"K9SQG" wrote
From my research I've found indications that radial length beyond a
quarter
wavelength is indeed significant out to about two wavelengths.

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Only indications?

At what frequency?

At a distance of two wavelengths you are in the far field. Any improvement
in distant signal strength has little to do with antenna/transmitter
radiating efficiency which depends only on what takes place in the near
field. More to do with less-lossy ground reflections part way along the
propagation path.

Very long radials behave similarly to large ground mats laid half way along
a two-hop path.
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Reg, G4FGQ