As expected, the discussion appears to have fizzled out.

Having for the first time allowed myself to be led astray by the
academic professors and authors and their Bibles on the subject, I
still have the problem of correcting a bug in my computer program. The
program itself, GRNDWAV3, is too interesting, useful and educational
to simply withdraw it.

Lets not be confused by fallible human ideas and notions on -

Reflections from the ground.
Mirror images in the ground.
Antenna gains relative to isotropic.
Antenna gains relative to isotropic with a ground plane.
Antenna gains relative to isotropic of dipoles.
Half hemispheres.
What on Earth is an isotropic antenna anyway?
And now we are being introduced to waveguides.

Thanks to Roy's investigations and clarification, the solution to my
problem is perfectly simple -

"The effective height of a short vertical antenna is half of its
actual height and the voltage induced in it is half of the field
strength in volts per metre."

Which gives the correct answers from my program.

And which was proven and well known 100 years ago by the early radio
engineers who were really the first amateurs in the game.

Having got that off my chest, I can now finish the second half of a
bottle of Australian, Bantock Station, Special Reserve, Cabernet
Sauvignon Shiraz which I can thoroughly recommend.
----
Reg, G4FGQ