Why verticals have got radials?

The past week we tried to analyse a vertical monopole 1/2 wl, no radials, compared with the vertical dipole and the horizontal dipole. The last image illustrated how the verticals are not so effective while over real ground. Let reaffirm the fact with a further analysis over very-poor ground. Both the antennas have the feed point 1/2 wl high, so the monopole is all over the horizontal dipole.

Note how the vertical is somewhat better now than over average ground, because of the squashing of high lobes.

But now is the time to add radials.
Four 1/4 wl radials, horizontally disposed.

What? There is no change in the pattern? If one, no-radial is slight better... Mmmm, the antenna is high over ground, maybe the radials will be more effective with a low one. OK. We will lover it, at .02 wl, so around 20 cm. (sic !) at 27 mhz.

Still equals? Where is the white trace? Is the software defective? Let we came back at the source of knowledge.

From Cebik - A Modeling Perspective on "Ground" Planes

We are very careless with the ground. We tend to treat it as a single homogenous entity. In simplest terms, that means that we think about the ground in the same way, no matter in what radio context it appears.
We tend to think of the ground relative to an antenna as a single ground. Hence, we tend to lump together the ground from which signals reflect to contribute to antenna far field patterns and the ground directly under a monopole antenna. The "only" difference is their relative distance from the antenna itself. However, let's see where separating the two ideas leads.
Far field reflective ground: ... ON4UN did some modeling with some vertical radiators that suggests the ground kicks in as a reflective medium somewhere around 2 and a half wavelengths from the antenna--possibly more for highly elevated antennas. Although the ground immediately under the antenna has some effect on antenna effectiveness relative to far field patterns, the effect is small (unless the ground is needed to complete the antenna). Dipoles, for example, exhibit only small gain changes as the quality of soil is ranged from very poor through very good.

The first killer idea is *radials can't affect pattern* because they're too near to the antenna. But there is much more. What unless the ground is needed to complete the antenna means?

Antenna-completion ground: Monopole antennas are generally analyzed as having their missing pole (relative to a dipole) within the ground. This is often pictorially presented as an "image" antenna sticking straight into the earth. While this portrayal allows the solution to certain basic equations, it is actually a very poor picture of what is going on. It is the surface volume of the ground that provides the completion of the antenna. Signals penetrate the ground to depths that vary directly with wavelength and inversely with frequency. However, even with a monopole, the penetration does not act like a spear into the ground ...

When we run a 1/4 wl monopole, it needs *the other half of the antenna*. We can obtain that with another straight wire, and ... we've a dipole. We can with some elevated radials, and that's named a GP. Or we use the surface volume of the ground, but

In fact, the so-called ground plane is never a GROUND plane, ... Hence, the so-called antenna-completing ground is not a ground at all--even though we sometimes use the ground to do the work of the plane. This is not the first time we have misnamed something in radio. It took a long time to weed out the term "condenser." It will likely take even longer to drop the term "ground" from ground plane.

Now where should be that *missed half of antenna* in the case of 1/2 wl monopole? When it's an off-center feed dipole, as all analysis demonstrate? So such an antenna don't needs *radials*, also at very low high. However when at 20 cm. by soil, who can negate any interference... But the 1/2 has also the advantage of very low currents (teorically zero) at tip, while the 1/4 has a maximum at feed point.

Now, because I would still to verify, here the same arrangement but with 1/4 wl stick.

Now the four elevated radials add some 2dB gain. But only if the antenna is low a lot. See below, when the GP is 3m above ground...

So my thought is: in the clear and at decent high, radials don't deal with radiation pattern. When the antenna is 1/4, of course, they deal with feed-point impedance. But the 1/2 monopole needs anyway a matching network, so I really can't figure what a radial system can add to a Antron-like antenna... maybe when not in the clear and maybe somewhat related to rfi, I'm waiting for hints...

Now you'd think I hate verticals, and A99 in particular. So here my roof, with the Moxon rectangle and, in top of it, an Antron-like monopole, the Sigma Simply-27. The analysis take in count of two distinct levels of ground, the first one (the roof) 6m under the aerials, the second one (the real ground) 10m under the roof.
Have fun. 1 AT 1839 Paolo