How to Calculate the Maximum Distance of LOS Coverage in

known Tx Height By Justin MA

Created: 2015_0524 Updated: 2015_0525

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 towerH1 m

The altitude of hillH2 m

Sea level

D km =?Ref: Question man: http://www.foodcentral.com.au/

Assumption: Without regard to the power issue

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/

LOS is stopped here!

The Earth is a ball

Descriptions

The earth surface is round.

The LOS of ray will travel until it touch-down the farest point on the earth surface.

So, lets calculate it now!

Radius of the earth6371km

Height of tower + AltitudeH mMax. LOS distanceD km

Calculation:

D^2 + 6371^2 = (6371 + H)^2D^2 = (6371 + H)^2 6731^2D^2 = (6371 + H + 6731) x (6371 + H - 6731)D^2 = (2 x 6371 + H) x HD^2 = 2 x 6371 x H + H^2

General Calculation of maximum distance of LOS

Example: What if Tx is on top of Taipei 101

The Altitude of Taipei 101: 508m

Ref: http://zh.wikipedia.org/

Taipei 101

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

Height of tower + Altitude 508 m

D^2 = 2 x 6371 x 508 + 508^2D = 80.5 km

Calculation of maximum distance of LOS for Taipei 101

Max. LOS distanceD km

Radius of the earth6371km

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.

Thank you for your reading!!

Any feedback is welcome.

My email: majachang@gmail.com