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Sphere to Spheroid Comparisons

  • Michael A. Earle (a1)

Extract

The notion of the earth as a perfect sphere has served navigators quite well over the centuries and it continues to provide a basis for instruction and practical navigation. Aside from the fact that modern navigators employ refined models of the earth such as the WGS84 ellipsoid, which together with satellite positioning gives unprecedented positioning accuracy, the question arises as to just how good are the spherical results for distance when compared to the results for distance obtained from the spheroidal model. In this document a comparison is made of great circle distance (GCD) on the sphere with great ellipse distance (GED) on the spheroid. This comparison is then repeated for rhumbline distances. In each case it is concluded that the difference in using the sphere when compared to the spheroid is near 0·5%.

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Copyright

References

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[1] Snyder, J. P. Map Projections-A Working Manual. Professional Paper. No.1395. Pub. U.S. Geological Survey
[2] Earle, M. A. A Comment on Navigation Instruction The Journal of Navigation, 58, 337340
[3] Walwyn, P. R. The Great Ellipse Solution for Distances and Headings to Steer between Waypoints. The Journal of Navigation, 52, 421424.
[4] Williams, R. Geometry of Navigation, Ch.7. Horwood Publishing. ISBN. 1-898563-46-2.

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