Elementary Surveying, Global Edition

Charles D. Ghilani / Paul Wolf  
Total pages
April 2015
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Elementary Surveying, Global Edition
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For Surveying courses offered in Civil Engineering departments


This highly readable, best-selling text presents basic concepts and practical material in each of the areas fundamental to modern surveying (geomatics) practice. Its depth and breadth are ideal for self-study. Elementary Surveying, Fourteenth Edition, is updated throughout to reflect the latest advances and technology.


Teaching and Learning Experience

This program will provide a better teaching and learning experience—for you and your students. It will help:

  • Emphasize the Theory of Errors in Surveying Work: Common errors and mistakes are listed to remind students to exercise caution in their work.
  • Use Strong Pedagogy Tools to Teach: Numerous worked example problems, figures, illustrations, and end-of-chapter problems help students apply concepts.
  • Reflect the Latest Advances in Technology: To keep your course current and relevant, this edition covers the latest advancements in surveying technology.


Emphasize the Theory of Errors in Surveying Work

  • At the end of each chapter, common errors and mistakes related to the topic covered are listed to remind students to exercise caution in their work.
  • Practical suggestions from the authors’ years of experience are interjected throughout the text. 

Use Strong Pedagogy Tools to Teach

  • More than 400 figures and illustrations help clarify discussions.
  • Numerous worked example problems illustrate computational procedures.
  • Over 1000 end-of-chapter problems help students apply concepts.
    • UPDATED: Many of the 1000 after-chapter problems have been rewritten so that instructors can create new assignments for their students.
  • Solutions to Selected Problems are available in an Appendix for students to check their work.
  • The Companion Website features the following resources:
    • UPDATED: Updated versions of Stats, Wolfpack, and Matrix are included on the Companion website www.pearsonhighered.com/ghilani.
      • These programs contain options for statistical computations, traverse computations for polygon, link, and radial traverses; area calculations; astronomical azimuth reduction; two-dimensional coordinate transformations; horizontal and vertical curve computations; and least squares adjustments.
      • Mathcad® worksheets and Excel® spreadsheets are included.
      • The Mercator, Albers Equal Area, Oblique Stereographic, and Oblique Mercator map projections are included to give students extra experience with map projections.
    • Every new copy of the book comes with access to Video Solutions and a Pearson eText. Video solutions are complete, step-by-step solution walkthroughs of representative homework problems. The Pearson eText is a complete on-line version of the book that includes highlighting, note-taking and search capabilities. These resources can be accessed on the Companion Website.
      • NEW: Seven new Video Solutions demonstrate instrumental procedures and record keeping.
    • An Instructor’s Manual is available to qualifying instructors on the Companion Website. Contact your Pearson Representative for information on how to access them.

New to this Edition

Reflect the Latest Advances in Technology

  • An emphasis on total stations as the instruments for making angle and distance observations provides an up-to-date presentation of surveying equipment and procedures.
    • NEW: Images of new instruments and field book pages that match today’s instruments.
    • UPDATED: Increased discussions on the changes in reference systems.
    • NEW: Discussion on planning a ground-based laser-scanning survey.
    • NEW: Discussion on the landxml format to exchange mapping files.
    • REVISED: Discussion on point codes in field-to-finish surveying.
    • EXTENDED: Coverage on errors present in electronic distance measurements.
    • NEW: Introduction to mobile mapping systems.
  • Several sections on machine control, localization of GPS surveys, and construction staking using GPS are included.
  • Coverage of both automatic and digital levels for elevation determination.
  • An appendix on Introduction to Matrices.

Table of Contents

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

Part I ∉ Units and Significant Figures

2.1 Introduction

2.2 Units of Measurement

2.3 International System of Units (SI)

2.4 Significant Figures

2.5 Rounding Off Numbers

Part II ∉ Field Notes

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

2.15 Advantages and Disadvantages of Survey Controllers



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 Percent Errors

3.17 Error Propagation

3.17.1 Error of a Sum

3.17.2 Error of a Series

3.17.3 Error of a Product

3.17.4 Error of the Mean

3.18 Applications

3.19 Conditional Adjustment of Observations

3.20 Weights of Observations

3.21 Least-Squares Adjustment

3.22 Using Software



4  Leveling–Theory, Methods, and Equipment

Part I ∉ Leveling–Theory and Methods

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

4.5.1 Measuring Vertical Distances by Taping or Electronic Methods

4.5.2 Differential Leveling

4.5.3 Barometric Leveling

4.5.4 Trigonometric Leveling

Part II ∉ Equipment for Differential Leveling

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

4.15 Testing and Adjusting Levels

4.15.1 Requirements for Testing and Adjusting Instruments

4.15.2 Adjusting for Parallax

4.15.3 Testing and Adjusting Level Vials

4.15.4 Preliminary Adjustment of the Horizontal Cross Hair

4.15.5 Testing and Adjusting the Line of Sight



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

5.9.1 Staking and Stationing the Reference Line

5.9.2 Field Procedures for Profile Leveling

5.9.3 Drawing and Using the Profile

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

5.11 Use of the Hand Level

5.12 Sources of Error in Leveling

5.12.1 Instrumental Errors

5.12.2 Natural Errors

5.12.3 Personal Errors

5.13 Mistakes

5.14 Reducing Errors and Eliminating Mistakes

5.15 Using Software



6 Distance Measurement

Part I ∉ Methods for Measuring Distances

6.1 Introduction

6.2 Summary of Methods for Making Linear Measurements

6.3 Pacing

6.4 Odometer Readings

6.5 Optical Rangefinders

6.6 Tacheometry

6.7 Subtense Bar

Part II ∉ Distance Measurements by Taping

6.8 Introduction to Taping

6.9 Taping Equipment and Accessories

6.10 Care of Taping Equipment

6.11 Taping on Level Ground

6.11.1 Lining In

6.11.2 Applying Tension

6.11.3 Plumbing

6.11.4 Marking Tape Lengths

6.11.5 Reading the Tape

6.11.6 Recording the Distance

6.12 Horizontal Measurements on Sloping Ground

6.13 Slope Measurements

6.14 Sources of Error in Taping

6.14.1 Incorrect Length of Tape

6.14.2 Temperature Other Than Standard

6.14.3 Inconsistent Pull

6.14.4 Sag

6.14.5 Tape Not Horizontal and Tape Off-Line

6.14.6 Improper Plumbing

6.14.7 Faulty Marking

6.14.8 Incorrect Reading or Interpolation

6.14.9 Summary of Effects of Taping Errors

Part III ∉ Electronic Distance Measurement

6.17 Introduction

6.18 Propagation of Electromagnetic Energy

6.19 Principles of Electronic Distance Measurement

6.20 Electro-Optical Instruments

6.21 Total Station Instruments

6.22 EDM Instruments Without Reflectors

6.23 Computing Horizontal Lengths From Slope Distances

6.23.1 Reduction of Short Lines by Elevation Differences

6.23.2 Reduction of Short Lines by Zenith or Altitude Angle

6.24 Errors in Electronic Distance Measurement

6.24.1 Personal Errors

6.24.2 Instrumental Errors

6.24.3 Natural Errors

6.25 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

Part I ∉ Total Station Instruments

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

Part II ∉ Angle Observations

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

8.19.1 Adjustment of Plate-Level Vials

8.19.2 Adjustment of Tripods

8.19.3 Adjustment of Tribrachs

8.19.4 Adjustment of Plummets

8.19.5 Adjustment of Circular Level Bubbles

8.20 Sources of Error in Total Station Work

8.20.1 Instrumental Errors

8.20.2 Natural Errors

8.20.3 Personal Errors

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

9.2.1 Traversing by Interior Angles

9.2.2 Traversing by Angles to the Right

9.2.3 Traversing by Deflection Angles

9.2.4 Traversing by Azimuths

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

9.9 Radial Traversing

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

10.7 Traverse Adjustment

10.7.1 Compass (Bowditch) Rule

10.7.2 Least-Squares Method

10.8 Rectangular Coordinates

10.9 Alternative Methods for Making Traverse Computations

10.9.1 Balancing Angles by Adjusting Azimuths or Bearings

10.9.2 Balancing Departures and Latitudes by Adjusting Coordinates

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 Measurements

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

12.4.1 Regularly Spaced Offsets

12.4.2 Irregularly Spaced Offsets

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

12.8.1 Trial and Error Method

12.8.2 Use of Simple Geometric Figures

12.8.3 Coordinate Method

12.9 Area by Measurements from Maps

12.9.1 Area by Counting Coordinate Squares

12.9.2 Area by Scaled Lengths

12.9.3 Area by Digitizing Coordinates

12.9.4 Area by Planimeter

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

13.4.1 The Satellite Reference Coordinate System

13.4.2 The Geocentric Coordinate System

13.4.3 The Geodetic Coordinate System

13.4.4 Evolution of WGS84 Reference Frame

13.5 Fundamentals of Satellite Positioning

13.5.1 Code Ranging

13.5.2 Carrier Phase-Shift Measurements

13.6 Errors in Observations

13.6.1 Clock Bias

13.6.2 Refraction

13.6.3 Other Error Sources

13.6.4 Geometry of Observed Satellites

13.7 Differential Positioning

13.8 Kinematic Methods

13.9 Relative Positioning

13.9.1 Single Differencing

13.9.2 Double Differencing

13.9.3 Triple Differencing

13.10 Other Satellite Navigation Systems

13.10.1 The GLONASS Constellation

13.10.2 The Galileo System

13.10.3 The Compass System

13.10.4 Summary

13.11 The Future



14 Global Navigation Satellite Systems–Static Surveys

14.1 Introduction

14.2 Field Procedures in Satellite Surveys

14.2.1 Static Relative Positioning

14.2.2 Rapid Static Relative Positioning

14.2.3 Pseudokinematic Surveys

14.3 Planning Satellite Surveys

14.3.1 Preliminary Considerations

14.3.2 Selecting the Appropriate Survey Method

14.3.3 Field Reconnaissance

14.3.4 Developing an Observation Scheme

14.3.5 Availability of Reference Stations

14.4 Performing Static Surveys

14.5 Data Processing and Analysis

14.5.1 Specifications for Static Surveys

14.5.2 Analysis of Fixed Baseline Measurements

14.5.3 Analysis of Repeat Baseline Measurements

14.5.4 Analysis of Loop Closures

14.5.5 Baseline Network Adjustment

14.5.6 The Survey Report

14.6 Things to Consider

14.7 Sources of Errors in Satellite Surveys

14.7.1 Instrumental Errors

14.7.2 Natural Errors 378

14.7.3 Personal Errors 378

14.8 Mistakes in Satellite Surveys



15 Global Navigation Satellite System–Kinematic Surveys

15.1 Introduction

15.2 Planning of Kinematic Surveys

15.3 Initialization

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 Adjustments by Least Squares

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

16.9.1 Linearizing Nonlinear Equations

16.9.2 The Distance Observation Equation

16.9.3 The Azimuth Observation Equation

16.9.4 The Angle Observation Equation

16.9.5 A Traverse Example Using WOLFPACK

16.10 The Error Ellipse

16.11 Adjustment Procedures

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

17.9.1 Radiation by Total Station

17.9.2 Coordinate Squares or “Grid” Method

17.9.3 Offsets from a Reference Line

17.9.4 Topographic Detailing with GNSS

17.9.5 Laser Scanning

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

17.14.1 Equipment for Making Soundings

17.14.2 Locating Soundings

17.14.3 Hydrographic Mapping

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

18.8.1 Manually Plotting by Coordinates

18.8.2 Plotting Using CADD

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

18.17 Sources of Error in Mapping

18.18 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 Deflection of the Vertical

19.6 U.S. Reference Frames

19.6.1 North American Horizontal Datum of 1927 (NAD27)

19.6.2 North American Horizontal Datum of 1983 (NAD83)

19.6.3 Later Versions of NAD83

19.6.4 National Geodetic Vertical Datum of 1929 (NGVD29)

19.6.5 North American Vertical Datum of 1988 (NAVD88)

19.6.6 Future Reference Frames in the United States

19.7 Transforming Coordinates between Reference Frames

19.7.1 Helmert Transformation and Its Variant

19.7.2 The Two plus One Approach

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

19.13.1 Triangulation

19.13.2 Precise Traverse

19.13.3 Trilateration

19.13.4 Combined Networks

19.14 Field Procedures for Vertical-Control Surveys

19.15 Reduction of Field Observations to Their Geodetic Values

19.15.1 Reduction of Distance Observations Using Elevations

19.15.2 Reduction of Distance Observations Using Vertical Angles

19.15.3 Reduction of Directions and Angles

19.15.4 Leveling and Orthometric Heights

19.16 Geodetic Position Computations

19.16.1 Direct Geodetic Problem

19.16.2 Inverse Geodetic Problem

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

20.5 State Plane Coordinates in NAD27 and NAD83

20.6 Computing SPCS83 Coordinates in the Lambert Conformal Conic System

20.6.1 Zone Constants

20.6.2 The Direct Problem

20.6.3 The Inverse Problem

20.7 Computing SPCS83 Coordinates in the Transverse Mercator System

20.7.1 Zone Constants

20.7.2 The Direct Problem

20.7.2 The Inverse Problem

20.8 Reduction of Distances and Angles to State Plane Coordinate Grids

20.8.1 Grid Reduction of Distances

20.8.2 Grid Reduction of Azimuths and Angles

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

20.12.1 Oblique Stereographic Map Projection

20.12.2 Oblique Mercator Map Projection

20.13 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

21.11 Adverse Possession and Easements

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 Lands 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

23.2.1 Visible Laser-Beam Instruments

23.2.2 Reflectorless Total Stations

23.2.3 Laser Scanners

23.3 Horizontal and Vertical Control

23.4 Staking Out a Pipeline

23.5 Staking Pipeline Grades

23.6 Staking Out a Building

23.7 Staking Out Highways

23.8 Other Construction Surveys

23.9 Construction Surveys Using Total Station Instruments

23.10 Construction Surveys Using GNSS Equipment

23.11 Machine Guidance and Control

23.12 As-Built Surveys with Laser Scanning

23.13 Sources of Error in Construction Surveys

23.14 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

24.16.1 Passing a Circular Curve through a Fixed Point

24.16.2 Intersection of a Circular Curve and a Straight Line

24.16.3 Intersection of Two Circular Curves

 24.17 Compound and Reverse Curves

24.18 Sight Distance on Horizontal Curves

24.19 Spirals

24.19.1 Spiral Geometry

24.19.2 Spiral Calculation and Layout

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

25.5.1 Example Computations Using the English System of Units

25.5.2 Example Computations Using the Metric System

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

26.6.1 End Areas by Simple Figures

26.6.2 End Areas by Coordinates

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

27.14.1 Basic Concepts in Stereoplotters

27.14.2 Analytical Stereoplotters

27.14.3 Softcopy Stereoplotters

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

28.4.1 Simple Spatial Objects

28.4.2 Vector and Raster Formats

28.4.3 Topology

28.5 Nonspatial Data

28.6 Data Format Conversions

28.6.1 Vector-to-Raster Conversion

28.6.2 Raster-to-Vector Conversion

28.7 Creating GIS Databases

28.7.1 Generating Digital Data from Field Surveys

28.7.2 Digitizing from Aerial Photos with Stereoplotters

28.7.3 Digitizing Existing Graphic Materials

28.7.4 Keyboard Entry

28.7.5 Existing Digital Data Sets

28.7.6 Scanning

28.8 Metadata

28.9 GIS Analytical Functions

28.9.1 Proximity Analysis

28.9.2 Boundary Operations

28.9.3 Spatial Joins

28.9.4 Logical Operations

28.9.5 Other GIS Functions

28.10 GIS Applications

28.11 Data Sources



A Tape Correction Problems

A.1 Correcting Systematic Errors in Taping

B Example Noteforms

C Astronomical Observations

C.1 Introduction

C.2 Overview of Usual Procedures for Astronomical Azimuth Determination

C.3 Ephemerides

C.4 Definitions

C.5 Time

C.6 Timing Observations

C.7 Computations for Azimuth from Polaris Observations by the Hour Angle Method

C.8 Azimuth from Solar Observations

C.9 Importance of Precise Leveling

D Using the Worksheets on the Companion Disk

D.1 Introduction

D.2 Using the Files

D.3 Worksheets as an Aid in Learning

E Introduction to Matrices

E.1 Introduction

E.2 Definition of a Matrix

E.3 The Dimensions of a Marix

E.4 The Transpose of a Matrix

E.5 Matrix Addition

E.6 Matrix Multiplication

E.7 Matrix Inverse

F U.S. State Plane Coordinate System Defining Parameters

F.1 Introduction

F.2 Defining Parameters for States Using the Lambert Conformal Conic Map Projection

F.3 Defining Parameters for States Using the Transverse Mercator Map Projection

G Answers to Selected Problems