Re: Wire Length (fwd)

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Gerry Reynolds <greynolds@xxxxxxxxxx>



---------- Forwarded message ----------
Date: Sat, 16 Dec 2006 11:04:32 -0700
From: resonance <resonance@xxxxxxxxxxxx>
To: Tesla list <tesla@xxxxxxxxxx>
Subject: Re: Wire Length (fwd)




Yes, but it's not a very practical value for TC work due to flashover 
problems.

I can not recall who did this work at Sandia (Albuquerque), but it was 
published in one of their papers back in the early 70's when they had their 
FRZZ  coil (3 mev) in operation.

 Dr. Resonance


>
> Let me see if I am getting this right.  For any given wire length and 
> number
> of turns-per-inch there is a unique solonoid height-to-diameter ratio at
> which maximum inductance occurs, and this H/D ratio is approximately .9/1.
> Is that correct?
>
> Gary Peterson
>
>
>> Inductance is good and it's usually excepted than max inductance occurs
>> when coil height/dia ratio is 0.9H .  This gives max inductance which
>> provides maximum potential from  Vsec = - L x dI/dt.  A very large, 
>> short,
>> fat, coil.  One reason Tesla used a 52 ft. dia for his Col. Springs
>> magnifier
>> coil.
>>
>> However, this is not the only consideration.  Build a coil this way and 
>> it
>> will always be arcing to the primary!
>>
>> A 4.5 to 6.0 to 1.0 height/dia ratio almost always results in a very
>> smooth
>> running coil.
>>
>> Dr. Resonance
>
>>> From: Mddeming@xxxxxxx
>>>
>>>    IIRC, back in Nov 2002, a paper was posted to the list which showed
>>> that for any given length of wire and turns/inch there is a unique
>>> solenoid and a unique flat spiral which give maximum inductance  for
>>> each configuration.  While it was an interesting mathematical 
>>> derivation,
>>> I'm not sure that anyone ever found it practical for TC  building. . . .
>>>
>>> Matt D.
>
>>>> Most of the coils that my friend Larry and I have built  are multiple
>>>> wavelength. The speed of light and frequency determine the  location
>>>> of voltage and current nodes along the wires  length.
>>>>
>>>> The Neumann equation can be found in many electromagnetic
>>>> textbooks.
>>>>
>>>> L does depend on geometric  considerations and the equation that
>>>> you have shown is correct (in the  abstract).
>>>>
>>>> Visualize a long piece of wire being like a wet  noodle.  We have a
>>>> collection of jars, and when we place the noodle in a  long skinny
>>>> jar it coils up against the walls of the jar giving us a large  number
>>>> of turns (but a low inductance).  Now we take the wire and place it
>>>> in a short jar and it coils up to give us far fewer turns then before.
>>>> But  the inductance is much larger then with the skinny  jar.
>>>>
>>>> L = u (wire length)sqrd / 4pi H
>>>>
>>>> The  wire length remains constant but the Height of the solenoid
>>>> has decreased with the short jar.  Can you now, see why the
>>>> inductance is greater even  though we have less turns?
>>>>
>>>> Now there is a practical matter.  In  real life a short solenoid 
>>>> departs
>>>> significantly from a uniform magnetic  field (a condition of the
>>>> derivation).  So the inductance is not really as  large as the 
>>>> equations
>>>> would suggest.  But is very close to true for long  solenoids where the
>>>> bulk of the magnetic field is uniform.
>>>>
>>>> Sincerely: Jared  Dwarshuis
>
> Original poster: Jared E Dwarshuis <jdwarshui@xxxxxxxxx>
>
> The classic equation for an air cored inductor, derived with Maxwell's
> equations is:
>
> L = u Nsqrd Area / length
>
> However the numerator and denominator can be multiplied by 4pi,
> yielding:
>
> L = u (2pi R N) sqrd / 4pi l
>
> Since: 2pi R N is wire length ,  we can write:
>
> L = u (wire length)sqrd / 4pi l*
>
> I put a star next to the length because solenoids in the real world do
> not have a perfectly uniform magnetic field. We then need to make our
> solenoid length just a little bit longer to get the correct
> inductance.
>
> Now we can talk about standing wave resonance in a Tesla coil.  We
> will use a simple version of capacitance in the lc equation.
>
> We can use a sphere for our top end capacitor. The capacitance of a
> sphere is:
>  c = 4pi e R*
>
> I put a star next to the radius because a Tesla coil inductor has self
> capacitance that must be accounted for. We find that  R, in real life
> is going to be a bit smaller due to the self capacitance of the
> inductor.
>
> Now we examine Tesla's equation:
>
> C/4 Wire length = 1/ 2pi sqrt (lc)
>
> Substituting from above for L and c, we get:
>
> C/4 Wire = C/ Wire'  x  1/2pi  sqrt (l*/R*)
>
> Set:  2pi = sqrt (l*/R*)
>
> Then:
>
> C/ 4 Wire = C/Wire'
>
> Inverting frequency gives us the period:
>
> 4 Wire /C = Wire'/C
>
> A casual inspection shows that this equation can only be satisfied if
> Wire' = 4 Wire
>
> Now we apply the Lorentz equation, as we are observing time dilation
> and distance contraction.
>
> With a Gamma of 4, we predict that the velocity of waves down the
> length of wire in our inductor will measure the sqrt(15/16)C
>
> Thus, the actual wave velocity is reference frame dependant.
>
> Tesla must not have understood all of this (in the late 1880's) or he
> would have found the general form of the equation which describes node
> formation.
>
> n/2  C/w = 1/2pi sqrt ( u  x  (w/2n)sqrd x 2n/ 4pi l* x 4pi e  R*)
>
> Where n = 1/2, 2/2, 3/3...........
>
> The nodality equation also yields a gamma of 4
>
>  Sincerely: Jared Dwarshuis (and by proxy),  Lawrence Morris
>
>
>
>