## True Meaning of Bifilar/ 2-d Bifilar Calculations

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• Hi all, I just wanted to point out some common misconceptions. Teslas coil for electromagnets patent does not represent bifilar windings. Yes it does store
Message 1 of 14 , Dec 21, 2002
Hi all, I just wanted to point out some common misconceptions.
Teslas "coil for electromagnets" patent does not represent bifilar
windings. Yes it does store more energy between winds, by virtue of
of the wire being adjacent to another wire winding that causes
internal capacitance as 1/2 CV^2.

Tesla notes the following;
Let it be assumed that the terminals of this coil show a potential
difference of one hundred volts, and that there are one thousand
convolutions; then considering
any two contiguous points on adjacent convolutions let it be assumed
that there will exist between them a potential difference of one-
tenth of a volt. If now, as shown in Figure 2, a conductor B be wound
parallel with the conductor A and insulated from it,
and the end of A be connected with the starting pointof B, the
aggregate length of the two conductors being such that the assumed
number of convolutions or turns
is the same, viz., one thousand, then the potential difference
between any two points in A and B will be fifty volts, and as the
capacity effect is proportionate to the square of this difference,
the energy stored in the coil as a whole will now be two hundred and
fifty thousand as great.
(If we use calculus to determine an integration for 1/2CV^2 for
0-1000, one should see more TOTAL Voltage squared between winds for
the TRUE Bifilar example, than the conventional adjacent layering
method that Tesla here employs. However that calculus implies a
smooth curve, when in actuality this would be what is known as an
geometric progression that adds discrete quantities, so below I will
show what that results in using the discrete squares of quantites in
of 1000.)

An inspection of the drawings of this coil at
http://www.keelynet.com/tesla/00512340.htm

clearly shows in figure 2 that the second coil system B enters in the
clockwise fashion identical to coil system A. Nowhere in the patent
is mention made of the use of bifilar coils.
A BIFILAR COIL AS AN EXAMPLE IS WOUND CLOCKWISE FROM THE
OUTSIDE IN. AND THEN FOR THE SECOND LAYER IT IS WOUND CLOCKWISE FROM
THE INSIDE OUT. It is essentially a zig zag layering. ANY multiturn
layered coil will store more energy,( a misnomer), or contain more
internal capacitance as a consequence of it having a higher voltage
between adjacent layers. However we can enhance that effect in one
dimension by employing bifilar layering. The added internal capacity
will reduce the resonant frequency of the coils in comparison.

To make an understanding here, first we must understand what a 1
dimensional bifilar coil consists of. It does not merely consists of
a returned wind adjacent to the first layer, as Tesla's often
noted "Coil for Electromagnets" shows. No where in that patent is the
word "bifilar" used. It is only the further commentators in history
of that patent that consider that method to be a "bifilar" winding.
No it is merely a returned layer winding. Suppose we then have 10
winds in two spirals starting from the outside in. The returned
layer winding method, ( which Tesla shows in that above mentioned
patent) would have all the windings going in one direction as
clockwise from the outside in, with the ordering appearing as
(RETURNED LAYERED SPIRAL WINDING)
1 2 3 4 5
6 7 8 9 10

Now let us compute the internal capacity by (.5) C V^2. Lets us
just call the first portion .5C a constant determined by the
insulation distance and width of the wire, and just be concerned with
the addition of the squared voltages. Technically for a spiral, and
this is where it differs from a solenoid: for the spiral case the
outer windings will have more voltage between the outer winds, then
they will for the inner winds, because the outer winds have a longer
distance between adjacent spots in the layerings on the wire path
itself: therefore with respect to the voltage being imposed on the
spiral itself, a longer wire path between those points implies a
larger voltage between the windings of larger circumference. What
this further implies, is that if we are going to series resonate a
spiral, the way we connect it in the LC series may deliver different
results if the inside winding is in the middle of the LC series, or
if the outside winding is in the middle of the LC , since it is at
the midpoint of the LC resonance that the high voltage rise point
occurs. We might want to make the outside winding connection as the
middle of the LC, since it already has the highest voltage reference
point as voltage between winds, and then suspect that this method
might give a slightly higher resonant rise of voltage, or perhaps
maybe it might actually be lower, only further experimentation will
tell if there is a relationship there. This is only mentioned in
passing, since it is not relevant to what is being discussed here.
Here we will just assume 10 volts imposed on these 10 winds in two
layers of spirals, and also assume no differences in voltage between
layers, which could be approximated to be true if the spiral was a
large diameter with respect to the inner diameter.

For the horizontal voltage differences between winds, each of
these layers would then be 1^2 *4, which for two layers becomes 8.
The vertical layer voltage differences are also constant values of 5
in five repetitons, making the calculation 5^2* 5= 125. Thus we have
a voltage squared internal value of (125 + 8) = 133 for the method
mentioned in Tesla's adjacent layered winding method.

Now let us compare what the bifilar wind method will deliver.
Also realize that bifilar does not imply magnetic cancellation, that
would be a definition of scalar, as it is bandied about. So on the
zig zag layering inherent in a bifilar, the magnetic field from each
layer is in unison, meaning as an example, the first layer might be
wound clockwise from the outside in, and the second layer would also
be wound clockwise, but instead from the inside out.
01 2 3 4 5
10 9 8 7 6
Again we have 8 for the two horizontal layers.
For the vertical now we have (10-1)^2+ (9-2)^2+ (8-3)^2+ (7-4)^2+ (6-
5)^2 =
9^2 + 7^2 + 5^2 + 3^2 + 1^2 = 81 + 49 + 25 + 9 + 1 = 165, and adding
this to the horizontally derived 8, this gives a total of 173
internal squared volts for the bifilar method, compared to 133 for
the adjacent wind method Tesla mentions. 30 % more internal capacity
was made by the bifilar method in this case example.

Now let us look at a real case example of bifilar vs standard
adjacent winds of spirals being stimulated to their resonant
frequencies and being scoped out. The method here was to energize a
unmagnetized ferrite cylinder via series neon discharge from
alternator resonant sources. This causes the ferrite to emit
longitudinal EM, similar to a radio signal, but no specific frequency
itself is being emmited, the process rather causes those adjacent
spirals to ring at their own natural resonant frequencies. The EM
should also be polarized in three dimensions, and in fact, although
this was never tested yet for this specific example, if we turned the
spirals in the direction facing the emmitor, they should also
register a different frequency again as a conventional EM reception!
This was not realized back about a year ago, when these things were
done, because normally we just accept the fact that frequency is just
frequency, but of course here we can see that this is not true for
this emmision case, as both of these recievers are also "recieving"
different frequencies from the same source. Both of these 4 layer
spirals have equal lengths of 50 ft in the 4 layers. However the
effect of "voltage between vertical layers" is very minimized
compared to the voltage between horizontal winds, because the wire
itself is flat braided wire, therefore most of the internal capacity
is between the layers on each spiral , and not between the edges of
the wire on that vertical relationship, which causes these
differences of resonant frequency to be registered in equal lengths
of wire: where the bifilar staggered windings have slightly more
internal capacity, thus a slight reduction in resonant frequency.
(Additionally here is the fact that only one layer between the dual
identically wound speaker wire cables are in the true bifilar
relationship, that is the layer BETWEEN the two dual spirals when one
spiral is placed in an opposite winding relationship to the other.
The windings as no.s connected to numbers was also STAGGERED so that
additionally a higher voltage between all the winding layers was
attained to, but of three of these interlayer winding voltage
differences, only one layer difference was truly bifilar. The purpose
here however was to only note that MORE interwinding voltage
difference COULD reduce the resonant frequency behing measured on
identical wire lengths of spirals. The particular routing method for
the reduced resonant frequency spiral wiould have been noted in that
post. This is when I first got the camera, and the sizing of the
first pictures came out too large, so one may have to scroll things
around to see the entire picture. The scope is set on dual channel
with both spiral sets hooked to separate probes; so that both
resonant frequencies can be seen simultaneously.

http://groups.yahoo.com/group/teslafy/files/Outer%20DSR/Dsc00010.jpg
shows the two 4 layered spiral sets placed on either side of the
ferrite rod. Since we now have a neon in series with the ferrite as
an interphasal pathway, it is easier to understand how the ferrite
can emit EM, since the hf actions of excited plasma are connected in
series. In any case the neon seems to make reading the amperage
consistantly an easier job, which for either component alone becomes
difficult, if not impossible. ( This is now not so certain of a fact,
but it was noted then a year ago). The scope in the background is set
for 50 mv voltage deflection at 1 us/div, or 10 us per screen sweep.
The ordinary return wound coil spiral set has a cycle in ~3 us or
333,000 hz. The bifilar set having a reverse wound dual set spiral,
and employing more interwinding voltage difference by staggered
windings has a reduced frequency of 4 us/cycle or 250,000 hz.

A closer shot of the scoping;
http://groups.yahoo.com/group/teslafy/files/Outer%20DSR/Dsc00011.jpg
The above was from the posting;
Sony Camera trials/ Dual channel scopings of bifilar spirals.
http://groups.yahoo.com/group/teslafy/message/149

Now let us take the example given here where the dual spiral
sets consisted of a total 200 ft of wire and see what the natural
resonant frequency would be by the 1/4 wave calculation. To do this
we consider the 200 ft to be one quarter of the wavelength that the
inductor would resonate to. Again that only strictly applies to a
straight length antenna, what happens is that soon as that length is
put into a coiled form, that changes the resonant frequency to some
degree. Here however the great amount of internal capacitance,
relatively speaking changes it to a great degree... Thus the
wavelength of the frequency would be 800 ft or 800/5280=.1515 mile.
Dividing the quantity by c, the speed of light at 186,000 miles per
second yeilds the time of one cycle or 8.14 * 10^-7 seconds. The
reciprocal of this yeilds the frequency at 1,227,600 hz. Thus this
shows how the wide variance of introduced inductance and internal
capacitance can change the resonant frequency an assembly will
resonate to. The bifilar spiral scopings showed values ~ 5 times
less this frequency, thus we can essentially say that the electrical
impulse was reduced ~5 fold down from that of the speed of light.
It also becomes important in modern days to note that in tesla
coils, the reverse effect also takes place, and we can instead arrive
at a frequency HIGHER than what the quarter wavelength calculation
gives, which may have not been a widely noted fact in Tesla's time.
http://groups.yahoo.com/group/teslafy/message/250
http://www.abelian.demon.co.uk/tssp/misc.html
( This 2nd URL IS A MUST READ FOR RESONANT FREQUENCY CALCULATIONS OF
SINGLE LAYER SOLENOIDS
Now most importantly here, I want to extend the concept of a
dimension, and we can use the same cited example to show even another
increase in internal squared voltage by doing this second dimensional
bifilar example :and some further comments on the three separate
methods to be employed for achieving such a thing. Now resonance
itself implies "equalization", we use equal capacitive and inductive
reactances in series to achieve it. For a 2 dimensional bifilar
coil, we want to make an additional voltage increase on the
horizontal winding numberings, where formerly only 1 volt existed
between those winds. To achieve this we will now use a larger square
coil, also with 5 windings to an edge, or 25 winds total, with 25
volts instead across the entire set of windings, so that the same
circmstance holds, if there were 25 winds in a single layer, we could
still approximate 1 volt between each wind, because now we are using
25 volts in the new case example. The reader might initially be
stumped on how we are going to wind such a creature, where here we
are assuming now that square circumference windings will be employed
to maximize both the differences of voltage in both horizontal and
vertical dimensions: if we wind it horizontally that leaves low
voltages for the spaces between vertical winds, and vice versa, if we
wind it vertically that leaves low voltages between the horizontal
layerings, so what must be done? You guessed it, it will be wound in
a diagonal manner! However there is a little more to this picture
than initially gets realized, we must also make the wind
numberings "resonant" or equalized, and to do this, every numbered
wind must add in a horizontal row to the same total number, and also
every number wind must sum to that same number in all of the vertical
rows! It is what they call a "magic square". This subject gets very
involved, as there are three different types of magic squares, but
here we will be dealing with the first type. Other types may not
employ this diagonal progression as will be seen. One may think this
problem is very simple, for example, taking just the first magic
square of 9 numbers we can draw it out in layered orderings
1 2 3 = 6
4 5 6 = 15
7 8 9 = 24
Transposed vertically in layers we have;
1 4 7 = 12
2 5 8 = 15
3 6 9 = 18
And also with magic squares the additional requirement can be
added that the diagonals also sum to this same number, so here the
diagonals are already correct, and so are the two middle
1 +5 + 9 = 15 : 7 + 5 + 3 = 15,
So out of 8 possible ways to make this 15, four of them are
already in place, but there is a subconscious assumption here that
will prevent you from ever finding that magic square solution, until
you overcome the assumption! Just TRY moving things around to make
everything 15! You may be sorely pressed to find that answer, because
there are 45,360 different unique combinations that can be had for
that array, and only one of them is correct!
So now I will show you "how" that solution is made. We will go
to the next "group 1" magic square of 25 numbers, draw it out, and
then see if you can fathom the three laws of diagonal progression
that are involved. When you recognize those laws that make the
pattern, you can quickly solve the above problem of the first magic
square.
17+24+01+08+15 = 65
23+05+07+14+16 = 65
04+06+13+20+22 = 65
10+12+19+21+03 = 65
11+18+25+02+09 = 65
----------------------
65 65 65 65 65 65
Now let us recall that for the adjacent layer internal voltage
square summation we arrived at 133, for the 1 dimensional bifilar
layering the result was 30% higher at 173.
Let us do the same procedure for the first two layers of the 2-d
bifilar and find the percentage of increase from the one dimensional
bifilar value. This entails making two horizontal calculations, and
one vertical, and then adding these three results. Actually this
would not be a complete analysis for comparisons, since to do that we
should analyse the complete set of 25 winds, both vertically and
horizontally, and here for analysing just the first two layers, for
the purpose of showing this percentage comparison we should revise
things for three layers instead of just two to make that comparison,
so that we have two sets of data for BOTH vertical AND horizontal
voltage measuring differences.
So for the first case then we have
01*02*03*04*05
06*07*08*09*10
11*12*13*14*15
We have formerly obtained 133 in adding two horizontal voltage
squared differences between winds, but only used one vertical voltage
squared differences between layers, so now we will add the extra
vertical squared difference of 5^2*5 =125 to that figure so that we
have equal amounts now of calculated squared voltage differences, two
for the horizontal, and two for the vertical differences, thus they
are equalized as a representation and the new no. of voltage squared
values becomes 258.
For the one dimensional bifilar case;
01*02*03*04*05
10*09*08*07*06
11*12*13*14*15
formerly we had 173 for adding the two horizontal and one vertical
summation, so we need to add one more vertical summation to that case
also, where we find that is also
1^2 +...+ 9^2 = 165: adding this to the former 173 giving a new
value of 338 for the 1-d bifilar made with equalized horizontal and
vertical no samplings. 338/258 =1.31, so in this better
representation for comparisons we can say the first bifilar has 31%
more internal capacity than the adjacent layering method. Now
reposting the 25 magic square for easy recognition to the
calculations;
17+24+01+08+15 = 65
23+05+07+14+16 = 65
04+06+13+20+22 = 65
10+12+19+21+03 = 65
11+18+25+02+09 = 65
1st horiz; (24-17)^2 +(24-1)^2 +(8-1)^2 +(15-8)^2
= 7^2 + 23^2 + 7^2 + 7^2 = 49 + 529 + 49 + 49 = {676}
2nd horiz; (23-5)^2 +(7-5)^2 +(14-7)^2 +(16-14)^2
= 18^2 + 2^2 + 7^2 + 2^2 = 324 + 4 + 49 + 4 = {381}
1st vert across horiz values; (23-17)^2 +(24-5)^2 + (7-1)^2 +(14-8)^2
+ (16-15)^2
= 6^2 + 19^2 + 6^2 + 6^2 +1^2 = 36 + 361 + 36 + 36 + 1 = {470}
{666, my favorite equal numerological combo of three fold nines! =
18, 1+8 =9}
2nd vert across horiz values; (23-4)^2 +(6-5)^2 +(13-7)^2 +(20-14)^2 +
(22-16)^2
= 19^2 + 1^2 + 6^2 + 6^2 + 6^2 = {470}
Also just for the heck of it lets also take a horiz. sampling that is
actually vertical
(24-17)^2 +(23-5)^2 +(6-4)^2 +(12-10)^2 +(18-11)^2
= 7^2 + 18^2 + 2^2 + 2^2 + 7^2 = 49 + 324 + 4 + 4 + 49 = {430}, heh
lets try that again for the next column!
(24-1)^2 +(7-5)^2 +(13-6)^2 +(19-12)^2 +(25-18)^2
= 23^2 + 2^2 + 7^2 + 7^2 + 7^2 = {680}, oh well, I thought we might
find some kind of pattern here, but evidently nothing is there, just
wondering why we got two 470's above....
Huh pretty interesting! Sometimes we find out things about
assumptions that might later be prooved to be false! This is the
first time I have made these calculations, because of all the work of
math involved, but when I began "I assumed" that the vert. and
horizontal samplings should be vitually the same procedure, and then
in this writing I noticed: "Why does the horiz. voltage difference
samplings only contain 4 terms, but the vert.difference samplings
contain 5 of them? Well there are only 4 sets of vert samplings to
be made that way, but there are also 5 sets of horiz. samplings
containing the 4 terms, and in each case THEN they both would add to
20 total samplings of voltage differences if we continued the process
for the whole square. Actually the vert. samplings were made across
the horiz row, but if we started out with the intention of doing the
whole square, we would logically take the vertical samplings across
the vetical column, instead of across the horiz, as was done in this
case. To stick to the original intention here anyways, we can note
then that 676 + 381 + 470 +470 = 1997
1997/338 = 5.908...
Thus by this data then the 1-d bifilar has 31% more internal
capacity as measured by these samplings then does its adjacent
layering method, and further then the 2-d bifilar then has 590% more
internal capacity than its 1-d method!
To make things even more interesting here, I have already scoped out
some time ago the resonant frequency of a bifilar inductor of some 20
by 30 zig zag windings,~ 600 ft of wire length and found that it
slows down the speed of light electrical impulse down to about 13
fold of what a normal solenoidal resonator of the same length of wire
would be. It is ~ 1ft/wind.

Bifilar spiral coil/ longitudinal reception for rf ringdown/ 1 x
probe/ .2 volt/div: 10 us /div
http://groups.yahoo.com/group/teslafy/files/BRS/Dsc00355.jpg

This shows about 2.8 cycles in 100 us, or 1 cycle in 35.7 us, or
28,000 hz. Now lets assume that instead I actually had a 2-d bifilar
coil, with 5.9 times more internal capacity, and then its resonant
frequency might even be further reduced 5.9 times, to about 4745 hz.
Alternators can easily produce 500 hz, so here we might also assume
that this hypothesised 2-d coil would only need to be 10 times as
large, or 10 times the length of wire for us to create the condition
where the generator will send out an electrical impulse that
technically never reaches the end of its wire path, before the
electrical source changes polarity. We would essentially be trapping
electrons in the coil, and it is the electron movement itself that
creates a magnetic field. The generator might act as if it were
driving an open ended coil, and no return current from the coil load
means no lenz law, and no lenz law means minimal work to turn the
field rotor! Then if we wished to make this coil the primary of an
air core transformer, the secondaries could output energy also with
no lenz law effect on the primary, which typically makes a primary
draw more amperage the moment we load down the secondary. IN FACT, we
might even also make this into a longitudinal embodiment on the air
core transformer itself, just as I have done in the jpeg with huge
induction coils as the air core primary, where the secondary coil
being scoped out, is in the wrong angle to recieve flux change from
the magnetic field source. That additionally implies that the primary
would not get "loaded down" from the secondaries amperage draw, and
then the secondaries could be wound orthogonally at right angles over
that special 2-d bifilar primary coil. But to accomplish that we
would need a resonant bifilar arc gapped resonance that puts out high
frequency, and we have negotiated any high frequency out of the
picture here, so that does sound a little unfeasible, so conventional
air core transformation sounds more resonable.
Now lets even go a bit further out there with these things, and
propose how Tesla's propagation of electricity through the earth
itself might occur using these principles.
This takes a little more knowledge about magic squares, because
industry still demands that the consumers pay for their electricity,
and we dont want people just sticking antennaes in the earth and
getting their juice for free. Someone has to pay for the cost of the
coils and generation station, after all! There are three types of
magic squares, the even numbered side squares are probably more
advantageous to use in the first place anyways. So what we do next
is instead of the generation coil having a return path to the
generator, we make that return path the ground of the earth. It aint
gonna get to the generator as a return path anyways, so why not just
use that earth ground instead to pump the free electrons of the earth
ground. Now it aint that hard to explain and show how a magic square
winding of merely 100 winds can have over 10 trillion possible
combinations for it to still be a magic square. The even magic
squares divisible by 4, such as 12, having 144 winds, have a special
option, only half of the pathways need to be switched for it to
convert from an ordinary winding of adjacent layerings, to that of a
magic square winding. This is the advantage of even magic squares,
they can be put together in vastly different ways and still be magic
squares. Now the power company gives the customer a magic square
coil device which is also grounded at one ending. At every switching
junction where the next wind meets its next winding path in the coil
are switching devices like diodes, and where it will go in its next
winding pathway on the coil can be determined by a master
controller. That master controller is the radio signal containing
coded information the power Co sends out, that tells those diodes to
switch on or off on the recieving magic square, to perfectly mimic
how the power station itself is altering those pathways on its own
sending coils into the earth. In one AC cycle, one of those random 10
trillion magic square possible combinations are chosen, and that
information of the correct switching to make on the pathways that
switch to convert it to a magic square on the recieving coil is
transmitted via wireless! How do I think up these science fiction
stories? Maybe I was Tesla in a past life! When this picture was
taken, apparently both us accidently cut ourselves shaving that day
mirror image on the photographs. One has to have an original
photograph of Tesla to see where he did it. I was wondering about all
of this later on, and then I discovered our birthdays were also
mirror image, and we were both 37 when those pics were made. Tesla
was born near midnight, but I was born 55 minutes afternoon. I was
born exactly 12 2/3 years after Tesla died. Numerologically, there
are also seven nines in my name, Harvey D Norris, which is also
Teslas birthday, 7/9/1856, and mine at 9/7/1955, 99 some years
later. I have always thought these things were bizarre, but the
picture takes the cake!
http://groups.yahoo.com/group/teslafy/files/ALT/DSC00062.jpg
Sincerely Harvey D Norris

"I have found that in every coil there exists a certain relation
between its self-induction and capacity that permits a current of
given frequency and potential to pass through it with no other
opposition than that of ohmic resistance, or, in other words, as
though it possessed no self-induction. This is due to the mutual
relations existing between the special character of the current and
the self-induction and capacity of the coil, the latter quantity
being just capable of neutralizing the self-induction for that
frequency. It is well-known that the higher the frequency or
potential difference of the current the smaller the capacity required
to counteract the self-induction; hence, in any coil, however small
the capacity, it may be sufficient for the purpose stated if the
proper conditions in other respects be secured. In the ordinary coils
the difference of potential between adjacent turns or spires is very
small, so that while they are in a sense condensers, they possess but
very small capacity and the relations between the two quantities,
self-induction and capacity, are not such as under any ordinary
conditions satisfy the requirements herein contemplated, because the
capacity relatively to the self-induction is very small. "
"In order to attain my object and to properly increase the
capacity of any given coil, I wind it in such way as to secure a
greater difference of potential between its adjacent turns or
convolutions, and since the energy stored in the coil considering -
the latter as a condenser, is proportionate to the square of the
potential difference between its adjacent convolutions, it is evident
that I may in this way secure by a proper disposition of these
convolutions a greatly increased capacity for a given increase in
potential difference between the turns."
Nikola Tesla on his 1894 patent for internal capacity, COIL FOR
ELECTROMAGNETS
• Hi Harvey, Technically, you are correct. I have seen others point out that Tesla s coil for electromagnets is not a true bifilar over on the pupman list. But
Message 2 of 14 , Dec 21, 2002
Hi Harvey,

Technically, you are correct. I have seen others point out that Tesla's
coil for electromagnets is not a true bifilar over on the pupman list. But
over the years people who studied this patent have come to call it a bifilar
wound coil, and it pretty much has stuck. So perhaps bifilar now has two
meanings? Either that, or someone needs to convince the Tesla community to
use another name.

No matter what we call it, the coil is Tesla's invention and it works quite
well.

Dave

-----Original Message-----
From: Harvey D Norris <harvich@...> [mailto:harvich@...]
Sent: Saturday, December 21, 2002 4:17 PM
To: teslafy@yahoogroups.com
Subject: [teslafy] True Meaning of Bifilar/ 2-d Bifilar Calculations

Hi all, I just wanted to point out some common misconceptions.
Teslas "coil for electromagnets" patent does not represent bifilar
windings. Yes it does store more energy between winds, by virtue of
of the wire being adjacent to another wire winding that causes
internal capacitance as 1/2 CV^2.

Tesla notes the following;
Let it be assumed that the terminals of this coil show a potential
difference of one hundred volts, and that there are one thousand
convolutions; then considering
any two contiguous points on adjacent convolutions let it be assumed
that there will exist between them a potential difference of one-
tenth of a volt. If now, as shown in Figure 2, a conductor B be wound
parallel with the conductor A and insulated from it,
and the end of A be connected with the starting pointof B, the
aggregate length of the two conductors being such that the assumed
number of convolutions or turns
is the same, viz., one thousand, then the potential difference
between any two points in A and B will be fifty volts, and as the
capacity effect is proportionate to the square of this difference,
the energy stored in the coil as a whole will now be two hundred and
fifty thousand as great.
(If we use calculus to determine an integration for 1/2CV^2 for
0-1000, one should see more TOTAL Voltage squared between winds for
the TRUE Bifilar example, than the conventional adjacent layering
method that Tesla here employs. However that calculus implies a
smooth curve, when in actuality this would be what is known as an
geometric progression that adds discrete quantities, so below I will
show what that results in using the discrete squares of quantites in
of 1000.)

An inspection of the drawings of this coil at
http://www.keelynet.com/tesla/00512340.htm

clearly shows in figure 2 that the second coil system B enters in the
clockwise fashion identical to coil system A. Nowhere in the patent
is mention made of the use of bifilar coils.
A BIFILAR COIL AS AN EXAMPLE IS WOUND CLOCKWISE FROM THE
OUTSIDE IN. AND THEN FOR THE SECOND LAYER IT IS WOUND CLOCKWISE FROM
THE INSIDE OUT. It is essentially a zig zag layering. ANY multiturn
layered coil will store more energy,( a misnomer), or contain more
internal capacitance as a consequence of it having a higher voltage
between adjacent layers. However we can enhance that effect in one
dimension by employing bifilar layering. The added internal capacity
will reduce the resonant frequency of the coils in comparison.

To make an understanding here, first we must understand what a 1
dimensional bifilar coil consists of. It does not merely consists of
a returned wind adjacent to the first layer, as Tesla's often
noted "Coil for Electromagnets" shows. No where in that patent is the
word "bifilar" used. It is only the further commentators in history
of that patent that consider that method to be a "bifilar" winding.
No it is merely a returned layer winding. Suppose we then have 10
winds in two spirals starting from the outside in. The returned
layer winding method, ( which Tesla shows in that above mentioned
patent) would have all the windings going in one direction as
clockwise from the outside in, with the ordering appearing as
(RETURNED LAYERED SPIRAL WINDING)
1 2 3 4 5
6 7 8 9 10

Now let us compute the internal capacity by (.5) C V^2. Lets us
just call the first portion .5C a constant determined by the
insulation distance and width of the wire, and just be concerned with
the addition of the squared voltages. Technically for a spiral, and
this is where it differs from a solenoid: for the spiral case the
outer windings will have more voltage between the outer winds, then
they will for the inner winds, because the outer winds have a longer
distance between adjacent spots in the layerings on the wire path
itself: therefore with respect to the voltage being imposed on the
spiral itself, a longer wire path between those points implies a
larger voltage between the windings of larger circumference. What
this further implies, is that if we are going to series resonate a
spiral, the way we connect it in the LC series may deliver different
results if the inside winding is in the middle of the LC series, or
if the outside winding is in the middle of the LC , since it is at
the midpoint of the LC resonance that the high voltage rise point
occurs. We might want to make the outside winding connection as the
middle of the LC, since it already has the highest voltage reference
point as voltage between winds, and then suspect that this method
might give a slightly higher resonant rise of voltage, or perhaps
maybe it might actually be lower, only further experimentation will
tell if there is a relationship there. This is only mentioned in
passing, since it is not relevant to what is being discussed here.
Here we will just assume 10 volts imposed on these 10 winds in two
layers of spirals, and also assume no differences in voltage between
layers, which could be approximated to be true if the spiral was a
large diameter with respect to the inner diameter.

For the horizontal voltage differences between winds, each of
these layers would then be 1^2 *4, which for two layers becomes 8.
The vertical layer voltage differences are also constant values of 5
in five repetitons, making the calculation 5^2* 5= 125. Thus we have
a voltage squared internal value of (125 + 8) = 133 for the method
mentioned in Tesla's adjacent layered winding method.

Now let us compare what the bifilar wind method will deliver.
Also realize that bifilar does not imply magnetic cancellation, that
would be a definition of scalar, as it is bandied about. So on the
zig zag layering inherent in a bifilar, the magnetic field from each
layer is in unison, meaning as an example, the first layer might be
wound clockwise from the outside in, and the second layer would also
be wound clockwise, but instead from the inside out.
01 2 3 4 5
10 9 8 7 6
Again we have 8 for the two horizontal layers.
For the vertical now we have (10-1)^2+ (9-2)^2+ (8-3)^2+ (7-4)^2+ (6-
5)^2 =
9^2 + 7^2 + 5^2 + 3^2 + 1^2 = 81 + 49 + 25 + 9 + 1 = 165, and adding
this to the horizontally derived 8, this gives a total of 173
internal squared volts for the bifilar method, compared to 133 for
the adjacent wind method Tesla mentions. 30 % more internal capacity
was made by the bifilar method in this case example.

Now let us look at a real case example of bifilar vs standard
adjacent winds of spirals being stimulated to their resonant
frequencies and being scoped out. The method here was to energize a
unmagnetized ferrite cylinder via series neon discharge from
alternator resonant sources. This causes the ferrite to emit
longitudinal EM, similar to a radio signal, but no specific frequency
itself is being emmited, the process rather causes those adjacent
spirals to ring at their own natural resonant frequencies. The EM
should also be polarized in three dimensions, and in fact, although
this was never tested yet for this specific example, if we turned the
spirals in the direction facing the emmitor, they should also
register a different frequency again as a conventional EM reception!
This was not realized back about a year ago, when these things were
done, because normally we just accept the fact that frequency is just
frequency, but of course here we can see that this is not true for
this emmision case, as both of these recievers are also "recieving"
different frequencies from the same source. Both of these 4 layer
spirals have equal lengths of 50 ft in the 4 layers. However the
effect of "voltage between vertical layers" is very minimized
compared to the voltage between horizontal winds, because the wire
itself is flat braided wire, therefore most of the internal capacity
is between the layers on each spiral , and not between the edges of
the wire on that vertical relationship, which causes these
differences of resonant frequency to be registered in equal lengths
of wire: where the bifilar staggered windings have slightly more
internal capacity, thus a slight reduction in resonant frequency.
(Additionally here is the fact that only one layer between the dual
identically wound speaker wire cables are in the true bifilar
relationship, that is the layer BETWEEN the two dual spirals when one
spiral is placed in an opposite winding relationship to the other.
The windings as no.s connected to numbers was also STAGGERED so that
additionally a higher voltage between all the winding layers was
attained to, but of three of these interlayer winding voltage
differences, only one layer difference was truly bifilar. The purpose
here however was to only note that MORE interwinding voltage
difference COULD reduce the resonant frequency behing measured on
identical wire lengths of spirals. The particular routing method for
the reduced resonant frequency spiral wiould have been noted in that
post. This is when I first got the camera, and the sizing of the
first pictures came out too large, so one may have to scroll things
around to see the entire picture. The scope is set on dual channel
with both spiral sets hooked to separate probes; so that both
resonant frequencies can be seen simultaneously.

http://groups.yahoo.com/group/teslafy/files/Outer%20DSR/Dsc00010.jpg
shows the two 4 layered spiral sets placed on either side of the
ferrite rod. Since we now have a neon in series with the ferrite as
an interphasal pathway, it is easier to understand how the ferrite
can emit EM, since the hf actions of excited plasma are connected in
series. In any case the neon seems to make reading the amperage
consistantly an easier job, which for either component alone becomes
difficult, if not impossible. ( This is now not so certain of a fact,
but it was noted then a year ago). The scope in the background is set
for 50 mv voltage deflection at 1 us/div, or 10 us per screen sweep.
The ordinary return wound coil spiral set has a cycle in ~3 us or
333,000 hz. The bifilar set having a reverse wound dual set spiral,
and employing more interwinding voltage difference by staggered
windings has a reduced frequency of 4 us/cycle or 250,000 hz.

A closer shot of the scoping;
http://groups.yahoo.com/group/teslafy/files/Outer%20DSR/Dsc00011.jpg
The above was from the posting;
Sony Camera trials/ Dual channel scopings of bifilar spirals.
http://groups.yahoo.com/group/teslafy/message/149

Now let us take the example given here where the dual spiral
sets consisted of a total 200 ft of wire and see what the natural
resonant frequency would be by the 1/4 wave calculation. To do this
we consider the 200 ft to be one quarter of the wavelength that the
inductor would resonate to. Again that only strictly applies to a
straight length antenna, what happens is that soon as that length is
put into a coiled form, that changes the resonant frequency to some
degree. Here however the great amount of internal capacitance,
relatively speaking changes it to a great degree... Thus the
wavelength of the frequency would be 800 ft or 800/5280=.1515 mile.
Dividing the quantity by c, the speed of light at 186,000 miles per
second yeilds the time of one cycle or 8.14 * 10^-7 seconds. The
reciprocal of this yeilds the frequency at 1,227,600 hz. Thus this
shows how the wide variance of introduced inductance and internal
capacitance can change the resonant frequency an assembly will
resonate to. The bifilar spiral scopings showed values ~ 5 times
less this frequency, thus we can essentially say that the electrical
impulse was reduced ~5 fold down from that of the speed of light.
It also becomes important in modern days to note that in tesla
coils, the reverse effect also takes place, and we can instead arrive
at a frequency HIGHER than what the quarter wavelength calculation
gives, which may have not been a widely noted fact in Tesla's time.
http://groups.yahoo.com/group/teslafy/message/250
http://www.abelian.demon.co.uk/tssp/misc.html
( This 2nd URL IS A MUST READ FOR RESONANT FREQUENCY CALCULATIONS OF
SINGLE LAYER SOLENOIDS
Now most importantly here, I want to extend the concept of a
dimension, and we can use the same cited example to show even another
increase in internal squared voltage by doing this second dimensional
bifilar example :and some further comments on the three separate
methods to be employed for achieving such a thing. Now resonance
itself implies "equalization", we use equal capacitive and inductive
reactances in series to achieve it. For a 2 dimensional bifilar
coil, we want to make an additional voltage increase on the
horizontal winding numberings, where formerly only 1 volt existed
between those winds. To achieve this we will now use a larger square
coil, also with 5 windings to an edge, or 25 winds total, with 25
volts instead across the entire set of windings, so that the same
circmstance holds, if there were 25 winds in a single layer, we could
still approximate 1 volt between each wind, because now we are using
25 volts in the new case example. The reader might initially be
stumped on how we are going to wind such a creature, where here we
are assuming now that square circumference windings will be employed
to maximize both the differences of voltage in both horizontal and
vertical dimensions: if we wind it horizontally that leaves low
voltages for the spaces between vertical winds, and vice versa, if we
wind it vertically that leaves low voltages between the horizontal
layerings, so what must be done? You guessed it, it will be wound in
a diagonal manner! However there is a little more to this picture
than initially gets realized, we must also make the wind
numberings "resonant" or equalized, and to do this, every numbered
wind must add in a horizontal row to the same total number, and also
every number wind must sum to that same number in all of the vertical
rows! It is what they call a "magic square". This subject gets very
involved, as there are three different types of magic squares, but
here we will be dealing with the first type. Other types may not
employ this diagonal progression as will be seen. One may think this
problem is very simple, for example, taking just the first magic
square of 9 numbers we can draw it out in layered orderings
1 2 3 = 6
4 5 6 = 15
7 8 9 = 24
Transposed vertically in layers we have;
1 4 7 = 12
2 5 8 = 15
3 6 9 = 18
And also with magic squares the additional requirement can be
added that the diagonals also sum to this same number, so here the
diagonals are already correct, and so are the two middle
1 +5 + 9 = 15 : 7 + 5 + 3 = 15,
So out of 8 possible ways to make this 15, four of them are
already in place, but there is a subconscious assumption here that
will prevent you from ever finding that magic square solution, until
you overcome the assumption! Just TRY moving things around to make
everything 15! You may be sorely pressed to find that answer, because
there are 45,360 different unique combinations that can be had for
that array, and only one of them is correct!
So now I will show you "how" that solution is made. We will go
to the next "group 1" magic square of 25 numbers, draw it out, and
then see if you can fathom the three laws of diagonal progression
that are involved. When you recognize those laws that make the
pattern, you can quickly solve the above problem of the first magic
square.
17+24+01+08+15 = 65
23+05+07+14+16 = 65
04+06+13+20+22 = 65
10+12+19+21+03 = 65
11+18+25+02+09 = 65
----------------------
65 65 65 65 65 65
Now let us recall that for the adjacent layer internal voltage
square summation we arrived at 133, for the 1 dimensional bifilar
layering the result was 30% higher at 173.
Let us do the same procedure for the first two layers of the 2-d
bifilar and find the percentage of increase from the one dimensional
bifilar value. This entails making two horizontal calculations, and
one vertical, and then adding these three results. Actually this
would not be a complete analysis for comparisons, since to do that we
should analyse the complete set of 25 winds, both vertically and
horizontally, and here for analysing just the first two layers, for
the purpose of showing this percentage comparison we should revise
things for three layers instead of just two to make that comparison,
so that we have two sets of data for BOTH vertical AND horizontal
voltage measuring differences.
So for the first case then we have
01*02*03*04*05
06*07*08*09*10
11*12*13*14*15
We have formerly obtained 133 in adding two horizontal voltage
squared differences between winds, but only used one vertical voltage
squared differences between layers, so now we will add the extra
vertical squared difference of 5^2*5 =125 to that figure so that we
have equal amounts now of calculated squared voltage differences, two
for the horizontal, and two for the vertical differences, thus they
are equalized as a representation and the new no. of voltage squared
values becomes 258.
For the one dimensional bifilar case;
01*02*03*04*05
10*09*08*07*06
11*12*13*14*15
formerly we had 173 for adding the two horizontal and one vertical
summation, so we need to add one more vertical summation to that case
also, where we find that is also
1^2 +...+ 9^2 = 165: adding this to the former 173 giving a new
value of 338 for the 1-d bifilar made with equalized horizontal and
vertical no samplings. 338/258 =1.31, so in this better
representation for comparisons we can say the first bifilar has 31%
more internal capacity than the adjacent layering method. Now
reposting the 25 magic square for easy recognition to the
calculations;
17+24+01+08+15 = 65
23+05+07+14+16 = 65
04+06+13+20+22 = 65
10+12+19+21+03 = 65
11+18+25+02+09 = 65
1st horiz; (24-17)^2 +(24-1)^2 +(8-1)^2 +(15-8)^2
= 7^2 + 23^2 + 7^2 + 7^2 = 49 + 529 + 49 + 49 = {676}
2nd horiz; (23-5)^2 +(7-5)^2 +(14-7)^2 +(16-14)^2
= 18^2 + 2^2 + 7^2 + 2^2 = 324 + 4 + 49 + 4 = {381}
1st vert across horiz values; (23-17)^2 +(24-5)^2 + (7-1)^2 +(14-8)^2
+ (16-15)^2
= 6^2 + 19^2 + 6^2 + 6^2 +1^2 = 36 + 361 + 36 + 36 + 1 = {470}
{666, my favorite equal numerological combo of three fold nines! =
18, 1+8 =9}
2nd vert across horiz values; (23-4)^2 +(6-5)^2 +(13-7)^2 +(20-14)^2 +
(22-16)^2
= 19^2 + 1^2 + 6^2 + 6^2 + 6^2 = {470}
Also just for the heck of it lets also take a horiz. sampling that is
actually vertical
(24-17)^2 +(23-5)^2 +(6-4)^2 +(12-10)^2 +(18-11)^2
= 7^2 + 18^2 + 2^2 + 2^2 + 7^2 = 49 + 324 + 4 + 4 + 49 = {430}, heh
lets try that again for the next column!
(24-1)^2 +(7-5)^2 +(13-6)^2 +(19-12)^2 +(25-18)^2
= 23^2 + 2^2 + 7^2 + 7^2 + 7^2 = {680}, oh well, I thought we might
find some kind of pattern here, but evidently nothing is there, just
wondering why we got two 470's above....
Huh pretty interesting! Sometimes we find out things about
assumptions that might later be prooved to be false! This is the
first time I have made these calculations, because of all the work of
math involved, but when I began "I assumed" that the vert. and
horizontal samplings should be vitually the same procedure, and then
in this writing I noticed: "Why does the horiz. voltage difference
samplings only contain 4 terms, but the vert.difference samplings
contain 5 of them? Well there are only 4 sets of vert samplings to
be made that way, but there are also 5 sets of horiz. samplings
containing the 4 terms, and in each case THEN they both would add to
20 total samplings of voltage differences if we continued the process
for the whole square. Actually the vert. samplings were made across
the horiz row, but if we started out with the intention of doing the
whole square, we would logically take the vertical samplings across
the vetical column, instead of across the horiz, as was done in this
case. To stick to the original intention here anyways, we can note
then that 676 + 381 + 470 +470 = 1997
1997/338 = 5.908...
Thus by this data then the 1-d bifilar has 31% more internal
capacity as measured by these samplings then does its adjacent
layering method, and further then the 2-d bifilar then has 590% more
internal capacity than its 1-d method!
To make things even more interesting here, I have already scoped out
some time ago the resonant frequency of a bifilar inductor of some 20
by 30 zig zag windings,~ 600 ft of wire length and found that it
slows down the speed of light electrical impulse down to about 13
fold of what a normal solenoidal resonator of the same length of wire
would be. It is ~ 1ft/wind.

Bifilar spiral coil/ longitudinal reception for rf ringdown/ 1 x
probe/ .2 volt/div: 10 us /div
http://groups.yahoo.com/group/teslafy/files/BRS/Dsc00355.jpg

This shows about 2.8 cycles in 100 us, or 1 cycle in 35.7 us, or
28,000 hz. Now lets assume that instead I actually had a 2-d bifilar
coil, with 5.9 times more internal capacity, and then its resonant
frequency might even be further reduced 5.9 times, to about 4745 hz.
Alternators can easily produce 500 hz, so here we might also assume
that this hypothesised 2-d coil would only need to be 10 times as
large, or 10 times the length of wire for us to create the condition
where the generator will send out an electrical impulse that
technically never reaches the end of its wire path, before the
electrical source changes polarity. We would essentially be trapping
electrons in the coil, and it is the electron movement itself that
creates a magnetic field. The generator might act as if it were
driving an open ended coil, and no return current from the coil load
means no lenz law, and no lenz law means minimal work to turn the
field rotor! Then if we wished to make this coil the primary of an
air core transformer, the secondaries could output energy also with
no lenz law effect on the primary, which typically makes a primary
draw more amperage the moment we load down the secondary. IN FACT, we
might even also make this into a longitudinal embodiment on the air
core transformer itself, just as I have done in the jpeg with huge
induction coils as the air core primary, where the secondary coil
being scoped out, is in the wrong angle to recieve flux change from
the magnetic field source. That additionally implies that the primary
would not get "loaded down" from the secondaries amperage draw, and
then the secondaries could be wound orthogonally at right angles over
that special 2-d bifilar primary coil. But to accomplish that we
would need a resonant bifilar arc gapped resonance that puts out high
frequency, and we have negotiated any high frequency out of the
picture here, so that does sound a little unfeasible, so conventional
air core transformation sounds more resonable.
Now lets even go a bit further out there with these things, and
propose how Tesla's propagation of electricity through the earth
itself might occur using these principles.
This takes a little more knowledge about magic squares, because
industry still demands that the consumers pay for their electricity,
and we dont want people just sticking antennaes in the earth and
getting their juice for free. Someone has to pay for the cost of the
coils and generation station, after all! There are three types of
magic squares, the even numbered side squares are probably more
advantageous to use in the first place anyways. So what we do next
is instead of the generation coil having a return path to the
generator, we make that return path the ground of the earth. It aint
gonna get to the generator as a return path anyways, so why not just
use that earth ground instead to pump the free electrons of the earth
ground. Now it aint that hard to explain and show how a magic square
winding of merely 100 winds can have over 10 trillion possible
combinations for it to still be a magic square. The even magic
squares divisible by 4, such as 12, having 144 winds, have a special
option, only half of the pathways need to be switched for it to
convert from an ordinary winding of adjacent layerings, to that of a
magic square winding. This is the advantage of even magic squares,
they can be put together in vastly different ways and still be magic
squares. Now the power company gives the customer a magic square
coil device which is also grounded at one ending. At every switching
junction where the next wind meets its next winding path in the coil
are switching devices like diodes, and where it will go in its next
winding pathway on the coil can be determined by a master
controller. That master controller is the radio signal containing
coded information the power Co sends out, that tells those diodes to
switch on or off on the recieving magic square, to perfectly mimic
how the power station itself is altering those pathways on its own
sending coils into the earth. In one AC cycle, one of those random 10
trillion magic square possible combinations are chosen, and that
information of the correct switching to make on the pathways that
switch to convert it to a magic square on the recieving coil is
transmitted via wireless! How do I think up these science fiction
stories? Maybe I was Tesla in a past life! When this picture was
taken, apparently both us accidently cut ourselves shaving that day
mirror image on the photographs. One has to have an original
photograph of Tesla to see where he did it. I was wondering about all
of this later on, and then I discovered our birthdays were also
mirror image, and we were both 37 when those pics were made. Tesla
was born near midnight, but I was born 55 minutes afternoon. I was
born exactly 12 2/3 years after Tesla died. Numerologically, there
are also seven nines in my name, Harvey D Norris, which is also
Teslas birthday, 7/9/1856, and mine at 9/7/1955, 99 some years
later. I have always thought these things were bizarre, but the
picture takes the cake!
http://groups.yahoo.com/group/teslafy/files/ALT/DSC00062.jpg
Sincerely Harvey D Norris

"I have found that in every coil there exists a certain relation
between its self-induction and capacity that permits a current of
given frequency and potential to pass through it with no other
opposition than that of ohmic resistance, or, in other words, as
though it possessed no self-induction. This is due to the mutual
relations existing between the special character of the current and
the self-induction and capacity of the coil, the latter quantity
being just capable of neutralizing the self-induction for that
frequency. It is well-known that the higher the frequency or
potential difference of the current the smaller the capacity required
to counteract the self-induction; hence, in any coil, however small
the capacity, it may be sufficient for the purpose stated if the
proper conditions in other respects be secured. In the ordinary coils
the difference of potential between adjacent turns or spires is very
small, so that while they are in a sense condensers, they possess but
very small capacity and the relations between the two quantities,
self-induction and capacity, are not such as under any ordinary
conditions satisfy the requirements herein contemplated, because the
capacity relatively to the self-induction is very small. "
"In order to attain my object and to properly increase the
capacity of any given coil, I wind it in such way as to secure a
greater difference of potential between its adjacent turns or
convolutions, and since the energy stored in the coil considering -
the latter as a condenser, is proportionate to the square of the
potential difference between its adjacent convolutions, it is evident
that I may in this way secure by a proper disposition of these
convolutions a greatly increased capacity for a given increase in
potential difference between the turns."
Nikola Tesla on his 1894 patent for internal capacity, COIL FOR
ELECTROMAGNETS

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• Hi Harvey, Good mornin . I ve been reading and re-reading your post regarding the coils/magic square (for almost a week now) and I must admit I m terribly
Message 3 of 14 , Dec 22, 2002
Hi Harvey,
Thanks for addressing this. If you'd rather save bandwidth in your group you may reply personally if you prefer.                         thanks, Chuck Farrar
----- Original Message -----
Sent: Saturday, December 21, 2002 5:16 PM
Subject: [teslafy] True Meaning of Bifilar/ 2-d Bifilar Calculations

Hi all, I just wanted to point out some common misconceptions.
Teslas "coil for electromagnets" patent does not represent bifilar
windings. Yes it does store more energy between winds, by virtue of
of the wire being adjacent to another wire winding that causes
internal capacitance as 1/2 CV^2.

Tesla notes the following;
Let it be assumed that the terminals of this coil show a potential
difference of one hundred volts, and that there are one thousand
convolutions; then considering
any two contiguous points on adjacent convolutions let it be assumed
that there will exist between them a potential difference of one-
tenth of a volt. If now, as shown in Figure 2, a conductor B be wound
parallel with the conductor A and insulated from it,
and the end of A be connected with the starting pointof B, the
aggregate length of the two conductors being such that the assumed
number of convolutions or turns
is the same, viz., one thousand, then the potential difference
between any two points in A and B will be fifty volts, and as the
capacity effect is proportionate to the square of this difference,
the energy stored in the coil as a whole will now be two hundred and
fifty thousand as great.
(If we use calculus to determine an integration for 1/2CV^2 for
0-1000, one should see more TOTAL Voltage squared between winds for
the TRUE Bifilar example, than the conventional adjacent layering
method that Tesla here employs. However that calculus implies a
smooth curve, when in actuality this would be what is known as an
geometric progression that adds discrete quantities, so below I will
show what that results in using the discrete squares of quantites in
of 1000.)

An inspection of the drawings of this coil at
http://www.keelynet.com/tesla/00512340.htm

clearly shows in figure 2 that the second coil system B enters in the
clockwise fashion identical to coil system A. Nowhere in the patent
is mention made of the use of bifilar coils.
A BIFILAR COIL  AS AN EXAMPLE IS WOUND CLOCKWISE FROM THE
OUTSIDE IN. AND THEN FOR THE SECOND LAYER IT IS WOUND CLOCKWISE FROM
THE INSIDE OUT.  It is essentially a zig zag layering.  ANY multiturn
layered coil will store more energy,( a misnomer), or contain more
internal capacitance as a consequence of it having a higher voltage
between adjacent layers. However we can enhance that effect in one
dimension by employing bifilar layering. The added internal capacity
will reduce the resonant frequency of the coils in comparison.

To make an understanding here, first we must understand what a 1
dimensional bifilar coil consists of. It does not merely consists of
a returned wind adjacent to the first layer, as Tesla's often
noted "Coil for Electromagnets" shows. No where in that patent is the
word "bifilar" used.  It is only the further commentators in history
of that patent that consider that method to be a "bifilar" winding.
No it is merely a returned layer winding.  Suppose we then have 10
winds  in two spirals starting from the outside in.  The returned
layer winding method, ( which Tesla shows in that above mentioned
patent) would have all the windings going in one direction as
clockwise from the outside in, with the ordering appearing as
(RETURNED LAYERED SPIRAL WINDING)
1 2 3 4 5
6 7 8 9 10

Now let us compute the internal capacity by (.5) C V^2. Lets us
just call the first portion .5C a constant determined by the
insulation distance and width of the wire, and just be concerned with
the addition of the squared voltages. Technically for a spiral, and
this is where it differs from a solenoid: for the spiral case the
outer windings will have more voltage between the outer winds, then
they will for the inner winds, because the outer winds have a longer
distance between adjacent spots in the layerings on the wire path
itself: therefore with respect to the voltage being imposed on the
spiral itself, a longer wire path between those points implies a
larger voltage between  the windings of larger circumference. What
this further implies, is that if we are going to series resonate a
spiral, the way we connect it in the LC series may deliver different
results if the inside winding is in the middle of the LC series, or
if the outside winding is in the middle of the LC , since it is at
the midpoint of the LC resonance that the high voltage rise point
occurs.  We might want to make the outside winding connection as the
middle of the LC, since it already has the highest voltage reference
point as voltage between winds, and then suspect that this method
might give a slightly higher resonant rise of voltage, or perhaps
maybe it might actually be lower, only further experimentation will
tell if there is a relationship there.  This is only mentioned in
passing, since it is not relevant to what is being discussed here.
Here we will just assume 10 volts imposed on these 10 winds in two
layers of spirals, and also assume no differences in voltage between
layers, which could be approximated to be true if the spiral was a
large diameter with respect to the inner diameter.

For the horizontal voltage differences between winds, each of
these layers would then be 1^2 *4, which for two layers becomes 8.
The vertical layer voltage differences are also constant values of 5
in five repetitons, making the calculation 5^2* 5= 125. Thus we have
a voltage squared internal value of (125 + 8) = 133 for the method
mentioned in Tesla's adjacent layered winding method.

Now let us compare what the bifilar wind method will deliver.
Also realize that bifilar does not imply magnetic cancellation, that
would be a definition of scalar, as it is bandied about. So on the
zig zag layering inherent in a bifilar, the magnetic field from each
layer is in unison, meaning as an example, the first layer might be
wound clockwise from the outside in, and the second layer would also
be wound clockwise, but instead from the inside out.
01 2 3 4 5
10 9 8 7 6
Again we have 8 for the two horizontal layers.
For the vertical now we have (10-1)^2+ (9-2)^2+ (8-3)^2+ (7-4)^2+ (6-
5)^2 =
9^2 + 7^2 + 5^2 + 3^2 + 1^2 = 81 + 49 + 25 + 9 + 1 = 165, and adding
this to the horizontally derived 8, this gives a total of 173
internal squared volts for the bifilar method, compared to 133 for
the adjacent wind method Tesla mentions.  30 % more internal capacity
was made by the bifilar method in this case example.

Now let us look at a real case example of bifilar vs standard
adjacent winds of spirals being stimulated to their resonant
frequencies and being scoped out. The method here was to energize a
unmagnetized ferrite cylinder via series neon discharge from
alternator  resonant sources. This causes the ferrite to emit
longitudinal EM, similar to a radio signal, but no specific frequency
itself is being emmited, the process rather causes those adjacent
spirals to ring at their own natural resonant frequencies. The EM
should also be polarized in three dimensions, and in fact, although
this was never tested yet for this specific example, if we turned the
spirals in the direction facing the emmitor, they should also
register a different frequency again as a conventional EM reception!
This was not realized back about a year ago, when these things were
done, because normally we just accept the fact that frequency is just
frequency, but of course here we can see that this is not true for
this emmision case, as both of these recievers are also "recieving"
different frequencies from the same source.  Both of these 4 layer
spirals have equal lengths of 50 ft in the 4 layers. However the
effect of "voltage between vertical layers" is very minimized
compared to the voltage between horizontal winds, because the wire
itself is flat braided wire, therefore most of the internal capacity
is between the layers on each spiral , and not between the edges of
the wire on that vertical relationship, which causes these
differences of resonant frequency to be registered in equal lengths
of wire: where the bifilar staggered windings have slightly more
internal capacity, thus a slight reduction in resonant frequency.
(Additionally here is the fact that only one layer between the dual
identically wound speaker wire cables are in the true bifilar
relationship, that is the layer BETWEEN the two dual spirals when one
spiral is placed in an opposite winding relationship to the other.
The windings as no.s connected to numbers was also STAGGERED so that
additionally a higher voltage between all the winding layers was
attained to, but of three of these interlayer winding voltage
differences, only one layer difference was truly bifilar. The purpose
here however was to only note that MORE interwinding voltage
difference COULD reduce the resonant frequency behing measured on
identical wire lengths of spirals. The particular routing method for
the reduced resonant frequency spiral wiould have been noted in that
post. This is when I first got the camera, and the sizing of the
first pictures came out too large, so one may have to scroll things
around to see the entire picture.  The scope is set on dual channel
with both spiral sets hooked to separate probes; so that both
resonant frequencies can be seen simultaneously.

http://groups.yahoo.com/group/teslafy/files/Outer%20DSR/Dsc00010.jpg
shows the two 4 layered spiral sets placed on either side of the
ferrite rod. Since we now have a neon in series with the ferrite as
an interphasal pathway, it is easier to understand how the ferrite
can emit EM, since the hf actions of excited plasma are connected in
series. In any case the neon seems to make reading the amperage
consistantly an easier job, which for either component alone becomes
difficult, if not impossible. ( This is now not so certain of a fact,
but it was noted then a year ago). The scope in the background is set
for 50 mv voltage deflection at 1 us/div, or 10 us per screen sweep.
The ordinary return wound coil spiral set has a cycle in ~3 us or
333,000 hz. The bifilar set having a reverse wound dual set spiral,
and employing more interwinding voltage difference by staggered
windings has a reduced frequency of 4 us/cycle or 250,000 hz.

A closer shot of the scoping;
http://groups.yahoo.com/group/teslafy/files/Outer%20DSR/Dsc00011.jpg
The above was from the posting;
Sony Camera trials/ Dual channel scopings of bifilar spirals.
http://groups.yahoo.com/group/teslafy/message/149

Now let us take the example given here where the dual spiral
sets consisted of a total 200 ft of wire and see what the natural
resonant frequency would be by the 1/4 wave calculation. To do this
we consider the 200 ft to be one quarter of the wavelength that the
inductor would resonate to. Again that only strictly applies to a
straight length antenna, what happens is that soon as that length is
put into a coiled form, that changes the resonant frequency to some
degree. Here however the great amount of internal capacitance,
relatively speaking changes it to a great degree... Thus the
wavelength of the frequency would be 800 ft or 800/5280=.1515 mile.
Dividing the quantity by c, the speed of light at 186,000 miles per
second yeilds the time of one cycle or 8.14 * 10^-7 seconds. The
reciprocal of this yeilds the frequency at 1,227,600 hz. Thus this
shows how the wide variance of introduced inductance and internal
capacitance can change the resonant frequency an assembly will
resonate to. The  bifilar spiral scopings showed values ~ 5 times
less this frequency, thus we can essentially say that the electrical
impulse was reduced ~5 fold down from that of the speed of light.
It also becomes important in modern days to note that in tesla
coils, the reverse effect also takes place, and we can instead arrive
at a frequency HIGHER than what the quarter wavelength calculation
gives, which may have not been a widely noted fact in Tesla's time.
http://groups.yahoo.com/group/teslafy/message/250
http://www.abelian.demon.co.uk/tssp/misc.html
( This 2nd URL IS A MUST READ FOR RESONANT FREQUENCY CALCULATIONS OF
SINGLE LAYER SOLENOIDS
Now most importantly here, I want to extend the concept of a
dimension, and we can use the same cited example to show even another
increase in internal squared voltage by doing this second dimensional
bifilar example :and some further comments on the three separate
methods to be employed for achieving such a thing. Now resonance
itself implies "equalization", we use equal capacitive and inductive
reactances in series to achieve it.  For a 2 dimensional bifilar
coil, we want to make an additional voltage increase on the
horizontal winding numberings, where formerly only 1 volt existed
between those winds.  To achieve this we will now use a larger square
coil, also with 5 windings to an edge, or 25 winds total, with 25
volts instead across the entire set of windings, so that the same
circmstance holds, if there were 25 winds in a single layer, we could
still approximate 1 volt between each wind, because now we are using
25 volts in the new case example. The reader might initially be
stumped on how we are going to wind such a creature, where here we
are assuming now that square circumference windings will be employed
to maximize both the differences of voltage in both horizontal and
vertical dimensions: if we wind it horizontally that leaves low
voltages for the spaces between vertical winds, and vice versa, if we
wind it vertically that leaves low voltages between the horizontal
layerings, so what must be done?  You guessed it, it will be wound in
a diagonal manner!  However there is a little more to this picture
than initially gets realized, we must also make the wind
numberings "resonant" or equalized, and to do this, every numbered
wind must add in a horizontal row to the same total number, and also
every number wind must sum to that same number in all of the vertical
rows!  It is what they call a "magic square".  This subject gets very
involved, as there are three different types of magic squares, but
here we will be dealing with the first type. Other types may not
employ this diagonal progression as will be seen. One may think this
problem is very simple, for example, taking just the first magic
square of 9 numbers we can draw it out in layered orderings
1 2 3 = 6
4 5 6 = 15
7 8 9 = 24
Transposed vertically in layers we have;
1 4 7 = 12
2 5 8 = 15
3 6 9 = 18
And also with magic squares the additional requirement can be
added that the diagonals also sum to this same number, so here the
diagonals are already correct, and so are the two middle
1 +5 + 9 = 15 :  7 + 5 + 3 = 15,
So out of 8 possible ways to make this 15, four of them are
already in place, but there is a subconscious assumption here that
will prevent you from ever finding that magic square solution, until
you overcome the assumption!  Just TRY moving things around to make
everything 15! You may be sorely pressed to find that answer, because
there are  45,360 different unique combinations that can be had for
that array, and only one of them is correct!
So now I will show you "how" that solution is made.  We will go
to the next "group 1" magic square of 25 numbers, draw it out, and
then see if you can fathom the three laws of diagonal progression
that are involved.  When you recognize those laws that make the
pattern, you can quickly solve the above problem of the first magic
square.
17+24+01+08+15 = 65
23+05+07+14+16 = 65
04+06+13+20+22 = 65
10+12+19+21+03 = 65
11+18+25+02+09 = 65
----------------------
65 65 65 65 65 65
Now let us recall that for the adjacent layer internal voltage
square summation we arrived at 133, for the 1 dimensional bifilar
layering the result was 30% higher at 173.
Let us do the same procedure for the first two layers of the 2-d
bifilar and find the percentage of increase from the one dimensional
bifilar value.  This entails making two horizontal calculations, and
one vertical, and then adding these three results. Actually this
would not be a complete analysis for comparisons, since to do that we
should analyse the complete set of 25 winds, both vertically and
horizontally, and here for analysing just the first two layers, for
the purpose of showing this percentage comparison we should revise
things for three layers instead of just two to make that comparison,
so that we have two sets of data for BOTH vertical AND horizontal
voltage measuring differences.
So for the first case then we have
01*02*03*04*05
06*07*08*09*10
11*12*13*14*15
We have formerly obtained 133 in adding two horizontal voltage
squared differences between winds, but only used one vertical voltage
squared differences between layers, so now we will add the extra
vertical squared difference of 5^2*5 =125 to that figure so that we
have equal amounts now of calculated squared voltage differences, two
for the horizontal, and two for the vertical differences, thus they
are equalized as a representation and the new no. of voltage squared
values becomes 258.
For the one dimensional bifilar case;
01*02*03*04*05
10*09*08*07*06
11*12*13*14*15
formerly we had 173 for adding the two horizontal and one vertical
summation, so we need to add one more vertical summation to that case
also, where we find that is also
1^2 +...+ 9^2 = 165:  adding this to the former 173 giving a new
value of 338 for the 1-d bifilar made with equalized horizontal and
vertical no samplings.  338/258 =1.31, so in this better
representation for comparisons we can say the first bifilar has 31%
more internal capacity than the adjacent layering method. Now
reposting the 25 magic square for easy recognition to the
calculations;
17+24+01+08+15 = 65
23+05+07+14+16 = 65
04+06+13+20+22 = 65
10+12+19+21+03 = 65
11+18+25+02+09 = 65
1st horiz; (24-17)^2 +(24-1)^2 +(8-1)^2 +(15-8)^2
= 7^2 + 23^2 + 7^2 + 7^2 = 49 + 529 + 49 + 49 = {676}
2nd horiz; (23-5)^2 +(7-5)^2 +(14-7)^2 +(16-14)^2
= 18^2 + 2^2 + 7^2 + 2^2 = 324 + 4 + 49 + 4 = {381}
1st vert across horiz values; (23-17)^2 +(24-5)^2 + (7-1)^2 +(14-8)^2
+ (16-15)^2
= 6^2 + 19^2 + 6^2 + 6^2 +1^2 = 36 + 361 + 36 + 36 + 1 = {470}
{666, my favorite equal numerological combo of three fold nines! =
18, 1+8 =9}
2nd vert across horiz values; (23-4)^2 +(6-5)^2 +(13-7)^2 +(20-14)^2 +
(22-16)^2
= 19^2 + 1^2 + 6^2 + 6^2 + 6^2 = {470}
Also just for the heck of it lets also take a horiz. sampling that is
actually vertical
(24-17)^2 +(23-5)^2 +(6-4)^2 +(12-10)^2 +(18-11)^2
= 7^2 + 18^2 + 2^2 + 2^2 + 7^2 = 49 + 324 + 4 + 4 + 49 = {430}, heh
lets try that again for the next column!
(24-1)^2 +(7-5)^2 +(13-6)^2 +(19-12)^2 +(25-18)^2
= 23^2 + 2^2 + 7^2 + 7^2 + 7^2 = {680}, oh well,  I thought we might
find some kind of pattern here, but evidently nothing is there, just
wondering why we got two 470's above....
Huh pretty interesting! Sometimes we find out things about
assumptions that might later be prooved to be false!  This is the
first time I have made these calculations, because of all the work of
math involved, but when I began "I assumed" that the vert. and
horizontal samplings should be vitually the same procedure, and then
in this writing I noticed: "Why does the horiz. voltage difference
samplings only contain 4 terms, but the vert.difference samplings
contain 5 of them?  Well there are only 4 sets of vert samplings to
be made that way, but there are also 5 sets of  horiz. samplings
containing the 4 terms, and in each case THEN they both would add to
20 total samplings of voltage differences if we continued the process
for the whole square. Actually the vert. samplings were made across
the horiz row, but if we started out with the intention of doing the
whole square, we would logically take the vertical samplings across
the vetical column, instead of across the horiz, as was done in this
case. To stick to the original intention here anyways, we can note
then that 676 + 381 + 470 +470 = 1997
1997/338 = 5.908...
Thus by this data then the 1-d bifilar has 31% more internal
capacity as measured by these samplings then does its adjacent
layering method, and further then the 2-d bifilar then has 590% more
internal capacity than its 1-d method!
To make things even more interesting here, I have already scoped out
some time ago the resonant frequency of a bifilar inductor of some 20
by 30 zig zag windings,~ 600 ft of wire length and found that it
slows down the speed of light electrical impulse down to about 13
fold of what a normal solenoidal resonator of the same length of wire
would be. It is ~ 1ft/wind.

Bifilar spiral coil/ longitudinal reception for rf ringdown/ 1 x
probe/ .2 volt/div: 10 us /div
http://groups.yahoo.com/group/teslafy/files/BRS/Dsc00355.jpg

This shows about 2.8 cycles in 100 us, or 1 cycle in 35.7 us, or
28,000 hz. Now lets assume that instead I actually had a 2-d bifilar
coil, with 5.9 times more internal capacity, and then its resonant
frequency might even be further reduced 5.9 times, to about 4745 hz.
Alternators can easily produce 500 hz, so here we might also assume
that this hypothesised 2-d coil would only need to be 10 times as
large, or 10 times the length of wire for us to create the condition
where the generator will send out an electrical impulse that
technically never reaches the end of its wire path, before the
electrical source changes polarity. We would essentially be trapping
electrons in the coil, and it is the electron movement itself that
creates a magnetic field. The generator might act as if it were
driving an open ended coil, and no return current from the coil load
means no lenz law, and no lenz law means minimal work to turn the
field rotor! Then if we wished to make this coil the primary of an
air core transformer, the secondaries could output energy also with
no lenz law effect on the primary, which typically makes a primary
draw more amperage the moment we load down the secondary. IN FACT, we
might even also make this into a longitudinal embodiment on the air
core transformer itself, just as I have done in the jpeg with huge
induction coils as the air core primary, where the secondary coil
being scoped out, is in the wrong angle to recieve flux change from
the magnetic field source. That additionally implies that the primary
would not get "loaded down" from the secondaries amperage draw, and
then the secondaries could be wound orthogonally at right angles over
that special 2-d  bifilar primary coil. But to accomplish that we
would need a resonant bifilar arc gapped resonance that puts out high
frequency, and we have negotiated any high frequency out of the
picture here, so that does sound a little unfeasible, so conventional
air core transformation sounds more resonable.
Now lets even go a bit further out there with these things, and
propose how Tesla's propagation of electricity through the earth
itself might occur using these principles.
This takes a little more knowledge about magic squares, because
industry still demands that the consumers pay for their electricity,
and we dont want people  just sticking antennaes in the earth and
getting their juice for free.  Someone has to pay for the cost of the
coils and generation station, after all! There are three types of
magic squares, the even numbered side squares are probably more
advantageous to use in the first place anyways.  So what we do next
is instead of the  generation coil having a return path to the
generator, we make that return path the ground of the earth. It aint
gonna get to the generator as a return path anyways, so why not just
use that earth ground instead to pump the free electrons of the earth
ground.  Now it aint that hard to explain and show how a magic square
winding of merely 100 winds can have over 10 trillion possible
combinations for it to still be a magic square.  The even magic
squares divisible by 4, such as 12, having 144 winds, have a special
option, only half of the pathways need to be switched for it to
convert from an ordinary winding of adjacent layerings, to that of a
magic square winding. This is the advantage of even magic squares,
they can be put together in vastly different ways and still be magic
squares.  Now the power company gives the customer a magic square
coil device which is also grounded at one ending. At every switching
junction where the next wind meets its next winding path in the coil
are switching devices like diodes, and where it will go in its next
winding pathway on the coil can be determined by a master
controller.  That master controller is the radio signal containing
coded information the power Co sends out, that tells those diodes to
switch on or off on the recieving magic square, to perfectly mimic
how the power station itself is altering those pathways on its own
sending coils into the earth. In one AC cycle, one of those random 10
trillion magic square possible combinations are chosen, and that
information of  the correct switching to make on the pathways that
switch to convert it to a magic square on the recieving coil is
transmitted via wireless!  How do I think up these science fiction
stories?  Maybe I was Tesla in a past life! When this picture was
taken, apparently both us accidently cut ourselves shaving that day
mirror image on the photographs. One has to have an original
photograph of Tesla to see where he did it. I was wondering about all
of this later on, and then I discovered our birthdays were also
mirror image, and we were both 37 when those pics were made. Tesla
was born near midnight, but I was born 55 minutes afternoon. I was
born exactly 12 2/3 years after Tesla died. Numerologically, there
are also seven nines in my name, Harvey D Norris, which is also
Teslas birthday, 7/9/1856, and mine at 9/7/1955, 99  some years
later. I have always thought these things were bizarre, but the
picture takes the cake!
http://groups.yahoo.com/group/teslafy/files/ALT/DSC00062.jpg
Sincerely Harvey D Norris

"I have found that in every coil there exists a certain relation
between its self-induction and capacity that permits a current of
given frequency and potential to pass through it with no other
opposition than that of ohmic resistance, or, in other words, as
though it possessed no self-induction. This is due to the mutual
relations existing between the special character of the current and
the self-induction and capacity of the coil, the latter quantity
being just capable of neutralizing the self-induction for that
frequency. It is well-known that the higher the frequency or
potential difference of the current the smaller the capacity required
to counteract the self-induction; hence, in any coil, however small
the capacity, it may be sufficient for the purpose stated if the
proper conditions in other respects be secured. In the ordinary coils
the difference of potential between adjacent turns or spires is very
small, so that while they are in a sense condensers, they possess but
very small capacity and the relations between the two quantities,
self-induction and capacity, are not such as under any ordinary
conditions satisfy the requirements herein contemplated, because the
capacity relatively to the self-induction is very small. "
"In order to attain my object and to properly increase the
capacity of any given coil, I wind it in such way as to secure a
greater difference of potential between its adjacent turns or
convolutions, and since the energy stored in the coil considering -
the latter as a condenser, is proportionate to the square of the
potential difference between its adjacent convolutions, it is evident
that I may in this way secure by a proper disposition of these
convolutions a greatly increased capacity for a given increase in
potential difference between the turns."
Nikola Tesla on his 1894 patent for internal capacity, COIL FOR
ELECTROMAGNETS

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• ... you prefer. No, please respond to the group. I have worked with bifilar coils, both flat and solenoid, and would like to follow this discussion. Dave
Message 4 of 14 , Dec 22, 2002
> If you'd rather save bandwidth in your group you may reply personally if you prefer.

No, please respond to the group.  I have worked with bifilar coils, both flat and solenoid, and would like to follow this discussion.

Dave
• ... There seems to be little advantage to increasing internal capacity in a coil. The decrease in natural resonant frequency also reduces the voltage of the
Message 5 of 14 , Dec 22, 2002
--- Chuck Farrar <psymund@...> wrote:
> Hi Harvey,
> your post regarding the coils/magic square (for
> almost a week now) and I must admit I'm terribly
> confused. I believe I understand what you are
> proposing as an ability to obtain more volts/amps
> from an identical length, but by utilizing geometry,
> gain more in one or both directions above what would
> be normally available.
There seems to be little advantage to increasing
internal capacity in a coil. The decrease in natural
resonant frequency also reduces the voltage of the
resonant waveform, as can be seen in the scope
comparisons, where the lower frequency form is the
bifilar, also with respectively lower voltage on the
scoping. This is why aspects of internal capacity are
not desirable with tesla coils. It reduces the output
voltage to such an extent that secondaries are not
even made with multiturn layer windings because they
are impractical. What this speculation involves is
merely thinking out certain things where we can
IMAGINE what a practical purpose MIGHT become for
employing internal capacity, and certainly it might
only be applicable for things on a very large scale.

I feel I begin to lose the
> picture when we assume that Tesla's flat coil with
> adjacent winding is not bifilar. I realize that
> Webster didn't build any coils and has little or no
> knowledge of the topic but in the dictionary it
> clearly states that "....two filaments wound
> together..." , now because of this we could say his
> pancake coil(s) is wound bifilar or simply return
> path wound. My understanding is that it would be
> bifilar if it wound the length of the core before
> continuing on to the next layer, while being wound
> side-by-side.
Yes an ordinary vertically wound multiturn coil is
also bifilar, because the windings go up to the top of
the layer, and then back down again, these are not
return adjacent layerings, as would be the case if the
next winding was also routed from the bottom winding,
similar to the preceeding layer. Bifilar simply
implies this zig zag method of layering, where no
magnetic cancellation takes place. I cant do much more
to show that the zig zag layering method will deliver
more total "internal voltage squared " values between
windings, than the adjacent wind layering method,
which I would suppose is actually very seldom
employed, simply for the logistics of trying to wind
something that way would be impractical. I can only
cite the simple numbered wind example I have given as
proof of that. The zig zag layering has Non-linear
voltage values between winds, leading to more internal
capacity via the exponential .5CV^2 relationship. The
adjacent layering method preserves a constant voltage
difference between layers, but when we compare the
two, the geometrical progression of added square
voltages for the bifilar case is greater than that
given for constant voltage values.

This implies 2 wires wound side by
> side over a series of wraps of layers. I make this
> distinction only because I have another
> understanding of the pancake coils and their
> inherant gain. As a builder I know that when two
> circles are compared and one is twice the diameter
> of the other, the area of the smaller circle is not
> half of one of twice its diameter but the square
> root of the larger circle. When Tesla used the
> pancake series coil I felt he meant that it obtained
> its exponential gain from the geometry of the circle
> alone. When engaging bifilar winds there is a
> variety of means to attach the ends for voltage
> /amperage gains ie ... parallel ...pp-nn,
> series..p-n,p-n, anti-parallel p-n,n-p
> (magnetic-self-cancelling). I agree that clockwise
> from in to out is right-hand-rule and from inside
> out counterclockwise is no different. It is merely a
> regular coil with winds down to one end (of a core)
> and winds back to return (no break just keep
> winding). I have been working with Doug Konzen on
> his motors for a couple years now and am always
> interested in what you have to say and due to my
> confusion I felt the need to write in hopes of
> clarity? I have read some of Bearden's work and
> although I can't understand half the sh*t he rambles
> about (no insult to Mr. Bearden) I can make sense of
> laymans terms of relaxation times and parallel paths
> (both key in the motors of Doug's to get a higher
> volt AND amp return.
I'm not that familiar with the Konzen motor. I thought
it used rotation based on magnetic repulsion, no?

I have just returned to a spark
> gap for switching instead of mosfets and find the
> anomalous readings are back again. Another question
> I have is how do you re-arrange your coil to get the
> magic square you have to get your numbers in proper
> order ?
This of course presents the monstrosity of that
building problem. Fo the group 1 square cited, if you
follow the numbers in order you should see a diagonal
pattern. When the diagonal leaves the square, it goes
to the opposite side, If it leaves a corner, or finds
another number for the next diagonal winding in its
place, it goes down one level. It should not be
impossible to wind like that, but of course it would
still be difficult. Granted we have to allow for space
in a junction cut in some cases for the next return
wind to go to a "different" winding. Then we have the
wire going at right angles to get to the next winding
layer, in its journey across the square. For the cited
25 square then the first winding goes around till it
almost meets itself, then it makes a right angle turn
to go to the bottom of the square where winding number
2 is located. This wraps around until it meets itself
again, only the next winding move is simpler, it just
continues on the next diagonal layer... and so on,
till the entire square is completed. If you
constructed much larger group 1 magic squares, you
would see how the diagonal pattern begins to start
predominating the square, making most of the windings
to be made easier without all of the changes shown
with smaller ones such as this. Actually it would be
better to route some of the outside non diagonal
changes around the periphery of the square as right
angle turns.

The aspect of the even squares was not dealt with in
the previous article. Let us say that we have such a
square array, BUT it is not wound at all, each of the
loops in the array are just that: only independent
loops of wire, all in parallel loops. 64 independent
winds there. So for a 64 square array we have 64
independent loops. Now what we are going to do is just
completely cut a cross section in those loops, leaving
64 open ends of the loops on each side of the cross
section cut. Each of these endings on both sides go to
what looks like two old fashioned telephone
switchboards. Remember in the old movies what the
telephone switchboard operator does, she takes one
loop ending and connects it to a new loop ending for
the person to recieve the call. Likewise we can take
both of these switchboards and then arrange all of the
loops together so that it makes the pattern of a
return layered winding. Now it is basically just like
Tesla's coil layering idea. This is the uniform
winding state, where at the switchboard each switch
routes over to the next adjacent winding, till we
reach the end of the row, and the next winding switch
starts over at the beginning of the next row. Again
that is not the zig zag pattern of the bifilar method,
it is the return winding layered method. Now suppose
we wish to make this arrangement different so that it
instead is in a magic square state. For the squares
divisible by 4, this can be done in such a way, that
only HALF of all the switches need to changed for the
new arrangement, and there are quite a few
possibilities on how this switching can be made with
the switchings that DO move from their uniform state.
Since we are started from the uniform state, when we
pull one ending out to place it to a new location, for
the simplest case of switching, the new position where
the current goes in its next winding pathway will be
in a symmetry on the square itself, so at the start of
this procudure from a switch made on the upper left
corner, it will go to a new destination point symmetry
wise to a new position on the bottom right corner.
That position will already have a winding in place
from the previous winding uniform state, so we have to
also pull the ending out, for the new ending route to
be placed. What we do with that ending that had to be
removed, is to place it back to where the original
switching ending "used to be" before we pulled it from
its uniform pattern state. Thus the switchings that
occur, occur in symmetry.

Now suppose we wish to employ a different strategy.
For one half of the AC cycle we wish the coil to
conduct in a uniform winding state. For every spot of
the 50% windings that do switch to become magic, we
can then put a forward conducting diode in place. But
we can also put a reverse conducting diode on the same
wire junction that would go to the new winding place
if it were to conduct as a magic square. Now when the
polarity reverses, the former forward conducting
diodes now become blocking diodes, and the reverse
former blocking diodes. It this way we can make the
coil have normal function for 1/2 cycle, and then
magic state for the next half cycle. Provided such a
coil would be of huge size, it might be possible that
the magic state would slow the electrical propagation
of the impulse down so far that the impulse "doesnt
have the time" to reach its destination. In one half
of the cycle we are then allowing that impulse to be
complete, thus essentially supplying the coil with
electron movement, but in the next half cycle that
movement is made with very little input energy, as it
then appears as driving a load with no endings.

This of course is just a theory, nothing more. It will
take vast expenditures to proove such a thing. But I
am only saying that it should be possible, that is
all. I have quite a bit of a lifetime left, and
assurances of future funds to attempt to do such a
vast project in the future. Here I am just trying to
explain the idea of what that project would consist
of.

I understand the need to balance the square
> numerically but how is this accomplished in the coil
> when you only have a limited number of possibilities
> to consider when wrapping the coil ? I again agree
> that the numbers you present appear to be accurate
> (ya right,...like I could tell...*smile* no insult
> intended it's just I couldn't keep you honest if I
> had to ) but I don't seem to be grasping how you
> arrive at the return-wind, vs. bifilar, vs
> anti-parallel, vs regular continuous wrap in down
> the shaft to end-back up again. There is after all
> only so many ways to wrap and almost as few ways to
> connect.
Again I have tried to explain how such switching would
be accomplished, via the idea of a telephone
switchboard. Complex electronics might eventually be
made so that this switching could be incredibly
complex as on each cycle a different magic square
state might be coded into such a switching scheme. As
I have mentioned, there are easily over 10 trillion
switching possibilities for just a 100 square array.

( I did share your fascination with the
> radioshak speaker coils tho, and when I saw them,
> had to run out and buy a half dozen myself, just to
> play with ). Don't feel badly if you presume me to
> be just a bit ignorant ...I am, but I'm working to
> understand and with a bit of help ..... well, we'll
> see. I was terribly caught-up with your mention of
> a signal being trapped in the wire along its path
> and have the input signal change polarities before
> the original signal reached its destination as this
> seems to be along Tesla's idea in his patent for
> method of producing currents of high voltage and
> high pontential...(several patents, 568176,
> 568178,568179, 568180 ) which I believe to be key in
> his search for scalar (or as described by that
> infuriating Webster as scalar- a quantity such as
> mass, length, or speed that is completely measured
> by its magnitude as it has no direction). Tesla
> mentioned that he trapped the electricity in the
> circuit building a potential... your idea to have
> the source change polarities before it actually
> arrived is along those lines, at least in my mind..
Nothing is known on this category, only speculation at
this point in time. As I have indicated it might be
advantageous to have a situation where continuity DOES
exist for half of a cycle. There might be a problem
similar to that of trying to drive a Tesla secondary
at a higher frequency that what the natural resonant
freq of the secondary actually is. In that case we
might reason that we are also trapping electron
movements in a coil, but whats the benefit of it? All
we see is a mistuned coil that makes no effects. We
might need a mechanism to actually impart a complete
charge movement, and then make that charge movement
again occur with a minimal amount of energy
expenditure.
> Thanks for addressing this. If you'd rather save
> you prefer. thanks, Chuck
> Farrar
No thats okay, but its nice to highlight/ edit/ cut
portions of previous entries that are redundant to the
posting.
Sincerely HDN

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• Hi Harvey, The practical application of Tesla s bifilar coils was in increasing the magnetic strength of the coil. Is there a formula for calculating the
Message 6 of 14 , Dec 22, 2002
Hi Harvey,

The practical application of Tesla's "bifilar" coils was in increasing the
magnetic strength of the coil. Is there a formula for calculating the
magnetic strength of a coil? We might learn something from it.

Dave
• ... This is what makes me dubious. Tesla may have already been known as a very relevant inventor in his time, and his claims accepted on face value. No model
Message 7 of 14 , Dec 22, 2002
--- David Thomson <dave@...> wrote:
> Hi Harvey,
>
> The practical application of Tesla's "bifilar" coils
> was in increasing the
> magnetic strength of the coil. Is there a formula
> for calculating the
> magnetic strength of a coil? We might learn
> something from it.
>
> Dave
This is what makes me dubious. Tesla may have already
been known as a very relevant inventor in his time,
and his claims accepted on face value. No model was
presented for this electromagnet patent. For
electromagnet calculations, the primary influences
seems to be the H value; amp turns/inch.(length of
coil) The B term, flux density is simply the amp
turns/ unit area, (2pi r squared), opening of coil.

I think that ratios of B/H have something to do with
this also, but I'm pretty rusty in that magnetics
field. The steel piece to be used as an electromagnet
has a certain maximum value of H, the amp*turms /inch
that can be used before the steel material gets
"saturated", and no further amounts of amp turns will
significantly increase the resultant magnetic field. A
commercial magnet is already designed with a good B/H
ratio inherent in its geometry. If we stack a number
of these magnets together we do not get the same
linear total magnetic field increases proportional to
the additions of the magnets, because now the total
assembly is a different inherent B/H geometry. With an
AC application in transformers a somewhat unexpected
result of saturation is that the windings loose their
impedance down to the level of air core action; but
I'm rusty there too. But in any case I just cant see
how a special increase in magnemotive force, (mmf
determined by amp turns) can be had by Tesla's coil
example. If this were true, we should be able to
measure a difference in inductance for the bifilar vs
returned wind models. For the spirals tested, there
was no difference in inductance measurements between
one or the othher with increased internal capacity. So
I dont see how the windings could be anymore effective
with their use as electromagnets. Many commentators on
this patent have emerged, but no one has actually
commented on the fact as to whether they make a better
electromagnet. This would be a good thing to test for,
as to whether there is anything to the method itself.
I dont see any possible rationalizations for it to be
true however, but of course I could be wrong.
HDN

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• Hi all, Just a note, thanks for the clarification Harvey, and Dave I believe I recall you mentioning that you d like a formula to decipher coil strength ?
Message 8 of 14 , Dec 22, 2002
Hi all,
Just a note,   thanks for the clarification Harvey, and Dave I believe I recall you mentioning that you'd like a formula to decipher coil strength ? This may or may not be of interest to either of you.  www.quickfield.com or http://femm.berlios.de/ are both 2-3d magnetic field mock-ups assuming you have better math skills than I do. They also offer a free downloadable version to experiment with. Best of luck.
One other note along the lines of energizing a coil and trapping potential in it check this url    http://my.voyager.net/~jrrandall/CookCoil.htm
regards, Chuck Farrar

--- David Thomson <dave@...> wrote:
> Hi Harvey,
>
> The practical application of Tesla's "bifilar" coils
> was in increasing the
> magnetic strength of the coil.  Is there a formula
> for calculating the
> magnetic strength of a coil?  We might learn
> something from it.
>
> Dave

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• Hi Harvey, ... Let s see if we can find one. I ll bet my new physics model will handle it. ... I ll get brushed up a bit as we start laying the groundwork.
Message 9 of 14 , Dec 22, 2002
Hi Harvey,

>No model was presented for this electromagnet patent.

Let's see if we can find one. I'll bet my new physics model will handle it.

>I think that ratios of B/H have something to do with
>this also, but I'm pretty rusty in that magnetics field.

I'll get brushed up a bit as we start laying the groundwork.

>But in any case I just cant see how a special increase
>in magnemotive force, (mmf determined by amp turns) can
>be had by Tesla's coil example.

I have a web page up that is quite popular among children's science classes
around the world. It is a simple experiment that demonstrates Tesla's
"bifilar" wound electromagnetic coil.
http://www.tesla-coil-builder.com/bifilar_electromagnet.htm

>If this were true, we should be able to
>measure a difference in inductance for the bifilar vs
>returned wind models.

Maybe we will discover something is wrong with our magnetic model? That's
why I want to look at some equations first.

>For the spirals tested, there
>was no difference in inductance measurements between
>one or the othher with increased internal capacity. So
>I dont see how the windings could be anymore effective
>with their use as electromagnets.

And yet, if you actually build the experiment, you find it is true.

>This would be a good thing to test for,
>as to whether there is anything to the method itself.
>I dont see any possible rationalizations for it to be
>true however, but of course I could be wrong.

Give the experiment a try and report your findings.

Dave
• Hi Chuck, Thanks for posting the link to the Cook patent. I think I ll try building that. It doesn t look very difficult or time consuming. My immediate
Message 10 of 14 , Dec 22, 2002
Hi Chuck,

Thanks for posting the link to the Cook patent.  I think I'll try building that.  It doesn't look very difficult or time consuming.  My immediate thought was the device would benefit by replacing the two separate iron cores with a looped laminated steel transformer core.  This way the magnetic flux would also be in a loop.  Maybe I'll try it with Tesla's improved electromagnet design.  I've got to go look for a transformer I can butcher.

Dave
-----Original Message-----
From: Chuck Farrar [mailto:psymund@...]
Sent: Sunday, December 22, 2002 5:50 PM
To: teslafy@yahoogroups.com
Subject: Re: [teslafy] True Meaning of Bifilar/ 2-d Bifilar Calculations

Hi all,
Just a note,   thanks for the clarification Harvey, and Dave I believe I recall you mentioning that you'd like a formula to decipher coil strength ? This may or may not be of interest to either of you.  www.quickfield.com or http://femm.berlios.de/ are both 2-3d magnetic field mock-ups assuming you have better math skills than I do. They also offer a free downloadable version to experiment with. Best of luck.
One other note along the lines of energizing a coil and trapping potential in it check this url    http://my.voyager.net/~jrrandall/CookCoil.htm
regards, Chuck Farrar

--- David Thomson <dave@...> wrote:
> Hi Harvey,
>
> The practical application of Tesla's "bifilar" coils
> was in increasing the
> magnetic strength of the coil.  Is there a formula
> for calculating the
> magnetic strength of a coil?  We might learn
> something from it.
>
> Dave

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• In a message dated 12/21/2002 4:18:31 PM, harvich@yahoo.com writes:
Message 11 of 14 , Dec 31, 2002
In a message dated 12/21/2002 4:18:31 PM, harvich@... writes:

<< The generator might act as if it were
driving an open ended coil, and no return current from the coil load
means no lenz law, and no lenz law means minimal work to turn the
field rotor! Then if we wished to make this coil the primary of an
air core transformer, the secondaries could output energy also with
no lenz law effect on the primary, which typically makes a primary
draw more amperage the moment we load down the secondary. IN FACT, we
might even also make this into a longitudinal embodiment on the air
core transformer itself, just as I have done in the jpeg with huge
induction coils as the air core primary, where the secondary coil
being scoped out, is in the wrong angle to recieve flux change from
the magnetic field source. That additionally implies that the primary
would not get "loaded down" from the secondaries amperage draw, and
then the secondaries could be wound orthogonally at right angles over
that special 2-d bifilar primary coil. But to accomplish that we
would need a resonant bifilar arc gapped resonance that puts out high
frequency, and we have negotiated any high frequency out of the
picture here, so that does sound a little unfeasible, so conventional
air core transformation sounds more resonable. >>

A most interesting discourse on the bifilar coil. I have read it several
times and still do not follow some of it. I am somewhat of an amature in the
field, however have done some reading about Wardencliff. I have wound a
couple of "bifilar coils" and found them to have electromagnetic properties.
It is my understanding that electromagnets increase in strength relative to
the current in an electromagnetic. As we note from your astute calculations
the capacity in a bifilar coil increases greatly with each wind. If i follow
your reasoning I would suspect that additional increases would occur in a
stack of bifilar coils.
I would request, if you have the time, that you do calculations for the
following example. Suppose we have two 250 foot rolls of #12 wire wound in a
dual spiral. On top of that layer we continue to add additional identical
layers until the height is equal to the diameter of the coils. I estimate it
would take a 3 foot diameter coil to wind two spirals.
288 layers of coils would equal to 3 foot in height. In the Wardencliff
project the primary was connected to a disruptor coil tank circuit on one
end, and if my speculation is correct, the primary was grounded to 16 lake
sized capacitors.
Paul
• ... I would also request that you do the calculations also. They have these things called guardian angels who have aided me against man and his police
Message 12 of 14 , Dec 31, 2002
--- xyme3@... wrote:
> I would request, if you have the time, that you
> do calculations for the
> following example. Suppose we have two 250 foot
> rolls of #12 wire wound in a
> dual spiral. On top of that layer we continue to add
> layers until the height is equal to the diameter of
> the coils. I estimate it
> would take a 3 foot diameter coil to wind two
> spirals.
> 288 layers of coils would equal to 3 foot in height.
I would also request that you do the calculations
also. They have these things called "guardian angels"
who have aided me against "man and his police state."
The police state comes in to rob you of your assetts.
When it is possible for that to happen, get your
calculator out for duty. HDN
> In the Wardencliff
> project the primary was connected to a disruptor
> coil tank circuit on one
> end, and if my speculation is correct, the primary
> was grounded to 16 lake
> sized capacitors.
> Paul
>
>
>

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• ... One can only guess for such a thing. The outside of the spiral windings would have more capacity between them then what the inside winds would have. The
Message 13 of 14 , Jan 1, 2003
--- xyme3@... wrote:
> I would request, if you have the time, that you
> do calculations for the
> following example. Suppose we have two 250 foot
> rolls of #12 wire wound in a
> dual spiral. On top of that layer we continue to add
> layers until the height is equal to the diameter of
> the coils. I estimate it
> would take a 3 foot diameter coil to wind two
> spirals.
> 288 layers of coils would equal to 3 foot in height.
> In the Wardencliff
> project the primary was connected to a disruptor
> coil tank circuit on one
> end, and if my speculation is correct, the primary
> was grounded to 16 lake
> sized capacitors.
> Paul
>
One can only guess for such a thing. The outside of
the spiral windings would have more capacity between
them then what the inside winds would have. The
predominant capacity would be between the layers. At
best we MIGHT find a 13 fold reduction in resonant
freq. So first we take the quarter wavelenght value.
250 ft * 288 layers = 72,000 ft =13.63 miles: this
would be the quarterwavelength, making the entire
wavelength 4 times that value, or 54.54 miles.
Dividing by the speed of light at 186,000 miles/sec
yeilds a cycle time of 2.93 * 10^-4 seconds, where the
inverse of this would be the frequency of 3410 hz. If
this were reduced 13 fold by the internal capacitance,
this would be the very low frequency of 262 hz. This
would qualify as a coil that might "trap" electrons in
the coil when driven at a frequency past that 262 hz.
Nothing is much known on these categories however. The
geometry of the spiral coils themselves,having zig zag
windings, and having the best inner diameter might be
large factors for this theorized resonant frequency
reduction. Undoubtably this is a very large coil.

Sincerely HDN

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• In a message dated 1/1/2003 2:40:16 PM, harvich@yahoo.com writes:
Message 14 of 14 , Jan 4, 2003
In a message dated 1/1/2003 2:40:16 PM, harvich@... writes:

<< This
would qualify as a coil that might "trap" electrons in
the coil when driven at a frequency past that 262 hz. >>

first time I have had time to look at calculations for the Tesla coil
primary. My primary interest is in Tesla turbine and disk generator designs
although particle acceleration is a fascination.