Transformations and OSGM02 user guide - Leica Geosystems

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