Before revision: Classification of Formulae based on Approximation Tunnel-distance based approximations: Flat surface, Gauss-mid-latitude () 0-th-order approximation: Spherical surface () higher-order approximations based on Ellipsoid: : Andoyer(1932) , Andoyer-Lambert-Thomas(1970), : Vincenty(1975), : Kaney(2011) ( on the hemisphere) The estimations of approximation are noted and is the flattening of the Earth in above.
After revision: ; Andoyer-Lambert(1942)theoreticalClassification of Formulae based on Approximation Tunnel-distance based approximations: Flat surface, Gauss-mid-latitude () 0-th-order approximation: Spherical surface () higher-order approximations based on Ellipsoid: : Andoyer(1932) , Andoyer-Lambert-Thomas(1970), : Vincenty(1975), : Kaney(2011) ( on the hemisphere) The estimations of approximation are noted and is the flattening of the Earth in above.