Re: AWG WIRE TABLE for Coilers (fwd)

---------- Forwarded message ----------
Date: Fri, 01 May 1998 14:03:19 -0700
From: Jim Lux <jimlux-at-earthlink-dot-net>
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: AWG WIRE TABLE for Coilers (fwd)

Tesla List wrote:
> ---------- Forwarded message ----------
> Date: Thu, 30 Apr 1998 20:32:50 -0700
> From: "Antonio C. M. de Queiroz" <acmq-at-compuland-dot-com.br>
> To: Tesla List <tesla-at-pupman-dot-com>
> Subject: Re: AWG WIRE TABLE for Coilers (fwd)
> Jim Monte wrote:
> > Using exp(a+b) = exp(a) * exp(b) and
> >       x = exp(ln(x)), x>0,
> > Alfred's formula translates to
> > d = exp(-0.1159489226967782 * gague - 1.125292573941649)   -- in inches
> > d = exp(-0.1159489226967782 * gague + 5.782462705040488)   -- in mils
> >
> > So the two are essentially the same -- it's good to see formulas that
> > agree!  From a computational standpoint, this form is somewhat better
> > than the one Alfred gave since it trades an addition/subtraction for a
> > division.
> Do someone know what is the official formula? and the reason for it?

I suspect the original selection of wire gauges has to do with the 
drawing process, and the amount of reduction that is achievable in one 
step through a die, which is to a large part determined by the 
mechanical properties of the wire. It is interesting, because, the 
ratios of nominal dimensions are not always the same ratio, nor are 
there fixed ratios between the areas.  Looking at my MWS catalog, the 
max and min ranges over the nominal (per ASTM spec) appears to be 1% or 
1 mil, whichever is greater.

>From a 1924 edition of Marks' Handbook, p1685: 
American (or Browne and Sharpe) gage is the standard for copper wire 
used for electrical purposes. The diameters in this system form a 
geometric series in which No 0000 has a diameter of 460 mils and #36 a 
diameter of 5 mils and follows the law d = 324.9/ 1.123^n, where n is 
the gage number and d is the diameter in mils..... Number 10 gage has a 
diameter of .1 inches and a resistance of 1 ohm per 1000 ft.

(of course, the very next page has a table showing that #10 is .9972 
ohms per foot at 20 deg C)

For sheet metal, the gauge has to do with how many square feet of sheet 
you get out of a fixed weight of metal, i.e. it is inversely 
proportional to the thickness. The "standard" weight for the steel is 
480 lb/cu ft.

For shotgun barrels, the gauge is the number of spheres of that size 
that can be cast from a pound of lead, so the diameter goes as the 
inverse cube root (!).

So, the short answer is that it isn't any particular relation, the 
official spec just codifies a 100 yr old manufacturing tradition....

> All these expressions generate some error when compared with the values in
> my table in the Ref. Data for Radio Eng. My expression I obtained from the
> values for #10 and #30. It is precise for these gauges, but disagrees
> slightly (<0.1%) for other gauges.

Given the size tolerance of 1%, a 0.1% error would always be within