Chapter One – Coordinate Geometry
Analytic Geometry
Vectors
Coordinate Axes
Basis for Two Dimensional Space (R2)
COGO Operations
Computational Error
Forward
Polar Coordinates
Inverse
Math/Science System
The Surveyor’s System
Rectangular/Polar Conversions
Line-Line Intersections (Brg-Brg)
Line-Line Intersections (Dist-Dist)
Line_Circle Intersections
Problem 1.1 Line-Line Intersection (Brg-Brg)
Problem 1.2 Line-Circle Intersection
Problem 1.3 Circle-Circle Intersection
Chapter Two – Stationing the Alignment
Definitions and Purpose of the Alignment
Stationing the Alignment
Layout and Use of a Simple Alignment
Measurements for the Plan View
Profile Leveling
Plotting the Plan View of the Plan and Profile Sheet
Plotting the Profile View of the Plan and Profile Sheet
Importance of Alignment and Grade
Definition of Grade and Gradient
Relationship between Percent and Station
Chapter Three – Horizontal Circular Curves
Geometry of the Circular Curve
Formulas for Curve Elements in terms of I and R
Four Fundamental Properties of a Circular Curve
Degree of Curve
Highway Definition
Railroad Definition
Layout of the circular Curve
Method of Radial Stakeout
Method of Stakeout by Deflection Angles
Moving up on the Curve
Compound Curves
Vertex Angle Method
Solution by Traverse
Reverse Curves
Chapter Four – Spiral Curves
Drawing a Curve System
Design of Curve System containing Spiral Transitions
Elements of the Simple Spiral (Notation)
Degree of Curve of the Simple Spiral
Radius of the Spiral
Spiral Angle
Computing Chord Distances on the Spiral
Layout from the TS or ST Stations
Layout form the SC or CS Stations
Moving up on the Curve
Problem 4.1 Computing Spiral Elements and Spiral Layout Tables
Coordinates on the Spiral Curve System (COGO)
Problem 4.2 Computations on the First Path
Problem 4.3 Computations on the Second Path
Problem 4.4 Computations on the Third Path
Chapter Five – Vertical Curves
The Algebra of the Quadratic Function
Geometry of the Parabola
Elevation Curve
Grade Curve
Rate of Change Curve
Relationship between Curves
Typical Computations on Equal Tangent Vertical Curve with Known Length
Unequal Tangent Vertical Curves
Unequal Vertical Curve Problem
Chapter Six – Vertical Curve Fitting
Review: Geometric Relationships between the Curves
Case I: High or Low Point Fixed; PVC Station and Elevation Known
Case II: High or Low Point Fixed; PVI Station and Elevation Known
Case III: Point on Curve Fixed; PVC Station and Elevation Known
Case IV: Point on Curve Fixed; PVI Station and Elevation Known
Case V: Fit Sag Curve to a Grade
Chapter Seven – Route Design Elements
Superelevation
Equilibrium Condition
Non-Equilibrium Condition
Superelevation Conditions
Transitions
Stopping Distance
Perception and Brake Reaction Distance
Braking Distance
Passing Sight Distance for 2-Lane Highways
Stopping Distance vs. Sight Distance
Sight Distance on Horizontal Curves
Sight Distance on Crest Vertical Curves
Problem 7.1: Sight Distanceon Crest Curve
Problem 7.2: Find Length of Curve to accommodate Stoping Sight Distance
Sight Distance on Sag Vertical Curves
Headlight Beam Distance
Rider Comfort
Drainage
Appearance
Sight Distance at Underpass Structures
The Measurement of Data for Route Design
Chapter Eight – Cross-sections and Volumes
Use of Abney Level
Cross-section Areas
Area Calculations
The Level Section
The Three Level Section
Special Three Level Sections
Five-Level Section
Side-Hill Section
Irregular Section
Volumes (Earthwork)
Average End-Area
Prismoidal Formula
Mass-Haul Diagram
Chapter Nine – Slope Staking
Cross-section Areas
Determination of Existing Ground
Slope Staking
Grade Rod
Ground Rod
Example in Cut Section
Clearing Stakes
Reference Stakes
Right of Way
Chapter Ten – Construction Control
Background
Horizontal Control
Vertical Control
Chapter Eleven – topographic Mapping
The Sparse Surface Model
Sampling
Visual Perception
Triangulated Irregular Network (TIN)
Breaklines
Interpolation
Conclusions
Kriging
Least Squares Collocation
Landform
Small Scale Mapping Considerations
Local Variation
Mapping Accuracy Standards
U.S. National Map Accuracy Standards of 1947”
NSSDA Horizontal Accuracy Statistic
NSSDA Vertical Accuracy Statistic
Analysis of the NSSDA Vertical Statistic
Actual Error Distribution at Large Scale
Ideal Check Point Sample Size
Large Scale Topographic Survey Design
Introduction
Background
Effect of Sampling Density
Profiles
Applications
The Drain
The Forested Hillside
Conclusions
Attachment A – Triangulation Study
Bibliography
Index
Chapter One – Coordinate Geometry
Analytic Geometry
Vectors
Coordinate Axes
Basis for Two Dimensional Space (R2)
COGO Operations
Computational Error
Forward
Polar Coordinates
Inverse
Math/Science System
The Surveyor’s System
Rectangular/Polar Conversions
Line-Line Intersections (Brg-Brg)
Line-Line Intersections (Dist-Dist)
Line_Circle Intersections
Problem 1.1 Line-Line Intersection (Brg-Brg)
Problem 1.2 Line-Circle Intersection
Problem 1.3 Circle-Circle Intersection
Chapter Two – Stationing the Alignment
Definitions and Purpose of the Alignment
Stationing the Alignment
Layout and Use of a Simple Alignment
Measurements for the Plan View
Profile Leveling
Plotting the Plan View of the Plan and Profile Sheet
Plotting the Profile View of the Plan and Profile Sheet
Importance of Alignment and Grade
Definition of Grade and Gradient
Relationship between Percent and Station
Chapter Three – Horizontal Circular Curves
Geometry of the Circular Curve
Formulas for Curve Elements in terms of I and R
Four Fundamental Properties of a Circular Curve
Degree of Curve
Highway Definition
Railroad Definition
Layout of the circular Curve
Method of Radial Stakeout
Method of Stakeout by Deflection Angles
Moving up on the Curve
Compound Curves
Vertex Angle Method
Solution by Traverse
Reverse Curves
Chapter Four – Spiral Curves
Drawing a Curve System
Design of Curve System containing Spiral Transitions
Elements of the Simple Spiral (Notation)
Degree of Curve of the Simple Spiral
Radius of the Spiral
Spiral Angle
Computing Chord Distances on the Spiral
Layout from the TS or ST Stations
Layout form the SC or CS Stations
Moving up on the Curve
Problem 4.1 Computing Spiral Elements and Spiral Layout Tables
Coordinates on the Spiral Curve System (COGO)
Problem 4.2 Computations on the First Path
Problem 4.3 Computations on the Second Path
Problem 4.4 Computations on the Third Path
Chapter Five – Vertical Curves
The Algebra of the Quadratic Function
Geometry of the Parabola
Elevation Curve
Grade Curve
Rate of Change Curve
Relationship between Curves
Typical Computations on Equal Tangent Vertical Curve with Known Length
Unequal Tangent Vertical Curves
Unequal Vertical Curve Problem
Chapter Six – Vertical Curve Fitting
Review: Geometric Relationships between the Curves
Case I: High or Low Point Fixed; PVC Station and Elevation Known
Case II: High or Low Point Fixed; PVI Station and Elevation Known
Case III: Point on Curve Fixed; PVC Station and Elevation Known
Case IV: Point on Curve Fixed; PVI Station and Elevation Known
Case V: Fit Sag Curve to a Grade
Chapter Seven – Route Design Elements
Superelevation
Equilibrium Condition
Non-Equilibrium Condition
Superelevation Conditions
Transitions
Stopping Distance
Perception and Brake Reaction Distance
Braking Distance
Passing Sight Distance for 2-Lane Highways
Stopping Distance vs. Sight Distance
Sight Distance on Horizontal Curves
Sight Distance on Crest Vertical Curves
Problem 7.1: Sight Distanceon Crest Curve
Problem 7.2: Find Length of Curve to accommodate Stoping Sight Distance
Sight Distance on Sag Vertical Curves
Headlight Beam Distance
Rider Comfort
Drainage
Appearance
Sight Distance at Underpass Structures
The Measurement of Data for Route Design
Chapter Eight – Cross-sections and Volumes
Use of Abney Level
Cross-section Areas
Area Calculations
The Level Section
The Three Level Section
Special Three Level Sections
Five-Level Section
Side-Hill Section
Irregular Section
Volumes (Earthwork)
Average End-Area
Prismoidal Formula
Mass-Haul Diagram
Chapter Nine – Slope Staking
Cross-section Areas
Determination of Existing Ground
Slope Staking
Grade Rod
Ground Rod
Example in Cut Section
Clearing Stakes
Reference Stakes
Right of Way
Chapter Ten – Construction Control
Background
Horizontal Control
Vertical Control
Chapter Eleven – topographic Mapping
The Sparse Surface Model
Sampling
Visual Perception
Triangulated Irregular Network (TIN)
Breaklines
Interpolation
Conclusions
Kriging
Least Squares Collocation
Landform
Small Scale Mapping Considerations
Local Variation
Mapping Accuracy Standards
U.S. National Map Accuracy Standards of 1947”
NSSDA Horizontal Accuracy Statistic
NSSDA Vertical Accuracy Statistic
Analysis of the NSSDA Vertical Statistic
Actual Error Distribution at Large Scale
Ideal Check Point Sample Size
Large Scale Topographic Survey Design
Introduction
Background
Effect of Sampling Density
Profiles
Applications
The Drain
The Forested Hillside
Conclusions
Attachment A – Triangulation Study
Bibliography
Index