# Re: AWG WIRE TABLE for Coilers (fwd)

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---------- Forwarded message ----------
Date: Wed, 29 Apr 1998 03:11:12 +0500
From: "Alfred A. Skrocki" <alfred.skrocki-at-cybernetworking-dot-com>
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: AWG WIRE TABLE for Coilers

On Thursday, April 09, 1998 1:38 PM Antonio C. M. de Queiroz
[SMTP:acmq-at-compuland-dot-com.br] wrote;

> About the AWG wire table, some time ago I tried to see what was
> the relation between the AWG gauge and the wire diameter, and found:
>
> diameter in mils=exp(-0.11592*gauge+5.7832)
>
> where exp(x)=e^x=2.71828^x
>
> For 00, 000, and 0000, use -1, -2, and -3.
> This expression is precise for #10 and #30, and gives less than 0.1% of
> error for the other gauges. (A regression algorithm can refine the
> coefficients for better mean precision, if someone want to try).
> Most of the other values of the table can be easily derived from the
> wire diameter, conductivity, and density of the material.

Antonio, I also worked on the relationship between the AWG (B&S) gauge and
wire diameter back around 1991 while working on a program dealing with
wire gauges I analized the relationship between B&S wire gauges and the
wire diameter in inches and arived at an equation to calculate the wire
gauge given the wire diameter, thereby eliminating the need to include the
values in a large data statement area.

Even though it may seem unnecessary to use calculations acurate to 15
decimal places, the fact is that if you were to round off to just 14
decimal places the equation will start to generate noticable errors! As the
equation is it will give answers that perfectly match the official
B&S wire tables as found in the CRC handbook of Chemistry and Physics, the
Machinist's Handbook, and the Radio Amature Handbook by the ARRL.

Given the wire diameter d in inches, the B&S wire gauge = the integer of;

-8.624487202999999 * natural LOG(d / .3245574964)

and if the resultant gauge is less than 1 make gauge = gauge - 1 to correct
for 0 gauges, ie. 0 gauge would be -1, 00 gauge would be -2, ect.

NOTE: even though this equation will give results like 000000 gauge and
larger at one extreme and 60 and smaller at the other, the official AWG
(B&S) wire gauge starts at 00000 and ends with #40 gauge respectively.

Given the AWG (B&S) wire gauge you can calculate the diameter of the wire
in inches;

d = .3245574964 * 2.718281829 ^ (gauge / -8.624487202999999)

(you may notice 2.718281829 is e or the base of natural logarithms) If the
gauge is less than 1 (the 0 gauges) then make gauge = gauge + 1

NOTE: when entering the 0 gauges (0,00,000,ect you would enter a -1, -2, or
-3 respectively.

Then to calculate the various wire values ie. feet per pound, feet per ohm,
fusing current, ect. I use;

turns per inch = 1 / d
diameter in mils m = d * 1000
cross-sectional area in circular mils = m ^ 2
cross-sectional area in sq. inches a = ((d / 2) ^ 2) * 3.141592654
feet per pound = 1 / (a * 3.853790614)
feet per Ohm = a * 122743.6823
fusing current for copper wire = 10244 * d ^ 1.5

Sincerely

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