=?646?Q?Saskia=3Fs_toroidal_secondary_?=

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

Original poster: "Jared E Dwarshuis" <jdwarshui-at-emich.edu> 

To  Mr. Garry Reynolds:

Hello from Larry Morris and Jared Dwarshuis.

Mr. Reynolds you seem very curious about our toroidal coil, so we will
explain to you how it works.  The inductance for the Saskia?s secondary
coil is frequency-dependent.  With a full wave you calculate the
inductance as L = u Nsqrd Area / length (where length is one fourth of
the average of the circumference).  With two wavelengths the inductance
is based on one eighth of the average circumference, with three
wavelength the length is one twelfth, and so on.  You base inductance
on inter-node distance, it?s really that simple, and of course:
Frequency = (n/2) x ( C/ wire length)

We have found that Medhurst?s is also inter-nodal and therefore
frequency-dependent as well, following the exact same trends as above.
So for a full wave you calculate the Medhurst from one quadrant and
subtract this from capacitance total before splitting the value between
the two voltage nodes.

It seems odd that Medhurst?s would not be cumulative, but if you start
looking at calculations carefully you will see that this must be true
or the coil would be completely swamped with self capacitance and not
function properly at any predicted frequency.  We do not have an exact
value for the Medhurst capacitance with this topology, so for now we go
with the inter-node length and radius and use the cylinder equivalent.

Periodicity implies that each periodic section experiences the same
changes in potential and current. It should not be a big surprise that
the inductance and self capacitance are both inter-nodal.

Some features of our L.C. formulae and correspondence: Our wire length
L.C. formulae are rather simple, it extends the original equations of
Tesla to the general case and reflects the periodicity of standing
waves. You will see that these equations are all consistent with
remarks in the first paragraph above.

(n/2)( C/wire-length) = 1/  2pi sqrt [  ( u x (N/2n)sqrd x Area x
(2n/heith) ) Capacitance ]

Examples: a quarter wave represents one half of a node so n = 1/2.
Plug in this value and the formulae reduces to the old familiar quarter
wave equation where you solve for capacitance and subtract Medhurst?s
to find the top end capacitance. (The old familiar!)

A half wave has two half nodes so n = 1.  Then C/ twice the wire length
= 1 / 2pi sqrt [ (1/2 the length of  the solenoids  L  ) x cap].  So in
a nut shell for a half wave we calculate  C/ twice the solenoids total
wire to find the tank frequency. Then we solve for capacitance total,
from this you subtract the Medhurst value of 1/2 of the solenoid
height. Since we have two voltage nodes we split this top end
capacitance value between both ends (like setting the tension on a rope
by using a split spring on both ends).


With a Marsha configuration you have a split system, so the rules are a
bit different, but not much. Strictly speaking Marsha?s configuration
is a full wave, but it represents a full wave as two disjointed half
waves running anti ?symmetrically. We can describe this system with n =
2 for the wire length frequency but you must consider each coil as its
own L.C. The upshot is that each individual coil from the pair follows
the same math as the half wave where n = 1. So you are really making
two half waves that react and have the equivalence of a full wave where
n = 2.  This sounds a bit like a song and dance, but it?s not, it all
follows directly from the rules. (Think ropes and tension.)

The Levi?s configuration could also be described in a complicated and
consistent fashion as n = 4 but again it is simpler to calculate it as
two individual coils where n = 2. And then simply split the top end
capacitance across the two coils as opposed to within a coil.

It is remarkable how much energy transfers across two part groundless
resonators through free space capacitive coupled displacement currents.

Our extended correspondence model predicts the behavior of new systems
so well that we have yet to build a system that hasn?t worked right the
first time.

  The rope derivations written by Jacob and Daniel Bernoulli are
frighteningly complicated, we got our extended correspondence with
careful substitutions borrowed from mass spring system correspondence
and some careful mapping with a relativistic argument.  These
substitutions all hold true logically, but of course we really need a
complete proof to describe standing wave resonant transformers in the
Maxwell/Heaviside vector calculus form.

One of the interesting features of our model is that it predicts that
the lumped form L.C.  (with math borrowed from mass spring) will
manifest itself at precise locations and at specific frequencies within
an inductor. It would be grand to see this formally resolved.

I don?t want to get into the details of rope resonance, it is something
that really needs to be played with to be understood in any sort of
intuitive way. Also the equations of a standing wave require a bit of
ink to explain.  In shorthand, we send an E.M, wave through a uniformly
distributed medium (the inductor).  If the wavelength is correct it
will form standing waves within the boundaries as the reflected waves
impose on transmitted waves. The Saskia secondary forms standing waves
all by itself without reflection, as transmitted waves are induced by
the primary in both directions (Lenz law), we can make Levi
configurations, but the price to pay is that we can only form resonance
with n = 2, 4 ,6, 8,?..

Send us your address and we will send you one of our prototypes. It was
only made as a proof of concept device, it has tiny wires and a high
frequency, don?t expect big sparks. I hope that it will be helpful to
you, it is a horribly addictive toy, and you will want two large ones
right away. (The inductor cores don?t need a perfect match but make
sure the wire length exactly the same or the Levi configuration just
work right).

A fun variation on the Levi configuration is the "Uncle Stumpy" this is
where you use a single coil with one capacitor and no breakout to drive
a full wave coil with breakouts, you get sparks across the un-driven
coil but not between the coils. We have just scratched the surface of
what is possible, haven?t even looked at the potential for Magnifier
designs.

You can send our cool toy to Paul in Manchester when you are done, some
fun would do him good. We are still going to tell his mom that he
called us names. We would sort of like the coil back by next summer. If
it gets busted somewhere, or you loan it out to someone who loans it
out to?, don?t worry about it.

Enjoy your summer, Larry and Jared.