Capacitance of a cylinder coil (and coil model)

From:  Antonio C. M. de Queiroz [SMTP:acmq-at-compuland-dot-com.br]
Sent:  Thursday, April 09, 1998 1:37 AM
To:  Tesla List
Subject:  Re: Capacitance of a cylinder coil (and coil model)

Jim Lux wrote:

> Is that for a closewound or a spacewound coil? I assume it is some sort of
> empirical curve fit to the tabular data, much as the Wheeler equations are
> an empirical fit to inductance data.

Apparently, the formula is intended to work for any reasonable turn spacing.
Obviously it must fail for a single turn...
I don't have the original paper (see my other post) to see how was this
formula derived.

A large (actually, any) coil behaves as a transmission line, not as a simple 
inductor with a parasitic capacitance, what is only a (good) approximation.
But the model is not a simple TEM mode transmission line. I have checked this
making measurements of the resonance frequencies (applying a grounded signal 
generator with a resistor in series to the lower end of a vertical coil and
searching for the voltage minima at the base of the coil). I found that the
resonances are all significantly shifted to low frequency, not following the
relation f, 3f, 5f, 7f, ..., where f is the frequency of the first resonance,
predicted by the model for a TEM line with open end (no top load).
The experiment is simple, and it is easy to observe the standing wave pattern
in the coil by just sliding a finger along it. With the finger over the voltage
nodes the voltage at the base returns to (close to) the minimum value.
Could someone try to make this measurement? I would be interested in see what
are the resonances found and if the voltage nodes are at the expected positions
(in my tests they are).

Antonio Carlos M. de Queiroz