Question

A transmitting antenna at the top of a tower has a height of 32 m and the height of the receving antenna is 50 m. What is the maximum distance between them, for satisfactory communication in Line of Sight (LOS) mode? ( Radius of earth = 6400 km)

Answer 1

Given height of,

Trasmitting antenna $\left(h_T\right)=32m$

Reciveing antenna $\left(h_R\right)=50m$

and radius of earth $\left(R_E\right)=6.4\times {10}^{6}m$

In line of sight $\left(LOS\right)$ communication, maximum distance of communication $\left(dmax\right)$ is given by :

$dmax=\sqrt{2h_T{R}_E}+\sqrt{2h_R{R}_E}$

putting values ,

$dmax=\sqrt{2\times 32\times 6.4\times {10}^6}+\sqrt{2\times 50\times 6.4\times {10}^6}$

$=(\sqrt{409.6}+\sqrt{640})\times {10}^{3}m$

$dmax\simeq 45.54km$