Distance between two antennas

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?

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

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