### D2 - - GRAPHICAL GREAT CIRCLE SAILING - - 07/13/2000

A navigation chart constructed by means of the gnomonic projection has the characteristic that any great-circle that is plotted will be a straight line. The Lambert-conformal charts are similar, but not as accurate. Both of the above charts are called great-circle charts. The Lambert charts are preferred for aircraft navigation, and the gnomonic charts are preferred for maritime use.

The obvious use involves drawing a line from the point of departure to the great-circle destination, and then tabulating the latitude and longitude of points along the path, usually at intervals of five degrees of longitude. The reference points can be transferred to a Mercator chart or Mercator plotting sheet and rhumb line courses can be sailed from point to point.

If you were to sail a rhumb line course from San Francisco to Yokohama Japan you could pick a destination point a few miles outside of Yokohama harbor, but if you were to try and use that point for a great circle course you would run aground many miles from your destination. Using a great-circle chart it would be obvious that you would be approaching Japan from the North-Easterly direction and that there would be land in the way, so it would be better to pick a great-circle destination up the coast to avoid collision.

If you were to sail a great-circle course from Seattle Washington to Yokohama the course would cross the Aleutian islands, so the procedure would be to sail the great-circle to a maximum safe latitude, sail directly West until you meet the great-circle again, and then to continue following the great-circle to the great-circle destination point off the coast of Japan. This procedure is known as composite sailing.

The vertex of a great circle path is that point that is nearest the North or South poles of the earth and where the direction is exactly East and West.
A second method of composite sailing involves placing a vertex on the limiting latitude that will give a great-circle path from the point of departure, or to the great-circle destination. This can be done graphically on a great-circle chart by placing a ruler from the point of departure to a tangent on the limiting latitude (drawing in the limiting latitude by hand if necessary). In this case, the composite course is in three sections, the starting great-circle path, the East or West path along the limiting latitude, and a second (different) great-circle path to the destination point.

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