Odd... I can think of a lot of elevated radial 'groundplane' antennas that work just dandy. What's the difference between a metal roof being used as that "groundplane" and with a few radials?
You're probably right, there'z a 'dumbazz' here. But I don't think it's us...
BYW - I don't remember that being taught 30 - 40 years ago when I was in school. Guess I'm just not 'most' engineering students? Ya'think? Ever??
Read what you just wrote - elevated ground plane antenna.
Lets use a Hy Gain 117 Super Magnum as a example.
The Hy Gain Super Magnum - right out of the box was designed and cut for channel 12 - or there abouts, because when it was manufactured there was only 23 channels in the chicken band.
It was designed to be installed 33' or more AGL and there was 4 radials - evenly spaced around the bottom of the base of the antenna. Each radial was probably 12' long.
The base plate was only about 3 inches square.
The end result was there was a slight droop of the - radials - actually called counterpoise - not called ground planes - that is a misnomer.
The purpose of the radials is that it would in theory increase local reception.
It's range - in the mountains of Pennsytuckey was about 37 miles in any direction with a 3 watt AM signal and good propagation.
If you could see the strong points of the signal - what we call a lobe - and if you wanted to talk more then a couple of miles - you would want a increase in height - which would make the main lobe at the bottom reach out further.
At times when propagation is good, a mobile can talk thousands of miles with a simple antenna.
When propagation is bad - you can barely talk to the next county.
All signals reduce at the square of the distance away - hence all reliable communications is line of sight.
The higher you put the antenna, the more you increase your horizon.
Simple 101 stuff her guys...
The downfall of the Super Magnum was not its design, it was that the ground planes were too long to droop 45* and it had no wind resistance when you redesigned it to 45* and no durability and it was expensive to manufacturer and the cell phones and two meters / 440 repeaters took away 90% of the CB radio traffic, once the truckers took over the 11 meters and the non truckers became ham radio operators - most of which did so around about 1982 in my area of the country.
In the 1970's there was 2 meter radios, but they were real expensive and did not usually have PL's built into them and the repeaters were more or less unreliable because a repeater frequency VHF 100 - 1000 miles away could trigger your local repeater and fill it up with traffic from other areas of the country and because before 1972 there was not any good radios made because phase lock loop wasn't perfected for FM before that - and that was the reason why automobiles only came with AM radios before 1972.
The signal would drift up and down the band and two people trying to have a conversation together would chase each other up and down the band trying to zero beat each others signals.