wrote:
It seems to me Cecil now agrees the system can be modeled as a lumped
components and loads and we do not need to use standing waves.

A 100% false statement but we are accustomed to such from
W8JI. Since the lumped circuit model is a subset of the
distributed network model, if there is any disagreement
between the two models, the distributed network model wins
every time. They are both right under certain conditions
and the lumped circuit model is wrong under certain
conditions.

Quoting from: http://www.ttr.com/corum/index.htm

"There are no standing waves [allowed] on a lumped element
circuit component. ... for coils whose WIRE LENGTH exceeds
1/6WL", the distributed network model is required.

Quoting from: http://www.ttr.com/TELSIKS2001-MASTER-1.pdf

Concerning the *impedance only* of a loading coil:

"The formula will NOT (and, being lumped, can not) give the
voltage magnification by VSWR dur to physically true
current standing waves on the structure ... If impedance is
the only item of interest, the empirical Medhurst approximation
is acceptable out to about 60 degrees."

But we haven't been arguing about impedance. We have been
arguing about phase. Here's what the above paper says about
phase shift through a loading coil.

"Further, the voltage distribution passes from the loop of a
sinusoid (at 90 degrees) to the linear portion of the sinusoid
(for heights less than 15 degrees)."

It is necessary to use the distributed network model if the
phase shift through the coil is greater than 15 degrees.

Continuing the quote: "Lumped elements 'have no physical
dimensions and no preferred orientation in space; they
can be moved around and rotated at will.' Not so for real
world coils. ... The concept of coil 'self capacitance' is
an attempt to circumvent transmission line effects on small
coils when the current distributions begins to depart from
its DC behavior."
--
73, Cecil http://www.qsl.net/w5dxp