ON THE GEOMETRICAL SOLUTION OF THE NAVIGATIONAL TRIANGLE

John A. Russell

Peer Reviewed

Abstract: The Ukted States Naval Institute Proceedings for March, 1952, contain a paper by Joseph B. Breed III entitled "The Navigational Triangle: How to Solve It by Drawing It." In this paper Mr. Breed capably expresses the conviction that although the supplanting of the trigonometric solution of the navigational triangle by tabulated solutions represents a great forward step in celestial navigation, instruction in the newer methods often leaves the student in ignorance of the basic relationships in the navigational triangle. Mr. Breed does not propose that spherical trigonometry be reinstated in the navigational curriculum. Instead, he suggests, as an instructional tool, a geometrical solution of the navigational triangle that requires only a protractor, a straight edge, and a pair of compasses. The paper describes with admirable clarity how to obtain the computed altitude of a celestial object by constructing the triangular pyramid whose vertex is the center of the earth; whose three sides are the extended radii of the earth through the nearer geographic pole, the geographical position of the celestial object, and the navigator’s position; and whose base is the intersection of the pyramid with a plane tangent to the earth at the nearer pole.
Published in: NAVIGATION, Journal of the Institute of Navigation, Volume 4, Number 6
Pages: 249 - 250
Cite this article: Russell, John A., "ON THE GEOMETRICAL SOLUTION OF THE NAVIGATIONAL TRIANGLE", NAVIGATION, Journal of The Institute of Navigation, Vol. 4, No. 6, 1955, pp. 249-250.
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