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- 1. Surv 222 - Geodesy/State Plane<br />STATE PLANE COORINATES<br />Computing Project Average Combined Scale Factor and Convergence angle (Gamma)<br />
- 2. Purpose<br />To reduce ground measurements to project grid values by reducing to the ellipsoid and then scaling to the grid equivalent (two-step procedure)<br />To calculate the value of convergence (Gamma angle) to allow determination of true north from grid north observations <br />Surv 222 - Geodesy/State Plane <br />
- 3. Features<br />Calculations are made on NGS site using Geodetic Tool Kit, State Plane Conversion Routine <br /> Go to NGS site at: http://www.ngs.noaa.gov/<br />Select Geodetic Tool Kit (See slide) from left-hand side of menu <br /> Select ‘State Plane Coordinates’ (See Slide)<br />Input the values for Latitude & Longitude for the four corners of perimeter rectangle encompassing project site<br /> Either select zone or let software determine zone<br />Hit submit and program will process the data providing grid scale factor and convergence (gamma angle) for position<br />Surv 222 - Geodesy/State Plane <br />
- 4. NGS SITE<br />Geodetic Tool Kit <br />Surv222 Geodesy/State Plane <br />
- 5. Conversion Program<br />State Plane Coordinates <br />Surv 222 - Geodesy/State Plane <br />
- 6. Geodetic to SPC<br />Surv 222 - Geodesy/State Plane<br />
- 7. Conversion Output<br />Grid Scale Factor & Convergence (Gamma Angle)<br />Surv 222 - Geodesy/State Plane<br />
- 8. Surv222 - Geodesy/State Plane<br />Reduction of Ground Surveyed Distance to the Ellipsoid<br />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. <br />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.<br />
- 9. Surv 222 - Geodesy/State Plane<br />Determination of Elevation Factor<br />Calculate the elevation factor using the formula (Ra/Ra+H+N) <br />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.<br />Since Geoid separation is around -20 meters (65’) in Washington, this component can be dismissed as insignificant in this calculation.<br />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)<br />
- 10. Determination of Elevation Factor<br />From Ghilani & Wolf Elementary Surveying, 12th Edition Section 20.8.1<br />Surv 222 - Geodesy/State Plane<br />
- 11. Combined Average Scale Factor<br />Final step of calculation<br />Multiply elevation factor x average grid factor<br />Example 0.9999427 x 0.999921 = .9998637(CSF)<br />Average the convergence angle at each of the 4 corners of the survey project area to use for converting grid bearing to geodetic bearings.<br />The sign of the convergence angle is always from Grid azimuth to geodetic Azimuth.<br />Example: Grid Azim.= N 01°48’15”W-01°56’53”(convergence) =N 00°08’38” E (Geodetic Azimuth)<br />Surv 222 - Geodesy/State Plane<br />

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