WIRES AND WIRE CALCULATIONS
The wireman who is called upon to plan and install a system of wiring
will find it necessary first to have a knowledge of the various kinds
of wire so as to select the one best suited for the work, and to be
able to make simple calculations in order to determine the proper sizes
of wire for the various circuits.
Wires are generally made of circular cross section. The process
of manufacture consists in drawing the material through steel
dies, when its properties permit this treatment. In the case of
some substances, as for instance, tin and lead, difficulties
arise in the drawing process, and these are therefore
"squirted."
The metals most extensively used for wires are copper and
iron; German silver, tin and lead are also employed, but only
at points where it is desirable to have a comparatively high
resistance in the circuit.
=Copper Wire.=—Copper is used in nearly all cases of wiring because it
combines high electrical conductivity with good mechanical qualities
and reasonable price. In conductivity it is only surpassed by silver,
but the cost of the latter of course prohibits its use for wiring
purposes.
Copper wire is used for electric light and power lines, for most
telephone and some telegraph lines, and for all cases where low
resistance is required at moderate cost.
Hard drawn copper wire is ductile, and has a high tensile
strength; these properties allow it to be bent around corners
and drawn through tubes without injury.
Pure annealed copper has a specific gravity of 8.89 at 60°
Fahr. One cubic inch weighs .32 pound; its melting point is
about 2,100° Fahr.
Good hard drawn copper has a tensile strength of about three
times its own weight per mile length. Thus, a number 10 B. &
S. gauge copper wire, weighing 166 lbs. per mile, will have a
breaking strength equal to approximately 3 × 166 = 498 lbs.
=Iron Wire.=—This kind of wire is largely used for telegraph and
telephone lines, although it is rapidly being replaced by copper in
long lines.
There are three grades of iron wire:
1. =Extra best best (E. B. B.)= which has the highest
conductivity and is the nearest to being uniform, in quality,
being both tough and pliable;
2. =Best best (B. B.)=, which varies more in quality, is not so
tough, and is lower in conductivity. _It is frequently sold as_
=E. B. B.=;
3. =Best (B.)=, which is the poorest grade made, being more
brittle, and lowest in conductivity. Iron wire should be well
galvanized.
=German Silver Wire.=—German silver is an alloy consisting of 18 to
30% nickel, and the balance about four parts copper to one part zinc.
It is very largely used as a resistance material in making resistance
coils, and is sold in the form of wire, and strip. The resistance of
this wire varies with its composition.
The resistance of the 18% alloy at 25° C. is 18 times that of
copper, and of the 30% alloy about 28 times that of copper.
The safe carrying capacity of the wire in spirals in open air
for continuous duty is such that the circular mils per ampere
varies from about 1,500 in No. 10 wire to about 475 in No. 30.
For intermittent duty the capacity is twice as great.
=Standard of Copper Wire Resistance.=—Matthiessen's standard for
resistance of copper wire is as follows: _A hard drawn copper wire
one meter long, weighing one gramme, has a resistance of .1469 B. A.
unit at 32° Fahr._ Relative conducting power: silver, 100; hard or
un-annealed copper, 99.95; soft or annealed copper, 102.21.
A committee of the Am. Inst. Electrical Engineers recommends the
following form of Matthiessen's standard, taking 8.89 as the specific
gravity of pure copper: _A soft copper wire one meter long and one
millimeter in diameter has an electrical resistance of .02057 B. A.
unit at 0°C._[2] From this the resistance of a soft copper wire one
foot long and .001 in. in diameter (mil-foot) is 9.72 B. A. units at
0°C.
[2] NOTE.—The international ohm ÷ B. A. ohm = 1 ÷ .9866. The B. A. ohm
÷ International ohm = 1 ÷ 1.0136. Hence, to reduce British Association
ohms to International ohms, divide by 1.0136. or multiply by .9866.
For every degree Fahr., the resistance of copper wire increases
.2222%. Thus a piece of copper wire having a resistance of 10
ohms at 32°, would have a resistance of 11.11 ohms at 82°.
Relative Conductivity of Different Metals and Alloys.
(According to Lazare Weiler.)
Pure silver 100
Pure copper 100
Alloy, ½ copper, ½ silver 86.65
Telephonic siliceous bronze 35
Pure zinc 29.9
Brass with 35% zinc 21.5
Swedish iron 16
Pure platinum 10.6
Copper with 10% nickel 10.6
Pure lead 8.88
Pure nickel 7.89
Phosphor-bronze, 10% tin 3.88
=Conductors.=—Copper is used more than any other metal for
transmitting electrical energy, and for interior wiring it is used
exclusively. Copper conductors should be of the highest commercial
conductivity, not less than 97%.
For conductors up to sizes as large as No. 8 B. & S. gauge, single
conductors may be used, but for larger sizes the necessary conductivity
should be obtained by conductors made up of strands of smaller wires.
The size of these strands depend upon the size of the conductors and
the conditions under which they are to be used.
Where conductors are very large (as for instance dynamo leads),
and where it is essential that they should be as flexible as
possible, strands as small as No. 20 or 22 B. & S. gauge may be
used.
Conductors for flexible cords, pendants, fixtures, etc.,
should also consist of very fine strands, so that they may be
perfectly pliable and flexible.
The individual strands for instance, for a No. 16 B. & S. gauge
flexible cord should be as fine as No. 30.
[Illustration: FIG. 807.—Elevator cable for annunciators. This type
of cable is designed for connecting the movable elevator car with the
signal buttons upon the different floors, and is constructed so as to
secure strength and flexibility.]
=Covered Conductors.=—For most conditions of service, wires are
protected with an insulating covering. Wires used in interior circuits
should have a covering which shall act both as an electrical insulator
and as a mechanical protection. In some instances, however, the
insulating qualities are of secondary importance.
The various forms of covering now in use commercially for wires are:
1. Rubber;
2. Weather proof;
3. Slow burning;
4. Slow burning weather proof;
5. Armoured.
=Rubber Covered Conductors.=—This class of conductor consists of a
tinned copper wire with a rubber covering, protected by an outside
braiding of cotton saturated with a preservative compound.
=Ques. What are the advantages of rubber insulation for conductors?=
Ans. It is waterproof, flexible, fairly strong, and has high insulating
qualities.
[Illustration: FIG. 808.—Rubber insulated telephone and telegraph
wires. The inner coat of rubber should be free from sulphur or other
substances liable to corrode the copper.]
=Ques. What are the disadvantages of rubber insulation?=
Ans. It deteriorates more or less rapidly and is quickly injured by
temperatures above 140° Fahr.
=Ques. For what service are rubber covered conductors adapted?=
Ans. For interior wiring.
=Ques. Is pure rubber used?=
Ans. No. The covering should be made from a compound containing from 20
to 35 per cent. of pure rubber.
It would be difficult to place pure rubber on a wire,
and moreover a covering made of pure rubber would not be
durable and would deteriorate very rapidly, particularly at
temperatures above 120° Fahr. Accordingly, it is mixed with
other materials, such as French chalk, silicate of magnesia,
sulphur, red lead, etc.
=Weather Proof Conductors.=—In this class of conductor, the wire is
protected from the weather by a waterproof covering, consisting usually
of braided cotton of two or three thicknesses saturated with a moisture
resisting insulating compound.
=Ques. Where are weather proof conductors used?=
Ans. In places subject to dampness, such as cellars, tunnels, open
sheds, breweries, etc.
[Illustration: FIG. 809.—Twisted weather proof wires. The insulation
consists of two or three thicknesses of braided cotton saturated with a
moisture resisting insulating compound.]
=Ques. What are the advantages of weather proof conductors?=
Ans. The insulation is cheap, very durable, and does not deteriorate
unless exposed to high temperatures such as will melt the compound.
=Ques. State the disadvantages.=
Ans. The covering is more or less inflammable and is not very efficient
as an insulator.
=Ques. What precaution should be taken in using weather proof
conductors?=
Ans. On account of the inflammable character of the covering, care
should be taken in wiring at points where any considerable number of
conductors are brought together, or where there is much woodwork or
other combustible material.
=Ques. For what use are weather proof conductors especially adapted?=
Ans. For outside wiring where moisture is certain and where fireproof
quality is not necessary.
Obviously conductors of this class should not be used in
conduits, nor in fact, in any way except exposed on glass or
porcelain insulators.
=Slow Burning Wire.=—This class of conductor is defined as: _one
that will not carry fire_. The covering consists of layers of cotton
or other thread, all the interstices of which are filled with the
fireproofing compound, or of material having equivalent fire resisting
and insulating properties. The outer layer is braided and specially
designed to withstand abrasion. The thickness of insulation must not
be less than that required for slow burning weather proof wire and
the outer surface must be finished smooth and hard.—_Underwriters'
requirements._
[Illustration: FIG. 810.—Slow burning wire, formerly known as
Underwriter's Wire. The insulation is triple braided, saturated with a
white fireproof compound. Solid conductor.]
=Ques. Where should slow burning wires be used?=
Ans. In hot dry places, where ordinary insulations would be injured,
and where wires are bunched, as on the back of a large switchboard or
in a wire tower.
A slow burning covering is considered good enough when the
wires are entirely on insulating supports. Its main object is
to prevent the copper conductors coming into contact with each
other or anything else.
=Ques. What must be done before using weather proof wire?=
Ans. Permission to use the wire must first be obtained from the local
Inspection Department.
=Slow Burning Weather Proof Wire.=—The covering of this type wire
is a combination of the underwriters and weather proof insulations.
The fireproof coating comprises a little more than half of the total
covering. When the fireproof coating is placed on the outside, the wire
is called "slow burning weather proof."
[Illustration: FIG. 811.—Slow burning weather proof wire. The
insulation is composed of two braids thoroughly saturated with a fire
proof composition, over which is a highly polished weather proof third
braid. This wire was formerly known as "fire and weather proof" wire.]
=Ques. How does slow burning weather proof wire compare with weather
proof wire?=
Ans. It is less inflammable and less subject to softening under heat.
=Ques. Where should slow burning weather proof wire be used?=
Ans. In places where the wires are to be run exposed and where moisture
resisting quality is desired, also where at the same time it is
desirable to avoid an excess of inflammable covering.
=Ques. How should it be installed?=
Ans. It should be set on glass or porcelain insulators.
=Miscellaneous Insulated Conductors=
[Illustration: FIG. 812.—Armoured submarine cable. This type of cable
is insulated with a rubber compound containing not less than 30% of
pure Para rubber. The following specifications have been adapted by
various telegraph companies and the United States Government for
general use.]
+————————————-+————————————+————————-+——————————————+——————————+——————————-+
| No. of | Gauge of | No. of | Gauge of | Outside | Weight |
| Conductors | Conductors | Armour | Armour Wires | Diameter | per 1,000 |
| | (B. & S.) | Wires | B. W. G. | (inch) | Feet |
+————————————-+————————————+————————-+——————————————+——————————+——————————-+
| | | | | | |
| 1 | 14 | 12 | 8 | ⅞ | 1,150 |
| 2 | 14 | 16 | 8 | 1-31/32 | 1,675 |
| 3 | 14 | 14 | 6 | 1¼ | 2,400 |
| 4 | 14 | 16 | 6 | 1-5/16 | 2,750 |
| 5 | 14 | 19 | 6 | 1⅜ | 3,100 |
| 6 | 14 | 21 | 6 | 1½ | 3,500 |
| 7 | 14 | 21 | 6 | 1½ | 3,600 |
| 10 | 14 | 22 | 4 | 1⅞ | 4,600 |
| | | | | | |
+————————————-+————————————+————————-+——————————————+——————————+——————————-+
NOTE.—The above specifications refer only to river and harbor
cables. Ocean cables are of an entirely different character,
and consist of "shore end," "intermediate" and "deep sea" types.
[Illustration: FIG. 813.—Gas engine ignition cable. This is a special
cable made to stand the hard service necessary on automobiles. The
conductor is composed of 36 strands of No. 27 tinned copper wire, equal
to No. 14 in capacity, which gives it necessary flexibility. About this
conductor are woven two layers of cotton thread. Over this are woven,
in opposite directions, several layers of specially prepared tape which
has been given two coatings of fine insulating varnish. Two strong
braids of cotton form the outside covering, and each of these different
braids is passed through a bath of insulating liquid and baked in a
steam heated oven. With three layers of tape the cable will stand a
test of 18,000 to 20,000 volts, and with five layers, 30,000 volts.]
[Illustration: FIG. 814.—Paper insulated lead encased telephone
cable.]
=Ques. For what service is slow burning weather proof wire not suited?=
Ans. It is not adapted to outside work.
=Safe Carrying Capacity of Wire.=—All wires will heat when a current
of electricity passes through them. The greater the current or the
smaller the wire, the greater will be the heating effect. Large wires
are heated comparatively more than small wires because the latter have
a relatively greater radiating surface.
[Illustration: FIG. 815.—Pothead wires. The standard wire for pothead
work is either No. 19, 20 or 22 B. & S. gauge, either single conductor
or twisted pair, insulated to a diameter of 3/32 inch over rubber,
without any outer braid or protection. In the case of twisted pairs
one conductor is usually made of a differently colored rubber than the
other, so as to distinguish between them.]
The temperature of a wire increases approximately as the square of the
current, and inversely as the cube of the diameter of the wire.
The elevation in temperature of a wire carrying a current represents so
much lost energy.
From these considerations it must be clear that it is important not to
overload conductors in order to secure efficient working, and to avoid
risk of fire on inside installations.
The Board of Underwriters specifies that the carrying capacity
of a conductor is safe when the wire will conduct a certain
current without becoming painfully hot.
In the following table of carrying capacity, prepared by
the underwriters, a wire is assumed to have a safe carrying
capacity when its temperature is not increased by the given
current over 30° Fahr. above that of the surrounding air.
SAFE CARRYING CAPACITIES OF WIRES
(Maximum amperes allowed by the Underwriters.)
+————————+——————————————-+————————————+————————————+
| Brown | | Rubber | Other |
| and | | insulation | insulations|
| Sharpe | Circular mils | —————— | —————— |
| Gauge | | Amperes | Amperes |
| | | | |
+————————+——————————————-+————————————+————————————+
| | | | |
| 18 | 1,624 | 3 | 5 |
| 16 | 2,583 | 6 | 8 |
| 14 | 4,107 | 12 | 16 |
| 12 | 6,530 | 17 | 23 |
| 10 | 10,380 | 24 | 32 |
| 8 | 16,510 | 33 | 46 |
| 6 | 26,250 | 46 | 65 |
| 5 | 33,100 | 54 | 77 |
| 4 | 41,740 | 65 | 92 |
| 3 | 52,630 | 76 | 110 |
| 2 | 66,370 | 90 | 131 |
| 1 | 83,690 | 107 | 156 |
| 0 | 105,500 | 127 | 185 |
| 00 | 133,100 | 150 | 220 |
| 000 | 167,800 | 177 | 262 |
| 0000 | 211,600 | 210 | 312 |
| | 200,000 | 200 | 300 |
| | 300,000 | 270 | 400 |
| | 400,000 | 330 | 500 |
| | 500,000 | 390 | 590 |
| | 600,000 | 450 | 680 |
| | 700,000 | 500 | 760 |
| | 800,000 | 550 | 840 |
| | 900,000 | 600 | 920 |
| | 1,000,000 | 650 | 1,000 |
| | 1,100,000 | 690 | 1,080 |
| | 1,200,000 | 730 | 1,150 |
| | 1,300,000 | 770 | 1,220 |
| | 1,400,000 | 810 | 1,290 |
| | 1,500,000 | 850 | 1,360 |
| | 1,600,000 | 890 | 1,430 |
| | 1,700,000 | 930 | 1,490 |
| | 1,800,000 | 970 | 1,550 |
| | 1,900,000 | 1,010 | 1,610 |
| | 2,000,000 | 1,050 | 1,670 |
| | | | |
+————————+——————————————-+————————————+————————————+
The lower limit is specified for rubber covered wires to
prevent gradual deterioration of the high insulations
by the heat of the wires, but not from fear of igniting
the insulation. The question of drop is not taken into
consideration in the table on page 731.
The carrying capacity of Nos. 16 and 18 B. & S. gauge wire is
given, but no smaller than No. 14 is to be used, except as
allowed under rules for fixture wiring.—_Underwriters' Rules._
=Circular Mils.=—The unit of measurement in measuring the cross
sectional area of wires is the _circular mil_; it is the area of a
circle one mil (.001 in.) in diameter.
_The area of a wire in circular mils is equal to the square of the
diameter in mils._
[Illustration: FIG. 816.—Diagram illustrating circular mils. The
circular mil is used as a unit of cross sectional area in measuring
wires. It is equal to the area of a circle .001 in. diameter; its value
is .0000007854 square inch. In the figure the sum of the areas of the
nine small circles equals the area of the large circle. This is evident
from the following: Take the diameter of the small circles as unity,
then the diameter of the large circle is three. Hence, the sum of the
area of the small circles × (¼ π × 1²) × 9 = .7854 × 9 =
7.0686; area of the large circle = ¼ π × 3² = .7854 × 9 =
7.0686. Therefore since the area of the large circle equals the sum of
the areas of the small circles, the area of a wire in circular mils is
equal to _the square of its diameter expressed in mils_.]
Thus a wire 2 mils in diameter (.002 in.) has a cross sectional
area of 2 × 2 = circular mils. Accordingly to obtain the area
of a wire in circular mils, _measure its diameter with a
micrometer which reads directly in mils or thousandths of an
inch, and square the reading_.
The circular mil (abbreviated C.M.) applies to all _round_
conductors, and has a value of .7854 times that of the square
mil, that is, 1 circular mil = .7854 square mil. If the
diameter be expressed as a fraction of an inch, as for instance
⅓ in., the circular mil area may be found as follows: Reduce
the fraction ⅓ to the decimal of an inch, multiply the result
by 1,000 to express the diameter in mils, and square the
diameter so expressed, thus: ⅓ = 1,000 ÷ 3 = .333. .333 ×
1,000 = 333 mils; 333 × 333 = 110,889 circular mils.
The diameter of any wire may be found when its circular mil
area is known by extracting the square root of the circular mil
area.
=Square Mils.=—For measuring conductors of square or rectangular cross
section, such as bus bars, copper ribbon, etc., the square mil is used.
A square mil is the area of a square whose sides are one mil (.001 in.
long) and is equal to .001 × .001 = .000001 square inch.
[Illustration: FIG. 817.—Diagram illustrating square mils. A square
mil is a unit of area employed in measuring the areas of cross sections
of square or rectangular conductors. It is equal to .000001 square
inch. One square mil equals 1.2732 circular mils. The figure shows
an area of nine square mils; this is equal to 9 × 1.2732 = 11.4588
circular mils.]
EXAMPLE.—A copper ribbon for a field coil measures ⅝ inch by
⅛ inch. What is its area in square mils? What is its area in
circular mils?
⅝ = .625 in., or 625 mils; ⅛ = .125 in., or 125 mils.
Area in square mils = 625 × 125 = 78,125.
Area in circular mils= { 78,125 ÷ .7854 }
{or 78.125 × 1.2732} = 99,469.
=Mil Foot.=—This unit is used as a basis for computing the resistance
of any given wire. A mil foot means _a volume one mil in diameter and
one foot long_.
_The resistance of a wire of commercially pure copper one mil in
diameter and one foot long is taken as a standard in calculating the
resistance of wires, and has been found to be equal to 10.79 ohms at
75° Fahr._
The calculation is made according to the following rule:
_The resistance of a copper wire is equal to its length in feet,
multiplied by the resistance of one mil foot (10.79 ohms) and divided
by the number of circular mils, or the square of its diameter._
Expressed as a formula:
length of wire in ft. × 10.79
resistance in ohms = —————————————————————————————— (1)
circular mils
EXAMPLE. What is the resistance of a copper wire 1,500 feet
long and having a transverse area of 10,381 circular mils?
Substituting these values in formula (1)
1,500 × 10.79
resistance = ———————————————————— = 1.559 ohms.
10,381
_The transverse area of a copper wire is found by multiplying the
resistance of a mil foot (10.79) by its length in feet and dividing the
result by its resistance in ohms._
This is obtained directly from the formula (1) by solving the equation
for circular mils, thus:
length of wire in ft. × 10.79
circular mils = ——————————————————————————————- (2)
resistance in ohms
EXAMPLE. What is the circular mil area of a wire 1,500 feet
long and having a resistance of 1.559 ohms?
Substituting the values in equation (2)
1,500 × 10.79
circular mils = ————————————- = 10,381
1.559
[Illustration: FIGS. 818 and 819.—Diagrams illustrating the meaning
of the term lamp foot, and how to apply it in calculating a circuit.
As defined, _one 16 candle power lamp at a distance of one foot from
the fuse block or point of supply is called a lamp foot_; this is
equivalent to one 8 candle power lamp at a distance of 2 feet, or one
32 candle power lamp one-half foot from the fuse block. In fig. 819,
there are four 8 candle power lamps, and the distance to center of
distribution is 10 feet. The circuit then contains 4 ÷ 2 × 10 = 20 lamp
feet.]
=Lamp Foot.=—This unit facilitates laying out wiring and calculating
the drop. A lamp foot is defined as _one 16 candle power lamp at a
distance of one foot from the point of supply_. Accordingly the number
of lamp feet in any circuit is equal to the number of 16 candle power
lamps (or equivalent in other sizes) in the circuit multiplied by the
distance in feet from the fuse block to the center of distribution.
When no point is specified, the feet are always measured from
the supply point to the center of distribution. When other than
16 c.p. lamps are in the circuit they must be reduced to 16
c.p. lamps. Thus two 8 c.p. lamps would be counted one 16 c.p.
lamp, one 32 c.p. lamp would be counted two 16 c.p. lamps, etc.
=Ampere Foot.=—From the foregoing explanation of _lamp foot_, the
significance of _ampere foot_ is easily understood—the two terms are
in fact self-defining.
An ampere foot may be defined as _the product of one ampere multiplied
by one foot_.
The unit ampere foot is used in figuring motor circuits or currents
designed to carry a mixed load.
[Illustration: FIG. 820.—The center of distribution of a circuit
coincides with the geometrical center of the group of lamps when the
lamps are of uniform size and spaced equal distances apart. The center
of distribution is here indicated by the dotted line A B.]
The ampere feet of a main are found by _multiplying the maximum load in
amperes by the distance from the fuse block to the electrical center of
the load_.
Thus if the center of distribution be 50 feet from the fuse
block and the maximum load is 9 amperes, the number of ampere
feet is equal to 9 × 50 = 450.
=Electrical Center of Distribution.=—The electrical center of a
circuit depends upon the distances between the lamps and the fuse
block; also the relative sizes of the lamps.
It may be defined as _the sum of the lamp feet for each section divided
by the number of 16 candle power lamps in the circuit_.
If the lamps be of uniform capacity, and placed at equal distances
apart, the center of distribution will coincide with the geometrical
center of the group of lamps. However, if the lamps vary in size, and
be irregularly spaced, the electrical center will not coincide with the
geometrical center unless the lamps be symmetrically arranged so as to
compensate for the difference in sizes and spacing.
[Illustration: FIG. 821.—Diagram of an irregular circuit illustrating
method of finding the center of distribution. Rule: _Divide the sum of
the lamp feet for each section by the number of 16 candle power lamps
or equivalent in the circuit_; the quotient gives the distance in feet
from the fuse block to the center of distribution.]
In such cases, as shown in fig. 821, the electrical center can
be determined by adding together the lamp feet of the several
sections A, B, C, etc., of the main and dividing the result by
the 16 c.p. units. Thus the lamp feet of
Section A = 10 lamps × 10 feet= 100
" B = 9 " × 5 " = 45
" C = 7 " × 6 " = 42
" D = 6 " × 4 " = 24
" E = 5 " × 5 " = 25
" F = 4 " × 10 " = 40
" G = 2 " × 5 " = 10
——-
which added together gives a total of 286 lamp feet.
This when divided by the ten 16 c.p. units comprising four 16
c.p. lamps and three 32 c.p. lamps, gives a little over 28½
feet as the distance from the fuse block to the center of
distribution, the position of which is shown by the line M N in
fig. 821, while that of the geometrical center is shown by the
line K L.
When the center of distribution is at a considerable distance
from the supply circuit, and it becomes advisable to divide
the wiring into two distinct elements—a feeder and one or
more mains, the junction of the feeder and the mains should
be located at the electrical center of the mains whenever
possible. When this is done, it is obvious that the wire size
of only one half the main needs to be calculated, as both
halves of the main are identical.
[Illustration: FIG. 822.—Brown and Sharpe (B. & S.), or American
Standard wire gauge. This gauge was adopted by the brass manufacturers
Jan., 1858. The cut is full size, and therefore, shows the actual sizes
corresponding to the gauge numbers.]
=Wire Gauges.=—For the purpose of facilitating the measurement
of wire, a number of gauges have been designed by various wire
manufacturing concerns. The principal gauges used in the United States
are the American or Brown & Sharp's gauge; the English standard or
Birmingham gauge; Washburn & Moen's standard gauge; Imperial wire
gauge; Stubs' steel wire gauge, and the U. S. Standard wire gauge.
The several gauges are here given with explanation of their use.
=The American Standard or Brown and Sharp's Gauge.=—This gauge
is commonly designated as A. W. G. or B. & S., and has been
adopted by brass manufacturers and is used mostly in measuring
brass, copper, silver, German silver, and gold in both wire and
plate.
=Birmingham or Stub's Wire Gauge (B. W. G.).=—Old English
Standard and Iron Wire Gauge. _Birmingham or Stubs' Iron Wire
Gauge is not the same as Stubs' Steel Wire Gauge_. A table of
Stub's Steel Wire Gauge is given on page 741.
[Illustration: FIG. 823.—Micrometer screw gauge. It consists
essentially of a screw whose thread is accurately turned to a pitch
of some convenient fraction of an inch or centimetre. When the screw
is screwed home, the surfaces of A and B meet, and the instrument
should then read zero on both the straight and the circular scale. If
this be not so, there is a zero error which must be either allowed
for, or corrected by means of the screw provided for that purpose. If
the former course be adopted, the reading of the instrument is taken
when the faces A and B are in contact, and this number added to or
subtracted from the final reading according to whether the error makes
the wire apparently smaller or greater than its real size. The surfaces
A and B are now screwed apart and then, after the wire to be measured
(which should be clean and straight) has been introduced between them,
they are screwed together to lightly grip the wire. If the gauge be
screwed up too tightly the value of the measurement is destroyed, since
a copper wire can easily be crushed, and in addition the accurate
screw may be permanently damaged. To avoid the possibility of this
happening, screw gauges are provided with a ratchet which prevents an
excessive force being applied to the screw. If the pitch of the screw
in the gauge be ½0th of an inch, and the circular scale consist of
50 divisions, then for each revolution of the screw, the surface B
will travel a distance equal to the pitch, that is ½0th of an inch.
The graduations on an instrument of this kind are generally ⅒th of
an inch on the straight scale, with shorter lines to mark the half
divisions. The thickness of a wire on the straight scale can therefore
be read to the nearest ½0th inch. Each division of the circular scale
represents 1/50th of a revolution of the screw, which corresponds to a
change in distance between A and B, of 1/50 of 1/20 = 1/1,000 in. If
then the reading on the straight scale be 1 and on the circular scale
35, the distance between A and B is .1 + .035 = .135 inch.]
=Washburn and Moen's Standard Wire Gauge.=—Commonly designated
as W. & M. G. has been adopted by the U. S. Steel Corporation
in making their wire.
=New British Standard (N. B. S.).=—British Imperial English
Legal Standard and Standard Wire Gauge, and is variously
abbreviated by S. W. G. and I. W. G.
=Roebling Gauge.=—Washburn Moen, American Steel & Wire Co.'s
Iron Wire Gauge.
[Illustration: FIGS. 824 and 825.—U. S. wireman's calculating gauge;
views showing both sides. On the side shown in fig. 824, set the
required number of feet on the small circle opposite the required
number of amperes on the large circle, then set the small pointer at
the required voltage and loss. Then on the other side (fig. 825) the
large pointer will indicate the required size of wire in B. & S. gauge,
and will also indicate the safe carrying capacity, while the wire may
be gauged by slot A (fig. 824).]
=U. S. Standard Wire Gauge.=—This gauge is used for measuring
sheet and plate iron, and steel, by the U. S. Government in
assessing duties, and in making requisitions for supplies.
=Old English Standard Wire Gauge.=—The old English gauge is
the same as the Birmingham or Stubs' standard gauge, commonly
designated as B. W. G. It is used chiefly for measuring sheet
iron and steel, also soft steel and iron wire.
=London Gauge.=—Old English (_not Old English Standard_).
From the foregoing it is seen that great confusion exists with
such a multiplicity of gauges and emphasizes the importance of
specifying the gauge and of knowing what gauge to use.
In using the gauges known as Stubs' Gauges, there should be
constantly borne in mind the difference between the Stubs' Iron
Wire Gauge and the Stubs' Steel Wire Gauge. The Stubs' Iron
Wire Gauge is the one commonly known as the English Standard
Wire, or Birmingham Gauge and designates the Stubs' _soft_ wire
sizes. The Stubs' Steel Wire Gauge is the one that is used in
measuring drawn steel wire or drill rods of Stubs' make and is
also used by many makers of American drill rods.
=STUBS' STEEL WIRE GAUGE=
——————-+————————-++——————+————————-++——————+————————-++——————+———————-
| Size of || | Size of || | Size of || | Size of
Letter.| Letter ||No. of| Number ||No. of| Number ||No. of| Number
| in || Wire | in || Wire | in || Wire | in
|Decimals.||Gauge.|Decimals.||Gauge.|Decimals.||Gauge.|Decimals.
——————-+————————-++——————+————————-++——————+————————-++——————+———————-
Z | .413 || 1 | .227 || 28 | .139 || 55 | .050
Y | .404 || 2 | .219 || 29 | .134 || 56 | .045
X | .397 || 3 | .212 || 30 | .127 || 57 | .042
W | .386 || 4 | .207 || 31 | .120 || 58 | .041
V | .377 || 5 | .204 || 32 | .115 || 59 | .040
U | .368 || 6 | .201 || 33 | .112 || 60 | .039
T | .358 || 7 | .199 || 34 | .110 || 61 | .038
S | .348 || 8 | .197 || 35 | .108 || 62 | .037
R | .339 || 9 | .194 || 36 | .106 || 63 | .036
Q | .332 || 10 | .191 || 37 | .103 || 64 | .035
P | .323 || 11 | .188 || 38 | .101 || 65 | .033
O | .316 || 12 | .185 || 39 | .099 || 66 | .032
N | .302 || 13 | .182 || 40 | .097 || 67 | .031
M | .295 || 14 | .180 || 41 | .095 || 68 | .030
L | .290 || 15 | .178 || 42 | .092 || 69 | .029
K | .281 || 16 | .175 || 43 | .088 || 70 | .027
J | .277 || 17 | .172 || 44 | .085 || 71 | .026
I | .272 || 18 | .168 || 45 | .081 || 72 | .024
H | .266 || 19 | .164 || 46 | .079 || 73 | .023
G | .261 || 20 | .161 || 47 | .077 || 74 | .022
F | .257 || 21 | .157 || 48 | .075 || 75 | .020
E | .250 || 22 | .155 || 49 | .072 || 76 | .018
D | .246 || 23 | .153 || 50 | .069 || 77 | .016
C | .242 || 24 | .151 || 51 | .066 || 78 | .015
B | .238 || 25 | .148 || 52 | .063 || 79 | .014
A | .234 || 26 | .146 || 53 | .058 || 80 | .013
| || 27 | .143 || 54 | .055 || |
——————-+————————-++——————+————————-++——————+————————-++——————+———————-
The following table gives the diameters, in decimal parts of an inch,
of the various sizes of wire corresponding to the number of gauge
numbers of the different standard wire gauges used in the United
States.
=TABLE OF VARIOUS WIRE GAUGES=
=In decimal parts of an inch=
————————+————————-+————————-+——————————+——————-+——————-+——————-+——————-
Number | Ameri- | Birming-| Wash- | Tren- |G.W. | Old | Brit-
of | can, or | ham, or | burn & | ton | Pren- | Eng- | ish
Wire | Brown & | Stubs | Moen | Iron | tiss, | lish, | Stan-
Gauge | Sharpe | (B.W.G.)| Mfg. Co.,| Co., | Holy- | From | dard
| (B.&S.) | | Worces- | Tren- | oke, | Brass | (S.W.-
| | | ter, | ton, | Mass. | Mfrs' | G.)
| | | Mass. | N.J. | | List |
————————+————————-+————————-+——————————+——————-+——————-+——————-+——————-
0000000 | | | | | | | .500
000000 | | | .460 | | | | .464
00000 | | | .430 | .450 | | | .432
0000 | .46000 | .454 | .393 | .400 | | | .400
000 | .40964 | .425 | .362 | .360 | .3586 | | .372
00 | .36480 | .380 | .331 | .330 | .3282 | | .348
0 | .32486 | .340 | .307 | .305 | .2994 | | .324
1 | .28930 | .300 | .283 | .285 | .2777 | | .300
2 | .25763 | .284 | .263 | .265 | .2591 | | .276
3 | .22942 | .259 | .244 | .245 | .2401 | | .252
4 | .20431 | .238 | .225 | .225 | .2230 | | .232
5 | .18194 | .220 | .207 | .205 | .2047 | | .212
6 | .16202 | .203 | .192 | .190 | .1885 | | .192
7 | .14428 | .180 | .177 | .175 | .1758 | | .176
8 | .12849 | .165 | .162 | .160 | .1605 | | .160
9 | .11443 | .148 | .148 | .145 | .1471 | | .144
10 | .10189 | .134 | .135 | .130 | .1351 | | .128
11 | .090742 | .120 | .120 | .1175 | .1205 | | .116
12 | .080808 | .109 | .105 | .1050 | .1065 | | .104
13 | .071961 | .095 | .0920 | .0925 | .0928 | | .0920
14 | .064084 | .083 | .0800 | .0800 | .0816 | .08300| .0800
15 | .057068 | .072 | .0720 | .0700 | .0726 | .07200| .0720
16 | .050820 | .065 | .0630 | .0610 | .0627 | .06500| .0640
17 | .045257 | .058 | .0540 | .0525 | .0546 | .05800| .0560
18 | .040303 | .049 | .0470 | .0450 | .0478 | .04900| .0480
19 | .035890 | .042 | .0410 | .0400 | .0411 | .04000| .0400
20 | .031961 | .035 | .0350 | .0350 | .0351 | .03500| .0360
21 | .028462 | .032 | .0320 | .0310 | .0321 | .03150| .0320
22 | .025347 | .028 | .0280 | .0280 | .0290 | .02950| .0280
23 | .022571 | .025 | .0250 | .0250 | .0261 | .02700| .0240
24 | .020100 | .022 | .0230 | .0225 | .0231 | .02500| .0220
25 | .017900 | .020 | .0200 | .0200 | .0212 | .02300| .0200
26 | .015940 | .018 | .0180 | .0180 | .0194 | .02050| .0180
27 | .014195 | .016 | .0170 | .0170 | .0182 | .01875| .0164
28 | .012641 | .014 | .0160 | .0160 | .0170 | .01650| .0148
29 | .011257 | .013 | .0150 | .0150 | .0163 | .01550| .0136
30 | .010025 | .012 | .0140 | .0140 | .0156 | .01375| .0124
31 | .008928 | .010 | .0130 | .0130 | .0146 | .01225| .0116
32 | .007950 | .009 | .0120 | .0120 | .0136 | .01125| .0108
33 | .007080 | .008 | .0110 | .0110 | .0130 | .01025| .0100
34 | .006305 | .007 | .0100 | .0100 | .0118 | .00950| .0092
35 | .005615 | .005 | .0095 | .0095 | .0109 | .00900| .0084
36 | .005000 | .004 | .0090 | .0090 | .0100 | .00750| .0076
37 | .004453 | | .0085 | .0085 | .0095 | .00650| .0068
38 | .003965 | | .0080 | .0080 | .0090 | .00575| .0066
39 | .003531 | | .0075 | .0075 | .0083 | .00500| .0052
40 | .003145 | | .0070 | .0070 | .0078 | .00450| .0048
41 | | | | | | | .0044
42 | | | | | | | .0040
————————+————————-+————————-+——————————+——————-+——————-+——————-+——————-
NOTE.—The sizes of wire are ordinarily expressed by an
arbitrary series of numbers. Unfortunately there are several
independent numbering methods, so that it is always necessary
to specify the method or wire gauge used. The above table gives
the numbers and diameters in decimal parts of an inch for the
various wire gauges in general use.
=Wiring Terms.=—The various members of a complex wiring installation
are designated feeders, sub-feeders, mains, branches, and taps.
A _feeder_ is a stretch of wiring to which no connection is made except
at its two ends.
A _sub-feeder_ is of the same class as a feeder, but is distinguished
either by being one of two or more connecting links between the end of
a single feeder and several distributing mains, or by constituting an
extension of a feeder.
[Illustration: FIG. 826. Circuit diagram illustrating names of the
various parts. A circuit may consist of the following parts as defined
in the accompanying text: 1, feeder, 2, sub-feeders, 3, mains, 4,
branches, 5, taps. It is well to clearly distinguish between these
divisions because the terms are constantly used in wiring.]
A _main_ is a stretch of wiring supplied from one or more feeders or
sub-feeders and distributing current to a number of taps, or else to a
number of branches.
A _branch_ distributes current among a number of lamps, etc.
A _tap_ almost invariably delivers current to a single lamp or other
device.
Reference to fig. 826 will make these definitions clearer. This
diagram is intended merely to illustrate the above definitions
and does not represent any special plan of wiring.
[Illustration: FIGS. 827 and 828. Simplest forms of circuit, consisting
of a main with one or more lamps at the end. The smallest size wire
allowed (No. 14 B.&S. gauge) will generally be found amply large for
such circuits. Note carefully the difference between a main and a
branch by comparison with fig. 826. A main begins from a fuse block,
while a branch is an offset from a main without any fuse block.]
The simplest possible wiring installation is one in which a
single lamp or compact cluster of lamps is located at the
end of a main, as shown in figs. 827 and 828. In such cases
calculations are almost always unnecessary, for the reason that
No. 14 wire, the smallest size allowed by the underwriters,
will supply several lamps at a long distance (as interior
wiring goes) with a very moderate drop. For example, if the
three lamps shown at the end of the main in fig. 828, be of 16
candle power each, and the voltage of the supply circuit be
110 volts, a main of No. 14 wire would supply the lamps at a
distance of 135 feet from the fuse block with a drop of only 1
per cent.
When the lamps are strung along the main, however, as in fig.
826, it is sometimes necessary to choose the size of wire with
regard to the drop, and in order to do this the main must be
measured for either "ampere feet" or "lamp feet."
=Wire Calculations.=—The problem of calculating the size of wire will
be presented here in as simple a form as possible, with explanation of
the various steps so that any one can understand how the formula is
derived.
In determining the size of wire, there are four known factors which
enter into the calculation, viz.:
1. Length of circuit in feet;
2. Maximum current in amperes;
3. Drop or volts lost in the circuit, _in % of the impressed voltage_;
4. Heating effect of the current.
The calculation is based on the _mil foot_, which as previously
explained, is a foot of copper wire one mil in diameter and whose
resistance is equal to 10.79 ohms at 75° Fahr.
[Illustration: FIG. 829.—Wiring for lights requiring unusually long
feeders.]
The first step is to find an expression for the resistance of the wire
which may be later substituted in Ohm's law formula. Accordingly, the
resistance of any conductor is equal to _its length in feet multiplied
by its resistance per mil foot and the product divided by its area in
circular mils_, thus:
length in feet × resistance per mil foot
resistance in ohms = —————————————————————————————————————————
circular mils
feet × 10.8
or ohms = ————————————- (1)
circular mils
(calling the resistance per mil foot 10.8 instead of 10.79 to
facilitate calculation).
LAMP TABLE FOR RUBBER COVERED WIRES
Showing the maximum number of 16 candle power 110 to 240 volt
lamps in parallel that may be carried by the various sizes of
wire without violating the underwriters' rules.
+——————————+———————+——————————————+————————————————+————————————-+
|Wire size |Amperes|3.1-watt lamps|3.5-watt lamps. |4-watt lamps.|
|B. & S. | +——————————————+————————————————+————————————-+
| gauge | | At 110 220 | At 110 220 | 220 230 240 |
| | | volts V. | volts V. | V. V. V. |
+——————————+———————+——————————————+————————————————+—————————————+
|0000 | 210 | 462 924 | 412 825 | 722 754 787 |
| 000 | 177 | 389 778 | 347 695 | 608 636 663 |
| 00 | 150 | 330 660 | 294 589 | 515 539 562 |
| | | | | |
| 0 | 127 | 279 558 | 249 499 | 436 456 476 |
| 1 | 107 | 235 470 | 210 420 | 367 384 401 |
| 2 | 90 | 197 396 | 176 353 | 309 323 337 |
| | | | | |
| 3 | 76 | 167 334 | 149 298 | 261 273 285 |
| 4 | 65 | 143 286 | 127 255 | 223 233 243 |
| 5 | 54 | 118 237 | 106 212 | 185 194 202 |
| | | | | |
| 6 | 46 | 101 202 | 90 180 | 158 165 172 |
| 8 | 33 | 72 145 | 64 129 | 113 118 123 |
| 10 | 24 | 52 105 | 47 94 | 82 86 90 |
| | | | | |
| 12 | 17 | 37 74 | 33 66 | 58 61 63 |
| 14 | 12 | 26 52 | 23½ 47 | 41 43 45 |
| 16[3] | 6 | 13 .. | 11 .. | 20 21 22 |
+——————————+———————+——————————————+————————————————+—————————————+
[3] This size can be used only in the shape of flexible cord.
Now, according to Ohm's law,
volts = amperes × ohms (2)
hence, substituting in (2) the value for the resistance in ohms, as
obtained in (1):
feet × 10.8
volts = amperes × ————————————-
circular mils
or using the usual symbols
feet × 10.8
E = I × ————————————- (3)
circular mils
or expressed in words, formula (3) means that the volts lost or
_drop_ between the beginning and end of a circuit is equal to the
current flowing through the circuit multiplied by the product of the
conductors' length in feet multiplied by the resistance of one mil foot
of wire, divided by the area of the conductor in circular mils.
LAMP TABLE FOR WEATHER PROOF WIRES
Showing the maximum number of 16 candle power 120 to 240 volt
lamps in parallel that may be carried by various sizes of
weather proof wire without violating the underwriters' rules.
+———————+————————+———————————————+———————————————+———————————————-+
|Wire |Amperes |3.1-watt lamps.|3·5-watt lamps.| 4-watt lamps. |
|size | +——————————————-+——————————————-+————————————————|
|B. & S.| | 110 220 | 110 220 | 220 230 240 |
|gauge | | V. V. | V. V. | V. V. V. |
+———————+————————+———————+———————+————————+——————+———————————————-+
| 0000 | 312 | 686 | 1372 | 612 | 1225 | 1072 1121 1170 |
| 000 | 262 | 576 | 1152 | 514 | 1029 | 900 941 982 |
| 00 | 220 | 484 | 968 | 432 | 864 | 756 790 825 |
| | | | | | | |
| 0 | 185 | 407 | 814 | 363 | 726 | 636 665 693 |
| 1 | 156 | 343 | 686 | 306 | 612 | 536 560 585 |
| 2 | 131 | 288 | 576 | 257 | 514 | 450 470 491 |
| | | | | | | |
| 3 | 110 | 242 | 484 | 216 | 432 | 378 395 412 |
| 4 | 92 | 202 | 404 | 180 | 361 | 316 330 345 |
| 5 | 77 | 169 | 338 | 151 | 302 | 264 276 288 |
| | | | | | | |
| 6 | 65 | 143 | 286 | 127 | 255 | 223 233 243 |
| 8 | 46 | 101 | 202 | 90 | 180 | 158 165 172 |
| 10 | 32 | 70 | 140 | 62 | 125 | 110 115 120 |
| | | | | | | |
| 12 | 23 | 50 | 101 | 45 | 90 | 79 82 86 |
| 14 | 16 | 35 | 70 | 31 | 62 | 55 57 60 |
+———————+————————+———————+———————+————————+——————+———————————————-+
Now, since the length of the circuit is given as the "run" or distance
one way, that is, one half the total length of wire in the circuit,
formula (3) must be multiplied by 2 to get the total drop, that is:
feet × 10.8 X 2 I × feet × 21.6
E = I × ——————————————- = ———————————————- (4)
circular mils circular mills
Solving the last equation for the unknown quantity, the following
equation is obtained for size of wire:
[Illustration: FIGS. 830 and 831.—Symmetrical and unsymmetrical
distribution. When a main is supplied by a feeder, the junction of the
two, if practicable, is located at the electrical center of the main,
as indicated in fig. 830, so that the distribution is symmetrical, that
is, the ampere feet each way from the junction are the same. This is
nearly always practicable in surface wiring, and when it is practiced
it is only necessary to calculate the wire size for one-half of the
main, as the other half is identical. In fig. 830 there are four lamps
on each side of the junction, J; the center of each group is at a
distance, M, so that the lamp feet in each half of the main are 5 × M.
The lamp feet of the feeder would be 10 × N, N being the distance from
the feeder fuse block to the junction, J. In concealed work, however,
it does not always happen that a feeder can be made to join a main at
its electrical center; when this is not practicable, each end of the
main should be figured separately. In fig. 831, for instance, the main
has five lamps on one side and two on the other, and the distances from
the junction to the centers of the two groups are at unequal distances
S and S'. If the distance S be 14 feet, and the lamps, 16 c. p., the
lamp feet in the left hand main equals 5 × 14 = 70, while in the main
to the right, taking S' at 10 feet, there are only 2 × 10 = 20 lamp
feet. Hence what appears to be one continuous main in this case would
have to be treated as two mains, and each part figured separately.]
I × feet × 21.6 amperes × feet × 21.6
circular mils = ———————————————- = ————————————————————— (5)
E "drop"
The following practical example is given to illustrate the application
of the formula just obtained:
EXAMPLE.—What size wire should be used on a 250 volt circuit
to transmit a current of 200 amperes a distance of 350 feet to
a center of distribution with a loss of three per cent. under
full load?
The volts lost or drop is equal to 250 × .03 = 7.5 volts.
=PROPERTIES OF COPPER WIRE=
+————————+————————+——————————+—————————————————————————————+———————————————————————-+
| Number |Diameter| Area in | Weight in pounds | Resistance at 68° Fahr.|
|of gauge| in | circular |——————————————————————————————————————————————————————|
|B. & S. | mils | mils | 1,000 feet| mile |feet per| 1,000 feet | mile |
| | | | | | pound | | |
+————————+————————+——————————+———————————+—————————————————+———————————————————————-+
| 0000 | 460 | 211,600 | 640.5 |3,381 | 1.561 | .04893 | .2583 |
| 000 | 409.6 | 167,800 | 508 |2,682 | 1.969 | .06170 | .3258 |
| 00 | 364.8 | 133,100 | 402.8 |2,127 | 2.482 | .07780 | .4108 |
| 0 | 324.9 | 105,500 | 319.5 |1,687 | 3.130 | .09811 | .5180 |
| | | | | | | | |
| 1 | 289.3 | 83,690 | 253.3 |1,337 | 3.947 | .12370 | .6531 |
| 2 | 257.6 | 66,370 | 200.9 |1,062 | 4.977 | .1560 | .8237 |
| 3 | 229.4 | 52,630 | 159.3 | 841.1 | 6.276 | .1967 | 1.0386 |
| 4 | 204.3 | 41,740 | 126.4 | 667.4 | 7.914 | .2480 | 1.3094 |
| | | | | | | | |
| 5 | 181.9 | 33,100 | 100.2 | 529.0 | 9.980 | .3128 | 1.6516 |
| 6 | 162.0 | 26,250 | 79.46 | 419.5 | 12.580 | .3944 | 2.0824 |
| 7 | 144.3 | 20,820 | 63.02 | 332.7 | 15.87 | .4973 | 2.6257 |
| 8 | 128.5 | 16,510 | 49.98 | 263.9 | 20.01 | .6271 | 3.3111 |
| | | | | | | | |
| 9 | 114.4 | 13,090 | 39.63 | 209.2 | 25.23 | .7908 | 4.1754 |
| 10 | 101.9 | 10,380 | 31.13 | 166.0 | 31.82 | .9972 | 5.2652 |
| 11 | 90.74| 8,234 | 24.93 | 131.6 | 40.12 |1.257 | 6.6370 |
| 12 | 80.81| 6,530 | 19.77 | 104.4 | 50.59 |1.586 | 8.374 |
| | | | | | | | |
| 13 | 71.96| 5,178 | 15.68 | 82.79| 63.79 |2.000 | 10.560 |
| 14 | 64.08| 4,107 | 12.43 | 65.63| 80.44 |2.521 | 13.311 |
| 15 | 57.07| 3,257 | 9.858 | 52.05|101.4 |3.179 | 16.785 |
| 16 | 50.82| 2,583 | 7.818 | 41.28|127.9 |4.009 | 21.168 |
| | | | | | | | |
| 17 | 45.26| 2,048 | 6.200 | 32.74|161.3 |5.055 | 26.690 |
| 18 | 40.30| 1,624 | 4.917 | 25.96|203.4 |6.374 | 33.655 |
| 19 | 35.89| 1,288 | 3.899 | 20.59|256.5 |8.038 | 42.440 |
| 20 | 31.96| 1,022 | 3.092 | 16.33|323.4 |10.14 | 53.540 |
+————————+————————+——————————+———————————+—————————————————+———————————————————————-+
Substituting the given value in formula (5)
350 × 200 × 21.6
circular mils = —————————————————— = 201,600.
7.5
Diameter = 2 √201,600 = 449 circular mils or .449 in.
From the table (on page 731 or on page 742) the nearest
(=larger=) size of wire is 0000 B. & S. gauge.[4]
[4] =CAUTION.=—The size thus obtained should be compared with the table
of carrying capacity of wires as given on page 731 to see if the wires
would have to carry more than the allowable current.
WIRING TABLE FOR LIGHT AND POWER CIRCUITS
===================+=======================================================
VOLTS | PERCENTAGE OF LOSS
===================+=======================================================
2000 | 1.7 1.5 1.4 1.2 1.1 1.0 0.75 0.5
1000 | 3.4 2.9 2.7 2.4 2.2 2.0 1.5 1.0
500 | 6.5 5.7 6.2 4.8 4.3 3.9 2.9 2.0
220 | 13.7 12.0 11.0 10.3 9.3 8.3 6.5 4.4
110 | — — 20.0 18.5 17.0 15.4 12.0 8.4
52 | — — — — — — 22.4 16.1
===================+=======================================================
ACTUAL VOLTS LOST
=========+=========+=======================================================
Carrying | |
Capacity | Size | 35 30 27.5 25 22.5 20 15 10
Amperes. | B. & S. |
=========+=========+=======================================================
300 | 0000 | 345800 296400 271700 247000 222300 197600 148200 98800
245 | 000 | 274400 235200 215600 196000 176400 156800 117600 78400
215 | 00 | 217525 186450 170912 155375 139837 124300 93225 62150
190 | 0 | 172550 147900 135575 123250 110925 98600 73950 49300
160 | 1 | 136850 117300 107525 97750 87975 78200 58650 39100
135 | 2 | 108500 93000 85250 77500 69750 62000 46500 31000
115 | 3 | 86100 73800 67650 61500 55350 49200 36900 24600
100 | 4 | 68250 58500 53625 48750 43875 39000 29250 19500
90 | 5 | 54250 46500 42625 38750 34875 31000 23250 15500
80 | 6 | 43050 36900 33825 30750 27675 24600 18450 12300
60 | 8 | 26965 23130 21202 19275 17347 15420 11565 7710
40 | 10 | 16975 14550 13337 12125 10912 9700 7275 4850
30 | 12 | 10675 9150 8388 7625 6862 6100 4575 3050
22 | 14 | 6720 5760 5280 4800 4320 3840 2880 1920
5[5] | 16 | 4235 3630 3328 3025 2723 2420 1815 1210
————————-+————————-+——————————————————————————————————————————————————————-
===================+=====================================================
VOLTS | PERCENTAGE OF LOSS
===================+=====================================================
2000 | 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05
1000 | 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
500 | 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2
220 | 3.9 3.5 3.1 2.7 2.2 1.8 1.4 0.9 0.45
110 | 7.6 6.8 6.0 5.2 4.4 3.5 2.7 1.8 0.9
52 | 14.7 13.3 11.8 10.3 8.8 7.1 5.5 3.7 1.9
===================+=====================================================
ACTUAL VOLTS LOST
=========+=========+=====================================================
Carrying | |
Capacity | Size | 9 8 7 6 5 4 3 2 1
Amperes. | B. & S. |
=========+=========+=====================================================
300 | 0000 | 88920 79040 69160 59280 49400 39520 29640 19760 9880
245 | 000 | 70560 62720 54880 47040 39200 31360 23520 15680 7840
215 | 00 | 55935 49720 43505 37290 31075 24860 18645 12430 6215
190 | 0 | 44370 39440 34510 29580 24650 19720 14790 9860 4930
160 | 1 | 35190 31280 27370 23460 19550 15640 11730 7820 3910
135 | 2 | 27900 24800 21700 18600 15500 12400 9300 6200 3100
115 | 3 | 22140 19680 17220 14760 12300 9840 7380 4920 2460
100 | 4 | 17550 15600 13650 11700 9750 7800 5850 3900 1950
90 | 5 | 13950 12400 10850 9300 7750 6200 4650 3100 1550
80 | 6 | 11070 9840 8610 7380 6150 4920 3690 2460 1230
60 | 8 | 6939 6168 5397 4626 3855 3084 2313 1542 771
40 | 10 | 4365 3880 3395 2910 2425 1940 1455 970 486
30 | 12 | 2745 2440 2135 1830 1525 1220 915 610 305
22 | 14 | 1728 1536 1344 1152 960 768 576 384 192
5[5] | 16 | 1089 968 847 726 605 484 363 242 121
————————-+————————-+————————————————————————————————————————————————————-
[5] NOTE.—In case a larger loss than any given in the table is
required, proceed as follows:—Divide the ampere feet by 10 and then
refer to column of Actual Volts Lost divided by 10, from which the size
of wire is found as before.
RULE.—_Multiply current in amperes by single distance and refer to the
nearest corresponding number under column of actual volts lost, to find
size of wire._ It should also be noted that the underwriters prohibit
the use of wire smaller than No. 14 B. & S. gauge, except as allowed
for fixture work and pendant cord.
TABLE OF WIRE EQUIVALENTS
GAUGE NUMBER OF WIRES
B. & S. 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384
0000 0 3 6 9 12 15 18 21 24 27 30 33 36 39
000 1 4 7 10 13 16 19 22 25 28 31 34 37 40
_____
00 2 5 8 11 14 17 20 23 26 29 32 35 38| 0+6
0 3 6 9 12 15 18 21 24 27 30 33 36 39| 1+7
1 4 7 10 13 16 19 22 25 28 31 34 37 40| 2+8
_____|
2 5 8 11 14 17 20 23 26 29 32 35 38|3+9 4+6
3 6 9 12 15 18 21 24 27 30 33 36 39|4+10 5+7
4 7 10 13 16 19 22 25 28 31 34 37 40|5+11 6+8
_____|
5 8 11 14 17 20 23 26 29 32 35 38|6+12 7+9
6 9 12 15 18 21 24 27 30 33 36 39|7+13 8+10
7 10 13 16 19 22 25 28 31 34 37 40|8+14 9+11
_____|
8 11 14 17 20 23 26 29 32 35 38|9+15 10+12
9 12 15 18 21 24 27 30 33 36 39|10+16 11+13
10 13 16 19 22 25 28 31 34 37 40|11+17 12+14
_____|
11 14 17 20 23 26 29 32 35 38|12+18 13+15
12 15 18 21 24 27 30 33 36 39|13+19 14+16
13 16 19 22 25 28 31 34 37 40|14+20 15+17
____|
14 17 20 23 26 29 32 35 38|15+21 16+18
15 18 21 24 27 30 33 36 39|16+22 17+19
16 19 22 25 28 31 34 37 40|17+23 18+20
____|
17 20 23 26 29 32 35 38|18+24 19+21
18 21 24 27 30 33 36 39|19+25 20+22
19 22 25 28 31 34 37 40|20+26 21+23
____|
20 23 26 29 32 35 38|21+27 22+24
21 24 27 30 33 36 39|22+28 23+25
22 25 28 31 34 37 40|23+29 24+26
____|
23 26 29 32 35 38|24+30 25+27
24 27 30 33 36 39|25+31 26+28
25 28 31 34 37 40|26+32 27+29
____|
26 29 32 35 38|27+33 28+30
27 30 33 36 39|28+34 29+31
28 31 34 37 40|29+35 30+32
____|
29 32 35 38|30+36 31+33
30 33 36 39|31+37 32+34
31 34 37 40|32+38 33+35
____|
32 35 38|33+39 34+36
33 36 39|34+40 35+37
34 37 40|36+39
___|
35 38|37+39
36 39|38+40
37 40|
=Ques. If the calculated size of wire be larger than any in the table
how is the required area obtained?=
Ans. By using two or more smaller wires in parallel, whose combined
area is equal to the required area.
To facilitate finding the equivalent sizes the above table of
wire equivalents has been prepared.
=Ques. How is the table of wire equivalents used?=
Ans. To use the table, find in the vertical column at left the size
of conductor desired; then follow along horizontally until the size
of wire that is desired to use for the strands, and the corresponding
number at top of column will give the number of strands of that size
wire required.
[Illustration: FIG. 832.—Break down switch for use on three wire
circuit, enabling it to be operated break down fashion with the two
outers connected together and the neutral wire serving as one side
of the resultant two wire circuit. Such circuits must be figured as
two wire installations of one half the three wire voltage. The size
of the neutral wire of a three wire circuit depends on conditions of
operation. Three wire circuits for occasional two wire working, must
have a neutral wire whose cross section is equal to the combined cross
sections of the two outer wires. This plan is useful for buildings
supplied from a central station, as it will be satisfactory for two
wire operation in emergencies, and for three wire, two phase or three
phase distribution should the central station ultimately be changed
over to either of those alternating current systems. The expense for
the extra copper in the beginning will not be nearly so great as that
entailed by a change in the wiring later on should developments require
it. It is permissible, however, to make the cross section of the
neutral wire smaller than that of each outer wire, if one be reasonably
sure that there will never be any changes such as those just mentioned,
and if the drop in the two outer wires do not exceed 1½ per cent.
Under such conditions, it will be found a very good rule to calculate
the neutral wire of a principal feeder for a maximum unbalancing of 25
per cent, that is, a condition under which the current in one outer
wire will be 75 per cent of the current in the other one, the current
in the neutral being 25 per cent of that in the heavier loaded outer
wire.]
=Ques. What is the significance of the zig-zag line?=
Ans. The figures below this line give the gauge numbers of two wires
which will have the same conductivity as the corresponding conductor in
left hand column.
TABLE OF CABLE CAPACITIES
[Illustration: FIG. 833.—Diagram showing capacities of cables for both
open and concealed work as allowed by the underwriters.]
=Incandescent Lamps on 660 Watt Circuits.=—The standard incandescent
lamp is rated as equivalent to the light given by 16 candles, and may
consume, according to type and make, from 50 to 56 watts, or from 3.1
to 3.5 watts per candle power. Therefore, a 660 watt circuit will carry
thirteen 16 candle power 49.6 watt lamps, or eleven 56 watt lamps.
[Illustration: FIG. 834.—Diagram showing symmetrical and unsymmetrical
distribution. The two 5 lamp centers are located at equal distances
from the distributing pocket or cabinet, P, so that the sub-feeders,
A and A', have equal values of lamp feet. The sub-feeders, B, B',
have equal lengths, but as one supplies 10 lamps, and the other 16,
the lamp feet are different, and each sub-feeder must therefore be
figured separately. The main, G, should be considered as a part of
the sub-feeder, B, in order to avoid the necessity for a fuse at the
junction of the two. As it is symmetrically divided, only one-half of
it would be considered. Thus, if the sub-feeder, B, were 50 feet long,
and the main, G, 30 feet long, B would have 16 × 50 = 800 lamp feet and
one-half of the main would have 8 × 15 = 120 lamp feet (assuming all
16 c. p. lamps). Hence 800 + 120 = 920 lamp feet should be taken as
the load length and the proper size wire used for that figure, making
the sub-feeder, B, of the same size as the main, G. The same procedure
applies to the sub-feeder B' and main G'; also to the sub-feeder, E,
and the main, F. The proper sizes of wire for the different circuits is
easily found from the lamp feet table, after having calculated the lamp
feet assigned the drop.]
[Illustration: FIGS. 835 and 836.—The "tree" and "modified tree"
systems of wiring. The tree system consists of a feeder reducing in
size and supplying mains for each floor, the general arrangement
resembling the trunk and branches of a tree. Since fuses must be
inserted on each floor where the size of the feeder is reduced, the
system requires a large number of joints, and in the event of a fuse
blowing it could not be quickly located. The tree system is not to be
recommended, as it results in considerable drop, and at full load the
lamps nearest the point of supply will either burn too brightly or
those more remote will not give the rated candle power. In the modified
tree system, fig. 836, the size of the feeder is not reduced. With
this arrangement the losses are considerably reduced owing to the much
smaller losses on the feeder between those centers farthest away from
the point of supply.]
The proper size of wire for a 660 watt circuit will depend upon
the voltage for which the lamps are made. For example: a 16
candle power lamp which consumes 56 watts on 110 volt circuit
will take, 56 ÷ 110 = .5 or ½ ampere of current, while the
same lamp, if made for 220 volts, will take only 55 ÷ 220 = .25
or ¼ ampere. Therefore, eleven 16 candle power 56 watt lamps
will require a current of 5½ amperes at 110 volts, or 2¾
amperes at 220 volts.
According to the laws of resistance, the resistance of a round
wire is inversely proportional to the square of the diameter,
and if the circuit be taken at 100 feet, and the allowable
percentage of drop at 1 volt, then according to formula, (5)
on page 748, the wire required for a circuit carrying eleven
16 candle power 56 watt 110 volt lamps, will have a cross
sectional area of,
5.5 × 100 × 21.6
———————————————— = 11,880 circular mils.
1
while the same number of lamps on a 220 volt circuit will
require wire having a cross sectional area of,
2.75 × 100 × 21.6
————————————————- = 5,940 circular mils.
1
In order to conform to the underwriters' requirements, No. 8.
B. & S. gauge, wire must be used for the circuit carrying the
110 volt lamps, while No. 12, B. & S. wire, would be sufficient
for the 220 volt circuit.
In the case shown in fig. 829, the branch circuits A and B are
identical, each supplying four 16 candle power lamps requiring
3.5 watts per candle power at 110 volts or carrying a load of 4
× 16 × 3.5 = 224 watts, = 224 ÷ 110 = 2 _amperes_.
[Illustration: FIG. 837.—Distribution with sub-feeders (multi-center
distribution). The feeder connects at a central point, A, with several
sub-feeders which run to distributing centers, as at B, C, D, and E.
With this arrangement, compound wound dynamos may be so designed that
the pressure at A will remain nearly uniform for all loads. If, for
instance, the wiring be proportioned for 2% drop, the dynamos may
be over compounded to that extent, and the even illumination will
compensate for the extra cost in the installation.]
The distance from the feeder junction or cut out to the
electrical center of each branch circuit is 12.5 _feet_. The
compact area of distribution permits the reduction of the
loss of volts to 1 per cent, or 110 × .01 = 1.1 volts "drop."
Then substituting in formula (5) on page 748 the values for
_amperes_, _feet_ and _drop_ as obtained above
2 × 25 × 21.6
————————————- = 981 circular mils,
1.1
or a value far below that of even No. 18 wire, B. & S. gauge
(see table on page 731), but the smallest wire allowed by the
underwriters for the mains A and B is No. 14, B. & S. gauge.
In calculating the size of wire for the feeders the total load
must be considered. This is equal to eight 16 candle power
lamps, requiring 3.5 watts per candle power at 110 volts =
8×16×3.5 = 448 watts = 4 amperes.
The distance from the entrance cut out to the feeder cut out is
200 feet. The drop should not be greater than 1.5 per cent. or
110×1.5 = 1.6 volts. Then,
4×200×21.6
—————————— = 10,800 circular mils
1.6
a value which indicates that No. 8 wire, B. & S. gauge, must be
used for the feeders in order to keep the drop within the limit
of predetermined value.
TABLE FOR TAPS, BRIDGES OR OTHER WIRES AT NEGLIGIBLE DROP
—————————————————————————————————————————————————————————————————————————
Wire Nos. |0 |1 |2 |3 |4 |5 |6 | 7 |8 |10 |12 |14|16|18
—————————————————————————————————————————————————————————————————————————
Lamp Feet|52 v.| 300| 260|200|160|130|100| 80| 65| 50| 38| 24|15| 9| 6
|110v.|1,280|1,085|860|680|560|435|345|280|220|160|100|60|40|25
—————————————————————————————————————————————————————————————————————————
NOTE.—In using this table, it is only necessary to
calculate the lamp feet of the tap and take the size of wire
corresponding to the nearest greater number of lamp feet in
the table. The lamp feet specified by this table should not be
exceeded by more than 10 per cent. Thus, if a tap measure 108
lamp feet, in 110 volt lamps, No. 12 wire would be used. But if
it measure 115 lamp feet, it would be advisable to use No, 10
wire.
=Constant Voltage Arc Lamp Circuits.=—The branch conductor should
have a carrying capacity about fifty per cent. greater than the normal
current required by the lamp, so as to provide for the heavy current
required when the lamp is started. The underwriters prohibit the use of
any size wire under No. 12 for parallel connected arc light circuits.
=Constant Current Series Arc Lamp Circuits.=—The wiring for series
connected arc lamps should never be concealed nor encased unless
requested by the electrical inspector.
For all interior wiring of this class, approved rubber covered wire
should be used, and the wire should always be rigidly supported on
porcelain or glass insulators which will hold the wires at a distance
of at least one inch from the surface wired over. The wires on all
circuits up to 750 volts, should be kept at least 4 inches from each
other, and 8 inches apart on circuits of over 750 volts. No wires
carrying a current having a pressure exceeding 3,500 volts should
be carried into or over any building except central stations and
sub-stations.
[Illustration: FIG. 838.—Diagram showing "bridge wiring." This method
is used in the case of two parallel mains where one feeder is ample for
both. The feeder is run to a central point as shown and connected to
the two mains by a so called "bridge." The arrangement clearly gives
good distribution and effects a saving in copper and labor, for if the
bridge were omitted, two feeders would be necessary.]
=Wire Calculations for Motors.=—The proper size of wire for a motor
may be readily determined by means of the following formula:
H.P. × 746 × D × 21.6
circular mils = ————————————————————- (6)
E × L × K
in which
H.P. = horse power of motor;
746 = watts per H.P.;
D = length of motor circuit from fuse block to motor;
21.6 = ohms per foot run in circuit where wires are one mil in diameter;
E = voltage at the motor;
L = drop in percentage of the voltage at the motor;
K = efficiency of the motor expressed as a decimal.
The average values for K are about as follows: 1 H.P., .75; 3
H.P., .80; 5 H.P., .80; 10 H.P. and over, 90 per cent.
[Illustration: FIGS. 839 and 840.—Wrong and right methods of loop
wiring. In general, when a large percentage of loss is allowed with
lamps at short distances, the size of wire, calculated simply in
accordance with the resistance rules, will be found too small to carry
the current safely. This fact is often overlooked, and even though
wires may have been correctly calculated for a uniform percentage
of loss, they will become painfully hot simply because the table of
carrying capacity was not consulted. The cross connection of mains
wherever possible, for the purpose of equalizing the pressure, will
also often reduce the heating effects of the current. An example of
this is shown in the above figures. A circle of lights was wired as
in fig. 839, and after the current had been turned on, the wires of
the circle became hot, and there was quite a perceptible difference of
candle power between the lights near A and those near B. Investigation
disclosed the fact that the loop, contrary to instructions, had been
left open. A few inches of wire as shown in dotted lines remedied the
fault. A better arrangement, however, is shown in fig. 840.]
EXAMPLE.—What is the proper size of wire for a 10 H.P. motor,
run at 220 volts, allowable drop 2 per cent. on 200 foot
circuit.
Substituting the given values in the formula on page 758:
10 × 746 × 200 × 21.6
Circular mils = ————————————————————- = 36,991.
220 × 4.4 × .9
The nearest larger value to this result, in the table of
carrying capacities of copper wire (page 731), is 41,740,
corresponding to No. 4 wire, B. & S. gauge.
_In all cases the size of the wire thus formed should be
compared with that allowed by the underwriters for full load
current of motor, plus 25 per cent. of that current_, and if
the size calculated happen to be smaller than the allowable
size, it should be increased to the latter, otherwise it will
not pass inspection.
TABLE OF AMPERES PER MOTOR
——————————————————————————————————————————————————————————————————————————————-
H.P. Per Cent. Eff. Watts Input 50 Volts 100 Volts 220 Volts 500 Volts
¾ 70 800 16 7 4 2
1½ 70 1600 32 15 7 3
3 75 2980 60 27 14 6
5 80 4660 93 42 21 9
7½ 85 6580 132 60 30 13
10 85 8780 176 80 40 18
15 85 13200 264 120 60 26
20 85 17600 352 160 80 35
25 85 21900 438 199 100 44
30 90 24900 498 226 113 50
40 90 33200 664 301 151 66
50 90 41400 828 376 188 83
60 90 49700 994 452 226 99
70 90 58000 1160 527 264 116
80 90 66300 1330 608 302 133
90 90 74600 1490 678 339 149
100 90 82900 1660 755 377 166
120 90 99500 1990 905 453 199
150 90 124000 2480 1130 564 248
——————————————————————————————————————————————————————————————————————————————-
TABLE OF AMPERES PER DYNAMO
——————————————————————————————————————————————————————————————————————————————-
Appx. Appx.
K.W. 125 Vs. 250 Vs. 500 Vs. H.P. K.W. 125 Vs. 250 Vs. 500 Vs. H.P.
1. 8 4 2 1.3 30. 240 120 60 40.
2. 16 8 4 2.7 37.5 300 150 75 50.
3. 24 12 6 4.0 40. 320 160 80 53.
5. 40 20 10 6.7 50. 400 200 100 67.
7.5 60 30 15 10. 60. 480 240 120 80.
10. 80 40 20 13. 75. 600 300 150 100.
12.5 100 50 25 17. 100. 800 400 200 134.
15. 120 60 30 20. 125. 1000 500 250 167.
20. 160 80 40 27. 150. 1200 600 300 201.
25. 200 100 50 34. 200. 1600 800 400 268.
——————————————————————————————————————————————————————————————————————————————-
To determine the current required for a motor, as for instance,
the 10 H. P. motor under consideration, _multiply the
horsepower by 746, and divide the product by the voltage of the
motor multiplied by its efficiency as follows_: (10 × 746) ÷
(220 × .90) = 37.6 amperes.
This value increased by 25 per cent. of itself (37.6 × .25 =
9.4 amp.) is equal to 37.6 plus 9.4 = 47 amperes. In the table
of carrying capacities of copper wire (page 731), 46 amperes
is given as the allowable carrying capacity of No. 6, B. & S.
gauge, rubber covered wire; therefore No. 5 wire must be used.
=Calculations for Three Wire Circuit.=—In all cases of interior
conduit work, and in most cases of inside open work, the main feeders
from a three wire source of supply are installed on the three wire
plan, and the sub-feeders and distributing mains, on the two wire plan,
except where the application of the method necessitates the use of
unwieldy sizes.
In laying out sub-feeders and mains, the total load, under normal
operating conditions, should be divided as nearly as possible into two
equal parts, and one part connected on each side of the neutral part
of the entrance cut out, or the neutral bus bar of the switch board or
panel board in an isolated plant, thus making the load on each side of
the neutral wire of the feeder as near equal as possible.
Fig. 841 shows a three wire panel board with connection for
12 mains; those shown in solid lines as A, B, C, etc., being
connected between the neutral wire and the negative wire of the
feeder, and those shown by dotted lines as G, H, I, etc., being
connected between the neutral wire and the positive wire of the
feeder. The total load consists of ninety-one 16 candle power
lamps, which are so distributed that the positive wire of the
feeder carries the current for 46 lamps, and the negative wire,
45 lamps, the neutral wire carrying the difference or current
for 1 lamp.
The proper size of wire for the mains may be calculated as already
explained, but in calculating the outer wires of the three wire feeder,
the neutral wire should be disregarded and the outer wires connected as
a _two wire circuit carrying the total load of 91 lamps at the over all
pressure of 220 volts_.
EXAMPLE.—Ninety-one 16 candle power lamps consuming 3.1 watts
per candle power at a pressure of 110 volts, will require a
current of
16 × 3.1 × 91
————————————- = 41 amperes.
110
The distance from the entrance cut out to the main or feeder
switch is 200 feet, then for a 2 per cent. drop, or a loss of
110×.02=2.2 volts, the cross sectional area of the wire will be,
41 amperes × 200 feet × 21.6
———————————————————————————— = 80,509 circular mils.
2.2 volts
[Illustration: FIG. 841.—Three wire circuit panel board with
connections for 12 mains. The wires shown in solid lines as A, B, C,
etc., are connected between the neutral wire and the negative wire of
the feeder, and those shown by dotted lines, as G, H, I, etc., are
connected between the neutral wire and the positive wire of the feeder.]
The joint resistance of the lamps on a three wire system,
however, would be four times greater than on a two wire system;
consequently the resistance of the outer wires of the feeder in
this case will be four times greater for the same percentage
of loss, and the cross sectional area of each of the outer
wires will be, 80,509÷4=20,127 circular mils. According to the
underwriters' rules, this value compels the use of No. 6 B. &
S. gauge wire.
If the _lamp_ voltage, 110 volts, be used, the two wire formula (5)
given on page 748 must be modified to,
amperes × feet × 21.6
circular mils = ————————————————————-
drop × 4
but if an _over all_ voltage, (that is, the voltage between the outer
wires), of 220 volts be used, the two wire formula does not require any
modification.
The proper size of wire may also be calculated by means of the formula
drop
———————————————————————- = resistance per foot . . . . (1)
2 × distance × amperes
Example.—If in calculating a three wire feeder, the over all
voltage be 220 volts, the drop = 4.4 volts, twice the distance
= 400 feet, and the current = 20.5 amperes, then,
4.4 volts
————————————————————————- = .0005365 ohms per foot.
400 feet × 20.5 amperes
In the table of the properties of copper wire which gives the
resistance of various sizes of wire, it will be noted that
at all of the given temperatures No. 8 wire has a resistance
greater than the value just calculated, therefore, No. 6 B. &
S. gauge wire should be used for the outer wires of the feeder.
In the table the resistance is given per 1,000 feet, hence
it is only necessary to move the decimal point to obtain the
resistance per foot.
If the calculation be based on the lamp voltage, 110 volts, the formula
(1) must be modified to
drop × 4
———————————————————————— = resistance . . . .(2)
2 × distance × amperes
In this case, drop = 2.2 volts, 2 × distance = 400 feet, and current =
41 amperes, then,
2.2 volts × 4 8.8
———————————————————— = ———————— = .005364 ohms.
400 feet × 41 amp. 16,400
=Size of the Neutral Wire.=—In three wire circuits, the size of the
neutral wire will depend to a great extent upon operating conditions.
In the case of installations which occasionally have to be worked as
two wire systems, the cross section of the neutral wire should be equal
to the combined cross section of the two outer wires.
For interior wiring which must pass inspection, the neutral wire must
always be twice the size of one of the outside wires. However, for
general distribution, if it be reasonably sure that the system will
always be worked three wire and that the drop in the two outer wires
does not exceed 1½ per cent., the cross section of the neutral
wire may be made smaller than that of one of the outer wires. In such
a case the size of the neutral wire may be calculated for a maximum
unbalancing of 25 per cent., when the current in one of the outer wires
is 75 per cent. of the current in the other outer wire.
For instance, suppose that in a balanced system, the total load
on each of the outer wires of a feeder be 211 amperes, and that
on account of certain operating conditions, this load has to be
divided unequally so as to put 242 amperes on one of the outer
wires, and 181 amperes on the other outer wire. In this case
the neutral wire will carry 60 amperes, or 25 per cent. of the
current carried by the heavier outer wire.
If the drop in the outer wires exceed 1½ per cent., the
cross section of the neutral wire will have to be equal to or
larger than that of each of the outer wires, otherwise the drop
in the neutral wire will exceed ½ volt with an unbalancing of
25 per cent.