Ray height computation for a continuous nonlinear atmospheric refractive-index profile

An algorithm is described for machine computation of the height of a ray originating at or near the earth's surface, when the initial elevation angle and the ray-path length (as measured, for example, by a radar-antenna elevation angle and the echo signal delay time) are given, and the refractive-index profile is specified as a continuous but nonlinear function of the height. The numerical precision of the result is limited only by the number of digits carried in the computation, although faster computation is achieved with reduced precision. The computing time is less than Is for six significant figures using the CDC-3800 computer. The equations used (which include those for the ground range, true geometric range, and true elevation angle) have been manipulated to avoid formulations that destroy computational precision. The method requires that the refractive index be spherically symmetric with respect to the earth's center and that the height profile be representable as a piecewise continuous function. In the work described, a negative-exponential profile was assumed. Two algorithms for higher speed computation with reduced precision, suitable for radar-target height calculation, are also described.