<html>
<head>
<meta content="text/html; charset=windows-1252"
http-equiv="Content-Type">
</head>
<body bgcolor="#FFFFFF" text="#000000">
<div class="moz-cite-prefix">You ask a simple question to this group
and stunning brilliance floods my inbox. RE-Wrenches, You are
truly amazing. Thanks to all that discussed this for the knowledge
I have gained.<br>
<br>
Larry<br>
<pre class="moz-signature" cols="72">
On 12/2/14 3:47 PM, Daniel Young wrote:
</pre>
</div>
<blockquote cite="mid:012601d00e81$e7726bb0$b6574310$@com"
type="cite">
<meta http-equiv="Content-Type" content="text/html;
charset=windows-1252">
<meta name="Generator" content="Microsoft Word 12 (filtered
medium)">
<!--[if !mso]><style>v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style><![endif]-->
<style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
@font-face
{font-family:Consolas;
panose-1:2 11 6 9 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman","serif";
color:black;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
p
{mso-style-priority:99;
mso-margin-top-alt:auto;
margin-right:0in;
mso-margin-bottom-alt:auto;
margin-left:0in;
font-size:12.0pt;
font-family:"Times New Roman","serif";
color:black;}
pre
{mso-style-priority:99;
mso-style-link:"HTML Preformatted Char";
margin:0in;
margin-bottom:.0001pt;
font-size:10.0pt;
font-family:"Courier New";
color:black;}
p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
{mso-style-priority:99;
mso-style-link:"Balloon Text Char";
margin:0in;
margin-bottom:.0001pt;
font-size:8.0pt;
font-family:"Tahoma","sans-serif";
color:black;}
span.HTMLPreformattedChar
{mso-style-name:"HTML Preformatted Char";
mso-style-priority:99;
mso-style-link:"HTML Preformatted";
font-family:Consolas;
color:black;}
span.BalloonTextChar
{mso-style-name:"Balloon Text Char";
mso-style-priority:99;
mso-style-link:"Balloon Text";
font-family:"Tahoma","sans-serif";
color:black;}
span.EmailStyle22
{mso-style-type:personal;
font-family:"Calibri","sans-serif";
color:#1F497D;}
span.EmailStyle23
{mso-style-type:personal;
font-family:"Calibri","sans-serif";
color:#1F497D;}
span.EmailStyle24
{mso-style-type:personal-reply;
font-family:"Calibri","sans-serif";
color:#1F497D;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
<div class="WordSection1">
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">It
all boils down to how ampacity is determined in the NEC.<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Ampacity
is really related to temperature as far as the NEC is
concerned. The ampacity of a 1/0 wire at 90c is the constant
current it can carry in free air (30 C air) and not achieve
an internal temperature of more than 90 C. the 75 c ampacity
is the same, the amperage it can carry while not going over
75 C.<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Now,
if you double the diameter of a circle, the circumference
also doubles, but the cross sectional Area actually goes up
much more (4x more in fact) because cross sectional area is
based on the square of the diameter and circumference is
simply based on the diameter ^1 power.<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Wire
dissipates heat from its surface only, so the dimension
critical for the amount of heat a wire can dissipate is
circumference, not cross sectional area. So even though the
wire is larger and has a much lower resistance, the heat
dissipating area does not increase by as much, so in the end
the larger wire has a lower current carrying capacity per
unit cross sectional area, than a smaller wire.<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Here
is an example that lets me keep the math simple: (the #’s
are all round #’s and not based on real
ampacities/resistances, just to keep the math simple.)<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Wire
1:<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">A
diameter of 10 units and can carry 100A through it and stay
at 90C. It has a resistance of 1 ohm/1000ft.<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Wire
2:<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">A
diameter of 20 units. It has 4times the cross sectional
area, and double the circumference (which means 2x the outer
surface area) to dissipate heat. It has a resistance of .25
ohm/1000ft (1/4 that of wire 1 since it has 4x the amount of
copper to carry current).<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">For
wire 1 to stay at 90 C, it has to dissipate (P=I^2*R),
P=(100amps^2)*1 omh=10,000 watts per unit of outer surface
area.<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">So
if Wire 2 has double the surface area to dissipate heat, it
can dissipate about 2x the energy, or 20,000watts. So if we
work it backwards (P=I^2*R is the same as I=sqrt[P/R])
I=sqrt[20,000/.25]=sqrt[80000]=282amps<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">So
wire 2 can handle (282amps/100amps)=2.8 times the amperage,
even though it has 4times the cross sectional area, all
because it only has 2 times the surface are to get rid of
heat. There are other factors with heat transfer that make
the larger wire have even lower ampacity, but this
demonstrates the main contributing factor.<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">[In
the NEC table 310.15(B) we see that a 250kcmill copper wire
handles 255A @75C, and a 100kcmill (4x the area) can only
take 545A, or 2.2 times the current, so not too far from my
example].<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">I
hope the above helps more than it hurts.<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<div>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">With
Regards,<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Daniel
Young, <o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">NABCEP
Certified PV Installation Professional<sup>TM</sup>: Cert
#031508-90<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">NABCEP
Certified Solar Heating Installer<sup>TM</sup>: Cert
#SH031409-13<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">
<o:p></o:p></span></p>
</div>
<br>
</div>
</blockquote>
<br>
</body>
</html>