Conductor ampacity as a function of cross sectional area

[MTG]

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.

 

[Dennis Alwon]

Show him the tables. Not your job to go thru that trouble...You're the boss...

 

[infinity]

Not sure of a specific formula but you are correct that smaller conductors can carry more amps with less cross-sectional area when compared to larger conductors. This can also come into play when sizing a GEC, SBJ or MBJ.

 

[Dennis Alwon]

Use 3- 250 kcm's and keep the load down to 765 amps and you can use an 800 amp breaker

 

[charlie b]

A formula showing the relationship between ampacity and cross sectional area may help.

Sorry, but no such relationship exists. For starters, cross sectional area is not the only relevant factor. The definition of ampacity brings "conditions of use" into the discussion. Put two otherwise identical wires in two different installations, and their ampacity values may be very different. For example, Table 310.15(B)(16) assumes not more than three current-carrying conductors in the same raceway, and assumes an ambient temperature of 30C. Change either circumstance and you change the ampacity. Table 310.15(B)(16) also lists three different ampacity values for the same cross-sectional area, depending on whether the insulation system is rated for 60C, or 75C, or 90C. Start with two identical sections of bare copper wire and put different insulation systems on the two wires, and you may wind up with very different ampacity values.

 

[iceworm]

Somebody did not have enough to do today
I won't say what I think the somebody was doing, but I suspect this is an attempt to keep from going down from oxygen starvation brain death.

Not me - just somebody.

MTG -
Show them the attachment.
Smaller diameter conductors will carry more amps /kcmil

As for the formula:

kcmil	Table Ampacity	Formula Ampacity	Error %
250	255	258	+1.1%
350	310	310	0.0%
500	380	378	-.0.5%
600	420	418	-.0.5%
750	475	473	-.0.4%

Enjoy

the worm

 

[electrofelon]

Enjoy

the worm

Cool graph. I assume the decreasing ampacity per area is mostly due to more heat building up as the circumference to area ratio decreases, but skin effect plays a role too. Please provide a separate graph for each of these effects

 

[LarryFine]

. . . but skin effect plays a role too.

Not at 60 Hz.

 

[don_resqcapt19]

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.

You could use four 3/0s per phase (671.2 kcmil) for the 800 amp service and use less copper than the parallel 350 kcmils you used for the 600 amp service.

 

[GoldDigger]

The resistance of a given length of conductor or parallel conductors is directly proportional to the cross sectional area as long as you can ignore skin effect. Skin effect at 60Hz does not become significant until you get to rather large conductors. (Look at the AC resistance tables). The voltage drop is directly proportional to the parallel resistance and the total current.
The ampacity, however, is as stated, not just a function of resistance.

 

[winnie]

...but skin effect plays a role too. ...

Not at 60 Hz.

You might be surprised.

Skin depth at 60Hz in copper is 8.5mm, and the diameter of the largest cable in the NEC tables is 41mm (2000kcmil).

Skin effect will be getting noticeable at that point. See the wikipedia graph of current density versus ratio of skin depth to conductor diameter at https://en.wikipedia.org/wiki/File:Current_Density_in_Round_Wire_for_Variuos_Skin_Depths.png

That graph makes things look worse than reality, in that it is a 1 dimensional cross section of a 2 dimensional wire; the wire has more 'edge' then 'middle'.

I don't know if anyone actually uses 2000kcmil Cu in practice, but this would be a reason to use smaller conductors in parallel, in addition to the pull nightmare.

-Jon

P.S. Worm: thanks for the graph and calculation, or whomever did it.

 

[electrofelon]

Not at 60 Hz.

You might be surprised.

Skin depth at 60Hz in copper is 8.5mm, and the diameter of the largest cable in the NEC tables is 41mm (2000kcmil).

Skin effect will be getting noticeable at that point. .

I know it only is an issue with larger wire sizes. A 350 KCMIL is about where the skin depth will diverge from the center point. 750 is the largest "common" wire size, so shouldn't it be not negligible for 750?

 

[iceworm]

(1) Cool graph. (2) I assume the decreasing ampacity per area is mostly due to more heat building up as the circumference to area ratio decreases, (3)but skin effect plays a role too. (4) Please provide a separate graph for each of these effects

This is the Worm's evil twin, Snake. I can sneak in when he is going down from oxygen deprivation, near brain death, caused from excessive management meetingitis.

But he is awake today, so I only have a few seconds while he is getting coffee.

So:
1 thanks
2 I would agree
3 Yes, I have seen evidence that is true. I also saw a paper contending that for three conductors in conduit/cable (intimate - so to speak), the magnetic fields interact and push the current density toward the outsides of the cables. This would be the cause of conductors jumping or rattling inside of a conduit under high current short circuits.

It is all about the heat. So anything that concentrates the current into a smaller area, pushes up the effective resistance >>> gives more heat. ¿Quien Sabe? I could be right.

4 I'll get right on that

... P.S. Worm: thanks for the graph and calculation, or whomever did it.

You're welcome

snake

 

[charlie b]

Somebody did not have enough to do today. . .

Not me -just somebody.

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?

 

[Besoeker3]

Surface area has per unit length has not been mentioned unless I missed it.........
That's essentially why the current capacity for lower gauges is higher in proportion to their CSA.......

 

[charlie b]

Surface area has per unit length has not been mentioned unless I missed it.

Are you, by chance, thinking about resistance? It is proportional to length divided by cross-sectional area. Resistance is related to ampacity, in that a higher resistance (e.g., from a smaller area) releases more heat for the same current. That heat can damage insulation, and is the basic reason for ampacity limits.

 

[Besoeker3]

Are you, by chance, thinking about resistance? It is proportional to length divided by cross-sectional area. Resistance is related to ampacity, in that a higher resistance (e.g., from a smaller area) releases more heat for the same current. That heat can damage insulation, and is the basic reason for ampacity limits.

No. The ability to dissipate heat.

 

[iceworm]

Surface area has per unit length has not been mentioned unless I missed it.........
That's essentially why the current capacity for lower gauges is higher in proportion to their CSA.......

Ethan aluded to that

Cool graph. I assume the decreasing ampacity per area is mostly due to more heat building up as the circumference to area ratio decreases, but skin effect plays a role too. Please provide a separate graph for each of these effects

And charlie b brings up another important factor.

.... Start with two identical sections of bare copper wire and put different insulation systems on the two wires, and you may wind up with very different ampacity values.

Which I suspect (that means I don't know) is not just the insulation temperature rating, but also includes the insulation thermal resistance.

 

[Besoeker3]

Ethan aluded to that

Cool graph. I assume the decreasing ampacity per area is mostly due to more heat building up as the circumference to area ratio decreases, but skin effect plays a role too. Please provide a separate graph for each of these effects

Skin effect isn't normally an issue at power frequencies.
Surface area? Think about why busbars are tall and thin rather than square for the same cross sectional area.

 

[iceworm]

Holy Quizicals, Batman. Its time to investigate.[/SIZE]

If "somebody" is suggesting that the formula (from his orher attachment) is what the NEC authors used to create the "original"Table 310.16 (and its successors), ...

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

… 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. …

Charlie - I am always amazed at your inductive reasoning - unless it is your deductive reasoning, and that amazes me as well. Or, I guess it could be “geometric” reasoning (Caine Mutiny - Captain Queeg and the strawberries), which would be extra amazing.

… I would be interested in seeing authoritative evidence. …

As would we all.

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

Of course, there is ample evidence that will affirm or refute. It is the priority of the dreaded Secret Ironing Cord Police. This is the same group that also is the keeper of the “25 ohms or less” knowledge. An anonymous, knowledgeable source has said, “This is so secret, even they don’t where it is. It is classified above ‘Ultra’. It is ‘Burn Before Reading’”

I tried to type this “tongue in cheek”, but I don’t type with my tongue (or cheek). So I substituted typing with “fingers in mouth”, but that made for really difficult typing. Ah-Ha - I went with fingers in mouth and typed with toes. That worked.

Yours Truly,
Johnny Dollar

Anonymously peaking from a worm hole - the gravity of the situation is brutal.