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Spcs01a
Spcs01a
Spcs01a
Spcs01a
Spcs01a
Spcs01a
Spcs01a
Spcs01a
Spcs01a
Spcs01a
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Spcs01a

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  • 1. Surv 222 - Geodesy/State Plane
    STATE PLANE COORINATES
    Computing Project Average Combined Scale Factor and Convergence angle (Gamma)
  • 2. Purpose
    To reduce ground measurements to project grid values by reducing to the ellipsoid and then scaling to the grid equivalent (two-step procedure)
    To calculate the value of convergence (Gamma angle) to allow determination of true north from grid north observations
    Surv 222 - Geodesy/State Plane
  • 3. Features
    Calculations are made on NGS site using Geodetic Tool Kit, State Plane Conversion Routine
    Go to NGS site at: http://www.ngs.noaa.gov/
    Select Geodetic Tool Kit (See slide) from left-hand side of menu
    Select ‘State Plane Coordinates’ (See Slide)
    Input the values for Latitude & Longitude for the four corners of perimeter rectangle encompassing project site
    Either select zone or let software determine zone
    Hit submit and program will process the data providing grid scale factor and convergence (gamma angle) for position
    Surv 222 - Geodesy/State Plane
  • 4. NGS SITE
    Geodetic Tool Kit
    Surv222 Geodesy/State Plane
  • 5. Conversion Program
    State Plane Coordinates
    Surv 222 - Geodesy/State Plane
  • 6. Geodetic to SPC
    Surv 222 - Geodesy/State Plane
  • 7. Conversion Output
    Grid Scale Factor & Convergence (Gamma Angle)
    Surv 222 - Geodesy/State Plane
  • 8. Surv222 - Geodesy/State Plane
    Reduction of Ground Surveyed Distance to the Ellipsoid
    Derived by averaging the elevations throughout the survey area. This is an approximate value and should have 50% of area above and 50% below mean elevation, or alternatively on the perimeter if that is where you will be surveying, such as the perimeter of a section.
    Start by averaging the elevations at the top left, middle and right corners of mapping area; then middle left, middle of map and middle right; ending with lower left, lower middle and lower right.
  • 9. Surv 222 - Geodesy/State Plane
    Determination of Elevation Factor
    Calculate the elevation factor using the formula (Ra/Ra+H+N)
    Where: H (average orthometric height above the geoid); N (geoid separation); Ra=20,902,000’ (Mean radius of the Earth) From Ghilani & Wolf Elementary Surveying, Section 20.8.1 Grid Reduction of distances.
    Since Geoid separation is around -20 meters (65’) in Washington, this component can be dismissed as insignificant in this calculation.
    Simplified, this means for local surveys, such as section line retracements that the ratio is simply 20,902,000/Mean elevation of site (20,902,000+average ortho height)
  • 10. Determination of Elevation Factor
    From Ghilani & Wolf Elementary Surveying, 12th Edition Section 20.8.1
    Surv 222 - Geodesy/State Plane
  • 11. Combined Average Scale Factor
    Final step of calculation
    Multiply elevation factor x average grid factor
    Example 0.9999427 x 0.999921 = .9998637(CSF)
    Average the convergence angle at each of the 4 corners of the survey project area to use for converting grid bearing to geodetic bearings.
    The sign of the convergence angle is always from Grid azimuth to geodetic Azimuth.
    Example: Grid Azim.= N 01°48’15”W-01°56’53”(convergence) =N 00°08’38” E (Geodetic Azimuth)
    Surv 222 - Geodesy/State Plane

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