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Well, I’d wonder if a (3 m total length including any loading coils) dipole would actually amount to making the driven element shorter, since the “ground” side of the dipole also radiates as has been established many times in tech discussions here.
Now, something as simple as a dipole might not be more advantageous for a ground mounted system, considering the small fraction of a wavelength there is to work with inside the 3M rule.. In fact, as I recall, Rich did some work emulating a loaded dipole close to or directly on the ground and it actually came out as somewhat less efficient than a loaded vertical with a good ground.
Not to say there might not be room for improvement with the loaded vertical antenna. I’ve noted some QRP ham operators seem to swear by having a separate tuner for the ground, for example. A loading coil on the ground needn’t take much length away from the 3M total, and it might or might not help. No way to know for certain until someone tries it and makes some experiments and reports some observations. Most of the loading coils I’ve seen people speak of using have been simple linear air core coils, and it’s possible that something like a “pancake” coil or a conical coil might have some advantages, or they might not work as well..
I’d say that antenna development for part15 AM is a long way from “there is nothing new under the sun”. One advantage (sorta) of the 3M rule is that with such a physically small antenna, the cost of experimentation is considerably less than if (for example) 100 ft antennas were allowed.
Emulation is a valuable tool, but it shouldn’t discourage experimentation. Often the emulation is based on extrapolation of results from things like a 1kw xmitter at a distance of 1 km, and I feel that in many cases with part15 AM, the specific technology may have been less fully explored than other frequency ranges and physical limitation simply because the focus was always on large transmitters with antennas that could much more closely approach physical resonance because they did *not* have a 3M limit they had to be developed in. Emulations and equations certainly have their place and are useful tools for exploration/development, and they make a great place to start.. But they shouldn’t ideally be the place it ends.
With your idea of a loaded dipole with large diameter coils.. Well, it’d be easy enough to try and see, wouldn’t it? A bit of wire, a plastic barrel and maybe a bit of pipe and you could tinker with it and see how it compares to some fairly simple standard like a 3M wire with a simple ground.