NEC Ampacities Data

This data shows the Allowable Ampacities of Insulated Conductors Rated 0 to 2000V, for Copper conductors, as listed in the NEC NFPA 70E Table 310.16, used for estimating the current ratings for power cables. For the third column (blue), which are the closest specs for standard conductors, I made some basic fitting (red), with an expression like this:

$$I=590.15 (1-e^{-0.02410 S^{0.6453}})+238.18(1-e^{-0.0001241 S^{1.4925}})$$

Where $$\I\$$ is the ampacity in $$\A\$$ and $$\S\$$ is the cable section in $$\mm^2\$$, with $$\R^2=0.9999\$$ before rounding, which appears to be quite satisfactory.

Evidently as you can realize, this expression is absolutely wrong for higher sections, if ever built.

Question is, which is the real model behind this table, used to build this table and prepare this standard? • Minor comment: SI units named after a person have their symbols capitalised but are lowercase when spelled out. "A" or "ampere". Same with the periodic table: "Cu" or "copper". I'm not sure if "ampacity" is a real word. "Current rating" sounds so much nicer but maybe I'm getting old. Jan 31 '20 at 23:26
• I do not see how this could help to answer the question, but well.... Jan 31 '20 at 23:31
• It was intended to help ask the question. Your meaning is clear but correct capitalisation matters in technical writing. I thought you might be interested. Jan 31 '20 at 23:45
• en.wikipedia.org/wiki/Ampacity Feb 1 '20 at 0:23
• "Evidently as you can realize, this expression is absolutely wrong for higher sections, if ever built." I must be thick, because the wrongness is not evident to me. Can you explain in simple words how it is wrong? What do the graph axis represent? Feb 1 '20 at 0:30

Ampacity is always based on a certain safety margin for flammability of the insulation based on thermal resistance, temperature rise and thus temperature margin before outgassing toxic fumes. Consider that the temperature rise is a function of the electrical losses per unit length and the thermal insulation which results in the temperature rise.

Thus the area in mm² is not a good linear indicator of Ampacity. It is more likely to be related to the radius. (I'll)Plot that. It's not quite a power series of x^0.5 as the wire radius/insulation thickness ratio affects that and the slope changes after 300 mm^2

• This could explain why the $S^{0.64}$ and $S^{1.49}$ factors appeared. Including a 1/2 factor in the fitting just gave me the same result, multiplied by two :). The plot for $A$ vs $r$ looks like an S curve instead of negative exponential. Even more intriguing. Feb 1 '20 at 1:19
• I reviewed the fitting with polynomials $c_ix^{q_i}$ and up to three elements I cannot reach an $R^2$ better than 0.98 but with high sq. errors. Perhaps I am missing some adjustment making $x^{q_i}$ different from $1-e^{-x^{q_i}}$, which we know are the same for low values. Though, this linear loglog view brought to me a lot of ideas. Feb 1 '20 at 3:34

Question is, which is the real model behind this table, used to build this table and prepare this standard?

The model is based on the allowable temperature of the insulation, or of the wire itself. The actual temperature is determined by the heat developed in the wire, the thermal conductivity of the materials and the rate at which heat is dissipated into the surroundings. The heat developed is determined by the current and resistance of the wire. The resistance is determine by the cross sectional area. The rate at which the heat is dissipated is related to the surface are of the wire.

A graph of the wire surface area/unit length vs. ampacity might make more sense.

Another thing to consider is: at some point, the temperature gradient from the center of the wire to the surface may be an issue.

Note also that the table assumes three conductors in a cable or buried in the earth. That further restricts heat dissipation into the surroundings.

The flattening of the curve seems to say that it is pointless to use single conductors larger that 2000 MCM. If that is not large enough, you must use more than one conductor per phase and separate the phases.

Shown below is wire circumference vs. current capacity for both bare copper wire in free air (transmission line) and insulated wire with not more than three conductors in a raceway, cable or direct buried. • The surface (radius), instead of the volume (section) has complete sense, as shown in the obtained factors $S^{0.64}$ and $S^{1.49}$. And also the temperature gradient in the center could explain a more "linear" piece for higher currents. Feb 1 '20 at 1:18
• "Pointless to use single conductors". And again, the data justifies this common practice... Feb 1 '20 at 1:22