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Re: Arc length vs pwr

At 04:25 AM 10/23/96 +0000, you wrote:
>From cbailey-at-ideanet.doe.state.in.usTue Oct 22 21:43:31 1996
>Date: Tue, 22 Oct 1996 16:11:33 -0400 (EST)
>From: Christopher Bailey <cbailey-at-ideanet.doe.state.in.us>
>To: tesla-at-pupman-dot-com
>Subject: Re: Arc length vs pwr
>
>Hi all,  I have been lurking here for some time time now and I have found
>the discussion fascinating.  The posts about arc length vs power peaked my
>interest, so here's my two cents.
>
>I found (in several volumes) Charles Steinmetz's lectures at the local
>used bookstore.  In volume I, he gives the power consumed by an arc as
>
>p = c * l * sqrt(i) 
>
>(c is an empirical constant, l is length, i is current)
>
>The reasoning is that the current is proportional to the cross-section of
>the arc, while losses due to convection, radiation, etc. are proportional
>to the surface area of the arc.
>
>using the formula 
>
>input power = v^2 * 2 * PI * 60 * c
>
>and some rearranging, the formula is now
>
>l = (a * p^.75) / sqrt(Cs)
>
>p = power, Cs is capacitance (pf)
>
>IF YOU ASSUME CONSTANT CAPACITANCE, the formula matches with an R of
>.99980250 with the data posted by Jack Couture
>
>POWER               INCHES                CALC'd
>500                 11                    11.55
>1000                20                    19.43
>2000                32                    32.68
>5000                64                    64.97
>10000               110                   109.26
>
>using .10926411 for (a/sqrt(Cs))
>
>In light of this I am wondering whether Couture's data was from
>a single coil or coils which were run at various power levels -- instead
>of many different coils at many different power levels.
>
>Factoring in the capacitance means that coils with small secondary
>capacitance would have a somewhat bigger arc length at the same power.
>
>Just my two cents, feel free to disagree, standard disclaimers,
>
>Chris Bailey - cbailey-at-ideanet.doe.state.in.us
>

>Hi Chris -

You have discovered an interesting relationship between the JHCTES program
spark lengths and Steinmetz's equations. However, the relationship is only
coincidental.

I have never seen Steinmetz's equations that you mention above. Also, the
program spark lengths are based on equations I developed several years ago.
I have been told by Tesla List that they are outdated but I do not believe
this is correct. The spark lengths for the program were obtained from data
of coils that coilers had built and tested in past years. The data was from
many coils run at various power levels. This data could not be used directly
but had to be converted into equations that a computer could use and this
was done by math regression methods. I used Quattro and Eureka (Borland) and
other programs to end up with equations to make a graph and a program. The
graph is shown in one of my books and the equations are used in the JHCTES
computer program.

The agreement with the spark lengths, however, is misleading as anyone who
has the JHCTES program knows. The spark lengths in the program for the same
wattage can be changed by several parameters that do not show in the
Steinmetz's equations. The program spark lengths for the same wattage are
different for neon and pole transformers. The program spark lengths for the
same wattage can be increased by increasing the secondary inductance, etc.
Also, the above comparison is only for about 1/6 of the range covered by the
program. There could be big disagreements at other wattages.

Nevertheless, I believe this is an excellent example of how coilers who
build good coils and measure them accurately can help others make
theoretical and empirical equations agree with real world coils. Note that
the equations can be easily changed to agree with new coil data as it is
collected.

Jack C.