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

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  • harvich
    {Comments follow conclusion} Date: Fri, 11 Jan 2002 13:22:32 -0800 (PST) From: harvey norris Subject: Resonant Rings & CSN Calc.s for
    Message 1 of 1 , Jan 21, 2002
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      {Comments follow conclusion}

      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
      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

      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
      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


      "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) +

      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
      > 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
      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
      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

      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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