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Author Topic:   Increase in Radio Horizon with Height
jimh posted 04-27-2013 10:21 AM ET (US)   Profile for jimh   Send Email to jimh  
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

Radio-horizon-in-miles = (2 x height-in-feet)^0.5

The most practical increment for increasing antenna height is 4-feet. There are 4-foot extension masts made, and in many cases an antenna can be elevated by 4-feet 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 3-feet long exposed metal whip antennas, can be easily raised with a 4-foot 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 4-feet will be

New-radio-horizon-in-miles = (2 x (original height + 4-feet))^0.5

For example, if the original height were 1-foot, the radio horizon would be 1.414-miles. If this is raised to 5-feet, the new radio horizon will be 3.16-miles, and the increase in radio horizon due to raising 4-feet will be 1.75-miles.

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 4-foot increase. We can see the trend as follows:

1 1.75
2 1.46
3 1.29
4 1.17
5 1.08
6 1.01
7 0.95
8 0.90
9 0.85
10 0.82
15 0.68
20 0.60
25 0.54

Once the original antenna height was 6-feet, adding the 4-foot extension only adds one-mile or less to the distance to the radio horizon. If an antenna is already 25-feet high, adding 4-feet 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 4-feet and raised to 8-feet. The increase in range will be 1.172-miles, which represents a 41-percent increase. In comparison, if an antenna originally at 8-feet is increased to 12-feet, the increase in range will be 0.9-miles, which represents only a 22.5-percent 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 10-feet, 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 8-feet from 4-feet has a nice payoff.

jimh posted 04-27-2013 10:31 AM ET (US)     Profile for jimh  Send Email to jimh     
The above calculations are just mathematical, and they may not reflect the actual improvement in range that may occur if an antenna were raiseed 4-feet. Other factors can influence the outcome. One important factor is the location of the antenna relative to other objects, both conducting and non-conducting. 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 4-feet 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 04-27-2013 11:32 AM ET (US)     Profile for Buckda  Send Email to Buckda     
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 04-27-2013 11:50 AM ET (US)     Profile for Buckda  Send Email to Buckda     
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.
Original height - Percent increase when adding a 4’ extension
1’ – 80%
2’ – 67%
3’ – 57.2%

12’ – 25%

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 04-28-2013 10:29 AM ET (US)     Profile for jimh  Send Email to jimh     
The range increases only as the square-root of the height increase. Not only does a 4-foot increment become a smaller percentage of increase, but then that new height only increases the range at a rate of the square-root 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 10-feet above the water, there is not a great deal to be gained by moving it to 14-feet. Of course, if you could move it to 14-feet 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 3-feet above the water, say on part of a cabin superstructure, there is a 4-foot extension, and a 3-foot radiator is placed there, the antenna height would be calculated as 3 + 4 + 1.5 = 8.5-feet, 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 = 10-feet.

In many antennas housed inside an 8-foot-long fiberglass tube or radome, the actual radiating portion is limited to the upper 3-feet, the upper 5-feet, or perhaps the upper 6-feet, 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 18-inches 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 10-feet above ground level for a VHF Marine Band antenna, you can probably stop worrying about the 18-inch 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


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 04-28-2013 12:31 PM ET (US)     Profile for jimh  Send Email to jimh     
ASIDE to Dave:

When an antenna at an elevation of 1-foot is increased by 4-feet in elevation, the percentage increase it its elevation is 400-percent, not 80-percent.

When an antenna at 12-feet is increased 4-feet the increase is 33-percent, not 25-percent.

I don't quite follow your figures for these calculations.

AZdave posted 04-28-2013 11:16 PM ET (US)     Profile for AZdave  Send Email to AZdave     
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 04-29-2013 12:47 AM ET (US)     Profile for jimh  Send Email to jimh     
The link to Bowditch pdf


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 25-watt transmitter and a 3-dB 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 300-foot high antenna only has a radio horizon of 24.5-miles. A typical boat with a 10-foot high antenna has a radio horizon of 4.5-miles. The radio horizons overlap up to a range of 29-miles. That path is not very long, and with 25-watts 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.

Intervening terrain also has to be considered in any sort of calculation of the radio horizon and path. If there is a 6,000-foot high mountain between your station and another station 15-miles away, the path loss is going to be much different than if there were nothing but sea water between the two stations.

jimh posted 04-29-2013 08:59 AM ET (US)     Profile for jimh  Send Email to jimh     
Having a cup of coffee this morning, I worked out the path loss to the moon as follows:

The Earth-Moon distance is roughly 238,900-miles. At a frequency of 156-MHz, the path loss for a free-space model is -188dB. Using a 25-watt transmitter with 3-dB gain antennas and feedline loss of -1-dB, the received signal level is about -140-dBm, or a signal of 0.022-micro-Volt.

If you figure a typical receiver sensitivity is 0.5-micro-Volt, the received signal is too weak by a factor of about 22-times.

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