Distance Reduction

Distance Reductions1ObjectivesAfter this lecture you will be able to:Determine the spheroidal distance between two points on Earths surface from EDM measurements2Lecture OutlineDistancesNormal SectionsCurve of AlignmentDistance ReductionPhysical CorrectionsGeometric CorrectionsSP1Conclusion3Geodetic DistancesGreat Circle (sphere)Small CircleTwo Plane Sections (also called Normal Sections).Curve of AlignmentGeodesic (spheroid)4Plane Sections (Normal Sections)Instrument set at B Rotation axis is normal BNVertical plane containing A = ABN.Instrument set at A Rotation axis is normal AMVertical plane containing B = BAMLine A B Line B AABMN5Curve of AlignmentLocus 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 planeHorizontal angles are angles between curves of alignmentBut can assume normal sections because start off sameSpheroidal triangles are figures formed by 3 curves of alignment joining the 3 pointsCurve of AlignmentABNormal SectionB to ANormal SectionA to B6Heights and DistancesHAhANAHBNBhBSlope Distance (d2)hMMean Terrain HeightLevel Terrain DistanceEllipsoidal Chord Distance (d3)Ellipsoidal Distance (d4)Geoidal (Sea Level) Distance (S)Geoid orSea LevelEllipsoidTerrainAB(S)Measured Distance (d1)7Distance ReductionDistance Reduction involves:Physical CorrectionsGeometric Corrections8Physical Corrections1. Atmospheric correction First velocity correctionSecond velocity correction.2. Zero correction (Prism constant).3. Scale correction.4. First arc-to-chord correction.

9First Velocity CorrectionCovered in earlier coursesFormula available - function of the displayed distance, velocity of light and the refractive index.Correction charts normally availableto set an environmental correction (in ppm) orto determine the first velocity correction to be added manuallySome only require the input of atmospheric readings and the calculations

10Second Velocity Correction

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Zero Correction(Prism Constant)Obtained from calibration results12Scale CorrectionObtained from calibration results13First Arc-to-Chord Correction(d1-d2)

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

Geometric Corrections1. Slope correction2. Correction for any eccentricity of instruments3. Sea Level correction (or AHD correction)4. Chord-to-arc correction (sometimes called the second arc-to-chord) correction)5. Sea Level to spheroid correction16Slope Correction

To calculate level terrain distance17EccentricsTry to avoid them!If they cant be avoided - connect them both vertically and horizontallyInclude redundant observations18AHD (Sea Level) Correction

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Chord-to-Arc Correctiond3 to d4 or S to S if correct radius is usedCorrection is

Ellipsoidal Chord Distance (d3)Ellipsoidal Distance (d4)Geoidal (Sea Level) Distance (S)(S)20Sea Level to Spheroid CorrectionWhere N is the average height difference between spheroid and AHDs is required spheroidal lengthR is a non-critical value for earths radius

Ellipsoidal Chord Distance (d3)Ellipsoidal Distance (d4 or s)Geoidal (Sea Level) Distance (S)(S)NANB21Example from Study BookFollow example from study book for full numerical example 22Geoscience Australias FormulaCombined and separate formula availableSpreadsheetsWill be used in TutorialsAlso in Study Book23SP1 RequirementsIn Study Book

24ConclusionYou can now:Determine the spheroidal distance between two points on Earths surface from EDM measurements

Self StudyRead relevant module in study materials26Review Questions

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