The document explains how to calculate the maximum line-of-sight (LOS) distance for a radio tower based on its height and the local altitude. Using the formula derived from the earth's curvature, an example calculates that the maximum LOS distance for a tower at the altitude of Taipei 101 is approximately 80.5 km. It also provides assumptions regarding transmission power and isotropic transmission, emphasizing the impact of the earth's roundness on coverage calculations.

1. How to Calculate the Maximum
Distance of LOS Coverage in
known Tx Height
By Justin MA
Created: 2015_0524 Updated: 2015_0525

2. What is the maximum LOS distance of a radio
tower?
Ref: hill: http://misteraibo.deviantart.com/
Ref: Radio tower: http://www.szoges.com/
The Height of Radio tower：H1 m
The altitude of hill：H2 m
Sea level
D km =?Ref: Question man: http://www.foodcentral.com.au/
Assumption: Without regard to the power issue

3. Assumptions
• Transmission is isotropic.
• There is no limitation of transmission power.
• Only focusing on the LOS coverage.
So, what is the
limitation now?
Ref: Question man: http://www.foodcentral.com.au/

4. LOS is stopped here!
The Earth is a ball

5. Descriptions
• The earth surface is round.
• The LOS of ray will travel until it touch-down the farest point on the
earth surface.
So, let’s calculate it now!

6. Radius of the earth：6371km
Height of tower + Altitude：H mMax. LOS distance：
D km
Calculation:
D^2 + 6371^2 = (6371 + H)^2
D^2 = (6371 + H)^2 – 6731^2
D^2 = (6371 + H + 6731) x (6371 + H - 6731)
D^2 = (2 x 6371 + H) x H
D^2 = 2 x 6371 x H + H^2
General Calculation of maximum distance of LOS

7. Example:
What if Tx is on top of Taipei 101

8. The Altitude of Taipei 101: 508m
Ref: http://zh.wikipedia.org/
Taipei 101

9. What is the maximum LOS distance of a radio
tower on Taipei 101?
Sea level
D km =?
Assumption: Without regard to the power issue
Ref: http://zh.wikipedia.org/
508 m

10. Height of tower + Altitude： 508 m
D^2 = 2 x 6371 x 508 + 508^2
D = 80.5 km
Calculation of maximum distance of LOS for
Taipei 101
Max. LOS distance：
D km
Radius of the earth：6371km

11. The maximum distance
of LOS for Taipei 101
• It is about 80.5 km
• Now we learn how to
calculate the maximum
LOS coverage of a known
height radio tower with
the local altitude.

12. Thank you for your reading!!
• Any feedback is welcome.
• My email: majachang@gmail.com