Re: Propagation velocity in long helical coils.

Hi Malcolm and all,

>Original Poster: "Malcolm Watts" <malcolm.watts-at-wnp.ac.nz>
>Hi Bob,
>             I'd be very interested to read all the work when it's done.

You can have a draft if you like  but you will need mathcad 5.
I don't want to go too public until I include an equation for the real self
C of the coil as opposed to an estimate confirmed by Terry.  This does seem
daft as I have already posted the predictions.
It is extraordinary how the transmission line equation still mange to work.
This is just as amazing to me as it was previously that Medhurst worked.

>> Original Poster: "Robert Jones" <alwynj48-at-earthlink-dot-net>
>> Hi all,
>> Still checking my results.  Found one error and fixed it.  No major
>> in
>> form. The cyclic velocity at long wavelengths may be a numerical
>> in the numerical integration.   It does now appear to have a mathcad type
>> closed form. Four page widths long and containing unfamiliar constants,
>> Sinc type functions and summation of factorials along with regular trig.
>> It also contains an unexpected  integration factor.
>> I should point out that this a not a major feat of mathematics.  With
>> mathcad its just circuit analysis, maybe a feat of circuit analysis and
>> approximation. One more key point is I used a Wheeler derived coupling
>> function as I could not face the elliptical integrals this may have
>> the production of  the closed form. It also only has mag coupling, ie no
>> internal C.
>> I have decided that the real test is a comparison with the Medhurst
>> frequency for a secondary coil.  The classical ground plane trick appears
>> be valid with a minor variation  The infinity long constant parameter
>> is equivalent to a 1/2 wave coil between to ground planes.  You then just
>> cut the coil in half  and you have a Tesla coil.  Because the diameter is
>> significant the EM fringes out of the end of the coil due the  missing
>> half.  I estimate this will make the coil  appear to be between zero to
>> diameter longer.  I will assume an integrated square effect so I will
>> 1/3 diameter longer. (Note this has a dispersion effect) This can be
>> verified by measurement but as its unlikely to be more than 1/6 or 1/3 in
>> error this corresponds to only 3.33% or 6.67% for 5:1 H/D coil.  The same
>> can be done to remove the ground plane for a valid comparison with
>> which I believe is for an isolated coil.  The ground plane effect is said
>> be small. This methodology turns the constant parameter case into the
>> practical case without any analysis of the parameter distribution.
>I've found that a grounded resonator which resonates with some
>frequency F does not resonate at 2F when ungrounded and lying
>horizontal clear of ground. I think from memory it resonated at an
>unexpectedly high frequency well above 2F but would need to check
>again to be sure. It was either high or low but significantly so.

In the process of writing a justification I found an error in my chain of

The refection in the ground plain is not equivalent to a continuing coil.
It is equivalent to a coil with the opposite winding sense.

I can not repeat your practical measurements.  You do not appear  to be
talking about a 1/4 wave (monopole resonance) and a 1/4+1/4 wave (bipolar
resonance) which may have been the test you wanted.

I suggest you must chop the coil in two.  One half 'end on' on a ground
plain or both halves end to end attached at a ground point in the middle but
isolated.  Both coils with the same winding sense is equivalent to the
continuous coil case and opposite is equivalent to the grounded case.  So
by doing all three you can compare all cases.

My error may not be a total disaster for my analysis because its only the
end effects. But I was relaying on your observation that the F shift was
between ground plain coil and an isolated coil was small. I can no longer do
this. It is a different effect.

Now if the ground plain F shift is small.  How???.

The ground effect is equivalent to an other coil attached to the grounded
end with the opposite polarity of voltage on the high voltage end but with
the magnetic polarity reversed between the coils.  The continuos coil has
 the same magnetic polarity (a bipolar coil).

As the separation between the ground plane and coil decreases the real self
C of the coil increases and in particular the real self C of the turns near
the ground plain increases by a very large factor. Terry's work indicates
that the real self C can double with most of that due to the increase on the
lower turns.

As the separation between the ground plain and the coil decreases,  the
field of the refection  cancels the field of the coil.  The lower turns will
most effected with the last one dropping to zero at the ground plane.

Could it be the circuit laws have been kind and both effects cancel?????
i.e. the increase in C is compensated by the decrease in L.

Now consider the continuos coil case. The capacitance will increase but this
time the inductance will also increase because the other coil reinforces the
field so the effect will be much larger between the continuous coil and the
isolated end coil (grounded end) compared to the grounded plain coil and
the isolated end coil (grounded end).

So it is a disaster for my for attempt to extend the analysis to practical
Telsa coils. Because I have no practical evidence to support my view that
the end effects are small.  Well I could just guess and hope for the
best but you cant call that analysis. It also means I can not verify my
analysis by comparison to Medhurst F.

Are you going to repeat your experiment with a chopped coil and an extra
half wound the other way??

Let downs are more negative than revelations  are positive  :-((

Well it worked on your coil so can  I blame you?

>> My gaol is near the comparison between the wave and lumped equations.
>> practical applications
>> for this academic exercise may be a more accurate calculation of
>> and voltage with and without a top load.  Although there are much simpler
>> methods for both. The analysis may be extendible to distributed coupling
>> and transients using similar methodology but I will leave that for an
>> time or
>> others.
>> Regards Bob
>Many thanks for your work.