Tom Ring wrote:
Picking a nice round number, say 55 degrees, I would then need 35
degrees of whip above that coil to make a quarter wave resonant antenna,
correct?

No, that is a myth spread by some people as a strawman
argument. Please don't support that strawman.

The requirement for resonance at the feedpoint is that
the phasor sum of the forward and reflected voltages
be in phase with the phasor sum of the forward and
reflected currents. Therefore, 90 degrees is *NOT*
required in the round trip. Indeed, the round trip
for the voltage doesn't have to be the same number
of degrees as the round trip for the current. That is
a misconception spawned by the lumped-circuit model
where everything is perfect and waves travel faster
than the speed of light. The real world is not so
perfect.

Given that the resonant feedpoint impedance equals
(Vfor+Vref)/(Ifor+Iref) isn't it obvious that the
individual components are not required to have the
same phase? For instance, Vfor could be at +50 degrees,
Vref could be at -40 degrees, Ifor could be at +20
degrees, Iref could be at -10 degrees, and the feedpoint
impedance would still be resistive.

The coil distorts the heck out of the phase relationships
between the voltages and the currents. Why is it surprising
that the result is unpredictable and needs an antenna
analyzer to find the resonant frequency? Factor in that
the lowest 50 ohm SWR may not be at the purely resistive
point and what do you have?
--
73, Cecil http://www.qsl.net/w5dxp