Transformations and OSGM02 user guide - Leica Geosystems

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⎛ ⎛ 5 2 5 3 ⎞ ⎛2 21 3 ⎞⎞⎜ ⎜1+n + n + n ⎟(φ −φ0) −⎜3n+ 3n+ n ⎟sin(φ −φ0)cos( φ + φ0) ⎟⎜ ⎝ 4 4 ⎠ ⎝ 8 ⎠⎟= bF0⎜⎟⎜⎛152 15 3 ⎞35 3+ ⎜ n + n ⎟sin(2(φ − φ ))cos(2( + )) − sin(3( − ))cos(3( + ))⎟0φ φ0n φ φ0φ φ0⎝ ⎝ 8 8 ⎠24⎠M (B6)νIII = sin φ cos24νIIIA = sin φ cos720ν 5VI = cos φ120I = M + N 0νII = sinφcosφ253φ(5− tan2φ(61−58 tanIV = ν cosφ⎛ ⎞= ν 3 νV cos φ⎜− tan2 φ ⎟6 ⎝ ρ ⎠2φ + 9η)2φ + tan4φ)2422 2( 5 −18tanφ + tan φ + 14η− 58 tan φη)246N = I + II( λ − λ0 ) + III( λ − λ0)+ IIIA( λ − λ0)(B7)35E = E0 + IV(λ − λ0) + V( λ − λ0)+ VI( λ − λ0)(B8)Transformations and OSGM02 user guide appendix Bv2.1 9/2002 © crown copyrightPage 35
Worked example using the Airy 1830 ellipsoid and National GridIntermediate values are shown here to 10 decimal places. Compute all values using double-precision arithmetic.φλνρη 2MIIIIIIIIIAIVVVIEN52° 39' 27.2531" N1° 43' 4.5177" E6.3885023333e+066.3727564399e+062.4708136169e–034.0668829596e+053.0668829596e+051.5404079092e+061.5606875424e+05–2.0671123011e+043.8751205749e+06–1.7000078208e+05–1.0134470432e+05651 409.903 m313 177.270 mTransformations and OSGM02 user guide appendix Bv2.1 9/2002 © crown copyrightPage 36
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 34 and 35: Appendix BConverting latitude and l
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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