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

Thanks for pointing out this measured discrepancy. It

> <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.

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

R = radius, inches

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

radius of the loop, and a the smaller radius of the

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

noticed this let us return to Transtrom's definitions:

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

current had an

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

henry has also been called the quad, or quadrant

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

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

> 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.

>

>

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

Subject: Re: Ball Lightning

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

--- Tesla list <tesla@...> wrote:> Original poster: "Terry Fritz" <twftesla@...>

The idea here of triggering two frequencies does seem

>

> 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....

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

R = radius, inches

N = number of turns

B = coil length, inches

In my calculations in had mistakenly used 19 instead

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