On Sat, 11 Nov 2006 15:06:46 -0000, "David" nospam@nospam wrote:

Adding elements of the same length to a dipole does not produce much
benefit,

Hi David,

Benefit is in the eye of the beholder. Additional elements (I presume
you mean length) bring gain in some directions and nulls in others. If
by adding elements you mean in parallel (AKA fan dipole), then you
stand to benefit in bandwidth coverage. If by adding elements you
mean stacking them |||| then you are describing a primitive beam array
which has classic benefits (once you attend other details of length
and separation).

while in contrast adding more elements as radials to a quarterwave
vertical antenna produces a lot of benefit.

This is something of the double-shuffle. What you stand to benefit
from is you are reducing loss, and arguably loss that the dipole does
not suffer from (although there is a lot of room in that statement for
equivocation).

Many books claim that the
radials of a quarterwave vertical antenna form an image.

Many books are useful for leveling tables too.

It is said that the
greater the number of radials, the more 'perfect' this image is and the
greater the efficiency.

This "image" and efficiency are two wholly different considerations.
True, these considerations flow from the same design, but one is an
electrical issue of matching and load, whereas the second is what in
the science of Optics is called ray-tracing.

In contrast, adding elements of same length to
dipole increases bandwidth and creates an unusual radiation pattern e.g. fan
dipole.

2 theories on vertical groundplane antenna a

1) Radials reflect radio wave emitted by vertical radiating element. Radials
form a ground plane to reflect radio wave. Image theory applies where
radials form a 'mirror' image.

That is a fairly jejune theory as applied to antennas. You need only
consider yourself as being that vertical radiator standing on a
literal mirror that is no wider than you are tall.

Look down into that mirror and what do you see? The sky above. Not a
very compelling benefit when you are trying to see the horizon, is it?
How big a mirror would you have to stand on to see, say, 10 degrees
above the horizon in it? That mirror would be quite large, probably
20 times your height.

2) Radials are simply conductors carrying current, and radiate accordingly.

This is quite true.

But they are placed and fed so this radiated wave nearly cancels.

Again, quite true.

Radials do
not form a flat metal conductor many wavelengths in diameter. Radials do not
reflect the wave emitted by vertical. The radials are too short to reflect
the wave radiated by vertical.

As I've responded to point 1 above.

With elevated radials, the radials are normally a quarter wavelength long.

As a specific statement, yes, but not generally so. Drooping radials
are more useful (benefit) but are not the same length as orthogonal
radials.

If the radials are proper current carrying conductors instead of a metal
reflector, the radials will transform the high impedance at open circuit end
to a low impedance at base of antenna.

Wire or metal reflector is the same. Wire radials are simply a poor
approximation (or better by degrees as the count of radials
increases).

Low impedance means antenna is
current fed. If the radials are made a half-wavelength long or longer, does
the impedance and SWR of the antenna stay the same?

No.

Are there any tests to prove which of the above 2 theories is right?

Common sense comes to mind; however, it is the common sense that is
found with experience and a solid base of physics. A quick path to
that experience comes with modeling [sic, quick is quite variable].

The confusion of radials as being abstractions of Earth is found in
the blur between matching and propagation. Earth and radials are
principal actors in those activities, but unless you stand to plant an
extremely huge radial field, there are different mechanisms at work.

Clearly, the association of Earth with matching portends loss. In
this sense more radials shields the fields from that loss and this can
be achieved in the near distance of the antenna. However, you can
achieve the same benefit with fewer radials by simply increasing the
distance between the antenna and lossy earth: lift the antenna up.

When we speak of Earth as a reflector of waves (the propagation side
of the coin of antenna transmission), it is the degree of mismatch
between the wave in space and the wave in Earth at a distance that
bounces the wave at a shallow angle toward the horizon. This point
will be 10s of wavelengths away from the antenna. The wave in a
medium of 377 Ohms (free space) meets the ground medium of several
hundred Ohms to as low as 10s of Ohms (sandy conditions to swampy
conditions).

Here, it is a simple matter of the mechanics of SWR. 377:25 (or 15:1)
has a huge reflection component. That is why you want to live next to
water (but not in it, which is another misconception that is born of
the confusion between matching and propagation). If you live next to
a desert, you might experience a condition of 377:250 (or 1.5:1) and
your signal is plunging right into the dunes, never to be reflected
with any great benefit. The paradox of this is that planting your
vertical into the sand is the best of all worlds (when you consider
the proximal loss of earth).

Moral of this tale:
Erect the vertical (with a few radials) on a tall sand dune near
the sea.

73's
Richard Clark, KB7QHC