I'm having trouble resolving the values produced by Reg's "Radials2" program
and the excellent section in ON4UN's Low Band DX'ing, 4th Edition.

Reg's work seems to be saying that placing radials on the ground shorten
their resonant point such that having radials the recommended 1/4 wave
physical length is not necessary, or even desirable. When I played with the
program, the losses reported by Reg's program with radials as short as 10 or
20 feet were quite low, with sufficient number of them. Is this overly
optimistic? (1/4 wave vertical)

Here are the points of departure that I'm having trouble "resolving".

Quoting from Chapter 9, section 10, Part 2.1.2:

"A 1/4 wave wire that is resonant above ground, is no longer resonant on or
near the ground. Typically for a wire on the ground, the physical length for
1/4 wave resonance will be approximately 0.14 wavelength." (the exact length
depending on ground quality)" This seems to agree at least somewhat, with
Reg's assumptions in his program.

However, when we get to section 2.2.3 (again in Chapter 9, section 10), John
asserts:

"As soon as you use a larger number of equally spread radials, the RESONANCE
EFFECT DISAPPEARS, and the radials form a disk, which becomes a screen with
NO resonance characteristics. In this case, we no longer talk about length
of radials, but about the diameter of a disk hiding the lossy ground from
antennas." Unless I misunderstood Reg's program, it seems to maintain the
idea of velocity factor/resonance in radials, no matter how many there are.

John Devoldre (ON4UN), then goes on to describe the early work by Brown,
Lewis and Epstein, as well as the exquisite study done by N7CL where he
developed a formula for optimizing radial systems based on amount of
available wire.

The magic number for efficiency in a radial field appears to be 0.015
wavelength tip to tip spacing at the radial perimeter. Fewer wires and
larger spacing degrade the radial field performance. More wires and closer
spacing do not improve performance significantly. The formula looks like
this:

N = ((2*PI*L)^0.5)/A

Where N = the number of radials, L = the amount of available wire and A =
the tip to tip distance (1.3 meters for the 80m band)

For 500 meters of available wire, the most efficient use of the wire is:

N = ((2*PI*500)^.5)/1.3 or 43 radials.

The length of the radials is 500 meters/43 or 11.6 meters long. This
arrangement maintains the .015 wavelength tip to tip separation at the
perimeter.
================================================== ===

Now, the case for perfection:

Section 2.1.3.2

"From these almost 70 year old studies (BLE), we can conclude that 60 1/4
wave long radials is a cost-effective OPTIMAL, solution for amateur
purposes. The following rule was EXPERIMENTALLY derived by N7CL and seems
to be very sound and easy one to follow."

"Put radials down in such a way that the distance between their tips is not
more than 0.015 wavelength. This is 1.3 meters for 80 meters and 2.5 meters
for 160 meters." The circumference of a circle with a radius of 1/4
wavelength is 2*PI*0.25 = 1.57 wavelength. At a spacing of 0.015 wavelength
at the tips, this circumference can accommodate 1.57/0.015 = 104 radials.
With this configuration you are within 0.1 dB of maximum gain over average
to good ground. If you space the tips 0.03 wavelength, you will lose about
0.5 dB."

"In general, the number that N7CL came by experimentally, closely follow
those from Brown, Lewis and Epstein."
================================================== ===================

Now, Reg has in the past, objected to the BLE data because they didn't
measure ground conditions. This issue is dealt with by N7CL, but it is too
rigorous for me to type into this message. Suffice it to say, the formula
appears to hold NO MATTER WHAT the ground conditions are like....i.e., the
best use of an available length of radial wire (several hundred meters), is
the formula listed above, and there is no resonance effect, no velocity
factor effect (that is meaningful)...

This seems to challenge, at its core, Reg's assumptions for his program on
radials. Or am I missing something?

There is no doubt that there is some agreement with Reg, but there are
several points of departure, that strangely enough lead us back to B,L and E
as being the most authoritative and experimentally verified data. That is
not to say the B,L & E data is very well explained....but...with the
addition of N7CL's work, radials are now "manageable for the masses", and
the two studies appear to agree.

Anyway, I found this stuff a lot more interesting than the endless
bickering about magical properties of phasors, lumped constant vs.
distributed networks, and when is an inductor an inductance, ad nauseum, so
I thought I throw this out and see if anyone else finds it interesting and
would like to comment.

73,

....hasan, N0AN