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New Algorithm for Great Elliptic Sailing (GES)

Published online by Cambridge University Press:  15 June 2009

Athanasios Pallikaris  and
George Latsas
Athanasios Pallikaris*
Affiliation:
(Hellenic Naval Academy)
George Latsas
Affiliation:
(National and Kapodistrian University of Athens)
*
(Email: [email protected])
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Abstract

An analytical method and algorithm for great elliptic sailing (GES) calculations is presented. The method solves the complete GES problem calculating not only the great elliptic arc distance, but also other elements of the sailing such as the geodetic coordinates of intermediate points along the great elliptic arc. The proposed formulas provide extremely high accuracies and are straightforward to be exploited immediately in the development of navigational software, without the requirement to use advanced numerical methods. Their validity and effectiveness have been verified with numerical tests and comparisons to extremely accurate geodetic methods for the direct and inverse geodetic problem.

Keywords

NavigationSailingsGeodesicGreat elliptic
Type
Research Article
Information
The Journal of Navigation , Volume 62 , Issue 3 , July 2009 , pp. 493 - 507
Copyright
Copyright © The Royal Institute of Navigation 2009

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References

REFERENCES

Bowring, B. R. (1984). The Direct and Inverse Solutions for the Great Elliptic Line on the Reference Ellipsoid, Bulletin Geodesique 58, pp. 101–108.CrossRefGoogle Scholar
Earle, M. A. (2006). Sphere to Spheroid Comparisons, The Journal of Navigation 59, 491–496.CrossRefGoogle Scholar
Earle, M. A. (2000). A Vector Solution for Navigation on a Great Ellipse. The Journal of Navigation 53, 473–481.CrossRefGoogle Scholar
Earle, M. A. (2008). Vector Solutions for Azimuth, The Journal of Navigation 61, 537–545.CrossRefGoogle Scholar
Hairawa, T. (1987) Proposal on the modification of sailing calculations, The Journal of Navigation 40, 138–148CrossRefGoogle Scholar
Plythian, J. E., Williams, R., (1985), Cubic spline approximation to an integral function. Bulletin of the Institute of Mathematics and its Applications, 21, 130–131Google Scholar
Snyder, J. P., 1987. Map Projections: A Working Manual. US Geological Survey Professional Paper 1395. WashingtonGoogle Scholar
Sodano, E. M. (1965), General Non-Iterative Solution of the Inverse and Direct Geodetic Problems, Bulletin Geodesique, March, 75, 69–89CrossRefGoogle Scholar
Tobler, W.R. 1964. A comparison of spherical and ellipsoidal measures. The Professional Geographer, Vol XVI, 4, 9–12.CrossRefGoogle Scholar
Torge, W. 2001. Geodesy 3rd edition. Walter de Gruyter, Berlin, New York.CrossRefGoogle Scholar
TSO [The Stationary Office]. 1987. Admiralty Manual of Navigation. Vol I. BR 45(1). General Navigation, Coastal Navigation and Pilotage. London.Google Scholar
Vicenty, T. 1975. “Direct and Inverse Solutions of Geodesics on the Ellipsoid with Application of Nested Equations”. Survey Review, vol. XXII no 176. pp. 88–93. Directorate of Over-seas Surveys. Ministry of Overseas Development. Tolworth, Surrey [UK].Google Scholar
Walwyn, P. R. (1999). The Great Ellipse Solution for Distances and Headings to Steer between Waypoints The Journal of Navigation 52, 421–424CrossRefGoogle Scholar
Williams, R. (1996). The Great Ellipse on the surface of the spheroid. The Journal of Navigation 49, 229–234.CrossRefGoogle Scholar
Zukas, Tim (1994). Shortest Spheroidal Distance. The Journal of Navigation 47, 107–108CrossRefGoogle Scholar