Automotive Science and Mathematics Allan Bonnick

265 Pages·2008·4.87 MB·English

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Automotive Science and Mathematics
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Automotive Science and
Mathematics
Allan Bonnick
AMSTERDAM•BOSTON•HEIDELBERG•LONDON•NEWYORK•OXFORD
PARIS•SANDIEGO•SANFRANCISCO•SINGAPORE•SYDNEY•TOKYO
Butterworth-HeinemannisanimprintofElsevier
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Butterworth-HeinemannisanimprintofElsevier
LinacreHouse,JordanHill,OxfordOX28DP,UK
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Firstedition2008
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Contents
Preface xvii
Units and symbols xviii
Glossary xix
1 Arithmetic 1
1.1 Terminology of number systems 1
1.2 The decimal system 1
Addition and subtraction of decimals 2
Multiplication and division – decimals 2
1.3 Degrees of accuracy 4
Rounding numbers 4
1.4 Accuracy in calculation 4
1.5 Powers and roots and standard form 4
General rules for indices 5
1.6 Standard form 5
Multiplying and dividing numbers in standard form 5
1.7 Factors 6
1.8 Fractions 6
Addition and subtraction 6
Fractions and whole numbers 6
Combined addition and subtraction 7
Multiplication and division of fractions 7
Order of performing operations in problems involving fractions 7
1.9 Ratio and proportion. Percentages 8
Examples of ratios in vehicle technology 8
1.10 The binary system 10
Most significant bit (MSB) 10
Hexadecimal 10
Converting base 10 numbers to binary 10
Uses of binary numbers in vehicle systems 10
1.11 Directed numbers 11
Rules for dealing with directed numbers 11
1.12 Summary of main points 12
1.13 Exercises 12
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vi Contents
2 Statistics – An introduction 16
2.1 Definition 16
2.2 Collecting and sorting raw data 17
2.3 Making sense of data 17
Discrete variables 17
Continuous variables 17
2.4 Descriptive statistics – pictographs 18
Pie charts 18
2.5 Interpreting data. Statistical inference 19
Frequency and tally charts 19
The tally chart and frequency distribution 19
2.6 Importance of the shape of a frequency distribution 20
The histogram 20
The frequency polygon 20
Cumulative frequency 21
2.7 Interpreting statistics 22
Sampling 22
2.8 Features of the population that are looked for in a sample 22
Average 22
2.9 The normal distribution 23
Importance of the normal distribution 24
Other ways of viewing frequency distributions – quartiles, deciles,
percentiles 25
2.10 Summary of main points 26
2.11 Exercises 26
3 Algebra and graphs 29
3.1 Introduction 29
3.2 Formulae 29
3.3 Evaluating formulae 29
3.4 Processes in algebra 30
Brackets 30
3.5 Algebraic expressions and simplification 30
Expression 30
3.6 Factorising 31
3.7 Equations 31
Solving equations 31
3.8 Transposition of formulae 33
3.9 Graphs 34
Variables 34
Scales 34
Coordinates 35
3.10 Graphs and equations 36
The straight-line graph 36
3.11 Summary of main points 37
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Contents vii
3.12 Exercises 38
Exercises – Section 3.3 38
Exercises – Section 3.4 38
Exercises – Section 3.5 38
Exercises – Section 3.6 38
Exercises – Section 3.7 38
Exercises – Section 3.8 38
Exercises – Section 3.10 38
4 Geometry and trigonometry 41
4.1 Angles 41
Angular measurement 41
Angles and rotation 41
4.2 Examples of angles in automotive work 42
Angles and lines 43
Adding and subtracting angles 43
4.3 Types of angle 44
Adjacent angles 44
Opposite angles 44
Corresponding angles 44
Alternate angles 44
Supplementary angles 44
Complementary angles 44
4.4 Types of triangle 45
Acute angled triangle 45
Obtuse angled triangle 45
Equilateral triangle 45
Isosceles triangle 45
Scalene triangle 45
Right angled triangle 46
Labelling sides and angles of a triangle 46
Sum of the three angles of a triangle 46
4.5 Pythagoras’ theorem 46
4.6 Circles 46
Ratio of diameter and circumference (cid:2) 47
Length of arc 47
4.7 Timing marks 47
4.8 Wheel revolutions and distance travelled 48
4.9 Valve opening area 48
4.10 Trigonometry 48
4.11 Using sines, cosines and tangents 49
Sines 49
Cosines 50
Tangents 51
4.12 Summary of formulae 52
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viii Contents
4.13 Exercises 52
Exercises – Section 4.2 53
Exercises – Section 4.3 53
Exercises – Section 4.4 54
Exercises – Section 4.5 55
Exercises – Section 4.6 55
5 Forces 58
5.1 Force 58
5.2 Types of force – examples 58
5.3 Describing forces 58
5.4 Graphical representation of a force 58
5.5 Addition of forces 59
5.6 Parallelogram of forces 60
5.7 Triangle of forces 60
5.8 Resolution of forces 61
5.9 Mass 62
5.10 Equilibrium 62
5.11 Pressure 62
5.12 Pressure in hydraulic systems 63
5.13 Hooke’s law 64
5.14 Practical applications 65
5.15 Summary 65
5.16 Exercises 65
6 Materials – Stress, strain, elasticity 68
6.1 Introduction 68
6.2 Stress 68
Types of stress 68
6.3 Tensile test 69
6.4 Examples of stress and strain 70
6.5 Stress raisers 71
6.6 Strain 72
Shear strain 72
6.7 Elasticity 73
Stress, strain, elasticity 73
6.8 Tensile strength 73
6.9 Factor of safety 74
6.10 Torsional stress 74
6.11 Strain energy 75
6.12 Strength of materials 75
6.13 Other terms used in describing materials 75
6.14 Non-ferrous metals 76
6.15 Non-metallic materials 76
Kevlar 76
6.16 Recycling of materials 77
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Contents ix
6.17 Summary of main formulae 77
6.18 Exercises 77
7 Levers and moments, torque and gears 79
7.1 Levers 79
7.2 Principles of leverage 79
7.3 The principle of moments 79
7.4 The bell crank lever 81
A practical application of the bell crank lever 81
7.5 Axle loadings 82
7.6 Torque 83
7.7 Engine torque 83
7.8 Leverage and gears 84
Torque multiplication 84
Drivers and driven 85
7.9 Gear trains: calculating gear ratios 85
Spur gear ratios 85
7.10 Couples 85
7.11 Summary of main points 85
7.12 Exercises 86
8 Work energy, power and machines 89
8.1 Work 89
8.2 Power 89
8.3 Work done by a torque 90
8.4 Work done by a constantly varying force 90
Mid-ordinate method for calculating work done 91
8.5 Energy 92
Potential energy 92
Chemical energy 92
Conservation of energy 92
Energy equation 92
Kinetic energy 92
Energy of a falling body 93
Kinetic energy of rotation 93
8.6 Machines 94
Mechanical advantage 94
Velocity ratio (movement ratio) 95
Efficiency of a machine 95
Work done against friction 95
A steering mechanism as a machine 95
8.7 Summary of formulae 97
8.8 Exercises 98
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