Buck wrote:

Maybe I should change the subject line, but here goes.
First of all, i am fishing for information, not challenging anyone's
intelligence.

I understand from books I have read, that a ground mounted vertical
antenna needs many radials. IIRC, the point of diminishing returns on
adding radials falls somewhere between 64-128 radials. I imagine the
best radial-based ground I could have for 20 meters would be a solid
copper disk with about 16 feet radius, give or take. However, I
recall in the ARRL Antenna handbook, not the latest version, but one
prior to this one, there is no noticeable difference between a raised
ground plane antenna with 4 elements as opposed to 128. (From here,
or another antenna forum, I heard for the first time that it holds
true for two radials.)

When a ground system is a long distance above ground, only two radials
are needed for high efficiency and a circular pattern at zero elevation
angle. The pattern does become non-circular at higher angles, which can
be prevented by adding two more radials. A ground system which is above
but close to the ground requires fewer radials for good efficiency than
one with radials which are buried or much closer to the ground.

I am still trying to figure out why so many radials are needed on the
ground and a few feet higher so few are needed.

The ground is very lossy. When the radial system is on or in the ground,
current flowing to the radials is forced to flow through the lossy ground.

Actually, more important than the why, is how high is high enough to
reduce the optimum number of radials? For example, i want to build a
20 meter vertical. I understand the best place for it is on top of a
100 foot+ tower, but somewhere in between, there has to be a place
where 4 radials above ground is noticeably better than the same 4
radials on the ground.

That's a good question without a single good answer. It depends at least
on the ground conductivity and permittivity (down to a considerable
depth), frequency, and radial length. Modeling can give you a good idea
of the tradeoffs, although the very simple minded ground model might not
be adequate to make a very accurate comparison.

Another point I have heard in the forums, but not confirmed, is that a
reduced size vertical element doesn't gain much by adding radials
longer than the antenna is high.

I don't believe that's true. I'll gladly consider any supporting
evidence. Hearing something on forums is among the worst justification
for believing it, in my opinion.

Roy Lewallen, W7EL