# Re: copper magnet wire

Tesla List wrote:
>
> Original Poster: "Bill Noble" <william_b_noble-at-email.msn-dot-com>
>
> yes, it looks like you are right, but I did read somewhere that it is in
> fact the number of wires that fit through a ??? that determines the gauge.
> According to a 1954 reprint of Audel's mathematics and calculations for
> mechanics (that happens to be sitting here),  page 114, in a footnote: "
> note - the sizes of wire are ordinarily expressed by an arbitrary series of
> numbers.  unfortunately there are several independent numbering methods, so
> that it is always necessary to specify the method or wire gauge used."
>
> The table provided above the footnote lists "americal or brown and sharpe",
> Birmingham or stubs, washburn & moen mfg co, worchester mass, Trenton iron
> co, trenton NJ, gwprentiss, holyoke mass, old english from Brass mfrs list,
> and british standard.   I wonder which one we use today?
> your table matches "american".  For 0000 gague, the diameters for the above
> standares are respectively: 0.46000, o.454, 0.393, .400, N/A, N/A, .400.
>
> There is also a table for American gauge, showing that 0000 gauge is equal
> to two 0, four 3 gauge, eight 6, 16 -9, 32 -12, 64 -15, 128 -18 and so on -
> as
> you can see, for every doubling of the number of wires the equivalent gauge
> increases by 3  (like decibels)
>
> I swear I read somewhere, sometime that there was a relationship of the type
> I described, but for now, I can't find it.  maybe someone else on the list
> has the definitive answer?  I even tried my bosh automotive handbook, and it
> doesn't even use wire gauge, it refers to the diameter in mm (so no help
> there for the origin of the measurement).  But I did learn that the word
> gauge comes (according to the OED) from old french with a meaing of
> performing a measurment.

Here's an old posting on the subject of wire sizes and wire numbers.

"From:

SOLENOIDS, ELECTROMAGNETS, and ELECTROMAGNETIC WINDINGS
1914
SECOND EDITION, 1921
Charles N. Underhill
D. VAN NOSTRAND COMPANY
NEW YORK

page 215:  (The rather quaint language is exact quote.)

"109. American Wire Gauge (B.& S.)

This is the standard wire gauge in use in the United

States.  It is based on the geometrical series in which

No. 0000 is 0.46 inch diameter, and No. 36 is 0.005 inch diameter.

Let n = number representing the size of wire.

d = diameter of the wire in inch.

Then log d = 1.5116973 - 0.0503535 n,                     (187)

- 0.4883027 - log d
n = -------------------                               (188)
0.0503535

n may represent half, quarter, or decimal sizes.

If d represent the diameter of the wire in millimeters,

then    log d = 0.9165312 - 0.0503535 n,                   (189)

0.9165312 - log d
and 	n = -----------------                                 (190)
0.0503535

The ratio of diameters is 2.0050 for every six sizes,

while the cross-sections, and consequently the conduc-

tances, vary in the ratio of nearly 2 for every three sizes."

In a reference on the following page these expressions are

attributed to the "Supplement to Transactions of the American

Institute of Electrical Engineers", October, 1893.

As for wire resistance, the resistivity at a constant

temperature can vary by several percent, depending on the purity

of the copper and its mechanical treatment, so the values

for resistance given in the wire tables are approximations.

The resistivity of "pure annealed copper" is given as

1.584 x 10^-6 ohm-cm, while that of "hard-drawn copper" is given

as 1.619 x 10^-6 ohm-cm.

I have no idea of the tolerance on manufactured wire

diameter, but can't imagine it being much better than a percent

for large sizes and worse than that for very small sizes, so the

above formulae have more precision than circumstances warrant.

I, personally, find the standard wire tables quite adequate.

By the way, this book is now available from Lindsay

Publications, and I recommend it to anyone interested in the

design of solenoids or other electromagnets.

The equations above are exact quotes from the original

and may get screwed up in transmission.

These should be easier to send correctly:

n = (-0.4883027 - log d)/0.0503535  (d in inches)  (188)

n = (0.9165312 - log d)/ 0.0503535  (d in mm)      (190)"

Ed