Here some calculations/modeling:
All wires copper= #12
Vertical = 30 ft
Hat (resonating)= 58-60 ft (x4)
Ground = no losses
Case 1, horizontal hat Rr = 5.5 Ohm
Case 2, hat edges at 15 ft. Rr = 3.2 Ohm
Case 3, hat edges at 5 ft. Rr = 2.0 Ohm
Case 4, hat edges at 1 ft. Rr = 1.6 Ohm
Something more real.....
Assuming 5 Ohm of ground losses, a quite good ground plane
that would equal an 87% efficiency if used with a full size
quarter wave antenna. (Case 1 will be about -3dB of the full
size 1/4w vertical with same ground losses)
We shall have, accounting also for the #12 copper wire ohmic
losses, the following numbers:
Case 1 = Eff 47.5 % (rel. +0.0 dB)
Case 2 = Eff 32.3 % (rel. -1.8 dB)
Case 3 = Eff 21.0 % (rel. -3.5 dB)
Case 4 = Eff 16.5 % (rel. -4.7 dB)
Let's now consider the case of 30 ft vertical and an
hat made with 4 wires 30 ft. long and sloped 22.5 deg
(Rr= 3.6 Ohm) whose lead to have the low edges at
20 ft. from ground.
If resonating the structure using a reasonable good
but still real coil (Q=200) between the hat and the
vertical, and still considering the same envionment,
the calculated efficiency is 34.5% (or -1.7 dB from the
Case 1 as a reference).
Practically speaking, the example with coil and a
well elevated hat equals the case 2, those with
hat edges at 15 ft, is 3.1 dB better than the
example with only hat wires but reaching 1 ft from
ground and still is 2 dB better than the case with
hat wires edge at 5 ft from ground.
If I were to decide what to do, I'd surely go for
an hat and no lumped reactance since the coil it's for
me a mechanical complication.
After all with the same inclination and longer hat
wires it's possible to resonate the antenna and still
have hat edges at 15 ft from ground.
Beeing very practical, if I had a 30ft antenna I'd keep
as high as I can the hat wires and by purpose I'll
also keep the antenna impedance slightly capacitive using
a smaller hat than required. This I'd do in order to use
a coil at the antenna base that would serve both to
resonate the antenna and as a step up autotransformer.
73,
Mauri I4JMY
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