Elementary Surveying

Dr. Charles Ghilani is a Professor of Engineering in the B.S. Surveying Engineering and A.S. Surveying Technology programs at Penn State. He holds a Ph.D. and M.S. in Civil and Environmental Engineering from the University of Wisconsin-Madison, and a B.S. degree in mathematics and education from the University of Wisconsin-Milwaukee. He has been involved in education since 1974; teaching at various levels from elementary through graduate school.Dr. Ghilani has received numerous awards including: a Campus Innovation Award (1991) and Professional Development Award (1994), P.S.L.S. presidential commendation in 1990, Outstanding Club Advisor in 1992, a Distinguished Service Award from the Pennsylvania Society of Land Surveyors in 1995, an American Congress on Surveying and Mapping (ACSM) fellowship (1999), and the Earle J. Fennell Award (2001) for outstanding service in surveying and mapping education from ACSM. He is a member of the graduate faculty at Penn State and University of Maine. Dr. Ghilani is a member of the American Congress of Surveying and Mapping, the American Society of Photogrammetry and Remote Sensing, the Wisconsin Society of Land Surveyors, and the Pennsylvania Society of Land Surveyors.

• 1. Introduction1.1 Definition of Surveying1.2 Geomatics1.3 History of Surveying1.4 Geodetic and Plane Surveys1.5 Importance of Surveying1.6 Specialized Types of Surveys1.7 Surveying Safety1.8 Land and Geographic Information Systems1.9 Federal Surveying and Mapping Agencies1.10 The Surveying Profession1.11 Professional Surveying Organizations1.12 Surveying on the Internet1.13 Future Challenges in Surveying 2. Units, Significant Figures, and Field Notes2.1 Introduction2.2 Units of Measurement2.3 International System of Units (SI)2.4 Significant Figures2.5 Rounding Off Numbers2.6 Field Notes2.7 General Requirements of Handwritten Field Notes2.8 Types of Field Books2.9 Kinds of Notes2.10 Arrangements of Notes2.11 Suggestions for Recording Notes2.12 Introduction to Survey Controllers2.13 Transfer of Files from Survey Controllers2.14 Digital Data File Management2.15 Advantages and Disadvantages of Survey Controllers 3.Theory of Errors In Observations3.1 Introduction3.2 Direct and Indirect Observations3.3 Errors in Measurements3.4 Mistakes3.5 Sources of Errors in Making Observations3.6 Types of Errors3.7 Precision and Accuracy3.8 Eliminating Mistakes and Systematic Errors3.9 Probability3.10 Most Probable Value3.11 Residuals3.12 Occurrence of Random Errors3.13 General Laws of Probability3.14 Measures of Precision3.15 Interpretation of Standard Deviation3.16 The 50%, 90%, and 95% Errors3.17 Error Propagation3.18 Applications3.19 Conditional Adjustment of Observations3.20 Weights of Observations3.21 Least-Squares Adjustment 4.Leveling—Theory, Methods, and Equipment4.1 Introduction4.2 Definitions4.3 North American Vertical Datum4.4 Curvature and Refraction4.5 Methods for Determining Differences in Elevation4.6 Categories of Levels4.7 Telescopes4.8 Level Vials4.9 Tilting Levels4.10 Automatic Levels4.11 Digital Levels4.12 Tripods4.13 Hand Level4.14 Level Rods4.15 Testing and Adjusting Levels 5. Leveling—Field Procedures and ComputatIons5.1 Introduction5.2 Carrying and Setting Up a Level5.3 Duties of a Rodperson5.4 Differential Leveling5.5 Precision5.6 Adjustments of Simple Level Circuits5.7 Reciprocal Leveling5.8 Three-Wire Leveling5.9 Profile Leveling5.10 Grid, Cross-Section, or Borrow-Pit Leveling5.11 Use of the Hand Level5.12 Sources of Error in Leveling5.13 Mistakes5.14 Reducing Errors and Eliminating Mistakes5.15 Using Software 6. Distance Measurement6.1 Introduction6.2 Summary of Methods For Making Linear Measurements6.3 Pacing6.4 Odometer Readings6.5 Optical Rangefinders6.6 Tacheometry6.7 Subtense Bar6.8 Introduction to Taping6.9 Taping Equipment and Accessories6.10 Care of Taping Equipment6.11 Taping on Level Ground6.12 Horizontal Measurements on Sloping Ground6.13 Slope Measurements6.14 Sources of Error in Taping6.15 Introduction6.16 Propagation of Electromagnetic Energy6.17 Principles of Electronic Distance Measurement6.18 Electro-Optical Instruments6.19 Total Station Instruments6.20 EDM Instruments Without Reflectors6.21 Computing Horizontal Lengths From Slope Distances6.22 Errors in Electronic Distance Measurement6.23 Using Software 7. Angles, Azimuths, and BearIngs7.1 Introduction7.2 Units of Angle Measurement7.3 Kinds of Horizontal Angles7.4 Direction of a Line7.5 Azimuths7.6 Bearings7.7 Comparison of Azimuths and Bearings7.8 Computing Azimuths7.9 Computing Bearings7.10 The Compass and the Earth's Magnetic Field7.11 Magnetic Declination7.12 Variations in Magnetic Declination7.13 Software for Determining Magnetic Declination7.14 Local Attraction7.15 Typical Magnetic Declination Problems7.16 Mistakes 8. Total Station Instruments; Angle Observations8.1 Introduction8.2 Characteristics of Total Station Instruments8.3 Functions Performed by Total Station Instruments8.4 Parts of a Total Station Instrument8.5 Handling and Setting up a Total Station Instrument8.6 Servo-Driven and Remotely Operated Total Station Instruments8.7 Relationship of Angles and Distances8.8 Observing Horizontal Angles with Total Station Instruments8.9 Observing Multiple Horizontal Angles by the Direction Method8.10 Closing the Horizon8.11 Observing Deflection Angles8.12 Observing Azimuths8.13 Observing Vertical Angles8.14 Sights and Marks8.15 Prolonging a Straight Line8.16 Balancing-in8.17 Random Traverse8.18 Total Stations for Determining Elevation Differences8.19 Adjustment of Total Station Instruments and their Accessories8.20 Sources of Error in Total Station Work8.21 Propagation of Random Errors in Angle Observations8.22 Mistakes 9. Traversing9.1 Introduction9.2 Observation of Traverse Angles or Directions9.3 Observation of Traverse Lengths9.4 Selection of Traverse Stations9.5 Referencing Traverse Stations9.6 Traverse Field Notes9.7 Angle Misclosure9.8 Traversing with Total Station Instruments9.9 Radial Traversing9.10 Sources of Error in Traversing9.11 Mistakes in Traversing 10. Traverse Computations10.1 Introduction10.2 Balancing Angles10.3 Computation of Preliminary Azimuths or Bearings10.4 Departures and Latitudes10.5 Departure and Latitude Closure Conditions10.6 Traverse Linear Misclosure and Relative Precision10.7 Traverse Adjustment10.8 Rectangular Coordinates10.9 Alternative Methods for Making Traverse Computations10.10 Inversing10.11 Computing Final Adjusted Traverse Lengths and Directions10.12 Coordinate Computations in Boundary Surveys10.13 Use of Open Traverses10.14 State Plane Coordinate Systems10.15 Traverse Computations using Computers10.16 Locating Blunders in Traverse Observations10.17 Mistakes in Traverse Computations 11. CoordInate Geometry In SurveyIng Calculations      11.1 Introduction11.2 Coordinate Forms of Equations for Lines and Circles11.3 Perpendicular Distance from a Point to a Line11.4 Intersection of Two Lines, Both Having Known Directions11.5 Intersection of a Line with a Circle11.6 Intersection of Two Circles11.7 Three-Point Resection11.8 Two-Dimensional Conformal Coordinate Transformation11.9 Inaccessible Point Problem11.10 Three-Dimensional Two-Point Resection11.11 Software 12. Area      12.1 Introduction12.2 Methods of Measuring Area12.3 Area by Division into Simple Figures12.4 Area by Offsets from Straight Lines12.5 Area by Coordinates12.6 Area by Double-Meridian Distance Method12.7 Area of Parcels with Circular Boundaries12.8 Partitioning of Lands12.9 Area by Measurements from Maps12.10 Software12.11 Sources of Error in Determining Areas12.12 Mistakes in Determining Areas 13. Global NavigatIon Satellite Systems—Introduction and Principles of Operation13.1 Introduction13.2 Overview of GPS13.3 The GPS Signal13.4 Reference Coordinate Systems13.5 Fundamentals of Satellite Positioning13.6 Errors in Observations13.7 Differential Positioning13.8 Kinematic Methods13.9 Relative Positioning13.10 Other Satellite Navigation Systems13.11 The Future 14. Global Navigation SatellIte Systems—Static Surveys14.1 Introduction14.2 Field Procedures in Static GNSS Surveys14.3 Planning Satellite Surveys14.4 Performing Static Surveys14.5 Data Processing and Analysis14.6 Things to Consider14.7 A Method for Obtaining Orthometric Height Differences Using GNSS14.8 Sources of Errors in Satellite Surveys14.9 Mistakes in Satellite Surveys 15. Global Navigation Satellite Systems—KInematic Surveys15.1 Introduction15.2 Planning of Kinematic Surveys15.3 Initialization Techniques15.4 Equipment Used in Kinematic Surveys15.5 Methods Used in Kinematic Surveys15.6 Performing Post-Processed Kinematic Surveys15.7 Communication in Real-Time Kinematic Surveys15.8 Real-Time Networks15.9 Performing Real-Time Kinematic Surveys15.10 Machine Guidance and Control15.11 Errors in Kinematic Surveys15.12 Mistakes in Kinematic Surveys 16. Adjustments by Least Squares16.1 Introduction16.2 Fundamental Condition of Least Squares16.3 Least-Squares Adjustment by the Observation Equation Method16.4 Matrix Methods in Least-Squares Adjustment16.5 Matrix Equations for Precisions of Adjusted Quantities16.6 Least-Squares Adjustment of Leveling Circuits16.7 Propagation of Errors16.8 Least-Squares Adjustment Of GNSS Baseline Vectors16.9 Least-Squares Adjustment of Conventional Horizontal Plane Surveys16.10 The Error Ellipse16.11 Adjustment Procedures16.12 Other Measures of Precision for Horizontal Stations16.13 Software16.14 Conclusions 17. Mapping Surveys17.1 Introduction17.2 Basic Methods for Performing Mapping Surveys17.3 Map Scale17.4 Control for Mapping Surveys17.5 Contours17.6 Characteristics of Contours17.7 Method of Locating Contours17.8 Digital Elevation Models and Automated Contouring Systems17.9 Basic Field Methods for Locating Topographic Details17.10 Planning a Laser-Scanning Survey17.11 Three-Dimensional Conformal Coordinate Transformation17.12 Selection of Field Method17.13 Working with Survey Controllers and Field-to-Finish Software17.14 Hydrographic Surveys17.15 Sources of Error in Mapping Surveys17.16 Mistakes in Mapping Surveys 18. Mapping18.1 Introduction18.2 Availability of Maps and Related Information18.3 National Mapping Program18.4 Accuracy Standards for Mapping18.5 Manual and Computer-Aided Drafting Procedures18.6 Map Design18.7 Map Layout18.8 Basic Map Plotting Procedures18.9 Contour Interval18.10 Plotting Contours18.11 Lettering18.12 Cartographic Map Elements18.13 Drafting Materials18.14 Automated Mapping and Computer-Aided Drafting Systems18.15 Migrating Maps between Software Packages18.16 Impacts of Modern Land and Geographic Information Systems on Mapping18.17 The Importance of Metadata18.18 Sources of Error in Mapping18.19 Mistakes in Mapping 19. Control Surveys and GeodetIc ReductIons19.1 Introduction19.2 The Ellipsoid and Geoid19.3 The Conventional Terrestrial Pole19.4 Geodetic Position and Ellipsoidal Radii of Curvature19.5 Geoid Undulation and De ection of the Vertical19.6 U.S. Reference Frames19.7 Transforming Coordinates Between Reference Frames19.8 Accuracy Standards and Specifications for Control Surveys19.9 The National Spatial Reference System19.10 Hierarchy of the National Horizontal Control Network19.11 Hierarchy of the National Vertical Control Network19.12 Control Point Descriptions19.13 Field Procedures for Conventional Horizontal Control Surveys19.14 Field Procedures for Vertical-Control Surveys19.15 Reduction of Field Observations to their Geodetic Values19.16 Geodetic Position Computations19.17 The Local Geodetic Coordinate System19.18 Three-Dimensional Coordinate Computations19.19 Software 20. State Plane CoordInates and Other Map Projections20.1 Introduction20.2 Projections Used in State Plane Coordinate Systems20.3 Lambert Conformal Conic Projection20.4 Transverse Mercator Projection20.5 State Plane Coordinates in NAD 27 and NAD 8320.6 Computing SPCS 83 Coordinates in the Lambert Conformal20.7 Conic System20.8 Computing SPCS 83 Coordinates in the Transverse Mercator System 603 Reduction of Distances and Angles to State Plane Coordinate Grids20.9 Computing State Plane Coordinates of Traverse Stations20.10 Surveys Extending from One Zone to Another20.11 The Universal Transverse Mercator Projection20.12 Other Map Projections20.13 Ground Versus Grid Problem20.14 Map Projection Software 21. Boundary Surveys21.1 Introduction21.2 Categories of Land Surveys21.3 Historical Perspectives21.4 Property Description by Metes and Bounds21.5 Property Description by Block-and-Lot System21.6 Property Description by Coordinates21.7 Retracement Surveys21.8 Subdivision Surveys21.9 Partitioning Land21.10 Registration of Title21.11 Adverse Possession and Easements21.12 Condominium Surveys21.13 Geographic and Land Information Systems21.14 Sources of Error in Boundary Surveys21.15 Mistakes 22. Surveys of the PublIc Lands22.1 Introduction22.2 Instructions for Surveys of the Public Lands22.3 Initial Point22.4 Principal Meridian22.5 Baseline22.6 Standard Parallels (Correction Lines)22.7 Guide Meridians22.8 Township Exteriors, Meridional (Range) Lines, and Latitudinal (Township) Lines22.9 Designation of Townships22.10 Subdivision of a Quadrangle into Townships22.11 Subdivision of a Township into Sections22.12 Subdivision of Sections22.13 Fractional Sections22.14 Notes22.15 Outline of Subdivision Steps22.16 Marking Corners22.17 Witness Corners22.18 Meander Corners22.19 Lost and Obliterated Corners22.20 Accuracy of Public Land Surveys22.21 Descriptions by Township Section, and Smaller Subdivision22.22 BLM Land Information System22.23 Sources of Error22.24 Mistakes 23. ConstructIon Surveys      23.1 Introduction23.2 Specialized Equipment for Construction Surveys23.3 Horizontal and Vertical Control23.4 Staking Out a Pipeline23.5 Staking Pipeline Grades23.6 Computing the Bend Angles in Pipelines23.7 Staking Out a Building23.8 Staking Out Highways23.9 Other Construction Surveys23.10 Construction Surveys Using Total Station Instruments23.11 Construction Surveys Using GNSS Equipment23.12 Machine Guidance and Control23.13 As-built Surveys with Laser Scanning23.14 Sources of Error in Construction Surveys23.15 Mistakes 24. HorIzontal Curves24.1 Introduction24.2 Degree of Circular Curve24.3 Definitions and Derivation of Circular Curve Formulas24.4 Circular Curve Stationing24.5 General Procedure of Circular Curve Layout by Deflection Angles24.6 Computing Deflection Angles and Chords24.7 Notes for Circular Curve Layout by Deflection Angles and Incremental Chords24.8 Detailed Procedures for Circular Curve Layout by Deflection Angles and Incremental Chords24.9 Setups on Curve24.10 Metric Circular Curves by Deflection Angles and Incremental Chords24.11 Circular Curve Layout by Deflection Angles and Total Chords24.12 Computation of Coordinates on a Circular Curve24.13 Circular Curve Layout by Coordinates24.14 Curve Stakeout Using GNSS Receivers and Robotic Total Stations24.15 Circular Curve Layout by Offsets24.16 Special Circular Curve Problems24.17 Compound and Reverse Curves24.18 Sight Distance on Horizontal Curves24.19 Spirals24.20 Computation of “As-Built” Circular Alignments24.21 Sources of Error in Laying Out Circular Curves24.22 Mistakes 25. Vertical Curves      25.1 Introduction25.2 General Equation of a Vertical Parabolic Curve25.3 Equation of an Equal Tangent Vertical Parabolic Curve25.4 High or Low Point on a Vertical Curve25.5 Vertical Curve Computations Using the Tangent-Offset Equation25.6 Equal Tangent Property of a Parabola25.7 Curve Computations by Proportion25.8 Staking a Vertical Parabolic Curve25.9 Machine Control in Grading Operations25.10 Computations for an Unequal Tangent Vertical Curve25.11 Designing a Curve to Pass Through a Fixed Point25.12 Sight Distance25.13 Sources of Error in Laying out Vertical Curves25.14 Mistakes 26. Volumes      26.1 Introduction26.2 Methods of Volume Measurement26.3 The Cross-Section Method26.4 Types of Cross Sections26.5 Average-End-Area Formula26.6 Determining End Areas26.7 Computing Slope Intercepts26.8 Prismoidal Formula26.9 Volume Computations26.10 Unit-Area, or Borrow-Pit, Method26.11 Contour-Area Method26.12 Measuring Volumes of Water Discharge26.13 Software26.14 Sources of Error in Determining Volumes26.15 Mistakes 27. Photogrammetry      27.1 Introduction27.2 Uses of Photogrammetry27.3 Aerial Cameras27.4 Types of Aerial Photographs27.5 Vertical Aerial Photographs27.6 Scale of a Vertical Photograph27.7 Ground Coordinates from a Single Vertical Photograph27.8 Relief Displacement on a Vertical Photograph27.9 Flying Height of a Vertical Photograph27.10 Stereoscopic Parallax27.11 Stereoscopic Viewing27.12 Stereoscopic Measurement of Parallax27.13 Analytical Photogrammetry27.14 Stereoscopic Plotting Instruments27.15 Orthophotos27.16 Ground Control for Photogrammetry27.17 Flight Planning27.18 Airborne Laser-Mapping Systems27.19 Remote Sensing27.20 Software27.21 Sources of Error in Photogrammetry27.22 Mistakes28. Introduction to GeographIc Information Systems      28.1 Introduction28.2 Land Information Systems28.3 GIS Data Sources and Classifications28.4 Spatial Data28.5 Nonspatial Data28.6 Data Format Conversions28.7 Creating GIS Databases28.8 Metadata28.9 GIS Analytical Functions28.10 GIS Applications28.11 Data Sources      Appendix A: Tape Correction ProblemsAppendix B: Example NoteformsAppendix C: Astronomical ObservationsAppendix D: Using the Worksheets from the Companion WebsiteAppendix E: Introduction to MatricesAppendix F: U.S. State Plane Coordinate System Defining ParametersAppendix G: Answers to Selected Problems