In telecommunication, radio horizon is the locus of points at which direct rays from an antenna are tangential to the surface of the Earth. If the Earth were a perfect sphere and there were no atmospheric anomalies, the radio horizon would be a circle. To compute the radius of the circle drawn on the earth in such a case use the formula:

:$mathrm\left\{horizon\right\}_mathrm\left\{miles\right\} = 1.23 imes sqrt\left\{mathrm\left\{height\right\}_mathrm\left\{feet.$

This is the geometric straight line of sight horizon. For an equivalent formula for an antenna height in metres and a radio horizon in kilometres would be

:$mathrm\left\{horizon\right\}_mathrm\left\{km\right\} = 3.569 imes sqrt\left\{mathrm\left\{height\right\}_mathrm\left\{metres.$

These formulas are approximations for the case that the height is much smaller than the earth radius. The precise formula is

:$mathrm\left\{horizon\right\} = sqrt\left\{2 r h + h^2\right\}$

where "r" is the earth radius and "h" the height.

The radio horizon of the transmitting and receiving antennas can be added together to increase the effective communication range.

Antenna heights above 1 million feet (1966 miles, or 3157 kilometres) will cover the entire hemisphere and not increase the radio horizon.

VHF and UHF radio signals will bend slightly toward the earth's surface. This bending effectively increases the radio horizon and therefore slightly increases the formula constant. The ARRL Antenna Book gives a constant of 1.415 for the feet/miles formula for weak signals during normal tropospheric conditions. This can usefully be approximated as:

:$mathrm\left\{horizon\right\}_mathrm\left\{miles\right\} = sqrt\left\{2 imes mathrm\left\{height\right\}_mathrm\left\{feet.$

In practice, radio wave propagation is affected by atmospheric conditions, ionospheric absorption, and the presence of obstructions, for example mountains or trees. The simple formula above gives a best-case approximation of the maximum propagation distance but is not sufficiently adequate for determining the quality of service at any location.

References

* The ARRL Antenna Book, 19th Edition, R. Dean Shaw, pp 22-25
* Federal Standard 1037C, in support of MIL-STD-188

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