Just to add, you should never assume a 1/4 wave ground plane antenna is ground mounted with radials. They can of course be elevated successfully.. would you put a 1/4 wave GPA on the ground for VHF at home ?
A ground plane antenna can be a vertical 1/4 wave radiating element and a ground pin. It will be very inefficient. So add the radials to improve efficiency.. 4 minimum ideally, the more you put down (or up if elevated) to about 60 will give you a max of about 2.4dB less losses over none, that is worthwhile.
A 5/8 wave is actually electrically extended to be a 3/4 wave using the coil which also serves to match the impedance. (sometimes with a capacitor) but a coil alone works. I know as I have built and used them myself and get SWR of 1.2:1 with just a coil and extensive radials.
The way I see it is if the radiating element is vertical the antenna is known as a vertical. Radials or counterpoise are not even strictly necessary for a 1/4 wave. However without them performance will dive.
My own view on 1/4 waves, they do work but I have no idea why anyone would ground mount them if you have alternatives. You get -6.0dBi gain at 5 degrees using MMANA-GAL. Much of F2 layer ionospheric propagated RF comes in at very low angles on 10m. This can VERY easily be improved on by a great margin by elevating a 1/2 wave end fed for example. At higher frequencies the gain from elevating
is an astonishing improvement at low angles.
A 1/4 wave ground mounted will work DX but is
very easily outclassed for DX (especially on 10m band) a basic Sirio GPS27 1/2 wave correctly set up and elevated 7m - 10m AGL
will totally destroy a 1/4 ground mount on 10m for a lot of the very low angle DX. This will be most apparent when the conditions are weak, I will go as far as to say given low noise RX QTH it could make or break an F2 layer DX contact in marginal conditions).
GPE 5/8: 5/8 λ ground plane GPS 1/2: 1/2 λ, Omnidirectional, 26.4 ... 29.0 MHz Tunable, Systems: 10m-HAM
www.sirioantenne.it
Also a 5/8 wave is omnidirectional and it does potentially have gain. Not much, but 1- 2 dB or so in some situations is a real possibility, the main lobe is focused down a bit giving a little lower take off on the main lobe and a little extra gain from the far field ground reflection which has a constructive phase interaction at reasonably low angles.