Question

A transmitting antenna at the top of a tower has a height $32m$ and the height of the receiving antenna is $50m$. What is the maximum distance between them for satisfactory communication in line of sight (LOS) mode?

• A. $55.4km$
• B. $45.5km$
• C. $54.5km$
• D. $455km$

Answer 1

Answer: (B)

$45.5km$

The line-of sight can be calculated using the following equation:
$d_m=\sqrt{2R{H}_t}+\sqrt{2R{H}_r}$
Where,
$d_m$ = distance to radio horizon (miles)
$H_r$ = height of RX antenna (feet)
$H_t$ = height of TX antenna (feet)
$R$ is the radius of the Earth

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

$=6400\sqrt{10}+8000\sqrt{10}$

$=14400\sqrt{10}=45.5km$.