Dan, KB0QIL wrote:
"From a practical perspective it would seem to me that building a 40
foot crnter loaded dipole and putting it in the sttic or on the roof
would probably perform somewhat better."

The roof or attic may be noisy receiving locations.

The ionospheric spot which effectively reflects a high frequency signal
to a point beyond the horizon is variable so that the received signal
direction varies from the true bearing of the transmitter, The received
signal elevation angle also varies from that predicted by the assumed
layer height for any given path length, and may change from instant to
instant.

The differences between predicted and actual azimuth and elevation
angles may at any momement be several degrees. These differences make
high frequency direction finding complicated, but results may be good
enough for some pracical purposes. Optimum vertical and horizontal
angles are sought in directional antenna design but enough beamwidth is
needed to accommodate
the angular variations which occur.

Over sea water, ground wave propagation is good and loss is low as
compared with propagation over earth. Frequencies up to about 5 MHz are
used for communications beyond the line of sight between ships and
between ships and shore. These frequencies are also used for tropical
broadcasting among islands.

For ionospheric reflection to near spots beyond the line of sight, near
vertical incidence reflections are used. The frequency must be below the
maximum usable frequency for vertical incidence at the transmitting
site.

For ground wave propagation a vertical transmitting antenna is used.

Horizontally polarized antennas are often used for sky wave signals
because reflection from the ionosphere makes equal strength components,
horizontally polarized and vertically polarized, from the incident wave,
regardless of its initial polarization.

Most disturbing noise is that generated within ground wave range of the
receiving antenna. It is vertically polarized.There is no ground wave
propagation of horizontally polarized waves. Thus, a horizontally
polarized receiving antenna ignores much of the available noise.
However, it receives as much signal from the sky wave as a vertically
polarized antenna would.

If a single antenna is to be used for both transmitting and receiving a
shy wave, a forizontally polarized antenna may be the better choice due
to its noise rejection. See "Radio Antenna Engineering" by Edmund A.
Laport for details.

Best regards, Richard Harrison, KB5WZI