
ContinuousWave Whaler Moderated Discussion Areas ContinuousWave: Small Boat Electrical Increase in Radio Horizon with Height

Author  Topic: Increase in Radio Horizon with Height 
jimh 
posted 04272013 10:21 AM ET (US)
It is frequently said that increasing antenna height is the best way to increase range. This is based on the notion that the radio horizon will increase with increased antenna height. That is, of course, true. The radio horizon is calculated by the relationship Radiohorizoninmiles = (2 x heightinfeet)^0.5 The most practical increment for increasing antenna height is 4feet. There are 4foot extension masts made, and in many cases an antenna can be elevated by 4feet with one of these extensions without too much mechanical difficulty. A longer extension will usually required some special attention to the mechanical aspect, such as providing an intermediate support. Smaller and lighter antennas, such as 3feet long exposed metal whip antennas, can be easily raised with a 4foot extension. When the antenna is raised, the distance to the radio horizon increases according to the relationship shown above. The new distance to the radio horizon after raising 4feet will be Newradiohorizoninmiles = (2 x (original height + 4feet))^0.5 For example, if the original height were 1foot, the radio horizon would be 1.414miles. If this is raised to 5feet, the new radio horizon will be 3.16miles, and the increase in radio horizon due to raising 4feet will be 1.75miles. Because of the relationship between height and radio horizon, there is a tendency to have diminishing returns on the improvement in distance to the radio horizon for a 4foot increase. We can see the trend as follows:
Once the original antenna height was 6feet, adding the 4foot extension only adds onemile or less to the distance to the radio horizon. If an antenna is already 25feet high, adding 4feet increases the distance to the radio horizon only a half mile. The percent of increase is even more discouraging. Let us compare and antenna originally at 4feet and raised to 8feet. The increase in range will be 1.172miles, which represents a 41percent increase. In comparison, if an antenna originally at 8feet is increased to 12feet, the increase in range will be 0.9miles, which represents only a 22.5percent increase. In general a higher antenna is a better antenna, but the above calculations show that there is a point of diminishing returns for incremental increases in height. I would say that once an antenna is at 10feet, there is not a great deal of further increase in range to be obtained with small improvement in height. The best investment occurs when the original height was low. Moving an antenna to 8feet from 4feet has a nice payoff. 
jimh 
posted 04272013 10:31 AM ET (US)
The above calculations are just mathematical, and they may not reflect the actual improvement in range that may occur if an antenna were raiseed 4feet. Other factors can influence the outcome. One important factor is the location of the antenna relative to other objects, both conducting and nonconducting. If an antenna is mounted in a location where it is surrounded by metal objects like grab rails or canvas top support rails, or where it is close to people, such as the helmsman at a console, the performance of the antenna can be diminished by the influence of these nearby objects. Raising the antenna 4feet higher and putting it in the clear may have more profound effect on performance than just the increase in distance to the radio horizon. 
Buckda 
posted 04272013 11:32 AM ET (US)
I am no mathematician, however, isn’t it true that a big part of the reason that “the percentage of increase is … discouraging” is because the percentage of increase is in height is simply diminished by the fact that adding 4 feet to a 12’ tall tower is a smaller increase than adding 4’ to a 1’ tall tower? I mean, if you add 4’ of height to something that is 1’ tall, you’re increasing the height much more (when expressed as percentage increase in height) than when you add 4’ of height to an 100’ tall tower…something like 400% compared to 4%. Right? 
Buckda 
posted 04272013 11:50 AM ET (US)
Again – math is not my strong suite…so never mind the above post… I show that adding 4’ in height represents the following percentage of increase for each. So I see your point that there is a diminishing relationship to the percentage of increased height vs. the percentage of increased range. 
jimh 
posted 04282013 10:29 AM ET (US)
The range increases only as the squareroot of the height increase. Not only does a 4foot increment become a smaller percentage of increase, but then that new height only increases the range at a rate of the squareroot of the increase. What I have done is to quantify what I already knew in a rough approximation, that is, after about ten feet of elevation the increase in distance to the radio horizon by adding height soon reaches a point of diminishing returns for the practical limitation of an installation on a small boat. Often said is "the best way to increase range is to increase antenna height," but there are practical limitations to it for the small boat operator. If you can get your antenna to about 10feet above the water, there is not a great deal to be gained by moving it to 14feet. Of course, if you could move it to 14feet without having a mechanical monstrosity, there is nothing wrong with moving it up. More height is always welcome. Also, when I am talking about antenna height, I am talking about the effective height of the center of the antenna array, not the tallest part of the antenna. For example, if the base of the antenna is mounted at 3feet above the water, say on part of a cabin superstructure, there is a 4foot extension, and a 3foot radiator is placed there, the antenna height would be calculated as 3 + 4 + 1.5 = 8.5feet, which is the height above the water for the center of the actual radiating part of the antenna. The height is not 3 + 4 + 3 = 10feet. In many antennas housed inside an 8footlong fiberglass tube or radome, the actual radiating portion is limited to the upper 3feet, the upper 5feet, or perhaps the upper 6feet, varying with the design of the antenna. By the way, another reason for ignoring the height of the tip of the antenna is the notion that the antenna current at the tip of a vertical antenna is always going to be the least current in the antenna. The point of maximum current is where the signal really comes from. Most of the current in the antenna is going to be about 18inches lower than the tip for a VHF Marine Band antenna. This is just a characteristic of vertical antennas. The higher above ground an elevated vertical antenna is located, the less attention needs to be paid to where the current maxima will be. By the time you get to more than 10feet above ground level for a VHF Marine Band antenna, you can probably stop worrying about the 18inch offset for the current maxima. Regarding the distance to the horizon from an elevated location, there are three distances: the geometric distance, the optical horizon, somewhat longer, and the radio horizon, somewhat longer still Radio waves routinely travel over the geometric horizon and the optical horizon. Although "radio is line of sight" is often said, it is not true. Radio wave routinely travel farther than light waves in terms of bending over the horizon. Unusual refraction of light waves in the atmosphere occurs when certain conditions, such as stratified layers of air at different temperatures are in the path of the light, and this produces unusual effects called mirages. For some reports of optical refractions, see http://continuouswave.com/misc/redGreen.html and http://trodden.rssing.com/browser.php?indx=2291377&item=163 Radio waves are similarly liable to be refracted in abnormal manners, and may be bent over the horizon for long distances in certain conditions. In some cases, radio waves can travel by reflection between layers in the atmosphere, but usually at the VHF Marine Band frequency this effect is not as common. 
jimh 
posted 04282013 12:31 PM ET (US)
ASIDE to Dave: When an antenna at an elevation of 1foot is increased by 4feet in elevation, the percentage increase it its elevation is 400percent, not 80percent. When an antenna at 12feet is increased 4feet the increase is 33percent, not 25percent. I don't quite follow your figures for these calculations. 
AZdave 
posted 04282013 11:16 PM ET (US)
Jimh, I just looked at your reference article on radio horizon. It includes a table from Bowditch showing distance to the radio horizon for towers of varying heights. If a boat with modest antenna height is communicating with a much taller shore based antenna, can one simply add the horizon distances for the two antennas? 
jimh 
posted 04292013 12:47 AM ET (US)
The link to Bowditch http://msi.nga.mil//MSISiteContent/StaticFiles/NAV_PUBS/APN/Tables/T12. pdf in http://continuouswave.com/whaler/reference/radioHorizon.html is to a table of optical horizon distances, not radio horizon distances. When figuring a range of communication, you can determine if the radio horizons of two stations overlap by comparing their distance apart to the sum of their radio horizons. Whether or not the two stations can communicate depends on the transmitter power, receiver sensitivity, and path loss. For example, the Moon might be visible overhead, but that does not mean you can communication with the Moon using your VHF Marine Band radio. Even though the Moon is on your radio horizon, the path loss will be too great for a 25watt transmitter and a 3dB gain antenna to communicate. For typical ranges of the radio horizon for small boats, you can generally always communicate with another station if your radio horizon overlaps with their radio horizon, because the distances are usually not very far. Even a shore station with a 300foot high antenna only has a radio horizon of 24.5miles. A typical boat with a 10foot high antenna has a radio horizon of 4.5miles. The radio horizons overlap up to a range of 29miles. That path is not very long, and with 25watts you will have plenty of signal. Typically, you can generally count on being able to communicate that far with plenty of signal reserve. See my article on VHF Communication for a good example. http://continuouswave.com/whaler/reference/VHF.html Intervening terrain also has to be considered in any sort of calculation of the radio horizon and path. If there is a 6,000foot high mountain between your station and another station 15miles away, the path loss is going to be much different than if there were nothing but sea water between the two stations. 
jimh 
posted 04292013 08:59 AM ET (US)
Having a cup of coffee this morning, I worked out the path loss to the moon as follows: The EarthMoon distance is roughly 238,900miles. At a frequency of 156MHz, the path loss for a freespace model is 188dB. Using a 25watt transmitter with 3dB gain antennas and feedline loss of 1dB, the received signal level is about 140dBm, or a signal of 0.022microVolt. If you figure a typical receiver sensitivity is 0.5microVolt, the received signal is too weak by a factor of about 22times. 
Powered by: Ultimate Bulletin Board, Freeware Version 2000
Purchase our Licensed Version which adds many more features!
© Infopop Corporation (formerly Madrona Park, Inc.), 1998  2000.