Hacking the AWG WIRE TABLE (fwd)

---------- Forwarded message ----------
Date: Mon, 4 May 1998 15:21:25 -0400
From: Thomas McGahee <tom_mcgahee-at-sigmais-dot-com>
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Hacking the AWG WIRE TABLE

> ---------- Forwarded message ----------
> Date: Sun, 3 May 1998 17:56:01 -0700 (PDT)
> From: "Edward V. Phillips" <ed-at-alumni.caltech.edu>
> To: tesla-at-pupman-dot-com
> Subject: Re: AWG WIRE TABLE for Coilers (fwd)
> 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

Thanks for posting the interesting info about the official
definitions for AWG/B&S wire sizes.

Coilers may note that in the table that I posted to the 
Tesla List the diameter for #0000 is 459.99 mils, and #36 is
5.0000 mils. This corresponds almost exactly to the info in
the above article. 

Some of the more inquisitive among you may be interested in
knowing something about the method that I used to generate
such an accurate table. After all, I did not know any of the
gory details that Ed has revealed to us in his post. So
how did I go about hacking the AWG wire table? It was easy,
and did not involve any hairy math. Just simple common sense.

I had accumulated an assortment of wire tables, but it was
frustrating to discover that most of them did not agree
with one another! The one that I had the most confidence in was
the one in the Machinery's Handbook, 21st Edition. I am not
all that keen on entering lists of data, so I looked to see
if I could find a relationship between adjacent wire sizes
and their diameters. 

I found that the wire sizes and their diameters were related 
in the following manner:
If you took the ratio of diameters between any two adjacent
wire sizes, the ratio was constant. 


I then wrote a simple program that began by taking the 
diameters of wire sizes #0000 and #000 as the starting point
for finding the EXACT ratio.

I decided that I would use #50's diameter of .00099
as a "checkpoint".

The program would begin with .4600 and .4096 to give it a
starting ratio, and would then use this ratio to generate the
following diameters. When it got to size 50 it would determine
if the ratio it was using was generating an answer that was
too large or too small. It then used this information to
generate a new ratio. The new ratio was tested in the same
manner, and, after several iterations, #50 was coming up
.00099 on the nose. The ratio had been determined by the 
program to be 1.1229319 

The program actually determined the value to more decimal
places than shown, but what is shown is all that is needed
to generate a table with five significant digits.

[I detest using a number like 1.23456789123456789
when 1.2345 +/- 1 is what you really need. For the task at
hand it was determined that an 8 digit value would generate
answers that would match those in the Machinery's

The algorithm for generating the current diameter is:
Current Diameter=Previous Diameter/Ratio

I then wrote a program that incorporated that algorithm.
So that the first entry in the table would be for #0000 
I used the ratio to find the diameter for #00000, since my 
program uses a loop to calculate the NEXT size. The 
calculated diameter for size #0000 then came out to be 
459.999999 which the program print routine truncated to 459.99

My method may not be as "neat" as some of the methods some of
the list members have proposed, such as using log base e, 
but it has several good points:
(A) it generated all the right answers with 5 digit precision
(B) it generated them in a way that to me (at least) was intuitive.
(C) it used only very simple math 

I like to keep things as simple as possible, so long as the simple
method achieves the correct results.

I am not against hairy math, or even against math that just
*looks* a bit hairy to the unititiated. But let us not forget that
the mathematical expression is, after all, just that: an
expression.... a way of showing something. An algorithm
is also a way of showing something. I always prefer to teach
my students the PROCESS by which someting is done, rather
that just hitting them with the final mathematical 
expression that comes out of that process.

The wire table created by the program includes info that I 
thought other coilers might be interested in, such as resistance,
weight, and turns per inch. Note that amp rated capacity varies
depending on what you consider "max" to mean. I opted not to
go for fusing amps, but for current rating that are generally 
considerd safe under normal operating conditions. 

Once you have the proper diameter it is very easy to generate
all the other table entries such as circular mils and ohms/ft.

Hope this helps.
Fr. Tom McGahee