Scaled Illustration of Unit Sphere Geometry with Navigation Applications

The need for three-dimensional diagrams for the display and illustration of long-range navigation problems is discussed, and the adequacy of the spherical earth model pointed out. Formulas by which three-dimensional problems in navigation, adequately represented by points and arcs on the surface of a sphere, can be reduced to the two dimensions of a plane are derived. Use of these formulas yields a scaled illustration of any three-dimensional problem as viewed from any direction normal to the earth's surface from an infinite distance. Computational problems are discussed and sample illustrations are included.