Re: Wire length (fwd)

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Original poster: List moderator <mod1@xxxxxxxxxx>



---------- Forwarded message ----------
Date: Tue, 12 Dec 2006 20:23:29 -0800 (PST)
From: Mike <megavolts61@xxxxxxxxx>
To: Tesla list <tesla@xxxxxxxxxx>
Subject: Re: Wire length (fwd)

Hi Matt,
       I did that derivation and posted it.  I'm not sure if someone else
did as well.  I probably still have that somewhere, but it was on an old
computer, so I'd have to look for back CD's.  I remember I was bored on a
road trip and first crunched it out by 'brute force" on a spreadsheet
before I did the actual calculus derivation(which basically was taking the
derivative of the inductance equation and setting it to zero for the
maximum).  Both derivations I did were based on the Wheeler equation.  
For a given length, the numerator in the Wheeler equation is a constant
(R^2*N^2 = a constant) and can be factored out when taking the first
derivative, so the max inductance is simply the ratio of the denominator
terms.....  9/10 for a solenoid and 8/11 for a flat spiral.
  Mike
   
   
   
  Hi Shaun, Jared, et.al.
 
    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. If it's not
there any longer, I'll be happy to re-post it or send an off-list copy on
request.
    It is also possible to express power input of a coil in "equivalent
standard cartloads of buffalo chips per fortnight" instead of kilowatts,
or the surface area of memory chips can be expressed in nanoacres.  
Again, interesting exercises but it seems no one has recognized their
great theoretical value yet. ;^)
 
Matt D.




 
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