Re: Quarter Wavelength Frequency

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

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

Mr. Nicholson: Yes we believe that an envelope exists between L.C.
resonance and wire length resonance. When we run our full wave devices
we can only get them to work at the wire length frequency (or
multiples). Changes in top end capacitance do not destroy the
resonance; it appears to be fixed by the primary L.C. and the wire
length of the secondary.

Observing and understanding are different animals.  We suspect that
L.C. resonance requires an interplay of timed events between both the
inductor and the capacitor, where wire length resonance deals with
timed events along just the inductors length itself.

When we ran up the Levi configuration for the first time we got a slow
beat frequency between the two coils (a slow cycling of spark length).
We knew the wire length difference was very small, so we removed wire a
bit at a time from one of the coils and the beat frequency got slower
and slower.  When we had removed about a meter of wire, the beat
frequency disappeared entirely.  Now, subtracting a wind or two of wire
from an inductor with most of a mile of wire on it is a negligible
change in inductance.  And, on the surface it also seems to be a
negligible difference in wire length.  But this difference in wire
length was enough to eliminate the beat frequency.  Making two wires
nearly a mile long to almost exactly the same length is not too
difficult.  But, making two toroidal inductors by hand at different
times and of different gauge core material to exactly the same
inductance is very difficult (read impossible).  It is not possible
that removing two winds from one of the coils would match the
inductance that closely.

Yes the velocity appears to be very close to, if not exactly, the speed
of light. How close? couldn?t say. We have to base our conclusions
mainly on observations and calculations. Our instruments are only good
for two digits, so we have to look at a body of evidence to draw
conclusions. Naturally, all of our work needs confirmation,
re-examination and possible re-working by people with different skill
sets and interpretations than our own.

Mr. Watts I believe my choice of wording may have offended, and I
apologize. And add that we both have an enormous respect for the small
minority of coilers ( maybe a dozen or two active theoretical
experimenters ) such as yourself who have shown a keen interest in
understanding and developing theory.

I believe you were referring indirectly to our ideal resonance
formulae, There?s not much to this formulae, it is merely an extension
of already existing formulae to a general case.   ( a convenient
accounting tool) It is Ideal in the same sense that the classic
inductance formulae was ideal, it assumes a uniform magnetic field
throughout. Our formula also pre supposes that periodicity occurs at
quarter wave intervals, that inductance for purposes of establishing
resonance can be found within these intervals. This formulae
specifically states that it is only applicable to wire length
resonators.

  We use Wheelers formula for all of our primaries, for short inductors
it cannot be beat, but when we go to make a secondary we use the
altered classic form for inductance. The two formulae differ
significantly in the values they predict,  but they are both correct
for the applications intended.

Mr. Epp:  Suppose we make a hypothetical secondary with 1000 turns of
22 gauge around an 8 inch diameter pipe, Medhurst predicts about 11.7
Pf.  Wheelers formula gives .523 Henry while the classic inductance
formula gives .594 Henry, then the self resonant frequency of this coil
would be between 240,000 and 260,000 Hz
But the predicted quarter wave wire length frequency is only 118,000
Hz. The coil operating at 118,000 Hz will have much larger amplitudes
and be easier to tune.

As to the differences between a quarter wave, a half wave, and a full
wave. To simplify I will only consider the case where they are all wire
length dependent.

So I make the coil described above and resonate it at 118,000 Hz.
After a while, I get bored and decide I want to make a half wave.  Here
is what to do: make an extra coil exactly the same, remove the old
ground and solder the two coils together. Slap the same primary on as
before, centering it between the two coils. Remove the top end
capacitor and replace it with a capacitor that has ? of the capacitance
and stick another ? capacitor on the other end of the coil. Now you
have a half wave, but you can run it with one breakout or two.  It
looks like a quarter wave with just one breakout as the entire arc will
appear on the end with the breaker (assuming your radius is large
enough to suppress an arc without a breakout).  If you put the caps
close together you get a nice clean arc between them. Now mind you we
could also make a grounded half wave, but there would be no advantage.

    So I get bored again and I want a ? wave; no problem.  Make another
coil, stack it on top, put the quarter wave capacitor back on top.  Put
the primary on the bottom and ground it like a quarter wave.

This time I want a full wave.  We have some choice here. We could place
4 inductors in line and ground both ends then place the ? capacitors at
the ? and ? points.  We could also assemble a pair of ? waves,
described above, and drive just one of the pair and get a capacitor
coupled anti- symmetric mode arrangement (Marsha configuration).   We
can arrange one breakout or two between the coils.  Amazingly, we can
even take two Saskia coils, power just one of the coils, place just one
? capacitor on each coil and we will have satisfied the capacitance
requirements (Levi configuration). But you can see this is very much
like 8 quarter waves ( two sets of 4 quarter waves driven anti-
symmetric), where we drive just one pair and the rest go along for the
ride.

The role of Medhurst is not a cumulative one.  We calculated it, once
and only once, for a quarter-wave section, as it also follows the
trends of periodicity.

All of this is like rope resonance.  Once you find the driving
frequency and tension to get one anti-node (the bump part) you can
simply add more sections of the same length rope and get more
anti-nodes.  You don?t change the frequency, and you don?t change the
tension.                                                      ( see our
derivation of correspondence)

Good luck and don?t get hurt.