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(Fwd) Re: Formula for self C of a Coil (not Medhurst)

Hi Robert,
                I'm sure you will love what I'm about to say (maybe ;) :

> Original Poster: "Robert Jones" <alwynj48@earthlink.net> 
> 
> Hi all,
> 
> Does anybody have the formula or a link for the capacitance of an isolated
> cylinder that is not due to Medhurst?

Medhurst never claimed that his formula delivered the Cself of an 
isolated cylinder. He specifically stated that it delivered the Cself of 
a single layer solenoid which had one end grounded. He developed 
the formula after contesting the work of Palermo (sp?) on some 
theoretical grounds. I remember reading that he measured around 
40 coils in the course of his work. He produced a paper full of math
(which I'm now obliged to go back and read again :( 
       I read about your low frequency measurement. One might call 
this the sheet capacitance of the coil. Problem is: the resonator is 
not a sheet of metal at the frequencies we are using it. Is the object 
of this exercise to model it from DC - light?
       What does Tx line modelling have to say about using such 
capacitance figures? How are you going to distribute it? It seems to
me that using such a figure makes the L/C ratio far less favourable 
than it already is. Can you really use a "lumped" inductance figure 
with any degree of validity in a Tx line model (we must now 
remember that it has capacitance distributed over it so perhaps it is
just as "incorrect" as the sheet value of capacitance).

Before continuing, I note that some transmission line modellers have 
no hesitation in quoting the quantities in dispute here in the same 
breath as the Fr of the resonator (which appears to verify them).

> My suspicion is that the Medhurst formula is incorrect or it contains a
> fiddle
> factor. If you compare the values it generates to the C of spheres it
> appears
> to underestimate  C by at least a factor of 2.
> 
> I believe the formula actual produces a value that when used with the
> inductance of a coil  correctly  calculates the resonance frequency but it
> is not the self C of the coil.  Its just an imperical relation to calculate
> Fr.

That has been my feeling for years too but perhaps we are now 
heading into apples and oranges territory. For a long time I have 
regarded Medhurst's formula as a *useful recipe*, not a definitive 
work but again that presupposes that the coil is actually a solid cylinder
at the frequencies of interest. One can see an immediate difficulty if
one tries to use Fr to derive a value for Cself. Since Cself is distributed
over inductance one is effectively trying to measure portions of it via 
portions of an inductance.............  This also throws into doubt the use
of the 
energy equation *based on the use of Medhurst's Cs*  to derive a 
maximum figure for Vs. Perhaps it is overly optimistic?

       What are we now to make of the capacitance of the top terminal?
We know that it is part shielded by the coil itself and we also know that
filling
in a toroid makes virtually no difference to its capacitance (or at least
to the coil
operating frequency).

     So what are we now to make of Vs? Far lower than previously 
suspected? Or far higher due to energy running into a "nothing" at 
the top of the coil? How would either scenario square up with 
observed output lengths in sshot mode given a definitive lump of 
energy minus some losses ends up in the secondary? Or that being 
<< than a wavelength long electrically, the energy is never lumped in 
one portion of the secondary but distributed over it? Or the length of 
coil that is required to stop a particular voltage from flashing over the 
entire winding length?  The answers to these questions seem fairly 
consistent with observed sshot spark lengths and not unrealistic 
compared with claims of multi-MV for relatively short resonators 
(and these with no good explanation of how such short coils can 
withstand such voltages). I know there are considerable safety 
factors built into insulators built for use on a 220kV national grid 
pylon but in the end, we are dealing with surface tracking issues in 
both cases. What do your transmission line models predict for 
output voltages and how do these compare with COE voltages for a 
lumped model *IF the resonator ends up with a fixed amount of 
energy in it in both cases*?.

> I have assumed the formula in wintesla is an accurate Medhurst formula.
> 
> Thanks in advance.
> 
> Regards Bob

So let's ask all the questions.  How about this one:  are we in fact looking at
the resonator the correct way at all? Is it even valid to assign some
simplistic electrical parameters to it in an attempt to characterize it 
(this would surely apply to transmission lines as well as lumped 
models)?

Regards,
malcolm