In order to accurately calculate for downtilt, one needs to know the vertical beamwidth of the antenna. A typical collinear with 5 dBd gain has approximately a 14 degree vertical beamwidth. Therefore the lower 3 dB point would be at 7 degrees below the horizon. To calculate how far away from the site that would intersect with the terrain you need to do the following calculation: tan(90 minus 1/2 vertical BW) times height of antenna above terrain. (Level terrain assumed.)
Example for an application where the antenna is 500 feet above surrounding terrain:
Example to show how/where 1 degree of downtilt would make the main beam intersect with the terrain; where the antenna is 500 feet above surrounding terrain:
57.2899x500=28645 feet (5.4 miles)
Therefore for 1 degree of downtilt, your main beam would be 5.4 miles away. Remember your upper 3 dB point is still above the horizon, so there would still be adequate signal to the horizon. My suggestion in this case would be not to bother with downtilt because the antenna has a wide enough beam pattern, however a 10 dBd antenna at 2000' is another story.
PDF articles for reference:
Half Power Beamwidth (HPBW) Calculation.
Bryan K. Dorbert N3ST
Verizon Wireless--Northeast Area
Senior Engineer/System Performance
Bryan.Dorbert (at)@ VerizonWireless (dot) com
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Article Copyright © Bryan K. Dorbert N3ST
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