Question

Derive an expression for the range of transmission via space wave from a transmitting antenna of height h.

Answer 1

The required expression for range of transmission is d = √2Rh

Explanation :

Consider a transmission tower transmitting signals in all the direction

Let R be the radius of earth,

h be the height of the antenna

d be the range of transmission on either side

Net height of the tower from center of the earth = R + h

hence,

(R + h)² = R² + d²

=> R² + h² + 2Rh = R² + d²

=> d² =  h² + 2Rh

since h <<< R, so h² <<< 2Rh

hence neglecting h² we get,

d² =  2Rh

=> d = √2Rh

which is the required expression for range of transmission.