Accuracy of the Earth-Flattening Approximation in the Theory of Microwave Propagation

A study was made of the maximum ranges and elevations for which the earth-flattening approximation in the theory of microwave propagation is valid. It is found that at a range equal to half the radius of the earth the error introduced by the earth-flattening approximation is only 2 percent, and this independently of the wave-length. The fractional error $\Delta$ in the height-gain functions is found to be proportional to the 5/2th power of the elevation, and to the inverse power of the wave-length. Values of $\Delta$ for various wave-lengths and elevations are shown in Table I. For wave-lengths of the order of several centimeters the earth-flattening approximation breaks down at elevations greater than a few thousand feet.