Radials do have standing waves, and so the minimum impedance at the base
will appear when the radial is somewhat less than 1/4 wave long.
Of interest here is that the benchmark Brown, Lewis and Epstein I.R.E paper
on ground systems does not show such standing waves along buried radials
(clip below).
The clip also shows that the r-f current flowing on the buried wires at and
beyond 0.25 lambda (of their physical length in free space) are considerably
less for 15 and 30 radials than for 113 radials.
http://s20.postimg.org/oxj3qv59p/BL_E_Fig_7.jpg
R. Fry
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