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Library of Congress Cataloging-in-Publication Data:
Wong, J. Y. (Jo Yung)
Theory of ground vehicles I J.Y. Wong.-3rd ed.
p.
cm.
Includes bibliographical references and index.
ISBN 0-471-35461-9 (cloth : alk. paper)
1. Motor vehicles-Design and construction. 2. Motor Vehicles-Dynamics.
Ground-effect machines-Design and construction. I. Title.
TL240.W66
2001
629.2l.3-dc21
Printed in the United States of America

3.

00-043853


To May
Chak
Ben
Jing
Kay
Leo
Sang
Loretta
San
Nicholas
the memory of my parents
and the glory of the Almighty



CONTENTS

PREFACE

xiii

PREFACE TO THE SECOND EDITION

xv


PREFACE TO THE FIRST EDITION

xviii

CONVERSION FACTORS

xxi

NOMENCLATURE

xxii

INTRODUCTION

1

MECHANICS OF PNEUMATIC TIRES

1.1
1.2
1.3
1.4

Tire Forces and Moments / 7
Rolling Resistance of Tires / 8
Tractive (Braking) Effort and Longitudinal Slip (Skid) / 18
Cornering Properties of Tires / 30
1.4.1 Slip Angle and Cornering Force / 30
1.4.2 Slip Angle and Aligning Torque 1 38

1.4.3 Camber and Camber Thrust / 40
1.4.4 Characterization of Cornering Behavior of
Tires / 43
1.5 Performance of Tires on Wet Surfaces / 65
1.6 Ride Properties of Tires / 73
References / 87
Problems / 89

1

3


viii

CONTENTS

MECHANICS OF VEHICLE-TERRAIN
INTERACTIONTERRAMECHANICS

2.1
2.2
2.3

2.4

2.5

2.6


2.7

2.8

Distribution of Stresses in the Terrain Under Vehicular
Loads 1 92
Applications of the Theory of Plastic Equilibrium to the
Mechanics of Vehicle-Terrain Interaction / 100
Empirical Methods for Predicting Off-Road Vehicle
Performance / 120
2.3.1 Empirical Methods Based on the Cone Index / 120
2.3.2 Empirical Methods Based on the Mean Maximum
Pressure / 128
Measurement and Characterization of Terrain Response / 130
2.4.1 Characterization of Pressure-Sinkage
Relationship / 133
2.4.2 Characterization of the Response to Repetitive
Loading / 141
2.4.3 Characterization of the Shear Stress-Shear
Displacement Relationship / 144
A Simplified Method for Analysis of Tracked Vehicle
Performance / 153
2.5.1 Motion Resistance of a Track / 154
2.5.2 Tractive Effort and Slip of a Track / 156
A Computer-Aided Method for Evaluating the Performance of
Vehicles with Flexible Tracks / 164
2.6.1 Approach to the Prediction of Normal Pressure
Distribution under a Track / 165
2.6.2 Approach to the Prediction of Shear Stress
Distribution under a Track / 166

2.6.3 Prediction of Motion Resistance and Drawbar Pull
as Functions of Track Slip 1 168
2.6.4 Experimental Substantiation / 169
2.6.5 Applications to Parametric Analysis and Design
Optimization / 171
A Computer-Aided Method for Evaluating the Performance of
Vehicles with Long-Pitch Link Tracks 1 174
2.7.1 Basic Approach / 174
2.7.2 Experimental Substantiation / 175
2.7.3 Applications to Parametric Analysis and Design
Optimization / 178
Methods for Parametric Analysis of Wheeled Vehicle
Performance / 182


2.8.1 Motion Resistance of a Rigid Wheel / 182
2.8.2 Motion Resistance of a Pneumatic Tire / 186
2.8.3 Tractive Effort and Slip of a Wheel / 192
References / 197
Problems / 201
3 PERFORMANCE CHARACTERISTICS OF ROAD VEHICLES

3.1 Equation of Motion and Maximum Tractive Effort / 203
3.2 Aerodynamic Forces and Moments / 209
3.3 Vehicle Power Plant and Transmission Characteristics I 227
3.3.1 Power Plant Characteristics / 227
3.3.2 Transmission Characteristics / 233
3.4 Prediction of Vehicle Performance / 250
3.4.1 Acceleration Time and Distance I 25 1
3.4.2 Gradability / 255

3.5 Operating Fuel Economy / 255
3.6 Engine and Transmission Matching / 260
3.7 Braking Performance / 265
3.7.1 Braking Characteristics of a Two-Axle
Vehicle / 265
3.7.2 Braking Efficiency and Stopping Distance / 275
3.7.3 Braking Characteristics of a
Tractor-Semitrailer I 277
3.7.4 Antilock Brake Systems / 282
3.7.5 Traction Control Systems / 288
References / 289
Problems / 292
4

PERFORMANCE CHARACTERISTICS OF OFF-ROAD
VEHICLES

Drawbar Performance / 296
4.1.1 Drawbar Pull and Drawbar Power I 296
4.1.2 Tractive Efficiency / 300
4.1.3 Coefficient of Traction / 3 17
4.1.4 Weight-to-Power Ratio for Off-Road
Vehicles / 319
4.2 Fuel Economy of Cross-country Operations / 320
4.3 Transport Productivity and Transport Efficiency / 323
4.4 Mobility Map and Mobility Profile / 324
4.1

203



X

CONTENTS

4.5

5

Selection of Vehicle Configurations for Off-Road
Operations / 328
References / 332
Problems 1 333

HANDLING CHARACTERISTICS OF ROAD VEHICLES

Steering Geometry / 336
Steady-State Handling Characteristics of a Two-Axle
Vehicle / 339
5.2.1 Neutral Steer / 342
5.2.2 Understeer / 344
5.2.3 Oversteer / 344
Steady-State Response to Steering Input / 350
5.3.1 Yaw Velocity Response / 350
5.3.2 Lateral Acceleration Response / 35 1
5.3.3 Curvature Response / 352
Testing of Handling Characteristics / 355
5.4.1 Constant Radius Test 1 355
5.4.2 Constant Speed Test / 356
5.4.3 Constant Steer Angle Test 1 358

Transient Response Characteristics 1 359
Directional Stability / 363
5.6.1 Criteria for Directional Stability / 363
5.6.2 Vehicle Stability Control / 366
Steady-State Handling Characteristics of a
Tractor-Semitrailer / 369
Simulation Models for the Directional Behavior of Articulated
Road Vehicles / 376
References / 385
Problems / 387

6 STEERING OF TRACKED VEHICLES

6.1
6.2
6.3
6.4

Simplified Analysis of the Kinetics of Skid-Steering / 390
Kinematics of Skid-Steering / 396
Skid-Steering at High Speeds / 397
A General Theory for Skid-Steering on Firm Ground / 401
6.4.1 Shear Displacement on the Track-Ground
Interface / 402

388


6.4.2 Kinetics in a Steady-State Turning Maneuver / 408
6.4.3 Experimental Substantiation / 4 12

6.4.4 Coefficient of Lateral Resistance / 416
6.5 Power Consumption of Skid-Steering 1 41 8
6.6 Steering Mechanisms for Tracked Vehicles / 419
6.6.1 ClutcM3rake Steering System / 419
6.6.2 Controlled Differential Steering System / 421
6.6.3 Planetary Gear Steering System / 422
6.7 Articulated Steering / 424
References / 428
Problems / 429
7 VEHICLE RIDE CHARACTERISTICS

Human Response to Vibration / 43 1
7.2 Vehicle Ride Models / 436
7.2.1 Two-Degree-of-Freedom Vehicle Model for Sprung
and Unsprung Mass / 437
7.2.2 Numerical Methods for Determining the Response
of a Quarter-Car Model to Irregular Surface Profile
Excitation / 453
7.2.3 Two-Degree-of-Freedom Vehicle Model for Pitch
and Bounce 1 455
7.3 Introduction to Random Vibration / 462
7.3.1 Surface Elevation Profile as a Random
Function / 462
7.3.2 Frequency Response Function 1 470
7.3.3 Evaluation of Vehicle Vibration in Relation to the
Ride Comfort Criterion / 472
7.4 Active and Semi-Active Suspensions 1 474
References / 482
Problems / 483
7.1


8 INTRODUCTION TO AIR-CUSHION VEHICLES
8.1 Air-Cushion Systems and Their Performance / 485
8.1.1 Plenum Chamber / 485
8.1.2 Peripheral Jet / 493
Resistance
of Air-Cushion Vehicles 1 497
8.2
8.3 Suspension Characteristics of Air-Cushion Systems / 509
8.3.1 Heave (or Bounce) Stiffness / 510

431


xii

CONTENTS

8.3.2 Roll Stiffness / 513
8.4 Directional Control of Air-Cushion Vehicles 1 515
References 1 5 19
Problems / 519
INDEX


PREFACE

More than two decades have elapsed since the first publication of this book
in the United States in 1978. During this period the first edition went through
ten printings, and the second edition, which first appeared in 1993, went

through more than seven printings. An increasing number of universities in
North America, Europe, Asia, and elsewhere have adopted it as a text for
courses in automotive engineering, vehicle dynamics, off-road vehicle engineering, or terramechanics. Many professionals in the vehicle industry around
the world have also used it as a reference. It is gratifying indeed to see that
the book has achieved such wide acceptance.
As we enter a new millennium, the automotive industry is facing greater
challenges than ever before in providing safer, more environmentally friendly,
and more energy-efficient products to meet increasingly stringent demands of
society. As a result, new technologies have continually been developed and
introduced into its products. Accordingly, to better serve the changing needs
of the educational and professional communities related to ground transportation technology, this third edition has been prepared.
To improve competitiveness, shortening the product development cycle is
of critical importance to vehicle manufacturers. Virtual prototyping is therefore widely adopted in the industry. To implement this process effectively,
however, the development of reliable computer simulation models for vehicle
performance evaluation is essential. For a realistic simulation of the handling
behavior of road vehicles, a method referred to as the Magic Formula for
characterizing tire behavior from test data is gaining increasingly wide acceptance. A discussion of the basic features of the Magic Formula is included
in Chapter 1 of this edition. For performance and design evaluation of offroad vehicles, particularly with respect to their soft ground mobility, a variety
of computer simulation models have emerged, including those developed by
myself along with my associates. It is encouraging that our models have since
xiii


X~V

PREFACE

played a significant role in assisting vehicle manufacturers in the development
of a new generation of high-mobility off-road vehicles, as well as assisting
governmental agencies in evaluating vehicle candidates in North America,

Europe, Asia, Africa, and elsewhere. In recognition of our contributions to
the development of these simulation models, we have been presented with a
number of awards by learned societies. These include the George Stephenson
Prize, the Crompton Lanchester Prize, and the Starley Premium Award twice,
awarded by the Institution of Mechanical Engineers. The major features and
practical applications of these simulation models are described in Chapter 2.
New experimental data on the optimization of the tractive performance of
four-wheel-drive off-road vehicles based on our own investigations are presented in Chapter 4.
To further enhance the active safety of road vehicles, systems known as
"vehicle stability control" or "vehicle dynamics control" have been introduced in recent years. The operating principles of these systems are described
in Chapter 5. A new theory developed by us for skid-steering of tracked
vehicles on firm ground is presented in Chapter 6. It is shown that this new
theory offers considerable improvement over existing theories and provides a
unified approach to the study of skid-steering of tracked vehicles. Experimental data, obtained from our own research, on the performance of an electrorheological damper in improving the ride comfort of ground vehicles are
presented in Chapter 7.
While new topics are introduced and new data are presented in this third
edition, the general objective, contents, and format remain similar to those of
previous editions. The fundamental engineering principles underlying the rational development and design of road vehicles, off-road vehicles, and aircushion vehicles are emphasized.
To a certain extent, this book summarizes some of my experience of more
than three decades in teaching, research, and consulting in the field of ground
transportation technology. I would like to take this opportunity once again to
record my appreciation to my colleagues and collaborators in industry, research institutions, and universities for inspiration and cooperation, particularly Dr. Alan R. Reece, Professor Leonard Segel, and the late Dr. M. Gregory
Bekker. I wish also to express my appreciation to staff members of Transport
Technology Research Laboratory, Carleton University, and Vehicle Systems
Development Corporation, Nepean, Ontario, and to my postdoctoral fellows
and postgraduate students, former and present, for their contributions and
assistance. Thanks are also due to governmental agencies and vehicle manufacturers for supporting our research effort over the years.
Jo YUNGWONG
Ottawa, Canada



PREFACE TO THE SECOND EDITION

Since the first edition of this book was published in 1978, it has gone through
ten printings. A number of engineering schools in North America, Europe,
Asia, and elsewhere have adopted it as a text for courses in automotive engineering, vehicle dynamics, off-road vehicle engineering, agricultural engineering, etc. It was translated into Russian and published in Moscow, Russia,
in 1982, and into Chinese and published in Beijing, China, in 1985. Meanwhile, significant technological developments in the field have taken place.
To reflect these new developments and to serve the changing needs of the
educational and professional communities, the time is ripe for the second
edition of this book.
With the growing emphasis being placed by society on energy conservation, environmental protection, and safety, transportation technology is under
greater challenge than ever before. To improve fuel economy and to reduce
undesirable exhaust emission, in addition to improvements in power plant
design, measures such as improving vehicle aerodynamic performance, better
matching of transmission with engine, and optimizing power requirements
have received intense attention. To improve driving safety, antilock brake
systems and traction control systems have been introduced. To provide better
ride comfort while maintaining good roadholding capability, active and semiactive suspension systems have attracted considerable interest. To expedite
the development of new products, computer-aided methods for vehicle performance and design optimization have been developed. Discussions of these
and other technological developments in the field have been included in this
second edition. Furthermore, data on various topics have been updated.
As with the first edition, this second edition of Theory of Ground Vehicles
is written with the same philosophy of emphasizing the fundamental engineering principles underlying the rational development and design of nonguided ground vehicles, including road vehicles, off-road vehicles, and


XV~

PREFACE TO THE SECOND EDITION

air-cushion vehicles. Analysis and evaluation of performance characteristics,

handling behavior, and ride comfort of these vehicles are covered. A unified
method of approach to the analysis of the characteristics of various types of
ground vehicle is again stressed. This book is intended primarily to introduce
senior undergraduate and beginning graduate students to the study of ground
vehicle engineering. However, it should also be of interest to engineers and
researchers in the vehicle industry.
Similar to the first edition, this second edition consists of eight chapters.
Chapter 1 discusses the mechanics of pneumatic tires. Practical methods for
predicting the behavior of tires subject to longitudinal or side force, as well
as under their combined action, are included. New experimental data on tire
performance are added. Chapter 2 examines the mechanics of vehicle-terrain
interaction, which has become known as "terramechanics." Computer-aided
methods for the design and performance evaluation of off-road vehicles are
included. Experimental data on the mechanical properties of various types of
terrain are updated. Chapter 3 deals with the analysis and prediction of road
vehicle performance. Included is updated information on the aerodynamic
performance of passenger cars and articulated heavy commercial vehicles.
Procedures for matching transmission with engine to achieve improved fuel
economy while maintaining adequate performance are outlined. Characteristics of continuously variable transmissions and their effects on fuel economy
and performance are examined. The operating principles of antilock brake
systems and traction control systems and their effects on performance and
handling are presented in some detail. The performance of off-road vehicles
is the subject of Chapter 4. Discussions on the optimization of the performance of all-wheel-drive off-road vehicles are expanded. In addition, various
criteria for evaluating military vehicles are included. Chapter 5 examines the
handling behavior of road vehicles. In addition to discussions of the steadystate and transient handling behavior of passenger cars, the handling characteristics of tractor-semitrailers are examined. The handling diagram for
evaluating directional response is included. The steering of tracked vehicles
is the topic of Chapter 6. In addition to skid-steering, articulated steering for
tracked vehicles is examined. Chapter 7 deals with vehicle ride comfort. Human tolerance to vibration, vehicle ride models, and applications of the random vibration theory to the evaluation of ride comfort are covered.
Furthermore, the effects of suspension spring stiffness, damping, and unsprung mass on vibration isolation characteristic~,roadholding, and suspension travel are examined. The principles of active and semi-active suspensions
are also discussed. In addition to conventional road vehicles and off-road

vehicles, air-cushion vehicles have found applications in ground transportation. The basic principles of air-cushion systems and the unique characteristics
of air-cushion vehicles for overland and overwater operations are treated in
Chapter 8. New data on the mechanics of skirt-terrain interaction are included.
The material included in this book has been used in the undergraduate and
graduate courses in ground transportation technology that I have been teach-


PREFACE TO THE SECOND EDITION

~ ~ i i

ing at Carleton for some years. It has also been presented, in part, at seminars
and in professional development programs in Canada, China, Finland, Germany, Italy, Singapore, Spain, Sweden, Taiwan, the United Kingdom, and the
United States.
In preparing the second edition of this book, I have drawn much on my
experience acquired from collaboration with many of my colleagues in industry, research organizations, and universities in North America, Europe,
Asia, and elsewhere. The encouragement, inspiration, suggestions, and comments that I have received from Dr. A. R. Reece, formerly of the University
of Newcastle-upon-Tyne, and currently Managing Director, Soil Machine Dynamics Limited, England; Professor L. Segel, Professor Emeritus, University
of Michigan; and Professor E. H. Law, Clemson University, are particularly
appreciated. I would also like to record my gratitude to the late Dr. M. G.
Bekker, with whom I had the good fortune to collaborate in research projects
and in joint offerings of professional development programs, upon which
some of the material included in this book was developed.
The typing of the manuscript by D. Dodds and the preparation of additional
illustrations by J. Brzezina for this second edition are appreciated.

Jo YUNGWONG
Ottawa, Canada



PREFACE TO THE FIRST EDITION

Society's growing demand for better and safer transportation, environmental
protection, and energy conservation has stimulated new interest in the development of the technology for transportation. Transport technology has now
become an academic discipline in both graduate and undergraduate programs
at an increasing number of engineering schools in North America and Elsewhere. While preparing lecture notes for my two courses at Carleton on
ground transportation technology, I found that although there was a wealth
of information in research reports and in journals of learned societies, there
was as yet no comprehensive account suitable as a text for university students.
I hope this book will fill this gap.
Although this book is intended mainly to introduce senior undergraduate
and beginning graduate students to the study of ground vehicles, it should
also interest engineers and researchers in the vehicle industry. This book deals
with the theory and engineering principles of nonguided ground vehicles,
including road, off-road, and air-cushion vehicles. Analysis and evaluation of
performance characteristics, handling behavior, and ride qualities are covered.
The presentation emphasizes the fundamental principles underlying rational
development and design of vehicle systems. A unified method of approach to
the analysis of the characteristics of various types of ground vehicle is also
stressed.
This book consists of eight chapters. Chapter 1 discusses the mechanics
of pneumatic tires and provides a basis for the study of road vehicle characteristics. Chapter 2 examines the vehicle running gear-terrain interaction,
which is essential to the evaluation of off-road vehicle performance. Understanding the interaction between the vehicle and the ground is important to
the study of vehicle performance, handling, and ride, because, aside from
aerodynamic inputs, almost all other forces and moments affecting the motion

xviii


of a ground vehicle are applied through the running gear-ground contact.

Chapter 3 deals with analysis and prediction of the performance of road vehicles. Included in the discussion are vehicle power plant and transmission
characteristics, performance limits, acceleration characteristics, braking performance, and fuel economy. The performance of off-road vehicles is the
subject of Chapter 4. Drawbar performance, tractive efficiency, operating fuel
economy, transport productivity and efficiency, mobility map, and mobility
profile are discussed. Chapter 5 examines handling behavior of road vehicles,
including steady-state and transient responses, and directional stability. The
steering of tracked vehicles is the subject of Chapter 6. Included in the discussion are the mechanics of skid-steering, steerability of tracked vehicles,
and steering by articulation. Chapter 7 examines vehicle ride qualities. Human
response to vibration, vehicle ride models, and the application of random
process theory to the analysis of vehicle vibration are covered. In addition to
conventional road and off-road vehicles, air-cushion vehicles have found applications in ground transport. The basic engineering principles of air-cushion
systems and the unique features and characteristics of air-cushion vehicles
are treated in Chapter 8.
A book of this scope limits detail. Since it is primarily intended for students, some topics have been given a simpler treatment than the latest developments would allow. Nevertheless, this book should provide the reader with
a comprehensive background on the theory of ground vehicles.
I have used part of the material included in this book in my two engineering
courses in ground transport technology at Carleton. It has also been used in
two special professional programs. One is "Terrain-Vehicle Systems Analysis," given in Canada and Sweden jointly with Dr. M. G. Bekker, formerly
with AC Electronics-Defense Research Laboratories, General Motors Corporation, Santa Barbara, California. The other is "Braking and Handling of
Heavy Commercial Vehicles" given at Carleton jointly with Professor J. R.
Ellis, School of Automotive Studies, Cranfield Institute of Technology, England, and Dr. R. R. Guntur, Transport Technology Research Laboratory, Carleton University.
In writing this book, I have drawn much on the knowledge and experience
acquired from collaboration with many colleagues in industry, research organizations, and universities. I wish to express my deep appreciation to them.
I am especially indebted to Dr. A. R. Reece, University of Newcastle-uponTyne, England, Dr. M. G. Bekker, and Professor J. R. Ellis for stimulation
and encouragement.
I also acknowledge with gratitude the information and inspiration derived
from the references listed at the end of the chapters and express my appreciation to many organizations and individuals for permission to reproduce
illustrations and other copyrighted material.
Appreciation is due to Dr. R. R. Guntur for reviewing part of the manuscript and to Dean M. C. de Malherbe, Faculty of Engineering, Professor



XX

PREFACE TO THE FIRST EDITION

H. I. H. Saravanamuttoo, Chairman, Department of Mechanical and Aeronautical Engineering, and many colleagues at Carleton University for encouragement.
J o YUNGWONG
Ottawa, Canada
July 1978


CONVERSION FACTORS

Quantity
Acceleration
Area
Energy
Force
Length
Mass
Moment of a force
Power
Pressure or stress
Speed
Volume

U.S.
Customary Unit

ft/s2

ft2
in.2
ft - lb
lb
ft
in.
mile
slug
ton
lb . ft
hp
lb/ft2
lblin.' (psi)
ft/s
mph
ft3
in.3
gal (liquids)

SI
Equivalent

0.3048 m/s2
0.0929 m2
645.2 mm2
1.356 J
4.448 N
0.3048 m
25.4 mm
1.609 km

14.59 kg
907.2 kg
1.356 N . m
745.7 W
47.88 Pa
6.895 kPa
0.3048 mls
1.609 kmlh
0.02832 m3
16.39 cm3
3.785 liter


NOMENCLATURE

area, contact area
cushion area
frontal area
parameter characterizing terrain response to repetitive loading
acceleration
acceleration component along the x axis
acceleration component along the y axis
acceleration component along the z axis
tread of the vehicle
barometric pressure
working width of machinery
barometric pressure under reference atmospheric conditions
vapor pressure
width
cone index

aerodynamic resistance coefficient
ratio of braking effort to normal load of vehicle front axle
longitudinal stiffness of tire subject to a driving torque
aerodynamic lift coefficient
liftldrag ratio


NOMENCLATURE

aerodynamic pitching moment coefficient
ratio of braking effort to normal load of vehicle rear axle
restoring moment coefficient
longitudinal stiffness of tire during braking
ratio of braking effort to normal load of semitrailer axle
coefficient of skirt contact drag
coefficient of power spectral density function
speed ratio of torque converter
torque ratio of torque converter
cornering stiffness of tire
cornering stiffness of front tire
cornering stiffness of rear tire
cornering stiffness of semitrailer tire
camber stiffness of tire
cohesion
adhesion
equivalent damping coefficient
damping coefficient of shock absorber
damping coefficient of tire
diameter
discharge coefficient

hydraulic diameter
energy
energy available at vehicle drawbar
force, thrust
braking force
bralung force of vehicle front axle
braking force of vehicle rear axle
braking force of semitrailer axle
lift generated by air cushion
drawbar pull
thrust of vehicle front axle
hydrodynamic force acting on a tire over flooded surfaces

~~iii


XX~V

NOMENCLATURE

horizontal force acting at the hitch point of a tractorsemitrailer
thrust of the inside track of a tracked vehicle
lift generated by the change of momentum of an air jet
net thrust
thrust of the outside track of a tracked vehicle
resultant force due to passive earth pressure
normal component of the resultant force due to passive earth
pressure
thrust of vehicle rear axle
side force

force component along the x axis
force component along the y axis
cornering force of front tire
cornering force of rear tire
cornering force of tire
camber thrust of tire
force component along the z axis
frequency
center frequency
equivalent coefficient of motion resistance
natural frequency of sprung mass
natural frequency of unsprung mass
coefficient of rolling resistance
grade, sand penetration resistance gradient
lateral acceleration gain
yaw velocity gain
acceleration due to gravity
height of center of gravity of the vehicle
height of the point of application of aerodynamic resistance
above ground level
depth
clearance height
height of drawbar


NOMENCLATURE

XXV

mass moment of inertia

mass moment of inertia of wheels
mass moment of inertia of the vehicle about the y axis
mass moment of inertia of the vehicle about the z axis
slip
slip of
slip of
slip of
slip of
skid

front tire
the inside track of a tracked vehicle
the outside track of a tracked vehicle
rear tire

momentum flux of an air jet
shear displacement
shear deformation modulus
augmentation factor
proportion of total bralung force placed on vehicle front axle
proportion of total braking force placed on vehicle rear axle
proportion of total braking force placed on semitrailer axle
coefficient of thrust distribution
gear ratio of a controlled differential
engine capacity factor
passive earth pressure coefficient
coefficient taking into account the effect of ground porosity on
the flow and power requirement of an air-cushion vehicle
ratio of the angular speed of the outside track sprocket to that
of the inside track sprocket

torque converter capacity factor
understeer coefficient
understeer coefficient of semitrailer
understeer coefficient of tractor
ratio of the theoretical speed of the front tire to that of the rear
tire
weight utilization factor
cohesive modulus of terrain deformation


front suspension spring stiffness
stiffness of underlying peat for organic terrain (muskeg)
rear suspension spring stiffness
stiffness of suspension spring
equivalent spring stiffness of tire
parameter characterizing terrain response to repetitive loading
frictional modulus of terrain deformation
parameter characterizing terrain response to repetitive loading
wheelbase
characteristic length
wheelbase of semitrailer
wheelbase of tractor
length
cushion perimeter
nozzle perimeter
distance between oscillation center and center of gravity of the
vehicle
contact length
distance between front axle and center of gravity of the
vehicle

distance between rear axle and center of gravity of the vehicle
aerodynamic pitching moment
braking torque
engine output torque
moment of turning resistance
restoring moment in roll
torque converter output torque
wheel torque
moment about the x axis
moment about the y axis
moment about the z axis
mobility index
vehicle mass
pressure-sinkage parameter for organic terrain (muskeg)


NOMENCLATURE

mus

sprung mass
unsprung mass

N

exponent of power spectral density function

ms

XXV~


N,, N,, N , bearing capacity factors
N+
n

flow value for soils
exponent of terrain deformation

n,

engine speed
number of speeds in a gearbox

4,.

torque converter output speed
engine power
power required to sustain the air cushion
drawbar power
power required to overcome momentum drag
engine power under reference atmospheric conditions
power consumption of a tracked vehicle in straight line motion
power consumption of a tracked vehicle during a turn
pressure
pressure exerted by tire carcass
critical pressure
cushion pressure
dynamic pressure
ground pressure at the lowest point of contact
critical ground pressure

inflation pressure
total jet pressure

Q
4

volume flow
surcharge

R

turning radius

Ra
Rc
Rd

aerodynamic resistance
motion resistance due to terrain compaction

4

grade resistance

drawbar load