Editing Line-of-sight propagation (section)

=== Atmospheric refraction ===
{{main|Atmospheric refraction}}
The usual effect of the declining pressure of the atmosphere with height ([[vertical pressure variation]]) is to bend ([[refraction|refract]]) radio waves down towards the surface of the Earth. This results in an '''effective Earth radius''',<ref name="ITU 2021">{{cite web | title=P.834 : Effects of tropospheric refraction on radiowave propagation | website=ITU | date=2021-03-05 | url=https://www.itu.int/rec/R-REC-P.834/en | access-date=2021-11-17}}</ref> increased by a factor around {{frac|4|3}}.<ref>Christopher Haslett. (2008). ''Essentials of radio wave propagation'', pp&nbsp;119&ndash;120. Cambridge University Press. {{ISBN|052187565X}}.</ref> This ''k''-factor can change from its average value depending on weather.

====Refracted distance to horizon====
The previous vacuum distance analysis does not consider the effect of atmosphere on the propagation path of RF signals. In fact, RF signals do not propagate in straight lines: Because of the refractive effects of atmospheric layers, the propagation paths are somewhat curved. Thus, the maximum service range of the station is not equal to the line of sight vacuum distance. Usually, a factor ''k'' is used in the equation above, modified to be

: <math>d \approx \sqrt{2 \cdot k \cdot R \cdot h}</math>

''k''&nbsp;>&nbsp;1 means geometrically reduced bulge and a longer service range. On the other hand, ''k''&nbsp;<&nbsp;1 means a shorter service range.

Under normal weather conditions, ''k'' is usually chosen<ref>Busi, R. (1967). ''High Altitude VHF and UHF Broadcasting Stations''. Technical Monograph 3108-1967. Brussels: European Broadcasting Union.</ref> to be {{frac|4|3}}. That means that the maximum service range increases by&nbsp;15%.

: <math>d \approx 4.12 \cdot \sqrt{h} </math>
for ''h'' in metres and ''d'' in kilometres; or

: <math>d \approx 1.41 \cdot\sqrt{h} </math>
for ''h'' in feet and ''d'' in miles.

But in stormy weather, ''k'' may decrease to cause [[rain fade|fading]] in transmission. (In extreme cases ''k'' can be less than&nbsp;1.) That is equivalent to a hypothetical decrease in Earth radius and an increase of Earth bulge.<ref>This analysis is for high altitude to sea level reception. In microwave radio link chains, both stations are at high altitudes.</ref>

For example, in normal weather conditions, the service range of a station at an altitude of 1500 m with respect to receivers at sea level can be found as,

: <math>d \approx 4.12 \cdot \sqrt{1500} = 160 \mbox { km.}</math>