I think it's a BIG mistake to be writing about "velocity factor" in
this thread (and perhaps also in some current, related threads). The
reason is that it presupposes behaviour that is just like a TEM
transmission line, and clearly it is not when you get to the fine
details. Until we better understand just what is going on, I propose
that we simply say that resonance occurs for a wire shorter than 1/4
freespace wavelength, when that wire is fed against a ground plane to
which it is perpendicular, and that the thicker the wire, the shorter
it is at resonance when compared with the freespace wavelength. The
effect can be described with an emperical equation, of course. But to
invoke "velocity factor" assumes something about the solution which may
well lead you away from the correct explanation.

I don't really expect many will take this seriously--there seems to be
too much invested in explaining everything in terms of behaviour that
seems familiar. It's a bit like saying a photon is a particle (or a
wave). It is not--it is simply a quantum; and it behaves differently
from particles we know, and behaves differently from waves we know from
our macro-world experience.

The transmission-line analog is a very useful one for practical antenna
engineering, just as considering loading elements as lumped reactances
(perhaps with parasitic lumped reactance and resistance as appropriate)
is useful for practical engineering. But that doesn't mean it fully
explains the behaviour in detail.

Cheers,
Tom