Distance Reductions

ObjectivesAfter this lecture you will be able to:Determine the spheroidal distance between two points on Earths surface from EDM measurements

Lecture OutlineDistancesNormal SectionsCurve of AlignmentDistance ReductionPhysical CorrectionsGeometric CorrectionsConclusion

Geodetic DistancesGreat Circle (sphere)Small CircleTwo Plane Sections (also called Normal Sections).Curve of AlignmentGeodesic (spheroid)

Plane 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 AABN

Curve 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 pointsNormal SectionB to ANormal SectionA to B

Heights and DistancesEllipsoidal Distance (d4)Geoid orSea LevelEllipsoidTerrainAB

Understanding and Using Coordinates

Distance ReductionDistance Reduction involves:Physical CorrectionsGeometric Corrections

Physical Corrections1. Atmospheric correction First velocity correctionSecond velocity correction.2. Zero correction (Prism constant).3. Scale correction.4. First arc-to-chord correction.

First Velocity CorrectionFormula 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

Second Velocity Correction

Zero Correction(Prism Constant)Obtained from calibration results

Scale CorrectionObtained from calibration results

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

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

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 correction

Slope CorrectionTo calculate level terrain distance

EccentricsTry to avoid them!If they cant be avoided - connect them both vertically and horizontallyInclude redundant observations

AHD (Sea Level) Correction

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

Sea 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 radiusNANB

SP1 RequirementsIn Study Book

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

Review QuestionsReduksi sudut dan azimut

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