We often hear VHF and UHF radio frequencies referred to as "line-of-sigh= t". In reality, the calculated horizon for visual line-of-sight (i.e. the visua= l horizon) is not the same as the horizon for radio wave propagation. Unless = there is a mitigating factor (for example, the antenna-to-tower spacing causing a= pattern shift) the range and coverage of your repeater will be limited to y= our radio horizon. This horizon goes beyond the calculated visual horizon due t= o a combination of factors including direct radiation and reflected ground wave= , and occasionally refraction. Note that radio horizon does not care if it is AM = or FM or SSB. And it's just a measure of distance, not a guarantee of communicati= ons range. Many other factors will have an affect on communications range such = as receiver sensitivity, local noise floor, antenna gain, antenna pattern and= more... Even though both horizons (i.e. each end of the path) can be calcul= ated, the calculations do not take into account the reality of our planet. Dust, = fog (i.e. water vapor) and solid objects (hills, etc) have an effect... And don= 't forget mankind - EMI (electromagnetic interference) has a considerable effe= ct... be it incidental (i.e. the local noise floor at the radio site), accidental= (i.e. an adjacent channel transmitter "bleeding over" on to your channel drowning out the weaker signals, or even deliberate interference on your ch= annel which can totally block the signal you are trying to receive.
To understand the radio horizon you first need to understand visual hori= zon.
Calculating the Visual Horizon
In Statute (land) Miles
First, measure the height of the viewer above ground level (in feet). Ca= ll it "H", for height.
The visual horizon distance in statute miles will be the square root of = the result of H divided by 0.5736
Example:
Height to center of your eyeball(s) = 5.5ft
5.5ft divid=
ed by
0.5736 = 9.588
Square Root of 9.588 = 3.10 statute miles, the maximu=
m
distance you could theoretically see if standing on the beach in California=
looking out across the Pacific Ocean.
Note: If your feet are just in the water you might want to know what the= distance to the horizon is in nautical miles... If so, multiply statute mil= es by 0.869 (or just take 86.9% on your calculator). If you're curious, 3.1 statu= te miles is about 2.7 nautical miles.
In Kilometers:
The visual horizon distance in kilometers will be the square root of the= result of the height in centimeters divided by 6.752
Example:
167.6cm divided by 6.752 = 24.822
Square root of 24.822=
=
4.982 km or just a hair under 5km. This is the maximum distance you could=
theoretically see if standing on the beach in Portugal looking out across t=
he
Atlantic Ocean.
Trivia:
The visual horizon of a person standing on the beach of about 3 miles is= where the historical 3 mile territorial waters rule came from. The increase= in horizon for an increase in height is why the sailing ships had a "crows nes= t" observers platform as high up on the main mast as was safe, and why even submarines have specially built observers positions as high as they can get= them.
Raising the observer from 5.5 feet to 50 feet increases the horizon from= about 3 miles to about 9 miles. Some sailing ships had masts over 100 feet = (a crows nest at 100 feet gives about 13 miles), and some WW2 warships had observation baloons - an unlucky soul with binoculars and a compass was per= ched on a seat under a baloon which was towed behind the ship at altitudes up to= 500 feet (which gives almost 30 miles). If he saw something he'd write a note g= iving dexcription and compass bearing and place it in a message canister which wa= s slid down the tow rope. A telephone headset with the cable suspended from t= he tow rope was implemented in later designs (and let the ships captain talk b= ack to the observer... "You see a WHAT?"...)
Calculating the Radio Horizon
Since radio transmissions involve a transmitting antenna and a receiving= antenna, both need to be considered for these calculations. Where the heigh= t of your eyeball was the critical measurment in the exercises above, the height= of the radiation center of both the receiving and the transmitting antennas is= the critical item here. In most antenna designs the vertical center of the ante= nna is considered to be the radiation center. In the execises below, "H1" is th= e height of antenna #1 and "H2" is the height of antenna #2.
Note that the calcualtions assume absolutely optimum conditions - qualit= y base stations, quality feedline, properly installed connectors, a perfectly= flat terrain between the two antennas, perfectly circular antenna pattern, perfe= ctly silent noise floor, etc.
An example of what can affect the results is a noisy (RF-wise) vehicle: = I can be sitting at a stoplight chatting with a friend across town on 10m SSB and= someone pulls along side with a noisy air conditioning fan motor. The local= noise can drown out my friend. His signal to me hasn't changed, my equipmen= t and antenna hasn't changed, but I can no longer hear him. As saud above, the ra= dio horizon is just an number of theoretical distance, it's not a guarantee of= communications range.
Another example: an antenna mounted on a vehicle fender is directional, = and if that directional effect is reducing the pattern in the direction of the = other antenna then the range in that direction will be reduced (both transmitting= and receiving).
Even atmospherics can have an affect: At frequencies where water vapor h= as an effect you will find that a rain cloud in the path can ruin the communicati= ons. Even a large flock of geese flying through a UHF signal path will cause a= visible drop in signal strength.
In Statute (land) Miles:
Square root of H1 (in feet) x 1.415 = D1
Square root of H2 (in feet=
) x
1.415 = D2
The radio horizon (in statute miles) is the sum of D1 and D=
2.
Example:
Antenna #1 height = 100 feet (i.e. a base station antenna =
on top
of a tower)
Antenna #2 height = 8 feet (i..e a roof-mounted antenna on=
a
large truck)
D1 equals the square root of 100 = 10 x 1.415 = 14.15
D2 equals t=
he square
root of 8 = 2.828 x 1.415 = 4.00
D1+D2 = 14.15 + 4.00 = 18.15 st=
atute miles
(theoretical maximum distance)
So in theory, an antenna with a radiation center 8ft above perfectly fla= t terrain should be able to receive signals about 18 miles away from an anten= na that has its radiation center 100 feet above the same flat terrain.
In Kilometers:
Square root of H1 (in meters) x 4.124 = D1
Square root of H2 (in me=
ters) x
4.124 = D2
D1 + D2 = Radio Horizon in Kilometers
Example:
Antenna #1 height = 15m
Antenna #2 height = 5m
Square root of 15 = 3.873 x 4.124 = 15.972 (D1)
Square root of 5 =
= 2.236 x
4.124 = 9.221 (D2)
D1+D2 = 15.972 + 9.221 = 25.193 kilometers (the=
oretical
maximum distance)
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