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Distance Reductions

Distance Reductions. Objectives. After this lecture you will be able to: Determine the spheroidal distance between two points on Earth’s surface from EDM measurements. Lecture Outline. Distances Normal Sections Curve of Alignment Distance Reduction Physical Corrections

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Distance Reductions

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  1. Distance Reductions

  2. Objectives After this lecture you will be able to: • Determine the spheroidal distance between two points on Earth’s surface from EDM measurements

  3. Lecture Outline • Distances • Normal Sections • Curve of Alignment • Distance Reduction • Physical Corrections • Geometric Corrections • SP1 • Conclusion

  4. Geodetic Distances • Great Circle (sphere) • Small Circle • Two Plane Sections (also called Normal Sections). • Curve of Alignment • Geodesic (spheroid)

  5. M Plane Sections (Normal Sections) • Instrument set at B Rotation axis is normal BN • Vertical plane containing A = ABN. • Instrument set at A Rotation axis is normal AM • Vertical plane containing B = BAM • Line A ® B ¹ Line B ® A A B N

  6. A B Curve of Alignment Curve of Alignment • Locus of all points where Bearing to A = bearing to B + 180° is called Curve of Alignment. • Marked on ground - A surveyor sets up between A and B such that A and B are in same vertical plane • Horizontal angles are angles between curves of alignment • But can assume normal sections because start off same • Spheroidal triangles are figures formed by 3 curves of alignment joining the 3 points Normal Section B to A Normal Section A to B

  7. Measured Distance (d1) Slope Distance (d2) Mean Terrain Height HA Level Terrain Distance hM hA HB Geoidal (Sea Level) Distance (S’) hB (S”) NB NA Ellipsoidal Chord Distance (d3) Heights and Distances A Terrain B Ellipsoidal Distance (d4) Geoid or Sea Level Ellipsoid

  8. Distance Reduction Distance Reduction involves: • Physical Corrections • Geometric Corrections

  9. Physical Corrections • 1. Atmospheric correction • First velocity correction • Second velocity correction. • 2. Zero correction (Prism constant). • 3. Scale correction. • 4. First arc-to-chord correction.

  10. First Velocity Correction • Covered in earlier courses • Formula available - function of the displayed distance, velocity of light and the refractive index. • Correction charts normally available • to set an environmental correction (in ppm) or • to determine the first velocity correction to be added manually • Some only require the input of atmospheric readings and the calculations

  11. Second Velocity Correction

  12. Zero Correction(Prism Constant) • Obtained from calibration results

  13. Scale Correction • Obtained from calibration results

  14. First Arc-to-Chord Correction(d1-d2)

  15. First Arc-to-Chord Correction(d1-d2)

  16. Geometric Corrections • 1. Slope correction • 2. Correction for any eccentricity of instruments • 3. Sea Level correction (or AHD correction) • 4. Chord-to-arc correction (sometimes called the second arc-to-chord) correction) • 5. Sea Level to spheroid correction

  17. Slope Correction To calculate level terrain distance

  18. Eccentrics • Try to avoid them! • If they can’t be avoided - connect them both vertically and horizontally • Include redundant observations

  19. AHD (Sea Level) Correction

  20. Geoidal (Sea Level) Distance (S’) (S”) Ellipsoidal Chord Distance (d3) Ellipsoidal Distance (d4) Chord-to-Arc Correction • d3 to d4 or S” to S’ if correct radius is used • Correction is

  21. Geoidal (Sea Level) Distance (S’) (S”) Ellipsoidal Chord Distance (d3) Ellipsoidal Distance (d4 or s) Sea Level to Spheroid Correction • Where N is the average height difference between spheroid and AHD • s is required spheroidal length • R is a non-critical value for earth’s radius NB NA

  22. Example from Study Book • Follow example from study book for full numerical example

  23. Geoscience Australia’s Formula • Combined and separate formula available • Spreadsheets • Will be used in Tutorials • Also in Study Book

  24. SP1 Requirements • In Study Book

  25. Conclusion You can now: • Determine the spheroidal distance between two points on Earth’s surface from EDM measurements

  26. Self Study • Read relevant module in study materials

  27. Review Questions

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