Re: Saskia?s toroidal secondary

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

Original poster: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net> 

hi Jared,

It is very kind of you to put this together and offer to send me the
toroidal coil.  I am curious in general about coils and resonances and my
interest has been mostly one of learning more about this area.  I feel you
and Paul and Antonio are both at the Phd level and lot of the discussion is
beyond my MSEE level.  I still find it interesting and I'm able to relate to
enough of the discussion to keep my interest.

I'm not sure I would know what to do with the coil and probably Paul could
make better use of it.  I bet in the end the two of you would find more in
common agreement then not.  Thankyou for thinking of me.

Regards,
Gerry Reynolds

 > 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.
 >
 >