Cecil Moore wrote:
Here are some valid conclusions that can drawn from the
"Current through coils" thread.

A mobile antenna is a standing wave antennas. Some mobile
antennas use loading coils within that standing wave
environment.

There is no useful phase information in standing wave
current. Therefore, standing wave current cannot be used
to determine the percentage of a wavelength that is
occupied by the coil.

I think I disagree with this. A standing wave has one of two phases
with respect to time, but the two waves traveling through both the
antenna elements and any loading coils do have phase shifts, both with
respect to time and with respect to position. But when the two waves
are superposed, all that is left of this phase information is phase
with respect to position. The phase shift of both the single
direction waves can be inferred by the shift in position of where they
combine to form a node (if you make the (reasonable?) assumption that
the delay in both directions is equal.

Standing wave current cannot even be used to determine
what percentage of a wavelength is occupied by the whip
above the coil.

There is information about this in the amplitude versus position of
the standing wave. But the only very definite points in this
variation are the nodes, so is the length is less than a half
wavelength, you have only the node at the end to work with, so you
have to use the sinusoidal amplitude curve to work with.

Standing wave current has virtually
unchanging phase the entire length of the mobile antenna.

With respect to time, yes. With respect to position, no. The
amplitude is different at different locations, so you can use phase of
the wave with respect to position. It is just a bit of a mental
switch to change from phase in time to phase (fraction of a 180 degree
half cycle of amplitude wave from one node to the next).

The percentage of a wavelength occupied by any element
can be estimated using that element's velocity factor.

Or the velocity factor of the traveling waves can be measured by the
interference pattern they produce as a standing wave. One cycle of
the standing amplitude wave has to occupy the length that carries one
cycle of the traveling wave.

The velocity factor of the whip is known.

Lets say that it has been measured for some cases, and generalized to
others.

The velocity
factor of the coil can be measured or estimated using
applicable formulas.

If they apply to this particular coil construction. Or you could
measure the standing wavelength with an without the coil and, so,
measure the coil's "length" in standing wave (and thus, traveling
wave) lengths.

The presuppositions of the lumped-circuit model render
it ineffective in any attempt to analyze large coils
in a standing wave environment.

Or any other environment where they have a net delay (electrical
length) that is not insignificant with respect to the frequency in
question.

Either the distributed
network model or Maxwell's equations must be used to
obtain valid analysis results.

Or you work with amplitude measurements versus position of the
standing wave.