OK, I apparently drifted off the beaten path plus I seem to be
experiencing some serious brain fade.

What I was doing was preparing a short presentation for new hams on
the subject of vertical antennas. I was using EZNEC to produce some
antenna pattern graphics. It was then that I noticed that when I
overlayed the pattern from a vertical half wavelength dipole with that
of a horizontal half wave dipole at the same center height over real
ground that the pattern from the vertical was completely enclosed by
the horizontal dipole pattern, at least broadside to the horizontal
dipole that is. The vertical dipole pattern definitely showed a lower
angle of peak radiation but no greater gain a low angles than the
horizontal dipole.

At first, seeing the vertical dipole gain the same as the horizontal
dipole, even at low elevation angles, was a little confusing but I had
just scanned a bit of text on vertical antenna operation including
calculation for reflected waves and stuff like the pseudo Brewster
angle.

But then... I remembered talking to a couple guys in Germany on 75
meters the previous evening. From my location here in Missouri, I was
hearing their signals on my 75 meter inverted L much stronger at 10 to
20 over S9 than on my dipole at S4 to S5. They noted the same
difference in performance between the two antennas. As both the
Dipole height and the top of the inverted L were at 50 feet, I thought
this was a reasonable comparison. Also, the dipole is in the clear,
resonant, and has been performing as well or better than other
horizontal dipoles used by other hams in this area.

Furthermore, my experience switching between horizontal and vertical
antennas on 75 meters matched that of other guys with both. I was
starting to wonder why the mismatch between the theory I was familiar
with and my experiences.

Jumping back in to the text books and spending some time 'googling'
for more info I found nothing to conflict with the material I had
previously covered. That was disconcerting. About the only glimmer
of a solution to the question popped up when I looked at papers on
ground or surface wave propagation. There were some vague comments
about diffraction that seemed to indicate one of the loss factors
involved with ground wave propagation is that some of the signal does
not get diffracted low enough to keep in from being 'lost' to sky wave
radiation.

As I continued chasing that thought, I found that discussions of sky
wave propagation ignored ground wave and discussions of ground wave
propagation considered sky wave as lost RF.

Now, after all that windup, what am I missing? I acknowledge ahead of
time that I may be a dummy so don't bother explaining that to me. Why
do reasonable size vertical antennas with proper radial systems under
them outperform horizontal dipoles for DX operation for typical ham
antenna support structure heights of 50 feet or so?

The interesting question then: Is the improved performance of
vertical antennas over horizontal dipoles on 75 meters at DX distances
due to a combination of direct radiation plus radiation from the
ground in the area of strong ground wave strength out hundreds of
meters? Is the ground wave leakage providing additional low signal
strength in both transmit and receive?

Gary - N0GW