Talk:Great ellipse

Questions
Is an arc of a great ellipse the shortest distance between two points on a spheroid (as with a great circle on a sphere)? Duoduoduo (talk) 15:15, 28 March 2011 (UTC)
 * No, the shortest distance is the geodesic which in general does not even lie in a plane. cffk (talk) 14:11, 13 September 2014 (UTC)

Does every plane containing the center of an ellipsoid cut it in a great ellipse? —Tamfang (talk) 07:32, 19 June 2011 (UTC)
 * Yes. cffk (talk) 14:11, 13 September 2014 (UTC)

Solution via equivalent great circle problem
I've added material to this article giving the solution of great ellipse problems via an equivalent great circle. I've retained just the 3 older references for the great ellipse. Here are some newer ones: Nearly all of the papers on great ellipse problems make heavy weather of the subject. The transformation to a great circle hardly needs any explanation and nicely reduces the problem to a simpler one. cffk (talk) 19:34, 13 September 2014 (UTC) Add a 2nd ref. for Earle. cffk (talk) 09:21, 15 September 2014 (UTC) Add 3rd ref for Tseng. cffk (talk) 15:14, 18 September 2014 (UTC)
 * Earle, M. A. (2000). A vector solution for navigation on a great ellipse. Journal of Navigation, 53(3), 473-481.
 * Earle, M. A. (2008). Vector solutions for azimuth. Journal of Navigation, 61(3), 537-545.
 * Pallikaris, A., & Latsas, G. (2009). New algorithm for great elliptic sailing (GES). Journal of Navigation, 62(3), 493-507.
 * Sjöberg, L. E. (2012). Solutions to the direct and inverse navigation problems on the great ellipse. Journal of Geodetic Science, 2(3), 200-205.
 * Tseng, W. K., & Lee, H. S. (2010). Navigation on a great ellipse. Journal of Marine Science and Technology, 18(3), 369-375.
 * Tseng, W. K., Guo, J. L., Liu, C. P., & Wu, C. T. (2012). The vector solutions for the great ellipse on the spheroid. Journal of Applied Geodesy, 6(2), 103-109.
 * Tseng, W. K., Guo, J. L., & Liu, C. P. (2013). A comparison of great circle, great ellipse, and geodesic sailing. Journal of Marine Science and Technology, 21(3), 287-299.

special name for longitudinal great ellipses?
"Meridian" seems a semiellipse, e.g., antimeridian vs. prime meridian. Fgnievinski (talk) 03:39, 12 November 2014 (UTC)

Great ellipse as a special case of a section
I see that you've modified this page to steer reader to earth section paths for calculating the solution of the direct and indirect problem. However earth section paths is only a few weeks old and still seems to be a "work in progress": some of the math expressions are malformed; some of the text is copied directly from your paper with is "Copyright Institute of Navigation" (which may be a problem for Wikipedia); there's no pointer to an implementation of the method; there are no rigorous bounds on the errors compared to geodesics. So I think your changes to great ellipse may be premature.

Please provide an example of what you think is malformed! No pointer to an implementation is required, since it is the implementation! I disagree. Chuckage (talk) 20:56, 29 April 2018 (UTC)


 * By malformed I meant badly formatted. An example is
 * $${c_3}=-e6*(60 + 105*e2 - 528*e4)/12288$$
 * See the talk page for the article for other examples. cffk (talk) 22:47, 29 April 2018 (UTC)

I'm the the editor (mainly) who cast the solution for great ellipses in terms of great circle navigation. And I still see this as the best way of viewing the problem for the typical reader. If great ellipses aren't sufficiently accurate (and for many applications, they are not), then the average user should just the geodesic. The solution of geodesic problems is available as a library on many platforms. (Full disclosure: I am the author of this library and the author of Algorithms for geodesics.)

I suppose that your point of view is that a great ellipse is part of a family of earth sections and that it is easiest to treat it that way. But this just converts the great ellipse to a more complicated problem rather than reducing it to a simpler problem.

No. The general section problem is not more complicated, that's the point. All sections may be solved in exactly the same fashion. Chuckage (talk) 20:56, 29 April 2018 (UTC)


 * I understand your point that all sections are solved in the same way. However it's still the case that the great circle problem is simpler than the general section problem.  So reducing the great ellipse problem to a great circle problem is a simplification. cffk (talk) 22:47, 29 April 2018 (UTC)

I only have a cursory interest in great ellipses. I can't see why anyone interested in navigation would use them in preference to geodesics.

Great ellipses are not a very good approximation to the geodesic, but for many aviation applications the normal section is. The reason for using the normal section is that cross track error is computed by a simple dot product compared to an iteration scheme for geodesics. Chuckage (talk) 20:56, 29 April 2018 (UTC)

Here is a summary of my reasons.

I'll post some comments on earth section paths on that article's talk page.

cffk (talk) 14:04, 29 April 2018 (UTC)

Because it's simpler to solve a problem by reducing it to a simpler one rather than as a special case of a more general problem, I've switched the method of solving great ellipses back to solving great circles. However, I've retained a note that great ellipses are a special case of earth section paths. cffk (talk) 14:56, 27 February 2020 (UTC)