Richard Harrison wrote:
Suppose the vertical is only 2/3 the height needed for self resonance,
or 60-degrees high. The loading coil must replace about 30-degrees of
missing antenna to bring the vertical to resonance.

Here's the reason why. In a standing wave antenna,
like a mobile antenna, the forward current and the reflected
current are 180 degrees out of phase at the tip of the antenna
and their phasor sum is zero. That is one of the laws of reflection
physics. Their phasors are rotating in opposite directions so they
must each rotate 90 degrees to be in phase and additive at the
feedpoint. That's simple geometry. Your above antenna loading coil
must contribute ~60 deg to the rotation of the forward and reflected
currents. There is nothing else existing in the antenna that can
accomplish that absolutely necessary function.

Where is the myth?

The lumped circuit model is generating a logical blunder. That model
presupposes no phase shift through an inductance. Therefore, there
is no phase shift through an inductance. (Circular Logic) Fortunately,
the coil ignores our mis-applied man-made model and performs the phase
shift anyway. The actual myth is that there is no phase shift through
a 75m bugcatcher coil. That myth is rampant on ham radio web pages.

The lumped circuit model assumes the proof before a solution to
the problem is even attempted. It is a common mistake, known as
'petitio principii', in the solution of logic problems (also known
as 'begging the question').

Some folks have simply forgotten that the lumped circuit model
presupposes that no reflections exist. It cannot be used in a
standing wave antenna environment. Now that these folk have
been reminded of the technical facts, it will be interesting to
observe the results. Will the erroneous web page information be
corrected?
--
73, Cecil http://www.qsl.net/w5dxp