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RE: Variable Capacitance and Inductance

Original poster: "David Thomson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <dave-at-volantis-dot-org>

Hi Terry,

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

Everybody knows I've made greater mistakes than this.  As embarrassing as it
often is, I tend to have more error than trial in the trial and error
method.  But then, I guess every body makes mistakes.

>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.

I didn't doubt there would be a wider gap between measurement and
calculation.  My guess is that the classic formula for inductance minus the
EMF effect would give a value for inductance.  And the difference between
this value and Wheeler's might be the variation caused by proximity to the
earth.  If enough tests are done, there may arise a specific value of
inductance attributed to earth effect.  We could then write a more direct
formula for inductance that demonstrates all the actual factors contributing
to the value of coil inductance.

It may not mean much to the Tesla coil community, but it would be a major
milestone in physics.

>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.

I agree.  So far there is no evidence Tesla actually pinpointed the exact
value of EMF on coil inductance.  He seems to be vaguely aware of it, but at
this time his attention is on other things.

>"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.

The reason for using the classic formula as a reference point is because
inductance is defined in that equation.  In the classic inductance equation
inductance is defined as a specific set of physical characteristics of a
physical coil with regard to permeability of free space.  Obviously the
classic formula is not accurate because there is some other force acting on
the inductance of the coil.  Wheeler's formula empirically accounts for this
force, but does not define it.  Since science is about finding out all the
details of how our universe works, it would be good to identify this force
that deviates the coil's actual inductance from the formula that defines

It may be this was tried before, but folks weren't aware of the EMF effect
that you and Paul have identified and quantified.  Undoubtedly there are
numerous minor forces that affect coil inductance, but after the EMF, earth
proximity must be the largest factor.  Wheeler's formula, while it does
yield a close approximation of the inductance of a coil, does not define
inductance per se.  Besides proving a definition of coil inductance,
identifying a constant of inductive reactance imparted by the earth would
have significant scientific usefulness.  It could get you a science prize,
as the knowledge could be put to commercial use.

>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.

The distances Tesla raised the ball from the earth were in something like 20
feet increments.  Twenty feet is a lot of extra space and a lot of extra
influences can get between the ground and ball.  These extra influences are
likely from stray magnetic flux from various sources.  This needs to be
proved, but it is a real possibility.  The fact that Tesla measured the
capacitance variations that he did is reason enough to look into stray
magnetic flux or other possible increases in the dielectric field strength.

Unlike a small capacitor where a change of distance between the charged
bodies does not allow for a change of dielectric strength, Tesla's
experiment does allow for this.

>>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.

Did you deal with distances of from 9 to 47 feet between charged bodies?  If
so, you may have the evidence to contradict Tesla's claim.

>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.

Excellent point, Terry.  Just as we stand on the shoulders of geniuses, we
can also step on the backs of those who fall. (sounds sick but it's true.)
It's better to have tried and not succeed than to never get involved at all.
I have two dynamic kids.  When they were young I constantly told them that I
wanted them to go out and make mistakes, that it is OK to take calculated
risks.  They took my advice and both of them are now super achievers.  One
should be just as proud of their mistakes as they are in their successes.
No doubt, there could be no success without making mistakes.  Even Tesla
learned a lot from the School of Hard Knocks.

>>>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))

Life is Great!  Isn't it?  Live for the adventure.

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

Is this Fight Club?  Sounds like fun.

>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...

I disagree.  The data is clear in CSN.  What's lacking is the data for the
opposing arguments.  People are taking Tesla's conclusions out of context
with his experiments, and without even trying his experiments are claiming
he is wrong.  Malcolm mentioned he has some data.  I look forward to seeing
this data.  I also look forward to doing these experiments myself this
summer or fall.  When Tesla's work is closely analyzed, the possibility that
he is correct does appear.

>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 sleep.

Speaking of which.  Have you put a hair dryer to one of your coils and
watched the inductance?  Where is the evidence that temperature affects the
induction of a coil?

>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.

This sounds authoritative.  Where is the data to counter Tesla's work?  I'd
like to see it.  So far I'm seeing lots of conclusions concerning Tesla's
error, but no data to support those conclusions.  At least with Tesla I can
the data he presented in his CSN.  I can also look at the many awards this
man has won for his scientific contributions and this instills an automatic
sense of respect and "benefit of the doubt" for his claims.  Before someone
of this stature can have his worked summarily dismissed, there needs to be
good counter evidence to prove he is wrong.  In the interim, all doubts
about his work must be qualified as opinions and not as fact.  That is the
way of good science.

>The tables like on pages 209/210 would evoke wild laughter from the
audience as they carried our beaten carcasses out :o))

I'm ready to look at this with you.  What in particular do you have a
problem with?  I think it is very insightful as to how he carried out his

>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:

How accurate can you calculate a 30 inch sphere's capacitance when you
haven't even discovered the effect of the earth on inductance yet?  I
suggested the experiment and you blew it off, apparently because you don't
understand the importance of the effect of this huge ball of metal and clay
on a coil.  You are no doubt aware of the effect of having cement blocks
next to your coil.  Imagine a cement ball 8000 miles in diameter next to
your coil.  How can you possibly measure the capacitance of a 30 inch ball
50 feet from an 8000 mile ball when you don't know what reactive effects the
8000 mile ball imparts?  Then you have to look at the effects of the sun and
moon; minute to be sure, but still effects.

>But there is one question.  What on Earth will we find that is "unusual"?

What a question!  How about the earth, itself?

>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.

This is because you accept Wheeler's formula for inductance without
understanding why it is empirically based.  The "unexpected" is buried in
Wheeler's formula.  You need to dig it out and identify it.

""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.

Read carefully the notes from October 26 to the end of November.  Tesla
clearly and painstakingly takes each capacitance into consideration.

>Today, it seems obvious...  Could weather and all kinds of other things
have affected his original experiment?  Obviously,

Obviously not!  Do the hair dryer experiment and report your results.  There
is a real big problem with the temperature thing.  And this means the
humidity thing needs another look, too.  Temperature has absolutely no
meaningful effect on coil inductance, let alone capacitor capacitance.

>We could eliminate those effects, at least on the computer, and then pat
ourselves on the back for proving nothing...

Let's try it and see.  This is exactly what happened in the ping pong ball
experiment in my ninth grade science class.  The teacher was so certain he
was right, he wouldn't do the experiment.  He was startled to be proved
wrong by a freshman high school student.  Don't pat yourself on the back
just yet.  ;-)

>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...  ;-))

What could be proven is that the earth imparts reactance (or inductance) to
the coil.  This could be through magnetic flux within the earth.  The payoff
could be new technologies for measuring environmental changes, designing a
pocket speedometer that would tell how fast and how far relative to the
earth an individual was traveling, or even the simple fact of knowing the
exact nature of inductance near the surface of a planet.  It stands to
reason that if the inductance of a coil on earth has one value according to
Wheeler's formula, then it will have a different value on Mars if the
Martian reactance (or inductance) is different from earth.  Future Tesla
coilers will be delighted to know the adjustment they need to make in order
to make their coils put out big sparks on Mars.  Who knows Terry, you might
even be able to send one of your coils to Mars or the moon to prove a new