Is this a genuine quirk of the NEC or am I missing something?

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bdcubbage

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Hi :)

I'm building an NEC wire ampacity / VD% / circuit ampacity / OCPD rules calculator as part of my web design portfolio. Not meant as a serious thing. Don't worry, I'm making sure nobody uses it as a serious tool.

I think I found a quirk of the NEC 2023 code, though. But I want to make sure I'm understanding things properly. Here are the rules that comprise the quirk:

  • Bare, free air conductors get their base ampacity from Table 210.21;
  • According to 310.15(D), bare or covered conductors installed "with" insulated conductors should be considered the same insulation rating as the weakest link in the chain when derating:
Where bare or covered conductors are installed with insulated conductors, the temperature rating of the bare or covered conductor shall be equal to the lowest temperature rating of the insulated conductors for the purpose of determining ampacity."
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  • After derating for the bundled size, temperature corrections are applied as per Table 210.15(B)(1)(2);
  • According to Table 210.15(B)(1)(2), temperature correction factors for temperatures below 36 degrees are higher for lower-insulation wires. For instance, a 60 degree wire in <10C ambient is 1.58, whereas for a 90 degree wire it is 1.26
What this essentially means is that, for bare, free-air conductors installed in cold environments, their calculated base wire ampacity is going to be highest if they are installed "with" 60C-rated wire.

Example:
  • 2AWG Copper, Free Air, Bare, Maintained Spacing (no bundling derate for simplicity)
  • Installed "with" 60-degree wire
  • <10C ambient
  • Table 310.21: 209A Base
  • Table 210.15(B)(1)(2): * 1.58
  • Final Calculation: 209A * 1.58 = 330.22A
Contrast that with if we installed it alongside 90C wire:
  • Table 310.21: 209A Base (Unchanged)
  • Table 210.15(B)(1)(2): 1.26
  • Final Calculation: 209A * 1.26 = 263.34A!
It's lower when installed with better wire.

Am I missing something crucial here, or is this just a quirk of the code? Obviously it wouldn't matter in practice because the terminal rating is the limiting factor in this instance. But I'm genuinely wondering if I'm getting something wrong, here.
 
don_resqcapt19 said:
Can you give me a practical example of a bare current carrying conductor being installed in a raceway with insulated conductors?
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It's just a hypothetical. Reminder of what I said: "Obviously it wouldn't matter in practice"

Also, I'm not talking about bare CCC's being installed in a raceway. I'm assuming free air.
 
2023 NEC 310.21 says its ampacities for bare conductors are based on 40C ambient temperature and 80C conductor temperature, where the heat dissipation rate is based on a 2 ft/sec wind. I.e. a 40C temperature rise, which is different from the 30C, 45C, or 60C temperature rise on which Tables 310.16 and 310.17 are based.

If you installed such a conductor with a 90C insulated conductor, there would be no effect, as the 90C insulation rating is above the 80C bare condcuctor operating temperature. If instead you installed such a conductor with a 60C insulated conductor, then I take 310.15(D) to mean that the operating temperature for the bare conductor needs to be reduced to 60C. So the allowable temperature rise when the conditions of 310.21 apply is now only 20C. That will give an ampacity correction factor of sqrt(1/2) = 0.707. Meaning at 40C ambient, #2 bare free air would be 209A * 0.707 = 148A when the operating temperature is limited to 60C. [The 60C insulated conductor would need to have its Table 310.17 ampacity adjusted for 40C ambient, as that Table is based on 30C ambient.]

So I'd say the calculations for your example should be:

  • 2AWG Copper, Free Air, Bare, Maintained Spacing (no bundling derate for simplicity)
  • Installed "with" 60-degree wire
  • 10C ambient
  • Table 310.21: 209A Base
  • Allowable temperature rise is 50C (10C to 60C) rather than 40C (40C to 80C)
  • Ampacity adjustment factor is sqrt(50/40) = 1.118
  • Final Calculation: 209A * 1.118 = 234A
Contrast that with if we installed it alongside 90C wire:
  • Table 310.21: 209A Base (Unchanged)
  • Allowable temperature rise is 70C (10C to 80C) rather than 40C (40C to 80C)
  • Amapacity adjustment factor is sqrt(70/40) = 1.323
  • Final Calculation: 209A * 1.323 = 276A

As to why Table 310.21 chooses 80C for the operating temperature, while the insulated conductor tables allow higher operating temperature if the conductor insulation is rated higher, I have no idea.

Cheers, Wayne
 
bdcubbage said:
I'm building an NEC wire ampacity / VD% / circuit ampacity / OCPD rules calculator as part of my web design portfolio.
Click to expand...
BTW, if you always use Equation 310.15(B)(1) instead of Table 310.15(B)(1)(1) and (2), you'll get more accurate and sometimes slightly higher ampacity values. The tables are based on rounding the ambient temperature up to the next multiple of 5C, which is an unnecessary conservative approximation to keep the tables from being 5 times as long.

Cheers, Wayne
 
wwhitney said:
As to why Table 310.21 chooses 80C for the operating temperature, while the insulated conductor tables allow higher operating temperature if the conductor insulation is rated higher, I have no idea.
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OK, not quite true. I infer it is related to bare free air installations being generally between poles, where conductor sag may be an issue, and so the operating temperature is limited to 80C to limit sag. As far as I can see, if you know that the sag would acceptable, there's no technical reason not to run your bare free air conductor at a much higher temperature, adjusting the ampacities accordingly. [Or maybe at sufficiently high temperatures, oxidation can also be a long term issue?]

Cheers, Wayne
 
wwhitney said:
2023 NEC 310.21 says its ampacities for bare conductors are based on 40C ambient temperature and 80C conductor temperature, where the heat dissipation rate is based on a 2 ft/sec wind. I.e. a 40C temperature rise, which is different from the 30C, 45C, or 60C temperature rise on which Tables 310.16 and 310.17 are based.

If you installed such a conductor with a 90C insulated conductor, there would be no effect, as the 90C insulation rating is above the 80C bare condcuctor operating temperature. If instead you installed such a conductor with a 60C insulated conductor, then I take 310.15(D) to mean that the operating temperature for the bare conductor needs to be reduced to 60C. So the allowable temperature rise when the conditions of 310.21 apply is now only 20C. That will give an ampacity correction factor of sqrt(1/2) = 0.707. Meaning at 40C ambient, #2 bare free air would be 209A * 0.707 = 148A when the operating temperature is limited to 60C. [The 60C insulated conductor would need to have its Table 310.17 ampacity adjusted for 40C ambient, as that Table is based on 30C ambient.]

So I'd say the calculations for your example should be:

  • 2AWG Copper, Free Air, Bare, Maintained Spacing (no bundling derate for simplicity)
  • Installed "with" 60-degree wire
  • 10C ambient
  • Table 310.21: 209A Base
  • Allowable temperature rise is 50C (10C to 60C) rather than 40C (40C to 80C)
  • Ampacity adjustment factor is sqrt(50/40) = 1.118
  • Final Calculation: 209A * 1.118 = 234A
Contrast that with if we installed it alongside 90C wire:
  • Table 310.21: 209A Base (Unchanged)
  • Allowable temperature rise is 70C (10C to 80C) rather than 40C (40C to 80C)
  • Amapacity adjustment factor is sqrt(70/40) = 1.323
  • Final Calculation: 209A * 1.323 = 276A

As to why Table 310.21 chooses 80C for the operating temperature, while the insulated conductor tables allow higher operating temperature if the conductor insulation is rated higher, I have no idea.

Cheers, Wayne
Click to expand...
Ah, this makes so much sense! My mistake was in assuming 310.21 was designed with 60C / 75C / 90C in mind (which it can't be, because there's only one column).

So really, it's based off of 80C. You take the difference between the 40C basis and the 80C rating, and that's your denominator. The numerator is just the "new" ampacity range. Then you take the square root of that, since convection increases exponentially relative to ampacity. Multiply it by the "base" ampacity number derived from the table, and that's the temperature-corrected ampacity.

Basically, it's not that complicated under the hood. Just a ratio of real-world values to the base values the NEC gives us, with a bit of math.

Thanks for your answer, it's really helped me out
 
bdcubbage said:
Then you take the square root of that, since convection increases exponentially relative to ampacity.
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You take the square root of that, because waste heat generation is proportional to current squared (P = I2*R), while heat rejection is proportional to temperature difference. So 4 times the temperature difference will give you 4 times the heat rejection, which can only handle 2 times the current.

And this is not an exponential relationship, it is a power law relationship. Something exponential in current I would have the I in the exponent.

Otherwise, yes, that's the idea behind Equation 310.15(B)(1).

Cheers, Wayne
 
wwhitney said:
You take the square root of that, because waste heat generation is proportional to current squared (P = I2*R), while heat rejection is proportional to temperature difference. So 4 times the temperature difference will give you 4 times the heat rejection, which can only handle 2 times the current.

And this is not an exponential relationship, it is a power law relationship. Something exponential in current I would have the I in the exponent.

Otherwise, yes, that's the idea behind Equation 310.15(B)(1).

Cheers, Wayne
Click to expand...
Okay, so a more accurate thing for me to say would be "heat generation is quadratically proportional to current, while heat rejection (including convection) is linearly proportional to the difference between the conductor and the ambient temperature"
 
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