Question

Heights of transmitting and receiving antennas from earth surface are $h_T$ and $h_R$ respectively. Write the relation for maximum line-of-sight (LOS) distance between two antennas.

Answer 1

Let the radius of earth be $R$ and height of the antenna be $h$ as shown in figure (i).

From figure (i) $AC=\sqrt{A{B}^2-B{C}^2}$

$\therefore$ $x=\sqrt{(h+R{)}^2-R^2}=\sqrt{h^2+2hR}$

As $h<<R$ $⟹$ $x=\sqrt{2hR}$ .......(1)

Let the receiving and transmitting antennas are situated on earth as shown in figure (ii).

Maximum line of sight (LOS) distance between two antennas $X=x_R+x_T$

Using equation (1), we have $x_R=\sqrt{2h_{R}R}$ and $x_T=\sqrt{2h_{T}R}$

$⟹$ $X=\sqrt{2h_{R}R}+\sqrt{2h_{T}R}$