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Author Topic:   Radio Horizon
jimh posted 01-20-2013 10:30 AM ET (US)   Profile for jimh   Send Email to jimh  
There is a well-known formula for calculating the radio horizon which says the distance in miles will be the square-root of twice the height in feet. When I see a formula, I tend to be curious about how it was derived. I demonstrate the derivation of the radio horizon formula in

Increasing the radio horizon is only possible by increasing antenna height, but as the relationship states, range increases only come with the square-root of height increases. To double the range requires a four-times increase in height.

On a small boat any sort of antenna height increase beyond about 10-feet elevation is impractical. It is not workable to have a 40-foot-high antenna on a small boat to double the range. Most small boats will have antennas about 10-feet high, and thus have a range to the radio horizon of about 5-miles.

Increasing the radio horizon of a shore stations is also costly if accomplished with just an antenna tower. An antenna tower of 100-feet is a reasonable installation. To increase to a 400-foot tower, that is, to double the range, will require much greater expense. Typically shore station antennas are sited on high ground, perhaps some distance from the actual shoreline, to take advantage of the natural elevation.

The height of a tower is generally limited to about 1,000-feet by regulations and practicality. Even a 1,000-foot high antenna has only a radio horizon of about 45-miles.

It should also be understood that all radio communication does not suddenly and immediately stop at the radio horizon distance. Propagation of radio waves beyond the radio horizon at VHF frequencies often occurs, but the path loss will tend to increase markedly. Increasing transmitter power and antenna gain can help extend the range. It is my experience that two small boats with good radio installations can communicate at a range of more than 10-miles most of the time, assuming there is no intervening terrain between them, that is, over open water. On the other hand, sometimes terrain can help by refracting or reflecting signals.

dfmcintyre posted 01-21-2013 08:29 PM ET (US)     Profile for dfmcintyre  Send Email to dfmcintyre     
Personal best [longest boat-to-boat radio path]: years ago, sitting at rest in the big Revenge at Northernaire I got wondering where was Walt. Called him, and got a faint response. He was sitting at rest, at Turnbull Island, across the North Channel. Weather was perfect, both engines off and no other interference around us at that time. My radio was a Motorola crystal based heavy as a brick unit, Walt's was a newer Motorola.
jimh posted 01-22-2013 09:53 AM ET (US)     Profile for jimh  Send Email to jimh     
The path described by Don looks to be about 22-miles with some intervening terrain (Barrie Island).
jimh posted 01-22-2013 10:01 AM ET (US)     Profile for jimh  Send Email to jimh     
I have expanded the article to include a formula for calculating the optical horizon, which accounts for refraction of light. This material is from BOWDITCH. There is also an on-line calculator for optical horizon (as well as several other useful calculators) available from:

Nautical Calculators _pageLabel=msi_portal_page_145

Thanks to Dave Pendelton for pointing me to this.

jimh posted 01-25-2013 01:21 AM ET (US)     Profile for jimh  Send Email to jimh     
ASIDE: I happened to watch the last hour of a classic movie, ICE STATION ZEBRA, on a cable channel tonight. There were some rather glaring errors in the production which caught my attention. The plot requires a submarine to surface in the Artic region. The submarine conning tower is only shown projecting about 20-feet above the ice. On the conning tower an extremely compact RADAR antenna is seen to be rotating at a very fast rate of revolution. An expedition shore party is on the ice surface. The sub contacts them to warn that they have picked up approaching aircraft. The CO asks for the range and ETA. (Of course, this would probably have been given in the first place--no need to ask.) This is where things start to go awry.

The aircraft are reported to be at a distance of over 100-miles. The scene changes to the aircraft. They are shown flying in at an altitude of about 500-feet above the ice. My RADIO HORIZON alarm goes off.

If we compute the radio horizon for an antenna that is 20-feet high, we get about 6-miles. For a target 500-feet high, we get a horizon of 31-miles. The incoming planes could not be detected at a range of 125-miles by a RADAR antenna at 20-feet elevation if the planes are flying at 500-feet. This is known as "flying under the RADAR." This concept is apparently not known to screenwriters.

I found another problem, this one with the relationship of the sun to the location. See my comments in the Navigation Calculation thread.

Hoosier posted 02-04-2013 11:33 AM ET (US)     Profile for Hoosier  Send Email to Hoosier     
A possible explaination for the 22 mile propagation that Don experienced can be found here:
jimh posted 02-04-2013 11:52 AM ET (US)     Profile for jimh  Send Email to jimh     
Tropospheric ducting usually results in very long paths, typically hundreds of miles. It is more likely that some refraction and scattering by intervening terrain may have augmented propagation on the radio link of 22-miles. I think a range of 22-miles would be relatively routine if two boats with good radio installations were carefully listening for each other, the receivers were operating at maximum sensitivity, there was no local electrical noise or interference that would limit the ultimate sensitivity, and there was no other on-channel interference.

ASIDE: For many years I was involved in the use of wireless microphones whose transmitters operated in the frequencies normally occupied by broadcast television transmitters. It was common practice for a broadcaster to have wireless microphone that operated on a television channel that was vacant in their local area. In our case, we used wireless microphones that operated on television channel eight; we had local stations on channels seven and nine. In the winter months, particularly in the pre-dawn hours of the morning, it was very common for the wireless microphone receivers to pick up the transmission of a distant television station operating on channel eight. The station was located about 140 miles away, with the path between an all-land path with plenty of urban terrain. Just about every morning in the winter they would come in with good signals on the wireless microphone receivers. Once the sun came up and the atmosphere began to warm, the signals would fade out.

When the local transmitters for the wireless microphones were turned on, they were much stronger than the remote signals, and the long-distance signals did not tend to disrupt their use. I should also mention that the broadcast station was transmitting at much higher power than a VHF Marine Band radio. But it was surprising how consistently there was a path of 140-miles. Channel eight is at a frequency of 180 to 186-MHz, just 25-MHz or so higher than the VHF Marine Band.

Hoosier posted 02-13-2013 09:31 AM ET (US)     Profile for Hoosier  Send Email to Hoosier     
Since light and rf waves obey the same laws of physics, here's an interesing scientific analysis of a optical phenomenon that some of us were witness to:

dfmcintyre posted 02-13-2013 04:49 PM ET (US)     Profile for dfmcintyre  Send Email to dfmcintyre     
That response above reminded me of working dispatch in the very early 70's at my department. Late night, clear and usually in the winter we would have, traffic that we later figured out was from a Mexican fire department.
That was on the old LF 39.10 - 39.14mhz era.

Personally, I talked to our dispatch early one morning in Lansing, 90+ miles away when the departments were in the 450mhz band. Reception was fine both ways.


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