Hello all... As a long-time radio hobbyist, I was intrigued to find out that the FCC, in calculating an FM broadcast station's height above average terrain, considers points only between 3.2 and 16 km from the station -- on the theory that terrain variations "closer in" than this really don't affect signal strength.
This certainly seems to make sense even for a Class A that's a mere 200 feet above the ground (as the line-of-sight probably wouldn't come down to Earth for a good two miles)... but I'm wondering if this is an accurate supposition for LPFMs, which often transmit off places like the 4th-story roof of a bank building in a medium-sized town. If you're only 40 feet off the ground, wouldn't an 80-foot hill a mile away do some serious damage to your coverage? And if so, has anyone proposed an alternative system of HAAT measurement for LPFM stations? (E.g., 0.5 to 8 km, perhaps with a requirement to measure along a greater number of radials since fewer data points would be involved?)
I'm about to test the theory myself. I did some trial-and-error calculations on the FCC's online FMCurves program, which revealed that each 20% drop in HAAT knocks approximately 1.8 dB off the theoretical signal strength at a given fixed distance. This appears to be true almost linearly, at least for any initial value between 125 and 1000 feet HAAT -- 125 being the lowest value I could test, since the program will calculate only for heights above 100 feet.
Afterward, I plotted out a circular coverage map (70/60/50/40/30 dBu) for my pirate station, based on its power and that minimum 100-foot HAAT... then went and got FCC HAAT data (i.e., at 3.2-16 km distance) for each one-degree radial at my location and actual height above ground level (11m). I chose sixteen radials split by 11.25 degrees each (extrapolating from the heights along the two adjacent integer radials where necessary), then figured out, along each radial, approximately how many 20% iterations' worth of difference there were between my 11m AGL and the actual HAAT raster data. I then drew new points along the radial, based on how many dB of difference were expected. (This is why I included the 70 and 30 contours on my initial map -- to ease the modification of the 60, 50, and 40 contours I was really interested in.) After all this, I connected the new contour points... and voila, instant directional coverage map!
I admit there were some shortcomings, both real and apparent, in my methodology. For instance, along radials where the HAAT proved to be negative, I used the estimate from 2m HAAT (i.e. eight iterations of 20% down from 11m, or -14.4 dB) and just moved the contours in from that by a somewhat arbitrary amount... as I had no mathematical basis for what to do with negative HAATs. (I was confident that this wouldn't result in too severe an inaccuracy -- since I live in Minnesota, the worst HAAT along any radial was around -6m.) Also, I'm fully aware that the actual FCC licensing procedure treats omnidirectional FM signals as being on flat terrain for spacing/interference purposes (except, apparently, in some really egregious cases... like Denver). This is OK for my purposes because I'm not interested in doing an actual proof-of-performance, but rather, checking the real-world accuracy of the 3.2-16 km HAAT measurement method for low-powered signals. If I find out that my signal significantly underperforms predictions in a couple of directions, and subsequently find out that there's a large obstruction between 0 and 3.2 km away along that radial... then voila, curiosity satisfied.
I'll post results once I actually get the on-air observations made, probably tomorrow night.
This certainly seems to make sense even for a Class A that's a mere 200 feet above the ground (as the line-of-sight probably wouldn't come down to Earth for a good two miles)... but I'm wondering if this is an accurate supposition for LPFMs, which often transmit off places like the 4th-story roof of a bank building in a medium-sized town. If you're only 40 feet off the ground, wouldn't an 80-foot hill a mile away do some serious damage to your coverage? And if so, has anyone proposed an alternative system of HAAT measurement for LPFM stations? (E.g., 0.5 to 8 km, perhaps with a requirement to measure along a greater number of radials since fewer data points would be involved?)
I'm about to test the theory myself. I did some trial-and-error calculations on the FCC's online FMCurves program, which revealed that each 20% drop in HAAT knocks approximately 1.8 dB off the theoretical signal strength at a given fixed distance. This appears to be true almost linearly, at least for any initial value between 125 and 1000 feet HAAT -- 125 being the lowest value I could test, since the program will calculate only for heights above 100 feet.
Afterward, I plotted out a circular coverage map (70/60/50/40/30 dBu) for my pirate station, based on its power and that minimum 100-foot HAAT... then went and got FCC HAAT data (i.e., at 3.2-16 km distance) for each one-degree radial at my location and actual height above ground level (11m). I chose sixteen radials split by 11.25 degrees each (extrapolating from the heights along the two adjacent integer radials where necessary), then figured out, along each radial, approximately how many 20% iterations' worth of difference there were between my 11m AGL and the actual HAAT raster data. I then drew new points along the radial, based on how many dB of difference were expected. (This is why I included the 70 and 30 contours on my initial map -- to ease the modification of the 60, 50, and 40 contours I was really interested in.) After all this, I connected the new contour points... and voila, instant directional coverage map!
I admit there were some shortcomings, both real and apparent, in my methodology. For instance, along radials where the HAAT proved to be negative, I used the estimate from 2m HAAT (i.e. eight iterations of 20% down from 11m, or -14.4 dB) and just moved the contours in from that by a somewhat arbitrary amount... as I had no mathematical basis for what to do with negative HAATs. (I was confident that this wouldn't result in too severe an inaccuracy -- since I live in Minnesota, the worst HAAT along any radial was around -6m.) Also, I'm fully aware that the actual FCC licensing procedure treats omnidirectional FM signals as being on flat terrain for spacing/interference purposes (except, apparently, in some really egregious cases... like Denver). This is OK for my purposes because I'm not interested in doing an actual proof-of-performance, but rather, checking the real-world accuracy of the 3.2-16 km HAAT measurement method for low-powered signals. If I find out that my signal significantly underperforms predictions in a couple of directions, and subsequently find out that there's a large obstruction between 0 and 3.2 km away along that radial... then voila, curiosity satisfied.
I'll post results once I actually get the on-air observations made, probably tomorrow night.