Reg Edwards wrote:

What everybody forgets about is that the velocity factor along
ground-mounted radial wires is about half of the free-space value.

Consequently, the 1/4-wave resonant length is crudely only half of the
elevated value.

On the other hand, the resonant length is very non-critical because Q
is very small - Q is only 2 or 3 and is even smaller at the high end
of the HF band.

Actually, at HF and average ground, the velocity factor below the ground
is about 1/4 to 1/5 the free space value. And no resonance at all is
usually apparent because of the high loss.

EZNEC isn't among the "everybody" who's forgotten it. Choose any real
ground, open the Utilities menu and click Ground Info, and you'll see
the velocity factor along with other information. But it's seldom of any
practical use.

Roy Lewallen, W7EL