Distance between two antennas

soulphish · Thu May 09, 2013 12:52 am

I am trying to find out the formula to calculate how high antennas need to be for Line of Sight (LoS) propagation.

I found:

d = 3.57sqrt(h)

also

d = 3.57sqrt(Kh)

d can also be worked out using

d = 3.57( sqrt(K[h1]) + sqrt(K[h2]) )

Where d is the distance between an antenna and the horizon (or between two antennas) in kilometres, h is the height of the antenna(s) in meters, and K is used to account for the curvature of the earth (which is usually 4/3).

The problem with this equation is it is making the antennas ridiculously high for the distance I am trying to calculate. The question I am trying to answer is: “Two antennae are used for line of sight propagation. The antennae are spaced 150km apart. Determine the required antennae heights.”

My calculations:

d=3.57sqrt(4/3)(h)
d=3.57(sqrt[4/3])(sqrt[h])
d=3.57(1.1547)(sqrt[h])
150=(4.1223)sqrt(h)
150/4.1223=sqrt(h)
sqr(36.3875)=sqr(sqrt(h))
1324.05=h   1324meters = h1 + h2  -> each antenna needs to be 762meters high

Is this the correct method? Or have I chose the wrong equation totally?

cbrown · Thu May 09, 2013 1:37 am

You could use "Radio mobile" or towercoverage.com. They might be much easier.

CelticComms · Thu May 09, 2013 10:37 pm

You need to consider both curvature effects and the Fresnel zone so the final answer is frequency and distant dependent. Have a look at this site:

http://www.radiodata.co.uk/faqs/line-sight