Re: Breakdown Voltage Gradient and Paschen's Law - Doesn't make sense ?

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Original poster: "davep by way of Terry Fritz <teslalist-at-qwest-dot-net>" <davep-at-quik-dot-com>


>I'm looking at some derivations of Paschen's Law in Lucas'

>High Voltage Engineering Book which states the following:

>**********************
>>Under constant atmospheric conditions, it is found that

>>the breakdown voltage of a uniform field gap may be

>>expressed in the form:

>>V = A*d + B*SQRT(d)       where d is the gap spacing
>>For air under normal conditions:
>>A = 24.4kV/cm
>>B = 6.29kV/cm^1/2

>>It then states that the breakdown voltage gradient is

>>about 30kV/cm in gaps on the order of 1cm
>>and about 6kV/cm for large gaps on the order of several

>>meters
>**********************

>Using the above equation for say 1cm, I do indeed get

>approx. V = 30kV/cm

>However, if I use d = 300cm (3 meters), i get about

>24kV/cm, which is way off from 6kV/cm.
         As Expected, from the notes:


>>It then states that the breakdown voltage gradient is
>>about 30kV/cm in gaps on the order of 1cm
         3 m is different than 1 cm.

>Is there an error in the above equation,

         cf the note

>or am I missing something???
         cf the note.

         Its there for a reason.

         meta:
         There are two sorts of equations encountered
         in engineering.  Some (area of cicrle-pirsquare,
         F=MA, V=IR) are exact over all times and places.
         (OK: Quantum limits will bend F=MA).

         Some are simply useful approximations, applicable
         over DEFINED LIMITS.  (arguably, these should not be
         called 'laws'...  8)>>)  Paschen's _guideline_
         is one of the latter.  Sometimes called 'curve fit',
         in that one plots some data, defines a range, fits
         an some equation to the arbitrarily defined range...
         This can be quite useful over the range, utterly
         pointless outside the range...


         Its roughly analaogus to appealing a parking
         ticket in Moscow, based on the laws of NY City.
         8)>>

         I suspect that the engineering book, if investigated,
         will speculate or define why the change occurs.
         Possibly something to do with free ions from
         corona...  (I have SOME such, but not that one.)
         best
         dwp