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Line of sight

Introduction

Radio waves and light (both are types of electromagnetic radiation) propagate in straight lines. Because the earth is round, the range of a radio station is limited, like our view. The higher you are above the earth, the farther you can see.

Diffraction

Relatively long waves, with wavelength in the kilometers range), bend around the earth. That means that if the transmitter has enough power, radio communication is possible to any place on earth. This is also true of medium waves, but to a much lesser extent. Medium waves range to a few hundred kilometers during the day, but at night, as a result of changed atmospheric conditions which cause reflection layers, reception is possible more than a thousand kilometers away.

Reflection

Short waves (wavelength of tens of meters) are also reflected by layers in the atmosphere, which makes reception possible at very long distances. In principle, the whole world is reachable by short wave transmissions, but this requires a studied choice of frequencies, appropriate for the time of transmission and the intended reception areas.

Calculations

The calculations in the frame next to this text (if you don't see it, click here) do not consider diffraction, reflections or the presence of hills, mountains or buildings. They also do not take into account that the earth is somewhat flattened, so the "sphere's" radius isn't exactly the same everywhere. In the calculation module, the radius can be adapted if desired. Diffraction is sometimes accounted for by assuming an effective radius of 4/3 times the physical radius, or some 8,500 km in case of the earth.

In a literal line of sight, haze and fog also have an effect. The atmosphere is never quite clear, so it is hardly ever possible to see as far as would be possible in theory. For a radio transmitter too, the line of sight isn't the only factor: there must also be sufficient transmitting power to bridge the distance to the receiver, the sensitivity of which also makes a difference.

This link takes you to the formulas used in the calculations, and their derivations.

Examples:

Ultrashort wave

Ultrashort waves, like those of the FM broadcasting band (around 100 MHz, wavelengths ca. 3 meters) or GSM (900 MHz, 33 cm or 1800 MHz, 17 cm) bend a little, but not much. Due to reflections, they can enter buildings to a certain extent. In exceptional cases atmospheric conditions can enable reception at much greater distances, such as is much more usual with short waves (wavelengths between approx. 10 and 100 m). Perhaps this is caused not only by single reflections, but also by tunneling (ducts).

As an example, in the 1970s, when the Dutch station Hilversum 3 (later called Radio 3FM) did not yet transmit on FM channel 33 (96.8 MHz), I once received Radio Luxemburg in or close to Arnhem in the Netherlands, at a distance of about 300 km. This station was always heard at 208 meters in the medium wave band, especial in the evenings, in Dutch (Felix Meurders, Peter Koelewijn) and English, but in the FM band, this was highly unusual.

On Sunday, July 20, 2003 I experienced quite a convincing case of this phenomenon: we were at a camp site in Portugal, south of Porto Covo and Sines, when I heard Irish voices in the FM band (actually in the Irish language! they normally only send that in Ireland itself!). Later there were also English and German stations, and even programmes in Scots Gaelic, Radio na Gailge! (That's how I wrote it down in my notes, but now I find the Scottish spelling Radio nan Gaidheal and in Irish Raidió na Gaeltachta). Perhaps there was a kind of a radio mirror over the Bay of Biscay, right in the middle? If those Scots Gaelic programmes came from the vicinity of Edinburgh, we are looking at a distance of over 2000 km.

It is conceivable that something like this, but at a smaller scale, played a part in the Deventer murder case, and created GSM cell phone connection over a distance of much more than 20 km.

Some links (all in Dutch): Maurice de Hond's weblog, a blog by radio ham Brillie (page to 11 November 2006, "Leken moesten hun mond houden"), and theories by G.H. (look for "zendmast in Deventer"). Because the "radio mirror" might have been at a specific spot, G.H.'s assumption that all GSM masts of the same provider in circle shaped area could have played a role, need not be accurate. This is because during my Portuguese-Scottish experience I heard English, Irish, Scottish and German voices, but no French, Spanish, Italian or Moroccan stations. So the effect was clearly directional.

See also my article (in Dutch): Het voortschrijden der tijd.

See also these Wikipedia articles:
Ionosphere
Skywave
E-skip


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