Validation of Vincenty's Formulas for the Geodesic Using a New Fourth-Order Extension of Kivioja's Formula
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 wor...
| Main Authors: | , |
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| Format: | Journal Article |
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American Society of Civil Engineers
2005
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| Online Access: | http://hdl.handle.net/20.500.11937/36501 |
| _version_ | 1848754788030742528 |
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| author | Thomas, C. Featherstone, Will |
| author_facet | Thomas, C. Featherstone, Will |
| author_sort | Thomas, C. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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 (10 to 18,000km) 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 0.115mm, and the forward and reverse azimuths agreed to within 5 × 10 −6 seconds 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. |
| first_indexed | 2025-11-14T08:45:58Z |
| format | Journal Article |
| id | curtin-20.500.11937-36501 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:45:58Z |
| publishDate | 2005 |
| publisher | American Society of Civil Engineers |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-365012017-09-13T15:55:51Z Validation of Vincenty's Formulas for the Geodesic Using a New Fourth-Order Extension of Kivioja's Formula Thomas, C. Featherstone, Will Distance measurement Azimuth Geodetic surveys 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 (10 to 18,000km) 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 0.115mm, and the forward and reverse azimuths agreed to within 5 × 10 −6 seconds 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. 2005 Journal Article http://hdl.handle.net/20.500.11937/36501 10.1061/(ASCE)0733-9453(2005)131:1(20) American Society of Civil Engineers fulltext |
| spellingShingle | Distance measurement Azimuth Geodetic surveys Thomas, C. Featherstone, Will Validation of Vincenty's Formulas for the Geodesic Using a New Fourth-Order Extension of Kivioja's Formula |
| title | Validation of Vincenty's Formulas for the Geodesic Using a New Fourth-Order Extension of Kivioja's Formula |
| title_full | Validation of Vincenty's Formulas for the Geodesic Using a New Fourth-Order Extension of Kivioja's Formula |
| title_fullStr | Validation of Vincenty's Formulas for the Geodesic Using a New Fourth-Order Extension of Kivioja's Formula |
| title_full_unstemmed | Validation of Vincenty's Formulas for the Geodesic Using a New Fourth-Order Extension of Kivioja's Formula |
| title_short | Validation of Vincenty's Formulas for the Geodesic Using a New Fourth-Order Extension of Kivioja's Formula |
| title_sort | validation of vincenty's formulas for the geodesic using a new fourth-order extension of kivioja's formula |
| topic | Distance measurement Azimuth Geodetic surveys |
| url | http://hdl.handle.net/20.500.11937/36501 |