[RE-wrenches] Parallel Wire combining

[Jerry Shafer]

To All Here is the math from wikipedia

By definition, No. 36 AWG is 0.005 inches in diameter, and No. 0000 is
0.46 inches in diameter. The ratio of these diameters is *1:92*, and there
are 40 gauge sizes from No. 36 to No. 0000, or 39 steps. Because each
successive gauge number increases diameter by a constant multiple,
diameters vary geometrically. Any two successive gauges (e.g. A & B ) have
diameters in the ratio (dia. B ÷ dia. A) of [image: \sqrt [39]{92}]
(approximately 1.12293), while for gauges two steps apart (e.g. A, B & C),
the ratio of the C to A is about 1.12293² = 1.26098. The diameter of a No.
*n* AWG wire is determined, for gauges smaller than 00 (36 to 0), according
to the following formula:
[image: d_n = 0.005~\mathrm{inch} \times 92 ^ \frac{36-n}{39} =
0.127~\mathrm{mm} \times 92 ^ \frac{36-n}{39}]

(see below for gauges larger than No. 0 (i.e. No. 00, No. 000, No. 0000 ).)
or equivalently
[image: d_n = e^ {-1.12436 - 0.11594n}\ \mathrm{inch} = e^ {2.1104 -
0.11594n}\ \mathrm{mm}]

The gauge can be calculated from the diameter using
[image: n = -39\log_{92} \left( \frac{d_{n}}{0.005~\mathrm{inch}}
\right)+36 = -39\log_{92} \left( \frac{d_{n}}{0.127~\mathrm{mm}} \right)+36]
[3] <http://en.wikipedia.org/wiki/American_wire_gauge#cite_note-3>

and the cross-section area is
[image: A_n = \frac{\pi}{4} d_n^2 = 0.000019635~\mathrm{inch}^2 \times 92 ^
\frac{36-n}{19.5} = 0.012668~\mathrm{mm}^2 \times 92 ^ \frac{36-n}{19.5}],Do
you want moreJerry


On Tue, Dec 2, 2014 at 2:20 PM, boB at midnitesolar.com <boB at midnitesolar.com>
wrote:

>
> The only thing I can think that AWG/KCMIL means is that it is a ratio ?
>
> boB
>
>
>
> On 12/2/2014 4:18 PM, boB at midnitesolar.com wrote:
>
>
> I'm pretty sure that  Daniel Young's explanation of surface area explains
> the discrepancy.
>
> The surface area of a larger wire does not grow as fast as its cross
> sectional area so
> it does not cool as well.  It can carry more current but its surface and
> temperature
> rise is going to be higher if you simply put more amps through it
> proportional
> to the wire area.
>
> But the wire table does not show multiple wires in parallel and/or the
> distance
> between them.  Or is there such a table ?  If the distance between them
> are high
> enough so that the heat can be dissipated, then you ~should~ be able to get
> 3 times the ampacity of all 3 wires in parallel ?  Shouldn't he ?
>
> What exactly does the title of that column mean ?  AWG/KCMIL ?
> AWG and KCMIL are different.  AWG goes higher as the wire gets smaller.
> KCMIL (area) gets higher as the wire gets bigger.
>
> boB
>
>
>
>
> On 12/2/2014 3:32 PM, Larry wrote:
>
> Hey boB,
>
> This is the reference table I was using. They show 325 AWG and 325kCM
> refer to the same diameter cable but I should have used kcm for clarity.
>
> If all insulation/temp rating is the same we are back to my original
> question. Anyone else able to explain this? To be safe I am leaning toward
> using the combined CM number to size for current rather than 3 times the
> ampacity as that just makes no sense to me.
>
>
> On 12/2/14 3:54 PM, boB at midnitesolar.com wrote:
>
>
> The "area" of the conductor will be 3 times and you would think that the
> NEC Ampacity would also be 3 times
> that of one conductor.   But one LARGE conductor with the same area might
> not be as high as you think
> because of insulation.  I would think that ampacity of 3 cables in
> parallel would be 3 times.  But probably
> not when you take a single cable of the 3X area out of the NEC table.  (I
> haven't looked at this to verify)
>
> Also,  Larry,  325 AWG 750 AWG (gauge) wire is a bit too small for this,
> don't you think ?
>
> I know...  You mean circular mils...
> boB
>
>
>
>
>
>
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