wrote:
1.) I can build an antenna that has greatly uneven currents at the ends
of the loading coil, but the antenna rea above the inductor is wasted
and the system will be less efficient than a properly designed system.

Anyone with EZNEC can answer the question for himself.
For the following EZ files, the currents at the bottom and
top of the coil are viewed by clicking on the "Load Dat"
button. Load 1 is at the bottom of the coil and Load 2
is at the top of the coil. The loads are both zero so
they have no effect on the antenna system and are used
only to report the current at that point.

I previously modeled a bottom-loaded 5.89 MHz mobile
antenna. That EZNEC file is available at:

http://www.qsl.net/w5dxp/test316.EZ

Taking that antenna and *changing nothing* except adding
1/4WL of wire to the top of the whip, yields the EZNEC
file at:

http://www.qsl.net/w5dxp/test316c.EZ

The antenna has been changed from a base-loaded 1/4WL
antenna to a base-loaded 1/2WL antenna using the same
coil in the same relative position to the source and
ground. The changes in the currents through the coil
are obvious.

The frequency was not changed so the coil occupies the
same percentage wavelength of the antenna in both examples.
In the first example, we have 1.01 amps at the bottom of
the coil and 0.6984 amps at the top of the coil. That's
fairly typical for mobile antennas at the 5.89 MHz
frequency and agrees with the measurements presented
so far.

Now, changing nothing except the whip length by adding
40 feet (1/4WL) of whip, in the second example we have
1.239 amps at the bottom of the coil and 2.068 amps at
the top of the coil. How does the lumped-circuit model
explain that one? More current "flowing" into the coil
than is "flowing" out of the coil just by adding 40'
of wire to the top of the antenna?

The coil occupies the same electrical length in both
examples because they are at the same frequency. The
current through the coil depends upon where it is
physically installed relative to the standing waves
existing at the point of installation.

Using what EZNEC tells us about the self-resonant
frequency near 9 MHz, we can calculate the delay
through the coil as ~59 degrees. Thus the coil
occupies ~0.16 wavelength. (The wire used to wind
the coil is ~0.24 wavelength if stretched out
straight.) Nobody said it was a 1:1 replacement
but someone said it was *NOT* a replacement at all.

I would encourage the experimenters to add 1/4WL
of whip to their previously measured mobile antenna
systems and make additional measurement. That is, of
course, after matching the source to the new
impedance. Please report the results here.
--
73, Cecil http://www.qsl.net/w5dxp