There is a slippery slope in our language concerning slopers.
Pun intended.
Sloping 1/2 wave dipoles behave like dipoles, with perhaps some
reflection or absorption from the tower behind. Or reflection, if
you're dealing with multiple sloping dipoles. These can also be
bent back to the tower at the base, a la K8UR's design in Ham Radio,
many years ago. (kudos, Dennis.)
Sloping 1/4 wave antennas operate with the tower being the other half
of the antenna. The closer they get to the antenna, the more they look
like a feed/matching system.
In the case of the sloper which was almost vertical....it can be viewed
as a shunt-fed tower, where the shunt transmission line has variable
spacing.
As to the question of efficiency.... radials out from the tower base,
in the 1/4 wave situation, would improve things significantly.
If you've tried it and it matches...add radials, the efficiency will
improve, although the matching may change.
n2ea
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