A.V. Sokolov

The paper considers the two topics: - taking into account atmospheric refraction in calculating the height and range of aerial targets; - calculation of the reduction in the radar operation range due to signal attenuation during its propagation in the atmosphere. Despite the presence of an extensive reference material, available data are not applicable when calculating the propagation paths of radio waves in case of airborne radars. These data are based on the effective Earth radius standard model, which satisfactorily describes the refraction in the surface layer at altitudes of no more than 1-2 km. The more complex atmospheric models, which describe the dependence of the refractive index on the height up to the upper boundary of the troposphere, are considered. Numerical computations of radio beam trajectories in a certain range of heights and angles of sighting are carried out for one of these models. The closed formulas approximating the dependence of the height on the measured target range and elevation are obtained. The accuracy of approximation is given. Also, an analytical expression for the corrections to the measured range due to retardation of the propagation speed and path bending in refractive media is obtained. The two effects are considered when calculating the signal attenuation: the absorption of energy by atmospheric gases and the angular extension of the beam during its propagation in an inhomogeneous atmosphere. It is shown that in case of long-range detection the effect of the beam extension is comparable with the effect of absorption and requires obligatory consideration. Numerical solutions of implicit equation, which describes the dependence of the operation range reduction on the estimated range in the free-space, were obtained. These solutions are approximated by various analytic formulas for the three characteristic intervals of viewing angles: above the local horizon, in between local horizon and the earth horizon, below the earth horizon. The accuracy of approximation is given.