Conductor Ampacity Calculation – Part Eight

In Article " Conductor Ampacity Calculation – Part Three ", I listed the Methods for Ampacity Calculations of Conductors Rated 0–2000 Volts as follows: 

Methods for Ampacity Calculations of Conductors Rated 0–2000 Volts

As per 310.15(A)(1), The allowable Ampacities for conductors rated 0-2000 Volts shall be permitted to be determined by two methods:

  1. Tables as provided in 310.15(B) or
  2. Under engineering supervision, as provided in 310.15(C).

I explained the first method: Tables as provided in 310.15(B) in the following articles:

Today, I will explain the second method: Under engineering supervision, as provided in 310.15(C).

Second Method: Under engineering supervision, as provided in 310.15(C)

In the first method, we select the ampacity from different tables provided in 310.15(B), while in the second method: Under engineering supervision, we will calculate the ampacity, so the second method will be more complex and time consuming and requires engineering supervision. It can, however, result in lower installation costs in some cases, and if calculated properly, it provides a mathematically exact ampacity.

The tables provided in the first method under NEC Article 310.15(B) don't address every type of installation and If there is an installation case not covered by these tables, how can you get the correct minimum ampacity?

The answer is using the second method: Under engineering supervision, as provided in 310.15(C), The NEC helps clarify what that entails in Annex B through many tables and figures.

Rule#1: Equation for Conductor Ampacities Calculation Under engineering supervision, as provided in 310.15(C)

Under engineering supervision, conductor ampacities shall be permitted to be calculated by means of the following general equation:


Tc = conductor temperature in degrees Celsius (°C)
Ta = ambient temperature in degrees Celsius (°C)
Rdc = dc resistance of conductor at temperature Tc
Yc = component ac resistance resulting from skin effect and proximity effect
Rca = effective thermal resistance between conductor and surrounding ambient

The above equation was developed by J. H. Neher and M. H. McGrath and it is called The Neher–McGrath formula.

Note #1 : Using The Neher–McGrath formula in selection of conductor size at the terminations

Although conductor ampacities calculated using The Neher–McGrath formula may exceed those found in a table of allowable ampacities, such as Table 310.15(B)(16), the limitations for connecting to equipment terminals specified in 110.14(C) have to be followed. For equipment 600 volts and under, the conductor size at the termination must be based on ampacities from Table 310.15(B)(16) because the selection of conductors based on a tables other than Table 310.15(B)(16),  can result in overheated terminations at the equipment.

Note #2 : Common Uses of  The Neher–McGrath formula

The most common use of the Neher–McGrath formula is for calculation of conductor ampacity in underground electrical ducts (raceways), although the formula is applicable to all conductor installations.

Note #3 : Heat Sources Surrounding The Conductor

The conductor’s ampacity is based on the rate of heat dissipation through the thermal resistances from all heat sources surrounding the conductor.
For conductors in underground electrical ducts, there are several heat sources, as follows, (and as illustrated in Fig.1):

1- Conductor losses due to the load current I 2R.
These losses vary with the load current, conductor material, and conductor cross-sectional area (conductor size).

2- Skin-effect heating if the current is alternating current.
The heat developed by the skin effect is due to the shape of the conductor and is based on the configuration of the conductors (i.e., solid, stranded, or compact).

3- Hysteresis losses if the duct is steel or other magnetic material.
These losses are dependent on the magnetic properties of the electrical duct and the shape of the duct.

4- Heating from other conductors in the duct. 
This heating is based on the number, location, and proximity of other conductors as well as the losses in the other conductors. The more conductors in the raceway, the greater the heating effect from these conductors is likely to be. This factor replaces the adjustment factors in 310.15(B) (3)(a) to the ampacity tables.

5- Mutual heating from other ducts, cables, and so forth, in the vicinity.
The closer the other heat sources and the more they surround the duct for which calculations are being made, the greater the heating effect.
For example, in the case of a symmetrical nine-duct bank, three ducts high and three ducts wide, the center duct will receive the most heat as a result of mutual heating.
Heat generated by the following various types of losses is conducted through the different thermal barriers or resistances, as illustrated in above image.


Note #4 : Thermal Barriers Or Resistances Surrounding The Conductor

Heat generated by the above heat sources in note#3 are conducted/dissipated through the different thermal barriers or resistances, (as illustrated in Fig.1) there are many thermal barriers as follows:

1- Conductor Insulation
It presents a thermal resistance to heat generated by the conductor due to the I 2R losses, including any dielectric losses. This thermal resistance value depends on the thickness of the insulation and the type of insulating material used.

2- Airspace
The airspace between the conductor insulation and the surrounding wall or raceway. The thermal resistance of this airspace is based on the number of conductors in the duct, the assumed mean value of the temperature of the air in the duct, and the constants provided in the Neher–McGrath paper, which were determined from experimental data.

3- Duct Wall
This thermal resistance is based on the thermal resistivity of the type of material used and the thickness of the duct wall.  Metallic materials have less thermal resistance than nonmetallic materials. The thicker the wall, the greater the thermal resistance.

4- Earth Backfill
This resistance incorporates not only the thermal resistivity and ambient temperature of the earth but also the number of current-carrying conductors within the duct, the outside diameter of the duct, the burial depth, a loss factor, and the mutual heating factor caused by other nearby ducts. The deeper the duct is buried, the greater the thermal resistance.

Rule#2: Conductor Ampacities Calculation by The Neher–McGrath formula

Typical ampacities for conductors rated 0 through 2000 volts calculated by The Neher–McGrath formula are included in many tables and figures as follows:.

1- Tables:

  • TABLE B.310.15(B)(2)(1),
  • TABLE B.310.15(B)(2)(3),
  • TABLE B.310.15(B)(2)(5) in Accordance with Figure B.310.15(B)(2)(2),
  • TABLE B.310.15(B)(2)(6) in Accordance with Figure B.310.15(B)(2)(2),
  • TABLE B.310.15(B)(2)(7) in Accordance with Figure B.310.15(B)(2)(2),
  • TABLE B.310.15(B)(2)(8)  in Accordance with Figure B.310.15(B)(2)(2),
  • TABLE B.310.15(B)(2)(9) in Accordance with Figure B.310.15(B)(2)(2),
  • TABLE B.310.15(B)(2)(10) in Accordance with Figure B.310.15(B)(2)(2),
  • TABLE B.310.15(B)(2)(11).

2- Figures:

The following figures represent Underground electrical duct bank configurations:

  • Figure B.310.15(B)(2)(3),
  • Figure B.310.15(B)(2)(4),
  • Figure B.310.15(B)(2)(5).

These figures are utilized for conductors rated 0 through 5000 volts.

To download a PDF copy of Annex B tables and figures, click on the link.


In Figure B.310.15(B)(2)(2) through Figure B.310.15(B)(2)(5), where adjacent duct banks are used, a separation of 1.5 m (5 ft) between the centerlines of the closest ducts in each bank or 1.2 m (4 ft) between the extremities of the concrete envelopes is sufficient to prevent derating of the conductors due to mutual heating.



Thermal resistivity: it refers to the heat transfer capability through a substance by conduction. It is the reciprocal of thermal conductivity and is normally expressed in the units°C-cm/watt.

Typical values of thermal resistivity (Rho) are as follows:

  • Average soil (90 percent of USA) = 90
  • Concrete = 55
  • Damp soil (coastal areas, high water table) = 60
  • Paper insulation = 550
  • Polyethylene (PE) = 450
  • Polyvinyl chloride (PVC) = 650
  • Rubber and rubber-like = 500
  • Very dry soil (rocky or sandy) = 120                                                                             


If other factors remain the same, a soil resistivity higher than 90 reduces ampacities to values below those listed in Tables B.310.15(B)(2)(5) through B.310.15(B)(2)(10) for underground ampacity. Conversely, a load factor less than 100 percent increases ampacities if other factors remain the same.

In the next Article, I will explain how to use the NEC, Annex B tables and figures used for Ampacity Calculations by the Neher–McGrath formula. Please, keep following.

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