## Tesla List/Resonant Rings & CSN Calc.s for single looped primary.

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• {Comments follow conclusion} Date: Fri, 11 Jan 2002 13:22:32 -0800 (PST) From: harvey norris Subject: Resonant Rings & CSN Calc.s for
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Date: Fri, 11 Jan 2002 13:22:32 -0800 (PST)

From: "harvey norris" <harvich@...>

Subject: Resonant Rings & CSN Calc.s for single looped primary.

To: tesla@...

Found this in Notes, sorry for late reply; harvich

--- Tesla list <tesla@...> wrote:
> Original poster: "by way of Terry Fritz
> <twftesla@...>" <Mddeming@...>
>
> Hi All!
> Grandson #1 wants to reproduce some of
> Tesla's early designs for
> next year's Science Fair. While reading through the
> Tesla Patents on Energy
> Conduction through Rarefied Atmosphere (0.1 atm ~7
> miles), NOT the ionosphere
> (<0.0001 atm ~50 miles), I noticed that he gives
> very specific coil
> dimensions: Primary one Turn Diameter of 8ft (244
> cm) , capacitor 0.04 uf,
> fr=230kHz, V(in)=50KV.
> This seems to be contradictory. Using the flat
> spiral formula (NR)^2/(8R+11B)
> with N=1, R=48" and B=0.25", I get L= ~6 uH for the
> primary. Back-calculating
> from fr=1/(2pi(LC)^0.5) with C=0.04 and fr=230kHz) I
> get L= ~12 uH.
Thanks for pointing out this measured discrepancy. It
may be due to that formula being invalid for a single
turn. CSN of June 7,1899 mentions the inductance of
primary loop used in experimental oscillator on
verticle frame in New York. This is the same 13/16ths
inch diameter cable used in CSN calculations. Using
the equation using respective radii and the natural
log, tesla derives 7.2 uH for the answer for the 8 ft
loop. CSN employed a 50 ft loop, where that formula
using same 13/16 ths diameter cable gives .064 uH.

The Wheeler equation is normally used in coil
design to calculate inductance.
L = R^2*N^2 / (9*R + 10*B) uH
N = number of turns
B = coil length, inches
Thus in your example R^2=48^2=2304 which is the top
term because n squared = 1 The bottom term is
9(48)+10(.25)= 435.4 Making the division yeilds
2304/435.4= 5.3 uH. This is going by a similar formula
and I have also checked your back calculated figure
where 12 uH is obtained, which is correct. So a big
discrepancy does exist. I can only suggest trying to
derive the inductance the way tesla did for a single
loop primary, where only two input parameters are used
instead of 3, where these become A the larger total
actual cable or tubing primary. It is then necessary
to apply the 10^9 conversion factor of cm/henry to
obtain the modern expression of inductance in Heries.
That is because the natural logarithmic derivations
(cited below from CSN)gives such an answer in cm, not
henries.

On the other hand the problem might be addressed by
knowing a simple fact. If the quantity expressed by
wheelers equation are applied for a constant length of
wire, the top quantity NR squared also remains
constant. By knowing this an important axiom can be
developed. Given a specified inductance the remaining
quantities R and B are such that they satisfy a
parametric equation with two unknowns. Or the custom
of supplying a function with y=f(x) can be specified.
The simplest parametric equation is that of a circle
where the radius of the circle being 1, is established
by the equation x^2+y^2=1 If we further place this in
customary form for applying calculus to find
instantaneous rate change made by taking derivatives
we change the formula to y^2= 1 -x^2 further reduced
to y=sq rt{1-x^2} However when we do this, it only
shows the top half of the circle above the x axis, so
the true answer is both positive and negative the
above function. In other words given one quantity as
the parameter, and determining the matching parameter
that will satisfy the equation we do not find unique
answers but dual quantities that can satisfy the
equation. In a likewise analogy to Wheelers equation
the following fact is derived;

Given a coil of specified length of wire,with
identical
spacings between wires to determine B as a parameter
of ht of the coil, the radius of that coil can be
easily calculated to construct an entirely identical
inductance coil, but at a different H/d ratio. Like
the parametric example of two different solutions
presenting themselves for a given parameter input, we
can also conclude that two sets of R,B quantities can
present themselves as a solution, even WITH the
additional requirement of equal spacing between
windings be observed. This has been mathematically
approximated and shown for a single layer coil of
h/d=1.5 will have a ring shaped coil close to pi times
the radius of the first coil as the alternative
solution. However this is pure mathematical
speculation and ignores the Medhurst considerations of
geometry vs internal capacitance which can be viewed
as an exotic tesla coil magnifier system design
possibility expressed as the fact that every secondary
may have another coil of entirely different geometries
that will also respond equally to rf bursts on the
primary. To easily establish this (mathematically
only)we can make R any quantity and compute what the
height of the coil, or the parameter B will have to be
to secure the requirement of making a coil of
identical inductance. This is done by understanding
that since the top term is reduced to a constant with
the same length of wire, this gives the bottom term
the requirement of also becoming a constant value as
determined by its parameters of existing R and B
quantities, to be computed to deliver a constant value
of inductance. Thus given any solenoidal coil with
radius R, B is also a known quantity, and the
denominator 9R+10B becomes the new constant first made
by the existing coil. Thus by the equation 9R+10B=K we
can vary R and find the corresponding B ht that such a
coil would have to have to be identical inductance.
Now each of these linear R&B solutions provide all the
solutions, but those may be all but two that use
identical spacing between wires and also many
different solutions with different spacing between
wires, still delivering identical inductances by
Wheelers equation. In this way a hypothetical primary
of three winds can be made to initally formulate this
constant value. Given the established 48 inch value as
R then yeilds K =48(9)+10(1.25)= 444.5, given three
.25 inch radius winds with the same separation between
windings on a vertical primary. Now the same length of
primary with only two turns would logically then have
50 % more circumference length available for its
turns, and since the circumference length is
proportional to the radius by 2 pi, we can conclude
that the new radius is also expanded by 50% yeilding a
new figure of 48*1.5= 72 for the R quantity in inches.
Next we can then find how far apart those winds will
have to be to achieve indentical inductance by
Wheelers formula. Since K= 444.5, we subtract the 72
to find that 10B will have to be 372.5 to also hold
the denominator constant. This tells us that such a
primary coil would have to have an astounding 37 inch
height to be of equal inductance, using two winds of
equal length instead. The coresponding inductance
would also be decreased by the angle of winding
established as the ratio of 72*2=144 inches where this
actual 2 wind length would be reduced by the amount of
cot 144/37 to satisfy the equation, for a relatively
high slope on the winding. Seeing this, it is easy to
conclude if the same length of primary were only one
winding, the inductance could then never be identical
value for only a single wind, because the
corresponding B value would have to be too High to
make the variables fit. So there is an example of when
the idea is invalid. But of course it should be very
valid for coils of many turns. Their should be a ring
counterpart of identical inductance using the same
length of wire, and same spacing if desired.. I have
constructed such rings of close estimation, and
demonstrated the REVERSE scenario, where the outer
ring picks up energy from the tesla coil placed inside
that ring.

To establish whether this is a mistaken concept let
us explore using a different formula for obtaining the
inductance of a single loop primary. In CSN Tesla
estimates such an inductance knowing only the radius
of the loop and also the radius of the wire. The
following is extracted from H L Transtrom/Turn of
the century definitions for cm's of L and C quantities

http://groups.yahoo.com/group/teslafy/message/14

"Amazingly when Tesla first begins his
experimentation, his
secondary only consists of a conical 14 turns with
average width of
130 ft/turn. From there he rapidly deduces the extra
coil effect:
also properly considered as an autotransformer
application. Tesla
also refers to this inductance as L(s), which brings
some confusion
as what he is refering to in the single loop case must
be L(p) or
primary. In any case the formula he supplies for the
primary is
assumed to be widely used at the time as follows in
CSN; with all {}
as my comments also designated as interior
parentheses. Also in
Tesla's calculation he neglects the last term as
negligible. Having
a man
electrocuted in error of judgement, after noting
Teslas entry. June
7,1899 Approximate estimate of a primary turn to be
used in
experimental station. L(s){?}= 3.14{pi}[ {4A{ln
(8A/a)-2)} + 2a{ln (8A/a)-5/4} - a^2/16A{2 ln(8A/a) +
19}]

Here A radius of circle= 25 ft=300 inch=300
*2.54{cm/in}=762 cm

The smaller a value is likewise calculated from the
radius of a 13/32 inch cable or a =(13/32)*2.54= 1.03
cm. Using these two length figures for the input
parameters the above equation answer using the ln
function ,(log base e is denoted as ln, the calculus
convention for the natural logarithm)also gives the
answer in cm by this equation. Tesla then concludes a
single turn primary where in the notes this is
specified as L(s) then yeilds approximately 63,900
cm.{~.064 mH} Two turns in series should be
approximately 255,600 cm. {This is a nonlinear
relationship between turns no due to mutual
inductance of turns also specified in tesla coil
patent for electromagnets. The conversion factor
explained below gives an anwer reduced 10^9 so the
answer becomes .000255 H =.255mh or 255uH}

The following info gives this conversion factor for cm
vs L value which is 10^9 cm/henry. Thus for one turn
the equation of primary inductance can be solved by
that method if you can supply the a dimension from
your tubing. If you have a calculator that has a log
function, it may also have the Ln function. This is
not the 10 based log, but the natural logarithm based
on e. Then you can punch out the no.s and get a
different inductance figure for your calculations and
then see if there is still a discrepancy.

TRANSTROM'S Definition of
UNIT VALUES Now concerning the use of inductance
defined in terms of
cm , Transtrom also goes into this on pg 80-82. The
inductance of a
circuit is sometimes expressed in centimeters, one of
the cgs units
or absolute units. By definition a circuit has a self
induction of
one henry when it generates a counter emf of one volt
when the
current is varied at a uniform rate of one ampere per
second-- that
is the circuit cuts 10^8 lines per second: so a
circuit of one turn
which has a flux of one Weber (10^8) when one ampere
is flowing
through it, has an inductance of one henry. One volt
then represents
a movement of a single conductor of 100,000 cm per
second across a
unit field (1 line per square cm) In this way the emf
in volts can be
given the dimension of length, namely 10^8 cm. As a
circuit of one
henry inductance generates a counter emf of
1,000,000,000 centimeters
when a change of one ampere, or one tenth unit of
current per second,
it is plain that the counter emf would be ten times as
high, or ten
volts (1,000,000,000 cm) when the rate of current
change per second
is unity (or ten amps per second) Therefore one Henry
of inductance
is given the dimension of 1,000,000,000 cm. In a
circuit of only one
turn the inductance in centimeters can be directly
obtained from the
number of lines enclosed when a current of 10 amperes
is flowing
through the conductor. The Henry was once called the
secohm, because
a circuit having an inductance of one henry would only
permit a rate
of change of one ampere per second when the impressed
emf of one volt, and as the counter emf acted as one
ohm resistance,
we see from this that the inductance can be expresssed
in ohms. The
because in the
metric system a quadrant of the earth from the equator
to the pole
equals approximately 10^9 centimeters. Both terms
mentioned above are
now quite obsolete."

> Obviously, both cannot be right. The illustrations
> in the patent clearly show
> a ~2 turn primary.
> The secondary is also a flat spiral, of 50
> Turns #8 wire. (Tesla
> call this "thin wire") R=47" ,B=47", N=50-->
> Ls=14.68 mH, V(out)= ~2-4 MV.
> The Axes of the coils are horizontal. At this point,
> the equations that I am
> familiar with no longer apply. (e.g., self
> capacitance, etc.) Can any of the
> theoreticians, mathematicians, et. al. help with
> these calculations and
> resolve the apparent discrepancies?
>
> Matt D.
>
>

Date: Fri, 11 Jan 2002 11:24:03 -0800 (PST)

From: "harvey norris" <harvich@...>

Subject: Re: Ball Lightning

To: "Tesla list" <tesla@...>

--- Tesla list <tesla@...> wrote:
> Original poster: "Terry Fritz" <twftesla@...>
>
> Hi Nele,
>
> The Corums and Cabbott Sanders worked with a two
> coil system to try this.
> Cabbott could not reproduce the fireballs
> convincingly. Unfortunately,
> Tesla's notes on this are sketchy and it is not
> clear at all what he was
> doing.
>
> Tesla states that is Colorado Springs system
> produced fireballs in the
> arcs. I am not sure if he thought these as being
> just like those found in
> nature or maybe just similar. If Tesla could make
> such fireballs, the
> methods he used and those for reproducing natural
> ball lightning will have
> to be "rediscovered" since there is not enough
> verifiable information to go
> on from his known notes. However, he seems to have
> been more successful
> that others in getting "close".
>
> Cheers,
>
> Terry
>
>
> At 11:49 AM 1/11/2002 +0100, you wrote:
> >73
> >Hello All!
> >
> >As for the ball lightning: what about the fact that
> Tesla mentioned in
> >his experiments, that he generated sphere lightning
> using just
> >discharging of two diferent frequencies, using the
> high frequency coil
> >to arc to the low frequency coil, the low frequency
> coil would then
> >release it`s energy rapidly, in a burst. He was
> saying also something
> >about discharging the two diferent frequency
> streamers through the
> >larger pipe, and notice little spheres inside as a
> product of a
> >colision.
> >
> >"...it became apparent that the fireballs resulted
> form the interaction
> >of two frequencies, a stray
> > higher frequency wave imposed
> on the lower
> >frequency oscillations of the main circuit....
The idea here of triggering two frequencies does seem
relevent. The first tesla coil I had built many years
ago was based on a mistaken formula for the primary
inductance where;
The Wheeler equation is normally used in coil
design to calculate inductance.
L = R^2*N^2 / (9*R + 10*B) uH
N = number of turns
B = coil length, inches
of 10 for the B constant. This meant that the coil was
not tuned properly, and only several inch arcing
ensued. Now this secondary was actually 1500 ft of
insulated 14 gauge wire. wound on a 20 inch diameter
Sonotube. Each of the 500 ft segments was soldered. It
was noticed however that ~ 1FT WHITE BOLTS WERE
ACCIDENTLY MADE WHEN THE TOP TERMINAL WIRE WAS BROUGHT
INTO THAT VICINITY OF THE FIRST 500 ft solder segment.

What does this indicate? It seems possible that
perhaps the shorter 500 ft of wire may have been more
conducive to vibrate to the (mistuned)primaries. In
any case I dont think a secondary arcing to itself
would be very healthy thing to purposely do. On the
other hand there certainly does seem to be a rationale
for a beneficial aspect of reacting 3 times a source
frequency with itself.

To cite Tesla here from Sept 19, CSN, pg 191 on 6
different magnifier schemes;
In Figures 5 And 6 it is found best to make extra coil
3/4 wave length, and the secondary 1/4 for obvious
reasons.

Now it seems to me that since all the other schemes
show the secondary endings connected to the base of
the extra coil, and that in fact all the extra coils
being employed were in fact INSIDE the larger
secondary, it seems logical that Tesla also tried
schemes where this direct line connection between
coils was not employed, and the cited figures show
that no such connection exists. And then for OBVIOUS
REASONS an outer vibration can excite its first
harmonic, or 3 times the initial frequency.

So if anyone is considering obtaining ball lightning,
perhaps they might try shorting their secondaries at
1/3 the length, and mistuning the coils to begin with!
> > This condition acts as a
> trigger which may cause the
> >total energy of the powerful longer wave
> > to be discharged in a
> infinitesimally small interval
> >of time and the proportionately tremendously
> > great rate of energy movement
> which cannot confine
> >itself to the metal circuit and is released
> > into surrounding space with
> inconceivable violence.
> >
> > It is but a step, from the
> learning how a high
> >frequency current can explosively discharge a lower
> > frequency current, to using the
> principle to design
> >a system in which these explosions can be
> > produced by intent." -N.
> Tesla
> >
> >But he never really explained how he acchieved the
> generation of this
> >phenomenon.
> >
> >Regards,
> >Nele
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