Question

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 that radius of the earth is $6.4\times {10}^{6}m$

• A. 45.5 km
• B. 25.5 km
• C. 85.2 km
• D. 33.5 km

Answer 1

The correct option is A 45.5 km

Given: $h_T=32m,h_R=50m,R_E=6.4\times {10}^{6}m$

The maximum line of sight distance ($d$) between the two antennas is given by:

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

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

$d=20.24\times {10}^3+25.28\times {10}^3=45.5\times {10}^{3}m$ ,

$d=45.5km$