Transformations and OSGM02 user guide - Leica Geosystems

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Appendix BConverting latitude and longitude to easting and northingThe formulae in this appendix and appendix C require ellipsoid constants and projection constants, given in the tablesbelow.Important note: When converting OSGB36 coordinates between (easting, northing) and (latitude, longitude) in eitherdirection, use the Airy 1830 ellipsoid constants. When converting ETRS89 coordinates between (easting, northing) and(latitude, longitude) in either direction, use the GRS80 ellipsoid constants. Use the same National Grid projectionconstants for both ETRS89 and OSGB36 coordinates.The ITM (Irish Transverse Mercator) projection is required to obtain ETRS89 eastings and ETRS89 northings for use withthe OSGM02 Geoid model data files for Northern Ireland and the Republic of Ireland. The ITM projection should only beused with the GRS80 ellipsoid.Ellipsoid constantsEllipsoidSemi-major axisa (metres)Semi-minor axis b(metres)Used for thefollowing coordinatesystemAiry 1830 6 377 563.396 6 356 256.910 OSGB36National GridGRS80‡ 6 378 137.000 6 356 752.3141 ETRS89(WGS84)‡ Also known as the WGS84 ellipsoid.The ellipsoid squared eccentricity constant e 2 is computed from a and b by:2 22 a – be = (B1)2aTransformations and OSGM02 user guide appendix Bv2.1 9/2002 © crown copyrightPage 33
Projection constantsProjectionScale factoron centralmeridian (F 0)True origin(φ 0and λ 0)Map coordinatesof true origin (m)(E 0and N 0)NationalGrid0.9996012717 lat 49° Nlong 2° WITM 0.99982 Lat 53° 30' Nlong 8° WE 400 000N 100 000E 600 000N 750 000To convert a position from the graticule of latitude and longitude coordinates (λ, φ) to a grid of easting and northingcoordinates (E, N) using a transverse mercator projection, for example OSGB36 National Grid, ITM or UTM (UniversalTransverse Mercator), compute the following formulae. Remember to express all angles in radians. You will need theellipsoid constants a, b and e 2 and the projection constants listed below:N 0– northing of true origin;E 0– easting of true origin;F 0– scale factor on central meridian;φ 0– latitude of true origin; andλ 0– longitude of true origin and central meridian.ρna−ba+b= (B2)2 2 −0.5ν = aF (1−e sin φ)(B3)02 2 2 −1.5= aF ( 1−e )( 1−e φ)(B4)0sinν= −1ρ2η (B5)Transformations and OSGM02 user guide appendix Bv2.1 9/2002 © crown copyrightPage 34
Page 2 and 3: PrefaceThis grid transformation sof
Page 4 and 5: Data copyrightUser guide copyrightT
Page 6 and 7: Appendix A Transforming ETRS89 GPS
Page 8 and 9: Orthometric heights in these system
Page 10 and 11: ETRS89 explainedBenefitsOrdnance Su
Page 12 and 13: Chapter 2Data overviewBasic princip
Page 14 and 15: Where:1 the record number is a sequ
Page 16 and 17: Where:1 the record number is a sequ
Page 18 and 19: 4 the height of the Geoid above the
Page 20 and 21: For example, to find the record for
Page 22 and 23: Shifts for x, y are:se 0= east_shif
Page 24 and 25: The OSi/OSNI polynomial transformat
Page 26 and 27: The Ordnance Survey Geoid model: OS
Page 28 and 29: Chapter 4Quality statementCoverageO
Page 30 and 31: Appendix ATransforming ETRS89 GPS c
Page 32 and 33: The offset values are given by:dx =
Page 36 and 37: ⎛ ⎛ 5 2 5 3 ⎞ ⎛2 21 3 ⎞
Page 38 and 39: Appendix CConverting easting and no
Page 40 and 41: Worked example using Airy 1830 elli
Page 42 and 43: Geoid modelA model of the level sur

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