Transformations and OSGM02 user guide - Leica Geosystems

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Appendix CConverting easting and northing to latitude and longitudeObtaining (λ, φ) from (E, N) is an iterative procedure. You need values for the ellipsoid and projection constantsa, b, e 2 , N 0, E 0, F 0, φ 0and λ 0given in appendix B. Remember to express all angles in radians.First compute:⎛ N − N ⎞φ ′ =⎜ ⎟ +⎝ aF ⎠0⎟ φ00(C1)and M from equation (B6) in appendix B, substituting φ′ for φ .If the absolute value of (N – N 0– M) ≥ 0.01 mm, obtain a new value for φ′ using:and recompute M substituting φ′ for φ .⎛ N − N0− M ⎞φ ′ =⎜⎟ + φ′⎝ aF0⎠new(C2)Iterate until the absolute value of (N – N 0– M) < 0.01 mm, then compute ρ, ν and η 2 using equations (B3, B4 and B5) inappendix B and compute:tanφ′VII =2ρν2 22 2( 5 + 3 tan φ ′ + η − 9 φ ′ η )tan φ ′VIII =tan324ρνTransformations and OSGM02 user guide appendix Cv2.1 9/2002 © crown copyrightPage 37
24( 61+90 tan φ ′ + 45 φ ′)tanφ′IX =tan5720ρνX = secφ ′νsec ′ ⎛ vXI = ⎜ + 2 tan36ν⎝ pφ 2⎞φ ′ ⎟⎠2( 5 + 28 tan φ ′ + 24 φ ′)′ 4secφXII =tan5120ν24( 61+662 tan φ ′ + 1320 tan φ ′ + 720 φ ′)′ 6secφXIIA =tan75040ν= φ′ −VII(E − EEE2460) + VIII( −0)− IX( −0)Eφ (C3)λ = λ X ( E E XI E E E E E E(C4)3570+ −0)− ( −0)+ XII( −0)− XIIA( −0)ETransformations and OSGM02 user guide appendix Cv2.1 9/2002 © crown copyrightPage 38
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 36 and 37: ⎛ ⎛ 5 2 5 3 ⎞ ⎛2 21 3 ⎞
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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