Perhaps I could share a few thoughts on the "missing degrees" topic;
and again I apologise as the new boy if this has all been covered
before! I found the following argument helpful when trying to get my
head around some of the issues, and it may help others:

Picture the short, base-loaded, 6ft vertical antenna example I gave
earlier which resonates at 3.79MHz with the coil dimensions I quoted.
The 6ft whip represents an electrical length of about 9 degrees. Now
suppose I remove the 12" long loading coil leaving a 12" vertical gap
in the antenna. At this point I find it much more helpful to think in
terms of a "missing" +j2439 ohms reactance, rather than a "missing" 81
degrees, for reasons we shall see later.

Now I run out a couple of horizontal wires from where the top and
bottom of the coil were connected, and short them at the far end
thereby forming a short-circuit stub. That stub will insert some
"loading inductance" in place of the coil. How long do I need to make
the stub to bring the vertical back to resonance?

Using the simplified stub formula Xl=+jZo.tan(Bl), and assuming for
now that the characteristic impedance is 600 ohms, I find that the
electrical length needed to generate +j2439 is 76 degrees - well short
of any "missing" 81 degrees. And if I increase the characteristic
impedance of the stub to 1200 ohms I only need 64 degrees. The Corum &
Corum formulas tell me that the characteristic impedance of my
original loading coil is 2567 ohms at this frequency, so that only
requires an electrical length of 43 degrees.

So, for me, the "missing degrees" question is not really about missing
degrees; rather, it's about a missing inductive reactance which can be
provided by transmission line structures with a wide range of
electrical lengths depending on their characteristic impedance. The
"constant" is the reactance, not the electrical length.

I also find this picture helpful because I can visualize that,
although there must be forward and return waves on the stub, the net
current I would observe is a standing wave whose phase doesn't change
along the length of the stub. Incidentally, taking 43 degrees as the
length of my loading coil I would expect to see a change in current
amplitude along the length of the stub of cos(43); that's 0.73 -
pretty close to the 0.69 observed in the EZNEC model between the ends
of the coil.

Finally, I ask what the transmission line characteristic impedance
would need to be for its length to be exactly the "missing" 81
degrees? Answer: 2349/atan(81)=273 ohms. Isn't that in the right ball
park for the characteristic impedance of a single straight piece of
wire - in fact the piece of wire that's needed to turn the 6ft whip
into a full quarter-wave vertical?

And finally, finally, to Roy: I struggle with the "mental gymnastics"
needed to move from the simple stub model outlined above, to one where
the "transmission line" is a single wire, not two wires, and "in-line"
with the antenna elements. If you read the Curum & Corum paper I'm
sure it will be clearer to you than to me! But until I can understand
it better, I content myself with this thought: if we removed 56ft of
wire from our full-sized quarter-wave vertical to leave just the 6ft
whip, we'd be happy to analyse this 56ft straight piece of wire using
a transmission line approach (including considering forward &
reflected waves, and the resultant standing wave along it), and to
ascribe to it an equivalent inductive reactance. I don't understand
why I (we?) find it intellectually any more difficult to take the same
approach with a piece of wire once it is wound into a helix.

Regards,
Steve G3TXQ