A COMPARISON OF GREAT CIRCLE, GREAT ELLIPSE, AND GEODESIC SAILING

An analytical and numerical comparison of great circle (GC) sailing, great elliptic (GE) sailing, and geodesic (Geod) sailing is presented. The comparison between GC and GE sailing addresses some problems whether the navigator and navigational software developers promptly have to use GE sailing or use hybrid sailing mixed with features of the GC sailing and GE sailing. This fact found here presents that the formulae tackling relationship of latitude and longitude of GC sailing also can be suited to the GE sailing except some calculation of GE sailing involving distance and course. The validity of effectiveness of proposed GE sailing has been verified with numerical tests and compared with extremely accurate geodetic methods (Vincenty's method). The numerical tests calculate the standard deviation of large sample of distance differences comparing GE sailing and Andoyer-Lambert method to Geod sailing. The result reveals that the mean and the standard deviation of distance differences of GE is one half and one sixth of Andoyer-Lambert method. The significance gives the assertion that the accuracy of GE sailing is better than Andoyer-Lambert method which (UK) Royal Navy and (US) Naval Oceanographic Office preferred spheroidal mathematical solution. We also give a dynamic programming recursive algorithm attaining any requirement of accuracy for distance calculation of GE sailing and more compact computational procedure of intermediate points along the GE. The course of GE sailing can be obtained from the proposed course reduction of GC sailing.