[RE-wrenches] Parallel Wire combining

Tue Dec 2 14:47:08 PST 2014

It all boils down to how ampacity is determined in the NEC.

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.

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.

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.

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.)

Wire 1:

A diameter of 10 units and can carry 100A through it and stay at 90C. It has
a resistance of 1 ohm/1000ft.

Wire 2:

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).

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.

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

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.

[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].

I hope the above helps more than it hurts.

With Regards,

Daniel Young, 

NABCEP Certified PV Installation ProfessionalTM: Cert #031508-90

NABCEP Certified Solar Heating InstallerTM: Cert #SH031409-13

From: RE-wrenches [mailto:re-wrenches-bounces at lists.re-wrenches.org] On
Behalf Of Larry
Sent: Tuesday, December 02, 2014 4:49 PM
To: RE-wrenches
Subject: Re: [RE-wrenches] Parallel Wire combining

That's the part that is throwing me off. If I have 3 times the circular mil
and compare that to a single conductor of similar circular mil, how do I
have 3 times the ampacity? These are very different numbers.

Example: 1/0 @ 90c is 170 amps x 3 = 510 amps. 510A is what a conductor just
over 750 AWG will carry. The circular mils of 3 1/0 cables is only 325,050
or a 325 AWG cable which would be rated at about 330 amps. 

So, is it 510 amps (3x the ampacity) or 330 amps (3x circular mil)? And,
more importantly, why?

Larry

On 12/2/14 11:14 AM, Bill Turberville wrote:

I am sorry.  Bad fingers.  Three times the ampacity under the same
conditions.

From: RE-wrenches [mailto:re-wrenches-bounces at lists.re-wrenches.org] On
Behalf Of Larry
Sent: Tuesday, December 02, 2014 12:09 PM
To: RE-wrenches
Subject: Re: [RE-wrenches] Parallel Wire combining

OK, let's use 1/0 for the example. 108,350 x 3 = 325,050. Do I now have a
cable between 300 and 350 AWG?

Thank you,

Larry

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