Refraction of VHF Signals at Ionospheric Heights

It is not generally realized that while the refractive error due to the troposphere rapidly decreases with the elevation angle, its ionospheric counterpart behaves very differently. For target heights which are small or comparable to the Earth's radius the ionosphere refractive error initially increases with the elevation angle, attains the maximum value at elevation angles on the order of 100 milliradians and then gradually decreases. The size of this increase decreases with the distance from the Earth and at astronomical distances the initial slope of the ionospheric error at grazing incidence is zero. At ionospheric heights the elevation angle at which the ionosopheric bending is maximum is roughly proportional to the square root of the layer height. This somewhat unexpected behavior of ionospheric bending is examined and sample computations are made using realistic models of ionosphere and troposphere.