microwave tower separation

[schmidty99]

Hey guys! 6 days to go! I am working some communications problems and I ran across a conflicting formula and was wondering if someone could help out. For the distance between 2 line of site towers, the formula is simple enough: distance between towers = 4.1*sqrt of the height.

(d=4.1*sqrt of h)

This holds true in both the EERM 8th edition (eqn 62.3) and Camara's 6-minute solutions (problem 91). EXCEPT, in the 6-minute solutions, there is an errata stating that the 4.1 should be changed to 8.2. They are saying that "d" they listed was the distance to the horizon, not the distance to the other tower. Just wondering if anyone could confirm or debunk one or the other. Thanks!!

 

[CincinnatiControlsGuy]

Hey guys! 6 days to go! I am working some communications problems and I ran across a conflicting formula and was wondering if someone could help out. For the distance between 2 line of site towers, the formula is simple enough: distance between towers = 4.1*sqrt of the height.
(d=4.1*sqrt of h)

This holds true in both the EERM 8th edition (eqn 62.3) and Camara's 6-minute solutions (problem 91). EXCEPT, in the 6-minute solutions, there is an errata stating that the 4.1 should be changed to 8.2. They are saying that "d" they listed was the distance to the horizon, not the distance to the other tower. Just wondering if anyone could confirm or debunk one or the other. Thanks!!

I have to smile when hearing this problem as it dinged me back in September. When given the height it's pretty straightforward to calculate the distance, right? Well, the formula is for the radio horizon of line of sight signals. In other words, draw a straight line from the top of a tower to it's point of tangency with Earth. This length is d. Suppose there is another tower past the radio horizon, the same height as the previous tower, AND the same distance (d) past this tangency point. Now both towers have a radio horizon at the same point and, since the comms are line of sight, have a signal path. The distance between the two towers is 2*d, whereas the radio horizon is just d. The formula for the radio horizon is d=4.1*sqrt(h), not the distance between two towers.

 

[schmidty99]

Thanks for the clarification GB! I know its doubtful a problem like this will be on the exam, but if I didn't clarify it, it sure would have been! Thanks again, and stay tuned! I might have more this week!