Validation of Vincenty’s Formulas for the Geodesic Using a New Fourth-Order Extension of Kivioja’s Formula
Publication: Journal of Surveying Engineering
Volume 131, Issue 1
Abstract
Vincenty’s (1975) formulas for the direct and inverse geodetic problems (i.e., in relation to the geodesic) have been verified by comparing them with a new formula developed by adapting a fourth-order Runge-Kutta scheme for the numerical solution of ordinary differential equations, advancing the work presented by Kivioja in 1971. A total of 3,801 lines of varying distances and azimuths (0 to 90°, because of symmetry) were used to compare these two very different techniques for computing geodesics. In every case, the geodesic distances agreed to within , and the forward and reverse azimuths agreed to within of arc, thus verifying Vincenty’s formula. If one wishes to plot the trajectory of the geodesic, however, the fourth-order Runge-Kutta extension of Kivioja’s formula is recommended as a numerically efficient and convenient approach.
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Acknowledgment
The writers would like to thank Dr J. G. Olliver of Oxford University for useful discussions and for provision of additional references.
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Published In
Journal of Surveying Engineering
Volume 131 • Issue 1 • February 2005
Pages: 20 - 26
Copyright
© 2005 ASCE.
History
Received: Feb 4, 2004
Accepted: Jun 22, 2004
Published online: Feb 1, 2005
Published in print: Feb 2005
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