I'm afraid you are hopelessly mixed up.

What on Earth has it got to do with RG58?

As I have already said, using the well known formulae -

Calculate C pF/m
Calculate L uH/m
Insert L and C in Zo = Sqrt(L/C)

and Bingo! Zo = 3243 ohms.


What it has to do with RG58 is as follows:

C = 55.5 / (Ln( 2 * H / D ) - 1) picofarads per meter.

RG58 has 93.5 pF/meter. (from ARRL Antenna Book)

L = Square( N * Pi * D ) / 10 microhenrys per meter.

RG58 has 258 nH/meter. (from Zo=sqrt(L/C) and Zo from ARRL Antenna Book)

TransLine impedance, Zo = Sqrt( L / C ) ohms.

RG58 is sqrt(L/C) = 52.5 Ohms.

Propagation Velocity = 1 / Sqrt( L * C ) metres per second.

Vp = 1/sqrt(L*C) = 203.7 m/s

Take a length of H =1.5 metres of this helix and use it as a short
vertical
antenna above a good ground.

It will resonate as a 1/4-wave vertical at 3.5 MHz.

Using a 1 meter length of RG58, it will resonate at f = 1/(2*pi*sqrt(L*C)) =
32.4 MHz.

Zo = 3243 ohms.

Zo = 52.5 Ohms.

Velocity factor = 0.0701

Velocity factor = 203.6/300 = .68


In other words, Reg, I don't see why I can't apply the same equations to
determine the resonant frequency of a piece of RG58. Are you saying you can
use these equations and I can't? After all, you are implying you can analyze
your distributed coil/transmission line using non-distributed, lumped
components.

If you can explain my error, please do so rather than insulting me by saying
I am hopelessly mixed up.