Conductor ampacity as a function of cross sectional area

[iceworm]

... Think about why busbars are tall and thin rather than square for the same cross sectional area.

Bes - I am pretty sure (strike that) really, really sure we understand that.

 

[electrofelon]

If "somebody" is suggesting that the formula (from his or her attachment) is what the NEC authors used to create the "original" Table 310.16 (and its successors), I would be interested in seeing authoritative evidence.

I am more inclined to believe (with, I admit, no supporting evidence of my own) that the table was derived through experiment and deductive reasoning, and that the formula was derived (after the fact) as a mathematical model of observed results.

Does anyone have any historical information that would affirm or refute my belief?

I always assumed it was just the Neher McGrath method where the 310 charts came from, but thats a total ASSumption.....

Ice is right: the 25 ohm people know for sure.....

 

[charlie b]

Oh, no question, the formula is where the "original" Table 310.16 came from.

I must beg to differ (or at least to describe the same thing in a different way :happyyes. If you take a value, such as area, and raise it to the power of 0.500, you are taking the square root of that value. If (as the formula shows) you take the area and raise it to the power of 0.552, you are well into a college senior or even graduate level mathematical world. You are creating a formula that is a "best fit" for an observed phenomenon, by selecting the exponent that will give you the shape of the curve that your experiments revealed to you. They must have set up the experiments with the conditions described in the table (i.e., 75C insulation system, 30C ambient, and not more than 3 CCCs). Then they will have increased the current in the test conductor until they either saw signs of insulation degradation or simply measured a surface temperature higher than 105C (i.e., 30C ambient plus 75C rise). They would plot the "failure point current" against the wire size, and discover the curve that is in your attachment. Finally, they would derive the "best fit" formula.

I imagine they would have done the same with conductors that have a 60C insulation system and with conductors that have a 90C insulation system. The 60C curve would appear below the 75C curve, and thus would have an exponent higher than 0.552. The 90C curve would appear above the 75C curve, and thus would have an exponent lower than 0.552.

 

[charlie b]

I always assumed it was just the Neher McGrath method where the 310 charts came from, but that's a total Assumption.

It is not a bad assumption. Sadly, it is not correct. The Neher McGrath method applies to underground installations, for which the physical properties of the dirt (and perhaps concrete encasement) come into play.

 

[electrofelon]

It is not a bad assumption. Sadly, it is not correct. The Neher McGrath method applies to underground installations, for which the physical properties of the dirt (and perhaps concrete encasement) come into play.

:weeping:

 

[electrofelon]

It is not a bad assumption. Sadly, it is not correct. The Neher McGrath method applies to underground installations, for which the physical properties of the dirt (and perhaps concrete encasement) come into play.

Charlie,

I did some reading, and I see no reason why NM is or should be restricted to those types of installations.

 

[iceworm]

... If (as the formula shows) you take the area and raise it to the power of 0.552, you are well into a college senior or even graduate level mathematical world. ...

Graduate level? Me? Okay, maybe I am. But that doesn't change the secret ironing cord police repository or "Ultra" knowledge.

 

[iceworm]

Note: I have never used Neher - McGrath. I don't plan on using Neher - McGrath.

It is not a bad assumption. Sadly, it is not correct. The Neher McGrath method applies to underground installations, for which the physical properties of the dirt (and perhaps concrete encasement) come into play.

Okay, one more hint, then I need to leave this alone.

310.15.A.1, Tables or Engineering Supervision
310.15.C, Engineering supervision
The equation is not limited to underground.

Informative Annex B, Application Information for Ampacity Calculation
B.2 Typical Applications Covered by Tables
This cites the Neher - McGrath equation and references IEEE 835
Table B.310.15.B.2.1 is for conductors in raceway in free air, 30C ambient.
Table B.310.15.B.2.3 is for conductors in raceway in free air, 40C ambient.

IEEE 835 Std Power Cable Ampacity Tables
A.2.3 Example 3: 3-1/c 2000 kcmil copper, 15 kV, tape shielded, EPR cables installed in a 6 Inch PVC in still air.
Yes, this is a Neher - McGrath calculation

So, yes, N-M does apply in free air.

No, the Secret Squad formula is not derived from that. And I think Ethan already knew this.

Signed

A (for anonymous)

 

[Besoeker3]

Bes - I am pretty sure (strike that) really, really sure we understand that.

Perhaps not everyone does otherwise this topic would not have arisen....[h=1]Conductor ampacity as a function of cross sectional area[/h]
Just my thoughts.

 

[iceworm]

Perhaps not everyone does otherwise this topic would not have arisen....Conductor ampacity as a function of cross sectional area ....

You are correct perhaps not every one.

 

[ggunn]

What is the formula for conductor ampacity as a function of conductor cross sectional area? I noticed that the ampacity (at 75 degC) of 350 kcmil copper = 310A (so one would need parallel sets of 350 kcmil conductors for a 600A service). But to achieve an 800A service, one needs to almost double the size (area) of the conductors (parallel 600 kcmil = 420A). Difficult to explain to a customer. A formula showing the relationship between ampacity and cross sectional area may help.

Why not just use the tables? Conductor sizes move up in step functions and so do ampacities. You've got to go look up the x-sectional area, anyway; why not just look up the ampacity?

 

[circuit_girl]

Note: I have never used Neher - McGrath. I don't plan on using Neher - McGrath.


Okay, one more hint, then I need to leave this alone.

310.15.A.1, Tables or Engineering Supervision
310.15.C, Engineering supervision
The equation is not limited to underground.

Informative Annex B, Application Information for Ampacity Calculation
B.2 Typical Applications Covered by Tables
This cites the Neher - McGrath equation and references IEEE 835
Table B.310.15.B.2.1 is for conductors in raceway in free air, 30C ambient.
Table B.310.15.B.2.3 is for conductors in raceway in free air, 40C ambient.

IEEE 835 Std Power Cable Ampacity Tables
A.2.3 Example 3: 3-1/c 2000 kcmil copper, 15 kV, tape shielded, EPR cables installed in a 6 Inch PVC in still air.
Yes, this is a Neher - McGrath calculation

So, yes, N-M does apply in free air.

No, the Secret Squad formula is not derived from that. And I think Ethan already knew this.

Signed

A (for anonymous)

I found this thread, as I'm also looking at how to properly do this for maximum _IDEAL_ current - ie fuse point. Ideal means I don't care about any other factors (insulation, derating, temperature, resistance changes, etc)- I'm just looking for an ideal maximum point I can then work backwards from. The chart and the formulas are incorrect that @iceworm refers to in terms of maximum current possible. I have derived the calculations the NEC uses based on AWG, Specific Resistivity, and their own 'rule of thumb' which is that wire can handle 1Amp for every 700 cmils (very conservative safety margin).

Calc cmil in inches per foot and divide that by 700. That will get you the value NEC uses for max safe current (again, very conservative) in their tables @ 20C.

It relies on Specific Resistivity info here (@20C)

Silver	9.8​
Copper (Drawn)	10.37​
Gold	14.7​
Aluminum	17.02​
Carbon	22000​
Constantan	295​
Tungsten	33.2​
Brass	42.1​
Steel (Soft)	95.8​
Nichrome	660​
Iron	60​
Lead	126​
Manganin	265​
Mercury	590​
Nickel	52​
Platinum	66​

-C

 

[Julius Right]

In NEC it is a copy of the Neher and McGrath formula[ in 310.15 article]see attachment.
Up to Rca it is easy to go but the big problem is Rca. So, this thermal resistance differs from cable to cable , from different type and size of conduit or ducts, number of conductors in a cable ,number of cables in a duct, duct concrete thermal resistance, surrounding earth resistance and temperature and many, many other data.
I did programs [in Visual Basic 6] 20 years ago for about 20 different cable situations and always it appears a new different case.

 

[GoldDigger]

Not at 60 Hz.

Skin effect increases voltage drop noticeably for very large conductors at 60Hz, but does not contribute enough to heating to be considered.

 

[GoldDigger]

It is not a bad assumption. Sadly, it is not correct. The Neher McGrath method applies to underground installations, for which the physical properties of the dirt (and perhaps concrete encasement) come into play.

Allow me to rephrase that slightly:
The Neher McGrath method applies to any problem involving conductor heating, but normally it is only necessary to invoke it for underground installations, where there are too many geometric, material, and environmental variables to allow a simple table or set of tables to suffice. Simple tables and formulas for free air and conduit allow for a conservative but still workable code rule.