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A transmitting antenna at the top of a tower has a height \(32\;m\) and the height of the receiving antenna is \(50\;m\). What is the maximum distance between them for satisfactory communication in \(LOS\) mode? Given radius of earth \(6.4\times 10^6\;m\).

Answer

\(45.5\ \mathit{km}\)
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Solution

Given:
Radius of Earth, \(R=6.4\times 10^6\;m\)
Height of transmitting antenna,\(h_t=32\;m\)
Height of receiving antenna, \(h_r=50\;m\)
Maximum distance for satisfactory communication \((d_m)\)  is given by,
\(d_m=\sqrt{2h_tR}+\sqrt{2h_rR}\)
\(d_m=\sqrt{2\times 32\times6.4\times 10^6}+\sqrt{2\times 50\times 6.4\times 10^6}\)
\(d_m=20,238.57+25,298.22\)
\(d_m=45,536.79 \ m\)
\(d_m=45.5\ \mathit{km}\)
Hence, maximum distance between them for satisfactory communication in LOS mode is \(45.5\ \mathit{km}\).
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