Owen Duffy wrote:
One of the things that intrigues me is the common "expert" advice to
cut radials for 7MHz to 33' long and bury them. It seems to me that
when buried and considering the wire as a transmission line, the
velocity factor will be somewhere between 0.3 and 0.8 depending on the
soil type, so that 33' is likely to be closer to a half wave
electrically, and present a relatively high and reactive impedance at
the antenna base if it were not for the attenuation of the wave on the
radial.

You seem to be referring to the feedpoint impedance of a
single radial the virtual impedance of which would depend
upon the magnitude and phase of the forward and reflected
wave on the radial wire. The single-wire transmission line
formula gives a Z0 for each radial as less than 100 ohms.
Given the probability of a high degree of attenuation and
the number of radials in parallel, the impedance presented
at the base is likely to be relatively low no matter what
the length of the radials assuming an electrical length
of longer than 1/4WL.
--
73, Cecil http://www.qsl.net/w5dxp