In the aeronautical standard propagation model typical of VHF, UHF & Microwave frequencies, free space propagation conditions are assumed when the transmitter and the receiver are within the distance to the radio horizon (line of (radio) sight).
The distance to the radio horizon (4/3 Earth radius) can be calculated using following equation.
Drh=1.23 (√Htx) … (1)
where
Drh: the distance of the station to the radio horizon (NM)
Htx: the height of the transmitter above the Earth’s surface (feet)
Note: The same formula can be used to calculate the radio horizon of the receiver by substituting the height of the transmitter with the height of the receiver.
Applying this formula to both the transmitter and the receiver (e.g. between an airborne transmitter and an airborne receiver) formula below can be used for the calculation of the distance to the radio horizon between the transmitter and receiver.
Drh=1.23 (√Htx + √Hrx) … (2)
where
Drh: the radio horizon separation distance between the transmitter and receiver (NM)
Htx: the height of the transmitter above the Earth’s surface (feet)
Hrx: the height of the receiver above the Earth’s surface (feet).
It should be noted that the propagation of radio waves, typical of VHF, UHF & Microwave frequencies, is subject to a number of additional conditions, compared to the free space propagation.
Refraction and ducting as described below can extend the range over which this propagation model is applicable:
Refraction – Gradual changes in the refractive index of the [standard] atmosphere with altitude causes the bending of radio waves slightly towards (or in some cases away from) the Earth. The effect is that radio waves can propagate beyond the physical horizon to and can be received up to a distance which is commonly referred to as the radio horizon as shown in Figure 1. Along this path no other (significant) losses than the free space propagation loss between the transmitter and the receiver has to be considered. Variations in the refractive index of the atmosphere however cause the radio horizon to vary as well.The bending effect of refraction is corrected in radio propagation by calculation the distance to the radio horizonusing a 4/3 Earth radius. The 4/3 Earth radius approximation has been derived based on a standard atmosphere at sea level and is therefore not universally applicable. However, it is very widely used and provides a good approximation to describe the effect of radio path propagation globally.
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Figure 1 - Radio Horizon versus physical horizon
Ducting – The change in refractive index is normally gradual, but under certain atmospheric conditions a layer, of warm air may be trapped above cooler air, often over the surface of water. The result is that the refractive index will decrease far more rapidly with height than is usual. The rapid reduction in refractive index (and therefore dielectric constant) may cause complete bending down, as illustrated in the Figure 2. The unusual atmospheric condition traps the radio waves in a duct. Extreme bending of the radio waves between the top of the atmospheric duct and reflection of the radio waves from the surface of the Earth may propagate the radio waves over extreme long distances (e.g. more than 500 NM). Other phenomena such as sand storm may also cause ducting of radio waves.
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Figure 2 - Propagation through ducting
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