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RE: Variable Capacitance and Inductance

Original poster: "Terry Fritz" <twftesla-at-qwest-dot-net>

Hi Dave,

At 12:40 PM 5/24/2002 -0500, you wrote:
>I need to interject a comment here.  Despite Matt's insinuation that anybody
>who takes a sincere interest in Tesla's work worships him as an infallible
>god, I have found several errors in Tesla's work in my studies.  Apparently
>I have found another one.  In reviewing Tesla's notes specifically related
>to measuring the capacitance of a "large structure" on page 282 of his CSN,
>he states, "The rise in the effective capacity for 47 feet and 6" was ...
>26.2%.  Per one hundred feet it would be from this: 55.16% or a little over
>1/2% per foot."  It seems Tesla incorrectly remembered the details of his
>notes and wrote in his article "50 per cent per foot of elevation" when he
>should have written "50 per cent per one hundred feet of elevation."
>His CSN correctly state the difference is 1/2% per foot, which is consistent
>with the rest of his article on variable capacitance.

Neat!  I don't remember anyone seeing this before!  I hope no one ever goes
through "my" old notes :o))

>>He is now saying that the capacitance of the conductive body increases with
>While checking his math I discovered Tesla was using the classic formula for
>inductance instead of a calibrated formula like Wheeler's (which wasn't
>discovered yet).  Tesla apparently measured his inductances accurately as he
>noted his measurement was considerably less than the calculated inductance
>(page 253 CSN.)  

It would be interesting to do some graphs comparing the formula below and
Wheelers...  I wonder by what percentage they differed in Tesla's tests.

For the example in CSN, Tesla had a coil 94 inches long, 99 inches in
diameter, and 105 turns...

Tesla came up with 0.029369H

Wheelers, gives 0.019498H

Tesla measured 0.02042H

So the formula Tesla used gives an error of +30.47%, and wheeler's gives an
error of -4.5%.  If one assumes 106 turns (hard to say if it is 105 or 106)
then wheelers is only off by -2.76%

That's why we use wheelers formula  :o))))  I don't mean to be picky, but
Wheelers formula would have worked just as fine for Tesla as it does for us.

BTW - Check my math!  I am not known for doing these fast calculations
right  0;-p

>Sorry Terry, but Tesla was aware that the EMF affected the
>inductance of the coil.  He makes such a comment on page 273 of CSN.  He
>probably was aware of this much sooner, so now I'll need to go back and look
>for other references.

Interesting!  He does not say it explicitly but he was so close he
certainly may have recognized that the uneven currents in the coil were
affecting his inductances.  But his calculations were too far off to
pinpoint it.  He studied it a lot but was frustrated.  His experiment on
page 274 tries to study this but such a method disturbs the coils
surrounding fields greatly.  He was trying a lot of things, but he just
didn't have the tools need :-((  The numbers were to course to see the
effects and quantify them.

>What's interesting is that Tesla made his correction for EMF from the
>classic inductance formula values and not from Wheeler's as you and Paul are
>doing now.  Why don't you try making your adjustment from the classic
>inductance formula of:
>    4 pi^2 N^2 R^2
>L = --------------
>          H
>Where L is in 1000 inches.

Because Wheeler's is better ;-)  Just because Tesla used a poor formula is
no reason we should ;-)  Paul's programs don't use Wheelers but rather the
finite filament thing like Dr. Rzeszotarski's program MandK.  All the
modern formula's and computer methods agree to within a percent.  "i" don't
see a need to base anything off a formula that gave Tesla an answer 30% in
error.  While the study may be of some interest, it does not "help" things.

>To put it simply, Tesla was measuring the effect of elevation on a dynamic
>charged body, not a static charged body.  To see what effect elevation has
>on a static charged body a capacitor with a vacuum dielectric, (not any
>other dielectric,) and not connected to the earth, should be measured at
>various elevations.  A vacuum dielectric would show the most variation due
>to elevation (distance from influence of the earth,) _if any exists_.
>>>Thus a circuit vibrates a little slower at an elevation than when at a
>lower level.
>>There is a problem here too. Included in my series of measurements are some
>showing clearly that a *resonator* that is elevated shows a *rise* in its
>frequency of oscillation. That is what I would expect given that it has
>moved further away from the ground plane. i.e. - its capacitance to ground
>has *dropped*.
>As noted above, raising the terminal increases the amount of dielectric
>between the sphere and ground, allowing greater potentials on the charged
>bodies.  Greater potentials mean greater capacitance.  It you check CSN, you
>will see that Tesla specifically tuned for greatest potential.  To know how
>this affects your experiments, it would be necessary to understand the
>tuning method you used.  If you did not tune for maximum potential, then
>your experiment would not be comparable to Tesla's experiment.
>>And so it should with the sphere, should it not? Is that not reasonable?
>Please address this question and show me exactly why my reasoning is in

You say that as you raise the sphere, the capacitance to ground decreases
and the frequency goes up.  That IS correct according to "me too".  But
Maxwell knew that in 1873...  I thought we were worried with "unusual"
capacitance variations that Maxwell's field theory could not explain?
There is the big factor of the connecting wire which reverses the
situation, but still no new science there.

>As I pointed out, you're using static capacitance as a model for a dynamic
>capacitance.  The amount of extra dielectric that can get between the
>charged bodies increases.  And this is precisely why the capacitance in
>variable.  The amount of free flowing dielectric "material" is always in

In my tests and calculations over the years, the DC, AC, and resonant
capacitances have all worked out to the same value.

>>Suppose we had blindly accepted theories that the resonator was a lumped
>tuned circuit. Where would that have got us?

Lumped parameter models could be used to accurately predict voltages and
currents in a Tesla coil.  We all knew it was far more complex and knew we
were learning to crawl before we could walk.  Today, Paul's TSSP work has
pretty much shown the real actions but the lumped models are still used by
at least me with great success in basic design problems.  It got "me" a
lot!!  Rest assured that my paper:


Got all the errors pointed out in detail!!  But "they" were right so no
harm was done.  That paper did launch some great work to follow!!  So just
another stair step...  I think it's most important contribution in the long
run was to show that hard data could finally be made available to all.
Even if "I" was wrong, the data was suddenly there in plain sight for all
to see and interpret themselves.  Today those graphs looks old and obvious,
that was not the case in 1998!  The lumped models can still do a few tricks
TSSP can't.  However, I see Paul is starting to use my 220k + 1pF streamer
model and wishes to improve on it.  If TSSP can do as much for streamer
modeling as it has for secondary modeling, the lumped parameter model will
be left in the dust of history!!  Of course, history suggest that someone
will come along still and...

>I hope research was done before blindly knocking the guys who came up with
>the lumped tuned circuit?  If it wasn't, I'll bet there was a mud slinging
>contest over that.

There was :-)))

"#*-at-&%!! . . . Thor, you dumdum! You CAN't use lumped circuit modeling! . . ." 


I did, and it worked just fine.... 

>>Suppose we had accepted theories that the resonator could be modelled as a
>uniform transmission line. Where would that have got us?

It was a major stepping stone to the lumped models that were a stepping
stone to the TSSP models...  It's all a long chain of people trying to
prove the last guy wrong :o))

>I hope research was done before blindly attacking the guys who came up with
>that theory, too.  What could blind mud slinging accomplish?  Ultimately all
>these mud slinging contests are ended with hard core research.  So why not
>do the research first and avoid the mud slinging?

We like a good fight :o)))  And it makes winning sweeter ;-))  However,
watch your back since every champion has a challenger...

Of course, the "mud slingers" or not lightweights and they know a heck of a
lot!!  Their punches hit hard and a "new theory" had better be solid as a
rock or it's gonna get carried out on a stretcher!!  However, when a solid
theory does come along, it knocks them off like flies...

The problem with the thread here is we have an idea that has no data to
back it up.  It was Tesla's idea so we all respect it but...  We don't see
the data...  Tesla tells of it but his calculations are not "good enough"
by today's standards.  The more we look the more holes we find.  Also,
other modern tests that "should" show such unusual things do not.  We just
don't have that "line in the sand" bit of evidence that challenges us to
explain.  If we ALL could take a sphere and measure 20pF tonight and 50pF
tomorrow, things would explode like wild fire as we rushed to find out
why!!!  But the sphere is 20pF tomorrow too, so we just yawn and go back to

The paper of mine above came at a time when many people were sure the
currents between the top and bottom of the coil were 90 degrees out of
phase.  Having some guy claim (rather loudly) that they were in phase and
then provide nice scope pictures of them in phase was a "big problem" with
the status quo.  It could not be ignored.  I happily answered any question
as to the setup and helped others to reproduce the results and make fiber
probes so they could do such work too.  Rest assured, people searched for
the error in the data but they didn't find one.  However, they did find a
"few" errors in some of my conclusions ;-)  Lumped models followed that in
short order that also demonstrated that "it worked" and they put the direct
challenge "if it is not right, where is the error".  Those models are just
a valid today as they were then and they easily defended themselves against
the challenges of the Corum's paper above.  Of course, time marches on and
far far better models are now coming up.  If a new model works, it gain
acceptance easily.  "Too" easily as I and now Paul find.  Paul asks again
and again for challenges or peer review to find errors in TSSP, but no one
wants to challenge the champ when he's at his best!!  However, if an error
were to pop up, they will be on us like tigers!!

Getting back to the matter at hand...

We cannot trust Tesla's original data for sphere elevation vs. capacitance
in the Colorado Springs notes.  There are too many unknowns and unaccounted
for sources for error.  Whatever conclusion we would make from that data,
could be shot full of holes far far too easily.  Previous posts to this
thread mention many of them and they cannot be defended against.  The
tables like on pages 209/210 would evoke wild laughter from the audience as
they carried our beaten carcasses out :o))  

However, we are not "defenseless" ;-))  Programs like E-Tesla6, TSSP's
Tcap, and the new fastTesla can meet the challenge of finding a 30 inch
sphere's capacitance at various elevations.  The testing of that computed
data can be compared to real modern measurements easily enough:


But there is one question.  What on Earth will we find that is "unusual"?
Although "I" have never done "this" exact test, all the testing I have ever
done suggest that we will see nothing unexpected in either the computer
models or the actual tests.  We will see how well the models correlate to
actual results but I think we will simply discover we are wasting time
proving the obvious.  Tesla's "astonishing phenomenon" is simple physics
and electrostatics:

""Continuing the investigation of this astonishing phenomenon I observed
that the capacity varied with the elevation of the conducting surface above
the ground, and I soon ascertained the law of this variation. The capacity
increased as the conducting surface was elevated, in open space, from
one-half to three-quarters of 1 per cent per foot of elevation.""

Of course, the reason the capacity "increased" is because of the connecting
wire and such.  Tesla just did not see or have the tools to see what was
going on at that time.  Today, it seems obvious...  Could weather and all
kinds of other things have affected his original experiment?  Obviously,
yes!!  We could eliminate those effects, at least on the computer, and then
pat ourselves on the back for proving nothing...

To make a long story short, what on Earth could be proven or what advance
will this type of testing give us?  If it was easy, we could just do it for
fun.  But there is a full day's work there at least.  There are far greater
fights to be fought...  Measuring the top terminal voltage of a Tesla coil
(directly) is the big challenge of the day.  Never been done...  Big
payoff...  Big challenge...  ;-))