We're both mixing things up here... I re-read what I posted while stuffing lunch in my face and it was mental. Hah.
The original scenario was helicopters talking to an unknown, but assumably ground level station, installing 20W transmitters. Probably from 500' AGL, but I gave them 1000' AGL in my discussion.
You replied with "The theoretical range of a 1 watt transmitter and a 1 microvolt receiver using standard whip antennas is something on the order of 1500 miles. Altitude and a good installation are everything; power means little to nothing."
The helicopters we were discussing don't have any significant altitude. They're trying to make up for it with power, which I think we were both pointing out -- doesn't work. Not well, anyway.
So I replied (with a bunch of jumbled thoughts) saying that you were incorrect because I was assuming you were staying with the OP's scenario.
Re-reading what you said, you were correct, but it had nothing at all to do with the real-world scenario presented.
(And neither did most of my reply, which apparently was mostly to say "Hey, I've done this stuff... you aren't going to ever get 1500 miles from a helicopter at 1000' AGL!" And then additionally, "20W isn't that big of a power difference.")
So we kinda violently agree just in different ways, Jim. Me from the "that doesn't work" practical standpoint, you from the "The theory says if you get higher, you're great."
Anyway, I had no idea the FAA was using 50W. I'd seen some licenses for them in the past that said 20W, so I assumed they all were 20W. Bad assumption. Seems kinda ridiculous that they built such a lop-sided system. If they can hear me at 5W, I can hear them at 5W... unless someone's receiver is really broken.
Recently I reported an RCO that needed to be NOTAM'd out of service to LockMart after landing. It was obviously only putting out exciter power, since I was looking at it at a slant range of about 3000' and the LockMart guy remotely talking to me through it was noisy and almost uncopyable.
They said they'd need at least two more reports before they'd dispatch a technician. Stupid. I was tempted to call up two buddies with other tail numbers and ask them to call 800-WX-BRIEF and make two more reports that night, and the next day.
Don't they invest in remote power monitoring on that stuff? Especially on top of mountains that are snowed in and require a snow-cat to get to for 6 months out of a year?
Nice tail number, BTW. Do you really think the California to Hawaii hop was ionospheric? Most of those are tropo... happens with more regularity than most folks think, along that path... lots of those logged.
At least you have some real-world to go with the Physics. I've worked on a couple of RF systems designed by engineers who'd never keyed a mic, and had done all the "math" only... and they didn't work well, mostly due to multipath effects and other problems in FM systems that weren't accounted for.
My favorite was the "deaf" high-mountain system overlooking the city. The engineer always took a "It's not making book numbers, so let's figure out why" approach, which never got the system up to what similar systems on the same tower did easily, and he could have copied from. "What worked" on the already tried-and-true systems sitting in the cabinet right next to his, didn't matter... he was an ENGINEER! (LOL!)
He was convinced he was smarter than the previous six engineers that had worked on the same systems up there, I guess. It was a shared TX/RX antenna system, split antennas, between four systems.
It was fun to watch him squirm when another system on the same tower and identical antenna system out-performed his significantly. What he didn't know, was that the site noise floor was atrocious, and he never measured it.
He just pre-amplified the snot out of his UHF receiver and shoved it's receiver down well into the noise floor where it was overloaded with out of band noise, and was generally quite unhappy.
Once we showed him how to do a receiver usable-sensitivity test, injecting a test signal at an iso-T with the real-world antenna connected, the light bulb started to come on. Ripping the pre-amp out actually helped, as did building the correct bandpass filtering on the receiver, even with the inherent losses involved in adding the cavities. A much weaker pre-amp after that nicely filtered input, and ... hey... look at that... you've built exactly what was in this cabinet over here next to yours! (ROFL!)
They don't cover massive broad undefined noise floors in the visible RF horizon, in most textbooks. And most cities are becoming exactly that... massive undefinable noise floors.
Thus... (Yes, this is leading somewhere...)... my comment about the Linksys!
Tons of those cheap pieces of crap out there, and some percentage of those thousands probably all failed in the same way mine did... making noise all over the place.
Unless someone is a weak-signal guy in the neighborhood, no one cares... but they all add to the combined noise floor in populated areas.
Is the rambling starting to make any sense now? Ahh, maybe not. This reply is too long. Oh well.
Fun stuff.
As far as other aviation radio related topics go -- I wonder how many aviation antennas when swept really present a reasonable response across the entire aviation band. Ever done that on any installations you've seen? I haven't, mostly out of abject fear that some FAA wonk might find out an "unauthorized" schmuck like me actually disconnected an antenna cable and then reconnected it. My God man... the world might come to an end, you know?
That installation I saw in that homebuilt was probably losing half the usable signal coming in, and going out, it was probably all turning to heat in the coax. The new-ish Icom radio was probably folding back to protect itself, too.
The guy's test-method was to have his buddy drive away from the airport with a handheld and see where he could hear him and talk to him. No plan for where he would go (behind a hill, top of a hill, straight behind the hangar row, or out in the clear... where?) and how far away (just drive until you can't hear me anymore), and they had no idea how to check his real-world tests against any theory/math.
It was about as useless a test as I've ever witnessed.
I offered to at least check the power output of his radio (not knowing if I was allowed to do that, but hey... he had at least *TWO* BNC barrel connectors in that antenna setup between the rig and the homebrew antenna in the tail -- so it's not like plugging my IFR 1500 in-line would have been difficult or even detectable by anyone later anyway -- but he only called on the phone once and never called back when I couldn't come over to the airport mid-day on a Tuesday...
(When you retire, do you suddenly forget that the rest of the world has day jobs? LOL!)
If I see him at his hangar again, I'll ask how his radio problems are going. Trying to be neighborly and all... but $100-$200 at an avionics shop and they'd rip out that Rat Shack coax and all those extra/unnecessary BNC connectors, put a real antenna in the tail, and he'd be golden...
He said he'd learned everything he needed to know about installing his Comm radios from an Internet builders forum for his homebuilt.