## Contents

Preface ix

Acknowledgements xi

1 Introduction 1

2 General principles of surveying 5

3 Principal surveying activities 12

4 Angle measurement 24

5 Distance measurement 39

6 Levelling 44

7 Satellite surveying 53

8 Geoids and ellipsoids 68

9 Map projections 80

10 Adjustment of observations 97

11 Reduction of distance measurements 115

12 Reciprocal vertical angles 128

Appendices

A Constants, ellipsoid and projection data 135

B Control stations 137

C Worked example in transforming between ellipsoids 140

D Calculation of local scale factors in transverse Mercator projections 142

E Worked examples in adjustment 145

F Worked example in setting out 152

G Booking sheets 157

H Calculation sheets 162

Glossary 165

Bibliography 169

Index 171

## Preface

More than almost any other engineering discipline, surveying is a practical, hands-on

skill. It is impossible to become an expert surveyor, or even a competent one, without

using real surveying instruments and processing real data. On the other hand, it is

undoubtedly possible to become a very useful surveyor without ever reading anything

more theoretical than the instrument manufacturers’ operating instructions.

What, then, is the purpose of this book?

A second characteristic of surveying is that it involves much higher orders of accuracy

than most other engineering disciplines. Points must often be set out to an accuracy of 5

mm with respect to other points, which may be more than 1 km away. Achieving this

level of accuracy requires not only high-quality instruments, but also a meticulous

approach to gathering and processing the necessary data. Errors and mistakes which are

minute by normal engineering standards can lead to results which are catastrophic in the

context of surveying.

Yet in the real world, errors will always exist and approximations and assumptions

must always be made. The accepted techniques of surveying have been developed to

eliminate those errors which are avoidable, and to minimise the effects of those which are

not. Likewise, the formulae used by surveyors incorporate many assumptions and

approximations, and save time when the errors which they introduce are negligible by

comparison with the errors already inherent in the observations.

No two jobs in surveying are exactly the same. A competent professional surveyor

therefore needs to know the scope and limitations of each surveying instrument,

technique and formula—partly to avoid using unnecessarily elaborate methods for a

simple job, but mainly to avoid using simplifying assumptions which are invalidated by

the scale or required precision of the project. This knowledge can only be developed by

understanding how the accepted techniques have evolved, and how the formulae work—

and this understanding is becoming increasingly hard to acquire with the advent of

electronic ‘black box’ surveying instruments and software applications, which perform

elaborate calculations whose details are hidden from the user.

It is this understanding which this book sets out to provide. The methods for using

each generic class of surveying instrument have been described in a way which is

intended to show why they have evolved, and the calculations are similarly explained,

such that the inherent assumptions can be clearly identified. Wherever necessary,

practical guidance is also given on the range of distances for which a particular formula

or technique is both necessary and valid.

The material in this book is based on the surveying courses taught in the Engineering

Department at Cambridge University, and I am grateful to the many colleagues who have

both enhanced my own understanding of the subject and contributed to past editions of

the ‘Survey Notes’, from which this book has evolved. The philosophy of engineering

education at Cambridge has always been that an understanding of a subject’s fundamental

principles is the key to keeping abreast with the changes which technology inevitably

brings, and indeed to initiating appropriate changes, when technology makes this

possible. I hope that this book has succeeded in applying that philosophy to surveying, in

a way which will be of value to those who read it.