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Elementary Surveying
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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 SurveyingProblemsBibliography2 Units, Significant Figures, and Field NotesPart I ?Units and Significant Figures ? 2.1 Introduction ? 2.2 Units of Measurement 25t? 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 Data Collectors ? 2.13 Transfer of Files from Data Collectors ? 2.14 Digital Data File Management ? 2.15 Advantages and Disadvantages of Data Collectors Problems Bibliography 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 in a Product 3.17.4 Error in the Mean ? 3.18 Applications ? 3.19 Conditional Adjustment of Observations ? 3.20 Weights of Observations ? 3.21 Least-Squares Adjustment Problems Bibliography 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 Problems Bibliography 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 Problems Bibliography 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 ? 6.15 Tape Problems ? 6.16 Combined Corrections in a Taping Problem Part II ?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 Problems Bibliography 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 Problems Bibliography 8 Total Station Instruments: Angle Measurements 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 Measurements ? 8.7 Relationship of Angles and Distances ? 8.8 Observing Horizontal Angles with Total Station Instruments ? 8.9 Observing 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 Optical 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 Problems Bibliography 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 Problems 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 Lengths and Directions of Lines from Departures and Latitudes or Coordinates ? 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 Problems Bibliography 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 Conclusions Problems Bibliography 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 Sources of Error in Determining Areas ? 12.11 Mistakes in Determining Areas Problems Bibliography 13 The Global Positioning System-Introduction and Principles of Operation ? 13.1 Introduction ? 13.2 Overview of GPS ? 13.3 The GPS Signal ? 13.4 Reference Coordinate Systems for GPS 13.4.1 The Satellite Reference Coordinate System 13.4.2 The Geocentric Coordinate System 13.4.3 The Geodetic Coordinate System ? 13.5 Fundamentals of GPS Positioning 13.5.1 Code Ranging 13.5.2 Carrier Phase-Shift Measurements ? 13.6 Errors in GPS Observations 13.6.1 Clock Bias 13.6.2 Refraction 13.6.3 Other Error Sources 13.6.4 Geometry of Observed Satellites 13.6.5 Selective Availability ? 13.7 Differential GPS ? 13.8 Kinematic GPS 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 Galileo System 13.10.3 Compass ? 13.11 The Future Problems Bibliography 14 The Global Positioning System-Static surveys ? 14.1 Introduction ? 14.2 Field Procedures in GPS Surveys 14.2.1 Static Relative Positioning 14.2.2 Rapid Static Relative Positioning 14.2.3 Pseudokinematic Surveys 14.2.4 Kinematic Surveys ? 14.3 Planning GPS 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 GPS Surveys ? 14.5 Data Processing and Analysis 14.5.1 Specifications for GPS 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 Sources of Errors in GPS Work 14.6.1 Instrumental Errors 14.6.2 Natural Errors 14.6.3 Personal Errors ? 14.7 Mistakes in GPS Work ? 14.8 Future Outlook for GPS Problems Bibliography 15 The Global Positioning System-Kinematic GPS ? 15.1 Introduction ? 15.2 Initialization ? 15.3 Equipment Used in Kinematic Surveys ? 15.4 Methods Used in Kinematic Surveys ? 15.5 Performing Post-Processed Kinematic Surveys ? 15.6 Communication in Real-Time Kinematic Surveys ? 15.7 Real-Time Networks ? 15.8 Performing Real-Time Kinematic Surveys ? 15.9 Machine Control ? 15.10 Errors in Kinematic Surveys ? 15.11 Mistakes in Kinematic Surveys Problems Bibliography 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 GPS Baseline Vectors ? 16.9 Least-Squares Adjustment of Traditional 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 Error Ellipses ? 16.11 Adjustment Procedures ? 16.12 Other Measures of Precision for Horizontal Stations ? 16.13 Conclusions Problems Bibliography 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 Direct and Indirect Methods of Locating Contours 17.7.1 Direct Method 17.7.2 Indirect Method ? 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 Radiation by Stadia 17.9.3 Coordinate Squares or "Grid" Method 17.9.4 Offsets from a Reference Line 17.9.5 Topographic Detailing with GPS 17.9.6 Laser-Scanning ? 17.10 Three-Dimensional Conformal Coordinate Transformation ? 17.11 Selection of Field Method ? 17.12 Working with Data Collectors and Field-to-Finish Software ? 17.13 Hydrographic Surveys 17.13.1 Equipment for Making Soundings 17.13.2 Locating Soundings 17.13.3 Hydrographic Mapping ? 17.14 Sources of Error in Mapping Surveys ? 17.15 Mistakes in Mapping Surveys Problems Bibliography 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 Impacts of Modern Land and Geographic Information Systems on Mapping ? 18.16 Sources of Error in Mapping ? 18.17 Mistakes in Mapping Problems Bibliography 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 Transforming Coordinates between Reference Frames ? 19.7 Accuracy Standards and Specifications For Control Surveys ? 19.8 The National Spatial Reference System ? 19.9 Hierarchy of the National Horizontal Control Network ? 19.10 Hierarchy of the National Vertical Control Network ? 19.11 Control Point Descriptions ? 19.12 Field Procedures For Traditional Horizontal Control Surveys 19.12.1 Triangulation 19.12.2 Precise Traverse 19.12.3 Trilateration 19.12.4 Combined Networks ? 19.13 Field Procedures for Vertical Control Surveys ? 19.14 Reduction of Field Observations to Their Geodetic Values 19.14.1 Reduction of Distance Observations Using Elevations 19.14.2 Reduction of Distance Observations Using Vertical Angles 19.14.3 Reduction of Directions and Angles 19.14.4 Leveling and Orthometric Heights ? 19.15 Geodetic Position Computations 19.15.1 Direct Geodetic Problem 19.15.2 Inverse Geodetic Problem ? 19.16 The Local Geodetic Coordinate System ? 19.17 Three-Dimensional Coordinate Computations ? 19.18 Conclusions Problems Bibliography 20 State Plane Coordinates ? 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 Conversions between SPCS27 and SPCS83 ? 20.12 The Universal Transverse Mercator Projection ? 20.13 Other Map Projections 20.13.1 Oblique Stereographic Map Projection 20.13.2 Oblique Mercator Map Projection Problems Bibliography 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 Problems Bibliography 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 Problems Bibliography 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 ? 23.3 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 GPS Equipment ? 23.11 Machine Control ? 23.12 As-Built Surveys with Laser Scanning ? 23.13 Sources of Error in Construction Surveys ? 23.14 Mistakes Problems Bibliography 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 GPS 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 Problems Bibliography 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 Problems Bibliography 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 Sources of Error in Determining Volumes ? 26.14 Mistakes Problems Bibliography 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 Direct Optical Projection Stereoplotters 27.14.2 Mechanical Projection Stereoplotters 27.14.3 Analytical Stereoplotters 27.14.4 Softcopy Stereoplotters ? 27.15 Orthophotos ? 27.16 Ground Control for Photogrammetry ? 27.17 Flight Planning ? 27.19 Airborne Laser-Mapping Systems ? 27.20 Remote Sensing ? 27.21 Sources of Error in Photogrammetry ? 27.22 Mistakes Problems Bibliography 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 29.7.4 Keyboard Entry 29.7.5 Existing Digital Data Sets 29.7.6 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 Problems Bibliography A Dumpy Levels, Transits, and Theodolites ? A.1 Introduction ? A.2 The Dumpy Level ? A.3 Introduction to the Transit and Theodolite ? A.4 The Transit A.4.1 Parts of a Transit A.4.2 Circle Scales and Verniers A.4.3 Properties of the Transit A.4.4 Handling, Setting up, and using a Transit ? A.5 The Theodolite A.5.1 Characteristics of Theodolites A.5.2 Repeating Theodolites A.5.3 Directional Theodolites A.5.4 Handling, Setting Up, and Using a Theodolite 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 D Using the Worksheets on the Companion Disk ? D.1 Introduction ? D.2 Using the Files ? D.3 Using the 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 Index

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