# Elementary Surveying: An Introduction to Geomatics, 15th edition

• Charles D. Ghilani

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## Overview

A highly readable bestseller, Elementary Surveying: An Introduction to Geomatics presents basic concepts and practical material in each of the areas fundamental to modern surveying (geomatics) practice. While introductory, its depth and breadth also make it ideal for self-study and preparation for licensing examinations. The 15th Edition is updated throughout to reflect the latest advances and technology. It includes QR codes linking to video instructions on solving specific problems, and more than 400 figures and illustrations, with numerous example problems to demonstrate computational procedures.

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1. Introduction

1.1 Definition of Surveying

1.2 Geomatics

1.3 History of Surveying

1.4 Geodetic and Plane Surveys

1.5 Importance of Surveying

1.6 Specialized Types of Surveys

1.7 Surveying Safety

1.8 Land and Geographic Information Systems

1.9 Federal Surveying and Mapping Agencies

1.10 The Surveying Profession

1.11 Professional Surveying Organizations

1.12 Surveying on the Internet

1.13 Future Challenges in Surveying

2. Units, Significant Figures, and Field Notes

2.1 Introduction

2.2 Units of Measurement

2.3 International System of Units (SI)

2.4 Significant Figures

2.5 Rounding Off Numbers

2.6 Field Notes

2.7 General Requirements of Handwritten Field Notes

2.8 Types of Field Books

2.9 Kinds of Notes

2.10 Arrangements of Notes

2.11 Suggestions for Recording Notes

2.12 Introduction to Survey Controllers

2.13 Transfer of Files from Survey Controllers

2.14 Digital Data File Management

3.Theory of Errors In Observations

3.1 Introduction

3.2 Direct and Indirect Observations

3.3 Errors in Measurements

3.4 Mistakes

3.5 Sources of Errors in Making Observations

3.6 Types of Errors

3.7 Precision and Accuracy

3.8 Eliminating Mistakes and Systematic Errors

3.9 Probability

3.10 Most Probable Value

3.11 Residuals

3.12 Occurrence of Random Errors

3.13 General Laws of Probability

3.14 Measures of Precision

3.15 Interpretation of Standard Deviation

3.16 The 50%, 90%, and 95% Errors

3.17 Error Propagation

3.18 Applications

3.20 Weights of Observations

4.Leveling–Theory, Methods, and Equipment

4.1 Introduction

4.2 Definitions

4.3 North American Vertical Datum

4.4 Curvature and Refraction

4.5 Methods for Determining Differences in Elevation

4.6 Categories of Levels

4.7 Telescopes

4.8 Level Vials

4.9 Tilting Levels

4.10 Automatic Levels

4.11 Digital Levels

4.12 Tripods

4.13 Hand Level

4.14 Level Rods

5. Leveling–Field Procedures and ComputatIons

5.1 Introduction

5.2 Carrying and Setting Up a Level

5.3 Duties of a Rodperson

5.4 Differential Leveling

5.5 Precision

5.6 Adjustments of Simple Level Circuits

5.7 Reciprocal Leveling

5.8 Three-Wire Leveling

5.9 Profile Leveling

5.10 Grid, Cross-Section, or Borrow-Pit Leveling

5.11 Use of the Hand Level

5.12 Sources of Error in Leveling

5.13 Mistakes

5.14 Reducing Errors and Eliminating Mistakes

5.15 Using Software

6. Distance Measurement

6.1 Introduction

6.2 Summary of Methods For Making Linear Measurements

6.3 Pacing

6.5 Optical Rangefinders

6.6 Tacheometry

6.7 Subtense Bar

6.8 Introduction to Taping

6.9 Taping Equipment and Accessories

6.10 Care of Taping Equipment

6.11 Taping on Level Ground

6.12 Horizontal Measurements on Sloping Ground

6.13 Slope Measurements

6.14 Sources of Error in Taping

6.15 Introduction

6.16 Propagation of Electromagnetic Energy

6.17 Principles of Electronic Distance Measurement

6.18 Electro-Optical Instruments

6.19 Total Station Instruments

6.20 EDM Instruments Without Reflectors

6.21 Computing Horizontal Lengths From Slope Distances

6.22 Errors in Electronic Distance Measurement

6.23 Using Software

7. Angles, Azimuths, and BearIngs

7.1 Introduction

7.2 Units of Angle Measurement

7.3 Kinds of Horizontal Angles

7.4 Direction of a Line

7.5 Azimuths

7.6 Bearings

7.7 Comparison of Azimuths and Bearings

7.8 Computing Azimuths

7.9 Computing Bearings

7.10 The Compass and the Earth's Magnetic Field

7.11 Magnetic Declination

7.12 Variations in Magnetic Declination

7.13 Software for Determining Magnetic Declination

7.14 Local Attraction

7.15 Typical Magnetic Declination Problems

7.16 Mistakes

8. Total Station Instruments; Angle Observations

8.1 Introduction

8.2 Characteristics of Total Station Instruments

8.3 Functions Performed by Total Station Instruments

8.4 Parts of a Total Station Instrument

8.5 Handling and Setting up a Total Station Instrument

8.6 Servo-Driven and Remotely Operated Total Station Instruments

8.7 Relationship of Angles and Distances

8.8 Observing Horizontal Angles with Total Station Instruments

8.9 Observing Multiple Horizontal Angles by the Direction Method

8.10 Closing the Horizon

8.11 Observing Deflection Angles

8.12 Observing Azimuths

8.13 Observing Vertical Angles

8.14 Sights and Marks

8.15 Prolonging a Straight Line

8.16 Balancing-in

8.17 Random Traverse

8.18 Total Stations for Determining Elevation Differences

8.19 Adjustment of Total Station Instruments and their Accessories

8.20 Sources of Error in Total Station Work

8.21 Propagation of Random Errors in Angle Observations

8.22 Mistakes

9. Traversing

9.1 Introduction

9.2 Observation of Traverse Angles or Directions

9.3 Observation of Traverse Lengths

9.4 Selection of Traverse Stations

9.5 Referencing Traverse Stations

9.6 Traverse Field Notes

9.7 Angle Misclosure

9.8 Traversing with Total Station Instruments

9.10 Sources of Error in Traversing

9.11 Mistakes in Traversing

10. Traverse Computations

10.1 Introduction

10.2 Balancing Angles

10.3 Computation of Preliminary Azimuths or Bearings

10.4 Departures and Latitudes

10.5 Departure and Latitude Closure Conditions

10.6 Traverse Linear Misclosure and Relative Precision

10.8 Rectangular Coordinates

10.9 Alternative Methods for Making Traverse Computations

10.10 Inversing

10.11 Computing Final Adjusted Traverse Lengths and Directions

10.12 Coordinate Computations in Boundary Surveys

10.13 Use of Open Traverses

10.14 State Plane Coordinate Systems

10.15 Traverse Computations using Computers

10.16 Locating Blunders in Traverse Observations

10.17 Mistakes in Traverse Computations

11. CoordInate Geometry In SurveyIng Calculations

11.1 Introduction

11.2 Coordinate Forms of Equations for Lines and Circles

11.3 Perpendicular Distance from a Point to a Line

11.4 Intersection of Two Lines, Both Having Known Directions

11.5 Intersection of a Line with a Circle

11.6 Intersection of Two Circles

11.7 Three-Point Resection

11.8 Two-Dimensional Conformal Coordinate Transformation

11.9 Inaccessible Point Problem

11.10 Three-Dimensional Two-Point Resection

11.11 Software

12. Area

12.1 Introduction

12.2 Methods of Measuring Area

12.3 Area by Division into Simple Figures

12.4 Area by Offsets from Straight Lines

12.5 Area by Coordinates

12.6 Area by Double-Meridian Distance Method

12.7 Area of Parcels with Circular Boundaries

12.8 Partitioning of Lands

12.9 Area by Measurements from Maps

12.10 Software

12.11 Sources of Error in Determining Areas

12.12 Mistakes in Determining Areas

13. Global NavigatIon Satellite Systems–Introduction and Principles of Operation

13.1 Introduction

13.2 Overview of GPS

13.3 The GPS Signal

13.4 Reference Coordinate Systems

13.5 Fundamentals of Satellite Positioning

13.6 Errors in Observations

13.7 Differential Positioning

13.8 Kinematic Methods

13.9 Relative Positioning

13.11 The Future

14. Global Navigation SatellIte Systems–Static Surveys

14.1 Introduction

14.2 Field Procedures in Static GNSS Surveys

14.3 Planning Satellite Surveys

14.4 Performing Static Surveys

14.5 Data Processing and Analysis

14.6 Things to Consider

14.7 A Method for Obtaining Orthometric Height Differences Using GNSS

14.8 Sources of Errors in Satellite Surveys

14.9 Mistakes in Satellite Surveys

15. Global Navigation Satellite Systems–KInematic Surveys

15.1 Introduction

15.2 Planning of Kinematic Surveys

15.3 Initialization Techniques

15.4 Equipment Used in Kinematic Surveys

15.5 Methods Used in Kinematic Surveys

15.6 Performing Post-Processed Kinematic Surveys

15.7 Communication in Real-Time Kinematic Surveys

15.8 Real-Time Networks

15.9 Performing Real-Time Kinematic Surveys

15.10 Machine Guidance and Control

15.11 Errors in Kinematic Surveys

15.12 Mistakes in Kinematic Surveys

16.1 Introduction

16.2 Fundamental Condition of Least Squares

16.3 Least-Squares Adjustment by the Observation Equation Method

16.4 Matrix Methods in Least-Squares Adjustment

16.5 Matrix Equations for Precisions of Adjusted Quantities

16.6 Least-Squares Adjustment of Leveling Circuits

16.7 Propagation of Errors

16.8 Least-Squares Adjustment Of GNSS Baseline Vectors

16.9 Least-Squares Adjustment of Conventional Horizontal Plane Surveys

16.10 The Error Ellipse

16.12 Other Measures of Precision for Horizontal Stations

16.13 Software

16.14 Conclusions

17. Mapping Surveys

17.1 Introduction

17.2 Basic Methods for Performing Mapping Surveys

17.3 Map Scale

17.4 Control for Mapping Surveys

17.5 Contours

17.6 Characteristics of Contours

17.7 Method of Locating Contours

17.8 Digital Elevation Models and Automated Contouring Systems

17.9 Basic Field Methods for Locating Topographic Details

17.10 Planning a Laser-Scanning Survey

17.11 Three-Dimensional Conformal Coordinate Transformation

17.12 Selection of Field Method

17.13 Working with Survey Controllers and Field-to-Finish Software

17.14 Hydrographic Surveys

17.15 Sources of Error in Mapping Surveys

17.16 Mistakes in Mapping Surveys

18. Mapping

18.1 Introduction

18.2 Availability of Maps and Related Information

18.3 National Mapping Program

18.4 Accuracy Standards for Mapping

18.5 Manual and Computer-Aided Drafting Procedures

18.6 Map Design

18.7 Map Layout

18.8 Basic Map Plotting Procedures

18.9 Contour Interval

18.10 Plotting Contours

18.11 Lettering

18.12 Cartographic Map Elements

18.13 Drafting Materials

18.14 Automated Mapping and Computer-Aided Drafting Systems

18.15 Migrating Maps between Software Packages

18.16 Impacts of Modern Land and Geographic Information Systems on Mapping

18.18 Sources of Error in Mapping

18.19 Mistakes in Mapping

19. Control Surveys and GeodetIc ReductIons

19.1 Introduction

19.2 The Ellipsoid and Geoid

19.3 The Conventional Terrestrial Pole

19.4 Geodetic Position and Ellipsoidal Radii of Curvature

19.5 Geoid Undulation and De ection of the Vertical

19.6 U.S. Reference Frames

19.7 Transforming Coordinates Between Reference Frames

19.8 Accuracy Standards and Specifications for Control Surveys

19.9 The National Spatial Reference System

19.10 Hierarchy of the National Horizontal Control Network

19.11 Hierarchy of the National Vertical Control Network

19.12 Control Point Descriptions

19.13 Field Procedures for Conventional Horizontal Control Surveys

19.14 Field Procedures for Vertical-Control Surveys

19.15 Reduction of Field Observations to their Geodetic Values

19.16 Geodetic Position Computations

19.17 The Local Geodetic Coordinate System

19.18 Three-Dimensional Coordinate Computations

19.19 Software

20. State Plane CoordInates and Other Map Projections

20.1 Introduction

20.2 Projections Used in State Plane Coordinate Systems

20.3 Lambert Conformal Conic Projection

20.4 Transverse Mercator Projection

20.6 Computing SPCS 83 Coordinates in the Lambert Conformal

20.7 Conic System

20.8 Computing SPCS 83 Coordinates in the Transverse Mercator System 603 Reduction of Distances and Angles to State Plane Coordinate Grids

20.9 Computing State Plane Coordinates of Traverse Stations

20.10 Surveys Extending from One Zone to Another

20.11 The Universal Transverse Mercator Projection

20.12 Other Map Projections

20.13 Ground Versus Grid Problem

20.14 Map Projection Software

21. Boundary Surveys

21.1 Introduction

21.2 Categories of Land Surveys

21.3 Historical Perspectives

21.4 Property Description by Metes and Bounds

21.5 Property Description by Block-and-Lot System

21.6 Property Description by Coordinates

21.7 Retracement Surveys

21.8 Subdivision Surveys

21.9 Partitioning Land

21.10 Registration of Title

21.12 Condominium Surveys

21.13 Geographic and Land Information Systems

21.14 Sources of Error in Boundary Surveys

21.15 Mistakes

22. Surveys of the PublIc Lands

22.1 Introduction

22.2 Instructions for Surveys of the Public Lands

22.3 Initial Point

22.4 Principal Meridian

22.5 Baseline

22.6 Standard Parallels (Correction Lines)

22.7 Guide Meridians

22.8 Township Exteriors, Meridional (Range) Lines, and Latitudinal (Township) Lines

22.9 Designation of Townships

22.10 Subdivision of a Quadrangle into Townships

22.11 Subdivision of a Township into Sections

22.12 Subdivision of Sections

22.13 Fractional Sections

22.14 Notes

22.15 Outline of Subdivision Steps

22.16 Marking Corners

22.17 Witness Corners

22.18 Meander Corners

22.19 Lost and Obliterated Corners

22.20 Accuracy of Public Land Surveys

22.21 Descriptions by Township Section, and Smaller Subdivision

22.22 BLM Land Information System

22.23 Sources of Error

22.24 Mistakes

23. ConstructIon Surveys

23.1 Introduction

23.2 Specialized Equipment for Construction Surveys

23.3 Horizontal and Vertical Control

23.4 Staking Out a Pipeline

23.6 Computing the Bend Angles in Pipelines

23.7 Staking Out a Building

23.8 Staking Out Highways

23.9 Other Construction Surveys

23.10 Construction Surveys Using Total Station Instruments

23.11 Construction Surveys Using GNSS Equipment

23.12 Machine Guidance and Control

23.13 As-built Surveys with Laser Scanning

23.14 Sources of Error in Construction Surveys

23.15 Mistakes

24. HorIzontal Curves

24.1 Introduction

24.2 Degree of Circular Curve

24.3 Definitions and Derivation of Circular Curve Formulas

24.4 Circular Curve Stationing

24.5 General Procedure of Circular Curve Layout by Deflection Angles

24.6 Computing Deflection Angles and Chords

24.7 Notes for Circular Curve Layout by Deflection Angles and Incremental Chords

24.8 Detailed Procedures for Circular Curve Layout by Deflection Angles and Incremental Chords

24.9 Setups on Curve

24.10 Metric Circular Curves by Deflection Angles and Incremental Chords

24.11 Circular Curve Layout by Deflection Angles and Total Chords

24.12 Computation of Coordinates on a Circular Curve

24.13 Circular Curve Layout by Coordinates

24.14 Curve Stakeout Using GNSS Receivers and Robotic Total Stations

24.15 Circular Curve Layout by Offsets

24.16 Special Circular Curve Problems

24.17 Compound and Reverse Curves

24.18 Sight Distance on Horizontal Curves

24.19 Spirals

24.20 Computation of “As-Built” Circular Alignments

24.21 Sources of Error in Laying Out Circular Curves

24.22 Mistakes

25. Vertical Curves

25.1 Introduction

25.2 General Equation of a Vertical Parabolic Curve

25.3 Equation of an Equal Tangent Vertical Parabolic Curve

25.4 High or Low Point on a Vertical Curve

25.5 Vertical Curve Computations Using the Tangent-Offset Equation

25.6 Equal Tangent Property of a Parabola

25.7 Curve Computations by Proportion

25.8 Staking a Vertical Parabolic Curve

25.9 Machine Control in Grading Operations

25.10 Computations for an Unequal Tangent Vertical Curve

25.11 Designing a Curve to Pass Through a Fixed Point

25.12 Sight Distance

25.13 Sources of Error in Laying out Vertical Curves

25.14 Mistakes

26. Volumes

26.1 Introduction

26.2 Methods of Volume Measurement

26.3 The Cross-Section Method

26.4 Types of Cross Sections

26.5 Average-End-Area Formula

26.6 Determining End Areas

26.7 Computing Slope Intercepts

26.8 Prismoidal Formula

26.9 Volume Computations

26.10 Unit-Area, or Borrow-Pit, Method

26.11 Contour-Area Method

26.12 Measuring Volumes of Water Discharge

26.13 Software

26.14 Sources of Error in Determining Volumes

26.15 Mistakes

27. Photogrammetry

27.1 Introduction

27.2 Uses of Photogrammetry

27.3 Aerial Cameras

27.4 Types of Aerial Photographs

27.5 Vertical Aerial Photographs

27.6 Scale of a Vertical Photograph

27.7 Ground Coordinates from a Single Vertical Photograph

27.8 Relief Displacement on a Vertical Photograph

27.9 Flying Height of a Vertical Photograph

27.10 Stereoscopic Parallax

27.11 Stereoscopic Viewing

27.12 Stereoscopic Measurement of Parallax

27.13 Analytical Photogrammetry

27.14 Stereoscopic Plotting Instruments

27.15 Orthophotos

27.16 Ground Control for Photogrammetry

27.17 Flight Planning

27.18 Airborne Laser-Mapping Systems

27.19 Remote Sensing

27.20 Software

27.21 Sources of Error in Photogrammetry

27.22 Mistakes

28. Introduction to GeographIc Information Systems

28.1 Introduction

28.2 Land Information Systems

28.3 GIS Data Sources and Classifications

28.4 Spatial Data

28.5 Nonspatial Data

28.6 Data Format Conversions

28.7 Creating GIS Databases

28.9 GIS Analytical Functions

28.10 GIS Applications

28.11 Data Sources

Appendix A: Tape Correction Problems

Appendix B: Example Noteforms

Appendix C: Astronomical Observations

Appendix D: Using the Worksheets from the Companion Website

Appendix E: Introduction to Matrices

Appendix F: U.S. State Plane Coordinate System Defining Parameters

Appendix G: Answers to Selected Problems