Considering a loading coil to be a section of transmission line -


To the first approximation, which in many applications is good enough -


Coil inductance = Sqr( N*Pi*d)/10 uH per metre.


Coil capacitance = 55.5/(Ln(2*H/d)-1) pF per metre.


Line Zo = Sqrt(L/C) ohms.


Velocity of propagation = 1/(sqrt(L*C) metres per second.


Where H is length of coil, d is diameter of coil former, and N is number of
close-wound turns per metre.


All of which can be found in Terman, who himself plagiarised his
predecessors and I have plagiarised from Ohm, Ampere and Volta. So why
couldn't YOU? "It's elementary my dear Watson."


To provide some numbers let -

H = 1m, d = 25mm, N = 500 turns per metre of 2mm diameter wire.

From which -

C = 16.43 pF, L = 154.2 uH,

Zo = 3064 ohms,

Velocity Factor Relative to Light = 0.0662.

And so a 1 metre height helical antenna, of the above dimensions, above a
ground plane will be 1/4 wavelength resonant at 4.967 MHz. (I do hope my
arithmetic is OK)


The foregoing demonstrates how a coil with its distributed capacitance
behaves as a transmission line or even as an entire antenna. When short
sections are used as loading coils in antennas exactly the same transmission
line calculations apply.


Beware of old wives hopelessly displaying their pseudo knowledge,
ridiculously overcomplicating situations and reducing the facts to
unbelievable nonsence. All in the good name of World-wide Amateur Radio.


I'm on "Rouwke's Drift" tonight, a South African, Western Cape, medium-dry
white. I can recommend it.
----
Reg, G4FGQ