The calculation of field strengths over a spherical Earth

Curves and formulae are given for the calculation of field strength at any height and distance from the transmitter for the case of horizontally-polarized electromagnetic waves over a curved Earth or sea. Sufficiently within the optical range the field is calculated by ray theory, and appropriate quantities for calculating path difference and divergence of reflected ray are given. At exact optical cut-off the field is calculated by an approximate method believed to be accurate to 1 db, and is presented in the form of contour curves of equal field strength on a plot of receiver height against transmitter height. Sufficiently far beyond optical cut-off the field is given by the first term in the diffraction-formula series. To calculate the field near optical cut-off, a curve should be drawn of field against distance for the heights of transmitter and receiver in question which joins smoothly the ray-theory curve for inside optical range to the one-term curve for the region beyond and passes through the point determined for the actual cut-off distance. The case of vertically polarized waves is also briefly discussed, and curves and formulae are given for the reflection coefficient (including surface-wave term) where ray theory is applicable, and for one term of the diffraction formula in the region well beyond optical cut-off.