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Re: Using skin effect (are our conductors to heavy?)
Subject: Re: Using skin effect (are our conductors to heavy?)
Date: Mon, 05 May 1997 15:17:57 -0500
From: David Huffman <huffman-at-FNAL.GOV>
To: Tesla List <tesla-at-pupman-dot-com>
----------
>
> >
> > On Mon, 28 Apr 1997 20:18:06 -0700 Bert Hickman
> > <bert.hickman-at-aquila-dot-com> wrote;
> >
> > > All,
> > >
> > > Alas, the perils of an early morning post! The above gives the
factor
> > > (x) of AC resistance divided by DC resistance, not skin depth!
Sorry
> > > 'bout that!
> > >
> > > Skin depth = 1/SQRT(Pi*f*Uo*a) for a cylindrical conductor
(meters)
> > > where f = Hertz
> > > Uo = 4*pi*10-7 Henry/meter
> > > a = 5.80x10^7 mho/m (conductivity of copper)
> > > = 6.17x10^7 mho/m (conductivity of silver)
> > >
> > > Copper skin depth = 66.1/SQRT(f) millimeters
> > > = 2602/SQRT(f) mils
> > >
> > > Silver skin depth = 64.1/SQRT(f) millimeters
> > > = 2523/SQRT(f) mils
> > >
> > > Comparing skin depths (in mils = 0.001") of the two metals at
various
> > > frequencies:
> > > Skin Depth (mils)
> > > f Silver Copper
> > > ====== ====== ======
> > > 10 kHz 25.2 26.0
> > > 50 kHz 11.3 11.6
> > > 75 kHz 9.2 9.5
> > > 100 kHz 8.0 8.2
> > > 200 kHz 5.6 5.8
> > > 300 kHz 4.6 4.8
> > > 400 kHz 4.0 4.1
> > > 500 kHz 3.6 3.7
> > > 750 kHz 2.9 3.0
> > > 1000 kHz 2.5 2.6
> > >
> > > As can be seen, copper tubing is very hard to beat! At typical
Tesla
> > > Coil frequencies, smooth copper tubing is almost as good as it
gets!
> > > Only pure silver or relatively thick silver plating can beat
it.
> >
> > Interesting equation Bert, where did you get it from?
_/
>
> Alfred and all,
>
> This particular form, for a good cylindrical conductor, came from
> "Engineering Electromagnetics, 2nd ed." by William H. Hayt, Jr.,
> McGraw-Hill Book Co., 1967, page 344. This is the result of taking
the
> more complex equations for potential and current density (presented
> earlier in the chapter), and solving for the depth at which the
current
> decreases to 1/e or 37% of the value seen at the outer surface of
the
> conductor. The only thing I've changed are the units to go to CGS
or
> English equivalents.
>
> Skin depth REALLY means that the average power loss in a conductor
with
> skin effect is exactly the same as that if the total current flow
was
> uniformly flowing through a tube whose wall thickness was exactly
one
> skin depth.
>
Hi Bert,
The first time I heard that at 60Hz the skin depth was 1/3" I was
amazed. Also the current vector you mentioned in a previous post is
most interesting. I can imagine a current curving into and out of a
conductor which is thicker that necessary.
Holey conductive phase shift Batman!
Dave Huffman
> Even at relatively low frequencies skin effect can still be
significant.
> For example, skin depth at 60 Hz for copper is about 8.53mm, or
about
> 1/3 of an inch. A 4" x 2" high-current busbar in a power plant can
be
> made tubular, with only 1/2" wall thickness, and will still be
virtually
> as effective as a solid conductor.
>
> -- Bert --
>