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 |  موضوع: كتاب Electric Vehicle Technology Explained الجمعة 25 نوفمبر 2022, 12:52 am | |
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أحضرت لكم كتاب
Electric Vehicle Technology Explained
James Larminie
Oxford Brookes University, Oxford, UK
John Lowry
Acenti Designs Ltd., UK
و المحتوى كما يلي :
Contents
Acknowledgments . xi
Abbreviations xiii
Symbols xv
1 Introduction 1
1.1 A Brief History 1
1.1.1 Early days . 1
1.1.2 The relative decline of electric vehicles after 1910 3
1.1.3 Uses for which battery electric vehicles have remained popular 5
1.2 Developments Towards the End of the 20th Century 5
1.3 Types of Electric Vehicle in Use Today 7
1.3.1 Battery electric vehicles . 8
1.3.2 The IC engine/electric hybrid vehicle 9
1.3.3 Fuelled electric vehicles . 15
1.3.4 Electric vehicles using supply lines 18
1.3.5 Solar powered vehicles . 18
1.3.6 Electric vehicles which use flywheels or super capacitors . 18
1.4 Electric Vehicles for the Future 20
Bibliography 21
2 Batteries 23
2.1 Introduction . 23
2.2 Battery Parameters 24
2.2.1 Cell and battery voltages 24
2.2.2 Charge (or Amphour) capacity 25
2.2.3 Energy stored . 26
2.2.4 Specific energy . 27
2.2.5 Energy density . 27
2.2.6 Specific power . 28
2.2.7 Amphour (or charge) efficiency 28
2.2.8 Energy efficiency . 29vi Contents
2.2.9 Self-discharge rates 29
2.2.10 Battery geometry . 29
2.2.11 Battery temperature, heating and cooling needs . 29
2.2.12 Battery life and number of deep cycles . 29
2.3 Lead Acid Batteries . 30
2.3.1 Lead acid battery basics 30
2.3.2 Special characteristics of lead acid batteries . 32
2.3.3 Battery life and maintenance 34
2.3.4 Battery charging . 35
2.3.5 Summary of lead acid batteries 35
2.4 Nickel-based Batteries 35
2.4.1 Introduction 35
2.4.2 Nickel cadmium 36
2.4.3 Nickel metal hydride batteries . 38
2.5 Sodium-based Batteries . 41
2.5.1 Introduction 41
2.5.2 Sodium sulphur batteries 41
2.5.3 Sodium metal chloride (Zebra) batteries 42
2.6 Lithium Batteries . 44
2.6.1 Introduction 44
2.6.2 The lithium polymer battery 45
2.6.3 The lithium ion battery . 45
2.7 Metal Air Batteries 46
2.7.1 Introduction 46
2.7.2 The aluminium air battery . 46
2.7.3 The zinc air battery 47
2.8 Battery Charging . 48
2.8.1 Battery chargers 48
2.8.2 Charge equalisation . 49
2.9 The Designer’s Choice of Battery 51
2.9.1 Introduction 51
2.9.2 Batteries which are currently available commercially 52
2.10 Use of Batteries in Hybrid Vehicles . 53
2.10.1 Introduction 53
2.10.2 Internal combustion/battery electric hybrids 53
2.10.3 Battery/battery electric hybrids 53
2.10.4 Combinations using flywheels . 54
2.10.5 Complex hybrids . 54
2.11 Battery Modelling 54
2.11.1 The purpose of battery modelling . 54
2.11.2 Battery equivalent circuit 55
2.11.3 Modelling battery capacity . 57
2.11.4 Simulation a battery at a set power . 61
2.11.5 Calculating the Peukert Coefficient . 64
2.11.6 Approximate battery sizing . 65Contents vii
2.12 In Conclusion . 66
References . 67
3 Alternative and Novel Energy Sources and Stores 69
3.1 Introduction . 69
3.2 Solar Photovoltaics 69
3.3 Wind Power 71
3.4 Flywheels 72
3.5 Super Capacitors . 74
3.6 Supply Rails 77
References . 80
4 Fuel Cells 81
4.1 Fuel Cells, a Real Option? . 81
4.2 Hydrogen Fuel Cells: Basic Principles . 83
4.2.1 Electrode reactions 83
4.2.2 Different electrolytes . 84
4.2.3 Fuel cell electrodes 87
4.3 Fuel Cell Thermodynamics – an Introduction . 89
4.3.1 Fuel cell efficiency and efficiency limits . 89
4.3.2 Efficiency and the fuel cell voltage 92
4.3.3 Practical fuel cell voltages . 94
4.3.4 The effect of pressure and gas concentration . 95
4.4 Connecting Cells in Series – the Bipolar Plate 96
4.5 Water Management in the PEM Fuel Cell . 101
4.5.1 Introduction to the water problem 101
4.5.2 The electrolyte of a PEM fuel cell 101
4.5.3 Keeping the PEM hydrated 104
4.6 Thermal Management of the PEM Fuel Cell . 105
4.7 A Complete Fuel Cell System . 107
References . 109
5 Hydrogen Supply 111
5.1 Introduction . 111
5.2 Fuel Reforming 113
5.2.1 Fuel cell requirements 113
5.2.2 Steam reforming 114
5.2.3 Partial oxidation and autothermal reforming . 116
5.2.4 Further fuel processing: carbon monoxide removal . 117
5.2.5 Practical fuel processing for mobile applications 118
5.3 Hydrogen Storage I: Storage as Hydrogen . 119
5.3.1 Introduction to the problem . 119
5.3.2 Safety . 120
5.3.3 The storage of hydrogen as a compressed gas . 120
5.3.4 Storage of hydrogen as a liquid 122viii Contents
5.3.5 Reversible metal hydride hydrogen stores . 124
5.3.6 Carbon nanofibres 126
5.3.7 Storage methods compared . 127
5.4 Hydrogen Storage II: Chemical Methods 127
5.4.1 Introduction 127
5.4.2 Methanol 128
5.4.3 Alkali metal hydrides . 130
5.4.4 Sodium borohydride . 132
5.4.5 Ammonia 135
5.4.6 Storage methods compared . 138
References . 138
6 Electric Machines and their Controllers . 141
6.1 The ‘Brushed’ DC Electric Motor 141
6.1.1 Operation of the basic DC motor . 141
6.1.2 Torque speed characteristics 143
6.1.3 Controlling the brushed DC motor 147
6.1.4 Providing the magnetic field for DC motors 147
6.1.5 DC motor efficiency . 149
6.1.6 Motor losses and motor size 151
6.1.7 Electric motors as brakes 153
6.2 DC Regulation and Voltage Conversion 155
6.2.1 Switching devices . 155
6.2.2 Step-down or ‘buck’ regulators 157
6.2.3 Step-up or ‘boost’ switching regulator . 159
6.2.4 Single-phase inverters 162
6.2.5 Three-phase 165
6.3 Brushless Electric Motors . 166
6.3.1 Introduction 166
6.3.2 The brushless DC motor 167
6.3.3 Switched reluctance motors 169
6.3.4 The induction motor . 173
6.4 Motor Cooling, Efficiency, Size and Mass . 175
6.4.1 Improving motor efficiency . 175
6.4.2 Motor mass . 177
6.5 Electrical Machines for Hybrid Vehicles 179
References . 181
7 Electric Vehicle Modelling 183
7.1 Introduction . 183
7.2 Tractive Effort . 184
7.2.1 Introduction 184
7.2.2 Rolling resistance force . 184
7.2.3 Aerodynamic drag 185
7.2.4 Hill climbing force 185Contents ix
7.2.5 Acceleration force . 185
7.2.6 Total tractive effort 187
7.3 Modelling Vehicle Acceleration 188
7.3.1 Acceleration performance parameters 188
7.3.2 Modelling the acceleration of an electric scooter 189
7.3.3 Modelling the acceleration of a small car . 193
7.4 Modelling Electric Vehicle Range 196
7.4.1 Driving cycles . 196
7.4.2 Range modelling of battery electric vehicles 201
7.4.3 Constant velocity range modelling 206
7.4.4 Other uses of simulations 207
7.4.5 Range modelling of fuel cell vehicles 208
7.4.6 Range modelling of hybrid electric vehicles 211
7.5 Simulations: a Summary 212
References . 212
8 Design Considerations . 213
8.1 Introduction . 213
8.2 Aerodynamic Considerations . 213
8.2.1 Aerodynamics and energy 213
8.2.2 Body/chassis aerodynamic shape . 217
8.3 Consideration of Rolling Resistance . 218
8.4 Transmission Efficiency . 220
8.5 Consideration of Vehicle Mass 223
8.6 Electric Vehicle Chassis and Body Design . 226
8.6.1 Body/chassis requirements . 226
8.6.2 Body/chassis layout 227
8.6.3 Body/chassis strength, rigidity and crash resistance . 228
8.6.4 Designing for stability 231
8.6.5 Suspension for electric vehicles 231
8.6.6 Examples of chassis used in modern battery and hybrid electric
vehicles . 232
8.6.7 Chassis used in modern fuel cell electric vehicles 232
8.7 General Issues in Design 234
8.7.1 Design specifications . 234
8.7.2 Software in the use of electric vehicle design . 234
9 Design of Ancillary Systems . 237
9.1 Introduction . 237
9.2 Heating and Cooling Systems . 237
9.3 Design of the Controls . 240
9.4 Power Steering 243
9.5 Choice of Tyres 243
9.6 Wing Mirrors, Aerials and Luggage Racks 243
9.7 Electric Vehicle Recharging and Refuelling Systems 244x Contents
10 Electric Vehicles and the Environment 245
10.1 Introduction . 245
10.2 Vehicle Pollution: the Effects . 245
10.3 Vehicles Pollution: a Quantitative Analysis 248
10.4 Vehicle Pollution in Context 251
10.5 Alternative and Sustainable Energy Used via the Grid . 254
10.5.1 Solar energy 254
10.5.2 Wind energy 255
10.5.3 Hydro energy 255
10.5.4 Tidal energy 255
10.5.5 Biomass energy 256
10.5.6 Geothermal energy 257
10.5.7 Nuclear energy 257
10.5.8 Marine current energy 257
10.5.9 Wave energy 257
10.6 Using Sustainable Energy with Fuelled Vehicles . 258
10.6.1 Fuel cells and renewable energy . 258
10.6.2 Use of sustainable energy with conventional IC engine vehicles 258
10.7 The Role of Regulations and Law Makers . 258
References . 260
11 Case Studies 261
11.1 Introduction . 261
11.2 Rechargeable Battery Vehicles 261
11.2.1 Electric bicycles 261
11.2.2 Electric mobility aids 263
11.2.3 Low speed vehicles 263
11.2.4 Battery powered cars and vans 266
11.3 Hybrid Vehicles 269
11.3.1 The Honda Insight 269
11.3.2 The Toyota Prius . 271
11.4 Fuel Cell Powered Bus . 272
11.5 Conclusion . 275
References . 277
Appendices: MATLAB Examples 279
Appendix 1: Performance Simulation of the GM EV1 279
Appendix 2: Importing and Creating Driving Cycles . 280
Appendix 3: Simulating One Cycle 282
Appendix 4: Range Simulation of the GM EV1 Electric Car 284
Appendix 5: Electric Scooter Range Modelling 286
Appendix 6: Fuel Cell Range Simulation 288
Appendix 7: Motor Efficiency Plots 290
Index .
Index
4 quadrant controller, 8, 241
Acid electrolyte fuel cell, 84
Aerodynamics, 185, 213, 217, 268
Air conditioning, 239
Alkaline fuel cells, 86
Ammonia, 135
Amphour capacity
effect of higher currents on, 57
modeling, 57
term explained, 25
Apollo spacecraft, 86
Armature, 142
Autothermal reforming, 116, 118, 128
Balance of plant, 107
Batteries
charge equalisation, 49, 50
different types compared, 52, 67
equivalent circuit, 24, 55
Modeling, 54
Battery charging, 35, 48, 244
Battery electric vehicles
applications, 5, 8, 262, 263
effect of mass on range, 224
emissions from, 250, 251
examples, 8, 189, 193, 261, 265
performance modeling, 189, 193, 279
range modeling, 201, 218, 224, 284, 286
simulation, 207
Battery life, 49
Bicycles, 261
Bipolar plates, 96
Blowers, 107
Body design, 226, 228
Brushless DC motor, 167, 275
Buses, 16, 19, 83, 272
C notation, 25
California air resources board, 12, 48, 259, 268
Capacitors, 19, 74
Carbon monoxide, 246
removal, 117
Carbon nanofibres, 126
Carnot limit, 89, 92
Catalysts, 87, 116, 136
Charge equalisation, 49, 50, 75
Charging, 35, 48, 244
Charging efficiency, 28, 50
Chassis design, 226, 228
Chassis materials, 230
Chopper circuits See DC/DC converters, 157
Coefficient of rolling resistance, 184, 218
Comfort, 231, 237, 243
Commutator, 142
Compressors, 107
Controls, 240
Cooling, 238
Copper losses, 149
Crash resistance, 228
DC/DC converters, 108, 155
efficiency of, 159, 161
step-down, 157
Digital signal processors, 171
Direct methanol fuel cells, 85
Drag coefficient, 185, 214
Driving cycles, 196, 280
10–15 Mode, 196
ECE-15, 196
ECE-47, 199, 206, 281
EUDC, 196
FHDS, 196
FUDS, 196
MATLAB, 280
Electric Vehicle Technology Explained James Larminie and John Lowry
2003 John Wiley & Sons, Ltd ISBN: 0-470-85163-5294 Index
Driving cycles (continued)
SAE J227, 198
SFUDS, 196, 205, 211
Driving schedules See Driving cycles, 196
Dynamic braking, 153, 275
Efficiency
DC/DC converters, 158, 161
limit for fuel cells, 92
motors, 149, 175, 202, 290
of fuel cells defined, 91
Electric scooters, 189, 200, 206, 286
Electronic switches, 155, 156
Emission
from different vehicle types compared, 251
Energy density
Batteries and fuel compared, 3
term explained, 3
Enthalpy, 90, 91
Equivalent circuit
batteries, 24, 55
Ethanol, 129, 245, 258
Exergy, 90
Faraday, unit of charge, 90
Flywheels, 18, 54, 72
Ford, 266, 276
Fuel cell powered vehicles
examples, 17, 83, 272
Fuel cell vehicles
buses, 16
cars, 16
emissions from, 249, 258, 259
examples, 15, 17, 83, 272
main problems, 81
range modeling, 208, 288
Fuel cells
basic chemistry, 84
cooling, 105, 108, 273
different types (table), 84
efficiency, 91
efficiency defined, 92
efficiency/voltage relation, 92
electrodes, 87
leaks, 101
Nernst equation, 96
osmotic drag, 104
pressure, 96
reversible voltage, 92
temperature, 87, 92
thermodynamics, 91
voltage/current relation, 94
water management, 101, 104
Gasoline
use with fuel cells, 118
Geothermal energy, 257
Gibbs free energy
changes with temperature, 91
explained, 90
GM EV1, 193, 205, 211, 215, 239, 267, 279,
284
GM Hy-wire, 107, 226, 233, 241
Greenhouse effect, 247
Harmonics, 163
Heat pumps, 239
Heating, 237, 238
High pressure hydrogen storage, 120, 122
Hill climbing, 185, 224
Hindenburg, 120
History, 1
Honda Insight, 53, 179, 217, 232, 269
Hybrid electric vehicles
battery charge equalisation, 50
battery selection, 53
electrical machines, 179
emissions from, 250, 251, 259
examples, 13, 269, 271
grid connected, 259
parallel, 10, 180, 270
series, 10
supply rails, 79
term explained, 9
with capacitors, 19, 77
Hydroelectricity, 255
Hydrogen
as energy vector, 124
from gasoline, 118
from reformed methanol, 115, 117
made by steam reforming, 114
physical properties, 120
safety, 120, 122–124
storage as a compressed gas, 120, 275
storage as a cryogenic liquid, 122
storage in alkali metal hydrides, 130
storage in chemicals, 127
storage in metal hydrides, 124
storage methods compared, 138
Hydrogen fueled ICE vehicle, 249, 259
IGBTs, 157
Induction motor, 173
Inductive power transfer, 78
Internal resistance, 24, 30, 38
Inverters
3-phase, 165
Iron losses, 149Index 295
Kamm effect, 217
Lead acid batteries
basic chemistry, 30, 32
internal resistance, 30
limited life, 34
main features, 31
modeling, 56
sealed types, 32
Liquid hydrogen, 122
Lithium batteries
basic chemistry, 45
main features, 45
Low speed vehicles, 263
Marine current energy, 257
Materials selection, 230, 232
Metal air batteries
aluminium/air, 46
zinc/air, 47
Metal hydride storage of hydrogen, 124
Methanation of carbon monoxide, 117
Methane, 116, 120
Methanol, 250, 259
as hydrogen carrier, 115, 130, 134
Methanol fuel cell, 85
Mobility aids, 263
Molten carbonate fuel cell, 86
MOSFETs, 156
Motors
BLDC, 275
brushed DC, 141
brushless DC, 167
copper losses, 149
efficiency, 149, 175, 202, 290
fuel cells, used with, 108
induction, 173
integral with wheel, 180, 221, 223
iron losses, 149
mass of, 177
power/size relation, 151
self-synchronous, 167
specific power, 177
switched reluctance, 169
torque/speed characteristics, 143
Nafion, 102
Nickel cadmium batteries
basic chemistry, 36
charging, 37
internal resistance, 38
main features, 37
modeling, 56
Nickel metal hydride batteries
applications, 41
basic chemistry, 39
main features, 39
Nuclear energy, 257
Orbiter spacecraft, 86
Osmotic drag, 104
Partial oxidation reformers, 116, 118
PEM fuel cells
electrode reactions, 84
electrolyte of, 101
introduced, 85
reformed fuels, use with, 115
Perfluorosulphonic acid, 102
Performance modeling, 188
Peugeot, 189, 200, 266
Peukert Coefficient, 57, 64, 203
Phosphoric acid fuel cells, 86
Pollution, 245, 248, 251, 259
Power steering, 243
Propane, 120
Proton exchange membrane, 84, 101
PTFE, 102
Rear view mirrors, 243
Regenerative braking, 9, 153, 206, 225, 270
Regulators, 155, 157, 159
Rolling resistance, 184, 218
Selective oxidation reactor, 117
Self discharge of batteries, 32
Shift reactors See Water gas shift reaction, 117
Shuttle spacecraft See Orbiter spacecraft, 86
Sodium borohydride
as hydrogen carrier, 132
cost, 135
Sodium metal chloride batteries See Zebra
batteries, 42
Sodium sulphur batteries
basic chemistry, 41
main features, 42
Solar energy, 18, 69, 254
Solid oxide fuel cells, 86
Specific energy
relation to specific power, 28
term explained, 27
Stability, 227
Stack, 96
Steam reforming, 114, 118
Sulphonation, 102
Super-capacitors See Capacitors, 19
Supply rails, 18, 77296 Index
Suspension, 231
Switched reluctance motors, 169
Thyristors, 157
Tidal energy, 255
Total energy use, 254
Toyota Prius, 13, 41, 53, 271
Tractive effort, 187
Transmission, 221
Types of fuel cell (table), 85
Tyre choice, 243
Ultra-capacitors See Capacitors, 19
Water gas shift reaction, 114, 117
Watthour
term explained, 26
Well-to-wheel analysis, 248, 251
Wind energy, 71, 255
Windage losses, 150
Zebra batteries
basic chemistry, 42
main features, 43
operating temperature, 43
Zinc air batteries, 16
Abbreviations
AC Alternating current
BLDC Brushless DC (motor)
BOP Balance of plant
CARB California air resources board
CCGT Combined cycle gas turbine
CNG Compressed natural gas
CPO Catalytic partial oxidation
CVT Continuously variable transmission
DC Direct current
DMFC Direct methanol fuel cell
ECCVT Electronically controlled continuous variable transmission
ECM Electronically commutated motor
EMF Electromotive force
EPA Environmental protection agency
EPS Electric power steering
ETSU Energy technology support unit (a government organisation in the UK)
EUDC Extra-urban driving cycles
EV Electric vehicle
FCV Fuel cell vehicle
FHDS Federal highway driving schedule
FUDS Federal urban driving schedule
GM General Motors
GM EV1 General Motors electric vehicle 1
GNF Graphitic nanofibre
GTO Gate turn off
HEV Hybrid electric vehicle
HHV Higher heating value
IC Internal combustion
ICE Internal combustion engine
IEC International Electrotechnical Commission
IGBT Insulated gate bipolar transistor
IMA Integrated motor assist
IPT Inductive power transferxiv Abbreviations
kph Kilometres per hour
LHV Lower heating value
LH2 Liquid (cryogenic) hydrogen
LPG Liquid petroleum gas
LSV Low speed vehicle
MeOH Methanol
mph Miles per hour
MEA Membrane electrode assembly
MOSFET Metal oxide semiconductor field effect transistor
NASA National Aeronautics and Space Administration
NiCad Nickel cadmium (battery)
NiMH Nickel metal hydride (battery)
NL Normal litre, 1 litre at NTP
NTP Normal temperature and pressure (20◦C and 1 atm or 1.01325 bar)
NOX Nitrous oxides
OCV Open circuit voltage
PEM Proton exchange membrane or polymer electrolyte membrane: different
names for the same thing which fortunately have the same abbreviation
PEMFC Proton exchange membrane fuel cell or polymer electrolyte membrane
fuel cell
PM Permanent magnet or particulate matter
POX Partial oxidation
ppb Parts per billion
ppm Parts per million
PROX Preferential oxidation
PWM Pulse width modulation
PZEV Partial zero emission vehicle
SAE Society of Automotive Engineers
SFUDS Simplified federal urban driving schedule
SL Standard litre, 1 litre at STP
SOFC Solid oxide fuel cell
SRM Switched reluctance motor
STP Standard temperature and pressure (= SRS)
SULEV Super ultra low emission vehicles
TEM Transmission electron microscope
ULEV Ultra low emission vehicle
VOC Volatile organic compounds
VRLA Valve regulated (sealed) lead acid (battery)
WTT Well to tank
WTW Well to wheel
WOT Wide open throttle
ZEBRA Zero emissions battery research association
ZEV Zero emission vehicleSymbols
Letters are used to stand for variables, such as mass, and also as chemical symbols in
chemical equations. The distinction is usually clear from the context, but for even greater
clarity italics are use for variables, and ordinary text for chemical symbols, so H stands
for enthalpy, whereas H stands for hydrogen.
In cases where a letter can stand for two or more variables, the context always makes
it clear which is intended.
a Acceleration
A Area
B Magnetic field strength
Cd Drag coefficient
C Amphour capacity of a battery OR capacitance of a capacitor
C3 Amphour capacity of a battery if discharged in 3 hours, the ‘3 hour rate’
C
p Peukert capacity of a battery, the same as the Amphour capacity if
discharged at a current of 1 Amp
CR Charge removed from a battery, usually in Amphours
CS Charge supplied to a battery, usually in Amphours
d Separation of the plates of a capacitor OR distance traveled
DoD Depth of discharge, a ratio changing from 0 (fully charged) to 1 (empty)
E Energy, or Young’s modulus, or EMF (voltage)
Eb Back EMF (voltage) of an electric motor in motion
E
s Supplied EMF (voltage) to an electric motor
e Magnitude of the charge on one electron, 1.602 × 10−19 Coulombs
f Frequency
F Force or Faraday constant, the charge on one mole of electrons, 96 485
Coulombs
Frr Force needed to overcome the rolling resistance of a vehicle
Fad Force needed to overcome the wind resistance on a vehicle
Fla Force needed to give linear acceleration to a vehicle
Fhc Force needed to overcome the gravitational force of a vehicle down a hill
F
ωa Force at the wheel needed to give rotational acceleration to the rotating
parts of a vehicle
Fte Tractive effort, the forward driving force on the wheels
g Acceleration due to gravityxvi Symbols
G Gear ratio OR rigidity modulus OR Gibbs free energy (negative
thermodynamic potential)
H Enthalpy
I Current, OR moment of inertia, OR second moment of area, the context
makes it clear
Im
Motor current
J Polar second moment of area
kc Copper losses coefficient for an electric motor
ki Iron losses coefficient for an electric motor
kw Windage losses coefficient for an electric motor
KE Kinetic energy
K
m Motor constant
k Peukert coefficient
L Length
m Mass
m˙ Mass flow rate
mb Mass of batteries
N Avogadro’s number, 6.022 × 1023 OR revolutions per second
n Number of cells in a battery, OR a fuel cell stack, OR the number of
moles of substance
P Power OR pressure
Padw Power at the wheels needed to overcome the wind resistance on a vehicle
Padb Power from the battery needed to overcome the wind resistance on a
vehicle
Phc Power needed to overcome the gravitational force of a vehicle down a hill
Pmot-in Electrical power supplied to an electric motor
Pmot-out Mechanical power given out by an electrical motor
Prr Power needed to overcome the rolling resistance of a vehicle
Pte Power supplied at the wheels of a vehicle
Q Charge, e.g. in a capacitor
q Sheer stress
R Electrical resistance, OR the molar gas constant 8.314 JK−1 mol−1
R
a Armature resistance of a motor or generator
RL Resistance of a load
r Radius, of wheel, axle, OR the rotor of a motor, etc.
ri, ro Inner and outer radius of a hollow tube
S Entropy
SE Specific energy
T Temperature, OR Torque, OR the discharge time of a battery in hours
T1, T2 Temperatures at different stages in a process
Tf Frictional torque, e.g. in an electrical motor
ton, toff On and off times for a chopper circuit
v Velocity
V VoltageSymbols xvii
W Work done
z Number of electrons transferred in a reaction
Total magnetic flux
δ Deflection
δt Time step in an iterative process
Change in . . ., e.g. H = change in enthalpy
σ Bending stress
ε Electrical permittivity
η Efficiency
ηc Efficiency of a DC/DC converter
ηfc Efficiency of a fuel cell
ηm Efficiency of an electric motor
ηg Efficiency of a gearbox
η0 Overall efficiency of a drive system
θ Angle of deflection or bend
λ Stoichiometric ratio
µrr Coefficient of rolling resistance
ρ Density
ψ Angle of slope or hill
ω Angular velocity
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