Reg Edwards wrote:
. . .
The attenuation due to skin effect and wire inductance along lossy
radial wires is rather high. There's negligible current flowing in
them at distances greater than 1/4-wavelength at their own velocity.
The wires may just as well not be there.
. . .

I'm afraid your oversimplified model of how radials work has once again
led you astray. B, L, & E's measurements show the following:

For an 88 degree high vertical, where n is the number of radials, the
following fraction of the current at the center is flowing in the radial
1/4 wavelength (at a velocity factor of 0.2, the approximate VF in the
radial's environment), from Fig. 42 of their paper:

n Fraction
15 0.67
30 0.68
60 0.90
113 ~ 1.0

1/4 *free space* wavelength from the center:

n Fraction
15 0.19
30 0.14
60 0.26 [This is a minimum; it rises then drops further out]
113 0.61 " "

Note that the results are quite different when the radiator is only 22
degrees high (Fig. 43) -- the resonant effects apparent on the 60 and
113 radial measurements are absent, and the currents decay
monotonically. There isn't nearly as much difference between 15 and 113
radials. But with 15 radials, the current 1/4 in-ground wavelength from
the center is still about 67% of the current at the center.

Again I see evidence that your analysis overlooks the interaction among
radials. There's less interaction when there are only a few, but even
with 15 your analysis has led you badly astray. And does it account for
the considerable differences with different radiator heights?

But I've pointed this out to you before yet you keep promoting this
myth, so I guess you just don't want to be confused by the facts.

If B. L & E, made any errors, they made sure they erred on the safe
side regarding numbers.

One of their key results is that ". . .the ground system consisting of
only 15 radial wires need not be more than 0.1 [free space] wave length
long, while the system consisting of 113 radials is still effective out
to 0.5 [free space] wave length."

Their results agree reasonably well with NEC-4 modeling. But I'm sure
glad we've got you to set us straight about how well they did and how
they could have improved their methods. You've surely got a clearer
perspective, not having been prejudiced by actually reading their paper.

Oops, here I am nitpicking again -- pointing out that .67 doesn't equal
zero.

Roy Lewallen, W7EL
Certified Reg's Old Wife and Nit-Picker