Of course I understand that both L and C are distributed. But the C in
the transmission line formula isn't a longitudinal C like the C across
an inductor; it's the (distributed, of course) shunt C between the two
conductors of the transmission line. I don't believe you can justify
claiming that the C across an inductor is even an approximation for the
C from the inductor to whatever you consider to be the other
transmission line conductor.

Roy Lewallen, W7EL

Reg Edwards wrote:
L and C are neither in series or in parallel with each other.

They are both DISTRIBUTED as in a transmission line.

To calculate the self-resonant frequency what we are looking for is an
equivalent shunt capacitance across the ends of the inductance.

Turn to turn capacitance is is a very small fraction of the total
capacitance. If there are 10 turns then there are 10 turn-to-turn
capacitances all in series. After a few turns there is very little
capacitance which can be considered to be across the coil.

Consider two halves of the coil. We have two large cylinders each of
half the length of the coil. Diameter of the cylinders is the same as
coil diameter. Nearly all the capacitance across the coil is that due
to the capacitance between the two touching cylinders (excluding their
facing surfaces).

The formula for VF is true for any transmission line with distributed
L and C. And a coil has distributed L and C.

Agreed, L and C are approximations for very short fat coils. But any
approximation is far better than none at all. All antennas have to be
pruned at their ends.
----
Reg.
"Roy Lewallen" wrote

Velocity = 1 / Sqrt( L * C) metres per second
where L and C are henrys and farads per metre.

What seems to be getting lost in the discussion is that L is
*series* L
per meter and C is *shunt* C per meter -- that is, the C to another
conductor(*). C is not the self-capacitance of the inductor.

(*) Conductors also have capacitance to free space, but I'm not at
all
sure the transmission line equations for such things as velocity are
valid if this is used for C. The equation for the resonant length of
a
wire in space is very complex and can't be solved in closed form,
and
even approximate formulas are much more complex than those for
transmission lines. So while transmission lines and antennas -- or
radiating inductors -- share some characteristics, you can't blindly
apply the equations for one to the other and expect valid results.

Roy Lewallen, W7EL