wrote:
Can you state in a few clearly written lines what you have learned or
concluded?

http://www.qsl.net/w5dxp/current.htm (bottom of page)

1.) If a loading coil has compact form and is terminated in a
capacitance that presents a reasonably low impedance compared to
inductor capacitance to the outside world, current taper will be
minimal. As a matter of fact, it can be immeasurable.

Current taper depends upon where the coil is installed in the
standing wave antenna system. It can be flat, positive, or
negative. If properly placed, it can even have current flowing
into both ends of the coil at the same time, i.e. a 180 degree
phase shift in the currents at each end.

The coil distorts the current waveform away from the pure cosine
envelope presented by a 1/2 wavelength thin-wire dipole but then
so does a large diameter conductor.

2.) Current taper and phase shift do not correspond to the electrical
degrees the loading coil "replaces", except as the physical size of the
loading coil might increase stray capacitance to the outside world.

Phase shift corresponds to the delay through the coil.
It can be estimated from the self-resonant frequency
measurement where the delay is known to be 90 degrees.
This is a common method of estimating the delay (electrical
length) of a transmission line stub.

3.) Phase shift of current is anything from zero to a reasonably small
number of degrees, and does not correspond to the electrical degrees
the inductor replaces.

My 75m bugcatcher coil occupies about 60 degrees at 4 MHz,
2/3 of the electrical length of the antenna. 60 degrees doesn't
seem to meet the definition of "reasonably small". IMHO, that
would qualify as "reasonably large", i.e. more than half the
electrical length of the 75m mobile antenna.

4.) There are at least two ways to get a good answer. One is by a
circuit model with enough L and C sections, the other is with a wave
theory approximation. Both models have limits.

It is impossible to get a good answer with a model that presupposes
faster than light propagation through the coil with equal amplitudes
and phases at each end of the coil. The error is the same as assuming
such for a piece of transmission line. Dr. Corum's suggested crossover
point where the lumped-circuit model fails is 15 degrees or 0.04 of a
wavelength. Either the distributed-network model or Maxwell's equations
must be used beyond that point in order to obtain valid results.

I think that pretty much is it. What did you conclude? Can you get it
into a few clear words?

A 75m bugcatcher coil is a "slow wave structure" described by Ramo and
Whinnery, by the IEEE Dictionary, and by Dr. Corum. The velocity factor
of my 75m bugcatcher coil has been measured at ~0.017 which agrees with
the published formula.
--
73, Cecil http://www.qsl.net/w5dxp