Distance Reductions

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

Lecture Outline n Distances n Normal Sections n Curve of Alignment n Distance Reduction –Physical Corrections –Geometric Corrections n SP1 n Conclusion

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

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  Line B  A A B M N

Curve of Alignment Locus of all points where Bearing to A = bearing to B  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 Curve of Alignment AB Normal Section B to A Normal Section A to B

Heights and Distances HAHA hAhA NANA HBHB NBNB hBhB Slope Distance (d2) hMhM Mean Terrain Height Level Terrain Distance Ellipsoidal Chord Distance (d3) Ellipsoidal Distance (d4) Geoidal (Sea Level) Distance (S’) Geoid or Sea Level Ellipsoid Terrain A B (S”) Measured Distance (d1)

Distance Reduction Distance Reduction involves: Physical Corrections Geometric Corrections

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.

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

Second Velocity Correction

Zero Correction (Prism Constant) Obtained from calibration results

Scale Correction Obtained from calibration results

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

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

Slope Correction To calculate level terrain distance

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

AHD (Sea Level) Correction

Chord-to-Arc Correction n d 3 to d 4 or S” to S’ if correct radius is used n Correction is Ellipsoidal Chord Distance (d3) Ellipsoidal Distance (d4) Geoidal (Sea Level) Distance (S’) (S”)

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

Example from Study Book n Follow example from study book for full numerical example

Geoscience Australia’s Formula n Combined and separate formula available n Spreadsheets –Will be used in Tutorials n Also in Study Book

SP1 Requirements n In Study Book

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

Self Study n Read relevant module in study materials

Review Questions