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Re: Hacking the AWG WIRE TABLE (fwd)
---------- Forwarded message ----------
Date: Mon, 04 May 1998 22:08:32 -0700
From: "Antonio C. M. de Queiroz" <acmq-at-compuland-dot-com.br>
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: Hacking the AWG WIRE TABLE (fwd)
Thomas McGahee wrote:
> > It is based on the geometrical series in which
> >
> > No. 0000 is 0.46 inch diameter, and No. 36 is 0.005 inch diameter.
> 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.
Let me tell then how I arrived to the exponential expression. I plotted
some gauge-diameter pairs with logarithmic scale for the diameter, and
obtained a straight line.
Such a line must correspond to a relation Ln(d)=a*g+b (d=diameter; g=gauge).
I picked two pairs, and solved the system of two linear equations:
Ln(d1)=a*g1+b
Ln(d2)=a*g2+b
The solution is:
a=-Ln(d1/d2)/(g2-g1)
b=(g2*ln(d1)-g1*ln(d2))/(g2-g1)
Using the definition above, the exact expressions for the two coefficients,
and so the "official formula" would be (using gauges 0000=-3 and 36):
a = -Ln(460/5)/39 = 0.115943296847
b = (36*ln(460)+3*ln(5))/39 = 5.78339659892
and diameter in mils = exp(a*gauge+b)
My original formula was obtained from the listed values for gauges 30 and 10.
(From the tables Ref. Data for Radio Eng., or the Radio Amateur's Handbook, that are identical.)
Due to rounding errors in the original computation of the table, slightly different
results are obtained depending on the pair chosen.
For confirmation, I run a fitting algorithm over the entire table, and obtained
something very close to the values above (first five digits identical).
The relative difference is greater for gauges 30, 27 and 5, and always smaller that 0.05%.
Antonio Carlos M. de Queiroz
http://www.coe.ufrj.br/~acmq