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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.
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.
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.
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.
Even at only 5 cm (2 inches) above the ground the horizon is already some 800 meters away. Of course at this scale, the earth is far from an ideal sphere, so this result is largely of theoretic value.
A person carrying a walkie-talkie at a height of 1.70 m has a visual reach of over 4.5 km. If the person at the other side of the radio link is at the same height, the total maximum distance is about 9 km.
A cell phone transmitter on a twelve storey building, at a height of some 30 m, has a "view" of about 19.5 km (12 miles). The mobile phone's horizon (as we found above: approx. 4.5 km) adds up to this, so the total range is around 24 km.
Antennas of radio and TV
transmitters are usually installed on high
masts, or on low masts on high mountains.
Even a small country like the Netherlands
needs several to cover the whole country.
The highest mast, the Gerbrandy tower, is located
(as was to be expected) in the centre of the
(formerly also called Lopik), not far from Utrecht.
The top of that mast is at a height of about 385 meters.
That is much higher than the Eiffel Tower in Paris,
but because the largest part of the tower is not
self-supporting, but held upright by guy wires,
it doesn't count as a building.
Consider that most of the antennas are not at the highest point of the mast: because many are needed, and some are rather large (TV transmitters in low bands) they are spread along the mast. Be that as it may, the optical horizon from the top can be calculated as being 70 km. It so happened that I lived at about 60, later almost 70 km from the TV/radio tower of IJsselstein. Indeed reception was possible, but poor there. The lower but closer station Markelo gave a better reception.
I heard about Canada and Russia having even higher TV and radio towers. Calculations show, however, that the considerable costs of builder higher towers does not outweigh the gain in geographical range. Suppose such a tower is 200 meters higher, making it 585 meter high (1920 feet). Then the extra range is a mere 16 kilometers.
In countries with mountainous areas they tend to build transmitter masts on or near high peaks. Their theoretical range of course only applies to far away places at see level: closer by at places that are also at high altitudes, the calculations are incorrect.
The highest mountain of Portugal
(mainland) is 1993 m in height. The theoretical line of sight
there is almost 160 km, strangely enough only 90 km more
than on the 385 meters high IJsselstein tower.
If we include Portugal's autonomous regions, the volcano called Pico, on the Azores island of the same name, is much higher: 2351 m. This results in a line of sight of 173 km. I don't know if the summit is accessible (I never visited the islands), but if so, a glimpse of another high altitude point, Pico de Vara on the eastern island of São Miguel, should be visible. (In practice, if only because of the haze, no doubt nothing can be seen.)
That other peak is 1103 meters high, for a horizon of 118.5 km, giving a total of both lines of sight of 291.5 km, while the distance between the summits, according to my calculations is slightly less: 289 km.
In the opposite direction, towards the island of Flores in the north-western Azores, chances are better in theory: 941 m for 108 km, a total of 281 km, with a distance between summits of 268 km.
Passenger jets often fly at altitudes between 8 and 11 kilometers (26 and 36 thousand feet). At 32,000 feet (9753,6 m) for example, the line of sight is 352.5 km. This means an aeroplane over Paris cannot reach Schiphol tower in Amsterdam over VHF or UHF, as I sometimes imagined, because the distance is around 426 kilometers. To be reachable at these non-bending wavelengths, the airport's antennas should be at an altitude of 425 meters!
Satellites of course are much higher. In that case we see that the difference between the distances through the air (d) and that along the earth's surface (D) becomes considerable. Of course the limit for D is a quarter of the sphere's perimeter, and the calculation module has a restriction for that value, for calculations that take D as input.
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:
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