Modifications of Sailings-II : Partial Modification of Great Circle Sailing

Abstract

From ancient times, the methods of calculating a ship's position by dead reckoning have been carried out by treating the earth as a sphere, or as a sphere in part and a terrestrial spheroid in part. However, there have arisen some questions concerning the results obtained by using these approximate methods. In his former paper, the author pointed out the problems and described alternate plans concerning plane sailing, parallel sailing, middle latitude sailing and Mercator sailing; moreover, he pointed out the shortcomings of a theory of traverse sailing. In this paper, he examines the usefulness of great circle sailing. As this sailing is an approximate method, it has great significance for calculating the changing points in a course, since we cannot sail on the geodesic line which is the shortest length connecting two points on the terrestrial spheroid. Therefore, the problem is to determine how the sum of the loxodromic distances between changing points approximate the geodesic line distance. Fig. 1〜Fig. 9 show the correcten values for guiding geodesic line distances from great circle distances. Fig. 10〜Fig. 15 show the relationships between the actual sailing distances and the geodesic line distances, when the changing points in the former were all taken at 5 degrees of D. Long. The lengths calculated by Σ(D.L.P.×sec Co.) agree with the gedesic line distances within lg.m. The method used to calculate changing course points on the sphere, as well as to calculate the length between two changing course points on the terrestrial spheroid, is effective in practice because the sum of loxodromic distances approximates the geodesic line distance.