Staff Members - Benha University
“A New Approach for Determining the Geodetic Latitude from Isometric Latitude”, Civil Engineering Research Magazine CERM, Faculty of Engineering, Al-Azhar University, Cairo, Egypt, Vol 28, No. 3, pp. 1096 – 1103, October .
Civil Engineering Research Magazine CERM, Faculty of Engineering, Al-Azhar University, Cairo, Egypt • 2006
Publication Information
Authors
Saiid A. Shebl, Ashraf ghoneim, Khaled M. Zaky
Keywords
Geodetic Latitude, Map Isometric Latitude, Ellipsoidal Earth, Residue Function, Polynomial Function.
Journal
Civil Engineering Research Magazine CERM, Faculty of Engineering, Al-Azhar University, Cairo, Egypt
Publisher
Faculty of Engineering, Al-Azhar University
Volume
28
Issue
3
Pages
1096 – 1103
publication.type
Local
Paper Link
Not Available
Supplementary Materials
Not Available
Abstract
Abstract
A solution for the problem of determining the Geodetic Latitude on the ellipsoidal earth, in terms of the Map (Isometric) or Mercator Latitude is presented in this research. The proposed model relies mainly on the spherical case by contributing a residue function which anticipates the disparity between spherical and ellipsoidal cases. The residue function is proposed as 8th degree polynomial equation whose independent variable is the Map Isometric Latitude. The coefficients of this function are constants derived from the values of earth’s size via the adaptation of the Least Squares approach applied along the entire earth’s meridian (i.e. < ). The output formula is uncomplicated and easy applicable with fair accuracy of value degree at latitude near the pole (φ =89°) if the WGS84 model is considered. This accuracy may be increased by increasing the power of the polynomial function. The major benefits of the formula are the allowance of the opportunity for the geodetic analytical analysis conduction and the validity of the formula for all values of the Geodetic Latitude.
A solution for the problem of determining the Geodetic Latitude on the ellipsoidal earth, in terms of the Map (Isometric) or Mercator Latitude is presented in this research. The proposed model relies mainly on the spherical case by contributing a residue function which anticipates the disparity between spherical and ellipsoidal cases. The residue function is proposed as 8th degree polynomial equation whose independent variable is the Map Isometric Latitude. The coefficients of this function are constants derived from the values of earth’s size via the adaptation of the Least Squares approach applied along the entire earth’s meridian (i.e. < ). The output formula is uncomplicated and easy applicable with fair accuracy of value degree at latitude near the pole (φ =89°) if the WGS84 model is considered. This accuracy may be increased by increasing the power of the polynomial function. The major benefits of the formula are the allowance of the opportunity for the geodetic analytical analysis conduction and the validity of the formula for all values of the Geodetic Latitude.