Surveying and Coordinates Systems

Introduction to Earth Surface Representations

  • Surveying involves measurements on the Earth's surface, which is subject to inherent inaccuracies.

  • Coordinates obtained through measurements are based on models, usually ellipsoids, rather than the actual surface of the Earth.

Ellipsoids and Their Definitions

  • Various ellipsoids exist globally.

  • Example ellipsoids discussed include:

    • Clark Ellipsoid (1886)

    • GRS80: Geodetic Reference System 1980

    • WGS84: World Geodetic System 1984, which underlies GPS technology.

  • GPS interprets the Earth as an ellipsoid, leading to complications in determining precise elevations.

Coordinate Systems

  • Fundamental horizontal coordinates are derived using Cartesian systems (X, Y).

  • Comparison of spherical coordinates (geodetic) with Cartesian coordinates:

    • Geodetic Coordinates: phi (Φ) and lambda (Λ) with height (h) above the ellipsoid.

    • 3D location requires conversion with complexity akin to astronomical calculations, which relate to surveying principles.

Geoid vs Ellipsoid

  • Geoid: An irregular surface representing mean sea level across the Earth.

    • GPS systems (such as GLONASS) cannot determine geoid but assume the Earth to be the ellipsoid.

  • GPS outputs heights above the ellipsoid, not mean sea level, which can present elevation discrepancies.

Defining Datums and Their Importance

  • A datum fixes the position of the ellipsoid relative to the center of the Earth and aids in establishing coordinates.

  • For horizontal measurements, a datum pertains to a fixed reference point (like sea level for vertical measurements).

Projected Coordinate Systems

  • Conversion from a 3D ellipsoid to a 2D map involves Map Projections.

  • Three types of surfaces for projections are:

    • Cone

    • Cylinder

    • Flat surface

  • Distortion is an essential theme, as projections may distort distances and angles between points.

Distortion in Map Projections

  • If a point is projected, it may shift significantly away from its true location when not on the tangent or secant of projection:

    • Distortion increases as distance from tangent/ secant increases.

  • Projections attempt to minimize distortion,
    and U.S. State Plane Coordinate System ensures no distortion exceeds 1 in 10,000.

Zone Concept in Projection Systems

  • The concept of zones relates to minimizing error in projections:

    • Zone Size: Boundaries defined by allowable distortion (e.g., 158 miles zone).

    • Tangent and secant projections minimize error, leading to efficient coordinate systems.

Specific Projection Uses

  • Transverse Mercator Projection: Commonly used where states extend vertically (north-south).

  • Conical Projection: More suited for states that extend horizontally (east-west).

The State Plane Coordinate System

  • The system ensures all measurements are positive, improving usability across regions.

  • Defined using datum based on the ellipsoid for the area and its specific projections.

  • Requires an understanding of the two state zones (North and South).

Standards and Zones Details

  • North American Datum (NAD)

    • NAD27 and NAD83 differ due to variations in the underlying ellipsoid and model definitions.

    • Emphasizes the necessity for awareness of the system being used to avoid significant errors in measurements.

The Upcoming North American Datum 2022

  • This newer system incorporates a fourth dimension representing time, focusing on up-to-date measurements with better accuracy overconnected geographical data.

Practical Considerations for Engineers and Surveyors

  • Emphasis on maintaining the integrity of projections by ensuring consistency in the data being utilized to avoid costly mistakes.

  • Importance of understanding overlaps between the North and South zones when conducting cross-zone measurements.

  • Coordinate transformations are often required between zone systems to ensure measurements fall within acceptable accuracy limits.

Conclusion

  • Understanding these fundamental concepts is crucial for effective surveying and accurate representation of spatial data. Differences between horizontal (x,y) and vertical (height) coordinates should be accounted for to avoid significant surveying errors due to distortions stemming from projection systems.