N1AHH

About line of sight. (So, how far can we communicate?)

Gloria and I, carry small radios in the 1 to 5 watt range. The most common question is, How far apart can you be and still communicate? Well the simple answer is 2 miles. But there is a complex answer as well.

The Simple Answer Explained: From experience we have observed that using our radios with the antennas we use in the normal areas we travel, we can usually communicate about 2 miles. This means we are both outside, not behind buildings, not behind a mountain, not in heavy wet foliage, not in areas with high radio frequency noise levels and a host of other conditions. Less distance inside of a large Mall, more over water.

In the old days, maps of unknown areas usually had a notation “Beyond here thar be beasties”. So be warned, Beyond Here Thar be MATHEMATICS!

A more complicated answer: It depends on the conditions between us. Suppose you are standing on a seashore. There is a person right on the Horizon. Assuming you are 6' tall and the other person is right down on the water.. How far away is that? Well under normal circumstances it is about 3 miles. The common formula is

Horizon in miles = 1.23 x (square root (height in feet))

or 1.23 * (square root (6)

or 1.23 * 2.25

or 3.01 miles.

But If they are 6' tall (and standing in a boat perhaps), and all you need to see is their head, then you can add another 3 miles for a total of 6 miles of separation between the two of you. The curvature of the earth limits your vision to Line of Sight. However Radio has a bit of an ability to bend just a bit so it can see a slight bit beyond the visible horizon. The rule of thumb is that the radio horizon is about 1.4 times the visible horizon.

The number 1.23 represents a “fudge factor” that includes the conversion between the measured feet of the antenna and the measured miles of the distance to the horizon as well as the radius of the earth. Unfortunately, the earths radius is a pretty huge number whose actual value depends on where on the earth you are located. Also, most calculations assume the ground is absolutely level between the antennas. So the earths radius of 3964 miles which = 20,929,920 feet and the antenna height of 6 feet means that the earths radius makes up a much larger component of the formula than the antenna height. Therefore the formula will not provide very good real world results. Still it is useful to help in understanding line of sight.

But as I said before, The Radio Horizon is 1.4 x the visible horizon. So if we are talking about antennas, one at 25' the second at 36', then they can be 30 x 1.4 or 42 miles apart. Sounds good. All we need to do is get a bit of height and we can talk for 42 miles. Well, that is not quite the whole story.

Although the above is true, it assumes that everything is working at it's theoretical maximum. The best radios (very sensitive receivers), with the best antennas with the best signal path (no obstructions) etc. In practice, it is never that good. Well, How good is it?

To find out, I have run a number of tests. I won't get into the detail of the tests now as this post is getting long enough. But in general, I have a method of sending digital information between my truck and camper while I drive around. The system I created logs my position and the signal quality. The result is plotted on a topographical map. Sounds complicated, which it is, but it is mostly automatic now, so it is pretty easy to do. So I try different antennas at various heights, change the power levels and in general play with the system.

Using the above formulas. Camper Antenna Ht = 12', Truck antenna Ht, 5'. Doing the math (1.4*(1.23((Sqrt(12) *1.23(sqrt(*5))) = 9.8 miles.

What I find is that reliable communications using high power (50 watts) from my standard truck antenna to my camper is about 9 miles. Well, it seems to be similar to the theoretical answer.

So pushing the concept to extremes, Line of sight, when applied to radio means just that. If you can see it, ;you can communicate with it. It is common for Radio Amateurs (Hams), to communicate with the International Space Station using 5 watts and a hand held radio. The nominal height of the Space Station is 250 miles. I talked with the Space Station while I was in Maine and the Space Station was over Florida. I did not compute the :slant angle:, but it was quite a long distance. The point being that in the proper situation you can talk for a long distance with a hand held radio. But one needs to understand the relationship between height and range. Higher is better, but how much higher is how much better?

Lets say you want to put up an antenna in your backyard. How high should it be? I usually make a short mast with two 10' pieces of PVC Tubing. Total of course is 20 feet. Very easy to do. Is it worth my effort to make it 30 feet tall? The construction is much more difficult because the forces on the PCV pipe begin to exceed the pipes strength. So here is a table using the theoretical calculations.

Notice that at 10' the range is 9.7 miles. Doubling the height of the mast to 20 feet changes range to 12 miles. But adding the next 10 feet to 30 only changes the distance to 13.6 miles. 100 feet = 21 miles and 200 feet = 28 miles. That is why most of the radio towers you see are so tall.

So height does matter, but it takes quite a change of height to make much range difference.

OK, so you have enough height to talk as far as you want. Why would anyone want a 50 watt radio? Why not just ½ watt? And what is a watt anyway? .... well that is next.

# posted by Ron @ 7:44 PM