient condition.” Further away from the organism’s
decreases as inertial forces become more important. surface, the velocity of fluid movement increases
Because drag also depends on the fluid’s density, it parabolically up to the “free-stream” velocity of the
exerts a much larger force at a given speed in water fluid moving past the organism (Fig. 5.2b). For an
compared with air. Consequently, swimming ani­ organism swimming through stationary fluid, the
mals typically encounter much higher l­evels of free-stream velocity is equal and opposite to the
drag and move at much slower speeds than flying organism’s forward swimming velocity. This ­velocity
animals. Finally, except at extremely small size, gradient represents friction drag, which depends
shape is important to determining the magnitude on the viscous interaction of fluid layers that are
of drag. Streamlined shapes that reduce drag by sheared as they move over the surface of the organ­
reducing the amount of energy lost to the wake ism. Friction drag increases in proportion to the sur­
(described in more detail in Section 5.3) are there­ face area of the organism exposed to flow, and this
fore favored over blunt or irregular shapes. causes a net deceleration in the flow of fluid past the
organism.
Flow asymmetry is also produced by pressure
drag. Pressure drag develops in real situations,
5.3 Steady flow: drag and streamlines
because the dynamic pressure exerted by the water
The physical basis for viscosity and drag is best moving past the front of the organism is greater than
seen by considering streamlines of a fluid’s motion the pressure developed at its back. The reason for
under conditions of steady flow past a solid object this difference in pressure is that the energy trans­
(Fig. 5.2). Streamlines represent the paths of indi­ ferred to the water when it is accelerated as it passes
94 A N I M A L L O C O M OT I O N

(a) Re<10

(b) Re<10

distance
velocity

(c) 10<Re<40

40<Re<200,000

(d) Re>200,000

Figure 5.2 Depending on the Reynolds number, fluid moving across a cylinder oriented perpendicularly to flow yields distinct patterns. (a) In low
Reynolds numbers (Re), streamlines pass over the cylinder without the formation of vortices when modeled with an idealized fluid with zero viscos-
ity. (b) However, for real fluids with viscosity, low Re causes the formation of a velocity gradient such that at decreasing distances from the cylinder,
the velocity decreases (velocity graph overlaid on streamlines). This parabolic gradient is a consequence of the shear imposed by fluid drag. (c) Flow
at low to moderate Re shows stationary and shed vortices and (d) flow at high Re generates a turbulent wake. Adapted from Vogel (1994).

around the sides of the organism is not completely organism (Fig. 5.2c). Vortices are rings of circulating
returned to the organism as the water moves along flow (think smoke rings) that form due to differ­
its downstream end. This loss of energy occurs due ences in pressure and friction drag as a fluid moves
to flow separation alongside or downstream of the past an object. They may remain “attached” if the
organism. When flow separation occurs at low to fluid forces that form them are stable, or they may be
moderate Re, attached or shed vortices develop that “shed” into the wake, when fluid forces change. We
dissipate the energy of the fluid as it moves past the will see that attached or bound vortices may form on
 M O V E M E N T I N W AT E R 95

the fin of a fish or the wings of a bird (Chapter 6), shape of the propulsive element and the volume of
and that vortices are then typically shed into the water that it accelerates. Similar to the drag coeffi­
wake at the end of a fin (Section 5.4.4) or wing. At cient, the added mass coefficient is lower for more
higher Re, the vortices break down and the flow streamlined bodies. The acceleration reaction is
becomes turbulent (Fig. 5.2d). Turbulent flow behind likely to be most important at slow speeds or when
the organism causes an even greater loss of fluid an animal accelerates from rest. Acceleration reac­
energy. The loss of energy results in a decrease in the tion forces are estimated in a variety of ways, r­ anging
pressure on the downstream side of the organism, from inferences based on accounting of other fluid
making the dynamic pressure difference between forces (e.g. Ngo and McHenry, 2014), particle image
the upstream and downstream sides greater. As a velocimetry of flow fields around the body (e.g.
result, pressure drag increases. Tytell, 2004) and sometimes direct measurements
(e.g. Martinez, 2001).

5.3.1 Steady versus unsteady flow

5.4 Swimming fish, mammals and
Before considering specific examples of aquatic
cephalopods: movement at high Re
locomotion, one more issue needs to be addressed.
This is the matter of steady versus unsteady flow. Aquatic locomotion at high Re (>>100) is dominated
Nearly all that we have discussed until now assumes by inertial forces. Viscous forces become relatively
a steady or constant state of flow past the organism. unimportant in the Re regime at which many fish,
However, in most biological cases, propulsion by humans and cetaceans operate (105–108). Small
reciprocating appendages or an undulating body invertebrate swimmers (e.g. crustaceans, copepods
necessarily involves unsteady flow which is defined and water beetles) in the range of Re 300–10,000 rely
as flow with changing conditions over time (Daniel, largely on inertial mechanisms for propulsion. At
1984; Dickinson, 1996). This is because the move­ high Re, drag is dominated by pressure drag, rather
ments of the body and/or the appendages must be than skin friction drag. Hydrodynamic efficiency is
accelerated from rest to generate propulsive force therefore enhanced by keeping the drag coefficient
and must then be decelerated before initiating a (Eq. 5.3) as small as possible. This is best achieved
subsequent propulsive stroke. Consequently, in most by having a streamlined body shape (Fig. 5.3a). The
cases, fluid propulsion not only involves overcom­ reason that a tuna would coast several body lengths
ing the force due to drag, which depends on the if it stopped swimming is largely due to its stream­
steady speed of the animal, but also involves respond­ lined body shape. In contrast, streamlining is unim­
ing to forces brought about by changes in the vel­ portant at the low Re regime of a swimming bacterium
ocity of flow. (see Section 5.6).
Changes in the velocity of flow introduce what is To achieve efficient aquatic locomotion at high
known as an “acceleration reaction” force that adds Reynolds numbers, it is important to reduce flow
to (or may subtract from) the drag force acting on separation and turbulent wakes and instead enhance
the animal (Daniel, 1984). When any part of an ani­ the parallel and orderly streamlines of laminar
mal’s body accelerates through a fluid, it entrains flow. Streamlined bodies have a bluff shape in front
and must also accelerate an additional mass of but a gradual taper to the rear. The taper is the trick.
fluid. The acceleration reaction force (Far) depends With a gradual taper, flow is less likely to separate
not only on the mass of the animal’s own body that and become turbulent as it moves by the body. Flow
is being accelerated (ma), but also on the “added separation is more likely to develop at faster flows
mass” of the fluid that is being accelerated: or with more bluff body shape (Fig. 5.3b). Having a
tapered body allows the fluid to gradually deceler­
Far = ma + Ca ρVa = a ( m + Ca ρV ) (5.5)
ate as it moves back along the animal, favoring the
where V is the volume of fluid that is being acceler­ maintenance of laminar flow. As a result, the body
ated, ρ is its density and Ca is the “added mass coef­ is essentially pushed along by the wedge-like clos­
ficient.” The added mass (= Ca ρV ) depends on the ure of fluid behind it. In contrast, bluff bodies result
96 A N I M A L L O C O M OT I O N

(a)

(b)

Figure 5.3 A streamlined shape in idealized fluids (a) minimizes the formation of turbulence and boundary layer, whereas a bluff body (b) causes
turbulence in front of and behind the body while enhancing the boundary layer.

in abrupt separation and rapid fluid deceleration, fin propulsion is typically associated with faster,
which create a turbulent wake, and the loss of pres­ open water swimming that depends on lift-based
sure behind the body, which leads to a large pres­ propulsion. These propulsive mechanisms and the
sure drag. Animals that swim or jet over a broad effects of body shape on swimming style are dis­
range of moderate to high Re, such as fish, whales, cussed in the following sections.
dolphins, squid and crayfish, generally have stream­
lined body shapes. Although streamlining incurs
5.4.1 Undulatory swimming
greater skin friction drag (due to the increase in sur­
face area associated with a long tapered length of Undulatory (or anguilliform) swimmers typically
the body), this is largely unimportant at high Re have relatively elongate bodies. Thrust along the
and is greatly offset by the reduction in pressure undulating body of a fish, salamander or sea snake
drag. can be considered in the context of the thrust that a
At moderate to high Re, the general mechanism local segment of the body produces (Fig. 5.4). At
for thrust production is to accelerate a mass of fluid high Re, thrust is dependent on the rate at which
backward so that a net reaction thrust is exerted momentum is transferred, or shed, to the fluid. This
on the animal to propel it forward. By accelerating can be summed up over the length of the animal to
fluid backward, the animal’s muscles generate thrust calculate the total average thrust that a steadily
by transferring momentum to the fluid. This is the undulating body produces. Undulatory swimming
case whether thrust is produced along most of the involves sinusoidal waves of body bending that
animal’s body axis (e.g. an eel), concentrated at a cau­ travel down the body axis. Anguilliform swimmers
dal fin (e.g. a tuna), a pectoral fin (e.g. a stingray) or originate waves at the front of the body that are
a fluke (e.g. a killer whale), or achieved by ejecting a quite similar to any fish, and as with other undula­
bolus of fluid from within the animal’s body (e.g. a tory swimmers, the amplitude of the wave increases
squid). These different styles typically emphasize as it passes to the tail. As any segment of the body
differing aspects of swimming ­performance. Whereas becomes incorporated into the backward-traveling
pectoral fin propulsion in fish is more commonly wave, it forms an angle to the direction of the ani­
associated with slower, more maneuverable swim­ mal’s forward movement and produces a local force
ming and depends on drag-based propulsion, caudal on the animal’s body that has two components
 M O V E M E N T I N W AT E R 97

Flat R

Flat R

Figure 5.4 In an undulatory swimmer, thrust (T) is produced by exerting a rearward component of the reaction force (R) on the fluid adjacent to
the body surface. This results from the angled orientation of the body that is achieved by the sinusoidal waves of bending that travel down the
animal’s body. This produces a Flat as well as a component of thrust. The lateral forces are cancelled out over time as the animal’s body bends back
and forth. These forces are summed across a portion of the animal’s body. Undulatory swimmers typically generate most of their useful thrust with
the posterior half of their body.

(lateral and backward). The lateral force is cancelled of most biological situations, because of the
out by symmetric lateral oscillations of each seg­ unsteady nature of flow. Unsteady flow occurs
ment as the body bends in opposite directions. The when the velocity of the water is not constant and
backward forces produced by these undulating body instead changes over time as it is accelerated by the
segments are summed to generate a net propulsive moving fin (Section 5.3.1). Nevertheless, the thrust
force (i.e. thrust) that accelerates the animal for­ equation (5.6) serves to illustrate two useful points.
ward. When the net thrust force is balanced by the First, by enlarging the surface area of the fin, more
resistive drag force, the animal swims at a constant water can be accelerated to generate thrust and
forward speed. thus, overcome drag. Second, a larger tail can be
Most fish, such as cod, perch and trout, exhibit a oscillated more slowly, thereby reducing drag.
more general style termed carangiform swimming,
in which the posterior third of the body undulates,
5.4.2 Caudal fin or fluke swimming
with the amplitude of undulation increasing toward
the tail where it is maximal. These fish are also dis­ At the opposite extreme of swimming style, thunni-
tinguished from anguilliform swimmers in that they form fish swimmers and cetaceans tend to avoid
are shorter with respect to the length of the bending undulatory movement over most of their body
wave that passes backwards. (Although, by defin­ length (in order to reduce drag) by emphasizing lat­
ition, carangiform fish have body lengths that are eral undulation of their caudal fins or flukes. The
less than one wavelength of the traveling bending lunate shapes of the fins and flukes of these animals
wave; fish body shapes and swimming styles span (Fig. 5.5a) and their similar swimming modes offer
a continuum from eel-like fish that ­utilize a large an example of convergent evolution. Aquatic mam­
majority of their body length to generate thrust to mals must contend with the same physical forces
fish that concentrate thrust at their caudal fin.) In for effective fluid propulsion as large swimming
order to enhance thrust, the surface area of the cau­ fish. Therefore, whales and dolphins have evolved
dal fin is enlarged. Because momentum is conserved, caudal flukes with a lunate shape, analogous to
thrust production of the swimming animal can be caudal fins of thunniform fish, but which they oscil­
most simply analyzed as balancing the momentum late in the dorsoventral plane (Fish, 1996). In con­
of the animal (mv) relative to that transmitted to the trast to the drag-based propulsion of undulatory
water as thrust (T): swimmers, these animals are believed to ­ produce
thrust by a lift-based mechanism. Lift is explored
mv + ∫ Tdt = − mw vw (5.6)
more extensively in Chapter 6 when discussing
where mw and vw are the mass and velocity of the flight, but its introduction is helpful here, as it pro­
water moving in the opposite direction of the ani­ vides an important mechanism for producing thrust
mal’s travel. This equation is an oversimplification in these fast swimming animals.
98 A N I M A L L O C O M OT I O N

on either side of the hydrofoil. Based on Bernoulli’s

(a) principle (pressure varies inversely to the velocity
of flow), water moving at a higher velocity (upper
T D side of hydrofoil in Fig. 5.5b, or fish’s right side)
exerts a lower pressure on the hydrofoil than water
moving at a slower velocity (on its left side). Hence,
a net lift force (L) is generated in the direction of
lower pressure. Given the hydrofoil’s angle relative
to the direction of oncoming water, the lift produced
by the hydrofoil has an anterior component. With
(b) L d the appropriate angle of attack, significant lift is
achieved relative to drag (d) on the tail, generating a
net anteriorly directed thrust force (T) that balances
T D
the drag force (D) on the fish’s body. Lateral compo­
nents of hydrodynamic force in the case of fins or
dorsoventral components in the case of flukes can­
Figure 5.5 Swimming animals, such as tuna and whales, can
achieve lift-based thrust. This is similar to the lift that flying animals cel out over successive tail beats. In contrast to dol­
achieve with their wings. (a) Tuna oscillate their caudal fin laterally to phins and whales, phocid seals and walruses use
generate thrust. Because the fins and flukes are inclined in the pelvic oscillations to undulate paired hind flippers
direction of swimming, they have an anterior component of thrust (T). in the lateral plane, whereas fur seals and sea lions
This fin orientation balances the total drag force (D) on the fish. (b)
use pectoral (fore) flippers as oscillatory hydrofoils
When viewed dorsally, and a cross-section of the caudal fin is
analyzed (dashed line in (a), corresponding to black hydrofoil shape of (Fig. 5.6). Both of these flipper-based propulsive
the fin shown in (b). The angle of the fin generates local lift (L) and mechanisms also achieve lift-based thrust (Fish,
drag (d) such that the fish experiences a net forward thrust. Lateral 1996).
and dorso-ventral forces are cancelled out by repeated beating of the The improved efficiency of lift-based propulsion
tail or fluke.
at faster speeds results from the increased water
flow past the fin induced by the animal’s own for­
ward movement, in addition to the movement of
When viewed in cross-section, the fins of tuna or
the fin with respect to the animal, similar to that of
flukes of dolphins have a streamlined shape (Fig.
airfoils (wings of insects and birds) in flight.
5.5b). As such, they can be considered hydrofoils. By
oscillating back and forth, they encounter the oncom­
ing water at a shallow angle, referred to as the
“angle of attack.” This induces an asymmetric flow
5.4.3 Tail shape: homocercal versus
of water and causes a velocity differential on either
heterocercal tails
side of the hydrofoil (the velocity of flow is greater
on the side of the hydrofoil with the greatest dis­ Tail shape is an important feature of fish, influencing
tance between the stagnation points of flow). This the way the tail works and how it generates thrust.
velocity differential represents the sum of a transla­ As noted above, high-speed long-distance swim­
tional velocity component and a circular component ming fish, such as tuna and mackerel, have sym­
(see Fig. 6.2a). Fluid doesn’t actually flow around metrical lunate-shaped tails that generate thrust
the hydrofoil (except when shed at its tip), but the through lift-based propulsion. In fact, most bony
effective circulation of flow (i.e. its vorticity) that fish possess symmetrically-shaped tails that are
is established each time the fin beats to either side described as being “homocercal.” Many of these
produces a net force perpendicular to the direction fish have shorter, more stocky tails which generate
of flow over the fin. This force is termed lift (for fur­ thrust by means of drag-based propulsion. Because
ther explanation of lift see Section 6.1). Lift can also of their symmetry, homocercal tails are thought to
be thought of as resulting from the pressure differ­ generate thrust in line with the animal’s movement.
ential that is established by the difference in velocity Kinematic analysis and flow visualization (Gibb
 M O V E M E N T I N W AT E R 99

d
T D
L

L
d

L
d

Figure 5.6 Various mammals that have evolved aquatic locomotor specializations use different structural appendages and propulsive
mechanisms (drag and lift based) to propel themselves through the water. T, thrust on the whole body; D, drag on the whole body; d, local drag on
the propulsive appendage; L, lift force. Adapted from Fish (1996) by permission of Oxford University Press.

et al., 1999) indicate that, in at least certain species thrust, heterocercal tails produce lift in a­ ddition to
with homocercal tails, differences in stiffness through thrust. Lift is achieved through the reduction of the
the depth of the tail (from top to bottom) result in ventral lobe of the tail in heterocercal tails, and the
non-uniform movement of the caudal fin as it beats extension and stiffening of the dorsal portion of the
back and forth. Indeed, recent research shows com­ tail. Three-dimensional kinematics and flow visu­
plex fluid dynamic coupling between the flow alization of tail and water movement (Fig. 5.7; Ferry
fields from the dorsal and pectoral fins with the and Lauder, 1996) confirmed this function of het­
vortices produced by the caudal fin (Flammang erocercal tails for swimming sharks, but subse­
et al., 2011). quent work indicates that lift production by the
In contrast to most fish that have homocercal heterocercal tail of sturgeon is less significant. The
tails, sharks and some other fish (e.g. sturgeon) lift produced by the heterocercal tail of sharks
have asymmetrical, or “heterocercal” tails (Fig. 5.7). helps to counteract the negative buoyancy of these
Whereas homocercal tails provide uniform forward animals, but also generates a pitching moment
100 A N I M A L L O C O M OT I O N

(a) Flow tank

Mirror
Water in
flow
flow

Cameras Lpect R
(c) L

T
CM

Freact
(d)
(b)

Lateral Posterior
view view Lateral view: dye stream

Figure 5.7 A flow tank and flow visualization are used to study swimming in many fish including leopard sharks (shown here). (a) By using two
video cameras and a mirror behind the animal, both lateral and posterior views of the tail’s motion can be analyzed (b). (c) The heterocercal tails of
sharks produce a net upward force, lift (L), that must be balanced by lift produced by the pectoral fins (Lpect) to prevent the shark from pitching
about its CM (open circle). Freact is the reaction force acting on the water; R is the resultant propulsive force. (d) Dye streams reveal the pattern of
flow produced by the heterocercal tail of the shark and confirm the downward direction of momentum transfer to the fluid that generates both lift
and thrust. Adapted from Ferry and Lauder (1996) with permission from the Company of Biologists, Ltd.

about the shark’s center of mass. This pitching tail shape to generate lift in order to maintain their
moment is resisted by additional lift produced by position in the water column.
the shark’s pectoral fins. Lift production and the The evolution of a swim bladder has enabled
presence of a heterocercal tail, therefore, are central a wide range of swimming morphologies and
to the body form and swimming function of many behaviors within teleost fishes and likely underlies
cartilaginous fishes, all of which are negatively much of their success as the most speciose class of
buoyant despite the retention of body oils to reduce vertebrates. Indeed, their ability to be neutrally
their negative buoyancy. Bony (teleost) fishes that buoyant has allowed them to become exception­
possess swim bladders, on the other hand, can ally maneuverable swimmers, and this has led to
achieve neutral buoyancy and, because of this, do the use of the pectoral fins as flexible, propulsive
not require constant swimming or an asymmetrical organs.
 M O V E M E N T I N W AT E R 101

5.4.4 Pectoral, dorsal and anal fin swimming stroke, the fin is rotated (“feathered” like the oar
movement of a human rower) parallel to the flow
Paired pectoral fin locomotion likely involves
(Fig. 5.8a, shown for the left fin) and, in some fish,
both drag- and lift-based mechanisms of propul­
reduced in breadth, so that its projected area is min­
sion. These mechanisms are the result of oscillatory
imized when the fin is protracted forward, keeping
movements of the pectoral fins on either side of the
drag low. This enables the fish to achieve a net pro­
fish’s body (Fig. 5.8). Simple rowing movements of
pulsive force in the forward direction. Left- versus
the pectoral fins represent a purely drag-based mech­
right-pectoral fin propulsive and recovery strokes
anism of propulsion (Blake, 1981). Like ciliary or fla­
have similar timing during forward swimming, but
gellar propulsion at low Reynolds numbers (Section
are varied when fish maneuver.
5.6), pectoral fin rowing requires a change in the
Particle image velocimetry (PIV) visualizes and
projected area of the fin relative to the direction of
quantifies flow, and has provided central insights
fluid flow in order to alter the drag produced dur­
into the hydrodynamic function of pectoral and
ing the propulsive and recovery strokes. During the
caudal fin propulsion in fish. PIV uses a laser-gen­
propulsive stroke, the fin is retracted back with the
erated “light sheet” to illuminate a thin plane of
fin plane oriented perpendicularly to its movement
water. By seeding the water with neutrally buoyant
(Fig. 5.8a, shown for the right pectoral fin), maxi­
particles, detailed patterns of flow can be tracked
mizing drag and hence, the reaction thrust force
and local flow velocities are quantified using high-
that the water exerts on the fin. During the recovery
speed video of the fluid movement (e.g. Wilga and

(a) Pectoral fin rowing (b) Pectoral fin ‘flying’

Drag-based propulsion Lift-based propulsion

vfin
vw

L
Recovery Propulsive
stroke stroke T
vnet
–vfin
Posterior view
vw

Figure 5.8 Many fish use their pectoral fins for either (a) drag based propulsion, in which the fin is used for rowing, or (b) lift-based, in which the
fin is used much like a wing or the tail fin of a tuna. (a) Taking a cross-section through the fins and body (dashed line, upper image) and then
looking anteriorly down the length of the fish (lower image), the effects of fin position on drag generation and reduction are evident. During the
propulsive stroke (right side, black fin), the fin is rotated perpendicularly to the flow to increase its cross-sectional area and enhance drag. During
the recovery stroke (left side, gray fin), the fin is oriented parallel to the oncoming flow during the recovery stroke, reducing its cross-sectional area
and hence, drag. (b) When fish use their pectoral fins for lift-based propulsion, the fins are actively moved through the water such that the fin’s
velocity (vfin) and velocity of water (vw) relative to the swimming fish sum (v net ) to generate lift (L) and forward thrust (T).
102 A N I M A L L O C O M OT I O N

Lauder, 2000). This computationally intensive experi­ the pectoral (as well as tail) fin produces. These, and
mental approach uses the same principles of track­ other, unsteady effects as propulsive mechanisms
ing dye to map streamlines, but allows fluid forces are central to swimming speed, gait transitions, and
to be calculated directly from the detailed pattern of energetic efficiency (Fish and Lauder, 2006).
flow velocities obtained from individual particles. In addition to drag-based thrust, paired pectoral
This also enables investigators to examine non- fins can also generate thrust by means of lift. Thrust
steady, as well as steady, flows associated with par­ generated by lift is produced when the pectoral fins
ticular locomotor mechanisms. Using this type of are used as hydrofoils rather than as simple paddles
analysis, Drucker and Lauder (2000) quantified the (Fig. 5.8b). In this case, the fins are moved primarily
thrust produced by the pectoral fins of a swimming in a dorsoventral plane and used as “wings” (this is
sunfish (Fig. 5.9), showing that donut-shaped rings in contrast to sharks, which hold their pectoral fins
of vorticity are shed at the end of each propulsive fairly steady, so that lift is generated mainly as a
stroke. Their analysis indicates that, in addition to a result of the shark’s own forward motion, Fig. 5.7c).
large posterior component of thrust, sunfish also Lift is generated as a force acting perpendicularly to
generate a large lateral hydrodynamic force that is the direction of flow over the laterally projected fin.
likely important to their stability and maneuvering By moving the fin downward with respect to the
ability. oncoming flow of water due to the fish’s forward
It also seems likely that the unsteady effect of velocity, a lift force is generated that has a forward
acceleration reaction due to the varying velocity of component acting to overcome drag. Just as for cau­
the fin, as it is accelerated and decelerated during dal fin propulsion in tunas, lift provides net forward
the stroke (Daniel, 1984), may be an important fea­ thrust. By rotating the fin in the opposite direction
ture of pectoral fin propulsion. The magnitude of during the upstroke, the horizontal component of
thrust that is produced, therefore, depends on the lift is maintained in the forward direction of the
rate of change of fin velocity, fin shape and stroke fish’s travel (the vertical components of lift and
angle. Fin velocity, flexibility, shape and angle drag cancel out during reciprocal downward
affect the magnitude and orientation of thrust that and upward motion of the fin). Consequently,

Shed vortex at end of

propulsive stroke

Figure 5.9 The pectoral fin of sun perches produces a shed vortex ring. The rotational momentum of fluid (curved arrows) in the ring produces a
net resultant propulsive force (R). Quantification of fluid movement was achieved by means of particle image velocimetry. Redrawn from Drucker
and Lauder (2000) by G. M. Farley.
 M O V E M E N T I N W AT E R 103

lift-based propulsion has the advantage of provid­ “invertebrate olympians” based on their explosive
ing thrust over the entire pectoral fin cycle (as it mode of locomotion (O’Dor and Webber, 1991). Jet-
does in caudal fin and fluke propulsion). In con­ propelled organisms eject a bolus of fluid at high
trast, drag-based propulsion can only provide velocity from an internal body cavity. Most jetters
thrust over 50 percent of the cycle. Generally, drag- do this by means of a muscle-lined wall that encloses
based propulsion is favored at slow speeds of swim­ a fluid-filled chamber. Once again, thrust is achieved
ming and lift-based propulsion at faster speeds in reaction to the momentum of the fluid discharged
(owing to the increased flow achieved by the ani­ by the jet. Contraction of circumferential muscle
mal’s forward movement in combination with the ­fibers decreases the diameter of the chamber, thereby
fin’s own movement). Nevertheless, the simple dichot­ causing the fluid to be ejected through a port. The
omy of drag- versus lift-based propulsive mech­ direction of the port allows the animal to orient its
anisms for slow versus fast swimming in fish that rely jet and thereby control the direction of its movement.
on paired p ­ ectoral fin propulsion can be mislead­ In the case of scallops, jetting is achieved by the con­
ing, as both mechanisms are likely employed dur­ traction of an adductor muscle which causes the
ing different phases of the fin stroke. Consequently, two valves (shells) of the animal to close against the
changes in fin kinematics and the relative import­ mantle cavity. In most animals, an antagonistic set
ance of these two mechanisms are likely to occur of muscles (longitudinal or transverse) causes the
over a range of swimming speeds within a species, cavity to expand and refill for the next jet. In scal­
as well as when comparing pectoral fin morpho­logy lops, however, an elastic hinge pad comprised of
and locomotor function among different types abductin serves as a compression spring that re-
of fish. opens the valves.
In addition to caudal and pectoral fin propulsion, At small sizes and low speeds, jet propulsion can
many fish also use elongated dorsal and anal fins be highly efficient, but at faster speeds, jet propul­
for swimming. These fins undergo lateral undula­ sion is costly. Some jellyfish (Aurelia aurita) exhibit
tions that are propelled as a traveling wave down cost of transport that is far lower than comparably
the length of the fin, often termed ribbon-fin loco­ sized swimming fish and crustaceans (Gemmell et
motion. Ribbon-fin locomotion has evolved multiple al., 2013). This is achieved through a combination
times across fish, and includes knifefish, bowfin and of lower metabolic costs associated with the minimal
seahorses (Jagnandan and Sanford, 2013). Many of layer of muscle used for bell contraction (and high
these fish hold their bodies fixed in place and loco­ proportion of metabolically inactive tissue), the
mote primarily with the dorsal or anal fin. One passive return of the elastic bell to its resting
remarkable example is found in knifefish which ­position, and the use of passive energy recapture
generate waves from both anterior and posterior through vortices formed within the bell. Even so, to
ends of the fin which meet at different nodal points; generate high velocities, jetting is an expensive
the location of these nodes determines whether the mode of locomotion. The basic problem lies in the
fish is hovering or swimming, as well as the swim­ required amount of momentum discharge (power
ming direction of the fish (Ruiz-Torres et al., 2013). output) relative to the kinetic energy of the dis­
charge (power input). As is also the case for swim­
ming fish, the thrust (T) of a jetter (from Eq. 5.6)
5.5 Jet-based fluid propulsion
depends on
Jet propulsion has evolved a number of times in a
T = mv (5.7)
diverse array of animals, resulting in a rather eclec­
tic assortment that includes many types of inverte­ where m and v are the mass and velocity of the
brates: jellyfish (DeMont and Gosline, 1988), scallops water ejected in each jet. Whereas thrust depends
(Marsh et al., 1992), and most notably, cephalopod on v, the kinetic energy of the discharge depends
molluscs (Nautilus, cuttlefish and squid). Squid are on v2. Consequently, jet propulsion is most efficient
best known for their prowess as jetters, reaching when the mass of fluid accelerated is increased
speeds of up to 8 m s–1, and have been described as rather than increasing the velocity of the jet. Greatest
104 A N I M A L L O C O M OT I O N

efficiency is achieved when the jet velocity approaches propulsive and recovery stroke. No net forward
the animal’s forward velocity. This can only be progression would be achieved.
achieved by very high-frequency, low-amplitude Consequently, at low Reynolds numbers there
jets. This is the basis of jet-propelled engines in air­ must be some asymmetry in the kinematics or shape
craft, but is not always a viable solution for biolo­gical of the propulsive and recovery strokes for any net
organisms. Instead, organisms must contain the mass thrust to be produced. Moving the cilia quickly dur­
of fluid within their body, which can limit efficient ing the propulsive stroke and slowly during the
high-rate motion. recovery stroke also does not work. This would
The scaling of jet propulsion is nicely illustrated only affect the rates of forward and backward
by the morphology and jetting frequency of jelly­ movement. The end result would be the same: the
fish. In a study of a five-fold range of jellyfish sizes organism would be in the same place at the end of a
(in Aurelia aurita), as body size increased, the shape full cycle of movement. Because viscous shearing of
of the body changed, the motion of the jellyfish’s the fluid is the sole mechanism available for gener­
bell increased, and the rate of jetting decreased ating thrust, low Re animals achieve net forward
(McHenry and Jed, 2003). The coordinated scaling thrust either by changing the shape of their propul­
of body shape, size and kinematics resulted in sors to maximize drag for thrust production during
larger animals swimming more slowly, but more the power stroke and reduce drag during the recov­
efficiently. Another study (Bartol et al., 2016) shows ery stroke (ciliates), or by taking advantage of helical
that squid use a combination of fin motion and jet­ or propagated bending waves (flagellates). Because
ting to locomote at intermediate speeds, but switch drag depends solely on the viscous interaction of
to exclusively jetting at higher speeds. Whether or the organism with the surrounding fluid (i.e. pres­
not this reduces or improves the efficiency of their sure drag is unimportant), the overall shape of the
movement remains to be determined. animal’s body is largely irrelevant to its ability to
move through the fluid. Consequently, the shapes
of these organisms are quite varied and no evidence
5.6 Movement at low Re: the of streamlining to reduce pressure drag is observed.
Indeed, streamlining is undesirable, because it tends
reversibility of flow
to increase skin friction drag by increasing the sur­
Life at low Reynolds numbers is a particularly face area of the body exposed to flow.
sticky business when compared to life at high Re.
Low Re flow dominates the world of single-celled
organisms. Although not animals, the locomotor
5.6.1 Flagellar swimming
movement of these organisms depends on low With the exception of bacterial (prokaryote) flagella
Re propulsion, and as such, we cover them here. which function as biological rotors, most eukaryote
Because viscous forces dominate at low Re, inertia flagella and cilia represent cellular projections that
can be ignored. At low Re, boundary layers are rela­ consist of a 9+2 arrangement of microtubules linked
tively thick because velocity gradients are slight, together by various microtubular-associated pro­
turbulence is absent and, because mixing across teins (Fig. 5.10a). Flagella and cilia bend as the
streamlines does not occur, flows are fully reversible. molecular motor, dynein, binds to a neighboring
The symmetrical oscillatory movements of fins and microtubule and ratchets along it, much like actin and
body surfaces that larger aquatic organisms use to myosin. The circumferentially paired microtubules
propel themselves through the water do not work overlap so that one pair is incomplete. This asym­
under these conditions, because a push in one direc­ metry ensures that the tail of the dyenin molecule
tion will be equally balanced by a push in the other is anchored to the “A” microfilament of the pair
direction—resulting in no net motion at all. For allowing the head end of the dynein to interact with
example, if the cilia of a paramecium or the flagella the “B” microfilament of the adjacent pair. ATP-
of a bacterium were to move back and forth sym­ dependent movement of the dynein toward the
metrically, the animal would simply move forward minus end of the “B” microfilament is similar to the
and then back to its original position during each movement of dynein along microfilaments within
 M O V E M E N T I N W AT E R 105

9 + 2 arrangment
(a) Microtubule pairs (b)

Bacterial
Dynein Eukaryote prokaryote

Bending
direction

Linking
proteins

Bend

–
– –

Figure 5.10 Eukaryotic and bacterial flagella and cilia use microtubules to generate movement. (a) Eukaryote flagella and cilia have a
characteristic 9 + 2 arrangement of microtubules. Bending of the microtubules and resulting hydrodynamic force are produced by the motor
protein, dynein. Dynein molecules operate like little “arms” that can bind and unbind along adjacent microtubules, much like the ratcheting action
of actin and myosin. As they ratchet along one side, it causes the cilium or flagellum to bend. (b) Bacterial flagella also are comprised of
microtubules, but have a different arrangement than in eukaryotes. In addition, they rotate at their base rather than passing waves of bending
along their length. Illustration by G. M. Farley.

cells for the purposes of cell transport. The local less flexible, and lack the characteristic internal
bending moments generated by microtubule trans­ 9 + 2 microtubular arrangement. The flagellum
lation induce planar or helical bending waves that itself is a helical tube consisting of a single protein
are transmitted along the length of the flagellum. subunit, flagellin. Prokaryotic flagella function by
Ciliary bending tends to be mainly planar. Despite rotating at their base rather than by bending along
differences in wave kinematics, flagella and cilia their length. Rotation is driven by a proton gradi­
are morphologically similar and of fairly uniform ent estab­lished across the plasma membrane of the
diameter (0.2 μm) across a wide range of taxa. They flagellum ­organelle and the inside of the bacterium
can, however, vary considerably in length (10–1000 (the details of which are beyond the scope of this
μm) and the number of waves (one to four) trans­ book). In fact, bacterial flagella represent the only
mitted. true biological rotary devices known. Helical rota­
Prokaryotic flagella (Fig. 5.10b) have distinct tion of the rest of the flagellum is believed to result
morp­hology and kinematics compared with eukary­ from passive transmission of the forces produced
otic flagella and cilia. They are typically much at the base. Bacteria, such as E. coli, swim toward
smaller (0.02 μm in diameter and up to 20 μm long), chemical attractants and away from repellents.
106 A N I M A L L O C O M OT I O N

Because the flagella have intrinsic “handedness”, attractant signal using a “biased random walk”
they draw together as a coherent bundle when the (Berg, 1983).
flagella rotate in a counterclockwise direction and Regardless of the detailed kinematics of motion or
splay apart when the flagella rotate in the opposite the molecular mechanism of power generation, fla­
direction. This results in either effective swimming gellar thrust is produced by the same mechanism.
in a fairly steady direction or a “tumbling” behavior A flagellum can be modeled as a cylinder. The drag
that produces a more chaotic motion. In the absence experienced by a cylinder perpendicular to the flow
of a chemical signal, flagellar rotation reverses (Fig. 5.11a) is about 1.8 times greater than the drag of
every few seconds. This causes the bacterium to a cylinder oriented parallel to the flow. By varying
tumble and change direction randomly over time, the angle at which segments of the flagellum move
so that interspersed “bouts” of swimming and tum­ relative to the fluid (Fig. 5.11b) a net drag-based pro­
bling constitute a random walk. In the presence of pulsive force (T) is generated perpendicularly to the
a chemotactic stimulus, tumbling is suppressed direction of the segment’s motion (similar to that for
and the bacterium swims more steadily toward the undulating fish and eels; Fig. 5.4). This is analogous

(a) Motion Drag

(b)
R

Motion with respect

to organism
(c) Propulsive stroke Recovery stroke

Figure 5.11 Drag-based propulsion is the sole means of achieving net forward thrust at low Reynolds numbers. (a) When a cylinder is
perpendicular to the flow, the drag that it encounters is 1.8 times greater than when it is oriented parallel to the flow. This difference in drag due
to orientation enables flagella (b) and cilia (c) to locomote. By orienting the cilia parallel to the flow during the recovery stroke, much lower drag
results than when the cilia beat in a more perpendicular orientation during the propulsive stroke.
 M O V E M E N T I N W AT E R 107

to the motion of a cylindrical object that is pulled fashion (Fig. 5.11c). During the power stroke, the
through the water at an inclined angle, which cilia are stiff and extended, oriented much like a
induces a slewing force (lateral to the direction of cylinder perpendicular to the flow. During the
pull) that is equivalent to the thrust force gener­ recovery stroke, the cilia are flexible and bent near
ated by a flagellar segment. The thrust developed their base. This allows them to slide parallel to the
by individual segments of the flagellum along its direction of flow, reducing their drag by as much as
entire length is summed to yield the overall thrust 50 percent. The two-fold difference in drag during
generated. For helically translating and rotating fla­ the power and recovery strokes accounts for much
gella, thrust can be generated along most of the of the net thrust production in these animals.
length of the flagella, but the animal’s body will However, because of their closely packed config­
tend to corkscrew in the opposite direction. Planar uration, cilia do not act as independent propulsors.
undulation of flagella restricts effective thrust to Hydrodynamic interactions among cilia can gener­
those regions of the flagella that are inclined (>20 ate coordinated motion that actually enhances the
degrees) to the direction of flow, but does not tend to propulsion velocity and efficiency (Elgeti and Gom­
destabilize the motion of the rest of the organism. pper, 2013). Complex hydrodynamic models have
This analysis of flagellar propulsion at low Re characterized the propulsive efficiency of single
ignores the interactive effects of fluid movement past and closely packed cilia (Elgeti et al., 2015). For
the body of the organism and its flagellum, as well as closely packed cilia, the summed interaction of the
between adjacent ciliary propulsors. This latter limi­ cilia can be reasonably predicted by treating the
tation is a problem when considering closely packed ciliary tips as a continuous surface of the organism
cilia near the surface of an organism. Because of the and analyzing the overall metachronal wave of
much greater size and length of the flagella compared ­ciliary motion that this surface generates to produce
to the body of most flagellates, the drag on the head hydrodynamic thrust. For less closely packed cilia,
or body of the organism is generally less than ten per­ other models have been developed to account for
cent of the flagellum and can be reasonably ignored. the flow between cilia in order to calculate a more
For bacteria, the requirement that rotation of the fla­ detailed velocity profile of flow within the ciliary
gella be conserved by angular rotation of the head field; these are also beyond the scope of this book.
suggests that rotational propulsion is only effective if How effective are flagella and cilia? One meas­
the radius of the head (modeled as a sphere) is greater ure of the effectiveness of fluid propulsion is hydro-
than five times the radius of the flagellum. dynamic efficiency, which measures the rate of useful
work performed relative to the total rate of work
done by the propulsors. Useful work represents a
5.6.2 Ciliary swimming
measure of the distance that the animal moves for a
Ciliary propulsion involves the coordinated beating given propulsive force. For flagellar propulsion,
(metachrony) of many hundreds to thousands of hydrodynamic efficiencies of 0.09–0.28 have been
short cilia (15 μm) along the surface of the organ­ estimated (Daniel et al., 1992); whereas, for ciliary
ism. Cilia are fundamental to the locomotion of propulsion a value of 0.25 has been estimated
ctenophores—the largest organisms that locomote (Vogel, 1994). The efficiency, modeling and synthe­
with cilia—as well as for the locomotion of the lar­ sis of cellular motion are the focus of a large body of
vae of a great diversity of marine invertebrates. The literature that connects biological and engineered
building blocks of sponges also use ciliary motion approaches to small-scale fluid dynamics (Elgeti
to generate water flows. Single-celled, protozoan et al., 2015).
ciliates generally have much larger body size
(25–1000 μm) than flagellates and are able to
5.6.3 Size considerations
achieve much faster speeds (where sizes overlap,
ciliates go about ten time faster; Sleigh and Ciliates, in general, are larger and swim faster rela­
Blake, 1977). In contrast to the sinusoidal or helical tive to body size than flagellates (Vogel, 2008). This
motion of flagella, cilia beat in an asymmetrical difference may arise from the mechanics of cilia
108 A N I M A L L O C O M OT I O N

v­ ersus flagella. Flagella don’t bend as a whole—they Water boatmen (Corixidae) make good use of
instead pass waves of bending along their length operating in the intermediate Re range by using
from an initial rotation at their base. By contrast, hairy appendages for drag-based propulsion (Ngo
cilia actively bend along their length. Therefore, and McHenry, 2014). When moved slowly, and thus
given that rates of working and bending moments at low Re, the hairy appendages act as thrust-gener­
scale to the cubed-length of the cilia (∝ l3) and resist­ ating paddles during the power stroke. When the
ance to bending only scales to the squared-length of appendages are moved quickly, the hairs flex, allow
the cilia (∝ l2), this means that increasing length can water to flow through the hairs, and reduce drag
compromise the structural and energetic effective­ during the return stroke.
ness of a propulsor. Such limits do not apply to fla­ Many other locomotor systems operate in the
gella, because they do not bend as a whole and instead intermediate Re regime, including young squid, lar­
pass waves of bending along their length. The solu­ val fish, and ascidians. The consequences for tiny
tion for larger body size is to have many short cilia locomoting fish, for example, are manifested through
or one to two long flagella. The disadvantage of fla­ distinctly different vortex generation and momen­
gella is that speed seems to be compromised, which tum transfer to the water compared to their adult
may explain why flagellates are generally much counterparts. A larval swimming fish contends with
smaller than ciliates. a boundary layer that is equivalent to its entire body
Limitations to larger body size seem to be set, at thickness and, as a result, almost immediately halts
least in part, by hydrodynamic efficiency. Hydro­ after even the most vigorous escape responses
dynamic efficiency is predicted to decrease with (Müller et al., 2008).
increasing size for both ciliates and flagellates. By
assuming a constant ciliary density over the body
5.8 Air-water interface: surface
surface and uniform propulsive efficiency of indi­
vidual cilia, the overall hydrodynamic efficiency of swimming, striding and sailing
ciliates is predicted to scale inversely to the animal’s Surface tension and waves are important factors
body length, or ∝ l–1. Consequently, an upper limit influencing the locomotion of animals at the water
to body size by means of ciliary propulsion appears surface. Fish typically swim underwater, rather
to be around 0.1 μm (however, see Section 5.6.2 con­ than at the surface (except for those species that
cerning ctenophores). leave the water to glide in the air or to strike their
prey). Most aquatic mammals and some birds also
5.7 Movement at intermediate Re: swim underwater, but many swim at the surface
and all must come to the surface to breathe. Animals
switching between paddles and rakes
that move at the surface encounter additional drag,
Given that Reynolds number is determined, in part, because their motion generates waves at the sur­
by velocity, it is possible for organisms to operate in an face of the water. This increase in drag can be as
intermediate Re regime in which the dominance of much as five times greater than the drag experi­
viscous and inertial forces depends on the speed of enced at a greater depth. As we discussed in
the body or appendage. This range spans Reynolds Chapter 3, this increases the metabolic cost of swim­
numbers from 100 to 102. For locomotor append­ages ming at the surface.
with hairs, the spacing of the hairs ­coupled with Wave formation incurs a drag penalty because it
varying speed during propulsive strokes can yield a involves work to elevate a mass of water against
gravity. The Froude Number ( = v / gl ; introduced
2
paddle-like and rake-like output of the appendages.
In other words, organisms can move a hairy append­ in Section 4.8) was originally defined by a ship
age slowly such that it operates like a paddle and eng­ineer (Froude) to express the relative importance
maximizes drag-based propulsion. They can then of a ship’s inertia versus its wave drag. At a low Fr
return it to the starting p ­ osition more quickly, such (i.e. low velocity and long length) only small waves
that the fluid flows through the hairs like a rake. are produced. At a higher Fr, wave-induced drag
 M O V E M E N T I N W AT E R 109

increases, reaching a maximum at Fr = 0.45 . Above a­ ccelerations. Smaller organisms using drag-based
this value, drag decreases because the boat moves at mechanisms tend not to develop notable forces from
a speed great enough to plane over the water surface. the acceleration reaction (Ngo and McHenry, 2014).
Planing is likely a rare event for animals, but is cer­
tainly used by water birds when they land from a
5.8.1 Striding and sailing on the water surface
flight and appears to be used by duck­lings when
they swim. For boats and animals that are unable to A few small invertebrates, notably water striders
plane, 0.45 represents their limiting ­performance: and fisher spiders (Fig. 5.12) take advantage of their
more propulsive energy will produce only larger size and hydrophobicity to use the surface tension
waves, not higher swimming speeds. Generally, low of water for locomotion (Bush and Hu, 2006; Hu et
speeds are favored at the surface. At low speeds, the al., 2007). Surface tension ( N/m ) equals a force
bow wave created in front of the ship moves out exerted per unit distance; it essentially represents
away at a faster speed than the ship, so that the ship the work ( Nm ) required to deform a liquid’s sur­
remains level. However, at faster speeds, the ship face over a unit area (m2). Water striders use surface
eventually moves at a greater speed than its bow tension to generate forces equal to or greater than
wave, causing it to “swim” uphill. their own weight in order to step over the surface of
The world record (2009) in the 100 m freestyle by ponds or streams. The force exerted upward on a
César Cielo is 46.9 s and is just above 2 m s–1. For leg is equal to the surface tension of the water times
perspective, a person walking fast along the side of the wetted perimeter of the leg. This force acts tan­
the pool could readily match this speed. Quite obvi­ gentially to the water surface. Consequently, as the
ously our athletic endurance and performance on leg sinks further into the water, its line of action
land outstrips our abilities in water. Interestingly, becomes more vertical, enhancing weight support
this is also about the sustained cruising speed of (Fig. 5.12b).
many large fish. For Cielo, this represents a swim­ It had been generally thought that in order to
ming speed of approximately one body length s−1, move forward, a rearward push of a leg causes an
making his Fr about 0.45. Consequently, Cielo’s asymmetrical reaction force from the fluid surface,
time represents the top performance for someone of giving the animal a forward acceleration. As it turns
his height. In general, surface swimmers must move out, fisher spiders use drag resistance of the moving
at rather low speeds in order to be economical, in leg in combination with the dimple that the leg
the range of Fr <0.2. The maximum speed of a mal­ creates on the water surface (Fig. 5.12) to exert a
lard duck with a hull length of 0.3 m should be propulsive force (Suter et al., 1997). However, Bush
about 0.7 m s–1. This is quite low compared with a and Hu (2006) concluded that the dominant forces
fish of similar size, which could easily achieve for surface tension locomotion are from the sub-
speeds of 2 m s–1 or higher, when swimming at surface vortices and secondarily from drag-generated
depth. Similarly, muskrats swimming on a pond waves of the moving leg and associated water dim­
rarely exceed speeds of 0.6 m s −1 ( Fr = 0.16 ) . Surface ple. Suter and Wildman (1999) found that the ability
swimming by ducks and muskrats represent clear to maintain the integrity of the dimple was size and
examples of drag-based propulsion. In addition to speed dependent (varying with size but inversely
overcoming drag, it is certainly the case (as for fish with speed). As a result, faster moving and/or
that are pectoral fin rowers) that these animals must smaller spiders switch from rowing, in which four
produce additional thrust to overcome the a­ cceleration limbs are used to propel the animal along the water
reaction of water that is propelled backward by their surface, to the use of a galloping gait, in which six
feet. The relative importance of drag and acceler­ limbs are used to propel the animal into the air in
ation reaction to thrust production has been exam­ successive strides (Fig. 5.12d). By doing so, the
ined in multiple studies which indicate that its role ­spider is released from the constraint of having to
shifts depending on size and kinematics, particu­ maintain contact with the water and the integrity of
larly affecting larger animals moving with high leg-surface dimple interaction. The recovery stroke
 (a)

(b)

R R
Surface tension
and depth

(c) Drag resistance during rowing

(d) Rowing (dorsal view)

Recovery Propulsive stroke Recovery

Galloping (lateral view)

(e)

λ vv
v
r
2r

Figure 5.12 Locomotion on the water’s surface at small sizes uses a combination of surface tension, vortex generation and capillary waves to
generate forward propulsive forces. (a) A fisher spider is buoyed by surface tension on the water’s surface. (b) Surface tension produces an upward
resultant force (R), which increases with the depth of the unwetted limb in the water. (c) Asymmetry in the surface tension acting on the limb can
be used by the spider and other surface striders to produce drag-based rowing propulsion when moving at slow speeds. (d) To move faster, the
fisher spider leaps into the air between periods of limb support. It also reduces the number of limbs that are in contact with the water surface,
enabling reduced drag and faster movement. Adapted from Suter et al. (1997) and Suter and Wildman (1999) with permission from the Company
of Biologists, Ltd. (e) Propulsion results from a combination of surface tension, vortex generation (vv= vortex speed, r=radius of vortex) and
subsurface capillary waves (wavelength, λ) Adapted from Hu et al. (2003) by permission from Macmillan Publishers Ltd.
 M O V E M E N T I N W AT E R 111

occurs while the spider is airborne, allowing it to pre­ 5.8.2 Running on the water surface at large
pare its limbs for the next propulsive support phase. size: integrating terrestrial and aquatic lifestyles
The size range for effective use of surface ten­
sion is quite limited. If an animal is too big, the There are at least two biological examples of verte­
water can’t support the animal’s weight. If too brates that can “walk on water,” albeit not at a walk.
small, the stickiness of the fluid—its viscosity— Western and Clark’s grebes run across the water for
becomes a problem, and the tiny beast can’t over­ their rushing display and iguanid basilisk lizards
come the fluid’s surface tension with its own (known popularly as “Jesus Christ lizards”) run
inertia. The switch to a galloping gait by fisher across streams and ponds (for predator escape) in
spiders, however, suggests a means for avoiding the Central American tropics with their head and
this problem at small size—by becoming airborne trunk elevated above the water (Fig. 5.13). These
in between support phases of the stride. At the animals are far too large to employ surface tension
large end of the size range, a 70 kg person would for support. Instead, they take advantage of the
need to have feet more than 30 m in length in mass density of water, which exerts a reactive force
order to support their body’s weight while walk­ when accelerated rapidly (the acceleration reaction
ing on the surface of water! force introduced in Section 5.3.1). Basilisks achieve

(a)

(b)
Slap Stroke Recovery

Figure 5.13 A basilisk lizard runs over the water surface by initially slapping the water surface (a) to generate an impact reaction force and
subsequently generating a cavitation reaction force produced by entraining air and displacing fluid from the foot cavity. (b) Through the use of
DPIV (digital particle velocimetry), the particle displacements and vortex generation reveal how forces are generated by the running lizard. The slap
and stroke of the foot into the water initiates vortex formation. The foot is removed from the water before the air pocket collapses. Then, fully
formed vortices are propagated opposite to the motion of the lizard. Adapted from Hsieh and Lauder (2004); copyright (2004) National Academy
of Sciences, USA.
112 A N I M A L L O C O M OT I O N

weight support by running rapidly with webbed feet As examples of how robotics and biology have
that produce both an acceleration reaction force when been synergistic, two simple models have been par­
their foot slaps the water surface followed by a fluid ticularly influential. The goal of the first model was
drag and buoyant force from the water cavity gen­ to simplify fish swimming down to the most essen­
erated as the foot strokes through the water, which tial parts—shape, materials and actuation. These
balances their weight and produces thrust (Fig. 5.13b; simple physical models, later named “Twid­dlefish”
Glasheen and McMahon, 1996). Just as for terrestrial when commercialized, were actuated by twisting a
running, the peak forces generated by this slapping flexible beam attached to the base of a rubber fish
and stroking mechanism must exceed the animal’s model’s head. Generating a body wave at the base
weight to compensate for periods in which lower of the head, coupled with a realistic shape and flex­
forces are exerted. By entraining a cavity of air, the foot ible material, was sufficient to generate realistic
not only generates a buoyant force (proportional to fish-swimming motion. A different, also very sim­
the entrained air volume), but the air cavity also ple, model looked at whether fish could locomote
allows the foot to be picked up out of the water with solely from the energy in the surrounding water—
minimal resistance. The actual propulsion force occurs as an example of energy harvesting (Beal et al.,
primarily during the stroke of the foot through the 2006). Here, a fish-like shape (either as a physical
water. The momentum of the lizard is transferred to model or an actual dead fish) was actuated solely
the water via vortices that are driven ventrally, lat­ by vortices passing along its body and was able to
erally and posteriorly to the lizard’s feet (Hsieh and propel itself. Therefore, in addition to high-tech,
Lauder, 2004). In comparison, recent analysis of the fully sensored and remotely operated robotic fish
slap dynamics of Western and Clark’s Grebe feet (Aditi and Atul, 2016), considerable basic under­
(Clifton et al., 2015) shows that during rushing, standing of aquatic locomotion has been achieved
grebes outperform basilisk lizards by about two- through physical modeling and robotics (Webb,
fold in terms of relative weight support achieved dur­ 2001).
ing the slap phase of their water running stride.

5.10 Summary
This chapter demonstrates how the physical prop­
5.9 Biological robotics in and on water
erties of water, and common hydrodynamic principles
The efficiency and diversity of organisms that loco­ that emerge from them, govern the swimming per­
mote on and in the water have inspired countless formance and diversity of aquatic propulsive mech­
robotic devices that include micro-scale swimmers, anisms. Although the buoyancy of water has
water-walking and jumping devices, synthetic water enabled a tremendous range in the size of aquatic
boatmen that are fueled with bacterial cells, robotic animals, body size still plays a crucial role in deter­
fish of all sizes, and even robotic jellyfish. These robots mining the physical regime of fluid propulsion that
are inspired by biological systems, yet address a can be successfully employed. Whereas moderate
wide range of goals, including testing fluid dynam­ and large animals must contend with drag resulting
ics hypotheses (such as momentum transfer in from their own inertia, the aquatic world of very
­surface-walking organisms and intermediate Re tran­ small animals is governed by viscosity. As a result,
sitions), surveillance, ocean current tracking, and the strategies that work for effective fluid propul­
innumerable other functions. Swimming robots sion at intermediate to large Re (streamlining and
are also used for testing biological hypotheses— lift) don’t work for very small animals. Instead,
for example, some robots are used for assessing they must overcome the reversibility of flow at low
the influence and evolution of vertebrae in swim­ Re by creating asymmetric patterns of drag-based
ming (Long Jr. et al., 2006). The plethora of water- propulsion, reminiscent of the strategies of both
based devices is a field in its own right that also pectoral fin and surface rowers. Within a given Re
informs the understanding of how biological systems regime, however, we find a spectacular diversity of
operate. body forms and hydrodynamic propulsors, ranging
 M O V E M E N T I N W AT E R 113

from lift-based caudal fins and bodies of fish, to the Additional reading
cilia and flagella of unicellular swimmers. Finally, as
Lauder, G. V. (2015). Fish locomotion: recent advances and
is often the case in biology, we also observe unusual,
new directions. Ann. Rev. Mar. Sci. 7, 521–45.
yet quite dramatic forms of aquatic ­propulsion, such Videler, J. J. (1993). Fish Swimming. London: Chapman & Hall.
as the jetting of squid and the surface running of Vogel, S. (1994). Life in Moving Fluids. The Physical Biology of
basilisk lizards and galloping fisher ­spiders. Flow. Princeton: Princeton University Press.
 CH A PT ER 6

Movement in Air

The aerial performance of flying animals is remark- Aerial flight involves the same fluid mechanical
able and has inspired human myth and experimen- principles that underlie aquatic locomotion. How­
tation over much of our history. The grace and beauty ever, because of the 800-fold lower density of air
of a heron in flight, the power and drama of a preda- compared with water, important differences exist.
tory attack by a diving hawk, the flitting maneuvers Unlike swimming, weight support is the key prob-
of a bat or the magnificent control of a bumblebee or lem when moving through air. Consequently, the
a hummingbird foraging for floral nectar all capture wings must produce lift to support the animal’s
the extraordinary performance of flying animals. weight as well as thrust to overcome drag on the
For comparison with human-made flying machines animal’s wings and body (Fig. 6.1). Because lift
that they inspired, the flight of a house fly at 3 m s–1 production in the low-density fluid of air requires
represents a speed of 430 body length s–1 (Table 6.1). a high flow velocity, flying animals move at much
When normalized for size in this way, a fly achieves higher speeds than swimming animals, or move
a speed that is more than 12-times greater than the their wings rapidly when flying at slow speeds. As
speed of a high-performance fighter jet and 80 times a result, the Reynolds number (Re) range for most
greater than the speed of a propeller driven air- flying animals is high enough (102–107) that inertial
plane. forces dominate. This means that pressure drag
In addition to such spectacular performance, flight contributes much more to the total force balance
has proven a highly successful mode of life for a than viscous (or friction) drag, except perhaps in
wide range of taxa, having contributed to the enor- the smallest fliers (e.g. at ~ 0.01 mg, fruit flies oper-
mous diversity of insects (>800,000 species), birds ate in the range of Re = 10 –100).
(>8000 species) and bats (>850 species), the latter In this chapter, we first examine the forces acting
constituting the second most speciose group of mam- on a flying animal and the various ways in which
mals. Though more expensive than swimming, flight these fluid forces can be calculated. We then con-
is a cheaper means of transport over a given dis- sider how basic features of the wings and body
tance than when moving on the ground (Chapter 3), affect flight forces. Building on this understanding,
particularly when changes in elevation must be we next examine the power requirements associ-
negotiated. Flight enables animals to migrate and ated with flight as a function of flight speed, based
forage over large distances, avoid harsh or challen- on conventional aerodynamics (i.e. steady airflow
ging environmental conditions (e.g. desert, ocean) past non-oscillating wings, which applies to most
and thereby reach otherwise inaccessible foraging engineered aircraft). Gliding flight is well described
sites. In addition, flight provides an exceptional means by steady-state theory and is discussed in this con-
of predator defense, as well as excellent access to text. However, because flying animals must flap
prey and other food resources. their wings to support weight and overcome drag,

Animal Locomotion. Second Edition. Andrew A. Biewener & Sheila N. Patek, Oxford University Press (2018).
© Andrew A. Biewener & Sheila N. Patek 2018. DOI: 10.1093/oso/9780198743156.001.0001
 MOVEMENT IN AIR 115

Table 6.1 Animal flyers can out-perform engineered systems when considered in terms of size-normalized speed (lengths/s).

Aircraft Mass (kg) Length (m) Speed (m/s) Speed (length/s)

DH-60 “moth” (biplane) 450 7.2 39 5.4

Cessna A-37B “dragonfly” 4500 8.6 219 25.5
Concorde 15,000 62.1 606 9.8
Airbus A340 240,000 63.7 253 4.0
MD F-4 “phantom” jet 20,300 19.4 639 32.9
Gossamer albatross (human-powered plane) 100 10.4 8.0 0.8
House fly 0.0001 0.0007 3 430
Butterfly 0.0002 0.05 1 20
Starling 0.070 0.15 15 100
Duck 1.0 0.28 25 89
Swan 8.0 0.8 18 23

R 6.1 Flight forces: lift, drag and thrust

L As we have noted for water movement past a hydro-
foil, when a wing (or asymmetric airfoil) encounters
an oncoming flow of air at a positive angle to the hori-
D zontal, the flow separates around the airfoil, such that
the air passing over the top of an asymmetrically
D’ shaped airfoil moves at a higher velocity (v) than
T
the air passing below (Fig. 6.2a). The angle that the
airfoil presents to the oncoming flow is referred to
as its “angle of attack.” In addition to being asym-
v metric in shape, airfoils usually have camber, which
means that their convex upper surface is more curved
BW than their lower surface (which may be nearly flat or
slightly concave). Camber (h/c’, Fig. 6.2b) is a meas-
Figure 6.1 During level flight, flying animals must generate a forward- ure of an airfoil’s curvature. Combined with asym-
directed aerodynamic lift (L) force with a horizontal component of thrust metrical shape, camber allows an airfoil to generate a
(T) that counters the horizontal component of drag (D´  ). Drag (D) acts
perpendicularly to lift and thus has a vertical component that sums with
greater velocity differential (and aerodynamic lift) for
lift (resultant force, R) to support weight (BW). a given angle of attack compared with a non-cam-
bered airfoil. Insects and hummingbirds have more
non-steady aerodynamic effects come into play. These symmetric (“uncambered”) airfoils because their wings
non-steady aerodynamic effects are revealed by track- generate lift during both downstroke and upstroke.
ing the flow over a moving wing or by the use of novel The fins of fish also tend to be symmetrical because
robotic models that allow non-steady flight forces to they, too, generate hydrodynamic thrust during alter-
be measured, and are subsequently discussed. The nating tail beats.
kinematics of flapping flight and the various flight According to Bernoulli’s principle, the velocity
styles that animals adopt are also reviewed. Finally, differential produced by the asymmetrical airflow
the neuromechanical and a­ erodynamic mechanisms velocity past the airfoil results in a pressure differ-
by which flying animals maneuver and control their ence (low, above and high, below). This pressure
flight are also discussed, as these are critical to suc- difference induces a net upward force on the airfoil
cessful flight performance in natural conditions. that acts perpendicularly to the incident airflow and is
116 A N I M A L L O C O M OT I O N

Overall lifting flow = Translational flow + Circulatory flow

(a)

(b) (d)
Leading Lift
Resultant
edge
aerodynamic force
Oncoming
Cross-section
wind
or profile
Angle Trailing
of attack Chord c’ edge

Drag
(c) wing span, b

Oncoming wind
(e)
c’ Top or plan view
area S
h

Chord c’

Figure 6.2 Key variables and vectors for flight are visible from cross-sectional (profile) or top (plan) views (a) Asymmetry of airflow past an
airfoil (faster above and slower below) can be decomposed into translational and circulation components. Flow is described by streamlines.
(b) Airfoil shape in cross-section and (c) planform, with definitions of important shape and aerodynamic variables. (d) Lift, drag and resulting
aerodynamic forces acting on an airfoil cross-section. (e) Cambered airfoil based on overall chordwise curvature, showing camber (h). (Adapted
from Vogel (1994), Figs 11.2 and 11.1; with permission from Princeton University Press).

termed lift. Lift can also be thought of as the net cir- air speeds create more circulation and greater lift. Lift
culation generated around the airfoil resulting from varies in proportion to the square of an animal’s air
this velocity differential (Fig. 6.2a). As for any fluid, speed (∝ v2), which depends on the animal’s airspeed
air molecules don’t actually circulate around the in ­combination with the velocity of its wing as it is
airfoil, but the asymmetric flow pattern represents flapped. The dependence of lift on the translational
the sum of a translational component and a circular free-stream velocity and rotational velocity is for-
component of airflow. The circulation developed mally defined by the Kutta–Joukowski equation,
along the length of the airfoil is shed at its tip as
L = lρ vΓ (6.1)
vortices (at which point, physical circulation, rotation
of the air does occur). Shed vortices from the wing where is Γ the magnitude of circulation, l is the
tips can be visualized by illuminating particles seeded length of the airfoil over which the circulation
into the air (Fig. 6.3) and represent the momentum develops, ρ is air density and v is the animal’s
transferred to the air associated with lift generation. ­velocity (for the more ambitious and mathematically
Increased airflow results in an increase in both transla- inclined reader, a readable but more formal discus-
tional and circular components. Consequently, faster sion of circulation and aerodynamic lift is presented
 MOVEMENT IN AIR 117

(a) (b)

Figure 6.3 Aircraft (a) and birds (b) shed vortices from their wing tips. Bound circulation about each wing is shed at the wing-tip as a “trailing
vortex” into the wake. During faster forward flight, vortices shed from bird (and bat) wing-tips form undulating vortical tubes that trail behind the
animal due to the flapping motion of the wings.

by Milne-Thomson, 1966). This means that an ani- decrease as drag continues to increase. At a critically
mal can generate more lift by flying faster, having large angle of attack, an airfoil will “stall” due to
longer wings, or increasing circulation via angle of flow separation along its upper surface, which causes
attack or camber. Similar to drag, lift can also be a sharp (and sometimes, catastrophic) reduction in
(and is conventionally) defined as circulation and drop in lift. However, under con-
trolled circumstances, such as when a bird lands, an
L = 0.5 ClSv 2 (6.2)
increased angle of attack leading to a stall enables a
where Cl is the lift coefficient (analogous to the drag bird to slow down (due to increased drag) and des-
coefficient). In this case, S represents the profile area cend lightly. Generally, flying animals can delay stall
of the wing (often referred to as its “planform”; during takeoff, when flying slowly and during land-
Fig. 6.2b). Like the drag coefficient, the lift coeffi- ing due to the rapid flapping motion of their wings
cient depends on shape, orientation, surface texture (compared with the fixed wings of aircraft). Two
and Re. However, the two coefficients depend in other interesting points emerge from Figure 6.5c.
differing ways on these factors, which underlies First, positive lift can be generated by airfoils even at
much of airfoil design. negative angles of attack if an airfoil has an asym-
We now see that the resultant aerodynamic force metrical shape (and camber), favoring a faster flow
acting on a wing can be distinguished as two basic velocity along the upper surface (a symmetrical air-
components: lift (which acts perpendicularly to the foil operating with a negative angle of attack will
resultant direction of airflow) and drag (which acts induce a reversed circulation and hence, experience
parallel to the airflow). For a given shape and Re, “negative” lift). Second, a tangent to the curve drawn
changing a wing’s angle of attack (orientation) alters from the origin defines the angle of attack at which
the amount of lift relative to drag that the wing lift:drag (L/D) is maximized. This represents the
experiences (see Fig. 6.5c). Increasing the angle of optimal performance that an airfoil can achieve.
attack initially increases the amount of lift relative to Maximum L/D ratios, in the range of 10–18, have
drag. However, beyond a certain angle of attack, been reported for soaring birds (see Section 6.3),
approximately 45° for animal wings, lift begins to such as falcons, condors and albatrosses (the latter
118 A N I M A L L O C O M OT I O N

having the highest L/D ratio due to their extremely larger gliding birds. Shorter, low AR wings are also
long narrow wings). Lower L/D ratios, in the range beneficial to sea birds (e.g. diving petrel, Table 6.2)
of 2–8, have been observed for smaller birds and that dive below the water surface to catch fish.
insects.
It is clear that lift acts in a direction that is
­favorable to counteracting a flying animal’s weight,
6.1.2 Wing loading
but in order to generate thrust to overcome drag, lift
must have a forward component (Fig. 6.1). This is The ability to generate lift depends on the wings’ sur-
achieved by moving the airfoil at an angle to the face area (Eq. 6.2). Consequently, in addition to chan-
direction of the animal’s forward travel (see Fig. 6.7) ging a wing’s angle of attack, increased lift can be
so that the lift vector has both upward and forward achieved by increasing wing planform area. For birds
components. This is the basis of flapping flight, in and bats, changing wing area is an important control
which the motion of the wing downward relative device for adjusting lift during landing and maneu-
to the forward (horizontal) movement of the animal vering. Changes in wing area also occur during each
induces a net airflow around the wing that is phase of a wing beat cycle. The ability to collapse the
inclined with respect to the horizontal. As a result, wing during the upstroke helps to reduce drag and
aerodynamic lift has a horizontal component (thrust) avoid negative thrust. Aircraft are similarly designed
that overcomes the drag acting on the animal and a with the ability, albeit to a much lesser degree, to alter
vertical component that counteracts its weight. It is wing area (and camber) during take-off and landing.
important to remember that lift always acts perpen- The weight of a flier relative to the area of its wings
dicularly to the resultant path of incident air flow (BW/S) defines its wing loading. Wing loading pro-
over the wing, which results from the wing’s velocity vides a quantitative comparison of how much lift a
relative to the animal, combined with the animal’s unit area of wing must produce to support the ani-
forward flight speed relative to any prevailing mal’s weight and any cargo that is carried.
wind. Differences in wing loading have important impli-
cations for flight performance. Slowly-flying birds
generally have large wings (low wing loading),
6.1.1 Aspect ratio
whereas fast fliers have higher wing loading. In
A key parameter that influences an airfoil’s lift-to- general, bats (Table 6.2) operate with lower wing
drag performance is its aspect-ratio (AR). Aspect- loading than similarly sized birds, which increases
ratio is defined most simply by the ratio of tip-to-tip their maneuverability for catching insects or negoti-
length (span, b) of the two airfoils versus their aver- ating dense foliage in search of fruit. In contrast,
age width, or chord (c’, Fig. 6.2b). Because wings the relatively small wings and high wing loading of
taper toward their tips, the mean wing chord is often ducks and geese requires that they fly quickly in
difficult to define. Consequently, AR is often defined order to generate sufficient lift to support their
2
as b / S (the square of span divided by the profile weight. These birds also operate their wings with a
area of the wings). Long, narrow wings have high small angle of attack, which helps to reduce drag at
AR (e.g. albatrosses: 15), whereas short, stubby wings fast flight speeds.
have low ARs (e.g. sparrows: 5.5). Generally, insects Wing loading introduces a basic problem of scaling.
have low aspect-ratio wings compared with birds. The need to produce lift can be expected to vary with
High aspect-ratio wings enhance lift relative to drag an animal’s weight, but the ability to generate lift
and are therefore a common feature of birds that at a particular speed depends on wing area. For
use dynamic soaring, such as albatrosses. The chief ­geometrically similar fliers this suggests wing load-
advantage of a low aspect-ratio wing, on the other ing scales ∝ BM 1/3, indicating that larger fliers have
hand, is improved maneuverability and a reduced greater difficulty generating enough lift to support
risk of damage due to collisions. Because size also their weight, especially at slower flight speeds and
affects maneuverability, small birds and insects with during takeoff. Clearly, a size limit to animal flight,
short stubby wings are far more maneuverable than using skeletal muscle as a motor, must exist. The
 MOVEMENT IN AIR 119

l­ argest living flying animal is a kori bustard, weighing Gossamer Albatross, which crossed the English
in at 13 kg. Although past extinct fliers (including Channel (36 km) in 1979, having been successfully
birds and pterosaurs) may have evolved greater engineered to achieve sufficient aerodynamic lift to
weights and sizes than the kori bustard, it is unlikely support its human pilot/motor (total gross weight:
that a vertebrate capable of powered (as opposed to 100 kg). With a wing area of 45 m2, it had a wing load-
gliding) flight has ever existed that exceeded 25 kg ing of only 22 N m–2, at the low end of the range of
in weight. One exception was the human-powered vertebrate fliers (Table 6.2).
It is also not surprising that larger fliers tend
Table 6.2 The scaling of wing loading and aspect ratio in relation to have relatively larger wings than smaller ones.
to body mass across biological fliers. Consequently, wing loading does not, in fact, scale as
strongly (∝ BW 0.22) as predicted by geometric scaling.
Species Body Mass Wing loading AR
By way of comparison, a 747 jet transport has a wing
(kg) (N m−2)
loading of 6000 N m–2, compared with an Andean
Vertebrates condor of 101 N m–2, a house sparrow of 26 N m–2, a
Wandering albatross 8.7 140 15 bumblebee of 20 N m–2 and a house fly of 5.9 N m–2
(Table 6.2). Nevertheless, the scaling of wing area is
Herring gull 0.54 51 9.5
insufficient to maintain a constant wing loading
Diving petrel 0.14 64 7
across different sized species. Larger fliers compen-
Andean condor 10.0 101 7.5 sate for their lower wing loading by generally flying
Buzzard 1.0 33 5.8 at faster speeds. Because lift varies with the square of
Sparrow hawk 0.2 28 6.5 speed (Eq. 6.2), faster flight can readily make up for
Mute swan 8.0 230 9.2 reduced wing loading. Gliding animals generally have
Canada goose 1.8 155 10.1 lower wing loading than non-gliders.
Mallard duck 1.0 113 9.1
Black grouse 1.0 85 5.9
Magpie 0.22 35 5.7
6.2 Power requirements for steady
Starling 0.075 37 7.2
flight
Budgerigar 0.035 34 7.2 In order to move at a steady forward speed, a
House sparrow 0.028 26 5.5 flying animal must generate sufficient lift to sup-
Swallow 0.024 16 8.0
port its weight and overcome drag (lift × speed =
total power) . The aerodynamic power requirements
Hummingbird 0.005 32 8.1
for flight can be separated into three main compo-
Archeopteryx a
0.27 55 6.3
nents associated with overcoming drag: induced
Pterosaura 15 32 10.5 drag, profile drag and body (parasite) drag. Induced
Rousettus bat 0.14 25 5.9 drag and profile drag operate on the wings, whereas
Fruit bat 0.014 12.3 6.5 body drag represents the parasitic cost incurred by
Greater horseshoe bat 0.023 12.2 6.1 resistance to airflow over the body. Each compo-
Little brown bat 0.007 7.5 6
nent of drag can be calculated in terms of its power
cost as a function of flight speed (Fig. 6.4). The total
Insects
aerodynamic power requirement for steady for-
House fly 0.00001 5.9 12.3
ward flight is, therefore, the sum of these three com-
Bumblebee 0.0002 20.0 10.0 ponents.
Butterfly 0.0003 0.9 2.6
Sphinx moth 0.0005 1.3 6.4
6.2.1 Profile and parasite drag
Dragonfly 0.0003 2.6 5.1
Profile drag results from pressure and skin friction
a
Extinct species. drag operating on the wings. As expected from
120 A N I M A L L O C O M OT I O N

(a)

Total power
(Hovering)

Profile power

Power

Parasite power

Induced power

vP-min vR-max
Speed
(b)

Total power
Power

Aerobic range

Speed Maximum sprint speed

Figure 6.4 The power demands of flight relative to speed can be decomposed into different drag sources and related to the flight capabilities of
the animal. (a) Total aerodynamic power requirements exhibit a “U”-shaped curve as a function of flight speed. Induced power is greatest during
hovering and slow flight, and decreases with increasing flight speed. In contrast, profile and parasite power (due to drag acting on the wings and
body respectively) increase at higher speeds. The combination of these power costs results in a minimum power at an intermediate speed (vP-min).
The tangent drawn from the origin (dashed line) to the total power curve defines the minimum cost of transport speed (or maximum range speed,
vR-max). (b) The aerobic (sustainable) range of flight speeds for most birds is quite restricted (bold black total power curve within the dashed
region), given the increase in power costs at slow and fast flight speeds. The maximum flight performance of most animals also limits their speeds
to either very brief periods of hovering, or short maximum speed sprints (region defined by gray horizontal and vertical lines). Most birds and bats
rarely perform at these performance limits and, as a result, may operate with more limited changes in metabolic and mechanical flight power
requirements than predicted by aerodynamic theory.

Eq. 5.4, profile drag increases with the square of the is greater than parasite power at low speeds, because
wings’ velocity relative to the surrounding air. Profile the wings must move at a much higher velocity than
drag also increases with increased angle of attack. the bird’s forward airspeed. As a result, the increase
Consequently, a reduction in angle of attack can help in profile power is less steep than the increase in para-
to diminish the increase in profile drag (and power) site power, which increases with the cube of the bird’s
at faster flight speeds. Parasite drag of the body forward airspeed. In addition to the wings, some lift
increases in a similar fashion to profile drag with is also likely produced by the animal’s body. Estimates
increasing flight speed. However, because the for body lift range from about five to 20 percent of the
wings have greater surface area than the body (and lift generated by the wings for a range of fliers that
move at a higher velocity), profile power exceeds include bumblebees, locusts and zebra finches.
parasite power. This is especially the case for large Because of this, the width of the body is typically
gliding birds with enhanced wing area. Profile power included in the measurement of wing span.
 MOVEMENT IN AIR 121

6.2.2 Induced drag: the cost of finite wings for forward flight is considered to have a character-
istic U-shape (Fig. 6.4). Total power is high at
The reason that low AR wings achieve lower L/D
hovering and low speeds due to induced power
performance than high AR wings results from the
requirements, but decreases over moderate speeds
fact that the circulation which develops around the
as induced power declines more rapidly than the
wing to produce lift is ultimately dissipated at the
increase in profile and parasite power. As a result,
wing tip as a shed vortex. Longer wings maintain a
total power has a minimum at an intermediate
greater proportion of the circulation bound to the
speed, before increasing at faster flight speeds due
wing compared to the momentum lost via shed vor-
to the rise in profile power and parasite power. The
tices (Fig. 6.3). On balance, a longer wing (if suffi-
U-shaped power curve for flight has two interesting
ciently narrow) produces more lift than the additional
implications. First, it indicates that there is a par-
drag incurred by increased length. In contrast to
ticular speed at which it is cheapest to fly (­minimum
real wings of finite length, infinitely long wings the-
power speed, vP-min). Second, it suggests there is a
oretically lose no energy due to tip vortices; momen-
speed at which the animal should fly to cover the
tum is lost only due to drag resulting from airflow
greatest distance as cheaply as possible (minimum
over the chord-wise section of the wing.
cost of transport, or maximum range speed, vR-max).
The extra drag and energy lost by finite wings at
This speed is defined by the tangent to the curve
their tips is referred to as induced drag. The air shed
drawn through the origin (which gives the ­minimum
from the airfoil is referred to as the “downwash,”
slope of power versus speed) and occurs at a higher
which has a downward component of kinetic energy.
speed than the minimum power speed.
Induced drag, therefore, is also considered to repre-
It is important to note that the U-shaped power
sent the component of drag associated with lift gen-
curve depicted in Figure 6.4 is largely based on
eration that produces this downwash. This means
steady aerodynamic theory for “fixed-wing” air-
that the product of induced drag and free-stream
craft, in which wing shape remains constant and
velocity (the animal’s airspeed) equals the induced
airflow over the wing does not change through
power cost for an animal to stay aloft with a wing of
time. While these assumptions are reasonable for
less than infinite span (or AR). Because a wing con-
gliding and soaring flight, both are unrealistic for
tacts more air per unit time at faster flight speeds, but
flapping flight. Consequently, changes in flight behav-
the lift required to stay aloft remains constant, less
ior and wing shape will modify the U-shaped power
induced power is required at faster speeds (that is, the
curve for flapping flight in different species. We
downwash represents a smaller component of the air-
discuss this in Section 6.5.2.
flow past the airfoil at faster speeds). Consequently,
in contrast to profile and parasite power, induced
6.3 Gliding flight
power is high for hovering and slow-speed flight but
decreases with increasing flight speed (Fig. 6.4). The The simplest form of flight to consider is gliding
higher induced power requirements at slower speeds because steady airflow conditions operate and
explains why hovering is energetically demanding classic aerodynamic theory can be readily applied.
and difficult to sustain. When an animal hovers, all Gliding represents unpowered flight. Although the
of the circulation for lift must be generated by the animal uses metabolic energy to keep its wings (or
flapping motion of the wings themselves. In contrast, other body surfaces) extended, it generates little or
at faster flight speeds the animal’s airspeed contrib- no mechanical power with its muscles. Instead, gliders
utes to circulation, reducing the amount that the convert their potential energy into ­aerodynamic
wings must provide by flapping. Consequently, the work, allowing them to cover a certain horizontal
induced power requirement for generating circulation distance as they descend. During equilibrium glid-
decreases as speed increases. ing, the resultant of lift and drag forces acting on a
Because the decrease in induced power opposes wing exactly balances the weight of the animal, so
the increases in profile and parasite power with that the animal descends along a fixed path at a con-
increasing flight speed, the total power requirement stant speed (Fig. 6.5a). Under these conditions, the
 (a) (b) Airspeed (m/s)
R 0 5 10 15 20 25 30
0
L
θ
0.5 C l /Cd = 40

Sinking speed (m/s)

D Butterfly
Butterfly Sailplane
1.0 Vulture
θ 25
1.5 Falcon
Descent path

2.0
BW

2.5
5 10

(c) 1.25
Slope = max L/D

12°
1.0 9° 15°
18°
6°
Lift coefficient (Cl )

0.75 3°

0° "Stall"
0.5
–3°
0
–6°
–9°
–0.25
0.05 0.10 0.15 0.20
Drag coefficient (Cd)
(d)

–1

–2
Vertical distance (m)

–3

–4

–5 R

–6
L
–7 D
Net
–8

–9 BW

–10
0 2 4 6 8 10 12 14 16 18
Horizontal distance (m)

Figure 6.5 The gliding performance of animals can be expressed in terms of standard force diagrams as well as the relationship between their
kinematics, drag coefficient and angle of attack. (a) The relative magnitude of lift (L) versus drag (D) determines a glider’s equilibrium glide angle
(θ) that balances weight (BW opposed by R) during gliding flight. (b). Glide polars illustrate the relationship between sinking speed and airspeed
and are shown for a butterfly, two bird wings and a sailplane. The tangent to each curve (dashed lines) gives the maximum ratio of lift to drag,
(L/D) indicating the maximum distance that a steady glider will travel from a given height. (c) The coefficient of lift (Cl) plotted versus the
coefficient of drag (Cd) as a function of angle of attack for an airplane wing. A tangent from the origin to the L/D polar gives the maximum ratio of
L/D for the airfoil and the angle of attack at which this is achieved. This angle of attack corresponds to the minimum glide angle shown in (a), but
the two angles are not equivalent. “Stall” occurs when lift drops suddenly relative to drag at high angles of attack. Similar L/D polars have been
observed for stationary bird and insect wings. (d) Gliding squirrels (and snakes) generally operate as non-equilibrium gliders, continuously adjusting
the L/D ratio to change their glide trajectory and velocity. (a) and (b) reproduced from Vogel (1994). Figure 11.4; with permission from Princeton
University Press. (d) from Bahlman et al. (2013); with permission from The Royal Society Publishing.
 MOVEMENT IN AIR 123

ratio of lift to drag (or Cl / Cd ) = cot θ (or = tan −1θ ) , The sinking speed of a glider plotted versus its hori-
where θ is the glide angle. Not surprisingly, birds zontal air speed ( vh = v g cosθ ; Fig. 6.5b) represents
that spend a great deal of their time gliding (see its “glide polar.” The glide polar shows how a glider
“soaring,” Section 6.3.1) typically have high L/D can alter its airspeed versus its sinking speed by
ratios. They achieve high L/D by having high AR changing its angle of attack, wing camber and wing
wings (see Table 6.2), which allow them to glide at span. A tangent drawn from the origin gives vs and vh
small angles. Albatrosses, with AR=15, have a L/D at the minimum glide angle. Changes in wing span,
ratio of 20, allowing them to glide at an angle of 3° which drastically affect wing area and aspect-ratio
or less. Hawks and vultures have L/D ratios that are the most effective mechanisms for changing
range from 10–15 (with a glide angle of 4–6°). By vh and vs. To remain aloft for as long as possible
minimizing its glide angle, an animal maximizes its (­minimize vs) gliders operate at the upper left of their
gliding distance. An albatross gliding from a height glide polar. In contrast, a raptor that wishes to descend
of 1 km above the ocean can travel 20 km in still air as fast as possible to pursue prey, operates at the
before reaching the water surface. Human-engi­ lower-right end of its glide polar. It does this by
neered sailplanes achieve a L/D of 40 (AR=20), retracting its wings back and reducing their span and
which ­enables them to travel a horizontal distance angle of attack, in order to maximize its sinking and
of 40 km for each km of descent. glide speeds (in addition to reducing profile drag).
For arboreal gliders, such as flying squirrels (which Because speed affects lift and drag similarly at
actually glide), gliding snakes or gliding lizards, a moderate to high Reynolds numbers, glide angle is
smaller glide angle means that less vertical eleva- largely independent of speed. Consequently, heavy
tion is lost when gliding between trees. Nevertheless, and light gliders with the same L/D ratio descend
these gliders commonly have lower - /D ratios (2 or along nearly the same path. However, because weight
less) than those of birds and bats. Gliding has is balanced by lift, which varies approximately with
evolved as an effective means of transport in a diverse v2, heavier gliders necessarily travel at faster speeds
array of arboreal animals which includes lemurs, than light ones. Fast glide speeds can be a problem,
opossums, frogs and snakes, in addition to the birds so gliders tend to be lightweight. As a final consid-
mentioned above. When the glide angle exceeds eration, scaling once again enters the picture.
45°, a distinction is commonly made between glid- Smaller gliders have lower L/D ratios because they
ing (L/D > 1) and parachuting (L/D < 1). Animals tend to have proportionately greater profile drag
that parachute typically exhibit less aerodynamic (higher S/BW, or lower wing loading). Consequently,
specialization. small size indicates a steeper glide angle. As a result,
Glide speed (vg) can be calculated by substituting insects having L/D ratios less than two are not gen-
L = mg into Eq. (6.2), such that, erally good gliders.
In contrast to equilibrium gliding, many gliding
vg = (2mg/rSC l ) 1/2 (6.3) animals operate as non-equilibrium gliders while
moving through their arboreal environment—that
which shows that, with a lower wing loading (mg/S) is, they accelerate in vertical and horizontal direc-
or a higher lift coefficient, an animal can glide at a tions, continuously changing their glide angle,
slower speed. An animal cannot glide more slowly rather than reaching an equilibrium balance of lift,
than the speed at which it would stall (maximum drag and body weight forces (Fig. 6.5d). This is the
Cl). The slotted primary wing tip feat­hers of hawks case for gliding squirrels (Bahlman et al., 2013), as
and vultures are believed to enable these birds to well as gliding snakes (Socha, 2002; Socha et al.,
delay stall and glide at slower speeds. In addition to 2010), which accelerate when taking off and then,
horizontal range, glide duration may also be by continuously adjusting their L/D ratio, control
­important to an animal. Glide duration depends on their glide trajectory. Gliding squirrels achieve high
the sinking speed of the glider, which is, L/D ratios, ascending and slowing down when land-
ing from a glide (Fig. 6.5d). Recent work (Socha,
vs = vg sin θ
(6.4) 2011) has highlighted the remarkable ability of
124 A N I M A L L O C O M OT I O N

gliding snakes (genus Chrysopelea) to ­dorsoventrally rising warm air beneath cooler air is unstable. The
flatten their body by splaying their ribs to expand warm air rises as a vortex ring “bubble” detached
their ventral surface after taking off. Gliding snakes from the earth’s surface (Fig. 6.6a; analogous to, but
also pass large amplitude lateral undulations down on a much larger scale than, the vortex ring shed from
their body to stabilize and enhance their glide per- the tip of a fish’s pectoral fin (see, for example,
formance, effectively configuring their body as a Fig. 5.9) or from the wing-tip of a bird). The circula-
“gliding wing.” Interestingly, increased L/D ratios tion of air within the thermal, means that the inner air
of gliders may enhance horizontal distance of the moves upward at a faster rate than the overall sys-
glide, but result in greater non-equilibrium glide tem. By gliding in a circular path aligned with the
performance (Socha et al., 2010) and require o­ ngoing upward current of air in the center of the torus, large
adjustments for gliding stability. With extremely raptors are able to gain altitude with respect to the
low L/D ratios and steep descents, parachuting ants ground while descending with respect to the local air.
(Yanoviak et al., 2005), for example, achieve stable These large birds are quite adept at moving from
equilibirum glides not observed for gliding squir- thermal to thermal as they hunt their prey on the
rels (Bahlman et al., 2013) and snakes (Socha et al., ground. Various arthropods (moths and spiders)
2010). also likely use thermals to balloon themselves via
an extruded length of silk as a dispersal mechanism
(Vogel, 1994).
6.3.1 Soaring
Dynamic soaring involves the use of energy
Soaring is specialized form of gliding flight in which available in the velocity gradient of air due to
a bird takes advantage of energy available in natural wind shear over the earth’s surface. At the surface,
air-movement patterns in order to remain aloft for the velocity is zero (due to the no-slip condition)
considerable periods of time without having to flap but increases parabolically with altitude. Dynamic
its wings regularly. Soaring allows these birds to gain soaring is favored by an open expanse with a steady,
substantial energy savings (estimated to be as high strong wind; conditions commonly found over the
as 67 percent) for travel, surveillance of prey, or ocean. Albatrosses take advantage of this velocity
actual feeding. There are two general forms of soar- gradient to oscillate in a spiral flight path (Fig. 6.6b),
ing: static soaring and dynamic soaring. Static soar- descending downwind (or at some cross-wind angle)
ing involves “slope soaring” and “thermal soaring.” to gain speed (and kinetic energy) before turning,
In the case of slope soaring, a wind moving uphill as they near the ocean’s surface, to fly upwind or
over a slope, as would be the case over the side of a to maneuver for feeding, using the kinetic energy
hill, a cliff face, or even an ocean wave, provides the gained during their descent. The low wind velocity
energy to keep a bird aloft. Glide descent is offset by near the surface allows the bird to reduce its drag as
the upward component of air movement, so that the it maneuvers, or when it begins to fly upwind. As
bird remains at a uniform vertical elevation with the bird flies upwind and begins its ascent, it not
respect to the earth. Slope soaring over a cliff face only exchanges kinetic energy for potential energy,
is a common practice of migrating hawks, swifts but by encountering increasingly faster moving
and swallows, but this involves a more complex air, the albatross gains additional altitude. Once it
air structure, which requires more variable flight regains sufficient altitude, the albatross then turns
behavior than static soaring. Slope soaring is also and begins another downwind descent. Dynamic
employed by human hang-gliders. Finally, petrels soaring allows albatrosses and petrels to travel long
and albatrosses use slope soaring over ocean waves distances and maneuver at much lower flight costs
to prey on fish. than if they relied on p­ owered flapping flight. When
Thermal soaring by vultures, hawks and eagles is foraging for insects, swallows also make use of
a common sight on hot summer days. These birds wind gradients close to the ground to dynamically
­utilize the energy of warm air rising from the earth’s soar, presumably ­reducing their energy cost of for-
surface when the air is fairly still during mid-day. The aging.
 MOVEMENT IN AIR 125

(a)

(b)

Figure 6.6 Birds can extract energy from moving air to soar without flapping by (a) thermal soaring when hot air rises relative to cool air above
and by (b) dynamic soaring using wind-shear gradients over open water (as shown) or air updrafts against cliff faces. (Reproduced from Vogel
(1994), Figs 10.10 and 11.15; with permission from Princeton University Press.)

6.4 Flapping flight wing (in s­ upination) to reverse its orientation, lift
and thrust can also be produced in insects and hum-
6.4.1 Kinematics mingbirds during the upstroke (Fig. 6.7a). This abil-
Insects, birds and bats evolved powered flight by ity allows these animals to hover for long periods.
oscillating their wings relative to their flight path to Unlike hummingbirds, which have evolved unique
produce lift for weight support and thrust (Fig. 6.7). shoulder and wrist articulations (Hedrick et
Hence, whereas the propellers (or jet engines) and al., 2010) that allow them to invert the wing to
fixed wings of aircraft carry out these functions achieve a positive angle of attack during the
­separately, the wings of flying animals accomplish upstroke, the ability to invert the wing during
both. Because of this, the kinematics of wing move- upstroke is more limited in other birds and bats.
ment during flapping flight are fairly complex. Consequently, many birds and bats flex the wing
The wing beat cycle is basically divided into two during the upstroke at slower speeds to reduce
phases: downstroke and upstroke. In vertebrates, drag and avoid “negative lift.” Notably, however,
the downstroke typically produces most of the recent work involving varying experimental
weight ­support and thrust required for flight. approaches shows that pigeons (Ros et al., 2011),
During the downstroke the wing is usually fully Pacific parrotlets (Lentink et al., 2015) and certain
extended to maximize wing area. By rotating the bats (Hedenström and Johansson, 2015) are able to
126 A N I M A L L O C O M OT I O N

(a) Hovering Slow flight Fast flight

Figure-of-eight wing stroke path Figure-of-eight wing stroke path Elliptical wing stroke path
L
L downstroke L upstroke L

(b)
V L L

(c) (d)

Stroke
plane angle Stroke
angle Hovering

Fast forward flight

Figure 6.7 Body angle and wing stroke patterns shift with flight speed. (a) The kinematics of wing motion and angle of attack (silhouettes of a
wing cross-section) vary with flight speed to adjust the magnitude and direction of aerodynamic lift during the downstroke and upstroke. (b) The
global motion of a wing’s path during forward flight is a combination of the bird’s forward velocity and the wing’s motion relative to the bird’s
body. Path asymmetries result from the relative upstroke and downstroke motions during forward flight. The net orientation of incident air flow
relative to the wing during the downstroke ensures that lift (L) generation includes a component of thrust (T) to overcome drag (D) on the bird’s
body and wings. For birds with pointed wings, such as swallows (depicted), upstroke is aerodynamically active, generating lift as well as negative
thrust. (c) Definitions of stroke plane angle (lateral view) and stroke angle (frontal view of animal). (d) Stroke plane angle changes with speed.
When hovering, stroke angle is nearly horizontal (net thrust = 0). Bees, hummingbirds and other forward-flying animals typically reduce body pitch,
increase their stroke plane angle, and adjust the wingtip stroke path to produce thrust as a component of lift.

generate useful upstroke lift by inverting their dis- This is not to be confused with the stroke angle,
tal hand-wing with a rearward “flick” in slow flight. which represents the angle through which the wing
At fast flight speeds, birds with high AR wings are moves during each half cycle (Fig. 6.7d) and deter-
generally able to sustain useful lift throughout the mines the amplitude of the wingbeat. At moderate
upstroke and downstroke by maintaining the circu- to fast flight speeds, wing rotation during upstroke
lation developed about their wings (see Section 6.4.2). is substantially reduced in birds and bats, and the
Associated with airfoil rotation, the wings of figure-of-eight pattern becomes a more elliptical
many insects, hummingbirds and other birds often stroke pattern (Fig. 6.7b). In birds, the wing gener-
make a figure-of-eight pattern relative to the wing’s ally moves downward along a path (relative to the
articulation at the body, oscillating with a stroke body) in front of the wing’s path during the upstroke;
plane that is angled relative to the body (Fig. 6.7b). whereas, in bats the elliptical path of the wing is
 MOVEMENT IN AIR 127

reversed, with the downstroke passing slightly behind during hovering, the wings of bumblebees and
the upstroke path. The fact that the wing stroke hummingbirds oscillate in a nearly horizontal plane
plane is inclined so that the wings are brought for- (Fig. 6.7a). To move forward at faster speeds, the
ward as they are swung down, may seem counter- animals incline their wing stroke angle to produce
productive to generating thrust for forward flight. increased thrust (Fig. 6.7e). Much of the change in
However, when the animal’s forward speed and stroke angle relative to the horizontal is, in fact,
wing rotation are taken into account, the trajectory achieved by changes in body pitch. In general, fly-
of the wing and its angle of attack with respect to ing animals have a high body-pitch angle while
the resultant vector of the oncoming airflow are hovering and flying at slow speeds, and reduce
effectively oriented for generating thrust as a com- their body pitch at faster speeds. This also helps to
ponent of lift during the downstroke (Fig. 6.7b). The reduce parasite drag, by reducing the body’s profile
resulting (global) motion of the wing relative to the area, countering the increase due to speed (Fig. 6.4).
air (its “profile path”) is asymmetrical; its slope dur- Ultimately, the increase in parasite (and profile)
ing the downstroke being much less steep than drag balances the thrust that can be produced by
during the upstroke. This results from the reversed the wings, setting a limit to the fastest speed an ani-
direction of the wing’s movement with respect to mal can fly.
the forward motion of the bird during each phase
of the cycle.
6.4.2 Changes in circulation and wake patterns
In birds and bats, this asymmetry also reflects the
with flight speed
relative timing of upstroke and downstroke, which
occurs with approximately a 1:2 ratio of time for As animals fly faster, the pattern of circulation and
each phase (i.e. the downstroke lasts about 2/3 of resulting aerodynamics of lift generation change.
the total cycle). However, this ratio can vary with Changes in circulation patterns are revealed by the
speed and between species. Cockatiels have close to wakes that flying animals produce. Originally stud-
a 1:2 ratio at slow speeds, but approach a 1:1 ratio as ied using helium bubbles (Spedding, 1987), modern
speed increases (Hedrick et al., 2002). The airspeed studies use fine oil droplets and automated video
of the wing during the downstroke (resultant wing tracking to image patterns of airflow. When hover-
velocity, vr) is high because of the wing’s own velocity ing and at slow flight speeds, circulation developed
(vflap) sums with the animal’s air speed (v). As a about the wings during each half stroke is shed as
result, aerodynamic lift is high and angled forward vortices from the wing tips, forming separate vor-
to provide a component of thrust. During the tex rings (Fig. 6.8a,b). This results from the dissipa-
upstroke, aerodynamic forces are lower because the tion of circulation as the wing slows down and
wing is flexed, reducing wing area, and the relative reverses direction. For many birds and bats, circula-
velocity of airflow over the wing is reduced. In tion is mainly generated during the downstroke at
addition, the feathers of birds may also rotate during slow flight speeds. However, as noted previously,
the upstroke to lower their profile drag. During the insects, hummingbirds and birds with more pointed
downstroke, the feathers re-engage to form an inter- wings (e.g. pigeons, swallows and thrush nightin-
locking array to achieve an effective airfoil shape. gales) also develop circulation (and lift) during the
With contiguous wings, this mechanism of drag upstroke.
reduction is unavailable to bats and insects. At faster flight speeds, circulation about the wings
However, as noted, rotation of their blade-like wings is more continuous and need not be reversed due to
allows many insects to generate useful lift during the influence of the animal’s forward airspeed rela-
the upstroke, as well as the downstroke. tive to the wings’ flapping motion, which reduces
In general, both the wing’s stroke plane and induced power requirements. As a result, vortices
stroke amplitude are adjusted, together with the shed at the wing-tips form a trailing (and undulat-
wing’s angle of attack, over a range of flight speeds ing) vortex “tube” within the animal’s wake at fast
in order to adjust the amount of weight support flight speeds (Fig. 6.8c), similar to those shed by
relative to thrust that is produced. For example, fixed-wing aircraft (Fig. 6.3), reflecting the steadier
128 A N I M A L L O C O M OT I O N

(a)

(b)

(c)

Figure 6.8 Idealized vortex wakes shed from the wings of a thrush nightingale flying (right to left) in a wind tunnel. Idealized wakes are
illustrated from a dorso-lateral view for slow (a) medium (b) and fast (c) flight speeds, measured using digital particle image velocimetry (DPIV).
Both upstroke (light grey) and downstroke (dark grey) phases of the wingbeat cycle generate aerodynamic force at each speed, with “cross-
stream” vortices present at the ends of half-strokes during slower flight (a,b) and throughout the wingbeat cycle during faster flight. Wake patterns
display vortex tubes of equal strength and are illustrated as having similar length but are actually three-fold longer for fast flight than slow flight
(Reproduced from Spedding et al., 2003; with permission The Company of Biologists, Ltd.).

nature of airflow over the wings of flying animals at and during accelerating flight are needed to con-
faster flight speeds. In addition to the shed vortices firm whether this shift in wake pattern occurs. If
behind the bird, “cross-stream” vortices are also this is the case, a bird’s top flight speed may be
ob­served, forming a “ladder-like” wake (Spedding determined by its ability to limit the rapid increase in
et al., 2003). drag, while at the same time maintaining sufficient
With more recent wake analyses of flying animals thrust, given that weight support is not the key
based on flow visualization studies, it has become challenge for flight at high speeds.
clear that distinct aerodynamic gaits do not apply to Differences in wing shape also affect the wake
flying birds and bats (Hedenström et al., 2007; Sped­ patterns and nature of lift generation that different
ding et al., 2003), or insects (Thomas et al., 2004). species use to fly at different speeds (Tobalske, 2007).
Instead, wake patterns and underlying kinematics Birds with short, rounded, low aspect ratio wings,
associated with lift generation change more grad- such as magpies and zebra finches, typically flex
ually as a function of flight speed (Tobalske et al., their wings during upstroke in slow flight and
2007). Interestingly, cockatiels and doves appear to likely have less steady circulation patterns at faster
revert to a less continuous wingtip vortex-shedding flight speeds. In contrast, birds with more pointed
pattern as a means for reducing upstroke drag at wings, such as pigeons and cockatiels, utilize a
their fastest flight speeds (Hedrick et al., 2002), wingtip reversal to generate useful upstroke lift dur-
which is also used when these species accelerate. ing slower flight. As a result, the shed wingtip vor-
Future wake analysis studies at high flight speeds tices in their wakes likely produce more complicated
 MOVEMENT IN AIR 129

wake patterns than the simple discrete vortex rings distinguished as undulatory flight, but both behav-
as depicted in Figure 6.8a & b. Birds with pointed, iors result in upward and downward oscillating
high AR wings also likely achieve more continuous flight paths). Both appear to reflect strategies for
circulation patterns over a broader range of inter- reducing energy expenditure and improving muscle
mediate to fast speeds. The continuity of the vortex ­performance. In flap-bounding, the bounding phase
shed from the wing tip is facilitated by the reduced occurs with the wings drawn in close to the animal’s
amplitude of the wing’s motion, which can occur at body. This eliminates profile and induced drag, so
faster flight speeds because of the decreased induced that the animal’s body flies through the air as a pro-
power requirement (Fig. 6.4). Maintenance of more jectile for brief periods. During the bound phase, the
uniform circulation about the wing throughout the animal loses altitude, which is regained during the
wingbeat cycle is also facilitated by moderate wing flapping phase. The relative time spent bounding
flexion at the wrist during the upstroke, which versus flapping depends on the overall speed of the
reduces drag, orients the shed wing tip vortex more animal, its size and wing geometry. The energy sav-
parallel to the animal’s flight path, and evades the ings by reducing drag during the bounding phase
production of negative thrust. must exceed the potential energy that is lost and
must be regained during the flapping phase for the
bird to achieve a net benefit. Otherwise, steady flap-
6.4.3 Intermittent flight ping flight is favored. This is most likely to be the
In addition to changing circulation many birds case at faster flight speeds, when profile power is
also vary their flight behavior by alternating periods high if the wings are extended. Flap-bounding is
of flapping flight with periods of bounding, or glid- more commonly observed in small birds (sparrows,
ing flight (Rayner, 1985; Tobalske, 1996; Tobalske finches, w­ arblers, etc.), but medium-sized birds (mag-
and Dial, 1994). This results in an undulatory flight pies and woodpeckers) also flap-bound (Tobalske
path for the animal (Fig. 6.9), referred to as flap- and Dial, 1996), with a glide-bound often preceding
bounding or flap-gliding (the latter is sometimes landing to a perch.

(a)

Continuous Flap-bounding Glide-bounding

flapping

Gliding

Continuous
flapping
(b)

Glide-bounding

Figure 6.9 Many smaller to mid-size birds exhibit intermittent flight behaviors, involving flap-bounding, glide-bounding, and gliding that are
frequently used in association with (a) foraging and landing. (b) The intermittent flight behavior of a Lewis’ woodpecker is shown when foraging.
(After Tobalske (1996)).
130 A N I M A L L O C O M OT I O N

Another potential advantage is that flap-bound- determine what selective forces would favor inter-
ing allows the bird to use a constant wing beat fre- mediate stages in the evolution of an incipient wing
quency and wing stroke amplitude, which may and the means by which, in the case of birds, a full-
allow their flight muscles to operate at maximum fledged flight feather may have evolved. The evolu-
efficiency (see Fig. 2.4). This “fixed-gear” hypothesis tion of feathers for insulation, protection and display
(Rayner, 1985) depends on the fiber characteristics represent reasonable hypotheses, but how feathers
of the pectoralis muscle being uniform (see Section and the forelimb wing of birds, bats (and pterosaurs)
6.5.1). According to this hypothesis, the bird varies evolved flight capacity remains a matter of debate.
the period of time that it flaps relative to bounding The problem of intermediate design is common to
flight in order to operate its muscle fibers at a uni- evolutionary biology, and the evolution of wings is a
form contraction rate (e.g. 0.3 × vmax ) that maxi- classic example. Originally, two theories were pro-
mizes their efficiency for converting metabolic posed for the evolution of flight in vertebrates:
energy into mechanical work, despite changes in a “trees-down” gliding theory versus a cursorial
flight speed. Nevertheless, studies of zebra finches “ground-up” theory (see Norberg, 1990 for a
(Tobalske et al., 1999) show that the angular velocity review). More recently, a third theory argues the use
of the wing increases with increasing speed during of a proto-wing to assist a ground bird’s ability to
flap-bounding that is correlated with an increased scale steep slopes may have provided a key select-
contraction speed of the bird’s flight muscles, limit- ive pressure for an avian-theropod ancestor (Dial,
ing their ability to operate as a simple “fixed-gear.” 2003; Heers et al., 2014). When available, modern
Flap-gliding involves intermittent gliding ­periods ground birds prefer elevated locations to reduce
interspersed among flapping periods when the ani- their risk of predation. In support of this scenario,
mal must regain the potential energy lost during the “wing-assisted incline running” (or “WAIR”) observed
glide. Here again, the energy savings during the in chukars and brush fowl during ontogeny involves
glide must offset the energy cost to regain altitude signature features of a lift-generating avian down-
during the flapping phase. In the case of flap-glid- stroke, enabling young galliform birds to scale
ing, this can occur at low to moderate flight speeds steep slopes toward safety before they can fly (Dial
because gliding is effective for generating lift over et al., 2008). Dial and colleagues provide evidence
this speed range and profile power is low. The par- that WAIR assists with foot traction against the
ticular flight path depends on the climb angle, the ground by directing aerodynamic force downward,
subsequent glide angle, and the relative time spent along with a thrust component to assist elevation of
gliding. Although flap-gliding is commonly con- the animal’s body as it climbs a steep slope. Juvenile
sidered to be a characteristic behavior of larger birds with short wings have difficulty climbing
birds and bats that have low wing loading and high steep slopes, but with the development of wings
aspect-ratio wings, which favor gliding performance, and feathers, larger older birds climb better (Dial,
many exceptions exist. For example, crows and jays 2003).
with intermediate wing loading and lower aspect- Ground-up theories have also argued that incipi-
ratio wings, as well as much smaller swallows with ent wings of birds may have been used for prey cap-
high aspect-ratio wings, all regularly flap-glide. ture, or for improved stability when maneuvering
High wing-loaded birds, such as ducks, however or running fast. However, the use of wings by
do not. ground birds to improve running stability and
maneuvering has yet to be demonstrated. Unlike
when running on a level surface, galliforms flap
their wings when ascending an incline. Whether
6.4.4 Origin and evolution of flapping flight
flapping of incipient wings might help a ground
Competing theories have been advanced for the bird or bipedal theropod ancestor to jump over
evolution of flight in animals. The role of a wing as obstacles or better navigate rough terrain when
an airfoil for flight is obvious, but its use for other running remains unknown. Future work that exam-
functions is less clear. Specifically, it is important to ines the use of a developing wing to aid in stability
 MOVEMENT IN AIR 131

when running over level or rough terrain would s­ econd possibility, similar to the ground-up theory
provide support for such a possibility. for birds, is that proto-wings evolved as extensions
There remain cogent arguments for a gliding ori- from the legs or from gill-like appendages in jump-
gin of powered flapping flight in birds and bats. ing insects. Any increase in ­aerial performance dur-
These arguments depend on the ability of proto-­ ing the jump (to escape predation) would presumably
fliers to climb, with the attendant advantages of being have been selectively advantageous. A third theory
­arboreal, and the use of a lift-producing airfoil to (Marden and Kramer, 1994) argues that wings may
navigate an arboreal environment. Early birds pos- have evolved initially as sails, allowing insects (mod-
sessed claws on their hands and feet, which would ern analogs being stoneflies) to sail over the water
favor their climbing ability. The earliest pterosaurs, surface, providing dispersal and foraging benefits.
like bats, were also small and probably used their This parallels the argument made by Hedrick (Hedrick,
forelimb claws to climb. Similar to the benefit for 2011) that asymmetrical flapping of gliding wings
modern ground birds being able to scale steep could enhance stability, favoring the evolution of
slopes, the advantages of being arboreal likely were powered flapping flight.
(and are) safety from predators and the availability All four theories seem plausible. However, cur-
of new foraging sources. Given the ubiquitous rent evidence indicates that insect flight arose once
forms of other gliding and parachuting arboreal in a common ancestral proto-flier (Dudley, 2000)
vertebrates, as well as arboreal ants (Yanoviak et so that only one of these, or some other, scenario
al., 2005), the selective advantage associated with occurred. Heinrich (1993) points out that the advan-
evolving an extended body surface for gliding and tage of lateral lobes (proto-wings) for more rapid
controlled descent seems clear. Gliding takes advan- heating is of little value to an animal as small as an
tage of gravity and provides a clear energetic sav- insect. Without their wings, butterflies still heat up
ings in terms of foraging cost. An incipient gliding at impressive rates (25°C min–1) (Heinrich, 1972).
airfoil leading to the evolution of flapping wings for Heinrich also notes that endothermy and thermo­
powered flight is not difficult to envision. Recent regulation are only associated with insects that fly.
work demonstrating that differential flapping of No known living insect basks or shivers to heat up,
wings contributes to flight stability by generating except just before flight. An attractive aspect of the
counteracting yaw and roll torques about the body sailing hypothesis for the origin of insect flight is
(Hedrick, 2011; Hedrick et al., 2009) suggests a that fossil insects possessed gills or gill covers, cap-
­plausible selection pressure favoring incipient flap- able of being moved for ventilation of the water,
ping of a gliding wing to enhance gliding stability, reminiscent of the reduced wings used for sailing.
leading to a more effective lift-generating wing for As for vertebrates, the evolution of flight in insects
flapping flight. Extant gliding animals, however, requires a plausible hypothesis for selective advan-
have not been observed to use small flapping move- tages associated with incipient airfoils and their ini-
ments for maneuvering or for prolonging glide tial and intermediate function. These requirements
duration, suggesting two distinct adaptive peaks are met by the thermoregulatory, sailing and stable-
selecting for gliding versus powered flapping flight. gliding models of insect flight evolution, in which
The evolution of flight in insects has been argued increased wing area would have improved lift-­
along three main theoretical lines. One theory generating capacity. Subsequent modification of the
(Douglas, 1981; Kingsolver and Koehl, 1994; Wasserthal, wing’s shape as an airfoil and internal modifica-
1975) argues that insect wings originally evolved as tions of the musculature and skeleton for active
thermoregulatory devices that allowed the animal generation of aerodynamic lift would have been
to regulate heat loss and gain (by solar radiation) favored by any initial benefits due to improved
through changes in surface area and wing orienta- gliding performance. That non-specialized append-
tion. Once evolved as thermoregulatory structures, ages enable canopy ants to control and direct their
selective advantages for gliding p ­ erformance and descent when falling from trees (Yanoviak et al.,
ultimately powered flapping flight, similar to those 2005) argues for selection to enhance aerodynamic
for birds and bats, could have been realized. A performance of incipient wing appendages of an
132 A N I M A L L O C O M OT I O N

arboreal ancestor. Finally, it is worth noting that the insect flight muscle antagonists are more similar in
same evolutionary origin for gliding or flapping size, which is associated with their ability to generate
flight need not have been shared by insects and ver- significant lift during the upstroke. Hummingbirds
tebrates. similarly tend to be distinguished by having rela-
tively larger wing elevators than other birds.
Whereas the flight muscles of flying insects oper-
ate at very high frequencies and contract over only
6.5 Flight motors and wing anatomy a small fraction of their length, the flight muscles
Because flapping flight requires considerable power, of larger birds operate at lower frequencies and
the flight muscles of vertebrates and insects achieve contract over much greater length ranges.
some of the highest capacities for sustained mech- In addition to the muscles that power flight,
anical power within the animal kingdom (in the many other muscles control wing orientation, wing
range of 200–400 W/kg muscle). These muscles are shape, and adjust the stroke plane. These muscles,
generally organized as antagonist groups that either referred to as steering muscles in insects, are important
depress or elevate the wing. Because wing depres- to the maneuvering flight of insects, as well as birds
sion generates most of the aerodynamic lift in bird and bats. Less is known about these muscles, which
and bat flight, the wing depressors are considerably are more numerous and smaller in size. Our focus
larger muscles than the wing elevators. In contrast, here will be on the larger flight muscles that are
with aerodynamic lift produced during both the most important to lift generation. In addition to the
upstroke and downstroke of most flying insects, flight musculature, the design of the skeleton is also

Extensor metacarpi
radialis Flexor carpi ulnaris
Biceps
Triceps
Tensor Scapulohumeralis
propatagialis caudalis

Shoulder joint

Pectoralis
(main wing depressor)
Supracoracoideus - deep to pectoralis
(main wing elevator)

Figure 6.10 The pectoralis is the primary downstroke flight muscle of birds, as illustrated here for the pigeon. The supracoracoideus (shaded),
which lies deep to the pectoralis, elevates the wing. These two large muscles span the shoulder joint (denoted by black circle). Smaller intrinsic
wing muscles control wing shape and orientation. (Reproduced from Dial (1992a); with permission Wiley-Liss, Inc.).
 MOVEMENT IN AIR 133

important to how the muscles transmit their force cles, which insert onto the dorsal aspect of the
to the wing. Finally, as we have discussed in some humerus.
detail, the wing’s design itself is critically important The pectoralis and supracoracoideus are pinnate
to its function as an airfoil. muscles in birds, enabling them to generate large
forces for their mass. The pectoralis has much
longer fibers than the supracoracoideus, associated
with its larger moment arm and need to produce a
6.5.1 Vertebrate flight musculature
large ventrally directed torque for generating mech-
In birds and bats, the pectoralis is the primary anical power during the downstroke. The fiber-type
­muscle that depresses the wing in order to produce characteristics of the pectoralis muscles of several
lift. The pectoralis originates from the body via the avian species have been examined (George and
sternum, ribs and clavicles (in birds the clavicles are Berger, 1966; Rosser and George, 1986). In general,
fused to form the furcula, or “wishbone”) and attaches the pectoralis of flying birds consists largely of
to the humerus, the most proximal bone in the wing fast-twitch muscle fibers. The majority (80–90 per-
(Fig. 6.10). In birds, the pectoralis muscles together cent) can be characterized as being fast-oxidative-­
constitute 12–22 percent of the body mass of the glycolytic (FOG, see Chapter 2, Section 2.7), with
animal. In many species, the pectoralis attaches most of the remaining being fast-glycolytic (FG).
locally to a bony process that projects ­anteriorly Hummingbirds and other small birds such as zebra
from the proximal humerus, termed the deltopecto- finches are most extreme having homogeneous pec-
ral crest. Its anterior insertion means that the pecto- toralis muscles with 100 percent FOG fibers (Welch
ralis also tends to rotate the wing in a nose-down and Altshuler, 2009). Because flapping flight gener-
direction (pronation). This is necessary to balance ally requires sustained high frequency contractions,
the opposing moment produced by aerodynamic the slow-oxidative (SO) fibers found in the muscles
force on the wing, which acts distally, but anterior of terrestrial animals and fish are largely absent
to the elbow. As a result, torsional loading of the from the flight muscles of most birds. However, in
humerus is common in the flight of bats (Swartz et soaring birds, such as turkey vultures and frigate
al., 1992) and birds (Biewener and Dial, 1995). In birds, specialized groups of SO twitch and/or slow
birds, the main elevating muscle of the wing, the tonic fibers have been identified. These fibers ­enable
supracoracoideus (homologous to the supraspina- economical and sustained isometric contraction of
tus and infraspinatus of bats and other mammals!), the pectoralis associated with prolonged gliding
has an unusual and intriguing anatomical arrange- flight. The uniformity of fiber-type characteristics
ment. It, too, arises from the keel of the sternum within the flight muscles of avian species is consist-
deep to the pectoralis. Consequently, the supracora- ent with the observation that wingbeat frequency
coideus has the same ventral position as the ­pectoralis and angular velocity change little over a range of
relative to the wing. However, the supracoracoi- flight speed and flight mode (Dial and Biewener,
deus elevates the wing by means of a pulley-like 1993; Tobalske and Dial, 1996; Dial et al., 1997).
arrangement of its long tendon, which passes anter- Hence, having flight muscles that operate at a fairly
ior to and over the shoulder attaching to the dorsal uniform contractile speed appears to be a general
aspect of the humerus. In most birds the supracora- feature of birds and is not necessarily limited to
coideus is about 1/8th the size of the pectoralis; smaller species that use intermittent flight. FOG
however, in hummingbirds it is about 50 percent and FG fibers similarly predominate in the flight
the size. This difference is consistent with the fact muscles of bats; however, greater variation exists
that lift is generated during the upstroke as well as among bats, including more prevalent populations
the downstroke in hummingbirds but is less in most of SO type fibers (see Norberg, 1990, for review). The
other birds. In bats, both the pectoralis major and ­heterogeneity of histochemically defined fiber types
minor act as depressors of the humerus at the across diverse taxa makes their classification and
shoulder; consequently, wing elevation is mainly the inference of their physiological properties prob-
achieved by the deltoid and other shoulder mus- lematic. Consequently, work that correlates muscle
134 A N I M A L L O C O M OT I O N

physiology with fiber-type characteristics is needed lis during flight of certain birds (Dial and Biewener,
for understanding how differences in flight muscle 1993; Biewener et al., 1998a; Jackson et al., 2011).
design are correlated with flight capabilities. These recordings (Fig. 6.11) show that the pectoralis
Other muscles contribute to motions of the wing generates work loops similar to those developed by
in birds, but they are mainly used to control wing fish axial musculature and bumblebee flight mus-
shape and airfoil orientation important to maneu- cles (see Section 6.5.3). In order to perform work,
vering and control of landing (Dial, 1992a & b). This the pectoralis lengthens only slightly, if at all, late
is also the case for bats, in which changes in wing in the upstroke (Fig. 6.11b) (“A”), allowing it to
shape by differential activation of several shoulder develop considerable force (“B”) before it, then,
and forelimb muscles, allow bats to achieve highly shortens during the downstroke to do aerodynamic
maneuverable flight (Altenbach and Hermanson, work (“C”). The muscle then relaxes, allowing it to
1987). Finally, because much of wing elevation may be passively lengthened during the upstroke (“D”).
be passively achieved by aerodynamic lift during The main difference between fish axial muscle
moderate- to fast-speed flight, the pectoralis repre- work loops and those of the pectoralis is that the
sents the primary power-generating muscle in birds avian pectoralis undergoes substantial length
and bats. changes (30–40 percent of resting length), associ-
ated with its need to move the wing through a
large angular excursion.
6.5.2 Avian pectoralis function: implications
Measurements of pectoralis force and kinematic
for power output during flight estimates of muscle length change in black-billed
The unique anatomy of the pectoralis and its inser- magpies while flying in a wind tunnel (Dial et al.,
tion on the humerus allows direct recordings of the 1997) indicate that the power requirements for
forces and length changes produced by the pectora- flight in magpies (Fig. 6.12a) differs substantially

Pigeon pectoralis (slow flight)

B
Downstroke Upstroke
55
55 In vivo work loop
Force (N)

EMG
Muscle force (N)

30
C
30
5

Energy/cycle = 0.75 J
Strain (ΔL/L0)

0.3
0.2 5
D A
0.1
0 –0.1 0 0.1 0.2 0.3
–0.1 Strain (ΔL/L0)
0.02 0.06 0.10
60 70 80 90
Time (s)
(a) (b) Muscle length (mm)

Figure 6.11 In vivo patterns of pectoralis force, activation (EMG) and fascicle strain in a pigeon over a complete wingbeat cycle allow its work
output to be measured during flight. (a) The pectoralis generates force and shortens (muscle strain) during the downstroke after being activated
late in upstroke and into the first half of the downstroke; it then passively lengthens during the upstroke. As a result, the muscle produces (b) a
positive (counterclockwise) “work loop” (force versus length) to power the bird’s flight. The area within the loop represents the net positive work
performed over one contraction cycle. Arrows denote the path of muscle force relative to length change versus time. The light shading denotes the
time during which the muscle is activated based on its EMG.
 MOVEMENT IN AIR 135

(a) Magpie
300 10

Frequency
250
8

Wing beat frequency (Hz)

200
Power (W/kg)
6

150

4
Power
100

2
50

0 0
0 2 4 6 8 10 12 14

(b) Cockatiel
300 10
Frequency
250
8

Wing beat frequency (Hz)

200
Power (W/kg)

150

Power 4
100

2
50

0 0
0 2 4 6 8 10 12 14
Speed (m/s)

Figure 6.12 Flight strategies and power costs at increasing speeds vary across birds. (a) The power costs of flight for magpies decreases and
then remains level with increasing flight speeds, in part because magpies maintain a fairly constant wingbeat frequency (Dial et al., 1997). (b) By
contrast, cockatiels increase their flapping speed at fast flight speeds, which contributes to a steeper increase in muscle power costs at higher
flight speeds compared to magpies (Tobalske et al., 2003).

from the U-shaped curve predicted by classical in power output due to increased profile and para-
­aerodynamic theory in which the wings are assumed site drag is observed at the highest flight speeds.
to be fixed in shape. Whereas the power require- Over the full range of speeds wingbeat frequency
ment is highest during hovering flight, it rapidly changes very little. The ability of magpies to fly
declines twofold to threefold as the bird increases with fairly uniform mechanical power over a range
its forward speed and remains fairly uniform over a of speeds most likely results from changes in flight
range of speeds from 4 to 14 m s–1. A slight increase behavior (relative phase of flap-gliding sequences)
136 A N I M A L L O C O M OT I O N

and wing shape (Tobalske and Dial, 1996). However, 6.5.3 Insect flight muscle mechanics
it also depends on whether magpies should be able
The flight muscles of insects consist of direct mus-
to sustain flight speeds at a power that equals or
cles that attach from the thorax to the wings and
exceeds that required during hovering flight (see
indirect flight muscles that lie within the thorax but
Fig. 6.4). For most birds the power required for
do not attach to the wing. The contractile proper-
­hovering likely requires anaerobic sources of energy
ties of these muscles are distinguished among
supply to the muscles and is, hence, non-sustainable.
flying insects by being either synchronously or
­
Consequently, birds are unlikely to favor fast flight
asynchronously activated. As their name suggests,
speeds that require non-sustainable power in the
synchronous muscles (found in locusts, beetles,
course of routine flight behavior.
moths, dragonflies and other large insects) contract
In contrast to magpies, studies of cockatiels and
in a 1:1 ratio with respect to the firing frequency of
turtle doves flying in a wind tunnel (Tobalske
their motor nerves, limiting their frequency in most
et al., 2003) indicate a clear U-shaped power curve
species to less than 150 Hz. In contrast, asynchronous
(Fig. 6.12b). Recent measurements of metabolic cost
flight muscles (found in bees, wasps and flies) oper-
versus flight speed in parakeets (budgerigars) and
ate at frequencies considerably above 200 Hz,
cockatiels (Bundle et al., 2007; Morris et al., 2010)
­ranging as high as 1000 Hz (the wingbeat frequency
reinforce earlier measurements (Tucker, 1968) that
of mosquitoes is about 500 Hz, which gives them
indicate a U-shaped power curve, matching fairly
their telltale and irritating “hum” as they fly close to
well the muscle-power curve observed for cocka-
one’s ear). Asynchronous muscles are not directly
tiels (Tobalske et al., 2003). Metabolic studies of
activated by their motor nerves. Instead, their high
other species, however, indicate flatter power curves
contractile frequency is achieved by means of being
(Fig. 3.15). Metabolic measurements are typically
stretch-activated by their antagonist in combination
limited to a fairly narrow range of flight speed
with having to contract against the inertial mass of
because they require longer periods of flight in
the wing and thorax. Motor neuron depolarization
order to obtain reliable (steady-state) aerobic meas-
serves to maintain calcium levels in the flight m
­ uscle,
urements. Mechanical measurements of muscle power
allowing the asynchronous muscle to contract mul-
can be made over a fewer number of wingbeats for
tiple times for a given motor neuron impulse.
both aerobic and anaerobic, non-sustainable flight.
Synchronous and asynchronous flight muscles can
Consequently, except for hummingbirds (and insects),
be generally divided into two antagonist groups:
metabolic measurements of flight cost are nearly
wing elevators and wing depressors. This is an
impossible to make during hovering and slow-
oversimplification because certain muscles within
speed flight, and are equally difficult to obtain for very
these groups also rotate the wing as it swings back
fast flight. Studies combining aerodynamics, muscle
and forth, as well as protract and retract the wing
biomechanics, and metabolic power approach­es are
between bouts of flight and rest. The relative size
needed to advance our understanding of how neu-
and organization of the direct and indirect flight
romotor and kinematic adjustments in wing shape
muscles, in part, reflects whether they are synchron-
and movement can alter the relationship of power
ous or asynchronous. The direct flight muscles of
versus flight speed from that predicated by conven-
synchronous insects generally are larger than the
tional aerodynamic theory.
indirect flight muscles. In asynchronous fliers that
The results obtained for muscle power in mag-
are small and must flap their wings at high frequen-
pies, pigeons (Dial and Biewener, 1993), starlings
cies, the indirect flight muscles have evolved to be
(Biewener et al., 1992), and most recently in cocka-
the dominant muscles powering flight. Two sets of
tiels (Bundle et al., 2007; Morris et al., 2010; Tobalske
indirect flight muscles exist: a dorsoventral pair and
et al., 2003), indicate that the pectoralis muscle
a dorsal longitudinal pair (Fig. 6.13). Their alternat-
operates with an efficiency in the range of 10 to 23
ing contractions deform the thorax, causing the
percent, ranging up to the maximum efficiency of
wings to be either elevated or depressed. Changes
vertebrate skeletal muscle (~ 25 percent).
 (a) (b)
Upstroke

(Indirect) Steering
power muscles muscles

Dorsoventral active

Downstroke Wing hinge

Longitudinal active

Longitudinal
Dorsoventral

Figure 6.13 Dorsoventral and longitudinal asynchronous flight muscles operate the insect flight “click mechanism”. (a) The dorsoventral and longitudinal muscles indirectly flap the
wings and smaller steering muscles control wing orientation and rotation. (b) This schematic model depicts a cross-section of an insect that uses a “click mechanism.” The dorsoventral
and longitudinal asynchronous flight muscles indirectly elevate and depress the wings at the wing hinge via deformations of the thorax (bold arrows). (Courtesy of M. Dickinson.)
138 A N I M A L L O C O M OT I O N

in thorax shape produced by alternating contrac- that are approximately half that of asynchronous
tions of these muscles induce wing rotation at the flight muscle, consistent with the view that the evo-
wing hinge by what is known as the “click mechan- lution of asynchronous muscle enabled an increase
ism.” The elasticity of the thorax relative to the in power output and flight performance via high
underlying contractions of the flight muscles is contraction frequencies (Josephson et al., 2000).
important to its operation as a high frequency Roughly 75 percent of flying insects have evolved
­resonant system. Contraction of the dorsoventral asynchronous flight muscles (Dudley, 2000). The
muscles compresses the thorax dorsoventrally and efficiency of invertebrate flight muscle has been
expands it longitudinally and laterally, elevating the determined to be in the range of 9 to 15 percent. As
wings. This also stretches the longitudinal muscles, with vertebrate flight muscles, lower efficiencies
causing them to contract, which compresses the likely reflect limits imposed by the need to operate
thorax longitudinally and expands it dorsoven- at higher contractile frequencies.
trally, producing wing depression. This, in turn,
stretches and activates the dorsoventral muscles,
causing the cycle to be repeated. Recent work on
6.5.4 Thermal issues related to flight
flies (Deora et al., 2015) indicates that in addition to
the wing hinge having a “gearbox” that modulates In order to operate at high frequencies, many flying
wingbeat amplitude, it also has a “clutch” that insects warm themselves before flight. This allows
engages the wing so that it can be driven by the their flight muscles to contract and relax at higher
indirect asynchronous muscles within the thorax. rates than would be possible at lower temperatures.
Activation by the motor nerves is important for Flight warm-up is a characteristic thermoregulatory
the initiation of flight activity and the maintenance behavior of most flying insects, particularly those
of muscle calcium levels to sustain the high-­ that inhabit more temperate climates and those that
frequency stretch-activated sequence of muscle are nocturnal and must fly during cooler night-time
contractions. Once motor neuron impulses cease, temperatures. For the interested reader, Heinrich
intrinsic operation of the asynchronous flight mus- (1993) describes in detail the physiology and related
cles quickly ends. Recent visualization by means of flight ecology of “hot-blooded” flying insects in his
synchrotron radiation imaging (Walker et al., 2014) engaging book. Many moths, butterflies, and dragon­
and by calcium imaging (Lindsay et al., 2017) of the flies either utilize flight muscle shivering thermogen-
indirect asynchronous and direct steering muscles esis or basking and solar heating to warm their thorax
of flies reveals, for the first time, fascinating details to temperatures of 32–40°C prior to flight. The large
of how the steering muscles operate in relation to wings of these species facilitate solar heating.
motions of the wing hinge and deformation of the Body size also affects insect flight performance due
thorax by the asynchronous muscles. to the effect of size on heating and cooling. Although
In contrast to the large strains that the avian pec- larger moths and butterflies require a longer period
toralis undergoes to power the motions of the wing, of time to warm up, once they reach an appropriate
estimates suggest that insect flight muscles operate flight temperature, they can sustain continuous flight
at much lower strains (± 5 percent of resting length). for longer periods than smaller species. Smaller
Blowfly steering muscles also operate over small species tend to cool when they fly due to convective
strain amplitudes < 7 percent (Walker et al., 2014). heat loss, limiting their flight to briefer durations.
The low strains of insect flight muscles are consist- Heinrich (1993) demonstrated that moths thermo­
ent with their highly structured organization (Fig. regulate during continuous flight by pumping
2.1) and their high contractile f­ requency. By operat- warmed blood that passes through their flight mus-
ing at high frequency, asynchronous flight muscles cles to their uninsulated abdomen where excess
achieve a power output in the range of 100–200 W/ heat produced by the flight muscles is lost to the air.
kg muscle, similar to the range for the pectoralis of During pre-flight warm up, blood flow to the abdo-
birds. Synchronous muscles achieve power outputs men is reduced so that heat loss is minimized at a
 MOVEMENT IN AIR 139

time when the moth elevates its t­horacic tempera- 6.6 Flight maneuvering and stability
ture as rapidly and economically as possible.
In contrast to tropical bees, temperate bumble- Not only must flying animals produce sufficient
bees and honeybees also exhibit pre-flight warm up aerodynamic force to support their weight and
to elevate their thoracic temperature. To do this, they overcome drag, they must also maneuver and be
contract their flight muscles ­synchronously via dir- stable in their aerial environment. Maneuverability
ect neurogenic stimulation. Once a sufficient thor- represents the ability of an animal to change its
acic temperature is reached (typically 30°C or more), orientation and/or direction of travel; whereas,
­
the flight muscles begin to contract asynchronously stability represents the ability to maintain a given
to achieve the high wing-beat frequencies neces- flight direction and body orientation. Despite their
sary for flight. Of all the flying insects, bumblebees fundamental importance, mechanisms underlying
exhibit the finest control and greatest capacity for flight maneuvering and stability have been less
thermoregulation during flight, utilizing similar well studied, in large part due to the challenging
mechanisms of heart and abdominal blood shunt- nature of suitable experiments. Encouragingly, with
ing control of heat loss to balance muscle heat pro- the advent of improved methods for a­ nalyzing the
duction, as moths and b ­ utterflies. In general, Heinrich three-dimensional kinematics and ­aerodynamics of
makes the argument that the evolution of thermo- flight, considerable progress has been made over
regulation is likely linked to large body size, at the past 15 years to advance our understanding of
which the danger of overheating (above 45°C) dur- animal maneuvering and flight stability. Indeed, fea-
ing flight due to excessive heat production by the tures of animal flight performance related to maneu­
flight muscles becomes a problem. verability and stability can now inform imp­roved
While many lepidopterans, dragonflies, bees, and designs of unmanned aerial vehicles (UAVs).
flies utilize pre-flight warm-up and thermoregulate
during flight, many smaller flying insects do not, but 6.6.1 Maneuvering flight
are able to fly with thoracic temperatures as low as
0°C. Clearly, the capacity to fly with low muscle tem- Maneuvering is not only important for negotiating
peratures required selection for faster myosin-ATPase obstacles, catching prey and avoiding predators, but
and metabolic enzyme rates, as well as more rapid also for ritualistic display and mating. Certainly,
Ca 2+ release and uptake, and neural properties that tradeoffs exist between wing designs that favor
enable fast contractile rates at low temperatures. Cold- more economical lift generation but which are poor
adapted species also exhibit other adaptations. Winter for maneuvering, such as the high AR wings of an
moths generally have low wing-loading, reducing albatross, versus those that enhance maneuvering
their aerodynamic power costs; and, in some species, ability. In general, smaller and shorter, more rounded
only males fly (females don’t attempt to carry their wings make an animal more maneuverable. Smaller
eggs). The males’ lack of a gut further reduces their flying animals therefore can successfully avoid preda-
transport cost. Finally, less-regular and shorter-dura- tory strikes of larger flying species and can exploit a
tion fliers, such as beetles and grasshoppers, do not broader array of spatial environments. Smaller birds
undergo pre-flight warm up and show little evidence also have greater muscle mass-specific power for flight
of temperature regulation in relation to flight. that increases their “marginal power” for maneu-
In contrast to many insects, birds face the ­opposite vering compared with larger birds (Ellington, 1991).
problem of dissipating heat generated by their flight Maneuverability has been fundamental to the evo-
muscles due to their well-insulated downy coat. lutionary success of flying insects, bats and birds.
Consequently, birds dissipate heat in selected areas Their aerial maneuvers represent some of the most
of their body (eyes, feet and shoulders). Also, the dramatic and spectacular acrobatic feats observed
role of the feet changes with flight speed; the feet in nature.
are dangled at slow speeds but folded out of the air- Maneuvering requires that asymmetrical forces
flow at faster speeds. be produced to generate torques causing rotation of
140 A N I M A L L O C O M OT I O N

(a) (c)
yaw
pitch
roll

2. bank stabilization
resulting flight path
z (left bank)
y
x

Lift
(b)

1. bank initiation

Wing downstroke
velocity
Aerodynamic force

Figure 6.14 Pigeons maneuver and turn during flight by producing aerodynamic torques that cause roll, pitch and yaw motions of their body.
(a) Rotations can occur about the body’s horizontal x-axis (roll), vertical z-axis (yaw) and mediolateral y-axis (pitch). (b) Posterior view showing that
when pigeons make 90° low-speed turns, the direction of aerodynamic force produced during the downstroke and upstroke (not shown) varies by
less than 8° relative to the pigeon’s body (three overlapping aerodynamic lift vector cones of varying shades of gray are shown for the three birds
studied). Pigeons, therefore, maneuver and turn like helicopters. (After Ros et al., (2011).) (c) Pigeons may also maneuver (left turn bank shown
from a posterior-dorsal view) by means of asymmetric wing motions (dashed arrows) leading to asymmetric aerodynamic forces (dark arrows
represent force vectors) by the two wings. In the process of performing a left bank turn, (1) the right wing’s velocity and force is greater, initiating a
leftward bank and associated body roll. This is followed in (2) by a reversed asymmetry of wing motion and force to arrest the bird’s banking
momentum (After Warrick and Dial (1998); with permission Company of Biologists, Ltd.).

the animal’s body about one or more cardinal axes aerodynamic force distribution between opposing
of roll (x-axis), pitch (y-axis) and yaw (z-axis; wings, enabling it to turn, dive, or ascend (Warrick
Fig. 6.14a). Force asymmetries may be produced by and Dial, 1998). Having initiated a turn, a flying ani-
various mechanisms, but most commonly are pro- mal must then produce a countertorque to arrest its
duced by differential aerodynamic forces generated roll, pitch and/or yaw motions, in order to establish
by the wings. Inertial forces can also play a role but a new stable flight trajectory.
are generally less important, as the reciprocating Flying animals most commonly make banked
motions of the wings largely cancel out inertia over turns similar to fixed-wing aircraft, or yaw-based
the course of a complete wingbeat cycle. The tail (if turns when hovering. These turns are accomplished
present) and body also often play a role. Changes by producing greater lift force on the outside wing
in incident air velocity over the wings, the wing’s or by producing greater drag force on the inside
angle of attack, and the wing’s area are three ­variables wing. Banked turns typically involve an initial (head-
important to lift generation which may be modu- up) body pitch and roll to redirect ­aerodynamic
lated by a flying animal to produce an asymmetric force acting on the animal into the turn. The change
 MOVEMENT IN AIR 141

in body pitch compensates for the loss of weight sup- issue for flying animals that can make subtle changes
port as lift is inclined into the turn. Yaw-based turns in wing and tail motion to counter unwanted yaw
are often initiated by hovering animals when for- when making a banked turn.
aging and making evasive maneuvers. The ability to turn with fine-scale adjustments of
In an early study of maneuvering during slow wing kinematics reflects the highly maneuverable
flight, Warrick and Dial (1998) observed that pigeons and small body moments of inertia of flying ani-
appeared to initiate and stabilize banked turns by mals, particularly about their roll axis. Consequently,
means of differential downstroke velocities of the small and subtle changes in aerodynamic force
bird’s wings: the outside wing achieved a larger ­produce sufficient torque to generate rapid body
velocity (greater aerodynamic force) than the inside rotations. Indeed, pigeons maintain the direction of
wing, causing a roll into the turn. In the next wing- net aerodynamic force within 8° of their body axis
stroke, an increased downstroke velocity of the inside through successive wingbeats while executing
wing was observed to counteract and reverse the turns (Ros et al., 2011) (Fig. 6.13b), paralleling the
angular momentum of the bird’s roll, while estab- redirection of aerodynamic force by changing body
lishing a new heading (Fig. 6.14c). More recent orientation, or “force-vectoring,” used by helicop-
experiments (Ros et al., 2015) benefitted by increased ters. Whereas wing movements relative to the body
kinematic resolution with improved video technol- are largely uniform, rotations of the body (mainly in
ogy, however, revealed no significant wing velocity roll and pitch) substantially shift the direction of
asymmetry when pigeons made level 90° low-speed aerodynamic force in the global coordinate system.
turns. Surprisingly, no significant asymmetries in Changes in aerodynamic force direction to acceler-
angle of attack, wing area or wingbeat amplitude ate during take-off and decelerate during landing
were observed that might underlie asymmetric are similarly achieved through changes in body
torque generation. Instead, pigeons subtly altered pitch rather than changes in wingstroke plane
their outside wing trajectory to ­produce pitch and ­relative to the bird’s body (Berg Robertson and
roll torques about their body; the outside wing Biewener, 2010).
was swept more anteriorly in a larger amplitude In addition to the banked turns observed for
path compared to the inside wing. The inside wing rapid evasive maneuvers of flying insects, and for
was also pronated earlier in downstroke compared turns of birds and bats, flying animals also perform
to the outside wing. These kinematic differences slower yaw-based turns, rotating about an axis nor-
were correlated with a redirection of aerodynamic mal to their wingstroke plane. Yaw maneuvers are
force needed to pitch and roll the body, by acting observed by hovering hummingbirds and by many
inward toward the turn and above the bird’s body insects when evading a looming stimulus or when
in the first-half of downstroke. turning away from a nectar source (Fry et al., 2003;
The subtle shifts in wing motion sufficient to Hedrick et al., 2009; Hesselberg and Lehmann, 2007).
redirect aerodynamic force that enable pigeons to Unlike banked turns that require active torque and
make tight bank turns are mirrored by flies making countertorque to roll the body into and out of the
evasive turns in reaction to looming stimuli (Muijres turn to establish a new flight direction, yaw-based
et al., 2014). Flies execute rapid banked turns by turns require active torque to initiate the turn but
means of body roll and pitch through active torque deceleration to arrest the turn can be active or pas-
and countertorque, generating mechanisms that, sive. Yaw rotations of the body induce a velocity
like those of pigeons, are similarly achieved by sub- asymmetry of the wings, even when the wings are
tle, fine-scaled changes of wing motion. Other insects flapped symmetrically (adding to or subtracting
(Dudley, 2000) and slow-turning bats (Iriarte-Diaz from each wing’s angular velocity). This produces a
and Swartz, 2008) also employ banked turns to maneu- force asymmetry, in which the animal’s yaw rota-
ver. Interestingly, for the species studied thus far, tion is damped by the increased force on the outside
adverse yaw (the tendency to yaw away from the wing, which resists the rotation. “Flapping counter-
direction of roll)—a common problem for fixed- torque” (FCT) (Hedrick et al., 2009) represents a
wing aircraft—does not appear to be a substantial passive mechanism by which yaw turns can be
142 A N I M A L L O C O M OT I O N

arrested. FCT may also provide stability about an phase asymmetries in the timing of wing rotation
animal’s roll axis when subjected to a perturbation, relative to wing translation by insects may reflect
such as a wind gust. the fact that airfoil shape is relatively constant com-
The challenge of linking wing and body kinemat- pared with the more variable wing shape that birds
ics to active aerodynamic (and inertial) mechanisms and bats are able to use throughout a wingbeat
of torque that rotate the body during a turn, or dur- cycle. Nevertheless, these kinematic adjustments of
ing a maneuver, reflect the low moment of inertia wing motion that affect lift generation and lead to
(I’) that flying animals have about their roll axis force asymmetries are subtle and challenging to dis-
(Fig. 6.14a). Though larger, moments of inertia for cern (Fry et al., 2003; Muijres et al., 2014).
body pitch and yaw are also low for flying animals, Finally, a recent study of falling and landing bats
especially smaller ones (given I’ ∝ BM 5/3 for isomet- (Bergou et al., 2015) shows that bats can perform
rically-scaled animals). As a result, subtle changes aerial roll and pitch maneuvers by changing wing
in wing (and tail) kinematics are sufficient to gener- inertia (due in part to their relatively heavier wings
ate the necessary torque and countertorque for turns, than other flying animals), rather than by producing
making them difficult to discern. In their study of asymmetric aerodynamic forces. Such inertial man-
evasive turning by flies, Muijres et al. (2014) used a euvers are important for bats that must land “heels-
scaled robot (Fig. 6.15) that allowed the subtle over-head” to roost. But evidence that bats and
changes in wing kinematics to be played into the other flying animals rely on inertial reorientation of
robot to validate the torques that were calculated their body through inertia-dominated asymmetric
from the three-dimensional kinematics of the fly’s wing motion during flight maneuvering remains
evasive flight movements. However, to date, a simi- less clear.
lar robotic approach has not been ­reliably achieved
for birds or bats.
6.6.2 Flight stability and control
That changes in angle of attack and wing area
may not be as important at low flight speeds could Being highly maneuverable conversely makes ­stability
reflect the fact that the wing’s stroke velocity is high a potential challenge for flying animals. Nevertheless,
relative to the animal’s forward flight speed under flying animals are highly maneuverable and yet
these conditions. At faster flight speeds, modula- ­stable, providing inspiration for improving the design
tion of angle of attack, wing shape and wing area to of human-engineered aerial vehicles, particularly at
adjust profile drag and lift may well be used to con- small-size scales. The intrinsic damping provided
trol an animal’s flight trajectory. Although obtain- by flapping countertorque likely plays one import-
ing accurate, detailed kinematics of wing and tail ant stabilizing role (Hedrick et al., 2009). Because
movement at high flight speeds is challenging, such FCT scales with wingbeat frequency, different-sized
mechanisms are likely to underlie the exceptional flying animals experience similar rotational damp-
maneuvering performance of insect foraging birds ing as a function of wingbeat duration. In addition
and bats. to FCT, however, flying animals have multiple sen-
Unsteady lift generating mechanisms (Dickinson sors (eyes, vestibular organs, halteres and anten-
et al., (1999); see Section 6.7) may also enable insects nae) that provide information about changes in
and other flying animals to execute steering maneu- their motion and feedback to control their flight
vers. These mechanisms depend in part on the tim- muscles. As a result, flying animals demonstrate
ing of wing translation relative to wing rotation exquisite sensorimotor control of flight maneuver-
associated with wing stroke reversal, affecting the ing and stability. Several recent neuromechanics
lift that a wing generates. For example, in order to studies have begun to explore how visual cues,
turn to the left a flying insect could phase delay rota- linked to optic flow (the angular motion of objects
tion of its left, (inside) wing and phase advance rota- moving over the visual field), or inertial cues sensed
tion of its right (outside) wing. This would result in by halteres or antennae, provide rapid sensorimotor
decreased lift by its left wing and increased lift by control for stability and maneuvering. Sensorimotor
its right wing, causing it to turn left. The use of control of movement will be discussed at greater
 MOVEMENT IN AIR 143

length in Chapter 8, but a few key points related to important understanding for the design require-
the control of flight are briefly summarized here. ments and performance of swimming and flying
The speed with which flying animals can respond animals, unsteady flow conditions also operate in
to visual stimuli (Muijres et al., 2014) or inertial per- the biological realm due to the fact that propulsion
turbations (Ristroph et al., 2010) and achieve rapid, is nearly always achieved by means of a reciprocat-
stable maneuvers highlights their ability to inte- ing appendage (wing, tail, fin) that must be acceler-
grate sensory information with motor output for ated and decelerated as it reverses its direction during
active flight control. Even so, passive control via each half cycle of movement. Consequently, whereas
wingbeat damping likely complements the active fixed-wing aircraft are well modeled and designed
control of flies, as well as hawkmoths, humming- according to conventional aerodynamics, unsteady
birds and other flying animals (Hedrick et al., 2009), flow conditions are important due to the rotational
because of inherent sensorimotor neural delays. and reversible movements of an oscillating wing or
Passive damping in combination with active torque hydrofoil (Dickinson, 1996). To emphasize this point,
generation (via differential wing forces) enables conventional mechanisms based on quasi-steady
flies to recover from yaw-induced perturbations aerodynamics do not provide sufficient lift for a fly-
within the space of ten wingbeats (~ 45 ms). This ing insect to support its weight in the air, let alone
parallels the intrinsic control resulting from muscle carry additional loads (Ellington, 1984). Hence,
force–length and force–velocity properties discussed unsteady mechanisms must operate to provide the
in Chapter 4 that helps running animals rapidly additional lift needed for weight support and load
­stabilize in response to perturbations (Daley et al., carrying. Because flows under non-steady conditions
2009). However, in the case of flight, it is the com- are necessarily complex, a detailed consideration of
bination of intrinsic damping mechanisms c­ oupled unsteady aerodynamic mechanisms is largely out-
with active asymmetric-aerodynamic force gener- side of the scope of this book. Nevertheless, a brief
ation that facilitates flight stability, while allowing introduction to and discussion of these phenomena
animals to be maneuverable. are warranted, given that much of the exciting and
Although vestibular cues can also play a role in continued recent discovery of novel lift-generating
stabilizing head position in birds and bats, it is clear mechanisms ­important to animal flight and maneu-
that birds rely on visual cues to avoid obstacles when vering at moderate to high Re is based on unsteady
navigating through cluttered environments (Lin et flow.
al., 2014; Ros et al., 2017) and to land (Davies and A major problem limiting the performance of a
Green, 1990; Lee et al., 1993). As for insects (Fry reciprocating airfoil (at slower flight speeds) is that
et al., 2009; Srinivasan et al., 1996), visual cues linked it must shed the vorticity developed during its previ-
to gaze stabilization also help hummingbirds control ous half stroke (e.g. downstroke) and, subsequently,
their flight trajectory (Ros and Biewener, 2016) as re-accelerate the fluid moving over it to develop a
well as their position in response to looming stimuli new (bound) circulation in the opposite direction
during hovering (Goller and Altshuler, 2014) and are during the next half stroke (e.g. upstroke). Once
crucial for aerial pursuit of flying and ground-based developed, the circulation must again be shed as
prey (Kane and Zamani, 2014; Mischiati et al., 2015). the wing reverses direction to begin the following
Similarly, echolocating bats rely on acoustic feedback downstroke. In the case of insects and hovering
to avoid obstacles and target insect prey. hummingbirds, the shedding of bound circulation
and subsequent re-development of circulation occurs
during each half stroke (given that useful lift is pro-
duced during the downstroke and upstroke of these
6.7 Unsteady aerodynamic mechanisms
animals). In the case of most birds, it is less clear if
Much of our discussion in this chapter and the pre- significant upstroke lift is developed during slow
vious chapter on swimming assumes conditions of flight, in which case the upstroke is considered aero-
steady fluid movement over an airfoil (or hydro- dynamically “inactive.” However, recent work pro-
foil). While conventional aerodynamics provides vides evidence that the tip-reversal upstroke of
144 A N I M A L L O C O M OT I O N

pigeons (Ros et al., 2011), and possibly other birds Reynolds number regime appropriate for flies (Re =
that exhibit this upstroke style, does achieve sig- 100–200; Fig. 6.15), Dickinson et al. (1999) found
nificant lift (~ 27 percent compared with down- that insect wings likely employ two additional
stroke) in slow flight. Nevertheless, the extent to unsteady mechanisms: rotational lift and wake
which vorticity is shed and the wing must re- recapture. Rotational lift is achieved by the rapid
develop circulation as it reverses direction (known angular rotation of the wing that occurs during
as the Wagner effect) diminishes the aerodynamic each half stroke at wing reversal. It is similar to but
performance of a reciprocating airfoil. more effective than the enhanced circulation that is
The first unsteady aerodynamic effect to be iden- achieved by a spinning ball as it moves through the
tified and considered important to insect flight was air, known as the Magnus effect. Due to the ball’s
a rotational mechanism called the clap and fling spin, the velocity of air flow is increased on one side
(Weis-Fogh, 1973). This involves rapid apposition of the ball (the side in which the rotational velocity
of the two wings at the end of upstroke (clap), is additive to the ball’s own motion) and reduced
which enhances the re-development of circulation on the opposite side. This creates a pressure differ-
as the air is flung out by the rapid rotation of the ential (lower pressure on the high-velocity side rela-
wings as they peel apart at the start of downstroke. tive to the low-velocity side), which causes the ball
Although important as an unsteady effect for enhan- to curve in the direction of its spin (explaining how
cing lift in small insects, and recently shown to be backspin causes a ball to rise or a baseball to curve
used by birds (Crandell and Tobalske, 2015), the due to the spin imparted by a pitcher as it is released
clap and fling is not used by all insects and so does from the pitcher’s hand). In the case of a fly wing,
not provide a general solution for meeting the force the lift produced by the wing’s rotation is consider-
requirements of slow flight. A second unsteady able, amounting to as much as 35 percent of the
mechanism, first observed using a robotic model of total lift generated. Finally, wake recapture pro-
a hawkmoth wing (Ellington et al., 1996), involves vides additional lift by means of the wing interact-
the spanwise development of a leading edge vortex ing with its own wake as it reverses direction and
(“LEV”) during the wingstroke that delays stall and passes back through the wake produced by its
enhances lift. It does this by enhancing the magni- movement in the previous half stroke. This allows
tude and duration of circulation developed during the wing to hasten the development of circulation
the downstroke and, in some instances, the upstroke. as it is re-accelerated following stroke reversal,
The leading-edge vortex grows in strength from the reducing the Wagner effect. The timing of wing
proximal to distal end of the wing, reflecting the dif- rotation relative to its translation has a significant
ferential velocity of a reciprocating wing. This also effect on the amount of lift generated. Hence,
allows the wing to maintain circulation at a higher ­alterations of the relative phase of wing rotation dur-
angle of attack than would be possible based on ing the stroke cycle provide insects with an effect-
conventional aerodynamic flow. Subsequent to ive means of producing lift asymmetries important
showing the importance of LEVs on a reciprocating to steering maneuvers.
hawkmoth wing model, LEVs have been found to Delayed stall by means of a leading-edge vortex,
enhance lift on real hawkmoth wings (Bomphrey et rotational lift and wake recapture represent three
al., 2005), as well as the flapping wings of flies (Birch distinct, yet interactive mechanisms of unsteady lift
and Dickinson, 2001), hummingbirds (Warrick et al., generation that enable flying animals to achieve the
2005), swifts (Videler et al., 2004), and bats (Muijres flight forces needed to support their weight and
et al., 2008). LEVs also operate to aid in the disper- carry loads. Conventional aerodynamic mechanisms
sal of rotating maple samara and other autorotating are insufficient to achieve this owing to the energy
plant seeds (Lentink et al., 2009); so, they appear to loss that occurs due to vortex shedding and the
be a general feature of lift augmentation of a recip- need to re-develop circulation about a reciprocating
rocating or rotating airfoil. wing that also must function as the animal’s propel-
In experiments using a robotic model fruitfly ler in order to generate aerodynamic thrust. These
wing operating in a vat of mineral oil scaled to the unsteady effects raise the lift coefficient for Drosophila
 MOVEMENT IN AIR 145

(a) Motor
assembly

Coaxial
activeshaft Mineral
oil
Force
sensor

Model
wing

(b)
Force
Force sensor
vector

Wing
Gear box
chord
Model wing

Downstroke

500
mN

Upstroke

Figure 6.15 The use of scaled models reveal new and dynamic explanations for insect flight capabilities. (a) A robotic model of a fly’s wings
driven back and forth in a large vat of mineral oil is used to study unsteady mechanisms of lift generation. The frequency of motion and enlarged
size of the model fly wings were matched to the viscosity and density of the mineral oil to achieve a Re appropriate for the flight of a real fly. (b)
By measuring the wing’s angle of attack and flow around the wing, the researchers calculated the forces (gray arrows) acting on the wings (black
lines). These force vectors were then concatenated to show their time-varying pattern at successive phases of a wing beat cycle. (Reprinted with
permission from Dickinson et al. 1999; Copyright American Association for the Advancement of Science.)

wings more than 2.5-fold compared with that frequencies. Without such physical models, which
achieved during steady-state conditions (Dickinson are amenable to study by virtue of being scaled up
et al., 1999). These studies also point to the import- in size, the ability to measure flight forces and to
ance of being able to model the Re regime appropri- image flow under unsteady conditions is challenging
ate to a small insect wing operating at high and limits the biological cases that can be studied.
146 A N I M A L L O C O M OT I O N

Such approaches continue to reveal exciting new of striated muscle to power flapping flight is impres-
perspectives on the complexity and beauty of fluid sive. This is particularly so, given the remarkable
propulsive mechanisms used by animals. It is par- maneuvering ability of most flying animals. The
ticularly interesting that unsteady mechanisms— diverse designs and contractile performance of
wake recapture and rotational lift—can be used to flight muscles reflect the differing biomechanical
control lift generation by means of the timing of mechanisms that have evolved to actuate flapping
wing rotation relative to wing translation, provid- wings over a broad size scale, and are linked to the
ing a mechanism for steering maneuvers as well as aerodynamic power requirements for flight across
lift augmentation. It was unclear at the time of this varying environmental conditions.
book’s first edition whether larger vertebrate fliers Because flying animals can manipulate the shape
make use of similar unsteady mechanisms to enhance and orientation of their wings (“wing morphing”)
the aerodynamic performance of their wings, but it within and across wingbeat cycles, they are able to
is now clear that such mechanisms as LEVs and employ unsteady aerodynamic mechanisms to gen-
clap and peel may broadly apply to animals that erate lift and maneuver effectively. This provides
flap their wings over a wide size range and Re scale. them with enhanced performance, exceeding that
predicted by conventional aerodynamics applied
to fixed-wing aircraft. However, it also provides
greater challenges for biologists and aerodynami-
6.8 Summary
cists interested in understanding the design, control
Flight has proven an enormously successful mode and performance of flapping airfoils. New experi-
of locomotion, witnessed by the impressive diver- mental techniques and robotics provide complemen-
sity of living insects, birds and bats. Relative to tary approaches to aerodynamic modeling analyses,
engineered aircraft, the flight performance of ani- offering novel insights into mechanisms that under-
mals is impressive. Recent bioengineering efforts lie the spectacular performance of flying animals.
to develop more flexible, maneuverable and stable Studies over the intervening 15 years since the first
unmanned aerial vehicle designs inspired by bio- edition of this book have also begun to reveal sen-
logical flight (Chirarattananon et al., 2017; Di Luca sory and neuromechanical mechanisms by which
et al., 2017; Nakata et al., 2011) represent a rapidly- animals maneuver and control their flight, allowing
growing field benefitted by insights gained from them to perform a captivating array of aerial acro-
studying the flight of animals. In this chapter, we batics.
reviewed fundamental features of animal wings
and body surfaces important to their aerodynamic
properties that allow animals to fly and glide. Similar
Additional reading
fluid mechanical principles underlie swimming and Dudley, R. (2000). The Biomechanics of Insect Flight. Form,
flying. In contrast to swimming, weight support is Function, Evolution. Princeton: Princeton University
key to successful flight performance because of the Press.
much lower density and viscosity of air versus Heinrich, B. (1993). The Hot-blooded Insects: Strategies and
Mechanisms of Thermoregulation. Cambridge: Harvard
water. This not only limits the size range of flying
University Press.
animals compared with swimming animals but also Norberg, U. M. (1990). Vertebrate Flight. In: Zoophysiology,
means that flying animals typically move at much vol. 27. New York: Springer-Verlag.
faster speeds. This also allows flying animals to for- Vogel, S. (1994). Life in Moving Fluids. The Physical Biology of
age and migrate over longer distances. The capacity Flow. Princeton: Princeton University Press.
 C H A PT ER 7

Jumping, Climbing and

Suspensory Locomotion

In contrast to the earlier chapters that addressed landed (one exception being the human triple jump).
locomotion in water, air, or on land, this chapter Some animals, like frogs, jump or hop, depending
focuses on locomotion that involves all three of these on the context. Other animals do not hop, but
media. We begin by examining jumping, which do jump, such as lemurs, cats, spiders and fleas.
includes launching from and landing on many types Jumping is important to animals that must cope
of s­ubstrates. Previous chapters have addressed with o­ bstacles in the environment, pounce to catch
the ­importance of elastic energy storage for a wide their prey, leap to avoid predators, or even (if suffi-
range of locomotor systems; however, it is during ciently small) launch from aquatic surfaces. Arboreal
jumping, especially catapult systems, when elastic animals jump between branch supports for move-
energy storage and release reach the outer extremes ment in complex three-dimensional environments.
known in animal systems. We also explore climbing Jumping also is an important component of take-off
and suspensory locomotion which are fascinating for flying birds and bats. While take-off is key to a
for their diverse mechanisms of attachment that controlled trajectory, landing often involves less
­enable movement up, under and through vertically- finesse. For example, some anurans do not land
structured terrestrial habitats. Jumping, climbing with much grace and balance. This likely reflects
and suspensory movement are central to rapid the fact that certain frogs jump into the safety of a
escape, prey capture and the navigation of complex pond and toads leap into tufts of grass to hide their
and varied habitats. In addition, they represent position and avoid predators. Presumably, in each
some of the remarkable extremes of animal locomotor of these instances, the need for a stable, balanced
capabilities and thus have inspired numerous syn­ landing is of less importance than it would be if
thetic and engineered devices. We conclude the they were hopping.
chapter by examining some examples of engineered Jumping most commonly involves the use of a
jumpers and a range of biologically-inspired robotic pair of rapidly extending limbs. For vertebrate quad-
climbers and synthetic adhesives. rupeds and insects this most often involves the use
of the hind limbs. Running jumps, on the other hand,
usually involve the use of a single limb. Despite their
7.1 Jumping
differences, all jumps commonly reflect two main
Jumping is a locomotor mechanism involving aerial goals: to jump high or to jump far. As we’ll see, sim-
launches from and landings on a variety of sub- ple equations of ballistic motion show that there is a
strates. Although certain types of jumps share simi- tradeoff between jump height and jump horizontal
lar features with hopping, jumping is distinguished distance and suggest that there is a particular take-
from hopping by the fact that it does not require off angle (generally about 45°) with which most jump-
that an animal rebound back into the air after it has ers achieve the greatest distance. Jump horizontal

Animal Locomotion. Second Edition. Andrew A. Biewener & Sheila N. Patek, Oxford University Press (2018).
© Andrew A. Biewener & Sheila N. Patek 2018. DOI: 10.1093/oso/9780198743156.001.0001
148 A N I M A L L O C O M OT I O N

and vertical distances are improved by various mech- shows that if an animal can double the vertical com-
anisms and techniques. These include longer limbs ponent of take-off velocity (vV), it can achieve a four-
with larger muscles than close relatives that do not fold increase in jump height.
jump, catapults that utilize springs and latches to In general, effects of drag and lift in airborne ani-
rapidly release energy, and counter-movement of mals are ignored for animals greater than 10 g (Vogel,
the animal’s center of mass preceding the jump. We 2009). Below this size, air resistance can be a consid-
will review these features after first discussing the erable hindrance. Drag reduces a flea’s jump range
basic physics of jumping. by 80 percent. By comparison, a locust loses only six
percent of its range due to drag (see Chapters 5 and
6). For small vertebrate jumpers, such as the kanga-
7.2 Jump take-offs and trajectories
roo rat, the loss due to drag drops to 1 percent. Lift
Jumping requires that animals generate sufficient is usually not considered important during jump-
kinetic energy (KE) to propel themselves into the ing for most animals, unless they have become spe-
air. This is accomplished during the take-off phase. cialized for gliding (see Chapter 6).
Beginning at rest, a jumping animal achieves its At the end of take-off, the final vertical and hori-
maximum kinetic energy at the end of take-off zontal velocities of a jump can be calculated by resolv-
when it leaves the ground (Fig. 7.1). Consequently, ing the vertical (vV) and horizontal (vh) components
to jump as far or as high as possible, an animal must of take-off velocity and angle (θ) (Fig. 7.1):
maximize its KE (= 1/2 mvt 2 ) via its take-off velocity
vh = vt cosθ (7.3)
(vt). This kinetic energy is converted into potential
energy as the animal travels a given horizontal and vv = vt sin θ (7.4)
vertical distance through the air before landing. For
vertical jumps, the potential energy (PE = mgh) that The horizontal distance (L) that the animal travels
an animal attains at the maximum height (h) of its during a jump is
jump equals the kinetic energy that was achieved at L = vhtair (7.5)
take-off (neglecting drag):
where tair is the time that it spends in the air. Jump
=
mgh 1=
/2 mvV2 E (7.1) height determines the time that the animal spends
such that, in the air, which can be derived as,

=h E=
/ mg and h vV2 / 2 g (7.2) tair = √ ( 2 h / g ) (7.6)

where vV is the animal’s vertical velocity and g is the These equations follow from the simple physics of
acceleration due to gravity, which decelerates the ballistic motion, for which the position (s) of a mov-
animal’s vertical motion after it has ceased acceler- ing object or projectile at any point in time that is
ating during the take-off phase of its jump. Eq. 7.2 subject to a constant acceleration is defined by:

vt
h
CM

LCM Ltot
θ
Lt L LL

Figure 7.1 The ballistic trajectory of jumps is determined by the angle (θ) and velocity (vt) of takeoff. The maximum velocity is dependent on the
distance over which takeoff occurs (Lt). Therefore, jumpers typically have long legs to enhance Lt and thereby increase takeoff velocity. CM, center
of mass; h, height of jump relative to CM; LCM, distance that CM is accelerated during takeoff; Ltot, distance from takeoff to landing; LL, distance
over which landing occurs.
 J U M P I N G, C L I M B I N G A N D S U S P E N S O RY L O C O M OT I O N 149

s = vt + 0.5 at 2 (where v is the initial velocity of the maximum speeds of movement regardless of body
object and a is its acceleration). Given that the ani- size (v = (l/t ) ∝ m0 ) . Similarly, Hill’s simple model
mal’s initial velocity is zero for standing jumps, this requires that all muscles have the same maximum
simplifies to s = 0.5 at 2 , from which Eq. 7.6 is derived speed of shortening (vmax). Any change in a muscle’s
( a = g ) . Using the previous equations, the horizon- intrinsic shortening velocity (v*, measured in
tal distance of a jump (while in the air) can also be lengths/sec ∝ m–1/3) is offset by the length of its
calculated as, ­fibers (lf ∝ m1/3 ) : vmax = v * × lf ∝ m−1/3 m1/3 ∝ m0 .
v 2 sin 2θ Muscle power (P, work/time) depends on the
L= t (7.7)
g product of force and velocity (P = Fv). Given that
muscle force varies with muscle cross-sectional
(recognizing that 2sinθ cosθ = sin 2θ ). This relation-
area (F ∝ A ∝ m2/3) and that the maximum speed of
ship predicts that animals should achieve a max-
muscle shortening is predicted to be constant, this
imum jump distance at a take-off angle of 45°. As
implies,
we shall see in the next section, actual take-off
angles, jump heights, and jump distances are deter- P ∝ m 2/ 3 m 0 ∝ m 2/ 3 (7.8)
mined by a suite of factors that relate to the scaling
Consequently, as we have seen for other forms of
of animals.
locomotion, mass-specific muscle power (P*, W/kg)
is predicted to decrease with increasing size:
7.3 Scaling of jumps P *(P m−1 ) ∝ m−1/3 (7.9)
A thorough understanding of animal jumping extends This decrease in muscle mass-specific power is off-
beyond the equations that govern the motion of ani- set by the greater take-off times tc of larger jumpers
mals solely after they have left the ground. In this (tc ∝ m1/3), so that according to geometric similarity
section, we begin with an examination of classic the total mass-specific work, or energy (E* = P * tc ),
questions about the scaling of jumps in the context derived from the animal’s muscles should be con-
of muscle capabilities, then consider the roles of body stant (E* ∝ m0). From Eq. 7.2, this again predicts that
weight and limb length. maximum jump height should be the same for ani-
mals of different size assuming that they have the
same proportion of muscle mass.
7.3.1 The role of muscle in jump scaling
As it turns out, the argument fails to hold when
The scaling of jumps has long fascinated scientists, smaller animals are incorporated into the calcula-
with analyses as far back as Borelli’s work in the tions. Smaller animals have shorter limbs; therefore,
1600s (Vogel, 2009). Building on the earlier discus- the distance and time available for acceleration dur-
sions, A. V. Hill (1950) proposed that all animals ing take-off is less than in larger animals with longer
should jump to the same height. As we shall see, this limbs. If the animal accelerates uniformly (constant
formulation is actually incorrect—animals do not ground reaction force) from rest to its take-off velocity
all jump to the same height. However, it is worth (vt), over a distance (Lt) that is proportional to their
working through the mathematical argument, because leg length, the time required to take-off (tc) is,
it expresses, in a simple framework, how the funda-
tc = 2Lt /vt (7.10)
mentals of muscle-based jumps can arise from ­muscle
dynamics. As a result, smaller animals must achieve greater
Hill based his argument on several key assump- acceleration (a) and force to jump a given height,
tions, including that all muscles can be expected to according to,
perform the same amount of work per unit mass
=a =
F/m vt 2/2Lt (7.11)
(J/kg). This follows from the proportional scaling of
length with respect to time (l ∝ t). Larger animals Because of their short legs, small jumpers simply
have longer limbs but move them at slower fre- cannot contract their muscles sufficiently quickly to
quencies (f ∝ t–1), resulting in the prediction of similar achieve the accelerations necessary to jump as high
150 A N I M A L L O C O M OT I O N

as larger animals (Alexander and Bennet-Clark, of 30 to 55°, horizontal jump distance is generally
1977). Consequently, Hill’s (1950) simple model for within 90 percent of the maximum possible dis-
jumping (and running) fails to hold when the time tance (Fig. 7.3). Consequently, jump performance is
available to perform the muscle contraction is taken not significantly reduced over a fairly broad range
into account. of take-off angles.
However, instead of an absence of small jumpers, The total work ( KE + PE ) of a jump is nearly con-
the very best jumpers are small (Table 7.1). How is stant over a broad range of take-off angles and
this possible? As we will cover in Section 7.4., the ground reaction force angles. This results from the
failure of this scaling argument to hold points to a offsetting changes in KE and PE required for differ-
jumping strategy that predominates in small ani- ent take-off angles, in which the more vertical the
mals—the evolutionary incorporation of mechanical jump take-off, the greater the PE component and the
power enhancements. lower the KE component of work (Fig. 7.3). However,
because jump distance varies with take-off angle,
the amount of work that a jumping animal’s mus-
7.3.2 Body weight and jump take-off
cles must perform to jump a given distance is
The weight of an animal influences the take-off strongly affected by take-off angle. Again, the opti-
angle that maximizes jump distance. The optimum mum (minimum work/distance) is close to a take-
angle of ground reaction force is always greater off angle of 35–40° (with a ground reaction force
than the angle of take-off, because a significant angle of 45°).
component of force is needed to counteract the ani-
mal’s weight. This is particularly the case for shorter
7.3.3 Limb length and jump scaling
jumps (Fig. 7.2). In general, larger animals can be
expected to use lower take-off angles, because they As demonstrated in the previous mathematical for-
exert relatively lower ground reaction forces for their mulations, limb length is a key part of jump scaling.
body mass (N/kg). For take-off angles in the range For example, the distance an animal travels during

Table 7.1 Jumping performance of various animals.

Animal Jump height Take-off distance Take-off time Mean acceleration Peak power
(m) (m) (msec) (g) (W/kg)

Antelope 2.5 1.5 430 1.6 115

(200 kg)
Human 0.6 0.7 350 1.0 34
(70 kg)
Cat 1.5 0.32 250 3.2 118
(2.5 kg)
Galago 2.25 0.16 100 7.3 410
(0.3 kg)
Cuban tree frog 0.65 0.108 60 6.1 213
(12.9 g)
Locust 0.45 0.04 26 12.0 330
(3 g)
Flea 0.10 0.0005 0.7 208 2750
(0.5 mg)
 J U M P I N G, C L I M B I N G A N D S U S P E N S O RY L O C O M OT I O N 151

80
Ground reaction force angle
60
30-g frog

Angle (°)
40

Take-off angle
20

2 4 6 8 10
Ground reaction force (N)

Figure 7.2 In order to maximize the horizontal distance of a frog’s jump, take-off angle and angle of ground reaction force vary depending on
the magnitude of the ground reaction force. The angles converge to approximately 45° at higher ground reaction forces. These data were collected
with a 30 g frog, but the angles persist regardless of body mass. Adapted from Marsh (1994).

5 10

Work/distance (J kg–1m–1)
Etot
4 8
Energy (J kg–1)

KE
3 6
Work/jump distance
2 4
30-g frog PE
1 2

15 30 45 60 75 90
Take-off angle θ (°)

Figure 7.3 Given a nearly constant total energy (Etot), the relative proportion of potential energy (PE) and kinetic energy (KE) shift as a function
of take-off angle for the jump of a 30 g frog. The minimum excursion of the work/jump distance curve indicates the optimal combination of PE, KE
and take-off angle to yield a maximum jump. Adapted from Marsh (1994).

the take-off (Lt) and landing (Ll) phases of a jump Consequently, given that LCM is proportional to hind
may constitute 20 percent or more of the total hori- limb length, for geometrically similar animals (l ∝
zontal distance (Ltot = L + Lt + Ll ) and height of a m1/3) this predicts Ltot ∝ (m1/3)2/3 ∝ m2/9 or m0.22.
jump (Marsh, 1994). In this case, the proportion of Indeed, within and across species, horizontal jump
these phases relates directly to the travel distance of distance scales with body size (Fig. 7.4). The scaling
different limb lengths (Fig. 7.1). relationships derived from phylogenetically-corrected,
In addition, predictive scaling equations can be cross-species datasets have yet to be s­ tatistically com-
generated based on limb length from the preceding pared to the predicted relationships. A few studies
equations. For example, maximum horizontal jump have incorporated phylogenetic relationships into
distance (Ltot) is predicted to scale according to the the statistical analysis of scaling (Gomes et al.,
product of mass-specific power (P*) and the dis- 2009; Jorgensen and Reilly, 2013) and these await
tance the animal’s center of mass (LCM) is acceler- comparisons to biomechanical scaling predictions.
ated during take-off, but raised to the 2/3 power: These phylogenetic analyses point to ecological
influences on jumping performance, such that the
Ltot ∝ (P *LCM )2/3 (7.12) scaling of leg length and jump performance differs
152 A N I M A L L O C O M OT I O N

Mean jumping distance (mm)

Semi-aquatic
High-canopy
1000 Low-canopy

Non-fossorials
100 Fossorials

–0.15 –0.10 –0.05 0.00 0.05 0.10 0.15

Residual hindlimb length

Figure 7.4 Hind limb length influences jump performance in anurans while both size and habitat type are also strongly associated. Comparative
analyses performed in the context of phylogenetic relationships and habitat types across anurans confirm the strong relationship between leg
length and jumping distance. When the individual species are coded for habitat (different labeled shapes), the key role of habitat on both body size
and jumping performance is illuminated. In this example, fossorial anurans (white triangles) are smaller and do not jump as far as the semi-aquatic
species (gray squares). From Gomes et al. (2009) with copyright permission from John Wiley and Sons.

depending on the environment (Gomes et al., 2009). For example, a 0.3 kg galago that jumps to a
The interface between morphology, jumping per- height of 2.25 m requires a take-off velocity of 6.64
formance, phylogeny, and habitat was extensively m s–1, which represents 6.62 J of energy (Hall-Craggs,
analyzed in another, larger dataset (Moen et al., 1965). Assuming that the galago achieves a constant
2013), which again points to the strong influence of acceleration during a 50 ms take-off, this represents
habitat and phylogeny on the scaling relationships an average power of 133 W. Given that the muscles
among the different muscles, leg lengths and jump contributing to the animal’s jump represent 40 per-
accelerations of jumping animals. cent of the animal’s body mass, this suggests an
average power output of 1108 W kg–1 of muscle.
This value is much greater than the peak power out-
7.4 Power enhancements to jump put measured for even the very fast glycolytic mus-
cles of frogs (270 to 371 W kg–1, Lutz and Rome,
performance
1994; Marsh and John-Alder, 1994). Given that jump-
In addition to increased limb length and enlarged ing animals cannot develop force instantaneously,
muscle mass relative to their non-jumping relatives, the galago’s peak power output during a jump must
jumping animals have evolved other specializa- be even greater than 133 W (peak power can be esti-
tions for enhancing jump performance, especially mated as roughly twice the average power, assum-
in terms of enhanced power output (Alexander, ing a half-sine pattern of force exerted on the ground;
1988). The release of elastic energy is fundamental see Chapter 4). In studies of galago jumping, for
to power enhancements during jumping, yet it is which ground reaction forces were recorded (see
not always obvious where or how this enhance- Section 7.5.), galagos achieved a peak muscle spe-
ment occurs in the animal (Alexander and Bennet- cific power of 1700 to 1820 W kg–1 (again assuming
Clark, 1977; Sutton, 2011). Biologists typically assess the jumping muscles represent 40 percent of the
the presence of power enhancement by calculating animal’s body mass) (Aerts, 1998; Gunther, 1985).
the power output of an animal’s movement based Aerts (1998) estimates a power amplification of
on its muscle capacity and then comparing that to 15-fold in the jump of a galago.
the actual power output of the movement. If the Similarly, in 1.4 m jumps of the Cuban tree frog
observed power output exceeds what is theoretically (Osteopilus septentrionalis), the frogs achieved an
possible by the animal’s muscles, then power ampli- average specific power output of 800 W kg–1 and
fication must be occurring in the system. peak power output of up to 1650 W kg–1, assuming
 J U M P I N G, C L I M B I N G A N D S U S P E N S O RY L O C O M OT I O N 153

that all of the hind limb muscles contributed simi- humans (Chapter 4), and even in the flight muscles
larly to the power of the jump (Peplowski and of birds (Chapter 6). Humans making a counter-
Marsh, 1997). The researchers measured an in vitro movement in squat jumps achieve greater heights
peak power output of 230 W kg–1 by the sartorius than if they jump from a stationary squat position.
muscle, which likely has contractile properties that In addition to increasing the power output of the
are similar to jumping muscles of the hind limb. muscles, the counter-movement also enables more
Even making the conservative assumption that all elastic energy to be stored and recovered during the
of the muscles contracted optimally to contribute jump than in jumps not preceded by a counter-
power for the jump, this is seven-fold less than the movement.
peak power indicated by the ballistics of the ani- Counter-movement jumps from rest use mech­
mal’s actual jump. anisms similar to those involved in running jumps.
The high power outputs that these jumps repre- When an animal jumps following a running start, it
sent are well beyond the capacity of the animal’s can store elastic energy and forcibly stretch its mus-
muscles, even if all of the jumping muscles con- cles when the foot is planted before springing into
tracted optimally to maximize their power output. the air. In addition to muscle stretch and elastic
This result, and many similar results for other jump- energy storage, running jumps also utilize the con-
ing animals, indicate additional enhancements to servation of an animal’s horizontal kinetic energy.
power output. The combination of kinetic energy transfer, muscle
stretch and elastic energy recoil are all important
components for achieving greater power and dis-
7.4.1 Counter-movement jumping
tance in running jumps. Various ­combinations of
Many animals that jump from rest use a counter- these are critical to the success of human long and
movement to stretch their extensor muscles (as well high jumpers. Whereas horizontal kinetic energy is
as elastic structures), which enables the muscles to likely most critical to long jumpers, the ability to
develop force more rapidly and to a greater magni- amplify muscle power through active stretch and
tude, thereby increasing the amount of power that can elastic energy recoil may be most ­important in high
be developed as the muscle shortens (see Chapter 2). jumping.
Although many frogs and toads jump from a station-
ary position, most jumping mammals and birds use
7.4.2 Power amplification via rapid release
a counter-movement during standing jumps to
in­crease their performance. A counter-movement
of stored elastic energy
represents an initial flexion of the limb, which lowers One particularly effective mechanism for enhan-
the body’s center of mass. During the counter-move- cing power amplification is through rapid release of
ment, the force exerted on the ground briefly falls stored elastic energy. As muscles develop force with
below the animal’s body weight (Fig. 7.5a). This is a limb in a fixed position, elastic energy can be
immediately followed by rapid extension of the limb stored in muscle apoeneuroses, tendons, apodemes,
to propel the animal into the air. By performing a ligaments and skeletal elements. These elastic elem-
counter-movement, the jumping muscles are forcibly ents amplify power output by releasing stored elas-
stretched while they are being activated. This allows tic energy over a shorter time period than would
the muscles to develop force more rapidly and to a have been possible with muscle contractions alone.
greater magnitude (see Fig. 2.4a). Because of this, the Frogs are superlative jumpers among the verte-
muscles can produce greater power when they sub- brates and have naturally attracted attention in
sequently shorten to extend the limb. As we have seen, the quest to understand the mechanisms of elastic
this pattern of active muscle stretch prior to shorten- energy storage and power amplification. Given
ing is a common behavior of many muscles involved that the location of elastic energy storage and the
in a wide range of locomotor activities. It occurs in latch that releases it have been exceedingly difficult
the leg muscles of hopping wallabies and kangaroos, to identify in frogs, researchers have instead
the leg muscles of running turkeys, dogs, horses, and ­determined where and how elastic energy enhances
154 A N I M A L L O C O M OT I O N

(a) HE KE AE
50

Force (N)
GV
25

GH
BW

−0.15 −0.10 −0.05 0

(b)
140

Ankle
Joint power (W)

70 Knee

Hip

−0.05 −0.025 0
Time (s)

Figure 7.5 Counter-movements enhance force development during jumping. (a) Ground reaction forces developed over the course of a standing
jump (GV and GH, vertical and horizontal components). The solid line shows a case for a galago in which no counter-movement occurs. The dashed
line shows the pattern of force developed when a counter-movement is made (GV only; GH is similar in both cases). These patterns of force
development relative to body weight (BW) are characteristic for a broad variety of vertebrate jumpers. The characteristic timing of the onset of hip
(HE), knee (KE) and ankle (AE) extension is indicated by arrows. (b) The pattern and timing of hind limb joint power (joint torque times angular
velocity) during the jump of a galago, shows that power is developed in a proximal to distal sequence, with the peaks in knee and then ankle power
matching the timing of peak propulsive ground reaction force. Note that the time scale is expanded in (b) relative to (a). Adapted from Aerts (1998).

power in frog jumps by tracking the timing of motion, then the tendon, rather than the muscle, is
­muscle contraction and joint motion (Astley and likely to be delivering the bulk of the work to the
Roberts, 2012; Astley and Roberts, 2014). If muscle jump. Indeed, this is how frogs power-amplify
contraction precedes and is decoupled from joint their jumps.
 J U M P I N G, C L I M B I N G A N D S U S P E N S O RY L O C O M OT I O N 155

Additional power amplification can be achieved 7.4.3 Extreme power amplification

through mechanisms that mediate the timing of elas- with springs and latches
tic energy release. For example, the shifting position
of the center-of-mass or changing torques and Devices that store elastic energy and then rapidly
mechanical advantage around joints during a jump release it via latches or catches to propel a mass with
can enhance power output of a jump (Astley and extreme power amplification are generally termed
Roberts, 2014). In frogs, gravitational loading of the catapults, click mechanisms, or latch mechanisms
body is insufficient to counteract the action of the (Gronenberg, 1996; Patek et al., 2011). Latches are
jumping muscles. However, the torques and shift- prevalent in the invertebrates, including froghop-
ing mechanical advantage of the proximal joints of pers, locusts, trap-jaw ants, and fleas.
the frog’s leg initially prevent motion during spring Locust jumps use a catapult mechanism that inte-
loading and then release it during the onset of a grates energy storage in apodemes and exoskeletal
jump to effectively amplify power output. These structures with a latch release system (Fig. 7.6).
authors term this type of energy release as a “dynamic Locusts jump by contracting a large extensor muscle
catch mechanism” that is mediated by torques and in the femur segment that operates to extend the tibia
mechanical advantage and, as such, distinguish it but initially do not extend their leg. To store energy
from the discrete catch mechanisms. and generate a power-amplified jump, the extensor

(a) Semilunar
process Muscle insertions
Femoro-tibial Femur
articulation Extensor
apodeme

Flexor
Cover Sclerotized apodeme
plate cuticle

Tibia

(b) Suspensory
Pocket in
ligament Semilunar Extensor
flexor apodeme
Flexible process tibiae
cuticle muscle

Flexible Flexor tibiae

part of muscle
apodeme
Heitler's lump

0 5 mm
Flexible
cuticle

Figure 7.6 Locusts use an elastic mechanism and latch to produce power-amplified jumps. In preparation for a jump, antagonist action of the
extensor and flexor muscles in the femur compress the semilunar process and stretch the extensor apodeme (arthropod tendon), both of which
store elastic energy. When ready to jump, the flexor’s apodeme slides over Heitler’s lump, which serves as a latch, and releases the tibia to initiate
the jump. Reproduced from Bennet-Clark (1975) with permission from the Company of Biologists, Ltd.
156 A N I M A L L O C O M OT I O N

tibia muscle contracts simultaneously with the antag- al., 2008; Burrows and Sutton, 2012a), which upended
onist flexor tibia muscle, thereby preventing any the classic assumption that arthropods use only
movement and allowing elastic energy storage in resilin to store elastic energy, such as in the flea’s
the extensor apodeme and exoskeletal springs located resilin pad. Resilin has superlative resilience, but
at the femur–tibia joint (called semilunar processes). such low stiffness that only minimal elastic energy
The small flexor muscle has a greater moment arm can be stored when solely using resilin. An under-
than the extensor muscle, allowing it to resist the standing of design principles of latches in catapult
large force developed by the extensor tibiae. This systems has remained relatively un-studied, except in
system also has a catch, called Heitler’s lump, over the multiple independent origins of trap-jaw ant
which the flexor muscle apodeme is braced during mechanisms, which some trap-jaw ants use for loco-
spring loading. The jump is initiated when the motor propulsion (Gronenberg et al., 1998; Patek et
flexor muscle quickly relaxes and is released over al., 2006). These remarkable systems leave open
Heitler’s lump. many questions about control prior to movement,
The sudden release of elastic strain energy from given that the release of elastic energy is often too
the compressed semilunar processes and the stretched fast for neural control (Kagaya and Patek, 2016; Sutton
extensor apodeme occurs much faster (25 to 30 ms) and Burrows, 2010), and that arthropods with cata-
than the speed of contraction of the extensor ­muscle pult systems often shift to muscles with long
which takes 350 ms or longer to develop maximum ­sarcomere lengths that contract more slowly, but with
tension. In addition, as the knee extends, the moment greater force, to store maximal elastic energy (Blanco
arm of the extensor muscle increases (Fig. 7.7), and Patek, 2014; Gronenberg and Ehmer, 1996).
which allows it to increase the force exerted on the
ground. A 1.7 g jumping locust (Schistocerca) accel-
erates from the ground within 30 ms, achieving a 7.5 Interactions with the substrate
take-off velocity of 3.2 m s–1 and a kinetic energy of
during jumping
8.7 mJ that is large enough to propel it nearly one
meter (Bennet-Clark, 1975). Half this amount of The pattern of forces against the substrate during
energy is stored in the apodeme and semilunar jumping and landing reveals the challenges of con-
processes of each hind leg. Without the release of trol and power development in these systems. When
stored strain energy from the apodeme and semi- an animal jumps from the ground, it exerts a force
lunar processes, the jump performance of the locust that rapidly exceeds its body weight (Fig. 7.5a).
would be greatly diminished. If the locust had to Initially the rise in force is slow, but progressively
rely solely on the power generated by the rather increases at a faster rate (increased slope). Ground
slow contraction of its extensor muscle, based on Eq. reaction force typically peaks late in the jump just
7.10, a ten-fold longer acceleration time would mean prior to take-off. This pattern of force development
that the locust could only achieve a take-off vel- is exhibited by a broad variety of jumping animals.
ocity 1/10th as high, resulting in a jump only 1/100th Unlike the constant take-off acceleration that simple
the distance (or 1 cm). Therefore, rapid release of ballistics equations assume, these patterns show
elastic strain energy via a catapult m ­ echanism is that the acceleration of the animal’s mass is not
essential to achieve reasonable jump performance. constant, but peaks late in the jump. This is why
Even though most power amplification mech­ the peak power output achieved by many jumpers
ani­sms have been identified only through the is much greater than their average power output,
mathem­atical comparisons of actual power output pointing toward the role of power amplification
versus maximum muscle power output, researchers mechanisms.
are increasingly focusing on the underlying struc- In vertebrate jumpers that do not use catapult
tures that enable enhanced power output. For mechanisms, the pattern of ground reaction force is
example, locust and froghopper springs integrate also reflected in the pattern of joint power devel-
both resilin (high-resilience arthropod rubber-like oped within their hind limbs (Fig. 7.5b). Charac­
protein) and stiff exoskeletal structures (Burrows et teristically, the hind limb joints extend in a proximal
 J U M P I N G, C L I M B I N G A N D S U S P E N S O RY L O C O M OT I O N 157

(a) Extensor apodeme (stretched)

Muscle
force
Moment
arm

Femur
Semilunar process
(compressed)

Tibia

(b) Extensor apodeme (recoiled)

Moment
arm

Semilunar process
(uncompressed)

Figure 7.7 This schematic demonstrates the elastic mechanism of the locust hindlimb which amplifies the power of the rapid leg extension
during a jump. (a) With the contraction of the extensor muscle, the apodeme is stretched and semilunar process is compressed. In this configur-
ation, the moment arm is short. (b) Once the latch is released (see Fig. 7.6), the semilunar process extends and pushes the tibia while the elastic
energy storage in the stretched extensor apodeme simultaneously pulls the tibia. Both actions rapidly rotate the leg through stored elastic energy
while effectively increasing the moment arm. Adapted from Alexander (1988).

to distal sequence: hip extension occurs early in reaction force and its sharp decline as the animal
take-off, followed by knee extension and then ankle leaves the ground. The late peak in knee and ankle
extension near the end of the jump. This pattern joint power indicates that energy stored in the elas-
allows muscle power to be transmitted within the tic elements by the extensor muscles is rapidly
limb to the ground. It also allows the large knee released and thereby enables the animal to achieve
and ankle extensor muscles to develop considerable power outputs that far exceed the capacity of the
force prior to shortening. When the joint extends, muscles alone.
muscle force (or the joint torque) falls rapidly. This This sequence of force and power development
coincides with the timing of maximum ground during jumping signifies that the properties of the
158 A N I M A L L O C O M OT I O N

substrate also affect power output and that animals in width and orientation. Therefore, many animals
may need to counteract or even co-opt the substrate have evolved specializations for moving effectively
behavior to achieve high performance. Jumping over such supports. One advantage of being small
click-beetles experience a 75 percent reduction of is that smaller animals can move more readily along
jump height when jumping from compliant leaves, branches of a certain diameter as if they were flat
which constitute the majority of their habitat (Ribak surfaces. However, in order to move up vertical sur-
et al., 2012). Evidently, click beetles do not change faces, an animal of any size must be capable of gen-
their jumping behavior to accommodate different erating a vertical reaction force between itself and
substrates. Anolis lizards also experience substan- its substrate that is equal to or greater than its
tial costs from the timing of perch compliance weight. Animals typically generate tangential force
relative to their ground reaction forces and actu- to the support surface by either interlocking with
ally prefer perches that are stiffer and enhance the substrate to generate a new non-vertical contact
jump performance (Gilman and Irschick, 2013). surface (Cartmill, 1985), or by developing an adhe-
Cuban tree frogs seem not to adjust their take-offs sive or suction force between the body and the con-
to varying perch compliance; however, they stay tact surface (Federle et al., 2006; Hanna et al., 1991).
on the perch long enough to actually use some of The first mechanism is used by animals that have
the elastic energy from the rebounding perch to evolved claws and the second by animals that have
enhance the jump take-off (Astley et al., 2015b). evolved specialized foot pads for gripping the sur-
The role of substrate compliance in jumping is at face. A friction grip can involve both mechanisms.
its most intriguing for water-jumping arthropods, Balancing above a support requires that an ani-
such as spring-tails and pygmy mole crickets mal maintain its center-of-mass in line with its sup-
(Burrows and Sutton, 2012b; Hu et al., 2007), that port. This is difficult for large climbing animals
must incorporate fluid dynamics (discussed in using small supports, because there is a reasonable
Chapter 5) to achieve sufficient reaction force for potential for developing a toppling moment (or
take-off. torque). The toppling moment equals the animal’s
body weight times the horizontal distance between
center of mass and the vertical axis of the support
7.6 Climbing and attachment
(W dh). To avoid falling when a toppling moment
mechanisms develops, an animal must be able to exert a counter-
The antics of animals climbing smooth walls and acting torque by achieving sufficient grip on the
locomoting upside down on ceilings inevitably support surface. Climbing animals reduce their risk
inspire our curiosity and also serve as a creative of developing large toppling moments by having
inspiration for new engineering capabilities evolved shorter limbs (for a given angle of pitch to
for humans. The diversity of attachment mechan- either side of the support axis, this reduces dh),
isms in animals is almost as rich as the habitats moving with more crouched postures (Schmitt,
that require vertical and upside-down locomotion. 1999) to bring their center of mass closer to the sup-
­Cli­mbing is important to many animals, particu- port axis (also effectively reducing dh), or being
larly those that are arboreal or must move over small. Large animals have difficulty with the ­limited
irregular and steeply sloping surfaces. In addition support provided by slender terminal branches,
to navigating above and below branches, animals where food resources are often found. This can be
use a ­variety of adhesive mechanisms to attach and mitigated to a certain extent by distributing body
detach quickly while locomoting along steep gradi- weight over multiple supports. Nevertheless, the
ents or even upside down on smooth surfaces. largest animals that habitually forage in trees are
orangutans which do not exceed 90 kg in weight.
Other arboreal specialists climb by hanging below
7.6.1 Navigating branches
the branch which ensures that their center of mass
Branches present particular challenges to locomo- is suspended in line with their support. Many climb-
tion, because they are discontinuous and variable ing animals, particularly primates and carnivorans,
 J U M P I N G, C L I M B I N G A N D S U S P E N S O RY L O C O M OT I O N 159

Fnorm=W sin𝛼
𝛼 Ffrict=W cos𝛼 η

Ftan=W sin𝛼
W

Figure 7.8 Frictional force (Ffrict) associated with an animal’s weight (W) on an inclined slope depends on the angle of the slope (α) in relation to
its static coefficient of friction (η). For the animal to stay attached, Ffrict must be greater than the tangential force to the substrate (Ftan).

also have prehensile tails that are capable of grip- leather, an animal could climb up a branch slope of
ping the primary or an adjacent support to better about 20° by friction alone before slipping.
resist toppling moments. Similarly, when grasping a circular support with
the digits of the hand or foot, a clawless animal
exerts an adductor force Fadd that produces tangen-
7.6.2 Static frictional gripping and claws
tial ( Ftan = Fadd sin β ) and normal ( Fnorm = Fadd cos β )
Without an interlocking, adhesive, or suction grip, a components of force, where β = (180° – θ ) / 2 and θ
static frictional grip (Ffrict) must be achieved that is the angle that the two points of grip subtend
supports an animal’s body weight: (Cartmill, 1985) (Fig. 7.9a). When θ = 180° , Fadd is
normal to the support surface; when θ = 0° , Fadd
Ffrict = W cos α η (7.13)
is completely tangential and no frictional grip is
where Ffrict is the frictional force, W is the animal’s ­possible. Similar to establishing a frictional grip on a
weight, α is the inclination angle of the support and sloping surface, when tan β = η the animal’s grip
η represents the coefficient of friction between the will fail. In practice, animals must achieve grip
animal’s foot and the support (Fig. 7.8). This condi- angles θ greater than the theoretical minimum because
tion is met when the tangential force (Ftan) due to some fraction of their weight will also act tangentially
body weight is less than the frictional force: to the support surface, and this too must be effectively
supported. In addition, when one surface is smooth
Ftan = W sinα ; W sinα < W cosαη (7.14)
and the other curved, with surface properties similar
or when tan α < η . For a vertical surface (α = 90°) to skin, the static coefficient of friction decreases with
this is impossible, and the animal must slip. With a increasing normal force (Car­tmill, 1985). Consequently,
coefficient of friction of 0.36, the value of wood on this also requires a greater angle for effective grip.
160 A N I M A L L O C O M OT I O N

(a) (b)

Fadd
𝜃

Ftan 𝛽
Fnorm
𝜃

𝛽 = (180°–𝜃)/2
Ftan = Fadd sin𝛽
Fnorm = Fadd cos𝛽

Figure 7.9 Clawed grips enhance frictional gripping capability. (a) A frictional grip of a circular support depends on the angle subtended by the
two points of grip and the coefficient of friction between the animal’s grip and the substrate. In the extreme case (not shown), when θ = 180° ,
Fadd is normal to the support surface, thereby giving maximal grip. (b) The angle subtended by a frictional grip is increased by using claws to grab a
surface at a greater angle (θ), demonstrating the added benefit of claws for climbing. Reproduced from Cartmill (1985) with copyright permission
from Harvard University Press.

Rather than relying solely on friction, most ­arboreal close range (< 0.5 nm). The close contact of adhesive
specialists have evolved an array of morphological structures has evolved numerous times and with
adaptations that allow them to achieve even greater different morphological mechanisms. Many species
grip forces. The most straightforward of these is to have evolved microscopic hair-like structures or
cling by developing an interlocking grip. Typically, exceedingly smooth pads—both of which can achieve
this involves the use of claws that penetrate into the close contact with the underlying surface. The scal-
surface of the substrate. By doing so, the claws cre- ing, performance and morphological diversity of
ate a new contact surface that is more nearly per- adhesive structures have inspired a vibrant field
pendicular to the gripping adductor force of their examining adhesion from microscopic forces to
digits. This greatly increases the effective gripping organism-environmental interactions.
angle, θ (Fig. 7.9b), which allows them to climb ver- Until recently, wet and dry adhesion were consi­
tically or even on overhanging surfaces. Many de­red fundamentally different mechanisms of adhe-
climbing animals have highly recurved claws with sion. Now, it is understood that, when examined
sharp tips, compared with their ground-locomoting more closely, many “dry” adhesives secrete fluids
relatives which have more blunt, gently curved that enhance adhesion and that “wet” adhesives
claws (Cartmill, 1985). often use mechanisms or morphologies to move
excessive fluid away from the surface to enable
closer contact. Nonetheless, the close contact of
adhesive structures can be enhanced through secre-
7.6.3 Locomoting with adhesion and friction
tion of fluids that can strengthen the surface contact
In addition to interlocking grips using claws, a wide through capillarity and viscous adhesion. Capillary
range of animals use adhesive pads to attach to the adhesion is achieved via the surface tension of the
substrate (Federle, 2006; Labonte et al., 2016). Adh­ fluid and its ability to wet the contact surface, such
esive pads make use of intermolecular forces between as found on the adhesive pads of tree frogs and
two surfaces, called van der Waals forces. These insects (Fig. 7.10) (Hanna et al., 1991). Viscous adhe-
forces arise from electron interactions among adja- sion occurs through fluid resistance to shear and is
cent molecules and therefore operate at extremely used by locomoting snails, ants and flies.
 J U M P I N G, C L I M B I N G A N D S U S P E N S O RY L O C O M OT I O N 161

(a) (b) (c) (d)

100 μm 5 μm 1 μm

Figure 7.10 Tree frogs use adhesion that couples wet surfaces with the adhesive forces of close surface interactions. White’s tree frog (Litoria
caerulea) (a) uses wet adhesive toe pads (b) to attach to the substrate. With a closer view, the toe pad is comprised of hexagonal cells (c) that are
further divided into smaller units (d). These small units allow for extremely close surface interactions and facilitate channeling most of the mucus
away from the adhesive surface. From Federle et al. (2006) by permission of the Royal Society.

In addition to the contribution of fluid forces to (a) (b)

adhesion, friction forces also play a role in adhesive
systems. Just as in the mechanisms described earlier
in this book, friction forces are generated by direct
contact between small or smooth processes in what
is called “boundary friction” (Federle et al., 2006).
Even in systems that secrete fluids, boundary friction
is possible if the fluid boundary forms such a thin
layer that it acts as a solid, and enables intermolecular
Figure 7.11 Geckos use dry adhesion to adhere to a wide diversity
forces. For example, the wet adhesive pads of tree of substrates. Tokay gecko (Gekko gecko) feet (a) are paved with
frogs must squeeze against the substrate to push microscopic setae (b, scale bar = 1 µm). These microscopic hair-like
excess fluid into the small channels that network structures form extremely close contacts with the substrate, such that
through the toe pad surfaces and ­ultimately enable intermolecular forces generate adhesion. Images reprinted with
personal permission from D. Irschick and M. Bartlett.
close contact.
Perhaps the most iconic adhesive organisms are
the geckos—renowned for the facility with which substrate. Adhesive pads can be moved directionally
they run over a diverse range of substrates in virtu- to either establish an effective adhesive bond or to
ally any body orientation. Geckos use adhesive pads release it, allowing the animals to move rapidly up
on their feet that consist of small 0.1 mm projections, smooth vertical surfaces. In geckos, as the foot is
or setae (Fig. 7.11) (Autumn, 2006). Individual setae placed on the substrate, the adhesive toe pad is
have hundreds of finer hair-like projections that ter- unfurled along its length to contact the surface. As the
minate on 0.2–0.5 μm spatula-like structures. A Tokay gecko moves over its foot support, the adhesive toe
gecko’s foot has about 5000 setae/mm2. pad then peels up and off the substrate surface,
For any adhesive organism, like rapidly running ­enabling the gecko to break its adhesive bond. The
geckos, it is essential to be able to attach and detach peeling action of the toe changes the o
­ rientation of the
quickly to enable rapid locomotion. Similarly, organ- setae, which presumably disrupts the van der Waals
isms must be able to keep the adhesive surfaces forces established between the spatula tips and the
clean as they traverse the naturally debris-filled bio- substrate surface. Even though they locomote
logical world. In geckos and other adhesive organ- through dirty and damp environments, somehow the
isms, adhesion actually increases as the surfaces slide setae remain clean and adhesive—achieving remark-
across each other, enabling distinct modes of attach- able performance using still-unresolved mechanisms.
ment and detachment, which are essential for rapid With this diversity in adhesive pad morphology and
locomotion as the animals walk and run across this scaling, coupled with a dynamic suite of mechanisms
162 A N I M A L L O C O M OT I O N

for enhancing or reducing adhesion and friction, it is 14 mammal lineages (Fujiwara et al., 2011). Vertical
perhaps unsurprising that animals have evolved a suspensory locomotion is exemplified by many pri-
range of capabilities even within a single foot or mates which swing between branches using their
across the various feet of a single individual. Insects forelimbs with their body in a vertical position, and
and spiders have distinct regions on their feet that is distinct from quadrupedal suspensory locomo-
perform different roles in adhesion. For example, the tion, such as used by sloths, in which all four legs
pads at the tip of the feet are used for adhesion, such are used to locomote while hanging below branches.
that they adhere when pulled p ­ roximally. In contrast, Brachiation is a specialized form of vertical suspen-
the pads at the “heels” of the feet (proximal tarsi), are sory locomotion and involves aerial flight phases
not particularly adhesive but instead utilize frictional interspersed between successive suspensory support
forces that are activated when pressed against the phases. Brachiation is used by gibbons, siamangs
ground. This means that an insect climbing up a ver- and spider monkeys.
tical surface will use the adhesive pads at the tips of The switch of the center-of-mass from above to
the front feet and the frictional pads on the rear feet below the points of attachment offers interesting
and then reverse the pattern when going back down potential for evolutionary analysis of origins of sus-
the surface. Likewise, jumping insects often use fric- pensory locomotion and the accompanying changes
tional pads to grip to the surface when jumping. in scaling, mechanics and efficiency. In terms of
Some of these distinct actions of the feet are actively scaling, smaller animals may not experience signifi-
controlled by the animal and in other cases they are cant mechanical changes in their limb forces to
passive consequences of joint dynamics or centralized accommodate this shift in the position of the center-
locomotor behavior. of-mass (other than for switching from gravitational
In the earlier sections of this book, the scaling compressive to tensile support of weight). However,
of forces and locomotor capabilities could be in larger animals, the forces on the limbs may change
explained through fundamental principles, equa- in the fore–aft direction with this shift in position.
tions and ­materials tests. The scaling of adhesive Some lemurs locomote quadrupedally below or
systems in biology is still not fully understood, in above branches; when they switch to below-branch
spite of intensive research on the comparative biol- locomotion, in addition to providing suspensory
ogy of adhesive structures and the scaling of adhe- support of weight, the forelimbs primarily provide
sive forces that should accompany increasing body propulsion and the hindlimbs serve as brakes,
mass. Some researchers have suggested that scalable whereas in the above-branch configuration the roles
adhesion requires two components—adhesive sur- and forces are the opposite (Granatosky et al., 2016).
face area and stiffness of the whole system (Bartlett Animals that switch over daily or evolutionary time-
et al., 2012). As we will discuss in Section 7.8, the scales to below-branch locomotion, also shift from
interdisciplinary nature of locomotor mechanics extensor to flexor muscle support in the forelimbs.
and engineering design reach an apex in the quest Indeed, the elbow flexor muscles are relatively larger
to learn from biological adhesion and build analo- than extensor muscles compared to non-suspensory
gous scalable, re-usable engineered devices that relatives, and the elbow joint angles maximize muscle
animals have been using effectively for millions of moment arms to oppose gravitational loading in the
years. suspended position (Fujiwara et al., 2011).
Slow, swinging suspensory locomotion in pri-
mates has been modeled as simple pendular loco-
7.7 Suspensory locomotion
motion (Preuschoft and Demes, 1984), but this model
The broadest characterization of suspensory loco- does not work in faster suspensory locomotion and
motion is the movement of animals while their brachiating gaits. Akin to the inverted pendular
center-of-mass is below the object supporting them, model of terrestrial walking gaits (Chapter 4), pen-
such as while suspended below a branch. Suspensory dular motion results from the out-of-phase exchange
locomotion includes the upside-down locomotion of potential and kinetic energy of the animal’s body
that is used by lizards, countless insects and at least as it swings from one overhead contact to another.
 J U M P I N G, C L I M B I N G A N D S U S P E N S O RY L O C O M OT I O N 163

However, the pendulum model only works during mechanisms and apply them to more futuristic
single-contact, slow swinging—alternative models designs, such as elastic bouncing balls.
must be used to address the aerial phase and colli- Climbing robots have explored frictional grip-
sion dynamics of brachiation (Betram and Chang, ping and dry adhesives, focusing especially on the
2001). Experiments based on measurements of the materials of the “feet” of the climbing robots (https://
reaction forces that gibbons exert on overhead sup- www.youtube.com/watch?v=XEMlkonimvQ).
ports (Chang et al., 1997) show that gibbons do not Synthetic dry fibrillar adhesives have been success-
simply rely on potential and kinetic energy exchange fully implemented on both climbing robots and
during pendular support, but they can also throw climbing people (https://www.youtube.com/wat
themselves into the air to achieve greater velocities ch?v=Mw-tol5ur84). Biologically-inspired scalable,
and stride lengths. In the absence of extensive elas- dry and smooth adhesives (not fibrillar) have also
tic energy storage in the system, researchers describe been applied to more general engineering challenges
brachiation as analogous to a stone skipping across of adhesives that can stick repeatedly to a range of
water, such that the collisional interactions between surfaces (e.g. GeckskinTM) (Bartlett and Crosby, 2014).
the grip and the substrate determine the dynamics This is a rich translational arena for integrating
of energy flow during brachiation (Usherwood and ­scaling, materials and locomotor environments in
Bertram, 2003). A similar collisional perspective has both biological and synthetic systems.
been applied to help explain the biomechanics of
legged locomotion over ground (see Section 4.11).
7.9 Summary
Another interesting difference between brachiation
and terrestrial locomotion is the relative timing of The diverse use and convergent evolution of jump-
horizontal deceleration and acceleration of the ani- ing in both large and small animals attests to its
mal’s body. Whereas terrestrial animals decelerate selective value for avoiding predation, catching prey
through the first half of limb support and re-accelerate and moving over obstacles in the natural landscape.
during the second half (Chapter 4), brachiating ani- Simple ballistic equations of motion provide a basic
mals accelerate during the first half and decelerate predictive framework for the jumping mechanics of
during the second half of the swing. This is consistent animals, yet neglect important aspects of hind limb
with the underlying difference in the pendular mech- extension during take-off and landing. Key mor-
anics of their motion (suspended versus “inverted”). phological adaptations are easily observed that can
Continuous pendular contact and richochetal support be linked to selection favoring increased jump per-
gaits can provide comparable and high mechanical formance. Most notably this includes long hind
efficiencies (Bertram et al., 1999). However, oxygen limbs with enlarged muscles. At small sizes, jump
consumption data indicate that the cost of locomotion performance becomes l­imited by the time required
is greater in spider monkeys when they brachiate ver- to take-off. Furthermore, because the muscles of small
sus when they walk quadrupedally (Parsons and animals cannot contract quickly enough, numerous
Taylor, 1977). species have evolved power-amplifying catapult
mechanisms. This allows their extensor muscles to
contract more slowly and to store elastic energy in
7.8 Inspiration for synthetic systems
spring e­ lements of their limbs. The use of elastic
Jumping and climbing are both locomotor mech­a­ strain energy greatly amplifies the power and per-
nisms that animals perform more effectively than formance of the jump. Although differently sized
current engineering robotics and materials. For jumpers cannot achieve similar jump ­performance
jumping, engineers have focused on scaling, effi- as simple isometric models of muscle contraction
ciency and the ability to navigate obstacle-laden suggest, small jumping insects can indeed achieve
environments (Armour et al., 2007). A range of elas- very impressive jumps when normalized to their
tic systems have been explored—from robots that body length.
actually look like jumping crickets and frogs to Climbing and suspensory locomotion represent
robots that take the principles from biological elastic two other specialized modes of locomotion that are
164 A N I M A L L O C O M OT I O N

well-suited to an arboreal environment. A number body as it swings by the arm appears pendular-
of morphological specializations, including coarse like, in fact the motion is not well-modeled by
pads, claws and adhesive pads enhance the fric- a simple pendulum. Instead these animals can
tional or adhesive contact that a climbing animal impart energy into the motion of their body during
can achieve with the surface of its substrate. suspensory support to adjust their speed and
Perhaps most impressive are the setae of gecko toe ­spacing of overhead supports, while minimizing
adhesive pads, which interact with the substrate collisional energy losses.
surface by means of van der Waals forces, allowing
geckos to scale vertical walls and run upside down
Additional reading
on ceilings with great ease. Larger climbing ani-
mals, such as primates, have the dual problem Alexander, R. M. (1988). Elastic Mechanisms in Animal
of limited branch strength for support and the Movement. Cambridge: Cambridge University Press.
increased risk of toppling moments. More crouched Alexander, R. M. and Bennet-Clark, H. C. (1977). Storage
of elastic strain energy in muscle and other tissues.
postures, grasping hands and feet and prehensile
Nature 265, 114–17.
tails all are adaptations that improve balance
Lutz, G. and Rome, L. 1994. Built for jumping: the design
and enable these animals to counteract toppling of the frog muscular system. Science 263(5145), 370–2.
moments. Suspensory locomotion at larger size is Roberts, T. J. and Azizi, E. 2011. Flexible mechanisms: the
observed in the richochetal brachiation of gibbons diverse roles of biological springs in vertebrate move-
and spider monkeys. Although movement of the ment. J. Exp. Biol. 214(3), 353–61.
 C H A PT ER 8

Neuromuscular Control
of Movement

The control of movement is essential for animals and perturbations encountered, thereby simplify-
traversing complex environments and operating ing the neural control task for maintaining balance
across a range of speeds and gaits. Previously, we and stability.
examined the organization and properties of mus-
culoskeletal systems in the context of the generation
8.1 Sensory elements
and support of locomotor forces. In this chapter, we
consider how animals process sensory information Local control of muscle function and movement is
and initiate motor responses, in what is termed mediated by various sensory elements across both
“sensorimotor integration.” This chapter primarily invertebrates and vertebrates. Three principal sensory
focuses on fairly simple motor responses that involve receptors local to the limbs (or wings) exist within
local reflex pathways of feedback and control, rather vertebrates and two main sensory receptors exist
than the more complex, longer-term responses that within insects. Due to limitations of space and because
require the broader integration of higher centers insects represent the best studied invertebrate group,
within the nervous system. We explore how local as well as representing species that exploit terres-
circuits facilitate decentralized coordination of trial, aerial and aquatic locomotive modes, our
locomotor rhythm and movement and examine the discussion here will focus largely on insects for
fundamentals of sensory receptors located in the comparison with vertebrates in order to highlight
muscles, tendons, joints and at the animal’s body common principles of sensorimotor integration and
surface. These sensors monitor the animal’s phys- function relevant to the control of locomotion.
ical environment and the action of its muscles. The
sensory information is then carried back to the ani-
8.1.1 Vertebrate sensory organs
mal’s nervous system by afferent n ­ eurons, provid-
ing feedback that is integrated at the level of the In vertebrates, two of the three main classes of
spinal cord of vertebrates and sensory-motor gan- sensory elements are located within the muscle
glia of invertebrates. This results in an appropriate itself, providing feedback on muscle-length change
efferent output via motorneurons that activate the (or muscle stretch), as well as velocity and muscle
muscles to control their action. An understanding force. Muscle stretch is monitored by muscle spindles
of reflexes and motor function at local levels pro- located in the belly (the center) of the muscle. Muscle
vides considerable insight into the fundamental force is monitored by golgi tendon organs, which
requirements for coordinated and ­stable movement. comprise free sensory nerve endings that terminate
In addition to local neuronal reflexes, ­mechanical at the muscle–tendon junction. Considered together,
properties intrinsic to the animal’s muscu­loskeletal muscle spindles and golgi tendon organs provide the
system enable rapid responses to changing demands means for controlling motor output (force, length

Animal Locomotion. Second Edition. Andrew A. Biewener & Sheila N. Patek, Oxford University Press (2018).
© Andrew A. Biewener & Sheila N. Patek 2018. DOI: 10.1093/oso/9780198743156.001.0001
166 A N I M A L L O C O M OT I O N

and velocity) in relation to movement and external Muscle spindles

forces imposed on the body. The third sensory Muscle spindles (Fig. 8.1) comprise a set of sensory
modality involves a general class of proprioceptive afferent neurons (“Ia”) and the special sets of modi-
feedback to the muscle, yielding tactile information fied intrafusal muscle fibers that they innervate. These
via pressure and pain receptors located in the skin, intrafusal fibers are found in various locations within
as well as mechanoreceptors located in the joints. the belly of the muscle. They do not contribute to the
These proprioceptive sensory elements will be dis- force produced by a muscle and, thus, are distinct from
cussed later in the context of the basic pathways of the force-producing extrafusal fibers that comprise the
local neural circuits.

Efferent
α motorneuron

Ia afferent
neuron

Spindle
Ia
capsule

Muscle spindle organ Intrafusal

muscle fiber

Ib afferent
neuron
Extrafusal
muscle fiber
Golgi tendon
organ

Figure 8.1 Two classes of sensory receptors operate in vertebrate muscle-tendon units: muscle spindles and Golgi tendon organs. Muscle
spindles (commonly termed “stretch receptors”) transduce muscle length changes and are found in multiple locations throughout the muscle.
Golgi tendon organs (GTO) transduce the force transmitted by the muscle‘s tendon and are found at the junction of the muscle’s fibers with its
tendon or aponeurosis. Muscle spindles are comprised of specialized non-force generating “intrafusal” fibers that relay changes of muscle length
via Ia afferent neurons back to the spinal cord. GTOs relay force information to the spinal cord via Ib afferent neurons. Of these two sensory
receptors, the muscle spindles represent the most important means by which muscle force is regulated (via α motorneuron activation) in relation
to muscle length.
 NEUROMUSCULAR CONTROL OF MOVEMENT 167

bulk of a muscle. The Ia neuron endings wrap in a result, the firing rates of the motorneurons that
helical fashion around the intrafusal fibers (two types innervate the muscle (and possibly its agonist
of intrafusal fibers exist—nuclear bag and nuclear ­muscles) is increased. Therefore, additional recruit-
chain—but differences in their response properties are ment of other motor units in the muscle increases
not critical to our discussion here. For more details, the force that the muscle generates to resist the
readers may consult a standard physiology textbook). stretch imposed by the applied load. By lightly strik-
The Ia afferents possess stretch receptors located ing a person’s patellar tendon (in front of the knee),
within the membranes of their dendrites. Thus, strain a routine medical examination often tests the integ-
of the muscle spindle’s intrafusal fibers stimulates the rity of this stretch response. The tendon tap stretches
membrane stretch receptors of the Ia afferents, causing and activates the spindles located in the knee exten-
their activation. (In addition to the main Ia affer- sor muscles (the quadriceps), normally resulting in
ents, secondary type II afferent neurons exist that knee extension and a forward kick of the leg.
also respond to stretch of the intrafusal ­ fibers. Muscle spindles, therefore, provide an ongoing
However, we again concentrate on the larger, more feedback of a muscle’s length in relation to its activa-
numerous and important Ia afferents.) Although tion as it resists external forces or torques. If a muscle
the intrafusal fibers do not contribute to force remains isometric or shortens as it contracts, the fir-
­generation by the muscle, they retain the capacity to ing rate of its spindle Ia afferents will remain low or
shorten, which is important to their ability to re-set be proportionately reduced, leading to weaker feed-
their response to different ranges of length change. back on motor recruitment (Fig. 8.2a). Modulation of
The intrafusal fibers are innervated by special gamma spindle Ia’s afferent response to length change over
(γ, or “fusimotor”) motorneurons that are distinct from the course of a contraction cycle can be achieved by
alpha (α) motorneurons. Recall that α motorneurons simultaneous activation of the gamma (γ) motorneu-
are organized as motor units in relation to the pools of rons, together with the recruited α motorneurons.
extrafusal fibers that they innervate. Many (10 to ~100) This is often referred to as “alpha-gamma motor co-
spindles are found distributed throughout a muscle, activation” and is frequently observed for both vol-
allowing changes in muscle length to be monitored untary and involuntary motor responses. This will
when different regions of a muscle are activated. cause the intrafusal fibers to shorten along with the
As we have discussed previously, when a muscle shortening of the whole muscle (Fig. 8.2b). Shortening
is activated and develops force, its extrafusal fibers of the intrafusal fibers means that spindle Ia afferents
may remain isometric, shorten to produce a pre- will shift their firing rate response to operate at
scribed movement at a joint, or be lengthened when shorter muscle lengths. By relaxing the intrafusal
resisting a joint torque. If the torque or force resist- ­fibers through inhibition of the γ-motorneurons, the
ing the muscle’s action is of sufficient strength that it spindle response to length change will shift in an
causes the muscle to be lengthened, the resulting opposite fashion, allowing more effective sensory
stretch of the muscle will also stretch the intrafusal feedback of the spindle Ia afferents when a muscle
fibers in the muscle spindles. The Ia sensory neuron operates at longer lengths.
that innervates the intrafusal fibers responds to this The ability to modulate spindle Ia afferent
stretch by increasing its firing rate (Fig. 8.2). The response is important for enabling muscles to con-
spindle organ also consists of intrafusal fibers that trol movements over differing ranges of length
are sensitive to the rate of stretch (i.e. velocity). change, depending on the motor tasks involved.
Consequently, muscle spindles provide feedback for Given that muscles may undergo time-varying pat-
both the magnitude and the rate of muscle stretch. terns of stretch, force development and shortening
The Ia afferent provides direct monosynaptic feed- over the course of a single contraction cycle (see
back to the motorneurons that innervate the muscle, Figures 2.5 and 4.12), the role of spindles for provid-
as well as synaptic input, via interneurons, to other ing length feedback is key to a vertebrate muscle’s
muscle agonists and antagonists. This synaptic relay ability to control length and position, as well as the
of the muscle’s stretch due to an externally applied manner in which it develops force and does mech-
force occurs within the spinal cord (Fig. 8.4). As a anical work. Further, because spindle Ia feedback
168 A N I M A L L O C O M OT I O N

(a) Ia
Ia

γ
γ

L + dL L − dL L
(b)

With γ co-activation

Ia firing
rate

No γ co-activation

Length

Figure 8.2 The firing rate of Ia spindle afferents increases in response to stretch (+dL) of the intrafusal fibers relative to the initial resting length
of the muscle (L) Other additional receptors within the spindle (not pictured here) also respond to changes in stretch velocity. The response of the
muscle spindle to changes in length can be adjusted by γ “fusimotor” activation of the intrafusal fibers, causing them to shorten (-dL). This allows
the spindle to respond to stretch when the muscle operates at shorter lengths. Without γ adjustment, stretch of the muscle from a shorter length
would result in a weaker (slower firing rate) Ia response to stretch. Two periods of stretch denoted by gray boxes are shown: From L to L + dL and
from L − dL to L at right.

involves a monosynaptic pathway, the time delay s­ keleton. Golgi tendon organs monitor muscle force
between sensing stretch within the muscle and recruit- by sensing the strain developed in the muscle’s
ing increased force is minimized. This reduction in ­tendon or aponeurosis in response to the force the
time delay is likely important for the control of bal- ­muscle develops. Relatively few, if any, GTOs are
ance during a limb’s support phase. In general, mus- found in parallel-fibered muscles which have min-
cles that control precise movements, such as finger imal ­tendinous and aponeurotic insertions on the
muscles, have a higher density of spindles than those skeleton. Consequently, their role in monitoring force
that control gross movements of the body. in parallel-fibered muscles appears less important.
Similar to the spindle Ia afferents, the Golgi Ib affer-
Golgi tendon organs ents sense force by means of membrane stretch
Golgi tendon organs (GTOs) consist of Ib sensory receptors located within their dendritric field. Strain
afferents that have free nerve endings that innervate within the muscle–tendon junction stimulates the
the collagenous connective tissue of the muscle membrane stretch receptors which leads to depolar-
aponeurosis and tendon (Fig. 8.1). Compared with ization and activation of the Ib sensory neuron in
muscle spindles, Golgi tendon organs are much sim- response to increasing force. The firing rate of the
pler in their organization and in how they function. Golgi Ib afferents increases proportionally to the
GTOs are most common and have been studied in force that a muscle develops. Although Golgi tendon
pinnate muscles that attach via tendons to the organs may exert an inhibitory feedback to a muscle
 NEUROMUSCULAR CONTROL OF MOVEMENT 169

and its synergists, ­limiting the force that the muscle thus sensed by the strains imposed on the campani-
develops to avoid damage, there is evidence that form sensillum’s sensory nerve endings.
GTOs provide excitatory, or positive, force-feed- In the insect leg, these strains result from the forces
back during locomotion (Pearson, 1995; Prochazka transmitted by the underlying muscles and apodemes
et al., 1997). Thus, motor drive to a vertebrate muscle, that stabilize and move the exoskeleton. In the wings
in principle, involves dual control: excitatory feed- of flying insects, the campaniform sensilla represent a
back via the spindles and excitatory or inhibitory network of pressure receptors that provide sen-
feedback, depending on context, via the Golgi ten- sory feedback of wing deformation in response to
don organs. Available evidence indicates that spin- ­aerodynamic loads. Similarly, sensilla also provide
dles exert the main control of a muscle’s motor drive sensory feedback to pressures developed in response
for most behaviors. to joint movement. Unlike vertebrates, there are few
known examples of insect muscles, or other inverte-
brate muscles, that possess a length-sensing element
comparable to the spindle organs of vertebrate mus-
8.1.2 Insect sensory organs
cles (one exception is the abdominal musculature of
Insects possess two classes of sensory receptors, crustaceans, such as lobster and crayfish, which has
commonly referred to as “exteroreceptors” and stretch receptors that are important to control of the
“proprioreceptors.” Exteroreceptors reside on the alternating dorsoventral beating movements of the
surface of the cuticle as hair-like projections of dif- tail, associated with the animal’s escape response;
ferent types that occur in varying densities and Hoyle, 1983). Hence, whereas vertebrate muscles
­distributions on the animal’s body. Like the proprio- operate more under length control via muscle spin-
ceptive skin receptors of vertebrates, the majority dles, insect muscles are largely controlled by force
of insect exteroreceptors sense tactile information feedback from a variety of mechanoreceptors.
that provides a mechanism for detecting when a
limb has contacted the ground or when it has con- 8.2 Sensorimotor integration via local
tacted an object during movement (others sense
reflex pathways
chemical stimuli or air movements). These recep-
tors can also often provide directional sensitivity in Control of muscle function by proprioceptive
response to displacements of the hair in differing (­tactile), force, and length reflex pathways provides
directions (Burrows, 1996). local feedback to the motorneurons that are activated
Proprioreceptive elements of insects generally act and responsible for a particular motor action. Local
as strain gauges (i.e. mechanoreceptors) that respond reflex control facilitates rapid motor responses to
to the forces and pressures exerted by muscles sensory stimuli and does not require higher-level
­internal to the insect’s exoskeleton and those result- signal processing by the central nervous system
ing from movement at the joints. Proprioceptive (CNS). Though critical for responding to more com-
elements located within the cuticle are generally
­ plex stimuli and for organizing and initiating more
referred to as “campaniform sensilla” (sensillum, sin- involved and prolonged motor behavior, CNS pro-
gular), due to their bell-like appearance (Fig 8.3). cessing takes longer to accomplish and requires
Proprioreceptors located within joints are represented greater attention to the motor task. This would not
by chordotonal organs and other types of joint recep- be an effective means for dealing with the rapid
tors. Proprioreceptors are less numerous than the and momentary disturbances that an animal often
exteroreceptors and are more densely distributed in encounters when moving through its environment.
areas near the joints where the muscles and apodemes Such disturbances are better dealt with at a “less con-
insert onto the cuticle. The campaniform sensilla are scious” and more local level of control. Thus, local
characterized by canals that extend through the cuticle, reflex pathways are an important component of the
through which dendrites of sensory neurons pass to distributed nature of neuromuscular control, which
attach to a thin membrane at the surface of the recep- is a general feature of most motor systems. We will
tor (Fig. 8.3). Localized deformations of the cuticle are begin by discussing vertebrate reflex pathways, as
170 A N I M A L L O C O M OT I O N

Hair receptors Campaniform sensilla

(dome-shaped)
Dendrite

Supporting
nerve cells

Sensory
nerve cell

Figure 8.3 Insect sensory elements are comprised of two kinds of extroreceptor elements (in addition to proprioreceptors) distributed over the
surface of their cuticle and concentrated near limb joints: hair receptors and campaniform sensilla. Whereas hair receptors respond to tactile stimuli
and air currents, campaniform sensilla act as mechanoreceptors. Each campaniform sensillum is comprised of a dome-shaped element that
responds to pressure or cuticular strain which activates the dendrite of the sensory neuron underlying the central region of the element.

these are the best studied and highlight principles of ing (contralateral) limb are operating. In this way,
neuromotor organization and control that are likely sensory information from one limb or side of the
common to a diversity of motor systems. body influences, and can be coordinated with, the
motor activity of the opposing limb or side of the
body. In vertebrates, the motorneurons are concen-
8.2.1 Vertebrate reflex pathways
trated within “motor pools,” or regions, located
Sensory information from proprioceptive elements, within the ventral region of the spinal cord. These
muscle spindles and Golgi tendon organs all passes motor pools are segmentally arranged along the
through the paired segmental dorsal root ganglia spinal cord in association with where the limb
that lie on either side of the vertebrate spinal cord extends from the body axis and where the muscles
(where the cell bodies of the sensory receptor of the limb are arranged (e.g. muscles that protract
­neurons reside). The sensory information then enters the limb are associated with more cranial vertebral
the spinal cord to synapse onto interneurons or, in segments of motor innervation, whereas muscles
the unique case of the spindle Ia afferents, directly that retract the limb are associated with more cau-
onto motorneurons innervating the same muscle dal segmental regions).
(Fig. 8.4). Most sensory feedback is transmitted via With foot contact on the ground, pressure recep-
one or more interneurons before being sent to tors within the base of the foot provide propriocep-
motorneurons innervating the muscles within the tive feedback via the dorsal root ganglia. This feedback,
limb. Interneurons also provide sensory feedback to together with increased stretch activation of the spin-
motorneurons that innervate muscles of the oppos- dle organs of certain limb extensor muscles, may
 NEUROMUSCULAR CONTROL OF MOVEMENT 171

Segmental spinal cord

Dorsal root Interneurons

ganglion Excitatory
Inhibitory
Ventral
motor pool

Extensor
α motorneuron
Afferent Ia Ventral root
neuron nerve trunk Contralateral flexors and extensors
Flexor
α motorneuron

Extensor
(stretch)

Flexor

Joint
flexion

Figure 8.4 Vertebrate motor reflex pathways are organized segmentally with respect to the limb and spinal cord. Afferent nerve fibers carrying
sensory information from muscle spindles (afferent Ia neuron shown, responding to stretch of an extensor muscle due to joint flexion), Golgi
tendon organs (Ib not shown) and proprioceptors (not shown) have their cell bodies in the dorsal root ganglion and transmit their information to
interneurons within the spinal cord. These interneurons relay sensory information to other regions within the spinal cord, to opposing muscles
within the same limb, as well as to flexor and extensors of the contralateral limb, by means of synapses with the dendrites of α motorneurons
(located in the ventral motor pool of the spinal cord). α motorneurons that innervate limb muscles to control movement and body support leave
the spinal cord via the ventral root nerve trunk. Spindle Ia afferents synapse directly with α motorneurons of the same muscle, forming a
monosynaptic pathway that facilitates rapid motor responses to stretch of the muscle. Interneurons mediate reciprocal inhibition (or activation) of
opposing sets of muscles within and between limbs.

increase the extensor muscles’ activation (Figs. 8.2 ing its support phase, proprioceptive and spindle
and 8.4). Increased activation involves an increased stretch receptor feedback act to stimulate more
firing frequency of motor units that are already forceful limb extension. As noted, recent evidence
active, as well as the recruitment of additional motor indicates that GTOs can also switch to positive
units to increase muscle force output. Thus, as a (excitatory) feedback to enhance extensor muscle
limb progressively experiences increasing load dur- activation and force output during limb stance. In
172 A N I M A L L O C O M OT I O N

contrast, if a sharp pain is felt, rather than stimulat- axons that facilitates rapid conduction of action
ing a more forceful activation of the extensor mus- potentials, as well as the mono-synaptic pathway of
cles, pain receptors initiate a “withdrawal reflex.” spindle Ia receptors, reflect the importance of reducing
This involves reduced excitation, or inhibition, of temporal delays in feedback to the motorneurons
limb extensors and activation of limb flexors in order controlling muscle recruitment. Even so, the extreme
to shift weight support away from the limb contact- size range of vertebrates indicates that delays may
ing the painful stimulus. To maintain balance, such a be problematic for larger animals with longer nerve
withdrawal reflex requires the ­coordinated activa- axons. In a study of axonal conduction velocity in
tion of extensor muscles of the opposing limb(s) to animals ranging from shrews to elephants, More et al.
allow for the shift in weight support. (2010) surprisingly found that maximum conduction
While useful and reasonably accurate, it should velocity was nearly constant across this large size
be recognized that these model descriptions for range (100-fold difference in limb length). As a result,
in­creased feedback and motor stimulation in neural conduction delays represent an increasing
response to load are likely oversimplified. In the fraction of the stance phase in larger animals, likely
actual movements of animals, the regulation of contributing to slower movements (e.g. stride fre-
motor recruitment involves a more complex inter- quencies). Longer delays may also favor predictive
action of reflex feedback from various sensors within (feed-forward) motor responses to anticipate future
a limb (and among different muscles), together with dynamics of limb and body movement (Biewener
feedforward motor activation driven by spinal cir- and Daley, 2007; Wolpert and Ghahramani, 2000).
cuits. In combination with descending control by
the central nervous system, much of the phasic
8.2.2 Insect reflex pathways
activity of limb muscles—that is, their alternating
flexor-extensor activation—is derived from local In insects, sensory information from surface hairs,
spinal circuits (see Section 8.5.). For example, the campaniform sensilla, and other mechanosensory
activation of certain limb extensors may show bi- elements provides feedback via reflex pathways
phasic stimulation patterns allowing the limb to that mirror the general organization described for
flex momentarily during the stance phase of the vertebrates. Whereas sensory feedback from hair
stride. As discussed in Chapter 4, this helps reduce exteroreceptors nearly always connects indirectly
the potential energy work of the body’s CM as it via interneurons to the motorneurons, feedback by
passes over the supporting limb when an animal mechanosensory neurons is generally direct (mono-
walks. Modulation of motor activation also influ- synaptic), similar to vertebrate spindle Ia afferents.
ences the temporal pattern of force development of Insects (and other arthropods) possess a ventral nerve
a muscle, determining whether its role is to produce cord that consists of segmental ganglia that provide
mechanical energy by shortening, absorb energy local integration of opposing limb (and wing) func-
by lengthening, or to facilitate spring-like function tion (Fig. 8.5). As in vertebrates, interneurons link
of the tendons (and the limb as a whole) by con- motorneuron pools to provide coordination of
tracting isometrically. Hence, the actual integration ­contralateral limb movements. In addition, inter-
of proprioceptive, spindle and Golgi tendon organ segmental interneurons running between segmen-
feedback with centrally coordinated patterns of tal thoracic ganglia underlie control of interlimb
motor drive is more complicated than the simple ­coordination for ipsilateral limbs (these ganglia are
schemes described previously. Nevertheless, they located in the anterior, middle and posterior regions
provide the basis for understanding how higher- of the insect thorax).
level, coordinated control of locomotor function is In contrast to vertebrates, the number of sensory
achieved. afferents in the limbs of insects greatly exceeds
Effective sensorimotor control also requires that the number of motorneurons that control their
sensory signals be transmitted rapidly to minimize muscles. Consequently, a large-scale convergence
delays in reflex feedback. Although not discussed of the thousands of sensory afferents occurs in
here, the myelinated nature of sensory and motor connections made with the much smaller number
 NEUROMUSCULAR CONTROL OF MOVEMENT 173

Thoracic segmental ganglia

Prothoracic Intersegmental
interneurons

Mesothoracic
(lateral view)

Metathoracic

Afferent sensory and

efferent motorneurons
(dorsal view)

Figure 8.5 Insects, such as the cockroach shown here, use motor reflex pathways that parallel the general organization observed within
vertebrates (see Fig. 8.4). Three ventral motor ganglia reside within the thorax of insects. Each motor ganglion controls the relative timing of flexor
and extensor activity within and between its associated paired set of limbs. Afferent sensory information from exteroreceptors and proprioreceptors
(found within the joints and the muscle’s apodemes) is relayed back to the motor ganglia where it converges on interneurons that control the
output to motorneurons supplying the limb muscles (see Fig. 8.6). Interneurons also relay local sensory information to the other motor ganglia to
coordinate the relative timing of muscle activation between sets of limbs. Visual, olfactory and tactile sensory information is transmitted from
higher centers within the head via interneurons to the thoracic motor ganglia. This information controls the overall motor behavior of the animal.

(< ~100) of motorneurons that control the limb mus- limbs. Evidence suggests that particular non-spiking
cles. This reflects one aspect of the fundamentally interneurons may control specific motions of a leg.
different motor unit organization of vertebrates ver- In almost all cases, the input from proprioceptive
sus that found in arthropods and other invertebrates. and exteroceptive sense organs is excitatory to the
This convergence largely occurs via a special class of interneurons and motorneurons of the segmental
“non-spiking” interneurons (in addition to spiking ganglia (“A” and “B” in Fig. 8.6a). Activation of
interneurons) located within and between the gan- mechanosensory neurons derived from campani-
glia (Burrows, 1996). As their name indicates, non- form sensilla or chordotonal organs that sense joint
spiking interneurons do not fire action potentials motion or force associated with extensor muscle
when depolarized (in contrast to the “all-or-none” activity may provide positive excitatory feedback to
properties of vertebrate neurons). Instead, they exert the extensor muscles of the limb, increasing their
graded voltage effects on the motorneurons and other resistance to joint flexion and providing greater
interneurons that they innervate. Consequently, weight support. Their feedback to motorneurons
non-spiking interneurons can be viewed as cellular innervating limb flexors (FLTi in Fig. 8.6a) is inhibi-
integrators that process the wide-ranging input tory, mediated via the inhibitory synapses of inter-
(from the same and other limbs) that converge onto neurons within the ganglion controlling the limb. In
them from a large number of sensory afferents. As addition, inhibitory feedback via interneurons within
such, they serve to regulate the output to the various a ganglion acts on the appropriate muscles of the
motor pools that control and drive the muscles of the opposing limb to reduce their role in weight support
174 A N I M A L L O C O M OT I O N

or to trigger their transition to a swing phase of suggests that intrinsic biomechanical properties of
the locomotor cycle (FETi and SETi in Fig. 8.6a). animal limbs likely facilitate stabilizing control
Comparable to vertebrates, the inhibitory action of responses to disturbances of an animal’s balance
interneurons thus provides reciprocal inhibition to (Jindrich and Full, 1999), simplifying the need for
control the appropriate action of the antagonistic centralized nervous system control.
muscles within a limb, as well as the actions of
muscles in the other limbs. Finally, insects also dis- 8.3 Muscle recruitment in relation
play a withdrawal reflex response similar to that
to functional demand: force, speed
of vertebrates, with limb retraction occurring in
response to a noxious stimulus applied to a particu- and endurance
lar appendage. We now turn our attention to the neuromuscular
Local reflex pathways that control the flexors and organization of vertebrate and invertebrate muscles,
extensors of a given limb are linked via the network which underlies the means by which motor recruit-
of interneurons within and between each ganglion ment is regulated for meeting the functional demands
to control the relative timing of muscle activation of changes in force output, speed and endurance.
among the various limbs associated with a given Considerable differences exist between vertebrates
gait. Since the relative phase and duration of arthro- and invertebrates in terms of how the nervous sys-
pod limb movement changes with gait, as it does in tem innervates and regulates motor recruitment
vertebrates, the interacting influences of local reflex (Table 8.1). This likely reflects, at least in part, the
pathways within a limb must be coordinated with constraints of size imposed on the organization of
the control of motor activation in opposing and the nervous system in invertebrates, which are, in
ipsilateral limbs. Although initiation of a particular general, much smaller than vertebrates.
limb-movement pattern may occur in response to
sensory stimuli received by higher centers within
8.3.1 Vertebrate motor recruitment
the nervous system, maintenance or modulation of
a particular pattern in response to external perturba- Motor innervation of vertebrate muscles is exclu-
tions or local stimuli is also likely a major compo- sively excitatory in nature and occurs via the neuro-
nent of an effective de-centralized motor control transmitter acetylcholine (Table 8.1). In almost all
system. Furthermore, while the finely graded con- cases, innervation of vertebrate muscle fibers is via a
trol necessary to maintain balance when an insect is single motorneuron that makes a connection with
moving rapidly almost certainly involves a complex individual fibers via a single local synaptic endplate
integration of sensory and motor signals via local junction. In contrast to many invertebrate motor
reflex pathways, the study of running cockroaches junctions, activation of vertebrate muscle fibers is

Table 8.1 Motor innervation features of invertebrate versus vertebrate skeletal muscles.

Feature Invertebrate Vertebrate

Synaptic Input Excitatory, inhibitory and modulatory Excitatory

Neurotransmitter l-Glutamate,a acetylcholine GABA and octopamine Acetylcholine
Motor nerve terminals Multiple and distributed Single or few, and localized
Muscle fiber innervation Polyneuronal Single neuronb
Activation Graded and twitch All-or-none, twitch
Force modulation Graded and frequency Motor unit recruitment

a
l-Glutamate is found in arthropods, but acetylchoine is the excitatory neurotransmitter in annelids, molluscs and echinoderms.
b
A few slow fibers of some fish and amphibian muscles, and eye muscles of mammals, receive polyneuronal innervation.
 NEUROMUSCULAR CONTROL OF MOVEMENT 175

a­ ll-or-none (i.e. “twitch”), in which the depolarization motorneuron. In such cases, polyneuronal innerv-
of a muscle fiber results in a rapid spread from the ation provides a means by which the activation of a
synaptic endplate along the fiber’s length. This depends muscle fiber may be influenced by the combined
on the presence of rapidly conducting voltage-depend- neural recruitment of more than one motorneuron.
ent sodium channels of vertebrate muscle fi ­ bers that
are not found in invertebrate muscle fibers. Orderly recruitment: the “size principle”
As was introduced in Chapter 2, vertebrate mus- Because of their uniform fiber type composition,
cles are comprised of subpopulations of twitch fibers vertebrate motor units exhibit characteristic proper-
that can be classified into three principal types. In ties that reflect those of their constituent fibers (see
most muscles, and almost exclusively in mammals Table 2.1). Motor units comprised of slow-oxidative
and birds, a single motorneuron innervates a distinct (SO) fibers are generally small, having a small diam-
population of muscle fibers of a single type forming eter motor nerve axon that innervates a small num-
a motor unit. Consequently, changes in force, speed ber of fibers with relatively small cross-sectional
and endurance are mediated by the manner in which areas (Table 8.2; Fig. 2.9). In contrast, fast-glycolytic
the nervous system recruits different motor units (FG) units are large, composed of a larger diameter
within the muscle. The number and size of motor motor axon that innervates a great number of larger
units varies among different muscles, ranging from diameter fibers. Consistent with their metabolic and
as few as ten or 20 to several hundred motor units contractile properties, FOG motor units possess inter-
per muscle. In general, smaller muscles consist of mediate organization.
smaller motor units (i.e. relatively fewer numbers of These differences in the relative sizes of the
fibers innervated per motorneuron). This allows for motorneurons and the total fiber area represented by
more fine-grained control of force and speed via each motor unit influence the excitability and the
recruitment of the muscle’s motor unit pool. For level of force output that can be recruited via activa-
example, the small muscles that control a person’s tion of a muscle’s motorneuron pool in the spinal
fingers are comprised of hundreds of small motor cord. At low levels of activation, the most excitable,
units. This is essential for grasping and manipulating low-diameter motor axons and smallest motor units
objects, as well as for performing motor tasks such as are excited first. As activation intensity increases
playing a musical instrument or typing on a key- (increased firing rate and, hence, greater summed
board. The effects of animal size on motor unit organ- synaptic excitatory input to the motorneuron), there
ization is not well understood. Partly, this reflects the is an orderly progression of recruitment from small
fairly daunting task of identifying and counting indi- to larger motor units as a greater number of the
vidual motor units within a muscle. Measurements motor units within a muscle’s spinal cord pool are
of motor unit size (number of fibers/motor unit) rela- recruited. This means that the smallest, most oxida-
tive to differences in muscle size may give some indi- tive and high endurance (SO) fibers are recruited
cation of scale effects on motor unit organization. first under conditions that typically require low
For example, the tibialis anterior muscle of a rat is levels of force output to be exerted over longer
­
approximately ten times smaller than that of a cat, ­periods of time (as, for example, when moving slowly,
but the average motor unit size within the muscle of shifting balance or maintaining posture). When
these two species varies by less than two-fold. This more rapid and forceful movements are required,
suggests that the number of motor units may decrease recruitment shifts to larger and faster motor units
with body and muscle size (in this example, a five- that possess less oxidative and more glycolytic
fold reduction) when compared across species. capacities (FOG and FG). This orderly recruitment of
The organization and properties of mammalian muscle fiber types from small (slow) to large (fast)
motor units have been most extensively studied and was first recognized by Henneman and his co-work-
are the focus of our discussion here. However, it should ers (Henneman, 1957; Henneman et al., 1965). It is
be noted that as in invertebrates, individual muscle now widely recognized as the “size principle” of
­fibers of other vertebrates (mainly fish and amphibians) motor unit recruitment. Although certain instances
occasionally may also be innervated by more than one have been observed in which FG units are recruited
176 A N I M A L L O C O M OT I O N

Table 8.2 Vertebrate skeletal muscle motor unit features based on fiber type.

Feature Slow-Oxidative (SO) Fast-Oxidative-Glycolytic (FOG) Fast-Glycolytic (FG)

(type I) (type IIa) (type IIb)

Innervation ratio* (motor unit size) Low Intermediate High

Motor nerve axon diameter Small Intermediate Large

and cell body size

Stimulation frequency Low Intermediate High

Excitability High Intermediate Low
Inhibitability [contractile] Low Intermediate High
Shortening speed Slow Moderate to fast Fast
Fatigue rate Low Intermediate Fast

* Defined as the number of fibers innervated per motorneuron.

before FOG or SO units, orderly recruitment accord- For muscles with less heterogeneous fiber-type
ing to motorneuron and motor unit size appears distributions, in which motor units with different
to hold quite generally for a broad range of motor properties are more compartmentalized into differ-
tasks in diverse vertebrate groups. This principle ent regions, differential recruitment within the
also explains the shifts in motor unit activation that ­muscle can be expected to result in a more regional
are observed as animals increase their speed and localization of force and length change within the
change gait during locomotion. muscle as a whole. However, the extent to which this
occurs depends on the degree to which force generated
Motor unit distribution by active muscle fibers is transmitted to surrounding
Motor units have varying distributions within dif- connective tissue components of the fibers. This will
ferent vertebrate muscles. The region of a muscle favor a more generalized transmission of force within
over which the fibers of a given motor unit are the muscle, even if its motor unit organization is
distributed constitutes a motor unit’s territory. compartmentalized into different regions.
In general, motor unit territories often represent Different muscles within an agonist group often
a third of the muscle’s total cross-section. can also have differing motor unit compositions. An
Consequently, in most cases, motor unit territories extreme and classic example of this phenomenon is
greatly overlap with one another. However, in found in the triceps surae, or ankle extensor muscles
some muscles, such as the lizard iliofibularis, their of the cat. The triceps surae is a group of leg mus-
distribution may be quite distinct, with one (cen- cles comprised of the medial and lateral heads of
tral) region being composed of SO units and the the ­gastrocnemius that, together with the soleus,
another (outer) region exclusively composed of transmit their force via the Achilles tendon to extend
FG units. Because motor units greatly overlap in the ankle joint. Whereas the cat medial and lateral
most muscles, their organization is typically het- ­gastrocnemius muscles are comprised mainly of FOG
erogeneously distributed throughout the muscle’s and FG fibers and a few SO fibers, the cat soleus is
cross-section. This means that as recruitment in a exclusively composed of SO fibers. Such differences
muscle shifts from slower to faster units, the force in motor unit organization among functional agonists
that individual units produce is likely summed in provides a means by which motor recruitment can be
a fairly uniform fashion throughout the whole of geared to changing demands of locomotor speed and
the muscle. force. In the cat (and many other mammals), the
 NEUROMUSCULAR CONTROL OF MOVEMENT 177

soleus is recruited for postural control and is the main gies that must be controlled relative to the much
ankle extensor muscle that is activated during walk- larger number of muscles within an animal’s limb.
ing. When cats increase their speed by changing their Recent work on limb self-cleaning (“wiping”)
gait from a walk to a trot or gallop, or when they movements in frogs, the control of balance and pos-
jump, the gastrocnemius muscles are recruited to pro- ture in cats and humans, and reaching movements
vide more rapid and forceful ankle extension. Shifts in humans provides evidence in support of the
in motor recruitment, both within and among mus- existence of muscle synergies, in which the control
cles, also affect the endurance capacity of the animal of movement is simplified by activating a reduced
associated with a given level of physical activity. As set of muscle synergies across a variety of motor tasks,
faster contracting, but more fatigable motor units are fewer than the number of muscles that might be inde-
recruited, an animal’s endurance capacity is reduced. pendently recruited to perform the task (for recent
discussions of these ideas and approaches, see Ting
Muscle synergies and global task control and McKay, 2007; Tresch and Jarc, 2009). However,
The challenge of understanding how the nervous work examining the control of human finger force
system coordinates the action of multiple muscles finds little or no evidence of muscle synergies as the
across multiple joints and limbs to produce a ­variety organizing basis of motor control to explain the
of motor tasks is a problem long recognized since at variability in the EMGs recorded while performing
least the time of Sherrington (1910). The orderly the task (Valero-Cuevas et al., 2009). Instead, the
recruitment of motor units within a muscle (from functional grouping of muscles recruited to per-
slow to fast) is one mechanism by which modula- form a particular motor task is considered to reflect
tion of force and contraction speed may help to the specific biomechanical requirements of the task
simplify the motor control task. It is still not well and not the underlying basis by which the ­nervous
under­stood how the nervous system regulates motor system regulates motor unit recruitment.
unit recruitment among multiple muscles, several Recent work also suggests that the coordinated
of which may have redundant (i.e. similar agonist) control of movement may be simplified by targeting
action at a joint, to coordinate a particular motor the level of the limb as a whole, rather than individ-
behavior (let alone a variety of behaviors). Given ual joints. In studies of peripheral nerve injury and
this apparent complexity, motor control research recovery (Chang et al., 2009), as well as during human
has sought to identify organizational schemes of hopping (Yen et al., 2009), the variability of affected
neural recruitment by which a motor control task joint motions and torques exceeds that for the limb
may be simplified. as a whole, suggesting that the nervous system adjusts
One conceptual framework proposes that the the activation among different muscle groups to main-
nervous system recruits muscles as functional tain consistent limb kinematics and ground force pat-
groups, reflecting flexible but repeatable activation terns. Adjustment of activation is also important for
patterns to execute specific coordinated motor controlling motion and the body’s CM, both of which
tasks. This grouping of muscle activation patterns, are critical to achieving robust responses to perturba-
originally proposed by Bernstein (1967), is currently tions of movement. Future work under conditions
referred to as a muscle synergy. Muscle synergies, of closed-loop (feedback) and open-loop (non-reflex
defined in this way, are extracted by processing mediated) control, with well-defined biomechanical
muscle EMG recordings to identify the recruitment measurements of the motor task, will be needed to
of specific subgroups of muscles that are activated further explore and test hypotheses for the exist-
to perform a given motor task. This is commonly ence of muscle synergies and the relative import-
done by means of non-negative matrix factorization ance of local versus global control of body movement.
or principal components analysis of the recorded
EMGs across differing motor behaviors. It has been
8.3.2 Invertebrate motor recruitment
argued that activating specific groups of muscles,
linked as a muscle synergy, simplifies the problem In contrast to vertebrate motor innervation, which is
of motor control by reducing the number of syner- exclusively excitatory in nature, motor innervation in
178 A N I M A L L O C O M OT I O N

insects and other invertebrates involves both exci- fiber. Consequently, in contrast to vertebrate motor
tatory and inhibitory synaptic input (Table 8.1). recruitment, motor recruitment in many inverte-
Excitatory motor junctions in arthropods utilize brate muscles is largely modulated by differences in
L-glutamate as the neurotransmitter, whereas inhibi- the phase and frequency of motorneuron stimula-
tory motor neurotransmission is via GABA (gamma tion of a muscle, which influences its level of
aminobutyric acid). Many arthropod muscles also depolarization and yields a graded response in
receive a third modulatory synaptic input via octo- terms of force output. This is correlated with the
paminergic neurons, which were originally thought fact that insect muscles are commonly innervated
to enhance the excitatory input to limb muscles by only one or two, and never more than a few (< 9)
through their secretion of octopamine locally on motor motorneurons (Hoyle, 1983).
junctions, but are now recognized to contribute more Hence, control of muscle force and speed within
complex neuromodulatory input to motorneurons insects must be achieved through activation of
and likely interneurons as well (Burrows and Pfluger, ­muscle by only a few motorneurons. This reflects a
1995). In annelids, molluscs and echinoderms, acetyl- much simpler organization for motor recruitment
choline serves as the excitatory neurotransmitter, in comparison with the graded recruitment of many
similar to vertebrate motor synapses. hundreds of motor units that often underlies the
Synaptic input from the motorneurons typically control of vertebrate muscles comprised of different
involves multiple terminals that have many branches muscle fiber types (Table 2.1). It also provides a
and are widely distributed over the ­muscle fiber’s more economical organization, requiring far fewer
surface. In distinct contrast to vertebrates, the motorneurons to control a muscle’s contractile func-
­neural activation of many invertebrate muscle ­fibers tion. Consequently, invertebrate motor recruitment
is graded locally within the muscle fiber, resulting depends on the graded activation of much larger
from the summed excitatory (and inhibitory) poten- fractions of the muscle as a whole, rather than the
tials that the various motorneuron terminals t­ ransmit summed recruitment of many individual motor
locally to the muscle fiber. Many insect motorneu- units, as in vertebrates. This likely reflects the import-
rons exhibit “spiking” properties, but in most ant constraint of size that extremely small animals
instances, these reflect local depolarization of the like insects and many other invertebrates face.
endplate junction and not an all-or-none activation
of the whole muscle fiber. Activation via multiple Invertebrate muscle fiber types
terminal endings of the motorneurons are there- Like vertebrates, different types of fibers are found
fore required to initiate contraction of the whole within the locomotor muscles of insects and other

Table 8.3 Invertebrate skeletal muscle fiber types (based largely on arthropods).

Feature Slow Intermediate Fast

Myosin ATPase Low Intermediate High

Metabolic enzymes Aerobic Mixed aerobic and glycolytic Glycolytica
Mitochondria Numerous Moderate/variable Few
Sarcoplasmic reticulum Sparse Moderate Extensive
Contraction speed Slow Moderate Fast
Fatigue rate (motorneuron) Low Moderate Rapid
Motorneuron axon diameter and cell-body size Small Intermediate Large
Excitatory synaptic potential Small Medium Large
Excitability High Intermediate Low

a
Except insect flight muscle.
 NEUROMUSCULAR CONTROL OF MOVEMENT 179

invertebrates. However, the limited number of controlling the muscles of each leg is largely inte-
muscles that have been studied and the varied grated via afferent input to both spiking and non-
properties of their fibers make it difficult to classify spiking populations of interneurons (Int. A and B,
them other than very generally and largely in terms Fig. 8.6a) within each ganglion (Burrows, 1989).
of studies of arthropods (Table 8.3). Similar to verte- Similar to vertebrates, these interneurons commonly
brates, three general classes of fibers are distin- exert opposing excitation (+) versus inhibition (−)
guished: slow, intermediate and fast. However, it is actions on antagonist pairs of leg extensors and
important to distinguish and note that the “slow” flexors on right relative to left limbs to coordinate
fibers of invertebrates are often much slower-con- alternating protraction and retraction movements
tracting and more resistant to fatigue than the slow of the limbs during walking and running. This is
“twitch” fibers of vertebrates. As a consequence, distinct from vertebrates in which spindle Ia affer-
they are often referred to as being “tonic.” In addition, ents synapse directly on to motorneurons of the
as with vertebrate muscle fibers, differences in con- same muscle. Spiking interneurons also synapse
traction rate and susceptibility to fatigue (fast fibers onto intersegmental interneurons (Fig. 8.5) to
being most readily fatigued) correlate with differ- integrate movements among sets of legs. In slow
ences in their enzyme characteristics and their cell movements and during walking, the slow extensor
architecture (extent of sarcoplasmic reticulum and neuron is mainly activated; however, some fast
number of mitochondria). As we noted in Chapter 2, extensor activation may also be observed. As
a key difference between invertebrate versus verte- speed increases, fast extensor activation increases.
brate muscle fibers is their sarcomere length. Whereas Although the roles of modulatory interneurons are
sarcomere length is fairly uniform among verte- still unclear (hence, synaptic inputs from OM are
brate skeletal muscles (2.2 to 3.0 μm), it varies con- not shown in Fig. 8.6), they are thought to serve a
siderably among invertebrates; ranging from 2.0 to similar role as adrenaline (or epinephrine) in verte-
13 μm in arthropods (and up to 40 μm in annelids). brates—to facilitate a rapid escape response by the
In general, muscles with longer sarcomere lengths animal.
contract more slowly than those with shorter sarco- In locusts and grasshoppers, which have evolved
mere lengths. a greatly enlarged metathoracic or hind limb for
jumping, the fast FETi nerve is only activated to
Examples of neuromotor organization power rapid contraction of the extensor tibiae when
in the locust and cockroach the animal jumps, whereas the SETi controls slow
The neural control of movement has been studied movements of the animal’s hind leg, as well as
in cockroaches, locusts and grasshoppers, as well as being activated during jumping. Jumping involves
stick insects. Each of these insects possesses paired three phases. In preparation for a jump, sensory
sets of prothoracic, mesothoracic and metathoracic input from the femoral chordotonal organ, as well
ganglia that control the movements of their fore, as hair receptors on the leg, first results in flexion of
middle and hind legs (Fig. 8.5). The extensor tibiae the femur-tibial joint by activating multiple flexor
muscle, which is located within the femur and motorneurons (FLTi; for simplicity only one is
extends the tibia (Fig. 8.6), or distal portion of each shown in Fig. 8.6b) of the flexor tibiae muscle. This is
leg, is one of the best-studied muscles, along with mediated by a central interneuron (Int. A) and is fol-
its antagonist the flexor tibiae muscle. In both locusts lowed by co-activation by the FETi motorneuron of
and cockroaches, the extensor tibiae of each leg is the extensor tibiae muscles of both hind limbs (Heitler
innervated by a pair of excitatory nerves, a slow- and Burrows, 1977). The FETi also has an excitatory
excitatory nerve (SETi) and a fast-excitatory nerve input to the FLTi, reinforcing the simultaneous
(FETi), which emanate from the motor ganglia of ­co-activation of the flexor and extensor tibiae mus-
each limb (Hoyle, 1983). In addition, the muscles of cles. Owing to the greater mechanical advantage of
all three pairs of limbs are influenced by octopamin- the flexor tibiae (see Section 7.4.3), this keeps the
ergic modulatory (OM) interneurons that act on the femur-tibial joint locked into position allowing
neural network. Activation of the motorneurons the extensor tibiae to develop maximal isometric
180 A N I M A L L O C O M OT I O N

Campaniform Chordotonal organs

(a)
sensilla
Hair
receptors
+ excitatory
inhibitory Extensor tibiae

Int A & B
+
FETi + Flexor tibiae
(& SETi)
FETi +
+ OM
(& SETi)

FLTi FLTi

Ventral segmental 'Generalized' motor organization (e.g. cockroach)

ganglion with alternating contralateral motor activation

(b)

Extensor tibiae
Int A
Sensory
afferents
CI

+ + +
FETi + FETi
+ Flexor tibiae
(& SETi) +
Extensor FLTi FLTi
Flexor

Ventral segmental
ganglion

Figure 8.6 In contrast to vertebrates, sensory-motor reflex pathways in the legs of insects, such as in a locust or grasshopper, use convergent
input from sensory afferents to interneurons in order to integrate and distribute their output to motorneurons, controlling specific motor behaviors
in response to stimuli. (a) The jumping leg of a locust (lateral view, top image) operates through the use of a reflex pathway (transverse section of
thorax below) coupled with sensory afferents. Sensory afferents from hair receptors, campaniform sensilla, chordotonal organs, and other receptors
converge on spiking (Int A, filled black circle) and non-spiking (Int B, open circle) interneurons in the ventral segmental ganglion (depicted as light
gray region within the transverse slice of the thoracic segment). Spiking interneurons also inhibit non-spiking interneurons (not shown). In walking
and running insects, such as cockroaches, interneuron stimulation to the contralateral extensor muscles through the slow (SETi) and fast (FETi)
extensor tibiae motorneurons is largely inhibitory, reflecting the out-of-phase nature of limb movement patterns similar to that observed in walking
and running vertebrates. Similar opposing inhibition (−) and excitation (+) of flexors via the flexor motorneurons, FLTi, of opposing limbs also
occurs. Octopaminergic modulatory (OM) neurons are believed to facilitate the transition of insect muscles from a resting to a dynamic state (their
synaptic inputs to the motor circuit remain unclear and are not shown). (b) In locusts and grasshoppers, the enlarged hind leg is used for jumping
as well as for slower movements. The extensor tibia muscle is innervated by two motorneurons, SETi (slow) and FETi (fast), which receive largely
excitatory stimulation via populations of metathoracic spiking interneurons (Int A) from sensory receptors in the limb. As discussed in Chapter 7
(Section 7.4.3), jumping in these insects involves three phases. First, activation of the flexor muscle flexes and locks the hind leg at the femur-tibial
joint. Second, co-activation of the extensor and flexor muscles via the FETi and FLTi motorneurons allows the extensor tibiae to develop isometric
tension and store elastic energy in the muscle’s apodeme, the semilunar process and the leg cuticle. Third, triggered release of the stored elastic
energy occurs via inhibition of the flexor motorneurons (FLTi) to both hind limbs by a common inhibitory interneuron (CI, grey circle; Heitler and
Burrows, 1977). The synchronous movements of the hind legs of locusts, grasshoppers and other jumping insects are therefore mediated by
simultaneous inhibition of the flexors of both limbs, releasing the catch of the hind limbs for the jump. The neuromechanical properties of this
circuit were confirmed by means of a computational model of these neurons (Cofer et al., 2010).
 NEUROMUSCULAR CONTROL OF MOVEMENT 181

tension and store elastic energy in the apodeme, vertebrates (Fig. 8.7). This causes the muscle to gen-
semilunar process and joint cuticle. This is followed erate greater force and at a higher rate, leading to
by a “triggered” release of the catch mechanism by more forceful and rapid limb movements. There is
simultaneous inhibition of the flexor tibiae muscles little evidence that insects and other invertebrates
to both hind limbs mediated by common “modula- have much ability to regulate their endurance
tory” inhibitory interneurons (CI) that receive capacity at differing intensities during locomotive
visual and olfactory inputs, as well as from an movement (other than, perhaps, by strategies of
inhibitory flexor motorneuron (also not shown). intermittent locomotion; see Section 3.10). This is
Having a separate trigger release via inhibition of largely because their ability to recruit different
the flexor muscle, rather than control via a change populations of muscle fibers within individual
­
in excitation of the motorneurons, assures precise muscles having different contractile properties is
timing of the release of elastic strain energy from limited by their simpler motor unit organization.
both hind limbs and a more stable jump. A recent However, studies of lobster swimmerets, which are
neuromechanical model of this neural circuit has innervated by three shared excitatory neurons that
confirmed past experimental results for the control produce motor synaptic potentials of different sizes
of kicking and jumping in these animals (Cofer (small, medium and large), provide evidence of
et al., 2010). recruitment to control slow, moderate and fast
swimming speeds by progressive activation of the
Invertebrate muscle activation patterns in three excitatory motorneurons (Hoyle, 1983). The
relation to speed fastest excitatory motor unit with the largest syn-
When insects move more quickly, the frequency of aptic motor potential also fatigues most quickly,
motorneuron bursts controlling different limb mus- whereas the slow excitatory motor unit with the
cles and the firing rate within each burst generally smallest motor potential is resistant to fatigue.
both increase—similar to the pattern observed in Finally, similarly to a general pattern observed in

Stance Swing
Left limb

Flexor EMG

Extensor EMG

Time Stance Swing

Contralateral (right) limb

Flexor EMG

Extensor EMG

Figure 8.7 Flexor and extensor EMGs of the right and left limbs of a walking or running animal alternate out-of-phase within each limb and
between limbs. This asynchronous motor activity is achieved via reciprocal inhibition by interneurons located within the spinal cord of vertebrates
or thoracic motor ganglia of insects. Activation of extensor motorneurons during the stance phase inhibits flexor motorneurons supplying muscles
of the same limb (antagonistic inhibition), but stimulates the flexor motorneurons and inhibits the extensor motorneurons of the opposite side
limb. EMG burst sizes are arbitrary and, other than for timing, are not intended to show left:right asymmetry.
182 A N I M A L L O C O M OT I O N

mammalian motor recruitment, the recruitment other limb) flexors results in inhibitory feedback of
order of the excitatory neurons and their motor the ankle extensors via interneurons within the
units appears to follow a progressive sequence from ­spinal cord. Thus, there is reciprocal inhibition via
slow → medium → fast. This is also similar to the spinal cord interneurons between the extensors and
pattern observed in ghost crabs, in which only the flexors within the same limb. This same general pat-
slow excitatory neurons to the principal limb mus- tern of reciprocal inhibition of flexors versus exten-
cles are activated during walking, whereas the sors within a limb also holds for invertebrates and
larger, fast excitatory neurons are recruited when other forms of locomotion.
the crab runs (Burrows and Hoyle, 1973). A second feature of legged locomotion is that
contralateral limbs commonly operate in reciprocal
8.4 Reciprocal inhibition: a basic feature fashion (Fig. 8.7 and see Chapter 4). This is true for
walking, running and trotting gaits (though not
of sensorimotor neural circuits
true for hopping and bounding gaits of vertebrates,
Two features of locomotor function underlie the or when many animals jump). It also characterizes
more general organization of the sensory and motor undulatory swimming (in which opposite sides of
systems of the body axis and limbs of both verte- the body axis are activated out-of-phase) but again,
brates and insects (as well as other invertebrates). is not the case for symmetrical motions of pectoral
These highlight the role that reciprocal inhibition fin swimming or flying. We concentrate here on the
plays in regulating the phasic activity of locomotor out-of-phase motions of the limbs associated with
muscles. First, because muscles can only shorten gaits commonly used by terrestrial animals. The
when developing force, the reciprocating move- reciprocal motion of the limbs means that when one
ments of any joint requires the arrangement of mus- limb is in contact with the ground and supporting
cles in opposing sets of antagonists (e.g. flexors and body weight, its extensors must be activated. At the
extensors). Therefore, sensory feedback to antagonist same time, the opposing limb is swung forward by
muscles acting at a given joint or across limb joints muscle flexors to anticipate the next support phase.
must stimulate one set of muscles while inhibiting The reciprocal, out-of-phase timing of the stance
the opposing set. For example, when a terrestrial phase extensor muscles and the swing phase flexor
vertebrate’s hind limb lands on the ground and its muscles is mediated by reciprocal inhibition within
ankle initially begins to flex as the joint moment the appropriate spinal cord segments (Fig. 8.4).
increases, the ankle extensors will be stretched as Again, using the ankle extensors and flexors of ter-
they begin to develop force, causing increased spin- restrial vertebrates as an example, activation of the
dle Ia afferent feedback drive to the α-motorneuron ankle extensors in the stance phase limb results not
pool of the ankle extensors (Fig. 8.4). As previously only in spindle feedback for enhanced motor drive
discussed, this occurs via a monosynaptic pathway to the same agonist muscles and inhibitory feed-
within spinal cord segments (lumbar vertebrae back to the ankle flexor antagonists, but also feed-
three, four and five in mammals) that contribute back to muscles of the contralateral swing-phase
sensory and motor innervation to the muscle. In limb via interneurons that cross between the left
addition to their excitatory feedback to the muscle’s and right motorneuron pools of the body. This same
own motorneurons, the Ia afferents of the ankle pattern also holds for invertebrates (Figs. 8.5 and
extensors also synapse onto interneurons located 8.6). In our example of terrestrial vertebrate ankle
within the spinal cord that, in turn, inhibit the extensors, this contralateral feedback exerts mainly
α-motoneurons of ankle flexor muscles. This ensures an inhibitory influence on the extensors of the oppos-
that ankle extensor activation due the stretch from ing limb, but may also provide an excitatory influ-
ankle flexion simultaneously prevents ankle flexor ence on the flexors of the opposing swing-phase
activation. At the end of the ground support phase, limb (Fig. 8.4). Thus, there is a second level of recip-
when the ankle must be flexed and the hind limb rocal inhibition that occurs via interneurons that
swung forward, the phase and pattern of motor transmit sensory feedback to contralateral limb
stimulation is reversed. Activation of the ankle (and muscles.
 NEUROMUSCULAR CONTROL OF MOVEMENT 183

8.5 Distributed control: the role body axis (lampreys and dogfish) can be initiated
of central pattern generators and maintained independently of any functional
link to higher brain centers.
Muscles may be controlled by higher brain centers One such model of a central pattern generator is
(e.g. motor cortex) to execute conscious behaviors depicted in Fig. 8.8a, which shows a “flexor-burst-
such as when reaching to pick up an object or choos- generator” model developed by Pearson (1976) to
ing to initiate locomotion, as when escaping a describe how the reciprocating activity of flexors
­predator or chasing prey. However, such command- and extensors within the limbs of walking cock-
driven motor behaviors require ongoing attention roaches is achieved. In this model, four ­interneurons
to perform the task. In contrast, many aspects of loco- within the nervous system are hypothesized to inter-
motor movement are achieved by unconscious con- act such that they produce an oscillating change
trol via local sensorimotor circuits operating at spinal in the membrane potential of a key i­nterneuron
(vertebrate) or thoracic ganglion (insect) levels. (Interneuron 1). The output of this network via
The coordinated timing of muscle activation Interneuron 1 exerts a reciprocal excitatory input to
within a limb and between limbs allows for more the flexor motorneurons and inhibitory input (via
distributed control of muscle function; simplifying another interneuron) to the extensor motorneurons
the command requirements of the central nervous of the limb. Descending central motor commands
system of both insects and vertebrates. Much of an from the brain and “higher centers” (to initiate and
animal’s regulation of its limb movement patterns sustain movement) are believed to exert an excita-
as it maneuvers or changes speed and gait is accom- tory effect on the flexor-burst CPG (establishing the
plished as an unconscious act, reflecting local con- frequency and amplitude of its oscillatory output)
trol for meeting the mechanical requirements for that drives the extensor motorneurons. Hence,
body support and movement. This allows the CNS ­inhibition of the extensor motorneurons (and mus-
to be attentive to other functions and needs of the cles) by this model is achieved via the inhibitory
animal. The motor response to the sight, sound, or input from the CPG at the time when the flexor
smell of a predatory threat involves the integration motorneurons are being activated, as evidenced by
of sensory stimuli via the central nervous system to the firing of a series of action potentials to activate
organize and plan the animal’s locomotive response. the flexor muscles.
However, once initiated, the motor response is largely A similar “half-center model” describes the rhyth-
controlled at local levels via the reflex pathways mic reciprocal pattern of flexor and extensor
described. motorneurons in the hind limb of a cat (Fig. 8.8b). In
Control of the relative timing and strength of contrast to the asymmetric flexor-burst generator
flexor-extensor activity within and between limbs is model that describes the control of the cockroach
thought to be mediated by networks of neurons limb, the half-center model is symmetric—with
called central pattern generators (or CPGs). Central mutually excitatory and inhibitory components
pattern generators represent clusters of nerve cells to control the out-of-phase activity of flexors and
located within the spinal cord of vertebrates or extensors. In the half-center model, the putative
nervous system ganglia of insects that have rhyth- interneurons that drive the CPG located within the
mic burst-generating properties. The organization spinal cord are linked with their associated flexor
and network properties of such CPGs are often or extensor motorneurons to form a “half-center.”
rarely identified in any discrete fashion, but models Reciprocal inhibition via interneurons within the
for their organization can be constructed that CPG network and between flexor and extensor
­accurately describe their motor output and their motorneurons results in an out-of-phase activation
response to changes in sensory input. The evidence of the flexor and extensor muscles of the limb. As is
for CPGs rests largely on experimental observations the case for the CPG network of the cockroach, the
of animals in which coordinated movement pat- cat CPG model also relies on descending motor
terns of the limbs (cats, turtles, cockroaches and commands from higher (brain) centers to excite the
locusts have been studied) or undulation of the half-center network and establish a basic frequency
184 A N I M A L L O C O M OT I O N

(a) Central
command
neurons

Interneuron 1

+ +

+ Flexor
motorneuron
Flexor- –
burst-generator +

Excitation +
Extensor
Inhibition – motorneuron

(b)
Interneurons Flexor
motorneuron
+
– + –
Flexor half-center +

+ +
– –
Extensor half-center
+
+
Excitation
Inhibition – Extensor motorneuron

Figure 8.8 Central pattern generators (CPGs) represent a network of neurons with synaptic connections and properties that result in phasic
activation (+, “on”) and inhibition (–, “off”) of opposing sets of muscles. CPGs are fundamental to the local control of rhythmic locomotor
movement patterns. Two hypothetical CPG circuits are shown: (a) A “flexor-burst-generator” model illustrates how the reciprocating activity of
flexors and extensors within the limbs of walking cockroaches may be achieved. This CPG network lies within one of the thoracic motor ganglia of
the cockroach. (b) A “half-center model” describes the rhythmic reciprocal pattern of flexor and extensor motorneurons in the hind limb of a cat.
The cat CPG likely resides within the spinal cord. Both flexor-burst-generator and half-center model CPG networks rely on reciprocal inhibition
mediated via interneurons to establish out-of-phase activation of motorneurons that excite flexor and extensor muscles within the limb. Central
commands from the brain can modulate CPG output and, hence, adjust locomotor behavior in response to sensory input, such as visual, auditory
or olfactory cues.

and magnitude of oscillatory change in membrane and neurons involved in such pattern-generating
potential to drive the alternating activation of the networks are still not well described. A key principle
flexors and extensors within the limb. The mutual of these networks is that they do not rely on a pace-
inhibition of each half-center facilitates the main- maker cell to establish and maintain a motor rhythm
tained rhythm of the motor pattern once it is estab- as occurs in a beating heart. Instead, external sen-
lished. Other more complicated CPG models have sory input—often integrated with reflex feedback
been developed. However, except for the most sim- resulting from activation of the muscles them-
ple invertebrate motor systems, the exact pathways selves—facilitates the rhythmicity and pattern
 NEUROMUSCULAR CONTROL OF MOVEMENT 185

established by the spinal CPG, in association with less of the distance that it traveled backward during
descending commands from higher CNS levels. the previous step.
These simple CPG network models can explain In another example, sensory feedback also modu-
the alternating rhythmicity of antagonist muscles lates the motor output to the limb when the top sur-
within a limb (e.g. flexors and extensors) that face of an animal’s foot is stimulated. In cats, activation
accompany the swing and support phases of a of proprioceptors in the skin causes the animal to flex
locomotor cycle. However, the existence of a CPG its limb more strongly, lifting the foot higher during
for each limb does not mean that sensory informa- the swing phase. This reflexive elevation of the limb
tion is unimportant. Indeed, the ability to adjust and foot enables an animal to step over obstacles that
limb movement patterns to accommodate irregu- it may encounter in its environment.
larities in the environment is an ongoing require- Reflexive sensory feedback thus has at least two
ment of stable coordinated locomotion. In fact, the important functions in controlling phasic motor
timing of muscle activation patterns that result in activity during locomotion. The first is to switch the
shifts in the relative onset, offset and duration of motor program from one phase to the other (e.g.
motor activation within a limb must be modulated from swing to stance), and the second is to modu-
by sensory feedback to the CPG and through feed- late the motor output within a single phase of the
back directly to the motorneuron pools that supply limb’s movement.
the muscles of a limb. Exactly how such shifts in The relative timing of limb movements must also
timing are mediated among functional agonist and involve the CPGs that control pairs of limbs, such as
antagonist muscles remains an important area of when an animal changes speed or gait. Hence, higher-
research. level networks within the nervous system must facili-
Because there is little change in the duration of the tate the coordinated timing of movement patterns
swing phase when animals move at different speeds, among multiple limbs of the animal, thereby main-
decreases in the duration of the support phase under- taining the appropriate phase of activation of muscles
lie faster speed movement. This suggests that com- within each limb. The reciprocal inhibition provided
pletion of the stance phase triggers activation of the by interneurons to opposing contralateral motor unit
next swing phase. In cats, two conditions appear to pools of a pair of limbs (e.g. the hindlimbs of a dog or
be necessary for this: 1) the hip must be extended, a cockroach) necessarily represents a key component
and 2) the extensor muscles must be unloaded. of local CPG control for the out-of-phase relationship
Similarly, in cockroaches, the removal of load on the of the paired limb movement. However, for those
limb is required to initiate the swing phase of the gaits (such as hopping or bounding) or modes of
stride. This is borne out by the observation that the locomotion (such as flight) that require synchronous
campaniform sensilla—which detect the strains in activation of paired appendages, any intrinsic pattern
the cuticle resulting from extensor activity during of reciprocal inhibition must be overridden (when an
stance—inhibit the flexor burst-generating system animal changes gait) or have been lost through the evo-
of interneurons. As the leg is extended and becomes lution of a new network that ensures paired synchrony
unloaded toward the end of stance, this inhibition is of limb-movement patterns. Owing to the greater
lost (cuticle strains decrease), facilitating activation complexity of central nervous system organization
of the limb flexors and the initiation of the limb’s and function, the anatomical and neurophysiological
swing phase. The switching from swing to stance is basis for such shifts in limb-movement patterns
also subsequently initiated by sensory input. In this remains an area of active investigation.
case, the leg-hair receptors—which are activated by
rapid leg motion—inhibit the flexor CPG and excite
8.6 Case examples of motor control
the extensor motorneurons. This input from hair
receptors causes the flexors to relax and the exten- Here we examine two modes of locomotion that
sors to contract, initiating stance. Moreover, sensory provide interesting and compelling case studies of
feedback from the hair receptors ensures consistent neuro-motor control and how changes in muscle
positioning of the limb at the start of stance, regard- recruit­
ment pattern accommodate changes in
186 A N I M A L L O C O M OT I O N

Wing flight muscles (Fig. 8.9). The halteres are small club-
steering Wing shaped structures that are mechanically coupled to
muscles
the wings (Deora et al., 2015). During flight, they
beat back and forth antiphase to the wings. Although
the halteres lack aerodynamic function, their mech-
anosensory components are enhanced relative to
those of the wings. In a blow fly (Calliphora spp.), for
Haltere
Haltere
example, each haltere is equipped with 335 cam-
steering paniform sensilla organized in distinct fields at the
muscles base of the haltere. Mechanosensory neurons inner-
vating these campaniform receptors encode Coriolis
forces that result from the cross-product of the hal-
tere’s linear velocity with its angular velocity result-
ing from rotations of a fly’s body about its pitch,
yaw and roll axes. Monosynaptic feedback from
Figure 8.9 Sensory motor pathways underlying flight control in flies these mechanosensors at the base of the halteres to
involve rapid mechanosensory feedback from the haltere to the wing the wing steering muscles (Fig. 8.9)—similar to ver-
steering muscles, as well as slower visual input from descending tebrate spindle Ia afferents—provides rapid com-
afferents to the steering muscles of both the wing and haltere. pensatory adjustment of wing motion to produce
Mechanoreceptors on the wing (dark gray) and haltere (medium gray)
aerodynamic forces that counter and ­stabilize the
make direct monosynaptic connections with steering muscles (light
gray) of the wing and haltere. The halteres are club-shaped organs fly’s body motion. If their halteres are removed,
(modified hindwings) that beat anti-phase to the wings responding to flies are unstable and cannot fly.
Coriolis forces generated by body rotations of the fly relative the The steering muscles of the wings and halteres
haltere stroke planes. Hence, mechanosensory feedback resulting from are also under direct control of motion-sensitive
body rotations influences how steering muscles control wing motion
visual afferents that synapse onto steering muscle
to stabilize the fly during flight or to produce body rotations during
maneuvering. Descending visual information (dark gray dashed lines) motorneurons (Fig. 8.9). They thus provide a sec-
converges on steering motorneurons providing guidance to ond, slower pathway that allows adjustments of
environmental features; however, the means by which this information wing motion to alter aerodynamic forces control-
is integrated with wing and haltere sensors remains unclear. (After ling the fly’s flight path. This visual-motor pathway
Dickinson, 2006; with permission Cell Press).
enables flies to respond to features in their environ-
ment. In response to visual stimuli, or experimental
locomotor ­performance. The first examines how a perturbations of the visual world (for example, by
fly’s underlying neuromuscular properties and reflex controlling the equatorial motion of vertical bands
pathways are organized to mediate and control of light that the fly sees while it is tethered to a force
maneuverability during flight. The second shows transducer), a fly will (or will attempt to, when teth-
how neuromuscular patterns of recruitment com- ered) alter its body orientation to change its flight
pensate for the physiological effects of temperature direction. Hence, visual stimuli strongly influence a
on fish swimming performance. fly’s flight behavior, and the halteres may well play
a role in this sensorimotor integration. However,
8.6.1 Mechanosensory and visual control clear evidence for the role of halteres in vision-
mediated flight control remains to be demonstrated.
of fly flight
The maneuvering ability of flies is quite excep-
In addition to their wings, dipteran flies possess a tional and is exemplified when a male fly tracks a
pair of equilibrium organs termed “halteres” evolved female fly during mating flight behavior (Wagner,
from the hind wings of their ancestors. As a result, 1986). This maneuverability depends on the stabil-
similarly to the muscles that control motions of the izing control that the halteres provide via their
fly’s wings, the halteres are also equipped with a rapid mechanosensory control of the wings, together
set of steering muscles and (smaller) asynchronous with the slower integration of descending visual
 NEUROMUSCULAR CONTROL OF MOVEMENT 187

motor control. The activity patterns across all steer- With decreasing temperature, myosin-mediated
ing muscles of tethered fruit flies have been revealed cross-bridge cycling decreases. By recruiting faster-
through the use of a genetically encoded fluorescent contracting white fibers at lower temperatures, carp
indicator (GCaMP6f) that causes Ca2+ to fluoresce, are able to achieve a similar contraction speed as
lighting up the cell when the muscle is activated. their red fibers at the higher temperature, allowing
These experiments revealed two classes of steering them to sustain a similar swimming speed. Although
muscles that control the position of four skeletal this enables many fish to compensate for and main-
elements at the wing hinge—a set of large phasi- tain performance in response to changes in environ-
cally controlled muscles for executing large changes mental temperature, it is likely that the increased
and a set of smaller tonically controlled steering reliance on white glycolytic fibers reduces their cap-
muscles specialized for continuous fine-scale adjust- acity for swimming endurance at colder temperat-
ments of wing motion (Lindsay et al., 2017). By ures. Certainly, the top speeds of fish are limited by
mathematically modeling the single motor unit temperature. Does this pose a significant ecological
innervation of the fly’s two classes of steering mus- threat to the fish? Possibly not, given that their prey
cles, researchers demonstrated that this arrange- and other ectothermic predators experience the same
ment provides sparse, but effective motor control temperature-slowing effects on locomotive per-
that ultimately yields exemplary maneuverability. formance. Of course, predators capable of maintain-
This mechanism for control likely applies to other ing elevated muscle, brain and eye temperatures
insects, given their similarly small size and shared (billfish, sea mammals and other swimming mam-
constraints on recruitment that arise largely from mals) likely have a distinct edge!
single motor unit innervation (Section 8.3.2). Similar patterns of temperature-dependent shifts
in motor unit recruitment have been observed in
other fish, as well as certain other lizards, but it is
8.6.2 Fish swimming: motor recruitment in
not a pattern that can necessarily be readily general-
variable temperatures ized to all ectothermic taxa. Nevertheless, it is a fas-
As ectotherms, most fish encounter seasonal and cinating mechanism by which some ectotherms
even daily changes in water temperature. As a are able to compensate for temperature-dependent
result, their axial musculature must operate over a effects on muscle contractile function and certainly
range of temperature. Due to the thermal effects on is an area of research that deserves additional study.
reaction rates, muscles contract more slowly at
lower temperatures. In general, approximately a
8.7 Summary
two-fold decline in contraction speed can be
expected for a 10°C decrease in temperature. In A fundamental set of sensory elements of verte-
order to maintain a uniform swimming capacity, brates and insects provide local feedback control to
fish that experience shifts in environmental tem- the limb and body muscles. Sensory feedback is
perature alter the recruitment pattern of their slow important for achieving coordinated and stable
red (SO) and fast white (FG) axial muscle fibers in movement. In vertebrates, muscle spindle organs
response to temperature changes (Rome et al., sense muscle length and velocity changes, Golgi
1984). At 20°C, swimming carp are able to sustain tendon organs sense the force transmitted to a mus-
a cruising speed of 0.45 m s–1 powered exclusively cle’s tendon, and various proprioceptors sense
by their red muscle fibers (Fig. 8.10a). When the pressure at the body surface and within joints. In
water temperature is lowered to 10°C, carp begin insects, hair-like exteroreceptors sense tactile stim-
to recruit their white musculature at 0.25 m s–1, in uli at the animal’s surface and mechanosensitive
addition to their red muscle fibers (Fig. 8.10b). The proprioreceptors sense stimuli at the cuticle surface
same pattern of slow-to-fast motor recruitment is or within the joints of the animal. Decentralized
observed at the two temperatures, but it is “com- control of locomotor movements is grounded in the
pressed” into a narrower speed range at the lower local sensorimotor integration provided by these
temperature. sensory elements and their reflex pathways.
188 A N I M A L L O C O M OT I O N

(a) (b)
Swimming 10°C 20°C
speed
Red
0.15 m/s muscle
White
muscle

Red
0.25 m/s
White

Red
0.40 m/s
White

Figure 8.10 EMG recordings show differential patterns of red and white axial muscle (see Figure 2.7) recruitment of a carp swimming at three
different speeds and at two different temperatures. To swim faster the carp (and other fish) must recruit more muscle and progressively shift
recruitment from red muscle fibers to white muscle fibers. At a higher temperature (20oC), carp can sustain swimming speeds up to 0.35 m/s by
recruiting only red muscle. At 0.40 m/s, carp begin to recruit faster white muscle fibers to sustain faster swimming speeds. In colder water (10oC),
the fish begins to recruit its white muscle fibers, in addition to its red fibers, at a slower speed (0.25 m/s) because its muscle fibers contract more
slowly and produce work at a slower rate. This “compression” of the fish’s muscle fiber recruitment order represents a motor strategy by which
ectothermic animals, such as carp, can sustain comparable levels of performance in the face of acute changes in temperature regime. Adapted
from Rome et al. (1984).

In both vertebrates and insects, direct mono- to faster contracting fibers within the muscle. In
synaptic pathways facilitate rapid motor responses vertebrates, the progressive recruitment from small,
to ­sensory stimuli, allowing animals to adjust rap- slow (oxidative) → intermediate → large, fast (glyco-
idly to their environment. Excitatory input to motor lytic) units is termed the “size principle” and is
units activates the muscles and increase their force largely considered the typical pattern of motor unit
output. Sensory afferents also commonly exert multi- recruitment.
synaptic inhibitory input to opposing (antagonist) Sensorimotor integration and control of muscle
muscles. In vertebrates, the “stretch reflex” of the activation within and between limbs is mediated by
spindles enhance motor recruitment and resist interneurons within the spinal cord of vertebrates
stretching of the muscle. Vertebrate motor recruit- and the motor ganglia of insects. These systems
ment involves the activation of discrete motor units control the out-of-phase activation of flexors and
in an all-or-none fashion. By contrast, recruitment extensors. Reciprocal inhibition plays a fundamen-
in insects and other invertebrates is achieved through tal role in mediating the relative phase of muscle
graded junction potentials that sum along muscle activation associated with, for example, the swing
fibers which are multiplied and innervated by dif- and stance phases of a limb. The rhythmic timing of
ferent motor neurons. In addition, whereas verte- limb and body movements is mediated by central
brate ­muscles are typically innervated by many pattern generators (CPGs) that constitute networks
motorneurons and are comprised of many motor of neurons that reside at local levels within the
units, invertebrate muscles are typically innervated ­spinal cord or motor ganglia. CPGs facilitate the
by one or only a few motorneurons. Motor recruit- decentralized control of basic motor patterns and
ment in both groups generally proceeds from slower locomotor movement. Higher centers involving
 NEUROMUSCULAR CONTROL OF MOVEMENT 189

the brain and specialized sensory organs provide control of animal movement across impressive ranges
“descending” input to local CPGs to initiate and of speed and maneuverability through complex
control more complex motor behaviors. However, environments.
the ability of local CPGs to maintain rhythmic
motor behaviors that can be modulated according
Additional reading
to local sensory feedback within and between limbs
is fundamental to the coordinated, stable move- Dickinson, M. (2006). Insect flight. Curr. Biol. 16, R309–14.
ment of an animal. Local CPGs are also key to the Goslow, G. E., Jr. (1985). Neural control of locomotion. In:
changing leg movement patterns accompanying Functional Vertebrate Morphology (eds M. Hildebrand,
D. M. Bramble, K. F. Liem, D. B. Wake). Cambridge:
shifts in gait and speed, as well as the wing move-
Harvard University Press.
ment patterns of maneuvering flight. We hope that
Grillner, S. (1985). Neurobiological bases of rhythmic
future research will integrate biomechanical, elec- motor acts in vertebrates. Science. 228, 143–9.
trophysiological, imaging, and computational ana­ Pearson, K. G. (2000). Neural adaptation in the generation
lyses of neural networks to more fully explain the of rhythmic behavior. Ann. Rev. Physiol. 62, 723–53.
 CH A PT ER 9

Evolution of Locomotion

The first chapter of this book began with the state- datasets and phylogenies to run meaningful ana-
ment that animals are the pre-eminent locomotor lyses. The goals of this chapter are two-fold—to
creatures on our planet. Yes, plants and fungi move, glean the fundamentals of locomotor evolution and
as do prokaryotes and single-celled eukaryotes, but to consider the pathways for performing rigorous
not with combination of the range of body size evolutionary biomechanical analyses. We will focus
scales and the diversity of mechanisms and terrains primarily on four areas: large-scale trends in animal
that are used by animals. How and why has the rich locomotor systems, the scales of study (genes to
diversity of animal locomotor systems evolved? organisms), basic methods for studying the evolu-
Scientists agree that the beginnings of life emerged tion of locomotor systems, and the integration of
from a primordial ocean, so it makes sense that the evolutionary analysis with the burgeoning fields of
cellular and tissue building blocks of motion are sur- robotic and synthetic locomotor systems.
rounded by salty fluid, coordinated through ion flow
and have been coupled together through cellular
interactions, neuromuscular connections, and on up 9.1 Large-scale trends in animal
to organ-level coordination. This means that the ori-
locomotion
gins and evolution of locomotor systems require
consideration of genes, cells, networks, whole sys- Animals form a single clade, formally known as the
tems and system-environment interactions over the Metazoa, that includes innumerable marine inver-
changing conditions of the planet over the past bil- tebrates, such as molluscs, cnidarians, a wide ­variety
lion years or so. of worm-like organisms, including the annelids
The evolution of animal locomotion straddles (e.g. earthworms), and is dominated by the arthro-
two big areas—what are the major trends in loco- pods which constitute the vast majority of animal
motion across the clade of animals (Metazoa) and species (Dunn et al. 2014; Fig. 9.1). The most famil-
how should the many principles and patterns of iar group to humans—the vertebrates—is found
locomotion be analyzed in the context of evolution- within a small group called the Chordata. The habi-
ary relationships? The first question is a broad tats and diversity of locomotor systems are mind-
examination across the metazoan tree and the sec- boggling when the full metazoan tree is considered.
ond is a methodological issue that is central to loco- However, as evidenced in previous chapters, the
motor analyses given the current abundance of bulk of research on animal locomotion has focused
phylogenies and the availability of computer power. on the vertebrates. There is little question that a fan-
Yet one cannot exist without the other. We need tastic diversity of animals and their locomotor sys-
proper analysis tools to figure out the evolution of tems is still open for discovery. Indeed, the place to
animal locomotion, and we need effective comparative start when learning the fundamentals of animal

Animal Locomotion. Second Edition. Andrew A. Biewener & Sheila N. Patek, Oxford University Press (2018).
© Andrew A. Biewener & Sheila N. Patek 2018. DOI: 10.1093/oso/9780198743156.001.0001
 E V O L U T I O N O F L O C O M OT I O N 191

Ctenophora

Animals Porifera
Placozoa
Cnidaria
Xenacoelomorpha
Parahoxozoa
Ambulacraria Echinodermata

Planulozoa Deuterostomia Hemichordata

Cephalochordata

Chordata Urochordata
Bilateria Craniata
Chaetognatha
Bryozoa
Entoprocta
Cycliophora
Nephrozoa
Annelida

Trochozoa Mollusca
Nemertea
Brachiopoda
Phoronida
Spiralia Gastrotricha

Protostomia Platyhelminthes
Gnathostomulida

Nucleariida Micrognathozoa
Gnathifera
Rotifera
Fungi
Orthonectida
Opisthokonta Filasterea
Dicyemida
Ichthosporea
Priapulida
Holozoa Animals Scalidophora
Loricifera
Choanoflagellata
Kinorhyncha
Nematoida Nematoda
Ecdysozoa Nematomorpha
Tardigrada

Panarthropoda Onychophora
Arthropoda

Figure 9.1 The evolutionary tree (phylogeny) of animals encompasses a rich diversity of locomotor systems. Animals constitute the clade
Metazoa. Their phylogenetic relationships remain uncertain at particular nodes (gray scale names and dots), especially at the base of the tree
where many distinct features of animal locomotion arose. Reproduced from Dunn et al. (2014) with permission of Annual Reviews, http://www.
annualreviews.org.
192 A N I M A L L O C O M OT I O N

locomotion is by becoming familiar with the meta- tats of today’s planet. Just as intriguing is a mysteri-
zoan tree of life—the metazoan phylogeny immedi- ous group of organisms, called the ediacarans, that
ately reveals the tremendous landscape of diverse had body plans not at all reflected in today’s ani-
forms and mechanisms worthy of study in the field mals and showed up in the fossil record approxi-
of animal locomotion. mately 640 mya and then disappeared around the
Yet even the structure of the metazoan tree of life time that today’s major animal groups emerged.
as it relates to locomotion is still intensely studied The ancient world of animal locomotor modes is
with its own uncertainty. The biggest areas of uncer- fundamentally important when considering the diver-
tainty remain at the base of the tree—right at the ori- sity of systems today—both in terms of the condi-
gin of controlled, dynamic locomotor movement. tions of their origins, but also the fact that these
The ­primordial origins of metazoans remain uncer- animals have been evolving within their own groups
tain, with the possibility that either the ctenophores for hundreds of millions of years and can be highly
(jellyfish-like creatures that locomote with bands of specialized to particular habitats. Although we
cilia) or the sponges root the tree. However, even spend little time on these questions in the scope of
with this uncertainty, the phylogeny of animals has this book, nearly all of the fundamentals of animal
yielded surprises in terms of the foundations of loco- locomotion we present in earlier chapters can be
motion. For example, nerves are found in every brought to bear on the interpretation of the locomo-
group except the sponges and placozoans (amoeba- tion of fossil animals. Indeed, many paleontologists
like multicellular animals), yet the use of electrical are also biomechanists—applying and testing their
signaling for controlling movement is present out- ideas from an understanding of today’s diversity of
side the animals: even single-celled paramecia con- animals to probe the functions, environments and
trol the direction of their movement through ion designs of ancient animals.
flow. The centralization of the nervous system is scat- Fundamental equations governing locomotion
tered throughout animals; the dorsal and ventral through different physical media, coupled with m­ aterial
nerve cords appear to have evolved or have been lost and mechanical property limits on locomotor systems,
multiple times across the tree. As we will discuss in have enabled scientists to successfully bring to life the
the next section, the multiple origins and conver- locomotion of fossil organisms. As a particularly
gence of systems that are considered fundamental to compelling example, by connecting the principles of
animal locomotion suggest a far more labile evolu- the limits on skeletal loading and the generation of
tionary process than thought previously, when verte- muscle moments (Chapter 2) with the forces of
brates were once considered the “apex” in an orderly bipedal locomotion on land (Chapter 4), researchers
ladder of increasingly complex locomotor design. were able to assess the limits on the locomotor ­abilities
As we examined the shared principles of the major of Tyrannosaurus rex: this massive dinosaur simply
locomotor modes in earlier chapters, it is intriguing could not have been a runner (Fig. 9.3) (Hutchinson
to consider the forces of natural selection that were and Garcia, 2002). This study performed analyses of
in place when these systems first appeared on the joint torque, muscle and bone loading, and ground-
planet. In fact, scientists and paleontologists have reaction forces that we covered in Chapter 4, ana-
uncovered a wealth of information about the timing lyzed with respect to the stress limits of muscle and
of the origins of major locomotor systems over the bone. Then, the actual dimensions of fossil dinosaur
planet’s history (Fig. 9.2). The major groups of ani- bones were incorporated into these general equa-
mals emerged during or just prior to the Cambrian tions. Once these lines of data were integrated, it was
period (540 mya) which means that the major loco- possible to place T. rex along a scaling continuum of
motor systems we study today were largely estab- organisms that can locomote at particular speeds.
lished hundreds of millions of years ago, raising This is only one example of a growing field that quan-
innumerable questions about the conditions of the titatively integrates the fundamentals of locomotor
planet at that time and how the cellular and tissue systems with fossil morphology to illuminate the
building blocks were shaped in environments that ancient world and the various successful and unsuc-
were profoundly different from the familiar habi- cessful pathways to today’s locomoting animals.
 E V O L U T I O N O F L O C O M OT I O N 193

Million
years
Ordovician
ago

Porifera Cnidaria Protostomia Deuterostomia

480

Bilaterian trace fossils

Chaetognatha

Burgess Shale-type preservation

Ambulacraria
Hexactinellid spicules
Ctenophora

Medusozoa
Archaeocyatha
500

Ecdysozoa
Anthozoa

Chordata

Calcite sea
Spiralia
Cambrian

Early skeletal fossils

Small shelly fossils

520

Aragonite sea
Doushantuo microfossils

540
Ediacaran fossils

560
Large ornamented Ediacaran microfossils

580 Gaskiers glaciation

Ediacaran

600

620

Marinoan glaciation
640
Cryogenian

Figure 9.2 The major groups of animals arose at varying time points over hundreds of millions of years ago with some groups, such as the
Ediacaran fossils, with body forms no longer in existence today. The environments and timing of the evolutionary origins of locomotion are key to
understanding and interpreting today’s diversity of locomotor systems. The solid gray bars indicate when major animal groups first appeared in the
fossil record (the lined bars indicate uncertain fossil evidence for these dates). Reproduced from Dunn et al. (2014) with permission of Annual
Reviews, http://www.annualreviews.org.

any level and ask about the foundations of v

­ ariation,
9.1.1 Origins of flight
origins and diversification of locomotion. Arguably,
Building on these very broad perspectives of loco- of all the classic unresolved questions in animal
motor evolution, it is possible to zoom in to nearly locomotion, the mechanical origins of flight remain
194 A N I M A L L O C O M OT I O N

(a) y

Pelvic pitch
Hip

Knee
Toe Ankle
x

(b)
100 200
6,000-kg chicken
90 180
IMPOSSIBLE Geometric 160
80
% extensor muscle mass per leg

chicken scaling

% total extensor muscle mass

70 140

60 120

50 Trex Lchick 100

NO RUNNING ABILITY Trex_1 (best guess)
Trex_2 80
40
Trex_Lgator
Trex_3
30 60
Small tyrannosaur
20 UNCERTAIN RUNNING ABILITY 40
Trex_4
Alligator Coelophysis Trex_lowest
10 20
Chicken BEST RUNNING ABILITY
0
100 101 102 103 104
Mass (kg)

Figure 9.3 By combining fossil morphology with information about the physiology and biomechanics of extant species, the locomotor
capabilities of extinct organisms can be estimated. A study of the running capabilities of Tyrannosaurus rex used the skeletal dimensions of fossil
specimens alongside the known limits of muscles and skeletal materials to predict T. rex’s running capabilities (or lack thereof). (a) A model of T.
rex was positioned in midstance and the moments around each limb segment were calculated. (b) The limits of running were then assessed based
on limb extensor muscle mass relative to body mass. Whether a single leg (left axis) or the total proportional extensor mass (right axis) relative to
body mass of T. rex were considered, fast running was impossible in these extinct animals. Adapted from Hutchinson and Garcia (2002) with
permission from Macmillan Publishers Ltd.

one of the most intensely examined and debated areas. out, and scientists have posited a wide range of
If one begins by simply examining the evolutionary ideas which they have tested through evolutionary,
tree of animals, it is clear that all flying animals do not physiological, developmental and physical m ­ odeling
share a common origin and that flight and wings have approaches. Like the T. rex example, scientists have
evolved multiple times through convergent evolu- applied the principles of flight in extant animals
tion. This process of mapping traits onto a tree is one and tested whether fossil organisms could have
of the simplest ways of incorporating evolutionary flown with particular morphologies and sizes (e.g.
thinking into locomotor studies. In this case, flapping Alexander et al., 2010); this kind of analysis is what
flight evolved independently at least four times: bats, led to the conclusion that some pterosaurs could fly
birds, insects and pterosaurs (flying reptiles). (Witton and Habib, 2010). In other approaches,
The evolutionary stepping stones to actual flight ­studies have examined animals that are almost flying,
capability have been exceedingly difficult to figure or that appear to be an example of a transitional form,
 E V O L U T I O N O F L O C O M OT I O N 195

and used those living examples to posit transitional 9.1.2 Evolution of legged terrestrial locomotion
forms in the origins of flapping flight (Marden and
Unlike the few, but significant origins of flapping
Kramer, 1995; Peterson et al., 2011).
flight, the origins and diversification of legs for ani-
Another approach is to look at earlier develop-
mal locomotion are so rich and variable that clear
mental stages of animals that fly as adults, but
transitions over evolutionary history are difficult to
don’t fly as juveniles to assess whether wings could
discern. Instead, the evolution of legged locomotion
have alternative or transitional functions. For
has emerged as a field that focuses on more central-
example, as we discussed in Chapter 6, one posited
ized developmental control and potential for vari­
pathway for the origins of flight in birds—that
ation that has enabled this rich diversity, rather than
was discovered through observations of chukkar
determining distinct transitions—with the one excep-
chicks—is that birds originally used flapping wing
tion of particular focus on the vertebrate-tetrapod
motion while running to help them ascend hills
transition from water to land.
and trees (Dial, 2003). Given that chicks do this
Again, with a simple glance at the metazoan tree
before they can fly, it seems plausible that natural
(Fig. 9.1), and given our knowledge that life origin­
selection might have acted on this initial capability
ated in a primordial ocean, it is not surprising that
to eventually transform the system to a fully air-
movement through water is present throughout
borne mechanism.
the tree. When and why marine animals transi-
While the chick example is a “ground-up”
tioned to land, and how their leg morphology and
hypothesis, others have proposed that flight origin­
mechanics changed with the transition, are not fully
ated from primordial gliding down from trees that
understood (Vermeij and Dudley, 2000). As just a
eventually evolved to controlled, wing-flapping
few ­examples: millipede ancestors moved to land in
flight. Support for these ideas come from today’s
the Late Ordovician, mites and ancient insects
organisms that glide from trees—such as snakes,
(apterygotes) transitioned by the start of the Early
rodents and a range of basal arthropods (Yanoviak
Devonian, ­tetrapod vertebrates and scorpions tran-
et al., 2005). However, these, and other theories for
sitioned in the Early Carboniferous. Numerous
the origins of flight, like the chick example, may
crustacean groups transitioned to land during the
simply be part of a broad array of effective mechan­
Cenozoic and even late Pliocene. Organisms also
isms used for navigating through air and do not
use legs for navigating on the benthos: many crabs
necessarily serve as evidence of the progenitor
can locomote in or out of water, echinoderms
mechanisms for true flight. These uncertainties
(such as sea stars) use a range of leg numbers and
have made it impossible thus far for scientists to
a myriad of tube feet to move through water and
definitively resolve the conditions and biomechan­
the intertidal, and even octopuses are known to
ical transitions that laid the groundwork for the
periodically “walk” along the seafloor (Huffard,
origins of flight.
2006).
Amidst these levels of uncertainty with the ori-
One arena that has received exceptional atten-
gins of flight, one long-standing debate related to
tion is the fish–tetrapod transition, specifically the
the evolution of flight has been resolved: the role of
key environmental shifts and associated morpho-
feathers. The role of or necessity for feathers in bird
logical changes of ancestral fish that accompanied
flight garnered considerable attention in early
the origin of tetrapod locomotion in ver­ tebrates
debates, but it is now clear that feathers preceded
(Fig. 9.4) (Long and Gordon, 2004; Shubin, 2009).
the origins of flight in the fossil record and that their
This is a particularly good example of how devel-
original function was most likely for thermoregula-
opmental processes, evolutionary diversification
tion—rather like fur (Xu et al., 2014). Therefore, the
and the fossil record can be combined to garner
more salient features of flight origins are the presence
major insights into the evolution of locomotion
of ­aerodynamic structures with muscular control
(Shubin et al., 1997). The fossil record contains
for flapping, essentially aerodynamic appendages
intriguing clues about the origin and diversification
that can generate lift and control movement through
of fin shapes and components that are homologous
the air.
196 A N I M A L L O C O M OT I O N

with the fore and hind limbs and digits of terres- Extinct taxa Extant taxa
trial vertebrate tetrapods. However, the linchpin for
Scyliorhinus
understanding the homologies of these systems canicula
was the discovery of the genes that control limb
development and diversification across body seg-
ments, called Hox genes. Once it was realized that a
Danio rerio
fairly short list of genes could control the presence,
absence and features of limbs and their processes,
the diversification of tetrapod limbs from fish fins
became not just probable, but highly supported by Polyodon
spathula
morphological, phylogenetic, paleontological, and
developmental genetic control (Zuniga, 2015). Even
with these fundamentals in place, much remains to be
Neoceratodus
resolved about these key transitions—innumerable forsteri
Sauripterus taylori
hypotheses have been posited for why tetrapods
moved to land, whether the transition occurred due
to limitations and competition in the aquatic environ-
ment or due to opportunities and new niches avail­
Eusthenopteron foordi
able on land.
In addition to sea-land transitions and the origin
of tetrapods, there have been many transitions
Panderichthys rhombolepis
in leg numbers—bipeds (primates, birds), quadru-
peds (mammals), hexapods (insects), octopods (2008 reconstruction)
(­spiders, ticks), decapods (some crustaceans) and the
animals with tens to hundreds of legs (remipedes).
The record is 750 legs found on a diplopod species Tiktaalik roseae
(the group including ­millipedes) (Marek and Bond,
2006)! The development of legs is a deep-rooted
aspect of animal biology that, at its most basic level, Acanthostega gunnari
is mediated through the control of Hox genes that
determine the types of appendages that develop at
particular body segments. Even within mammals, Tulerpeton curtum Gallus
gallus
the origin of bipedality, such as in jerboas (extreme
jumping rodents), the integration of genes, mechan-
ics and phylogeny have revealed both a centralized Homo
sapiens
control of morphology and an impressive potential
for diversification (Moore et al., 2015). However,
although the transition to the extremely long
Figure 9.4 Central to an understanding of the origin of vertebrate,
lengths of the jerboa’s hind legs is clearly related terrestrial tetrapod locomotion is the transition from fins to feet and
to jumping (and hopping), few studies have exam- the discovery of a “transitional” form, Tiktaalik roseae. The
ined the utility of having fewer or more legs in homologous bones of fins and feet (black) are depicted on a
particular environments or time points in evolu- phylogeny of extinct (left column) and extant (right column) fish and
tetrapods. Fossil morphological constructions and comparative
tionary history. While there are not easy answers
analyses of Hox genes have yielded a rich understanding of deep
for many fundamental questions in locomotion— homologies in evolution of limb bones and digits in terrestrial
even as basic as the origins and diversification of tetrapods. From Shubin et al. (2009) with permission from Macmillan
leg number—these kinds of questions are central to Publishers Ltd.
 E V O L U T I O N O F L O C O M OT I O N 197

understanding the costs and consequences of loco- Earlier in this chapter, we looked at the origins and
motor mechanisms. diversification of major systems of the whole organ-
ism, yet we can also gain tremendous insight at a
much finer level, such as at the tissue or cellular level,
9.2 From genes to locomotion
including the evolution of muscle itself. When actin
The evolution of animal locomotion began with the and myosin became organized within striated muscle
origin of movement at the cellular level—involving cells, the capabilities for animal locomotion exploded.
motor proteins, such as actin, myosin and dynein, Striated muscles have long been thought to be a
which operate motions ranging from intracellular shared, homologous feature of most animals; how-
organelle and ciliary movement to muscle contrac- ever, with new genetic approaches and a burgeoning
tions. Any kind of coordinated multicellular move- number of genomes available, scientists have recently
ment requires communication across cells and tissues. discovered that striated muscle evolved independ-
It is no coincidence that ions are used both for propa­ ently at least twice and possibly multiple times
gating action potentials in motor neurons and initi- (Fig. 9.5) (Steinmetz et al., 2012). One gene thought to
ating muscle contractions through the neuron-like be central to vertebrate striated ­ muscle (Myosin
membranes of muscle cells. The origins and evolution Heavy Chain, MyHC), was ­discovered to be present
of neurons and muscle cells are linked and probably even outside animals, demonstrating that it was not
share a cellular origin. The gradual specialization unique to vertebrate muscle. Further­ more, animal
into different cells is what eventually enabled the groups that have striated muscle (vertebrates, cnidar-
long-distance transmission and regionalization of ians and possibly ctenophores) do not all share the
the finely-tuned neuromuscular systems in many genes that code for critical components of vertebrate
animals. striated muscle, such as titin and the troponin

Only Euplokamis
(a) Cod (b)

Deuterostomia Protostomia Cnidaria Placozoa Porifera Ctenophora Choanozoa

(fish, frogs, (insects, (jellyfish) (Trichoplax) (sponges) (comb jellies) (unicellular
urchins) snails) flagellates)

Jellyfish

Figure 9.5 Striated muscle looks similar across metazoans when only using microscopy, but underlying genetics suggest that there were multiple
evolutionary origins of this muscle type. (a) Fluorescence microscopy of the striated muscles of cod and jellyfish revealed very similar structure
which has historically led to the conclusion that striated muscle only evolved once. (b) However, when the genes coding for the major structures of
striated muscle were analyzed, at least two independent origins of striated muscle were discovered. The stars indicate the clades in which striated
muscle evolved. An independent origin of striated muscle in ctenophores remains uncertain. From Hejnol (2012) with copyright permission from
Macmillan Publishers Ltd.
198 A N I M A L L O C O M OT I O N

complex. This indicates that striated muscle can be parative dataset is called phylogenetic comparative
built in different ways and this evolutionary conver- methods and is based on the use of independent
gence suggests strong selection pressure for aligned contrasts. Independent contrasts is the term for the
actin and myosin filaments for fine-tuned control of transformed data points that account for relatedness
animal locomotion. In sum, the organization of actin of the organisms underlying the dataset; with inde-
and myosin is based on genes shared even outside pendent contrasts, it is possible to perform ­statistics
the animals, with the result that different groups of correctly with properly independent data points.
animals locomote using striated muscle that evolved Now, there are numerous approaches, in addition
independently and is built of variable components, to independent contrasts, to correcting for phylo­
even though they look morphologically very similar. genetic relatedness and that enable more complex
This kind of integrative study—connecting phyloge- statistical analyses with both continuous and cat-
nies, genomes, genes, and cellular morphology— egorical data, such as phylogenetic least squares
exemplifies the power of these approaches in the field regressions (PGLS) (Nunn, 2011).
of animal locomotion and has fundamentally shifted One compelling example of the effects of includ-
our notion of the lability of locomotor evolution that ing the phylogenetic relationships of animals when
occurred at the very root of animal evolution. studying locomotor scaling emerged from an analysis
of adhesive scaling (Fig. 9.6) (Peattie and Full, 2007).
In this case, the density of fibrillar adhesive struc-
9.3 Comparative methods and animal
tures was plotted against the size of the animals—
locomotion including everything from flies to lizards. If the
In most of the examples thus far in this chapter, con- phylogenetic relationships of these animals were
clusions about locomotor evolution were based on not considered, then a clear and strong positive
the integration of multiple types of data and the relationship between an animal’s size and the density
mapping of trait origins and losses onto a phylogeny. of adhesive structures is evident. However, when the
These basic approaches tell us about independent evolutionary relationships were incorporated, this
origins, convergences, timing or sequences of traits. scaling relationship dissolved, and it was abun-
However, much of the richness of evolutionary ana- dantly evident that more closely related animals do
lyses can be found in methods that enable robust, not scale with the steep slope indicated when all the
quantitative and statistics-based hypothesis testing, species are treated as independent data points. A
which are the topic of this section. more recent study performed a series of statistical
In the 1980s, there was a seismic shift in the think- analyses of an even larger dataset that probed the
ing about how to quantitatively analyze compara- scaling relationships of adhesive area and animal
tive datasets (comparative datasets are compilations size, and again found that by incorporating phylo-
of data from multiple species) (Felsenstein, 1985). genetic relationships into the analysis, the scaling
Scientists might plot the data collected from loco- slope was reduced (Labonte et al., 2016).
moting animals, for example, in terms of stride fre- While capturing the actual scaling relationships
quency relative to body size, and then perform a can be essential for problems like adhesion, for which
regression to calculate the scaling relationship. the mechanism of supporting a particular body weight
However, Felsenstein’s seminal work recognized is central to its function, the deviation from scaling
that a foundational rule of statistics—the independ- rules can be equally informative when considering
ence of data points—was violated when comparing the particular effects of habitat or even tradeoffs
species with differing degrees of relatedness. In between key variables. As we saw earlier in Chapter
other words, just by virtue of being more closely 7 (Fig. 7.4), the scaling rules for leg length and jump
related, some species’ data should be more similar distance did not turn out to capture the full variation
to each other than to others and, therefore, the data of jumping frogs. In this case, scientists combined
are not independent and cannot be analyzed using morphological and kinematic data with a phylogeny
standard statistics. The first new set of methods that and comparative dataset of frog habitats (Gomes
accounted for phylogenetic relationships in a com- et al., 2009). They measured scaling using i­ ndependent
 E V O L U T I O N O F L O C O M OT I O N 199

(a) 108 (b) 0.8

0.6
107
Spatular density per mm2

Log(spatular density) ICs

0.4

6
10
0.2

105 0

–0.2
104

–0.4
10–3 10–2 10–1 100 101 102 103 0 0.5 1 1.5
Body mass (g) Log (body mass) ICs
wet dry

Figure 9.6 The incorporation of phylogenetic relationships into statistical scaling analyses can dramatically change the conclusions. In a classic
study on the scaling of fibrillar adhesives relative to body mass across numerous animal species, the density of the adhesive fibers (spatula density)
was plotted relative to the mass of the animal. When a linear regression was applied to all of the raw data together, a strong positive scaling
relationship resulted (solid line). However, when the data were split into two general mechanical categories, such as whether the fibrillar system is
associated with significant fluid (wet) or minimal fluid (dry), the scaling relationship disappeared (dashed lines). (b) The same data were analyzed
using independent contrasts (ICs) based on the phylogeny of animals. Here the phylogenetically-corrected dataset indicated a lack of a strong
positive relationship between spatula density and body mass. Adapted from Peattie and Full (2007); copyright (2007) National Academy of
Sciences, USA.

contrasts and then incorporated the categorical traits to analyses performed with the untransformed spe-
for environments using a regression approach. Their cies values (Garland and Janis, 1993; Losos, 1990;
study statistically demonstrated that fossorial anuran Vidal-García and Scott Keogh, 2017). A variety of tests
species were significantly different from jumpers in can be used for assessing the influence of ­phylogeny
other habitats, suggesting diversification into par- on trait distributions, most often through the calcu-
ticular habitats can necessitate specific shifts in morph­ lation of lambda (Freckleton et al., 2002), which is
ology. Taking these approaches even further, with equal to zero when the traits are distributed as if
more sophisticated phylogeny-based methods, a later they were from a star phylogeny (all equally similar
study examined the relative roles of historical con- to each other) and equal to one when the traits fol-
straints, geography and habitat on the diversification low a distribution that matches the phylogenetic
of frog jumping (Moen et al., 2013). The results of this tree (using a Brownian motion model of evolution
rich study clearly demonstrate the interacting and and the branch lengths of the tree). With the advent
potent influences of evolutionary contingency (such of PGLS and the use of R statistical programming to
as the morphology of ancestors) and the habitat- implement these calculations, the calculation of
based pressures that lead to convergent morphology lambda is now embedded in the process of account-
across distinct lineages that occupy similar habitats. ing for phylogeny, and if there is not a strong influ-
Given that many scientists who study locomotion ence of phylogeny (i.e. lambda = 0 ), PGLS simply
are fundamentally interested in the relationships runs as a regression of the raw, untransformed data
among traits, especially scaling, these methods are (Orme et al., 2012). Therefore, many of the earlier con-
central to correctly estimating trait correlations. cerns about first testing for the effects of phylogeny
However, phylogenetic relationships do not always are now alleviated through this streamlined process
strongly influence the distribution of the traits and of running comparative analyses using PGLS in R.
accounting for phylogeny through these methods It is widely recognized that when scaling ana­
need not always change the results when compared lyses are performed blind to the relationships of the
200 A N I M A L L O C O M OT I O N

organisms underlying the dataset, the scaling slopes on control principles exemplified by the banking turns
can be overestimated and incorrect (Harvey and Pagel, of swallows and swifts. These observations of animal
1991; Nunn, 2011; Taylor and Thomas, 2014). Even capabilities and the diversity of forms that e­nable
with this important step forward for correctly ana- distinct flying strategies both initially inspired and
lyzing comparative data, three major roadblocks continue to drive forward the engineering design of
stood in the way for most animal locomotor biolo- flying machines. Indeed, like these great inventors
gists until recently: the existence of resolved phylo- from human history, today’s engineers are focusing
genetic trees, the ability to collect large datasets about on emulating flying insects. Insects make use of
locomotion given the technical hurdles (such as using subtle energy-saving and stability ­mechanisms, espe-
reels of film rather than the today’s ease with digital cially through vortex formation and manipulation
image analysis) and computational limitations of by flexible airfoils, that engineered flying machines
running the phylogeny-based analyses. These road- are largely still unable to do.
blocks are no longer as much of a challenge for today’s Nonetheless, the study of animal locomotion and
biomechanicians (although this clearly depends on the the inspiration for engineering design has been
particular system and the technical hurdles of acquir- fraught by the problem of adaptationist story-tell-
ing substantial comparative datasets), such that the ing, or, as formalized in the 1970s and targeted espe-
focus revolves around which, of many, analyses to use cially at the fields of biomechanics and physiology, the
when analyzing comparative datasets and how to “Spandrels” problem (Gould and Lewontin, 1979).
draw strong conclusions given the inherent correla- While it can be quite easy to point to a particular
tive nature of many scaling studies. structure and ascribe special mechanical utility to
The power and diversity of phylogeny-based it, what appears to be a structurally important fea-
methods for analyzing animal locomotion consti- ture may simply be an ornament or a by-product of
tute a burgeoning field. Today’s evolutionary com- the vagaries of evolutionary history—like the span-
parative analyses can examine a host of central drels of the great European cathedrals. It is tempt-
issues in animal locomotion, including: (1) the tim- ing to look at animal locomotion as highly optimized
ing and statistical probability of locomotor origins, and worthy of emulation, yet biologists should be
such as particular modes (e.g, flight) or morpholo- familiar with the vagaries of evolutionary history
gies (e.g. bipedal jumping), rates and accumulation and the fact that changing environments leave
of evolutionary change; (2) the correlates of diversi- major footprints on any biological mechanism.
fication rates (how fast certain clades diversify); (3) Likewise, the history of humans tinkering with
the evolutionary integration and lability of locomotor device designs over time can also yield peculiar,
mechanisms and traits; (4) the influence and correl­ non-optimal designs, such as today’s computer
ation of ecology and habitat on locomotor features; “QWERTY” keyboards that were originally designed
and (5) one of the most fundamental of questions in with letters in particular locations to avoid jamming
animal locomotion—the scale effects of body size the arms of manual typewriters and do not opti-
on locomotor traits. This rich arena is beyond the mize today’s process of typing on computer key-
scope of this chapter, but continues to be covered boards. Teasing apart the key biological features for
extensively through new publications and books effective engineering design is much harder than it
(Nunn, 2011; Taylor and Thomas, 2014). initially appears and is a rich arena for the use of
evolutionary analysis to interpret the relevant prin-
9.4 The relevance of evolution to ciples in locomotion to engineering design.
As we have seen in early chapters of this book,
robotics and bio-inspired design
some engineers have resolved this issue by simply
Evolutionary diversity has served as an inspiration looking to animal locomotor mechanisms for inspir-
for human devices for as long as humans have been ation to broaden their creative ideas for e­ ngineering
documenting their design ideas. Da Vinci was design (i.e. bioinspiration), rather than as mechan-
­obs­essed with the soaring ability of kites in his isms for emulation (i.e. biomimicry) (Flammang
Codex on Flight. The Wright Brothers were focused and Porter, 2011). However, in this chapter, we
 E V O L U T I O N O F L O C O M OT I O N 201

look more closely at two other strategies that take a settings. For example, they identified three ­performance
more quantitative approach to engineering design objectives that are key determinants of soaring
based on biological systems (Patek, 2014). First, flight in birds—glide speed, sink rate and turning
some scientists and engineers consider biological radius—yet also are impossible to maximize simul-
comparative datasets as goldmines of information taneously. For example, increasing glide speed causes
of past evolutionary experiments that have the a decrease in turning performance (i.e. increasing
potential to reveal how fundamental tradeoffs in turning radius). Similarly, with increasing glide
design strategies and shifting environments have speed comes an increase in sink rate, which is also
yielded a dataset of trait combinations that could not ideal for maintaining effective soaring. Their
also be useful for engineering design. A second analysis reveals that soaring land (Accipitriformes)
strategy is to determine the fundamental physics or versus water (Procellariiformes) birds have resolved
underlying equations for a locomotor system, exam- these tradeoffs differently. For example, vultures
ining the biological dataset to explore congruence express a suite of equally optimal combinations of
or lack of congruence, and then making designs that turn radius and glide speed that exceed the resolution
are effective based on physical principles or the of this tradeoff in other species, whereas albatross
principles of evolution by natural selection. These species achieve equally optimal combinations of
strategies are not mutually exclusive—engineers sink rate and glide speed that place their soaring
can incorporate all of these processes in their ­creative capabilities—specifically in the context of these two
and strategic design process. variables—ahead of other species. Even though these
Taking a quantitative and strategic approach to results are not necessarily novel in the context of
biology-based engineering designs, rather than the understanding bird wing evolution, the application
more qualitative process of biomimicry and bioin- of these methods provides a pathway for analyzing
spiration, has involved a suite of approaches that comparative datasets that can enable engineers
are rapidly developing. Addressed in a recent book to exam­ine how evolutionary diversification has
on evolutionary biomechanics (Taylor and Thomas, ex­pressed the resolution of multiple competing
2014), one approach is to examine biological data- objectives while pinpointing the features that
sets not as a search for a single optimal performance should be useful for improving engineering design.
outcome—which is exceedingly difficult to define The above example incorporated tests of datasets
in the multi-faceted ecology of evolving organ- representing existing organismal diversity, yet it is
isms—but instead as a space of competing variables also possible to perform similar analyses using
that can produce equally good outcomes. Like the mathematically-modeled organisms. Using the
name implies, a method called multi-objective opti- same fundamental physical principles of locomo-
mization calculates how various parameters can be tion covered earlier in this book, virtual, locomot-
combined to yield multiple, equally good performance ing organisms can be evolved and compared to real
outcomes (termed Pareto sets). This approach moves evolutionary diversity, with the goal of pinpointing
away from the “Spandrels” problem of adaptationist engineering design principles that are informed by
thinking that assumes a universal performance opti- the resolution of competing design tradeoffs. For
mum and instead provides a quantitative founda- example, based on a mathematical model of muscle
tion for understanding how multiple, competing contraction, and the opposing objectives of reducing
variables can yield multiple combinations that are cost of transport and increasing swimming speed
equally effective—a rich and valid dataset for design through body shape and dimensions, researchers
principles for engineered systems. successfully simulated a realistic range of fish body
Taylor and Thomas (2014) examine this approach shapes and swimming speeds that reflect the evolu-
in an analysis of bird soaring, wing form and glid- tionary diversity of fish (Fig. 9.7) (Tokić and Yue,
ing aerodynamics to tease apart the competing 2012). The goal of this study was to probe how vir-
­variables that, over evolutionary history, have ­enabled tual fish shapes would evolve, given realistic axial
soaring, and flight more generally, to evolve and muscle activation models driving caudal fin pro-
operate in a variety of environments and ecological pulsion that were “virtually” presented with the
202 A N I M A L L O C O M OT I O N

Rainbow trout Atlantic cod Bottlenose dolphin

data prediction data prediction data prediction

L (m) 0.1 – 0.7 0.46 L (m) 0.4 – 0.7 1.28 L (m) 2.5 – 3.0 2.30
v (m s–1) 0.3 – 2 1.09 v (m s–1) 0.7 – 0.95 1.12 v (m s–1) 1–7 1.72
v/L (len s–1) 1.5 – 6.5 2.37 v/L (len s–1) 1.2 – 2.2 0.88 v/L (len s–1) 0.5 – 3.0 0.75
t (s) 0.2 – 0.75 0.32 t (s) 0.3 – 0.55 1.07 t (s) 0.3 – 2 1.15

Great sandeel Atlantic salmon Bluefin tuna

data prediction data prediction

L (m) 0.15 – 0.40 0.21 data prediction
L (m) 0.3 – 0.7 0.46
v (m s–1) 0.35 – 0.50 0.43 v (m s–1) 0.5 – 2.5 1.09 L (m) 1.7 – 2.5 1.32
v/L (len s–1) 1.4 – 1.8 2.05 v –1
(m s ) 1.2 – 3.5 0.38
v/L (len s–1) 0.8 – 3.6 2.37
t (s) 0.28 – 0.40 0.55 t (s) 0.2 – 0.75 0.40 v/L (len s–1) 0.6 – 1.65 0.29
t (s) 0.55 – 1.45 0.81

Figure 9.7 Computer simulations using realistic muscle dynamics coupled with tradeoffs between cost of transport and swimming speed yielded
fish body shapes that are similar to forms found in biological systems. Multi-objective optimization and evolutionary algorithms can be used to
“evolve” organisms that exist solely in a computer with the broader goals of finding general design principles to explain biological diversity and
inform engineering design. This study revealed close similarity in shapes of synthetic (prediction) and biological diversity (data). The authors
compared body length (L), swimming speed (v), relative swimming speed (v/L) and duration (t) across the modeled and real fish. Adapted from
Tokić and Yue (2012) by permission of the Royal Society.

challenge of resolving a fundamental tradeoff, such design. Researchers often also incorporate physical
as swimming speed versus cost of transport (COT). modeling and hypothesis-testing with live animals,
The results are striking—the model generated a alongside mathematical modeling. In sum, there is
range of recognizable fish forms, such as a tuna- great potential for new engineered devices based
shaped fish that has very low COT, but that was on animal locomotion and for integrative, first-
achieved through a shape and muscle activation principles approaches that explain the physics of
that simultaneously caused a reduction in swim- movement and thus inform both biological and
ming speed (in terms of lengths per second). The engineered locomotor systems.
tuna-like fish that evolved from the simulation
resolved the COT-swimming tradeoff quite simi-
9.5 Summary
larly to how tradeoffs during the evolutionary
diversification of actual tunas are thought have This chapter provided a brief glimpse into the
been manifested. As previously mentioned, this remark­able and innovative ways that researchers
type of analysis can inform engineering design are approaching the realm of locomotor evolution.
principles of aquatic locomotor systems that bal- Beginning at the broadest possible level—address-
ance the needs and tradeoffs of cost of transport, ing the topology of the metazoan tree—and then
size, shape and actuation of deployed devices in zooming in to various levels of analysis has yielded
diverse environments. rich findings about the origins of striated muscle,
These are only a few examples of the rich array of transitions to terrestrial legged locomotion, and
quantitative and principled approaches that are now even the genetic basis of the diversity of limbs. The
taken to examine locomotor evolution and have the methods used for analyzing locomotor evolution
potential to serve as a test-bed for novel engineering have advanced significantly over the past few dec-
 E V O L U T I O N O F L O C O M OT I O N 203

ades and now enable quantitative and statistical ana­ with a robust array of quantitative, comparative
lysis of fundamental questions, such as the relative methods and yielding considerable i­ nterdisciplinary
roles of evolutionary contingency and the selective impact on the fields of biomechanics, paleontology,
pressures of particular habitats on the diversity and evolutionary biology and e­ ngineering design.
convergence of locomotor mechan­isms. In previous
chapters, we touched on the various engineering
Additional reading
innovations arising from animal locomotion, and
here we examined the quantitative and principled Dunn, C. W., Giribet, G., Edgecombe, G. D. and Hejnol, A.
ways that researchers are gleaning engineering design (2014). Animal phylogeny and its evolutionary implica-
insights from ­locomotor diversity, such as through tions. Annu. Rev. Ecol. Evol. Syst. 45, 371–95.
Nunn, C. L. (2011). The Comparative Approach in Evolutionary
mathematical ­simulations and analysis of compara-
Anthropology and Biology. Chicago: The University of
tive datasets. The stunning diversity of locomotor
Chicago Press.
mechanisms and animal forms that populated the Taylor, G. K. and Thomas, A. L. R. (2014). Evolutionary
earlier chapters of this book are now being examined Biomechanics. Oxford: Oxford University Press.
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 Index

Note: Tables and figures are indicated by an italic t and f following the page number.

A body weight, jump scaling dinosaurs 192, 194f

acceleration reaction 95 150, 151f distributed control 183–5
actin 12–15, 197–8 bone fracture 29–30 diversity of animals 190, 191f, 192
activation-relaxation 49–52 bouncing gaits 79–80 dorsal root ganglia 170–2
added mass 95 boundary friction 161 downhill running 53
adhesion 160–2, 161f branches 158–9 drag 2, 40–1, 90–1, 93–5, 94f, 115–18,
adhesive scaling 198–200, 199f 116f, 148–9
aerobic capacity 59 C coefficient 92–3
aerobic metabolism 34–5, 42, 42f calcium 14 friction 91, 95, 119
afferent nerves 166f, 167, 185–6 campaniform sensillum 169 induced drag 121
air 2t carbohydrates 35 pressure 91, 95, 119
airflow 116f carbon dioxide production 35 dry adhesion 160
allometric (allometry) 8–9 carrangiform swimming 97 dynamic soaring 124
allometric equation 9 cartilage 29 dynamic viscosity 2t
anaerobic metabolism 34, 42, 42f cellular metabolism 34–5 dynein 103, 104–5
anguiliform (undulatory) swimming central pattern generators
96–7, 97f (CPGs) 183–5, 184f, 188 E
apodeme 169 cilia 107 ectotherm (metabolism) 37–8,
aspect ratio 117, 118, 119t circulation 115–17 38f, 40, 187
asynchronous muscle 136 circulatory airflow 116f energy patterns 41–2, 42f
ATP (adenosine triphosphate) 13–14, clap and fling 144 effective mechanical advantage
22–3, 27, 34–5, 36 claws 159–60, 160f (EMA) 87–8
attachment mechanisms 158–62 climbing 158–62 body size vs. 66–7
branches 158–9 definition 66f
B robots 163 efferent nerves 166f, 167,
balance 158 coefficient of drag 92–3 185–6
banked turns 140–1, 140f coefficient of friction 74 efficiency 3
bending 5–6, 6f collagen type I 29 hydrodynamic 107
biological wheels 61–2 collisional mechanics 80–2, 81f muscle 16–18
biomechanics of support 3–7 comparative evolution 198–200 elastic energy 85–8, 86f, 87f
loading, modes of 5–6 compression 5 elasticity
safety factors 6–7 cost of transport (COT) 41, 46f, 202 linear, non-linear 3
bipeds countercurrent heat exchangers 59 muscles 15–16
effective mechanical advantage counter-movement jumping elastic (Young’s) modulus 4
vs. 67 153, 154f elastic properties, muscle 15–16
evolution 196–7 CPGs (central pattern generators) electromyogram (EMG) 181–2, 181f,
running 72 183–5, 184f, 188 187, 188f
stride frequency and cross-bridge cycling 14 EMA see effective mechanical
length 71f advantage (EMA)
blood-flow measurements 50–1 D endoskeletons 27, 28–30, 29f
body mass, surface area and 10f deformation 4f endotherms 38f, 40
body size 47–52, 47f, 48f delayed stall 144–5 energy patterns 41–2, 42f
effective mechanical advantage density 2t, 91–2 endplate (motor) 174–5, 177
vs. 66–7 dimensions 9, 11 endurance 40
220 INDEX

energetics of movement 2–3, 34–60 flapping counter-torque (FCT) 140–1, genetics of locomotion 197–8
body size 47–52, 47f, 48f 142–3 geometric similarity (isometry) 7f
cellular metabolism 34–5 flapping flight 125–32 glide angle 123
comparison of costs 55–6, 57f circulation changes 127–9, 128f glide speed 123
endurance 40 flight speed 127–9, 128f gliding flight 121–4, 122f
fatigue 40 intermittent flight 129–30, 129f Golgi tendon organs 165–6, 168–9
flight 54–5, 56f kinematics 125–7 ground reaction force 62f, 63f, 75–6
incline running 52–3, 52f origins and evolution of 130–2,
increased aerobic capacity 59 192–5 H
intermittent exercise 56–9 wake patterns 127–9, 128f haltere 186–7
swimming 53–4, 54f, 57f flight heat capacity 2t
terrestrial speed 40–7, 41f, 42f dinosaurs 194–5 Heitler’s lump 156, 155f
time course of energy usage energetics of 54–5, 56f heterocercal tails 98–9
35–40, 36f evolution 201 hexapods 196–7
energy gliding flight 121–4, 122f Hill, A V 16, 149
costs of gait 43f, 44–7, 45f, 46f intermittent flight 129–30, 129f homocercal tails 98–9
costs of running 44, 47, 49 maneuvering 139–42, 140f hopping 43–4, 43f, 68
elastic 4 metabolic rate 55 potential and kinetic energy 79–80
metabolic 3 origins of 193–5 hovering 120f, 125, 126f, 136
time course of usage 35–40 speed of 127–9, 128f hydrostatic skeletons 27, 30–1
environmental media 1–2 stability 142–3 hydroxylapatite 29
locomotion effects 2t vertebrate flight musculature 133–4
physical properties 1–2, 2t see also flapping flight; soaring I
EPOC (excess post-exercise oxygen flight motors 132–9 incline running 52–3, 52f
consumption) 37, 37f, 57–8 insects 136, 137f, 138 increased aerobic capacity 59
evolution power outputs 134–6 induced drag 121
flight 201 thermal issues 138–9 induced power 120f
robotics and 200–2 vertebrate musculature 133–4 inertia 91–3, 114
swimming 201–2, 202f flow insects
evolutionary tree (phylogeny) turbulent 95 flight motors 136, 137f, 138
191f, 193f unsteady 95 local reflex pathways 172–4
excess post-exercise oxygen flow tanks 100f sensory organs 169
consumption (EPOC) 37, flow visualization 99–100, 100f see also invertebrates
37f, 57–8 FOG (fast-oxidative-glycolytic) intermittent exercise 56–9
excitation-contraction coupling muscle fibers 22–3, 22t intermittent flight 129–30, 129f
20–2, 21f force 2–3, 4f intermittent swimming 58–9
exoskeletons 21f, 27, 30 dimensions 11t interneurons 167, 170–2, 173–4,
exteroreceptors 169 generation by muscle 12–14, 183–5
extrafusal muscle fibers 166f 14–16, 15f, 16f intrafusal muscle fibers 166–7
response of materials 5f invertebrates
F units 9 motor recruitment 174t, 177–82,
factorial metabolic scope 39–40 force–deformation 5f 178t
fast-glycolytic (FG) muscle fibers force economy 26–7 muscle fibers 178–9
22–5, 22t, 24f friction 159–62 neuromotor organization 179, 181
fast-oxidative-glycolytic (FOG) drag 91, 95, 119 stride frequency and length
muscle fibers 22–3, 22t Froude number 51, 108–9 70, 71f
fatigue 40 fusimotor nerves 167 see also insects
fats (lipids) 35 isometric force-length relationship
FCT (flapping counter-torque) G 14–16, 15f, 16f
140–1, 142–3 gait phase 66f isometry (geometric similarity) 7f
feathers 195 galloping 68–9 isotonic contraction 12
FG (fast-glycolytic) muscle fibers energy costs 46f isotonic force-velocity 16–18, 17f
22–5, 22t, 24f potential and kinetic energy 79–80
fixed-gear hypothesis 129f, 130 ganglia J
flagella 104–7, 105f, 106f dorsal root 170–2 jetting 103–4
flagellin 104–5 motor 173f, 179, 181f, 183–4, 188 joint torques 32, 64–7
flap-gliding 130 segmental 173, 179 joint work 72–3
 INDEX 221

jumping 72–3, 147–57, 150t motion, range of 32–3 ‘non-spiking’ interneuron 173–4
power enhancements 152–6, 152f motor ganglia 173f, 179, 181f, 183–4, ubiquity of 192
robots 163 188 neuromotor organization,
running jumps 147, 153 motorneurons 21–2 invertebrates 179, 181
substrate interaction 154f, 156–8 motor recruitment 174–82 neurotransmitter 175, 177
jump scaling 149–51 invertebrates 174t, 177–82, 178t non-equilibrium gliding 123–4
body weight 150, 151f vertebrates 174–7, 174t, 176t ‘non-spiking’ interneuron 173–4
limb length 150–2 motor units 20–2, 167, 170–2, 172–3, non-steady state movement 72–3
muscle 149–50 174–7, 185, 187
distribution 176–7 O
K muscle 12–27 octopods 196–7
kinetic energy, running 79–80 antagonistic sets 31–2, 31f origins of locomotion 192, 193f
Krebs cycle 36–7 asynchronous 136 oxygen
efficiency 16–18 consumption 3, 35
L elastic properties 15–16 content of air and water 2t
laminar flow 93, 95 excitation-contraction post-exercise oxygen recovery 36–8
latches 155–6, 155f coupling 20–2, 21f rate of oxygen consumption
leading edge 116f fibers see muscle fibers (VO2) 35
leading edge vortex (LEV) 147 force development/generation storage 59
legged robotics 82 12–14, 14–16, 15f, 16f, 49–52, 50f oxygen debt 37, 38f
LEV (leading edge vortex) 147 isometric force-length relationship oxygen deficit 36–8, 37f, 38f
lift 98, 102–3, 115–18, 148–9 14–16
coefficient 116–17 jump scaling 149–50 P
rotational 144 molecular organization 12–14 paddles 108
limbless locomotion 82, 83f, 84 motor units see motor units parallel-fibered muscle 25–7, 25f, 26f
limbs 62–4 neural control 71–2 parasite power 119–21
effective mechanical advantage vs. power 16–18 particle image velocimetry
scaling 67 shortening mechanisms 12–14 (PIV) 101–2
length and jump scaling 150–2 spindle organs 165 PCr (phosphocreatine) 36
mechanical advantage 64–7 striated muscle 197–8, 197f pectoral fins 101f
limb swing 49–52 structure 13f pendular locomotion 162–3
linear maneuverability number work loops 18–20, 19f PGLS (phylogenetic least squares
(LMN) 76 muscle dampers 85–8, 86f, 87f regressions) 198–200, 199f
lipids (fats) 35 muscle fibers 32 phosphocreatine (PCr) 36
LMN (linear maneuverability architecture of 25–7, 25f, 26f phylogenetic least squares regressions
number) 76 extrafusal fibers 166f (PGLS) 198–200, 199f
loading, modes of 5–6 intrafusal fibers 166–7 phylogeny (evolutionary tree)
local reflex pathways 169–74 invertebrates 178–9 191f, 193f
insects 172–4 parallel-fibered 25–7, 25f, 26f physics of movement 2–3, 192
vertebrates 170–2 pinnate-fibered muscles 25–7, pinnate-fibered muscle 25–7, 25f, 26f
25f, 26f PIV (particle image velocimetry)
M types 22–5, 22t, 133, 175–9, 186–7 101–2
Magnus effect 144 muscle spindles 166–8, 166f polyneuronal innervation 21
maneuverability 73–6, 74f myosin 12–15, 197–8 post-exercise oxygen recovery 36–8
MAS (maximum aerobic speed) 41 posture changes 66f
mass-specific cost of transport 57f N potential energy, running 79–80
mass-specific metabolism 8, 47 nerves power 3
materials, force and stress responses afferent 166f, 167, 185–6 flight motor outputs 134–6
to 5f efferent 166f, 167, 185–6 induced 120f
maximum aerobic capacity 38f, 39–40 fusimotor 167 muscle 16–18
maximum aerobic speed (MAS) 41 Ia sensory 166f, 167, 168f, 182 parasite 119–21
mechanical properties of structure 4f Ib sensory 166f, 167, 168–9 profile 119–20
mechanosensory nerves 173–4, 186 interneuron 167, 170–2, 173–4, predictive scaling equations 151
metabolic energy cost 49–52, 50f, 51f 183–5 preferred speed 44
metabolic rate 41f mechanosensory 173–4, 186 pressure, drag 91, 95, 119
flying 55 (alpha) motor 167, 182, 183–4 proprioceptors (proprioceptive)
momentum 90, 97, 103–4 muscle control 71–2 166, 169
222 INDEX

Q size-normalized speed 115t swimming

quadrupeds ‘size principle’, 175–6 energetics of 53–4, 54f, 57f
evolution of 195–7, 196f skeletons 27–33 evolution 201–2, 202f
stride frequency and length 71f bone fracture 29–30 intermittent 58–9
hydrostatic skeletons 27, 30–1 surface swimming 108–9
R jointed levers as 31–3 thunniform swimming 97–8, 98f
rakes 108 SLIP limb mechanics 80, 82 undulatory (anguiliform)
range of motion 32–3 slow-oxidative (SO) muscle swimming 96–7, 97f
rate of oxygen consumption fibers 22–5, 22t, 24f work loops 20
(VO2) 35 soaring 124, 125f swing phase 62–4
reciprocal inhibition 167–8, 182 dynamic 124
reflex, stretch 188 thermal 124 T
resilin 156 see also flight take-off 147, 148–9, 148f
respiratory quotient (RQ) 35 SO (slow-oxidative) muscle take-off angle 147–8, 150
respirometry 35 fibers 22–5, 22t, 24f temperatures 59
Reynolds number 91–3, 92t, 104, spandrels 200–1 tendons 27–8, 28f, 31f
108, 114 speed 40–7, 49, 57 rupture 29–30
flow patterns 94f energy costs 44 springs 85–8, 86f, 87f
robots 82 flight 127–9, 128f tension 5–6, 6f
climbing 163 preferred speed 44 tetrapod locomotion see
evolution and 200–2 running maxima 69f quadrupeds
jumping 163 size-normalized speed 115t thermal soaring 124
legged robotics 82 spindle organs 165 thermoregulation 131–2
water locomotion 112 springs 155–6 thrust 90–1, 91f, 97–8, 99f, 102–3,
RQ (respiratory quotient) 35 stability 73–6, 74f 115–18
running 68 Standard International (SI) thunniform swimming 97–8, 98f
bipeds 72 system 9, 11 titin 14
downhill running 53 static frictional gripping 159–60, 159f tonic fibers 20
energy costs 44, 47, 49 steady flow 93–5 torsion 6
incline running 52–3, 52f steady state metabolism 36–8 trailing edge 116f
potential and kinetic energy 79–80 steady state movement 72–3 traveling wave 82, 84
speed maxima 69f step length 51f trotting 68
water surface 111–12, 111f stiffness 3 energy costs 44, 46f
see also galloping; trotting stored elastic energy 153–5, 157f potential and kinetic energy
running jumps 147, 153 strain 3–4, 4f 79–80
response of materials 5f turbulent flow 95
S streamlines 93–5, 94f, 96f turning 73–6, 74f
safety factor 6–7 strength 6 twitch 174–5
sarcomere 12–14, 13f, 15, 15f stress 3–4, 4f twitch fibers 20
scaling 7–9, 107–8, 117–19 dimensions 11t Tyrannosaurus rex 192, 194f
second moment of area 6 stress–strain graphs 5f
segmental ganglia 173, 179 striated muscle 197–8, 197f U
sensory elements 165–9 stride frequency 69–70, 71f undulatory (anguiliform) swimming
Ia sensory nerves 166f, 167, 168f, stride length 69–70, 71f 96–7, 97f
182 stroke angle 125–7, 126f units 9, 11
Ib sensory nerves 166f, 167, 168–9 stroke path 126f unsteady aerodynamic mechanisms
insect sensory organs 169 stroke plane 126–7 143–6
vertebrate sensory organs stroke plane angle 126f unsteady flow 95
165–9, 171f substrate, jumping 154f, 156–8 unsteady left generating
shear (stress) 91–2 support, biomechanics of see mechanisms 141
sidewinding 84 biomechanics of support
SI (Standard International) support phase 61–2, 62–4 V
system 9, 11 surface area, body mass and 10f van der Waals forces 160
size 7, 53, 90–3, 108–12, 117–19, surface swimming 108–9 velocity
131–2, 135f, 136, 138–9, 150–2, surface tension 108–12, 110f dimensions 11t
158, 161–2, 179–80 suspensory locomotion 162–3 units 9
see also body size sustainable activity 39–40 ventral spinal nerve root 171f
 INDEX 223

vertebrates W loading 118–19, 119t

flight musculature 133–4 Wagner effect 144 shape 128–9
motor recruitment 174–7, 174t, 176t wake patterns 127–9, 128f work 3
sensory organs 165–9 wake recapture 144 dimensions 11t
viscosity 2, 2t, 91–5, 104 walking 44, 46f, 47, 49 work loops 18–20, 19f
VO2 (rate of oxygen water 2t
consumption) 35 weight-support cost model 51 Y
vortex 90, 102–3, 102f wet adhesion 160 yaw-based turn 141–2
leading edge vortex 144 wing Young’s (elastic)
shedding of 117f anatomy 132–9, 132f modulus 4