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 02000 Volts
shall be permitted to be determined by two methods:

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.
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.
 Conductor Ampacity Calculation – Part One
 Conductor Ampacity Calculation – Part Two
 Conductor Ampacity Calculation – Part Three
 Conductor Ampacity Calculation – Part Four
 Conductor Ampacity Calculation – Part Five
 Conductor Ampacity Calculation – Part Six
 Conductor Ampacity Calculation – Part Seven
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:
where:
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 crosssectional area
(conductor size).
2 Skineffect 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
nineduct 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.

Fig.1 
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 currentcarrying 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:
2 Figures:
The following figures
represent Underground electrical duct bank configurations:
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.
Important!!!
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.

Definition:
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°Ccm/watt.
Typical values of thermal
resistivity (Rho) are as follows:

Important!!!
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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