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Does Size Really Matter ? Richard M1 RKH
It is often said that you need to get your antennas up as high as possible. In HF, the height above ground can have an effect on the take off angle. At VHF, the reason can be simpler, to get a better line of sight as most signals follow the direct path to the receiving station.
Most VHF signals arrive at the destination via a direct path, or by bouncing off something (for example rain scatter, a building etc) so the height of your mast is important if for example you are planning to talk to someone outside of Telford. Effects such as diffraction or other bending type propagation are less dominant at VHF. What this comes down to is if you can’t see the rx station you may have problems communicating between you both.
Step forward Bob. Bob lives somewhere around Stoke. Bob and I regularly have a very good signal between us on FM, even at 2.5W on my FT290. Why could this be so?
Lets assume we both have aerials at 5m height above ground, lets also assume that we are at sea level and then afterwards we’ll use some real data.
The diagram looks something like this, see Figure 1:
This is a hypothetical line of sight path between us. We need to know something about triangles and do a little mathematics to work out what the maximum line of sight path is.
Lets review what we know or can find out really easily:
Figure 2 shows some of the distances more mathematically and has been labelled as in the bullet points above. The important point here is the antenna heights are in addition to the radius of the earth. Where the line of sight touches the surface of the earth it makes a right angle to the centre of the earth (the distance is the earths radius), the distance to the left of this is D and to the right is F metres.
Also remember Pythagoras? The square of the hypotenuse is equal to the sum of the square of the other two sides?
Remember my aerial is at a distance T above ground. We need to know where about the horizon is, this will be “D” metres away. The distance of my aerial above the centre of the earth is “A+T”. Lets go (remember Pythagoras).
(A+T)2 = D2 + A2
Rearrange this to put D on its own (take A2 off both sides)
D2 = (A+T)2 - A2
We need to multiply out (A+T)2, remember this is the same as (A+T) x (A+T), it’s the same as 32 = 3 x 3, I will give you the answer: A2 + AT + AT + T2 = A2 + 2AT + T2. So:
D2 = (A2 + 2AT + T2 ) - A2
D2 = 2AT + T2
We can make an assumption now to simplify things. A is a lot lot lot bigger than T. Do you agree? So the T2 term becomes pretty small in comparison to the 2AT term.
D2 = 2AT
The same is true for the other triangle :
F2 = 2AR
If we know what “X” squared is, if we take the square root we get back to X. I don’t know where my square root sign is in this editor programme but we can write it out as X1/2, that is X to the power of a half. This is the same as taking the square root.
D = (2AT)1/2
And
F = (2AR)1/2
Now we know what the line of sight distance between our homes is, it is D + F:
D + F = (2AT)1/2 + (2AR)1/2
This can be rewritten as:
D + F = (2A)1/2 x (T1/2 + R1/2)
Obviously in this case, since both are at the same height D and F are the same and we know A (6350 km or 6,350,000 m), T and R so we can put them in a calculator.
Bob to Richards line of sight path with 5m high aerials is 15km. Wow, we should be able to shout to each other. So how do we start to model the real path.
Lets start by using some real antenna heights, again assuming we are both at sea level. My aerial is about 10m above ground. Bob’s is about 12m. Put these in the same formula and we get the line of sight path is about 23km. Now we are heading in the right direction. You can see that by adding just over 5m to each side we have almost doubled the line of sight range of our VHF stations. Those extra poles we put in the T-K brackets were useful after all.
I know my house is about 190m above sea level, Bobs is about the same. This increases my effective aerial height “T” to 200 and “R” to 202. Plugging these in gives a path of 101km.
But our path is not perfect, there is some lumpy land in the way. There is a big lumpy bit about 100m high, in the simplest case this effectively reduces our height above sea level by the same amount. This gives our line of sight path as 71km. In reality it depends on where the obstruction is, here I am assuming it is right in the middle, somewhere close to the point where we see the horizon (see the pictures above) in reality it is to one side. Where the obstruction is influences what we can see on the other side of it as the Earths surface is curved. Between Bob and I we not only have a good line of sight path but the obstructions are probably not too large to affect it.
Now to use a program that will calculate paths between locators that we can use for references (and some data to allow your own calculations):
UKV Loc. is IO82RR57, National Grid SJ639158 (52m ASL, 9m AGL (Above Ground Level))
Bob's locator is IO83VC26, National Grid SJ845572 (190m ASL, 12m AGL)
Mine is IO82SQ11, National Grid SJ670085 (190m ASL, 10m AGL)
UKV < RKH is 7.9 Km, 156.3 deg / 336.4 deg bearing to/from each other
UKV < RJS is 46.2 Km, 26.0 / 206.2 deg
RKH < RJS is 51.7 Km, 199.5 / 19.3 deg.
From the data above our “as the crow flies” distance between our antennas is 51.7km. We calculated our line of sight path, and it turned out that we could probably be up to 71km apart and still be able to transmit directly between each other, though this may mean adding antenna gain or output power to cover a few more kilometres of loss.
You can now see why for even the simpler cases getting those extra few metres on your VHF/UHF set up will vastly improve your line of sight path. Then you can start to take into account other obstructions. Or to put it another way, this is why Bob and I have a good chance of talking on FM to each other at such low powers over long signal paths. It’s also the reason why the microwavers climb up mountains to talk to each other, it has nothing to do with microwaves frying their brains and making them do odd things…….really.
Disclaimer: OK, it’s a very simplistic case, and doesn’t even start to take into account other variables such as diffraction, antenna gain etc, but it does illustrate the principle. One other way to measure paths is slightly different in perspective. You would use a power budget over the path and account for things like path loss, antenna gain, output power. Of course again, you need to have a way to see the rx station in the first place.
Richard M1 RKH