Cec sez,

My solution is to get Reg to write a new program. :-)

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My patience is wearing thin.

Nevertheless, once more into the breach.

There's no need to write a new program. There's not even any need for an old
one.

Knowledge of the current distribution along a loading coil has no practical
use except to assist with drawing pictures of it in books and magazines.

FOR PRESENT PURPOSES THE LENGTH AND IMPEDANCE OF THE ANTENNA BELOW THE COIL
IS NOT RELEVANT. IT CAN BE CONSIDERED TO BE PART OF THE GENERATOR.

LET THE ANGULAR LENGTH OF THE COIL = THETA DEGREES. OTHERWISE KNOWN AS THE
PHASE SHIFT. THIS IS A FIXED, IMMUTABLE QUANTITY SET BY THE PROPAGATION
VELOCITY = 1 / SQRT( L * C ).

THE MAGNITUDE OF THE CURRENT DISTRIBUTION ALONG THE COIL IS ALWAYS THE SAME
COSINE CURVE BUT WHICH IS TRUNCATED (SLICED OFF) AT VARYING ANGULAR DEGREES
AT EITHER OR BOTH ENDS.

THE ANGLE AT WHICH THE TOP END IS TRUNCATED DEPENDS ON THE INPUT IMPEDANCE
OF THE ANTENNA ABOVE IT. IT IS ALSO RELATED TO Zo OF THE COIL WHICH IS THE
USUAL SQRT( L / C ).

THE ANGLE AT WHICH THE BOTTOM END IS TRUNCATED IS ALWAYS THE TOP ANGLE MINUS
THETA. IT CANNOT BE ANYTHING ELSE.

THUS, WHEN THE TOP END IS OPEN CIRCUIT AND THETA = 90 DEGREES WE HAVE A
COMPLETE 1/4-CYCLE OF A COSINE CURVE - A 1/4-WAVE RESONANT HELICAL
ANTENNA.

The foregoing applies to both short, fat coils and long, thin coils,
close-wound or stretched-out.

Coil resistance is the uniformly-distributed radiation resistance plus
conductor resistance.

For useful calculations such as Q, bandwidth, efficiency, etc., you can
forget all about bewildering reflections, standing waves, forward and
reflected power and use the well-known classical transmission line formulae,
the everyday tools of all good engineers.
The final wanted characteristic, the radiation pattern, can be found with
number-crunching EZNEC-type computer programs which work in an entirely
different manner.
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Reg, G4FGQ