I have been searching for some descriptions of professional HF vertical antennas to see how professionals do it. WWV uses individual 1/4 wave verticals for each frequency used (2.5/20/25MHz with 2.5kW ERP and 5/10/15MHz with 10kW ERP). The description of each antennas comes from nist.gov so I’ll assume is reasonably accurate.
Each antenna is 1/2wavelength tall. The top 1/4 is the radiating element, the bottom 1/4 is isolated and used to raise the radiating element 1/4 wavelength above ground. There are 9 equal length radials, each of which slopes down at 45deg, each radial is sqrt(2)/4 wavelenth long. This is a little longer than the classic formula which suggests 1/4wavelength long (WWV length 0.3535 wavelength vs 0.25 wavelength). Antennas are fed with hardline coax and no coax crosses another coax feed.
This is what a professional service uses for a 1/4 omni antenna. It answers how high, how many radials, elevated or drooping on on the ground. Compared to amateurs, professionals will chose a location that meets their needs more that erect antennas in the location they have. Similarly cost is not really a problem relative to amateurs.
Now we’re not just amateurs but SOTA amateurs and we have a plethora of extra limitations on us that make using an antenna like that less suitable for SOTA. That design is going to get pretty damn unmanageable, heavy and a nightmare to setup very quickly for the more LF bands. But it’s good reference for what a professional chooses for an omni service.
So if you want to know how many radials you can get away with, or whether your loaded and shortened end-fed vertical or Buddistick is any good then make a reference and your intended SOTA antenna and run them using something like Richard CWI’s WSPR unit and see what others receive. Then you will have some numbers showing how they perform relative to what a professional uses.
When you have the numbers then you can then decide if the worse performance is acceptable to you for the relative ease of setup in a SOTA environment, weight, speed of band change etc. But you would have some kind of objective performance values to compare.