Re: Etesla6 math questions

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "robert & june heidlebaugh by way of Terry Fritz <teslalist-at-qwest-dot-net>" <rheidlebaugh-at-desertgate-dot-com>

I have been pleased with this discussion, but I wanted to add a curve or in
fact lack of a curve. I use a cone coil so my inductance follows a near sin
function and my charge is near a linier distrabution. Your program is based
on the persumption of a linier coil about a axis. The flat secondary group
of coilers have a compleatly different distrabution and a dialectric plate
added to the secondary / primary spacing not air . Yes I know the work of a
mathgenious / programer is never finished. I use a meter.
    Robert  H
-- 


 > From: "Tesla list" <tesla-at-pupman-dot-com>
 > Date: Fri, 31 Jan 2003 19:22:01 -0700
 > To: tesla-at-pupman-dot-com
 > Subject: Re: Etesla6 math questions
 > Resent-From: tesla-at-pupman-dot-com
 > Resent-Date: Fri, 31 Jan 2003 19:23:53 -0700
 >
 > Original poster: "Terry Fritz" <teslalist-at-qwest-dot-net>
 >
 > Hi Peter,
 >
 > At 04:12 PM 1/31/2003 -0800, you wrote:
 >> Terry,
 >> I've tried once again to figure out how Etesla6 works by trying
 >> to describe my limited understanding of it to someone who does have a
 >> fairly good knowlege of E&M.  Here is what we think is true, leading up
 >> to what we think is the gap in our understanding...
 >>
 >> 0. Capacitance = charge per volt, we need to compute the charge on the
 >> TC (toroid plus secondary) for some given arbitrary voltage on the top.
 >
 > Yes,  We use Gauss's law to find the charge given an impressed (arbitrary)
 > voltage on the coil.  Then, C = Q/V  "All" we need to know is the
 > capacitance of this charged object.  E-Telsa's only purpose is to find the
 > capacitance of this charged object in a given boundary condition space.
 >
 >
 >> 1. The voltage on the toroid can be chosen arbitrarily and that value
 >> will be constant across every point on the toroid, and the voltage
 >> on the secondary can be approximated to be linear from the top down
 >> to 0 at the base (or a better approximation can come from TSSP).
 >
 > The voltage along the secondary is curve fitted, first to my random guess,
 > but now to TSSP profiles supplied from Paul's work.  The program is not
 > super sensitive to the profile but accurate curves have help much.  Paul
 > has also shown that the secondary's inductance is "different" due to the
 > non-uniform current in it.  E-Tesla now corrects the secondary's inductance
 > from meter measured values.
 >
 >
 >> 2. The charge inside an enclosing surface can be computed by summing up
 >> the strength of the E-field normal to the surface at all points on the
 >> surface.  This calculation will be independent of the shape or size
 >> of the surface, in the case of Etesla6 it is a sphere that encloses the
 >> entire TC.
 >
 > Yes, gauss's law used to the extreme.  There is a text file that explains
 > this in the program's zip files.  I think it was called "original.txt".
 >
 >
 >> 3. The E-field at any point of the enclosing surface can be computed as
 >> the (vector) sum of the E-fields from all the points on the surface of
 >> the object(s) inside the enclosing surface.
 >
 > Yes, but the program just finds the 2D field voltages and does the
 > volts/distance thing.  Calculus adds it all up and does a cylindrical sweep
 > for the grand total.  The program assumes the coil is uniform about a
 > cylindrical axis and does the calculus thing around the center line.
 >
 >
 >> 4. The E-field at a point on the object(s) inside the enclosing surface
 >> depends on the charge density at that point.
 >
 > Proportional.  Not sure that matters.
 >
 >
 >> Minor questions:
 >>
 >> ? In statement (3) this is independent of whether the line from a point on
 >> the object's surface to the measurment surface crosses through the object
 >> or not (we're assuming the object(s) is conductive).
 >
 > E-Tesla computes the voltage profile around an object.  If there is
 > anything in the way, that will be compensated for.  See:
 >
 > http://hot-streamer-dot-com/andrewb/
 >
 > so a charged point that is between a grounded surface and the measurement
 > surface will be blocked.
 >
 >
 >> ? In statement (3) what if the line crosses significant amounts of
 >> dialectric.
 >
 > E-Tesla assumes either air or conductors.  Dielectric effects are
 > considered insignificant.  If half the coil were say in a pool of oil,
 > things would change...  It would not be terribly difficult to add 
dielectrics.
 >
 >
 >> Major question:
 >>
 >> ??? It seemed to us that even though the voltage on the toroid is constant
 >> across all points on its surface, the charge density would not be, ditto
 >> for the secondary solenoid. If the charge density is not constant we
 >> have
 >> a major problem computing it (and I think that is the "trick" in Etesla6,
 >> but I cannot remember what it is), otherwise the above gives a fairly
 >> straightforward outline of a numerical analysis approach (except that
 >> even if the charge density is constant across the object surface it is
 >> not clear what that density would be for a given voltage...).
 >
 > The charge density certainly is non-uniform.  But that is controlled by the
 > shape and E-Tesla does the "E-field relaxation thing" to find the E-field
 > (voltages) around the coil. Here we see the charges building up around the
 > toroid's outer edge:
 >
 > http://hot-streamer-dot-com/andrewb/models/soutput.jpg
 >
 > When we do the relaxation matrix, the charge density on the parts works
 > out!!  Sharp edges get high fields do to high densities.  Smooth edges get
 > low fields do to low densities.  The "relaxation" does this field density
 > adjustment for us.
 >
 >
 >
 >> I remember the last time I asked you this question I did not really
 >> follow the answer (something about "shrinking the sphere down to the
 >> object" in a mathematically smooth way), and my E&M friend could not
 >> figure it out either.
 >
 > Here is the file of a coil with the Gaussean measurement sphere added:
 >
 > http://hot-streamer-dot-com/andrewb/models/diag_contore.jpg
 >
 > One just finds the voltage difference across the sphere's surface and adds
 > it all up in a spherical integration (easier than it sounds ;-))
 >
 >
 >> For me part of the joy of coiling is getting to use my machine shop tools,
 >> part is watching the sparks, and part is learning some new math/physics.
 >> For the later I'ld really like to understand Etesla6 (and someday TSSP 
too).
 >
 > I like machine tools too :-))))  Sparks or sort of dull to me, rather watch
 > them on the scope :o)))  Math is something I find myself doing to make
 > things better.  I am not real good at fields stuff but Tesla coils force me
 > to do field theory ;-))  I still struggle greatly with fields...
 >
 > I see what Paul's programs do and why, but I never seem to have that
 > perfect intuitive view of things.  I really have to think about
 > it.  However, it appears Paul's program are truly reflecting what really
 > goes on and the results are astounding!!  Paul is far far better than I at
 > seeing the full theoretical picture and converting that to program code and
 > results!!
 >
 > I pulled up the "original.txt" file below.  This is what the whole mess is
 > based on.
 >
 > ============================
 > tesla-at-pupman-dot-com
 > Terry Fritz <twf-at-verinet-dot-com>
 > New Fo, Cself, Ctotal Program
 > 1/3/99  01:17pM
 >
 >
 >
 > Hi All,
 >
 > We have often wanted to know the resonant frequency, self capacitance,
 > and total capacitance of our secondary coils before they are 
built.  Wheeler's
 > formula gives us the secondary inductance to a very good accuracy so
 > calculating
 > the inductance of the secondary has never been a real problem.  The Medhurst
 > equation supplies us with a number for the secondary self capacitance 
that is
 > fairly accurate.  However, once you put a terminal on the top of the
 > secondary,
 > things get bad.  The terminal is placed within the self capacitance 
space and
 > has the effect of adding to the self capacitance.  There are rules and ideas
 > about how to guess at this situation but guesses are all there are.  People
 > have
 > done experiments but the experimental set up never seems to match our 
systems
 > well and the results may not be very good.  You won't find a good single
 > equation
 > for this situation.
 >
 > So.... the real problem is finding the total capacitance of our secondary
 > systems by calculation rather than building it and seeing how close we
 > guessed.
 > If one thinks about all the variables the problem quickly seems impossible.
 >
 > However, consider this.  The capacitance of an object is simply the 
charge in
 > Coulombs on the object divide by the voltage.  If we know the charge and the
 > voltage we know the capacitance (and Fo).  The voltage is really 
easy.  It can
 > be any arbitrary voltage  ( I use 100 volts... for no real 
reason).  Then the
 > problem is simply to find the charge, on the coil system, at that
 > voltage.  Sounds
 > hard to figure out and the mental effort behind the solution is in the
 > realm of
 > genius.  Fortunately, around 200 years ago Karl Friedrich Gauss (1777-1855)
 > figured it out for us.  It doesn't mater how complex or messy the
 > dimensions of
 > the charged object are.  All that matters is what the field around it looks
 > like.
 > Gauss came up with what is known as Guass's Relation.  It is:
 >
 > "The total flux passing outward through any closed surface equals (1/eo) 
times
 > the total electric charge inside the closed surface."
 >
 > In other words, if you throw any shaped charged object into a bag with 
lots of
 > little electric flux sensors sewn into it.  The charge on the object will be
 > equal to the sum of what all the sensors measure times eo.  Or...
 >
 > Q = Sum E x eo
 >
 > So... That still sounds harder than just building the darn thing and seeing
 > what happens :-)  However, we now know how a secondary coil's voltage is
 > distributed.  It is a sine shaped distribution along the length of the coil.
 > The top of the coil and terminal are at the same potential while the base is
 > grounded.  Thus we can set up a computer simulation to find the electric 
field
 > around the coil given it's dimensions.  The finite element analysis 
technique
 > to do this is well known by people who worry about such things.  It is 
really
 > very simple but takes a very large number of calculations.  So the computer
 > can crunch out the field distribution.  Our task (the computer's task) is to
 > simply place a virtual surface around the coil and add up all the flux 
passing
 > through it.  The surface can simply be a sphere with the Tesla coil 
contained
 > inside it.  This is the simplest surface to use for our needs.  There are no
 > unknowns here.  Just Gauss's wonderful relation, some simple math and 
one heck
 > of a lot of calculation.  We have the relation,  the math is straight 
forward,
 > and modern computers can easily do the calculations in some reasonable time
 > frame.
 > So we have all the parts.  So... would someone please write a program to do
 > this?...
 >
 > Too late! :-))   I couldn't wait.  It is still an alpha version but I
 > think it works well.  It is called TWFreq and is available at my site:
 >
 > www.peakpeak-dot-com/~terryf/tesla/misc/twfreq.zip
 >
 > I'll call this the Alpha version.  It is written in DOS's QBASIC (which is
 > included since modern OSs don't have it anymore).  It will run on any PC.
 > It will run in a DOS window on NT and the like.  If it works out, 
someone can
 > rewrite it in some nice language since it is short, simple, and
 > straightforward.
 > Programming is not one of my strong points...  I hear there are DOS
 > emulators for
 > Macs.  If so, it should work fine on those too.  This is a straight text 
based
 > program with no fancy stuff.  It can be converted to any computer's BASIC
 > programming language (it needs more than 8k of RAM :-)).  Nothing
 > fancy.  Expect
 > it to take at least a few hours to get down to a stable number.  The extra
 > cash
 > you paid for the faster computer will pay off now.  It writes the voltage
 > field
 > data to disk periodically so you can print the field plots out if you have
 > Excel97
 > or some other program that can do surface plotting.  It can be modified 
to do
 > field stress too very easily.  It only does one terminal but two terminals
 > or other
 > configurations would be easy to add.  Just a matter of putting the shape in.
 >
 > Basic instructions are included and any problems found or suggestions
 > should be
 > sent to me for fixing.  The program works fine on my system and the parts I
 > can
 > mix and match together but only a real field test will insure it "really"
 > works.
 > If you know your system well, please report the accuracy to me so I can
 > determine
 > if there are any weak spots and come up with a good number for claimed
 > accuracy.
 > There are no "fudge" factors in it now but that could change :-))
 >
 > This program has never been field tested before so the guarantees are zero.
 > However, it should work.  I hope it works out.  It will fill a one of 
the few
 > holes we have left in Tesla coil design for the armchair coiler...
 >
 > Good luck!    We'll blame Karl if it doesn't work :-))
 >
 > Terry
 > terryf-at-verinet-dot-com
 > ==================================
 >
 > Although the program has had many revisions, BASIC, Qbasic, complied BASIC,
 > C, C++......  It is still the same idea...  The program has been refined,
 > but the basics have never changed.  It is just a computer applying gausses
 > law....
 >
 > Let me know if I can help with further questions.  I spent uncounted hours
 > on this stuff, and others did too, to make E-Tesla what it is today.  It is
 > a pretty refined program at this point.  If I think a little, I can
 > probably recount a long story behind every letter of the code ;-))  But
 > remember, Paul's work is far far beyond E-Tesla!!!
 >
 > Cheers,
 >
 > Terry
 >
 >
 >
 >
 >> thanks,
 >> Peter Lawrence.
 >
 >