Radio horizon

The radio horizon describes the places where direct (i.e. not diffracted or reflected) radio waves emanating from a transmitter are exactly tangential to the earth's surface. It usually runs at a greater distance than the optical horizon . The decreasing height with increasing refractive index of the atmosphere causes a refraction of electromagnetic waves towards the ground. This refractive index gradient is greater for radio waves (up to around 100 GHz) than for light. Therefore, even those radio waves whose range is not increased by effects such as ionospheric reflection have a range that extends beyond the optical horizon.

Principle calculations

This range beyond the optical horizon to the radio horizon is approximately ${\displaystyle s}$

${\displaystyle s={\sqrt {2\,R\,h_{s}}}}$

with as the earth radius and as the height of the transmitting antenna above ground level. ${\displaystyle R}$ ${\displaystyle h_{s}}$

As a rough approximation, in practice an enlargement of the radio horizon by about 15% compared to the optical horizon can be assumed. Alternatively, this can be understood as an apparent increase in the radius of the earth. By default, the earth's radius is then assumed to be 4/3 larger.

If you put the mean earth radius of 6370 km into this formula multiplied by the factor of 4/3 for a normal atmosphere (about 8500 km), the distance from the radio horizon in km is calculated ${\displaystyle s}$

${\displaystyle s=4{,}1\,{\sqrt {h_{s}}}}$

with as the height of the transmitting antenna in meters above ground level. ${\displaystyle h_{s}}$

If the receiver is also at a relevant height above earth, the two radio horizons add up. The quasi-optical range can then be calculated using the following formula : ${\displaystyle d}$

${\displaystyle d={\sqrt {2R}}\,\left({\sqrt {h_{s}}}+{\sqrt {h_{e}}}\right)}$

with the radius of the earth, as the height of the transmitting antenna and the height of the receiving antenna, both on the ground floor. ${\displaystyle R}$ ${\displaystyle h_{s}}$ ${\displaystyle h_{e}}$

If the earth's radius of around 8500 km, increased by 4/3, is used, the quasi-optical range in km results ${\displaystyle d}$

${\displaystyle d=4{,}1\,\left({\sqrt {h_{s}}}+{\sqrt {h_{e}}}\right)}$

with the height of the transmitting antenna in meters and the height of the receiving antenna in meters. ${\displaystyle h_{s}}$ ${\displaystyle h_{e}}$

In a simplistic way, these formulas assume that the earth is a sphere. Differences in altitude in the propagation path such as mountains and valleys are not taken into account. These formulas agree very well with reality over level terrain or over the sea and are often used as a first estimate when calculating the path of propagation of radio waves.

Formulas for calculating the radio horizon from digitized terrain data can be found, for example, in corresponding sources from the International Telecommunication Union (ITU).

Tropospheric propagation effects such as diffraction, scattering and reflection are not taken into account when calculating the radio horizon. They cause the electromagnetic waves to propagate beyond the radio horizon (trans-horizon propagation).

Radar horizon

The radar horizon is calculated using the same formulas. In contrast to above-horizon radar , the functionality of a radar system is based on a quasi-optical propagation of radio waves. This is only given if the radio horizon of the radar system and the radar horizon of the target overlap or just touch one another.

See also

• Line of sight
• Visibility

Individual evidence

1. ↑ Definitions of terms relating to propagation in non-ionized media, ITU , Recommendation ITU-R P. 310-9: "The locus of points at which direct rays from a point source of radio waves are tangential to the surface of the Earth. Note 1 - As a general rule, the radio and geometric horizons are different because of atmospheric refraction. "
2. ^ The radio refractive index: its formula and refractivity data, ITU, Recommendation ITU-R P. 453-9
3. ↑ Definitions of terms relating to propagation in non-ionized media, ITU, Recommendation ITU-R P. 310-9: "For an atmosphere having a standard refractivity gradient, the effective radius of the Earth is about 4/3 that of the actual radius, which corresponds to approximately 8,500 km. "
4. ↑ ^{a b} Method for point-to-area predictions for terrestrial services in the frequency range 30 MHz to 3 000 MHz, ITU, Recommendation ITU-R P. 1546-3
5. ↑ Prediction procedure for the evaluation of microwave interference between stations on the surface of the Earth at frequencies above about 0.7 GHz, ITU, Recommendation ITU-R P. 452-12
6. ↑ Definitions of terms relating to propagation in non-ionized media, ITU, Recommendation ITU-R P. 310-9, Note 1 on the term "Trans-horizon propagation": "Trans-horizon propagation may be due to a variety of tropospheric mechanisms such as diffraction, scattering, reflection from tropospheric layers. [...] "
7. ↑ J. Detlefsen in Meinke, Friedrich-Wilhelm Gundlach : Pocket book of high frequency technology , 4th edition, chapter S1.1 Fundamentals of radar technology