LIBRARY
OF THE
UNIVERSITY OF CALIFORNIA.
Class
ELECTRIC POWER
CONDUCTORS
BY
WM. A. DEL MAR
* 4
A. C. G. I., Assoc. Mem. A. I. E. E., Assoc. I. E. E., Assistant Engineer of the
Electrical Transmission Department, New York Central Railroad,
Formerly with the Interborough Rapid Transit Co.. etc.
THE
R
OF
NEW YORK:
D. VAN NOSTRAND COMPANY
23 MURRAY AND 27 WARREN Sxs.
LONDON:
CROSBY LOCKWOOD & SON
7 STATIONERS' HALL COURT, LUDGATE HILT.
1909
GENERAL
Copyright, 1909
BY
D. VAN'NOSTRAND COMPANY
JScbrrl 0rummnnl anil (Company
Stofodt
PREFACE
THE purpose of this book is to present, for the
benefit of the users of power conductors, a clear
account of all the engineering considerations which
affect the purchase and use of such conductors.
The book will be found practical and up to date;
being based upon notes prepared by the author for
his own use, and there is nothing in the book which
has been copied from any published data without
having been thoroughly studied and found reliable.
The arrangement of the book follows the rational
order of the series of engineering considerations which
affect the purchase of conductors, namely, the deter-
mination of material, insulation, and size, the specifi-
cations, test, and installation.
The text is made as brief as possible, and where
explanation or theoretical discussion is advisable, the
text is supplemented by appendices.
The sections on Alternating Current Feeder Calcu-
lations and Stress in Spans, were written by Dr. Harold
Fender, who also suggested the method of calculation
given in the sections on Skin Effect and Kelvin's Law.
iii
203792
iv PREFACE
Dr. Fender's method of calculations are distinguished
for their thorough adaptability to practical work with
the minimum amount of labor and for their careful
scientific foundation. The author, therefore, has
pleasure in expressing his indebtedness to Dr. Fender
for his valuable contributions.
The author also acknowledges the courtesy of Mr.
W. W. Weaver of the Electrical World and of Mr. J.
H. Smith of the Electrical Age in permitting the use
of material from their respective journals.
W. A. DEL MAR
NEW YORK, June, 1909
\
TABLE OF CONTENTS
WIRES AND CABLES
ERRATA.
Page i. 2d line of table, 3d column, change ".995 " to "3.31."
Page 4. 22d line, change "4X6" to 4X10."
/D\ 2 /7rD\ 2
Page 14. 3d line, change I 1 to I ) .
Page 27. 4th line from bottom, change " 9.516 " to " 9.5916."
Page 49. To the note at the bottom of Table B, add " except for
smaller sizes than No. 0, B. & S., where the divergence between
experiments is greater."
Page 125. Cancel entire paragraph following words "Appendix
IV," from "If" to "practice" inclusive.
Page 284. Line after first formula " 8n " should be " o.oo8?r."
Page 292. Table I, column headed " Error Thickness," read in
reverse order, i.e., 5/64 in. heading the table and 3/i28ths in. ending it.
Page 296. i3th line, between "4000" and "respectively," add
"millions."
Page 298. Top of last column, the number "0.315625," change to
"0.515625."
IV
PREFACE
Dr. Fender's method of calculations are distinguished
for their thorough adaptability to practical work with
the minimum amount of labor and for their careful
scientific foundation. The author, therefore, has
pleasure in expressing his indebtedness to Dr. Fender
for his valuable contributions.
j^iic/x Acknowledges the courtesy of Mr.
TABLE OF CONTENTS
WIRES AND CABLES
CHAPTER I
MATERIALS AND GAUGES
PAGE
1 . Materials i
2. Wires 8
3. Mechanical Properties of Cables 12
CHAPTER II
ELECTRICAL PROPERTIES
1 . Resistance of Wires and Cables 22
2. Resistance of Networks 33
3. Skin Effect 40
4. Carrying Capacity 43
CHAPTER III
INSULATION AND INSULATED CONDUCTORS
1 . Insulation 59
2. Insulated Cables 76
3. Insulators 94
CHAPTER IV
DETERMINATION OF SIZE FOR GIVEN VOLTAGE DROP AND POWER Loss
1. Voltage and Systems of Distribution 104
2. Lamp Wiring Calculations 107
3. Continuous Current Railway Feeder Calculations in
4. Negative Booster Calculations 127
5. Alternating Current Transmission Line Calculations 133
6. Economical Size of Conductors and Kelvin's Law 156
V
vi TABLE OF CONTENTS
CHAPTER V
DETERMINATION or SIZE FOR GIVEN STRESS IN SPANS 159
CHAPTER VI
SPECIFICATIONS 179
CHAPTER VII
TESTING WIRE AND CABLE 200
CHAPTER VIII
INSTALLATION
1 . Underground Lines 220
2. Overhead Lines . 224
3. Splicing 227
CHAPTER IX
DEPRECIATION AND DETERIORATION
1 . Depreciation 238
2. Deterioration by Electrolysis and Miscellaneous Causes 240
CHAPTER X
THIRD RAIL CIRCUITS 245
CHAPTER XI
RAIL BONDS 252
CHAPTER XII
TABLES OF INDUCTANCE, REACTANCE AND CAPACITY
1 . Inductance 270
2. Capacity 277
APPENDICES
I. BASIS OF B. & S. GAUGE 281
II. BASIS OF SKIN EFFECT AND CARRYING CAPACITY FORMULA 284
III. METHOD OF CALCULATING THICKNESS OF RUBBER INSULA-
TION 291
IV. BASIS OF DIRECT AND ALTERNATING CURRENT TRANSMISSION
FORMULAE 299
V. BASIS OF FORMULA FOR STRESSES IN SPANS 308
VI. EXPLANATION OF SPECIFICATIONS 310
VII. BASIS OF TABLES OF INDUCTANCE 321
- *
OF THE
UNIVERSITY
OF
ELECTRIC POWER CON
DUCTORS
CHAPTER I
MATERIALS AND GAUGES
i. MATERIALS
COMPARISON OF ALUMINUM AND COPPER
General Properties.
Aluminum.
Copper
(Hard Drawn).
Copper,
Soft Drawn.
Specific gravity .
2 68
8Q-?
8 89
Relative specific gravity
I.OO
3? ?
Conductivity (Matthiessen's
Standard)
61 to 63
06 to 99
Elastic limit, solid wire (Ibs. per
sq.in.). .
14 ooo
^ 5 ooo to 40 ooo
Coefficient of expansion per de-
gree F. .
o ooo o i ^ 8
Modulus of elasticity, solid wire
8 to 16X10
Melting point (about)
i 200 F
2000 F
2000 F
Lbs. per cu.in
O OO7
O 32
Tensile strength, solid wire, Ibs.
per sq.in. .
(20,000 to
3 ^,000
45,000 to
68 ooo
25,000 to
3.*
ELECTRIC POWER CONDUCTORS
Comparison of Aluminum and Copper of Equal Length and
Conductance.
5 = specific gravity of aluminum ;
5= specific gravity of copper;
c = conductivity of aluminum ;
C = conductivity of copper ;
/ = tensile strength of aluminum, Ibs. per sq.in.;
T = tensile strength of copper, Ibs. per sq.iri.;
p = price of aluminum, per Ib.
P = price of copper, per Ib.
Then to compare a given aluminum wire with a
copper wire of equal length and conductance,
Relative cost,
Relative cross-section,
Relative diameter,
Relative weight,
Relative breaking strength,
Aluminum _ spC
Copper SPc
Aluminum _ C
Copper c
Aluminum _ \C
Copper ^ c
Aluminum sC
Copper Sc
Aluminum 1C
Copper Tc
-D , ,. Aluminum 4 IC
Relative current carrying capacity, =\|
Copper ^ c
MATERIALS AND GAUGES
The following table is calculated for s = 2.68, 5 =
25,000, and 7 = 55,000;
Conductivity (Matthiessen's
Standard).
Copper.
Aluminum
98
63
62
61
60
Relative cost
I. CO
I.OO
I. 00
I.OO
1.00
I.OO
0.467^
1.556
1.247
0.467
0.708
1.117
Q-474P
1.581
1.258
0.474
0.719
I. 121
0.48277
1. 606
1.268
0.482
0.731
I.I26
0.489?
I- 6 33
1.278
0.489
0.743
I.I30
Relative cross-section
Relative diameter
Relative weight
Relative breaking strength
Relative current carrying
capacity ^
* For wires of the same diameter aluminum will carry only 80% of the current
carried by copper.
Advantages of Aluminum Compared with Copper.
(1) For equal conductance aluminum is cheaper.
In the United States the price is held about 10% less
than that of copper.
(2) For equal conductance aluminum is lighter and
therefore easier to string.
(3) Sleet does not adhere so readily as to copper.
Disadvantages of Aluminum Compared with Copper.
(1) Aluminum wire must be strung with a greater
sag than copper wire of equal conductance due to its
lower tensile strength and greater surface exposed to
wind and sleet. For long spans higher towers are
therefore required.
(2) Low melting-point makes wire more liable to
break off under influence of an arc either at the insu-
4 ELECTRIC POWER CONDUCTORS
lators or when foreign wires fall on the line. Wires
must therefore be placed further apart, necessitating
the use of longer cross arms.
(3) Scrap value very small on account of artificial
price of new product.
(4) Aluminum is much softer than copper; greater
care must therefore be observed in stringing to avoid
denting or abrasion.
TENSILE STRENGTH AND ELASTIC PROPERTIES OF COPPER
The properties of commercial hard-drawn copper
seldom resemble those given in the old text-books, as
the commercial article used for aerial power wires is
much softer than that usually described as hard-
drawn copper. The modulus of elasticity instead of
being i6Xio 6 (in Ib.-in. units) varies from SXio 6 to
i6Xio 6 ; the tensile strength instead of being over
60,000 Ibs. per sq.in., varies from 45,000 to 68,000.
The point where the strain ceases to be proportional
to the stress, called the elastic limit, varies from
35,000 to 45,000 Ibs. per sq.in., 38,000 being a value
easy to obtain. These values apply to solid wire;
for stranded cables the modulus of elasticity varies
from 4 XJ0 to 12 X io 6 , the tensile strength from 45,000
to 60,000 Ibs. per sq.in.; the elastic limit from 25,000
to 35,000 Ibs. per sq.in.
If the elastic limit is considerably exceeded, the wire
becomes so attenuated that the actual stress, i.e.,
the force per sq.in. of actual section gradually in-
MATERIALS AND GAUGES 5
creases, and ultimately teaches a value sufficient to
break the wire. Therefore a stress considerably under
the nominal breaking stress will break a wire if con-
tinued for a sufficient length of time. Working a wire
having 60,000 Ibs. per sq.in. ultimate strength, at a
stress of 10,000 Ibs. per sq.in., therefore gives an
actual safety factor of less than six instead of six,
as is usually computed.
The hardness of copper depends upon the amount
of drawing it has been subjected to, and all degrees
of hardness are obtainable from soft annealed copper
to the hard material used for telephone wires. Tel-
ephone wires can be made very hard because they are
drawn to such a small size. It is therefore important
to take into account the size of wire in specifying its
degree of hardness and the various mechanical prop-
erties dependent thereon. This is well illustrated by
the curves of Fig. i.
Curve A is what is usually called half-hard drawn
and curve D is a very hard- drawn telephone wire of
i/ 10 inch diameter, having an elastic limit of 50,000
Ibs. and an ultimate strength of 69,000 Ibs. per sq.in.
with an elongation of i%.
It should be noted that in hard-drawn copper of
various degrees of hardness, the elongation at the
elastic limit is usually about J%, whatever the modu-
lus of elasticity.
Soft-drawn copper cannot be used alone in tension
on account of its low elastic limit, about 3000 to 5000
6
ELECTRIC POWER CONDUCTORS
Ibs. per sq.in. It is used with hard-drawn copper
wires for the cores of concentric cables, where a knowl-
edge of its stresses under various elongations is essen-
A B C
w
1
I
10
50
20 30 40
Stress, Thousands of Ibs. per Sq. In.
FIG. i. Typiral Stress-Strain Diagrams, Hard Drawn Copper Wire.
tial for the calculation of the strength of the cable.
Fig. 2 is a typical stress strain diagram for commercial
soft-drawn copper, and is based on the following
table:
GAUGES AND MATERIALS
Ultimate strength
Lbs. per Sq.in. of Original
Area Elastic Limit.
3,000
5,000
10,000
15,000
20,000
25,000
30,000
3Soo
40,000
41,000
41,500
42,000
15
10
Elongation Per Cent of
Original Length.
.2
-4
I.I
2.1
3-5
5-
6.7
9.0
12.5
13.6
15-0
45-o
I 5 10 15 20 25 30 35 40
Stress. Thousands of Ibs. per Sq. In.
FIG. 2. Typical Stress-Strain Diagram, Soft Drawn Copper.
45
The ultimate strength of soft-drawn copper is of no
practical importance as, when the elastic limit is some-
what exceeded and the load maintained, the wire
stretches until it breaks. The ultimate strength var-
ies from 25,000 to 45,000 Ibs. per sq.in. with an elon-
gation of from 25% to 45%.
8
ELECTRIC POWER CONDUCTORS
Wire used for the core of hard-drawn cables fre-
quently has an ultimate strength of about 45,000 Ibs.
per sq.in., with an elongation of 8% to 10%. The
elastic limit of such wire is about 20,000 Ibs. per sq.in.
and the modulus 8 to 10 millions.
2. SOLID WIRES.
RATING OF WIRES
American or Brown and Sharpe Gauge
A.W.G-
B. &S.
Diam-
eter.
Inches.
Area.
Copper.
Aluminum.
Circular
Mils.
Square
Mils.
Lbs. per
Foot.
Feet per
Lb.
Lbs. per
Foot.
Feet per
Lb.
oooo
0.460
211,600
166,190
0.6405
1.561
0.1929
5-185
ooo
0.4096
167,800
131,790
0.5080
1.969
0.1529
6-539
00
0.3648
133,100
104,518
0.4028
2.482
0.1213
8.246
0.3249
105,500
' 82,887
0-3195
3-130
0.09618
10.40
I
0.2893
83,690
65,732
0-2533
3-947
0.07629
13.11
2
0.2576
66,370
52,128
0.2009
4-977
0.06050
16.53
3
0.2294
52,630
41,339
0.1593
6.276
0.04797
20.85
4
0.2043
41,740
32,784
0.1264
7.914
0.03805
26.28
5
0.1819
33 5 ioo
25,999
O.IOO2
9.980
o.c 30I 7
33-15
6
0.1620
26,250
20,618
0.07946
12.58
0.02393
41-79
7
0-1443
20,820
l6,35l
0.06302
15-87
0.01898
52.69
8
0.1285
16,510
12,967
0.04998
20. 01
0.01505
66.44
9
0.1144
13,090
10,283
0.03963
25-23
0.01193
83-82
10
0.1019
10,380
8,155
0.03143
31.82
0.009462
105-7
ii
0.09074
8,234
6,467
0-02493
40.12
0-007505
133-2
12
0.08081
6,530
5,129
0.01977
50-59
0.005952
168.0
13
0.07196
5,i78
4,067
0.01568
63-79
.004720
211.9
14
0.06408
4,107
3,225
0.01243
80.44
-003743
267.2
15
0.05707
3, 2 57
2,558
0.009858
101.4
.002968
336.9
16
0.05082
2,583
2,029
0.007818
127.9
.002354
424.8
17
0.04526
2,048
1,609
0.00620O
161.3
.001867
535-6
18
0.04030
1,624
1,276
0.004917
203.4
.001480
675-7
19
0.03589
1,288
1,012
0.003899
256-5
.001174
851.8
20
0.03196
1,022
802
0.003092
323-4
.000931
1074.1
GAUGES AND MATERIALS
COMBINATION OF WIRES APPROXIMATELY EQUIVALENT
TO ONE WIRE
(Based upon approximate equivalence of \/2 and'Vga.)
B. & S.
No.
2 Of
B. & S.
No.
4 Of
B. & S.
No.
8 of
B. & S.
No.
16 of
B. & S.
No.
32 of
B & S.
No.
64 of
B. & S.
No.
One Each
of B. & S.
Nos.
oooo
3
6
9
12
15
000
i
4
7
10
13
16
00
2
5
8
ii
14
17
i arid 3
3
6
9
12
i-5
18
2 " 4
I
4
7
10
13
16
3 " 5
2
5
8
ii
14
17
4-6
3
6
9
12
15
18
....
5 " 7
4
7
10
13
16
6-8
5
8
ii
14
17
7 " 9
6
9
12
15
18
....
....
8 " 10
7
IO
T 1
16
" II
g
1 7
IO l * 12
9
12
15
18
ii - 13
T 'J
16
12 "l4
ii
14
17
13 " 15
I 2
I r
18
14 " 16
16
I ^ " 17
J 3
I 7
16 " 18
15
18
Circular Mils. A circular mil is the area of a circle
of i mil (thousandth of an inch) diameter. The area
of any conductor in circular mils is equal to the square
of its diameter in mils, or one million times the square
of its diameter in inches.
one square mil 4
one circular mil
10
ELECTRIC POWER CONDUCTORS
BIRMINGHAM OR STUBB'S WIRE GAUGE
B. W G.
Stubb's.
Diameter.
Inches.
Area.
Lbs. per Foot.
Copper.
Circular Mils.
Sq.Mils.
oooo
0-454
206,100
161,883
0.6239
ooo
0.425
180,600
141,863
0.5468
00
0.380
144,400
II3,4H
0.4371
0.340
115,600
90,792
0-3499
i
0.3000
90,000
70,686
0.2724
2
0.2840
80,660
6 3,347
0.2441
3
0.2590
67,080
52,685
o. 2031
4
0.2380
56,640
44,488
0.1715
5
0.2200
48,400
38,013
0.1465
6
O.2O30
41,210
32,365
0.1247
7
O.I80O
32,400
25,447
0.09808
8
0.1650
27,230
21,382
0.08241
9
0.1480
21,900
17,203
0.06630
10
0.1340
17,960
14,103
0-05435
ii
O.I20O
14,400
11,310
0-04359
12
O.IOQO
1 1, 880
9,33i
0.03596
13
0.0950
9,025
7,088
0.02732
14
0.08300
6,889
5,4n
0.02085
15
O.O72OO
5,^84
4,072
0.01569
16
0.06500
4,225
3.3i8
0.01279
17
0.0580
3,364
2,642
0.01018
18
O.O4900
2,401
1,886
0.007268
iQ
O.0420O
1,764
i,385
0.005340
20
0.03500
1,225
962
0.003708
GAUGES AND MATERIALS
11
TABLE OF COMPARATIVE SIZES OF WIRE GAUGES, IN
DECIMALS OF AN INCH
No. of
Wire
Gauge.
Brown &
Sharpe.
American
Steel & Wire
Co. or
Washburn
& Moen.
Birmingham
or Stubb's.
English
Legal
Standard.
Old English
or London.
ooooooo
O 4QOO
o 12 -f, etc.)
iv = weight of each wire or strand, Ibs. per foot;
p 6 = pitch factor of first or 6 wire layer;
Pn = pitch factor of second or 12 wire layer, etc.
(Definition of pitch factor on page 13.)
Pitch. The British standard pitch is twenty
times the pitch diameter, and is the only standard
pitch agreed upon by any large body of manufac-
turers. In America there is no standard pitch, this
being usually left to the manufacturers.
The cable user is interested in obtaining the largest
pitch with which the wires will hold together and
that obviously depends upon the size and number
of wires and upon their stiffness. The longer the pitch
the greater the conductance and tensile strength.
The cable manufacturers, on the other hand,
generally prefer a short pitch. The pitch to be used
should therefore be agreed upon by manufacturers
and buyers when specifications are to be prepared.
For cables of hard-drawn copper for aerial lines, a
*
GAUGES AND MATERIALS 17
pitch of from twenty to thirty-five times the pitch
diameter is usual practice.
Minimum Pitch. The minimum pitch or lay with
which n wires of diameter d can be coiled spirally on
a pitch diameter D, is
nD.nd
) 2 - (nd) 2
In the case of regular concentric cables in which
successive layers have 6, 12, 18, etc., wires, the mini-
mum pitch is i o.i times the pitch diameter if all the
wires are of equal size. The constant 10.1 equals
Ultimate Strength of a Seven-Wire Strand with Soft Core.
Let p = pitch factor of six- wire layer;
d = diameter of each wire (in.) ;
t = tensile strength of outer wires, Ibs. per sq. n. ;
e = elongation, per cent, at which outer wires
break ;
5 = stress in Ibs. per sq.in. in core with elonga-
tion e (see Fig. 2, p. 7, for soft-drawn
copper) .
Ultimate strength (Ibs.) =**&(s + -V
4 \ p/
Ultimate Strength of a Nineteen-Wire Strand with Soft Core.
Let pQ = pitch factor of six- wire layer ;
Pi2 = pitch factor of twelve- wire layer;
d = diameter of each wire (in.);
18
ELECTRIC POWER CONDUCTORS
t = tensile strength of outer wires, Ibs. per
sq.in.;
e = elongation, per cent, at which outer wires
break ;
5 = stress, Ibs. per sq.in. in core with elongation
e (Fig. 2, p. 7, for soft-drawn copper).
Ultimate strength (Ibs.) =-d 2 (s+ + V
4 \ PG Pl2/
With a 37-wire strand, the bracketed expression
should have a term for the 1 8- wire layer, namely,
18*
, and so on, for all sizes.
PlB
Space Wasted in Concentric-Strand Cables.
n = number of concentric layers around one central
wire;
R = ratio of copper area to area of circle circum
scribing the outside of cable;
3 (
This neglects the increase of ratio due to wires
being arranged in spiral form.
Number of
Layers.
Number of
Wires.
R.
_
I
I.OOO
I
2
7
iQ
0.778
0.760
3
4
37
61
0-755
o-753
5
9 1
0.752
GAUGES AND MATERIALS
19
RESISTANCE AND WEIGHT OF STANDARD BRITISH
CABLES
Wires in Cable.
Ratio of Resistance of Cable,
to Resistance of One Wire.
Ratio of Weight of Cable,
to Weight of One Wire.
7
0.14436
7.0736
J 9
0.05324
19.2207
37
61
0.02735
0.01659
37-4414
6i-735 6
9i
O.OIII2
92.1034
Based upon the British Institution of Electrical Engineers' Standard of a lay or
pitch of twenty times the pitch diameter which corresponds to a pitch factor of
i. 01 22. Both the weight and resistance of the strand are about one per cent higher
than for a solid wire of same cross section.
DIAMETER OF WIRES IN STRANDS
Size of
Number of Wires in Strand.
Cable.
7-
19-
37-
61.
91-
127.
Circ. Mils.
2,000,000
0-5345
0.3244
0.2324
0.1811
0.1482
o-i 2 55
1,750,000
o. 5000
0-3035
0.2175
0.1694
0.1387
0.1174
1,500,000
0.4629
0.2810
o. 2013
0.1568
0.1284
0.1087
1,250,000
0.4226
0.2565
0.1838
0.1431
0.1173
0.0992
1,000,000
-3779
0.2294
0.1644
0.1281
0.1048
0.0887
750,000
o-3 2 73
0.1986
0.1428
0.1109
i . 0908
0.0769
500,000
0.2673
o. 1622
O.Il62
0.0906
0.0661
0.0628
250,000
0.1889
0.1147
O.O822
0.0640
0.0524
B. & S.
0000
o-i739
0-1055
0-07563
0.0589
000
0.1548
0.09398
0.0674
0.0525
00
0-1379
o. 08369
0.060
0.1228
0.07453
I
0.1094
0.06637
2
0.0974
0.05911
3
0.0867
4
0.0772
20
ELECTRIC POWER CONDUCTORS
DIMENSIONS AND WEIGHTS OF CABLES
COPPER AND ALUMINUM
Size.
Number of
Wires in
Strand.
Diameter of
Individual
Wires in
Inches.
Diameter of
Bare Cables
in Inches.
Approximate
Weight of
Copper per
1000 Ft.
in Lbs.
Approximate
Weight of
Aluminum
per 1000 Ft.
in Lbs.
B. &S.
14
7
0.0243
0.0729
13
3-87
12
7
0.0306
0.0918
20
5-95
10
7
0.0386
0.1158
3 2
9-54
8
7
0.0485
0-1455
5*
15-2
6
7
o . 06 i 3
0.1839
81
24.1
5
7
0.0688
o. 2064
1OI
30.2
4
7
0.0773
0.2319
128
38-5
3
7
0.0867
o. 2604
161
48-5
2
7
0.0974
o. 2922
203
61
I
19
0.0664
0.3320
256
77
O
19
0-0745
0-375
3 2 3
97
00
19
0.0837
0.4190
408
123
000
19
. 0.094
0.4700
5U
i55
oooo
19
0.1055
0.5280
647
i95
CM.
250,000
37
0.0822
0-5754
765
239
300,000
37
0.0906
0.6342
919
276
350,000
37
0.0974
0.6818
1070
322
400,000
37
0.104
o. 7280
T22O
368
450,000
37
O.III
0.7770
1380
414
500,000
61
0.0906
0.8154
1530
460
550,000
61
0.095
0.8550
J680
506
600,000
61
0.0992
0.8928
1840
552
650,000
61
0.1033
0.9297
1990
597
700,000
61
0.1072
0.9648
2140
643
750,000
61
0.1109
0.9990
2300
690
800,000
61
0.1146
.031
2450
735
900,000
61
0.1216
.094
2750
834
1,000,000
61
o. 1281
-153
3060
920
1,000,000
oi
0.1048
-153
33
924
1,250,000
9 1
0.1173
.290
3830
1150
1,500,000
9i
0.1284
.412
4590
1380
1,750,000
127
0.1174
.526
536o
1610
2,000,000
127
- T2 55
-631
6120
1840
2,000.000*
133
0.1226
-84
6220
1850
Rope.
GAUGES AND MATERIALS 21
The above figures should be regarded as approxi-
mate only, as the cable diameters and weights de-
pend upon the pitch of the spirals.
An allowance of i% is made for increase of weight
due to spiralling.
The size of area is based upon the united areas
of the individual wires cut at right angles to their
axes and laid out straight.
CHAPTER II
ELECTRICAL PROPERTIES ' OF CONDUCTORS
i. RESISTANCE OF WIRES AND CABLES
MATTHIESSEN'S STANDARD
The recognized standard of conductivity of copper
wire is that established by Matthiessen, from experi-
ments on pure copper. Matthiessen's standard for
soft-drawn copper is that a wire one meter long, of
uniform cross-section, weighing one gram, has a
resistance of 0.141729 ohm at o C.
While Matthiessen's standard is often reached
and even exceeded in commercial copper, it is usual
to accept soft-drawn copper having 98% and hard-
drawn copper having 97% of the above standard
conductivity.
Matthiessen's special standard for hard-drawn
copper is not used in America.
The conductivity of aluminum is from 55% to
63% of Matthiessen's standard for copper, the usual
commercial figure being 62%, which is equivalent
to 15.47 ohms per mil-foot at o C.
22
ELECTRICAL PROPERTIES OF CONDUCTORS 23
The variation of resistance with temperature, both
for copper and aluminum, is about 0.42% per degree
Centigrade or 0.23% per degree Fahrenheit.
RESISTANCE OF A MIL-FOOT OF COPPER, OHMS
(One circular mil area, i foot long.)
Temperature Degrees.
Per Cent Conductivity Matthiessen.
Cent.
Fahr.
100.
99-
98.
97-
96.
32
9-59
9.69
9-79
9.89
9-99
10
15-5
5
60
9-99
10.2
10. I
10.3
IO. 2
10.4
10.3
i-5
10.4
10.6
2O
24
30
68
75-2
86
10.4
10.6
10.8
io-5
10.7
10.9
10.6
10.8
II.
10.7
10 9
ii. i
10.8
II.
II. 2
40
SO
60
104
122
140
II. 2
ii. 6
12.0
"3
11.7
12. I
II. 4
ii. 8
12.2
n-5
12.0
12.4
II.7
12. I
12-5
70
80
90
158
I 7 6
194
12.4
12.8
13.2
12.5
12.9
13-4
I2. 7
I3-I
13-5
12.8
13.2
13-6
I2. 9
13-3
I3-
100
212
13-6
13-7
13-9
14.0
14.2
Based on Matthiessen's Standard, 9.5916 ohms per mil-foot at e C. and the
A.A.I. E E. temperature coefficient, 0.0042 from o C.
For any other percentage conductivity divide the
number in the column headed 100 by the conductivity
expressed as a decimal fraction. For example, the
ohms per mil-foot for aluminum of 62% conductivity at
70 C. is - = 20.0.
0.62
24
ELECTRIC POWER CONDUCTORS
ii.U
109
,/
/
in R
I
\f/
107
il.
I
10 fi
/
7 ;
/
105
/
/
104
/J
/
. if) q
/
/
8m2
/,
/
^ 101
/
/
10.0
/
/
o q
/
7
98
/
/
97
/
G
t
q
/
/
9.5
/
/
10 20 30 40 50 60 70 80 90 100
Degrees Fahrenheit
FIG. 3. Resistance of Copper. Based on Standards adopted by A.I.E.E.
ELECTRICAL PROPERTIES OF CONDUCTORS 25
RESISTANCE OF SOLID COPPER WIRE
CONDUCTIVITY 100 PER CENT MATTHIESSEN'S STANDARD
Ohms per 1000 Feet.
Size.
oC.
32 F.
10 C.
50 F.
20 C.
68 F.
S o C.
122 F.
Millions
of C.M.
5
0.001918
0.001999
0.002079
O.OO232I
4
0.002398
0.002499
0.002599
0.002901
3
0.003197
0.003331
0.003466
0.003869
2
0.004796
0.004997
0.005199
0.005803
If
0.005481
0.005711
0.005941
O.OO6632
l
0.006394
0.006663
0.006932
0-007737
ii
0.007673
0.007996
0.008318
O.O09285
i
0.009592
0.009994
0.01040
o. 01161
f
0.01279
0.01333
0.01386
0.01547
i
0.01918
0.01999
0.02079
0.02321
I
0-03837
0.03998
0.04159
0.04642
B. &S.
oooo
0.04528
0.04718
0.04909
0.05479
000
0.05716
0.05956
0.06196
0.06916
00
0.07207
0.07510
0.07813
0.08721
0.09089
0.09470
0.09852
O.IIOO
i
0.1146
0.1194
0.1242
0.1387
2
0-1445
0.1506
0.1566
0.1749
3
0.1822
0.1899
0-1975
0.2205
4
0.2298
0.2394
0.2491
0.2780
5
0.2898
0.3019
0.3141
0.3506
6
0-3654
0.3807
0.3961
0.4421
7
0.4608
0.4801
0.4995
o-5575
8
0.5810
0.6054
0.6297
0.7029
9
0.7325
0-7633
0.7941
0.8863
10
0.9239
0.9627
I.OOI
1.118
1 1
1.165
1.214
1.263
1.410
12
1.469
I-53T
1.592
1.777
13
1.852
1.930
2.008
2.241
14
2-335
2-434
2.532
2.826
15
2-945
3.069
3.192
3-563
16
3-713
3.869
4-025
4-493
17
4.683
4.880
5-077
5-667
18
5.906
6-154
6.402
7.146
Based upon Matthiessen's Standard of 9-S9i6 ohms per mil-foot at o C. and the
A.I.E.E. temperature coefficient of 0.0042 per degree Centigrade temperature rise
above o C.
Resistance at t C. is equal to that at zero multiplied by (i +0.00420.
26
ELECTRIC POWER CONDUCTORS
RESISTANCE OF SOLID COPPER WIRE
CONDUCTIVITY 98 PER CENT MATTHIESSEN'S STANDAKD
Ohms per 1000 Feet.
Size.
oC.
32 F.
10 C.
50 F.
20 C.
68 F.
So C.
122 F.
Millions
of C.M
5
0.001957
0.002040
O.OO2122
O.OO2369
4
0.002447
0.002550
0.002652
0.00296l
3
0.003262
0.003400
0.003536
0.003948
2
0.004894
0.005099
0.005305
0.005921
If
0-005593
0.005828
0.006063
0.006767
I*
0.006525
0.006799
0.007073
0.007895
Ij
0.007830
0.008159
0.008488
0.009474
I
0.009787
0.01020
o. 01061
O.OII84
I
0.01305
0.01360
O.OI4I5
0-01579
J
0.01957
0.02O4O
0.02122
0.02369
J
0.03915
0.04079
'0.04244
0-04737
B. & S.
0000
0.04621
, O.04820
0.05009
0-05597
ooo
0-05833
0.06078
0.06323
0.07057
oo
o-o7355
0.07663
0.07972
0.08899
0.09274
0.09664
0.1005
O.II22
I
0.1169
O.I2I9
0.1268
0.1415
2
0.1475
0-1537
0.1598
0.1784
3
0.1860
0.1938
0.2016
0.225O
4
0-2345
0.2443
0.2542
0.2837
5
0.2957
0.3081
0.3205
0-3578
6
0.3728
0.3885
0.4042
0.45II
7
0.4702
0.4899
0.5097
0.5689
8
0.5928
0.6177
0.6426
0-7173
9
0-7475
0.7789
0.8103
0.9044
10
0.9427
0.9823
1.022
I.I4I
ii
1.189
I . 238
1.288
1.438
12
i-499
1.562
1.625
I.8I4
13
1.890
1.970
2.049
2.287
14
2-383
2.483
2.583
2.884
15
3-o5
3-I3 1
3- 2 57
3-636
16
3-789
3-948
4-107
4-585
i7
4-779
4.980
5.180
5-783
18
6.027
6.280
6-533
7.292
Based upon Matthies?en's Standard of 9.5916 ohms per mil-foot at o C. and the
A.I.E.E. temperature coefficient of 0.0042 per degree Centigrade temperature rise
above o C.
Resistance at t C. is equal to that at zero multiplied by (i +0.0042*).
ELECTRICAL PROPERTIES ~OF CONDUCTORS 27
RESISTANCE OF ALUMINUM WIRE
CONDUCTIVITY 62 PER CENT MATTHIESSEN'S STANDARD
Ohms per 1000 Feet.
Size.
oC.
32 P.
10 C.
50 F.
2C C.
68 F.
50 C.
122 F.
Millions
of C.M.
5
.003094
.003224
-003354
.003744
4
.003868
. 004030
.004192
. 004680
3
-005157
-005373
-005590
.006239
2
-007735
.008060
.008385
. 009360
l|
.008840
.009211
.009583
.01070
I*
.01031
.01075
.01118
.01248
I*
.01238
.01290
.01342
.01497
I
-01547
.Ol6l2
.01677
.01872
1
.02063
.02149
.02236
.02496
*
.03094
.03224
-03354
.03744
i
.06188
.06448
.06708
.07488
B & S.
0000
-07304
.07610
.07917
.08837
000
.09219
. 09606
.09994
.1116
00
.1162
.1211
.1260
.1407
.1466
.1527
.1589
-1774
I
.1848
.1926
.2004
-2237
2
-2331
.2429
-2527
.2820
3
-2939
-3063
.3186
-3556
4
.3706
.3862
-4017
.4484
5
.4674
.4870
-5066
-5655
6
.5893
.6141
.6388
-7131
7
-7432
-7744
.8056
.8992
8
-937
.9764
1.016
1.134
9
1.181
I.23I
1.281
1.430
10
1.490
i-553
1.615
1.803
ii
1.879
1.958
2.037
2.273
12
2.369
2.469
2.568
2.867
3
2.988
3-"3
3-239
3-615
14
3-7 6 7
3-925
4-083
4.558
15
4-750
4-949
5-149
5-747
16
5-989
6.241
6.492
7-247
i7
7-554
7.871
8.188
9.140
18
9.526
9.926
io-33
u-53
Based upon Mathiessen's Standard of 9.516 ohms per mil-foot at o C. and
the temperature coefficient of 0.0042 per degree Centigrade temperature rise
above o C.
Resistance at t C. is equal to that at zero multiplied by (i + .oo42/).
28 ELECTRIC POWER CONDUCTORS
The following rules, which are easily remembered,
enable one to determine approximately the constants
of any size of copper or aluminum wire on the B. & S.
gauge without reference to a wire table.
1. A No. 10 copper wire has a resistance of approxi-
mately one ohm per 1000 feet, a cross section of 10,000
C.M. and weight of 32 Ibs. per 1000 ft.
2. A No. 10 aluminum wire has a resistance of
approximately 1.6 ohms per 1000 feet, a cross section
of 10,000 C.M. and weights 9.5 per 1000 feet.
3. An increase of one in the number of a wire in-
creases the resistance 25 per cent; an increase of two
in the number increases the resistance 60 per cent ; an
increase of three in the number doubles the resistance
an increase of ten in the number increases the resist-
ance ten times.
4. The cross section and weight of a wire varies in-
versely as the resistance ; the diameter in mils is equal
to the square root of the cross section in circular mils
(a stranded wire has a diameter about 15 per cent
greater) .
Examples: The resistance of a number 18 copper
wire is 4 X 1.60 = 6.4 ohms per thousand feet; the cross
10,000 /
section is = i 560 C.M. ; the diameter is v 1 560
6.4
= 39.5 mils; the weight =5.00 Ibs. per 1000 feet.
6.4
The resistance of a number oo stranded aluminum
wire is : = 0.128 ohms per 1000 feet; the cross
10X1.25
ELECTRICAL PROPERTIES OF CONDUCTORS 29
section -X 10,000 = 125,000 C.M. ; the diameter
O.I2O
1.6
1.15^/125,000 = 406 mils; the weight - X9-5 = ii9
Ibs. per 1000 feet.
Increase of Resistance Due to Spiralling. The area
of a cable for electrical purposes is taken to be
the sum of the areas of the wires when laid out
straight and measured in a plane at right angles
to their axes. Hence, calculating the resistance of
a cable accurately we must take into account the
increase in effective length due to spiralling.
Let a = area of each wire in circular mils.
k = resistivity of the wires in ohms per mil-
foot.
PQ = pitch factor of layer of 6 wires.
piz= pitch factor of layer of 12 wires, etc.
The resistance of a seven-wire cable equals
k fin
ohms per foot.
a " ' "
The actual path of the current is along the spiral,
a very small proportion passing from wire to wire.
Formulae for larger cables are cumbersome, but
calculations may be made by considering the layers
individually and grouping them in multiple. The
proper value of p for each layer being assumed, we
have the following resistances.
30
ELECTRIC POWER CONDUCTORS
Wires in Layer.
Resistance of Each
Layer, Ohms.
I
k
a
6
*
12
~\2a ' ^^
18
A. #a
etc.
etc.
n
k
na
See p. 19 for Resistance of Standard British Cables, for which the pitch is twenty
times the diameter.
VARIATION OF RESISTANCE WITH TEMPERATURE
All materials suffer a slight increase of resistance
with rise of temperature. For all pure metals except
iron and nickel, this amounts to about two-fifths of one
per cent per degree Centigrade. Iron and nickel show
an increase of .005 and .007 respectively.
The law of increase of resistance, although for most
purposes proportional, is not always exactly so, and
depends not only on the metal but also on the physical
condition of the sample experimented on.
Measurements by Kennelly and Fessenden appear to
show that the resistance of commercial copper follows
a straight-line law, that is, the equation connecting
resistance and temperature is of the form,
R=r(i+at),
-
ELECTRICAL PROPERTIES OF CONDUCTORS 31
where R -resistance at t Cent. ;
r= resistance at o Cent.
The coefficient a appears to depend on the quality
of the sample. The following values are used:
Authority. Coefficient a.
American Institute of Electrical Engineers
Standardization Report, value used in U.
S. A. and accepted by American Authorities
as correct 0042
British Engineering Standards Committee 00428
German 0040
Matthiessen (Phil. Transac. 1862) gave the follow-
ing formula, which was used in making up the Ameri-
can Institute of Electrical Engineers' Wire Table:
C t = conductivity at t C.
C = conductivity at o C.;
C t = Co(l .O03,89O,I/ + .OOO,OOQ,OO9/ 2 ).
The second significant figure being doubtful, the
absurdity of having five is apparent. The reciprocal
formula is in the form of a convergent series and is
unwieldy. The following widely published formula is
obtained by omitting the terms containing the higher
powers of t than t 2 :
R =r(i + .00387^ + .000, 005, 968/2).
It was pointed out by F. B. Crocker (Elect. World,
Feb. 23, 1907), that the higher terms are not negligi-
32 ELECTRIC POWER CONDUCTORS
ble and that an error of over 1.7% is obtained at 100 C.
The following approximation is more nearly correct:
R=r(i + .004/ + . 000,002, 4/ 2 ).
The error at 100 C. is only i/io of i% compared with
Matthiessen's formula. Professor Crocker, in the
article above referred to, says that "the formula
adopted in the A. I. E. E. Standardization Report is
probably as nearly correct as any general expression
can be made."
The author's concurrence with this statement led him
to calculate new wire tables to supersede that of the A.
I. E. E., these tables being given on pages 25 and 26.
The temperature coefficient of aluminum is practi-
cally the same as that of copper, but is sometimes
given as .00423 per degree Centigrade.
Temperature - Resistance Calculations for Copper.
Slide-rule Method. The following method is of great
value on account of its simplicity, but requires a
slide rule marked as described below.
Mark slide (lower scale) as follows :
Slide Rule Number. Marking of New Scale.
238 o
248 10
258 20
268 30
278 40
288 5
298 60
308 7
318 80
328 90
338 100
etc. etc.
ELECTRICAL PROPERTIES OF CONDUCTORS 33
Example showing how to use temperature scale:
Suppose a copper wire to have a resistance of 300
ohms at 13 C., what will be its resistance at 100 C. ?
Set 13 on the new slide scale opposite 300 on the
lower scale and read on the lower scale the desired
resistance 404 opposite 100 on the new 7 scale.
This method is based on the coefficient 0.0042
adopted by the American Institute of Electrical En-
gineers, using the formula
238
(H. Fender, Elect. World, New York, April 13, 1907).
2. RESISTANCE OF NETWORKS OF CONDUCTORS
KIRSCHOFF'S LAWS
(1) In any branching network of wires, the alge-
braic sum of the currents in all the wires that meet
in any point, is zero.
(2) When there are several electromotive forces
acting at different points of a circuit, the total elec-
tromotive force around the circuit is equal to the
sum of the resistances of its separate parts multi-
plied each into the strength of the current that
flows through it.
Maxwell's Imaginary Currents. In any network of
conductors it is permissible, for purposes of calcu-
lation, to replace the actual currents through the
network, by imaginary currents flowing in the
34
ELECTRIC POWER CONDUCTORS
closed cricuits formed by each mesh. These imagi-
nary currents are taken as circulating in one direc-
tion, say the clockwise direction, and are all given
the same sign, say the positive. Should it be con-
venient, for any reason, to take a current flowing
in the opposite direction, it should be given a
negative sign. In each mesh the sum of the IR
drops equals the E.M.F. in the mesh, this being
zero unless there is a generator. If the generator
E.M.F. is in the same direction as the current,
the E.M.F. is positive; if it opposes the imaginary
current, its sign is negative.
Example. Let a, 6, c, d, e, f, g, h, and i be the
resistances of the various branches of the network
represented in Fig. 4, and w, x, y, and z the imaginary
currents in the various meshes as shown, the direc-
tion of each current being assumed to be clockwise.
The only E.M.F. in the system is E, produced by a
battery in the branch i. Then,
ELECTRICAL PROPERTIES OF CONDUCTORS 35
+ c)-Yg-Ze-Wc=o',
Y(g + b + d+f)-Xg- Zf-Wd^o
Z(e+f+h)-Xe-Yf-Wh =o;
+ h + d)-Xc-Yd-Zh=E.
Rearrange the equations so as to make them all
of the same form; thus,
-Yg-Ze =o;
Wd-Xg + Y(g + b + d+f)-Zf=o;
-Wh-Xe -Yf+Z(e+f+h) =o;
+ d)-Xc-Yd-Zh =E.
These equations may be solved in the ordinary
way or by determinants, as described below.
SOLUTION OF EQUATIONS BY DETERMINANTS
In order to solve such a series of equations the
following pair of " determinants " are written out:
W =
o (a -
\-g + e +
c) -g -e
-g
(g + b + d+f) -c
e
-f (e+f+h)
E
c
-g -h
c (a-
f- + ^ +
c) -g -e
-d
Q
(g + b + d+f) -c
-h
e
-f (e+f+h)
(i + c + h + d)
c
-g -h
36. ELECTRIC POWER CONDUCTORS
In the above equation it should be noted that the
denominator consists of the terms of -the four equa-
tions with the W, X, Y and Z omitted. The numera-
tor differs from the denominator only in that the
column of W terms is replaced by the terms on the
right-hand side of the four equations. Were X the
unknown, the second column of the numerator would
be replaced by the terms, o, o, o, and E.
The numerator and denominator of the above
equation, each constitute what is called a determi-
nant, and are simplified by the following rules. When
the value of W has been found, the resistance of
the circuit external to the generator is .
Rules, (i) If a determinant has two equal rows or
columns, it is equal to zero.
(2) To any row or column it is possible to add
or subtract any number of times any other row or
column without altering the value of the determinant.
(3) To multiply any row or column by a number
is equivalent to multiplying the whole determinant
by that number.
(4) If all the terms in a row or column except
one are zero, the determinant reduces to one of a
lower order which may be obtained by striking out
the row and column which intersect at the term in
question, and multiplying the whole by that term,
the sign of the determinant being settled in the
following way:
ELECTRICAL PROPERTIES OF CONDUCTORS 37
The line of terms beginning at the upper left-hand
corner and ending at the lower right-hand corner,
is called the principal diagonal of the determinant.
If the uncancelled term in the line of zeros is on the
principal diagonal or is removed from it by an even
number of terms, the term by which the determi-
nant is multiplied in lowering its order, is positive.
If, however, this term is removed from the principal
diagonal by an odd number of terms, the multiply-
ing terms is negative. Thus,
and
I
5
6
3
I
6
3
2
i
I
5
2
i
5
= 2
4
3
2
1
4
2
i
o
2
I
5
6
3
I
5
3
o
i
i
5
ry
2
i
5
4
3
2
i
4
3
i
2
the principal diagonal being that with the figures :,
2, and o. It is immaterial whether the distance
from the diagonal is counted along a row or a column.
(5) A determinant of the second order is ex-
panded in the following way
The reduction of determinants is effected by alter-
ing the terms according to the above rules until a
38
ELECTRIC POWER CONDUCTORS
row or column is obtained in which all terms but
one are zero. This enables a reduction or order to
be effected in accordance with rule 4. Reductions
are continued until one of the second order is
obtained.
Example i.
x+ y+ 3 = 6;
Then
6 i i
8 2 i
g i 2
III
121
I 12
i
2 I
i
~3 -i
2
I I
I 2
O
I I
I
2
I
-3
- I
i
I
i
2
I _
I
In the numerator, the following steps were taken.
Six times the last column was subtracted from the
first, and the last column was subtracted from the
second. In the denominator, the first column was
subtracted from the last. The determinants were
ELECTRICAL PROPERTIES OF CONDUCTORS 39
then reduced to the second order bv rule 4,
expanded by rule 5.
Similarly,
and
i 6 i
100
i 8 i
120
2
192
i 3 i
3 i
iii
I I
I I
121
120
I 2
112
III
= 2
Hence 2 = 3, by subtraction.
Actual cases are usually worked out without
copying the various steps of the determinant, the
changes being made with pencil and eraser.
Example 2. Reduce the following determinant.
2 4 7
2 5 8
3 8 9
Subtract twice the first column from the second,
and \ of the first column from the third.
21 I
3 2 -f
Reducing to the second order
Expanding
40 ELECTRIC POWER CONDUCTORS
3. RESISTANCE TO ALTERNATING CURRENTS OR
SKIN EFFECT
NATURE OF SKIN EFFECT
THE current induced in a conductor begins at
the surface and rapidly diffuses inward. When an
alternating E.M.F. is applied, the current started
by a positive impulse has only time to diffuse a
short distance from the surface before the succeed-
ing impulse starts an opposite current from the
surface. The effect is that the current never attains
its full value. A conductor therefore offers greater
resistance to alternating than to direct current.
Calculation of Skin Effect for a Cylindrical Wire. Let
R = ratio of alternating current resistance to direct
current resistance.
M = area of conductor, circular mils.
N = cycles per second.
jj. = permeability of conductor.
k = resistance of a mil-foot of the conductor at
the temperature under consideration.
=
The relation between R and Z is given by the
curve of Fig. 5, and by the following table.
TABLE I
APPROXIMATE VALUE OF R
Z less than i. 4 R=i
Z between 1.4 and 4.0 R is as given in Table II
Z is greater than 4.0 R=o.^4Z-\- 0.24
ELECTRICAL PROPERTIES OF CONDUCTORS 41
3.0
R
2.0
1.0
(
x
^
/
X
X
x^
/
/
/
>
/
/
/
/
/
s
s
2
X
^^
)
1
1
.
2
3
4 Z 5
FIG. 5.
TABLE II
6
7
8
9
z.
R.
Z.
R.
1.48
I. 01
2.80
1.16
1.64
1.02
2.84
1.17
1.78
1.03
2.89
1.18
1.90
1.04
2-94
1.19
2.OO
1-05
2-99
i. 20
2. II
I. 06
3-3
I. 21
2. 2O
1.07
3-o8
1.22
2.28
I. 08
3.12
1.23
2.36
1.09
3-i4
1.24
2-43
I.JO
3-20
J - 2 5
2.50
I. II
3-24
1.26
2.57
I. 12
3-27
1.27
2-63
I-I3
3-3i
1.28
2.68
I.I4
3-34
1.29
2-74
I-I5
3-38
1.30
42
ELECTRIC POWER CONDUCTORS
The calculation of skin-effect in copper and other
non-magnetic conductors presents no difficulties
because /* is unity. In the case of iron and other
magnetic metals, calculation is rendered difficult by
the necessity of using the proper value of / which
depends on the current. The following table gives
the results of tests by L. Lichens tein. (Electrician,
London, Aug. 23, 1907.)
TEST ON RAIL
Cycles per
Second.
Amperes.
A.C. Resistance.
Equivalent /-*.
D.C. Resistance.
58-5
49
4-34
8.0
48.7
153-8
5-55
7-2
Rail
28.2
62.5
2-85
14.8
bonded
25-4
108.4
3-76
15.0
with
19.4
3 6 -4
2-5
16.0
copper
17-3
123.2
2-93
i9-3
58.6
35
2.68
9.6 ]
48.6
152
3-42
r not
28.4
25-7
46.2
169
i-94
2.2
II. | , '
14.4 J bonded
Area of rail, 5160 sq.mrn. = 8 sq.in.
LARGE CABLES ON A.C. CIRCUITS
Owing to the fact that alternating current flowing
in large cables has greater density on the surface
of the conductor than in the center (so-called skin
effect), an ordinary cable will not carry as much
alternating current with the same temperature rise
ELECTRICAL PROPERTIES OF CONDUCTORS 43
as direct current. In order to overcome this it is
advisable on single conductor cables, 700,000 cm.
and larger, for 60 cycle circuits and 1,250,000 cm.
and larger for 25 cycle circuits, to make up the cable
with a fibre core and the copper stranded around
it. The weight of copper in this type of cable is
the same per foot as in an ordinary cable, but owing
to its annular cross section the cable is much more
efficient in carrying alternating current, and also
has a somewhat greater current carrying capacity
due to the larger radiating surface.
Size.
Diameter
Fiber Core
in Inches.
Number
of Wires
in Strand.
Size Wire
in Strand.
Overall
Diameter
Copper
Core.
Ampere Capacity.
30 C.
60 C.
2,000,000
7/8
2IO
0.099
2.065
1400
1750
1,750,000
25/3 2
210
0.091
.870
1300
1625
1,500,000
11/16
162
0.091
. 7 8o
1 200
1500
1,250,000
9/16
148
0.086
-590
1150
1400
1,000,000
15/32
98
O.T02
.280
900
1150
800,000
11/32
51
0.125
.100
775
925
700,000
9/32
51
O.II7
0.990
700
830
(G. E. Co. Bulletin.)
4. CARRYING CAPACITY
In the following table the lower limit is specified
for rubber-covered wires to prevent gradual deteriora-
tion of the insulation by the heat of the wires, not
from fear of igniting the insulation.
The carrying capacity of Nos. 16 and 18 B. S.
gauge wire is given, but no smaller than No. 14 is
used, except for fixture work and flexible cord.
44
ELECTRIC POWER CONDUCTORS
TABLE OF CARRYING CAPACITY OF COPPER WIRES AND
CABLES INTERIOR WIRING
(National Electric Code.)
B. & S. Gauge.
Table A.
Rubber Insulation.
Amperes.
TableB.
Other Insulations
Amperes.
Circular Mils.
18
3
5
1,624
16
6
8
2,583
14
12
16
4,107
12
17
2 3
6,53
10
24
3 2
10,380
8
33
46
16,510
6
46
65
26,250
5
54
77
33,i
4
65
92
41,740
3
76
no
52,630
2
90
131
66,370
I
107
156
63,690
O
l'2 7
185
105,500
oo
15
220
133,100
ooo
177
262
167,800
oooo
210
312
211,600
2OO
300
200,000
270
400
300,000
330
500
400,000
39
590
500,000
450
680
600,000
500
760
700,000
55
840
800,000
600
920
900,000
650
I OOO
,000,000
690
1080
,100,000
730
1150
,200,000
770
I22O
,300,000
810
1290
,400,000
850
1360
,500,000
890
143
,600,000
93
1490
,700,000
970
1550
,800,000
IOIO
1610
,900,000
1050
1670
2,000,000
ELECTRICAL PROPERTIES OF CONDUCTORS 45
For insulated aluminum wire the safe carrying
capacity is 84% of that given above for copper wire
with the same kind of insulation. (Nat. Elec. Code.)
CURRENT CARRYING CAPACITY OF INSULATED LEAD
COVERED COPPER CABLES IN DUCTS*
Initial Temperature, 20 C.
(G. E. Bulletin 4591.)
Low TENSION CABLE,
SINGLE CONDUCTOR.
HIGH TENSION
CABLE, THREE
CONDUCTOR.
Size of Cable
in Circular
Mils.
National
Electric
Code, 1907,
Rubber.
Rubber 30 C.
Rise.
Var. Cam.
or Paper
60 C. Rise.
Rubber and Var.
Cam. 30 C. Rise
Paper, 35 C. Rise
Amperes.
Amperes.
Amperes on Each
Conductor.
2,000,000
1050
1400
1750
1,500,000
850
1200
1500
1,000,000
650
900
1150
750,000
525
75
900
500,000
390
550
660
440
400,000
33
460
56o
360
300,000
270
37
45
290
250,000
235
230
390
250
2OO,OOO
200
270
310
2IO
150,000
1 60
220
260
175
125,000
140
1 80
210
140
IOO,ooo
120
1 60
100
125
80,000
104
140
I6 5
110
60,000
82
110
I 3
85
40,000
63
75
9
60
6 B. & S. solid
4 6
5
60
40
8B&S. solid
33
3
36
24
10 B. & S. solid
24
20
24
16
* The table gives the maximum continuous load in amperes for high and low
tension cables with rubber and varnished cambric or paper insulation, the ulti-
mate rise in temperature being marked at the head of each column. For high
tension single conductor, use figures given for single conductor rubber.
46 ELECTRIC POWER CONDUCTORS
Experience has shown that the maximum tem-
perature which cables should be permitted to attain
is 50 C. for rubber and 80 C. for varnished cambric
and paper insulated. (From G. E. Co. Bulletins.)
GENERAL FORMULA FOR THE CARRYING CAPACITY OF
COPPER WIRES AND CABLES:
/ = Current, amperes;
T = Temperature rise, deg. Cent.;
,
K
where
k is given by Table I
A " " II
B " " III
C " " IV
D " " V
For multiple conductor cables, the value of 7 is
for one conductor. The carrying capacity of Alumi-
num of 62% conductivity is 80% that of copper.
When / is known, and T is required, use the fol-
lowing formula
~i +0.0042 TO
N 0.0042
ELECTRICAL PROPERTIES OF CONDUCTORS 47
where
TO = initial temperature in deg. Cent. ;
L lABCD^.
~k (^^) '
k = value of k at o C., as given by Table I.
For Aluminum of 62% conductivity = 15.5.
TABLE I
VALUES OF k
RESISTANCE (OHMS) OF A MIL-FOOT OF COPPER
Use of Table
Find the temperature corresponding to the rise T by adding the initial
temperature thereto. Then take the value of k corresponding to that tem-
perature, from the table.
Temperature.
Values of k.
Temperature.
Values of k.
C
op
98%
Conduc-
99%
Conduc-
C
F.
98%
Conduc-
99%
Conduc-
tivity.
tivity.
tivity.
tivity.
3 2
9-79
9.69
55
13*
12.0
11.9
5
4i
10.
9-9
60
140
12.2
12. I
10
50
10.2
10. I
65
149
12.4
12.3
15-5
60
IO.4
10.3
70
158
12.7
12-5
20
68
10.6
10.5
75
157
12.9
12.7
24
75-2
10.8
10.7
80
176
13-1
I2. 9
30
86
II. O
10.9
85
185
13-3
I3-I
35
95
II. 2
n. i
90
194
13.5
13-4
40
104
ii. 4
n-3
95
203
13.7
13-6
45
U3
ii. 6
"-5
IOO
212
13-9
13-7
50
122
ii. 8
1.1.7
on Matthiessen's Standard and the A.I.E.E. temperature coefficient.
ELECTRIC POWER CONDUCTORS
TABLE II
VALUES OF A
where d= diameter of a solid wire of the size given, inches
Size of Conductor.
A.
Size of Conductor.
A.
Millions of C.M.
No. B. & S.
2
i-9
1.8
10.32
9-93
9-54
oooo
ooo
00
1.91
1.61
i-35
-7
.6
-5
9.14
8.74
8.32
o
I
2
1.14
-955
0.802
-4
-3
.2
7-9
7.46
7-03
3
4
5
0.675
0.566
0.476
I.I
1.0
0.9
6-59
6-15
5-67
6
7
8
0.400
o-337
0.282
0.8
5-i9
9
0.237
o-75
4-95
10
0.200
o-7
4-7
12
0.147
0.6
o-S
0.4
4.18
3-65
3-o8
14
16
18
0.0995
0.0703
0.0496
o-35
-3
2-79
2-49
20
22
0.0351
0.0248
0.25
2.17
ELECTRICAL PROPERTIES OF CONDUCTORS 49
TABLE III
VALUE OF B
W= watts dissipated per sq.in. of single conductor cable per deg. Cent.
Temperature rise.
Where Installed.
Type of Cable.
Bare.
Rubber Covered.
Paper or Cloth
and Lead.
Solid.
Stranded.
Solid.
Stranded.
Solid.
Stranded.
Open air ...
1 60
130
175
143
105
94
140
89
78
75
no
no
IOO
150
93
82
79
US
105
89
86
75
72
IOO
no
93
90
79
75
105
Still air
Wooden moulding..
3J" tile duct;
No. oooo B. & S. .
|M. .
iM
Under water, leaded
and armored
The values given in the above table are averages based on experimental data
from various sources ; the maximum variation from the average in the values thus
found was about 5%.
TABLE IV
VALUE OF C
(Standard Underground Cable Co. Handbook.)
Type of Cable.
C.
Single conductor
i
Two conductor, flat or round
o 87
Two conductor, concentric. . .
O 7c)
Three conductor, triplex
O 7?
Three conductor, concentric
o 60
50
ELECTRIC POWER CONDUCTORS
TABLE V
VALUES OF D
Number of Simi-
larly Loaded Cables
in Group of
Ducts.
D.
I
i .0
2
3
0.92
0.86
4
o-79
5
6
7
8
o-75
0.70
0.66
0.63
9
10
-59
0.56
12
0.&
The thickness of insulation probably has a considerable effect upon the radiation,
but experimental data on this point are not available. The above table is based
principally upon tests of low voltage cables.
Carrying Capacity of Wires of Various Metals. The
carrying capacity or current causing a given tem-
perature rise is inversely proportional to the square
root of the specific resistance of the metal, and
directly proportional to the square root of the heat
radiation per unit area. Assuming the latter to be
the same for all wires, the relative carrying capaci-
ties of wires of different metals, referred to Matthies-
sen's annealed copper as unity are given in the
following table;
ELECTRICAL PROPERTIES OF CONDUCTORS 51
Metal.
Relative Carry-
ing Capacity.
Silver, annealed
1 .04
Copper annealed
o oo to I 01
Copper, annealed, 100% cond...
Copper or silver, hard drawn. . . .
Gold hard drawn. . .
I
0.98 to i.o
o 87
Aluminum, annealed
0.74
Aluminum wire, 62*% cond
O 70
Zinc pressed. .
o. <3
Phosphor bronze
O 4 <
Platinum annealed.
o 42
Iron, annealed
0.40
Nickel annealed
o 36
Tin, pressed
O. "? ^
Lead pressed
O 2O
German silver, from
o 28
to
O 2 T.
Platinoid
O 22
Antimony pressed
O 21
Mancanin . -
O IO
Krupp metal
O 14
^tercury
O I 3
Bismuth. Dressed. .
0. 12
Knowing Heating with One Current, to Find Heating
with Another Current. The chart (Fig. 6) is used as
follows :
Suppose a switch or cable has a rise of 20 C. with
200 amperes, what will the rise be with 300 amperes?
Referring to the curve, the vertical line 200 is followed
upward until it intersects the diagonal which starts
at 20. This diagonal is followed upward until it
intersects a vertical line at 300 amperes. The hori-
zontal line intersecting the vertical line at this point
gives the rise in degrees, namely, 45.
52
ELECTRIC POWER CONDUCTORS
As noted on the diagram the current scale is cor-
rect for amperes, milli -amperes, or any other unit,
100
90
70
.i 60
5
. 80
40
30
20
15
10
//// I//// // //////// I/I
LLL
ILL
LL
LULL
J/ILIULULUL
7 A
'LL
'JL I
100 150 200 300 400 500 600 700 800 900 1000
Current in any Unit.
FIG. 6.
and the temperature scale is correct for either Centi-
grade or Fahrenheit. (Based on article by C. C.
Badeau, Elec. World, Jan. n, 1908.)
ELECTRICAL PROPERTIES OF CONDUCTORS 53
INTERMITTENT CARRYING CAPACITY
Let P = time of full period (minutes) assuming the
current periodically on and off;
a = portion of f till period (minutes) that current
is on;
T = time (minutes) in which temperature rise
becomes 0.633 times maximum tempera-
ture rise. This depends on size and type
of cable and is given in the following table :
C = maximum permissible constant current;
pC = maximum permissible intermittent current.
To find pC:
Find T for size of cable under consideration.
Thence calculate and and from the table
find the corresponding value of p.
VALUES OF T
CABLE INSULATED FOR 700 VOLTS
Sq.Mm.
Value of T.
Single Cond.
Triplex.
50
14
21
100
21
32
J 5
28
42
200
3 2
50
300
38
63
400
41
70
500
42
600
44
700
46
800
48
yoo
49
IOOO
50
54 ELECTRIC POWER CONDUCTORS
VALUES OF p
a
a
P
T
O. I.
0.15.
0.2.
0.3.
0.4.
0.5-
0.6.
0.7.
0.8.
0.9
o.o
3-15
2.65
2.25
.8
-55
-45
-3
1.2
I.I
-05
I
2. :<
2.T.Z
2.2
.7
. c;
4
.25
.Ot?
O 2
2 2
2.OZ
I n
.6
-4s
?c;
2C
oc
o 3
-0
.85
I -7
- ^
.4
. 7
ex
o 4
.7
.7
1.6
. <
.7C
. T.
-O
24.
3
24.0
19.2
16
11
14/32
40.
3 2
25.6
32
25.6
20.5
17
< I
14/32
42.5
34
27.2
34
27.2
21.7
18
1 '
15/32
45-
36
28.8
30
28.8
23.0
J9
<
15/32
47-5
38
3-4
38
3-4
24-3
:o
"
16/32
So.
40
32-
40
32.
25-5
21
( C
l6/ 3 2
52.5
42
33-6
42-
33-6
26.8
22
< <
17/32
55-
44
35-2
44
35-2
28.!
23
( (
17/32
57-
46
36.8
46
36.8
29.4
24
1 1
18/32
60.
48
38.4
48
38.4
3-7
25
tl
18/32
62.5
5
40.
50
40.
3i-9
G. E. Bulletin 4591-
I
INSULATION AND INSULATED CONDUCTORS 91
Belted and Unbelted Triplex Cable. In a three-
conductor cable for, say, 11,000 volts, the insulation
can be most advantageously disposed if each con-
dutor is insulated for half of 11,000, i.e., 5500 volts,
and the group insulated by a belt' good for 900 volts,
this being the difference between 5500 and 6400,
the voltage from conductor to ground. A triplex
cable built on this plan, i.e., with an exterior belt,
is therefore dielectrically the strongest as long as the
belt is intact. For this reason paper insulated cables
are almost invariably of the belted type.
Rubber cables differ from paper in not necessarily
breaking down when the sheath is punctured. It is
therefore desirable to design such cables so that they
will not be put out of service in the event of water
getting at the insulation. When a triplex cable of
the belt type is punctured so as to admit water under
the belt, the whole surface under the belt and between
conductors becomes rilled with water for a consider-
able distance on each side of the puncture, perhaps
even for the whole length of the cable. The result
of such a puncture is to put a stress of 6400 volts on
the 5500 volt insulation. The puncturing of a sheath
of an unbelted triplex cable is attended with no such
injurious result, and if the insulation of only one
conductor is injured, the other two are intact. The
former may be used if supplemented by a new single
conductor cable or by a similar uninjured wire
from another injured cable.
92 ELECTRIC POWER CONDUCTORS
The processes of manufacture of belted triplex
cables with rubber insulation also place this type at
a disadvantage compared with the unbelted type.
The insulation on the individual conductors being
vulcanized and tested before the conductors are
assembled is subjected to an additional cooking when
the belt is vulcanized. This is liable to alter its
electrical and mechanical characteristics after test,
which is very undesirable.
Diameter of a Triplex Cable.
Let d = diameter of each conductor ;
t= thickness of insulation around each con-
ductor ; ,
T = sum of thickness of sheath and outer belt
of insulation, if any.
Diameter - 2. i $d + 4.3* + 2 T.
Thickness of Sheath. The following sheath thick-
nesses are recommended as representing the best
practice for cables in tile ducts:
. Thickness of Sheath.
Inches.
14-8 B. & S 3/64
6-1 B. & S 4/64
o B. & S. to 250,000 cm 5/64
500,000 to 750,000 cm 6/64
1,000,000 cm 7/64
1,250,0002,000,000 cm 8/64
Triplex-ooo B. & S 8/64
Triplex-oooo B. & S 9/64
INSULATION AND INSULATED CONDUCTORS 93
Short Circuit Indicator. Direct-current feeders fed
through circuit breakers set for large currents may
be protected against the effects of short circuits by
means of the following device:
The automatic relay feature of the circuit breaker
is connected to a small wire or a pair of wires clipped
or taped to the feeder cable along its entire length
in such a way that a short circuit will burn these
wires and thereby open the relay circuit. The relay
is of the low voltage release type, so that the inter-
ruption of its circuit has the effect of promptly open-
ing the circuit breaker. A diagram of connections is
shown in Fig. 8.
*- Cable
FIG. 8.
A No. 12 B. & S. wire with ^ in. 30% Para rub-
ber compound taped and braided is usually suitable
for this service, but the correct size should be worked
out for each installation, taking into account both
the carrying capacity and potential drop. The fuse
on the negative side comes into service in case the
short circuit melts the indicator wire into contact
with the main feeder metal thereby maintaining the
94 ELECTRIC POWER CONDUCTORS
continuity of the circuit. In such a case, the rush
of current to ground blows the fuse and interrupts
the relay circuit. This system has been in suc-
cessful operation on the New York Central R. R. to
protect feeders along the Park Avenue viaduct and
tunnel. It was devised by the author early in 1906,
and is unpatented.
3. INSULATORS, PINS, ETC.
REQUIREMENTS OF A GOOD INSULATOR
1. Dielectric strength.
2. Resistance to surface arcing.
3. Mechanical strength.
4. Ease of erection.
5. Facility of cleaning.
6. Negligible electrostatic capacity, this oemg,
however, the least important qualification.
Dielectric Strength. This quality is affected by
dielectric strength of material, by thickness of mate-
rial, and by freedom from flaws.
Porcelain and glass are the omy materials used
extensively, although there are several composi-
tions which have had success particularly for low
tension work. Porcelain is almost universally used
for high tension work, notable exceptions, however,
being the use of glass for 57,000 volts by the
Missouri River Power Company, and for 40,000
*
INSULATION AND INSULATED CONDUCTORS 95
volts by the Madison River Power Company, Butte,
Montana.
A thick head adds to the dielectric strength but
reduces the mechanical strength. The " Italian "
type is solid and is provided with a wide petticoat
at each end and two small intermediate petticoats.
The usual American practice for high tension work
is to make the insulator in two or more pieces, each
individually tested and assembled with litharge and
glycerine cement. This construction adds consid-
erably to the dielectric strength.
Porcelain which absorbs water should be avoided,
although it is not uncommon to find an absorption
of i% or 2% in commercial porcelain..
Resistance to Surface Arcing. This quality is
affected by material, texture of surface, and shape
of insulator.
With regard to material, porcelain is universally
conceded to be superior to glass on account of its
less hygroscopic nature. The surface should be
very smooth and uniform.
The shape is a matter of great importance, and
there is a division of opinion as to the relative merits
of many petticoats or a wide umbrella or bell com-
bined with a long pin shield. Petticoats give long
leakage surface but shorter arcing distance, and
are more difficult to manufacture.
Mechanical Strength. Mechanical strength depends
upon strength of material, thickness of material, and
96 ELECTRIC POWER CONDUCTORS
judicious design. Porcelain is superior to glass
mechanically, and glass is more subject to internal
stresses developed in manufacture. Glass, however,
being transparent, has the advantage of enabling
flaws to be readily detected.
Facility of Cleaning. Facility of cleaning depends
upon the size of spaces between petticoats. The bell
and shield type is decidedly superior to the petticoat
type in this characteristic. Glass in some cases
has the advantage of permitting inspection more
readily on account of its transparency. The trans-
parency has the further advantage of preventing
insects from building cocoons under the petticoats.
Electrostatic Capacity. An insulator in service
acts as the dielectric of a condenser, the two con-
ductors of which are the wire and pin. The capacity
of the insulator should be as low as possible to
minimize operating troubles. This can be accom-
plished by having a considerable thickness of insu-
lation between line and pin, precaution being taken
to distribute the potential so as to make each shell
carry its share of the potential stress. In fact, a
multipart insulator acts as several condensers in
series, the voltage stress in the different shells being
dependent upon the relative capacities of the several
condensers.
Shape. In a severe rainstorm the wind and
spattering from the top surfaces of shells are liable
to wet practically all of the insulator surfaces,
*
INSULATION AND INSULATED CONDUCTORS 97
except possibly the under surface of the inner shell.
In order to keep this inner surface dry, the insulator
must be carefully mounted with respect to the
cross-arm. The ideal multipart insulator of the
umbrella type should therefore have its inside shell
so designed that alone it can carry the full line poten-
tial without puncture or arcing. This condition
usually obtains on low voltage insulators but seldom
on those for 60,000 volts or more.
With a given diameter and height, maximum
sparking distance between adjacent rim and shell
can be, obtained by using the curved type of shell,
but there is a point where this advantage is counter-
balanced by the increased risk of spattering from
the other shells. The flare of the shell is often
determined by a radius taken about the rim of
the upper shell as center, the curve beginning at the
hypothetical dry line, assuming that the rain falls
at an angle of 30 from the horizontal.
TEST VOLTAGE FOR INSULATORS
Dry Test, insulator assembled on metal pin ; fifteen
minutes at three times line voltage.
Wet Test, precipitation J in. per minute, 45 angle
spray nozzle; fifteen minutes at i^ times line voltage.
Puncture Test, for each shell; fifteen minutes at
from J to ij times line voltage, the former figure for
high voltages and the latter for low voltage.
98 ELECTRIC POWER CONDUCTORS
By line voltage is meant the normal voltage between
line and ground.
INSULATION FACTORS
Wet
Ratio of Arcing Distance . This ratio varies
Dry
from 0.3 to 0.9, averaging between 0.6 and 0.7
Ratio of Dry Creeping Surface with 45 Rain and Dry.
This ratio varies from 0.5 to 0.85 and averages be-
tween 0.75 and 0.7.
Working Volts per Inch Thickness of Insulation.
Above 10,000 volts this varies between 20,000 and
60,000, averaging between 30,000 and 40,000. Below
10,000 volts mechanical considerations settle the
thickness.
Factor of Safety (ratio of breakdown to working
volts). Above 20,000 volts the factor of safety varies
between 2j and 3 dry, and between ij and 2^ wet.
At voltages around 10,000 the factor is usually be-
tween 6 and 8 dry and between 3 and 6 wet.
Puncturing Voltage of Porcelain. C. J. Greene
(Eke. Rev., Lond., Apr. 24, 1908) says that the average
puncturing voltage of porcelain tested by him is
approximately 100 kv. per inch.
LINK INSULATORS
The insulator consists of a solid porcelain piece
having a flanged rim which affords a long creepage
surface between live parts and insures some portion
INSULATION AND INSULATED CONDUCTORS 99
of the surface sheltered from rain. There are two
interlinked holes in the center (Fig. 9) through which
the cables or guy wires are threaded, thereby bring-
ing a compressive strain on the porcelain.
An insulator of 10 in. diameter is suitable for 25,000
volt service and a 6V in. insulator for 12,000 volts.
For higher voltages, several disks are used in series
spaced at a distance approximately equal to their
diameter.
FIG. 9. Cross Section of Link Strain Insulator.
The advantages of this tvpe of insulator are as
follows :
(1) The material is subjected on_y to compress- ve
strains.
(2) By the use of the proper number of insulators
in series practically any line voltage can be used.
(3) High factor of safety both electrically and
mechanically.
100
ELECTRIC POWER CONDUCTORS
(4) Less likelihood of torsional strains in cross arms
in the event of a wire breaking.
The chief disadvantages are:
(1) Increased height of poles or towers.
(2) Necessity of frequent anchoring of the line
wire.
FIG. 10.
Where several discs are used in series, they should be
linked together by hard drawn copper cable held fast
by bolted clamps. Brass wire has been tried and found
unsuitable on account of its uneven structure, and
galvanized steel has been found to deteriorate rapidly.
INSULATION AND INSULATED CONDUCTORS 101
PINS
Wooden pins are largely used for low-tension
work, but are now considered risky for high-tension
lines. The most approved type of pin is that of the
Long Island R. R., a malleable cast-iron pin which
it attached to the cross arm by a U bolt passing
around the cross arm, as shown, in Figs. 10 and n.
Insulator Pin for H. T. Lines. Long Island R. R. Type.
Scale \ Full Size. Dimensions approx. only.
FIG. II.
This construction obviates the drilling of holes in
the cross arms. The advantages of metallic pins are
long life, and if grounded, rapid and clean short
circuit in the event of an insulator failing, thereby
102
ELECTRIC POWER CONDUCTORS
preventing protracted arcing and operating circuit
breakers with certainty
Locust and eucalyptus are the most approved
kinds of wood for insulator pins.
PROPOSED STANDARD PINS
(See Fig. 12.)
A.
7?.
c
C
D.
.
F.
C.
H.
7.
Nom-
Act-
inal.
ual.
5
4f
4*
I
iM
iA
I|
I
i
if
i
7
6f
4*
if
ifi
itt
i
9
81
4i
if
iff
itf
ri
N
|
2
N
2l
i
N
ii
iof
4f
2
i|J
itt
2|
"fl
13
xa|
4|
2f
2&
2^
13
9
"rt
i
15
15
I4l
4f
J
2^
2^
e
J|
<2
2i
5
17
*9
i6|
i8f
Si
Si
2f
2*
2^
2M
2^
2^
0)
1
0)
1
0)
1
2j
2j
1
Trans. Am Inst. E. E., vol. XX, p. 415.
FIG. 12.
CONDUCTIVITY OF ATMOSPHERE AT HIGH VOLTAGES
(From Amer. Inst. Elec. Eng., 1904, H. J. Ryan.)
E = maximum value of voltage curve (to obtain
R.M.S. value divide by V 2) ;
r= radius of conductor, inches;
5= distance between conductors, center to center;
D = strength of electrostatic field, coulombs per sq.in.,
causing atmospheric rupture.
* *
INSULATION AND INSULATED CONDUCTORS 103
d= distance from the surface of the conductor at
which atmospheric rupture is initially caused.
E = 2055 logw(^D(r+d) X 10.
The following table gives the relation between d,
D', and r at a pressure of 29.5 in. of mercury and a
temperature of 70 F. :
B. & S. Gauge.
27".
d.
D.
20
0.03196
0.0050
35oXio~ 10
15
0.05706
O.OIOO
300
10
0.10189
0.0180
275
8
0.12849
0.0220
258
6
0.16202
0.0350
200
4
0.20431
0.0700
171
2
0.25763
0.0700
170
up to 625 in. diam.
O.C7OO
I7O
Amended to allow for barometric pressure and
temperature, the above formula reduces to the follow-
ing, in which b = barometric pressure in inches of
mercury, and t= temperature, F. deg.,
17.946
459 + *
If the surface of the wire is rough, the voltage at
which it glows is less than given above.
Experiments of R. D. Mershon at Niagara give the
critical voltage approximately 40% less than the values
calculated from Ryan's formula. (See Proc. Am. Inst.
Elect. Eng. June 30, 1908.)
CHAPTER IV
DETERMINATION OF SIZE OF CONDUCTORS
i. VOLTAGE AND SYSTEMS OF DISTRIBUTION
GENERAL IMPORTANCE OF HIGH VOLTAGE
The amount of copper required to transmit a given
amount of power at a given loss over a given dis-
tance, other things being equal, is inversely pro-
portional to the square of the potential used, whatever
the system of distribution.
Comparison of the different systems, such as two-
wire single phase, three-wire three-phase, and quarter-
phase is given below on the basis of equality of
power delivered, loss and potential.
In low-potential circuits, as secondary networks,
where the potential is not limited by the insulation
strain in the transmission system but by the potential
of the apparatus connected into the system, as, for
example, incandescent lamps, the proper basis of
comparison is equality of the potential per branch
of the system, or per phase.
On the other hand, in long distance transmission
where the potential is not restricted by any con-
104
DETERMINATION OF SIZE OF CONDUCTORS 105
sideration of apparatus suitable for a certain maxi-
mum potential only, but where the limitation of
potential depends upon the proper insulation of the
conductors against disruptive discharge, the correct
comparison is on the basis of equal maximum
dielectric strain on the insulation; for overhead lines
this means equality of potential to ground as it is
between ground and wire that the insulation (other
than air) has to be provided.
COMPARISON OF SYSTEMS WITH EQUAL EFFECTIVE DIF-
FERENCE OF POTENTIAL ACROSS BRANCH OR PHASE
OF LOWEST DIFFERENCE OF POTENTIAL
No.
of
Wires
System.
Relative
Amount of
Copper.
c. or single-phase, neutral full
c. or single-phase, neutral half
Continuous current. .
Single-phase
Edison three-wire, d.
section
Edison three-wire, d.
section
Inverted three-phase (derived from two branches of a
-3-phase system by transformation by means of two
transformers, whose secondaries are connected in
opposite direction with respect to their primaries) . . .
Quarter-phase with common return
Three-phase
Three-phase with neutral wire, full section
Three-phase with neutral wire, half section
Independent quarter-phase
Edison five-wire, d. c. or single-phase, full neutral
Edison five-wire d. c. or single phase, half neutral
Four wire, quarter phase, with common neutral, full
section
Four wire, quarter-phase, with common neutral, half
section. .
TOO
100
37-5
31-25
56-25
72-9
75-o
33-3
29.17
100
i5- 6 25
10.93
31-25
28.125
106
ELECTRIC POWER CONDUCTORS
We see herefrom that in distribution for light-
ing, with the same minimum potential and with
the same number of wires, the single phase system
is superior to any polyphase system.
COMPARISON OF SYSTEMS WITH EQUAL MAXIMUM
POTENTIAL TO GROUND
No.
of
Wires
System.
Relative
Amount of
Copper.
Single-phase, either without ground * or with one wire
ground ed
Single-phase, center grounded
Continuous current, either without ground* or with
one wire grounded ,
Continuous current, center grounded
Three-phase, either without ground* or with one wire
grounded ,
Three-phase, neutral grounded
Quarter-phase with common return, without ground or
with either outer grounded
Quarter-phase with grounded common return
Independent quarter-phase, either without ground * or
with one wire grounded
100
25
I2 -5
75
25
M5-7
72.9
* Even when no part of the system is grounded each wire has to be insulated
from ground for a difference of potential equal to that between wires, since the
difference of potential between any wire and ground rnay be anything from zero
to full potential between wires.
Since the comparison is made on the basis of
equal maximum potential and the maximum poten-
tial of an alternating system is V2 times that of a con-
tinuous-current circuit of equal effective potential,
the alternating circuit of effective potential e com-
pares with the continuous-current circuit of potential
eV2, which latter requires only half the copper of
the alternating system.
(The author is indebted to C. P. Steinmetz,
DETERMINATION OF SIZE OF CONDUCTORS 107
" Alternating Current Phenomena," for much of
the above data.)
Standard Transmission Line Voltages. The following
three-phase voltages have been adopted by the Gen-
eral Electric Company as standard for railway work:
11,000 volts with delta connected transformers.
19,000 volts with delta connected transformers.
33,000 volts " Y " or delta connected transformers.
57,000 volts " Y " connected transformers.
These voltages step up in the ratio of the square
root of three to one, allowing the voltage of any
system to be raised in case of extensions from one
standard to the next higher, by changing the
transformer primary connections from delta to " Y."
The lowest voltage (11,000), is the only one suited
for direct generation without step-up transformers,
and is generally so installed. Such systems are
not readily changed over, for which reason 19,100
volt transformers are delta connected only. On
account of the prevailing use of 13,200 volts, trans-
formers and switching apparatus can be supplied
for this voltage also. (G. E. Review, May, 1908.)
2. LAMP WIRING CALCULATIONS
PRELIMINARY
THE following data are necessary for the wiring
calculations.
(i) Length of feeder from bus to branches. Use
length of wire, which is usually twice the distance.
108
ELECTRIC POWER CONDUCTORS
(2) Number of branches.
(3) Length of wire and current taken by each
branch.
(4) Permissible volts drop from bus to branches,
in both wires.
(5) Permissible volts drop in each branch. Usually
the same for all branches.
Calculation of Wire for Branches. Construct a
table as shown below, giving for each branch the
permissible drop, the length of wire, and the current.
Then by the formula C.M. =
10 . 8 X ampere-feet
Volts drop
, the
size of the wire is calculated.
TABLE FOR CALCULATION OF BRANCH WIRES
Branch
Number.
Permissible
Drop of
Volts in
Branch = v.
Length of
Wire in
Branch.
Feet = F.
Amperes
taken by
Branch = .<4.
io.8AF_
V
Circular Mils.
Size
B. & S
I
2
3
etc.
Calculation of Wire for Feeder or Main.
i o . 8 X total current X total length
Permissible volts drop
While the above form is the most usual, the formula
may also be written as follows:
1080 X total ampere-feet
C.M.
pXV.
DETERMINATION OF SIZE OF CONDUCTORS 109
where V = volts delivered,
p = drop in mains in per cent of volts delivered.
Slide Rule for Wiring. A simple slide rule for
wiring calculations devised by E. P. Roberts, is
made by constructing a table as shown below, and
cutting along the line between the first and second
columns.
Size of Wire.
Thousands of
Ampere Feet.
Thousands of
Circular Mils.
Volts Loss.
500
500
400
400
320
320
250
250
0000
2OO
ooo
1 60
oo
I2 5
o
IOO
I
80
2
64
3
50
4
40
5
6
32
25
7
8
20
16
9
12
10 >
IO
ii
8
12
6
13
5
14
4
15
16
3
2
17
2
110 ELECTRIC POWER CONDUCTORS
Then to use the rule all that is required is to put
the arrow-head opposite the figures in the second
column representing volts loss allowable, and oppo-
site thousands of ampere-feet, read in the second
column, will be found in the first column the size of
the wire required.
The action of the rule is based upon the fact that
No. 10 wire has a resistance of practically one ohm
per 1000 feet, and therefore with No. 10 wire 10,000
ampere-feet would give 10 volts loss. Also No. 10
wire has practically 10,000 circular mils cross-section,
and the size of the wire doubles for each third size
larger.
Three- Wire System. The outside wires are calcu-
lated by the above rules, ignoring the center or
neutral wire, and treating two lamps in series as
one lamp of double voltage.
The neutral wire of a branch is usually made the
same size as the outers, although in most cases a
smaller size would be possible.
Alternating Currents. The inductance of house
wiring, where the two wires of a circuit are run in
the same pipe or moulding, is negligible.
I
DETERMINATION OF SIZE OF CONDUCTORS 111
3. CONTINUOUS-CURRENT RAILWAY FEEDER
CALCULATIONS
PERMISSIBLE POTENTIAL DROP
The total drop of potential in the positive and
negative conductors is governed by four conditions,
namely: the possibility of starting the cars, the
brilliancy of the lights, the limiting of drop in the
grounded conductors and the relative economy of
low first cost compared with low energy loss. With
regard to the question of starting the cars, the voltage
required may be derived from a study of the motor
curves.
With the multiple-unit system of control, the limit-
ing voltage is usually that at which the contactors
will operate satisfactorily, this being about one-half
the normal running voltage. The voltage at which
the car lights become too dim is about 90% of the
rated voltage of the group of lamps. However, by
using lamps, rated considerably below the normal
bus voltage, it is^ permissible to let the voltage drop
more than 10% without affecting the lights too
seriously; although lamps thus used get an over-
voltage when the load is light, causing a shortening
of their life.
The drop in grounded conductors is usually covered
by city ordinances, which require it not to exceed a
specified amount.
112 ELECTRIC POWER CONDUCTORS
The investment in a system of conductors may be
expressed as an initial cost or as an annual interest
thereon. The value of the kilowatt-hours of energy
lost in these conductors is most conveniently expressed
as an annual expense. The sum of these two annual
items is the total annual expense of the feeders,
which it is desirable to make as small as possible.
AUXILIARY FEEDERS
Any direct-current feeder system consists of two
distinct parts, the conductors which supply current
from the power-house to the line and the contact
conductors which yield their current directly to the
cars. In many cases the contact conductors will be
sufficiently large to fulfil both functions, but more
often they are supplemented by auxiliary copper
feeders. The various steps at which auxiliary copper
may have to be added are given below in the order
in which they usually have to be treated.
I. If the drop in the grounded conductors exceeds
the legal limit or the limit prescribed by danger of
electrolysis, copper will have to be added to these
conductors.
II. If with this additional copper the total drop
in the positive and negative feeders is still too great
to enable the cars to start, additional copper must
again be resorted to, but this time it may be added
to either the positive or negative system. Whether
it will be more economical to add it to the positives
I
DETERMINATION OF SIZE OF CONDUCTORS 113
or negatives will have to be worked out for each case,
although an indication is given by the fact that if
the unit price of conductors installed is the same for
both, it is more economical to distribute the copper
so as to make the resistance of the two systems equal.
III. Having provided copper to maintain the voltage
high enough to start the cars, it remains to deter-
mine whether it is also high enough to keep the lamps
bright. If not, more copper must be added in the
way described above.
IV. The feeder system having been made of ample
dimensions to meet all the conditions of the service
it remains to determine whether the annual loss in
the conductors is great enough to justify the addition
of more copper in order to keep down the operating
expenses. If the conductivity is sufficient, there is
nothing to be done; but if the considerations of
operating economy call for more copper, the engineer
is justified in recommending it.
In order to determine the most economical copper
investment, it is convenient to compile a table show-
ing the following six quantities: (i) Value of pro-
posed additional conductors. (2) Total annual energy
loss (kilowatt-hours) in the entire positive and nega-
tive system, including the proposed additional con-
ductors. (3) Value of this lost energy. (4) Value
of the additional conductors. (5) Annual interest
on value of additional conductors. (6) Sum of value
of total annual energy loss and the interest on pro-
114 ELECTRIC POWER CONDUCTORS
posed additional conductors. When selecting the
figures for the first column two values should be
assumed initially and all the other columns worked
out for them, in order to give an indication of the
range of values which is most convenient to work
with.
An abbreviation of this calculation is given under
Kapp's and Fender's modifications of Kelvin's law. ,
V. If after these conditions are satisfied, the carry-
ing capacity is insufficient, more copper must be
added.
DISTRIBUTION OF CURRENT
A certain current passing from the positive to the
negative system at the end of the line farthest from
the power station being assumed to cause a total
drop of V volts, the same total current taken from
from the line in n equal amounts at n equidistant
points along the line will produce a total drop of
(i+ ) volts. If n is infinite, that is, if the drain
n] 2
of current is uniform along the line, the drop will
y
be . If, however, n is not infinite, the drop will
2
be greater than by - - per cent, a quantity which is
quite small when n is considerable. It is therefore
usual to assume a uniform drain of current, a procedure
*
DETERMINATION OF SIZE OF CONDUCTORS 115
which is further justified by the continuous motion of
the load which causes it to act as if more distributed.
Such an assumption, however, is by no means
justifiable on interurban or trunk line railroads, as
in such cases the trains are usually far apart. This
case is treated separately below.
DISTRIBUTION OF COPPER
The drop of potential depends largely on how
the copper is distributed along the line. It is there-
fore important to secure the most economical dis-
tribution of copper which will give the required
drop. The auxiliary copper may be connected
to the contact conductor at such frequent inter-
vals that it virtually forms a part of it; it may,
on the other hand, be connected at one end only,
or it may be connected at such distances as not to
be covered by either of the above cases. Each of
these schemes requires separate consideration, a
general method of treatment being given for each,
which covers the addition of copper to either the
positive or negative system, as the case may require.
AUXILIARY COPPER FREQUENTLY CONNECTED
The diagram in Fig. 13 shows the most economical
way of distributing the feeder metal; the formulas for
circular mils, volume of copper, watts lost and
116
ELECTRIC POWER CONDUCTORS
potential drop are also given.* The following symbols
are used in both Figs. 13 and 14.
C.M. =Area in Circular mils, where one C.M. is the
area of a circle of Viooo inch diameter.
FIG. 13.
C.M. -Ft. = Volume in Circular mil-feet, where one
C.M. -Ft. is the volume of a cylinder of one c.m. area
and one foot long. A volume of copper in c.m. -ft.
divided by any number of c.m. gives the number
of feet of cable of that area required to make up the
given volume of copper.
FIG. 14.
r=the resistance of a c.m.-ft. of copper, measured
along its length, at about 60 F.
r = 10.2 for copper of 100% cond
10.3 for copper of 99% cond.
10.4 for copper of 98% cond.
10.5 for copper of 97% cond.
* See Appendix 4.
*
DETERMINATION OF SIZE OF CONDUCTORS 117
If the conductors are partly of iron, as with a
third rail, it is usual to reduce the area of iron to its
equivalent area of copper.
F=drop of potential from the station bus to the
end of the line in either the positive or negative
conductors, as the case may be.
A = total current delivered from the station bus
to the section under consideration.
L= length of the section, feet.
00= distance (feet) of any point from the end of
the line farthest from the station.
V
Drop = -= x/* 3 ,
\/L 3
Watts lost =
5
It is, of course, impossible to exactly realize the
most economical distribution in practice, so that
a series of steps, as shown in the second diagram,
should be arranged so as to approximate as closely
as possible to the theoretical curve. It should be
remembered that the curve of most economical dis-
118 ELECTRIC POWER CONDUCTORS
tribution shows the total feeder metal, including
the contact conductors.
The approximation to the most economical dis-
tribution is calculated in the following way. Refer-
ring to Fig. 14:
X\ = distance ED, and Y\ =c.m. 01 copper in ED.
X 2 = distance EC, and Y 2 =c.m. of copper in DC.
X% ==-- distance EB, and Y% =c.m. of copper in CB.
X* = distance EA, and F 4 =c.m. of copper in BA.
Drop in DE =k-
" AB=k'
4 ^ v 3
Y*
Total watts lost -
DETERMINATION OF SIZE OF CONDUCTORS 119
The drop given by the above formula is from the
far end of the line. The drop from the station end
may be obtained by subracting this value from V.
AUXILIARY COPPER CONNECTED AT END
The auxiliary feeder, in this case being merely a
uniform conductor with the same current along its
entire length, may be treated by Ohm's law in its
simplest form. Auxiliary conductors of this sort are
useful in connection with grounded retjrns in which
it is desired to minimize the drop. Two or more
insulated conductors, connected to the line at various
points will each take off its proportion of the current
without making the entire current accumulate near
the station, as would be the case with a single con-
nection direct from the bus. This gives rise to a series
of rises and falls of potential along the line, but there
will be no serious drop in the grounded conductors,
irrespective of what the drop may be in the insulated
feeders connected thereto.
FEEDERS INFREQUENTLY CONNECTED
This condition occurs where a feeder cable runs
parallel to the line and is tapped in at intervals
through circuit breakers or switches. The expense
of the breakers renders it necessary to have as few
such connections as possible. Fig. 15 shows an
120
ELECTRIC POWER CONDUCTORS
example of such a system, comprising four conduc-
tors, some of which may be contact conductors and
others, auxiliary feeders. Fig. 16 shows this scheme
Positive Contact Conductors
C D
c
D
c
D
A | E
^Generator LoadQ)
H |G
3
Generator^
H
Ti#ck Kails
FIG. 15.
in diagrammatic form with corresponding points
indicated by identical letters.
The resistance of this system may be calculated in
two ways, the first of which is simpler, but the second
more complete, as it gives the point of maximum
resistance.
DETERMINATION OF SIZE OF CONDUCTORS 121
First Method. Referring to Figs. 15 and 16, the
resistances of the various sections are designated as
follows :
Points.
Conductors.
Resistance.
Ej to A
All tracks
C
E 2 to B
All tracks
d
CtoD
All feeders but one
e
A to L
One track
a
B to L
One track
b
F l to G
All tracks*
m
F 2 to G
All tracks*
n
* Including negative feeders.
Resistance from load to both substations equals
AF-
B
where
A + F-
A =
(Derivation of above formula given in Appendix IV.)
Second Method. Where the maximum resistance is
required, the following formulas may be used. The
resistances and lengths are as follows:
R = resistance of third rail per 1000 ft.;
r = resistance of all track rails per 1000 ft.
/ = length A B in thousands of feet;
x = distance from A to point of maximum resistance,
thousands of feet;
122 ELECTRIC POWER CONDUCTORS
c= resistance from EI to A, all tracks;
d = resistance from E 2 to B, all tracks;
k = resistance from F L to H , all tracks ;
y = resistance from F% to I, all tracks ;
, say;
*">+'
Then
^ ,^
Resistance
and resistance is a maximum where
(Derivation of above formula given in Appendix
IV.)
Third Method. Unlike the two previous methods,
this is intended to be used where there is only one
substation feeding the section, as shown in Fig. 17.
I
DETERMINATION OF SIZE OF CONDUCTORS 123
Let R = resistance in ohms per thousand feet of
single contact conductor;
r = resistance in ohms per thousand feet of
combined track rails;
e = multiple resistance of all conductors between
A and B except the loaded one;
M+*'
Auxiliary Feeders
Contact Conductors
h -x
L^ /,,..._ *-
i
(Only Positives Shown)
FIG. 17.
D = resistance from b to c. all conductors in
multiple ;
E = r X length be in thousands of feet;
x = distance from b to point of maximum re-
sistance from substation;
^4
= 28'
The resistance from substation to ooint of maxi-
mum resistance from substation,
124
ELECTRIC POWER CONDUCTORS
This may be applied to the section be as well as to
the section ab.
Fourth Method. The circuit, shown in Fig. 18, is
that of a feeder system in which both positive and
negative feeders are infrequently cross-bonded.
.Substation
li
FIG. 1 8.
O Substation
The resistances are designated by letters on the
diagram and by the following:
DETERMINATION OF SIZE OF CONDUCTORS 125
The total resistance from the load to both sub-
stations in multiple is given by the following expres-
sion:
DB
(The derivation of the above formula is given in
Appendix IV.)
If there are several trains between the two sub-
stations, the maximum drop in the section will be the
sum of the drops computed for each train as if it
were the only one on the line, and the trains should
be distributed so as to give the worst condition
that would arise in practice.
MISCELLANEOUS FORMULAE
The potential drop in any uniform conductor in
which the current varies along its length, is given by
Volts = ohms per ft. X area of current curve in
ampere-feet.
The \vatts lost in any conductor along which there
is a uniform drain of current are given by
Watts lost = amperes per ft. X area of drop curve
in volt-feet.
If a curve of potential drop in any feeder system
be plotted for one load, the drop curve for any other
126
ELECTRIC POWER CONDUCTORS
load similarly distributed may be derived from it by
merely changing the ordinates in the ratio of the two
loads in question.
VALUE OF CURRENT USED IN CALCULATIONS
Purpose.
Current.
Electrolysis.
Depends upon local ordinances.
Car starting
Average current during half minute of maximum load.
Car lighting?
If cars are closely spaced, the R.M.S. current during
hour of maximum load. If cart are infrequent, it
is better to use various unit train loads and esti-
mate whether their effect upon the candle-power
is excessive, when concentrated at various points.
Copper economy.. -
R.M.S. current of whole year. If the trains are too
infrequent to permit the assumption of uniform
current drain, the best approximation is to assume
the R.M.S. current for the year, concentrated at
the point of average resistance.
Heating of cables..
R.M.S. current taken over several periods of maxi-
mum load.
Let ii, 1*2, fc',3, etc., be the currents flowing for t\, 1%,
t 3 , etc., minutes respectively, and let -T be the minutes
in the total interval considered. Then the R.M.S. cur-
rent =
UNIVERSITY
( --
DETERMINATION OF SIZE OF CONDUCTORS 127
COST OF ENERGY
The cost of producing energy may be divided into
two items.
Fixed Charges, which are independent of varia-
tions of output, and
Operating Expenses, which are practically propor-
tional to the output. Fuel, water, and oil are
included in this item.
In feeder calculations only the operating expenses
should be used because the fixed charges exist inde-
pendent of any saving in line losses.
4. NEGATIVE BOOSTER CALCULATIONS
IN railway feeder work it is usual to assume the
load to be uniformly distributed along the line, so
that going towards the power station the current
+ 550, 25 500
ifl,
1 4-10 +20
J J
R
FIG. 19.
in the negative feeders, including the return rails,
uniformly increases. The current flowing in the feed-
ers to the bus bars will then be represented by a
straight line diagram, provided that all the feeders
are connected together so as to virtually form one
conductor. When, however, a booster cable is con-
nected to the negative feeders, as shown in Fig. 19,
128
ELECTRIC POWER CONDUCTORS
the booster cable being insulated from the other
feeders, except at one point, the current will be
drawn from the line into the booster cables and the
current diagram will take one of the forms shown in
FIG. 20.
Fig. 20, these four forms, however, being treated in
exactly the same way in the voltage calculations de-
scribed below. Case I shows a booster which entirely
neutralizes the drop in the booster cables and re-
.duces the point of connection, /, to the same po-
tential as the bus bar. In this case current is drawn
DETERMINATION OF SIZE OF CONDUCTORS 129
into the booster tables from both sides of the point of
connection, the current dividing at a point /, from
which the resistance to the bus equals the resistance
to the point /. In Case II, the booster only par-
tially neutralizes the drop in its cables, but draws
current from both sides of the point of connec-
tion. Case III shows a booster drawing current only
from beyond the point of connection, the whole of the
current on the other side returning to the bus by the
line feeders. In Case IV, the booster draws only part
of the current from beyond the point of connection,
the remainder returning to the bus through the
line feeders with the current from between the
station and that point. A fifth case might be added
to these, which is only useful when the permissible
drop is very small. In this case the point of con-
nection, 7, is maintained at a lower potential than
the negative bus itself.
The relation between line drop, booster E.M.F.
and current may be found either by calculation or
graphically. Considering the former method first,
let
a = amperes entering negative feeder system per foot
of line;
r = resistance of negative feeder system per foot ;
i = total amperes entering negative feeder system ;
io = total amperes taken off by booster ;
l=HI = = distance from H to the point at which
130 ELECTRIC POWER CONDUCTORS
the current in the negative feeders is zero. (Fig.
21);
t^'JD.
The volts drop in the various sections of the negative
feeder is
From Htol: D
/to/: D l -
JtoD: D 2
FIG. 21.
These drops can be read directly from a curve
plotted from the equation
The drop to the point / is (D Di) and the total
drop is (D-Di + D 2 ).
The booster voltage is
where R is the resistance of the booster cable.
In case /o < |/ the current curve takes the form
shown in Case IV, Fig. 20.
*
DETERMINATION OF SIZE OF CONDUCTORS 131
In this case there is no point in the negative feeders
at which the current is zero. Mathematically, how-
ever, we still define the distance HI by the formula
e- . The length /i is then negative, but since the
lengths are squared in the above formula for drop,
these formulas also hold in this case.
N
FIG. 22.
The voltage curves shown in Figs. 20 and 22 are
composed of parts of a general voltage curve, the
equation of which is
where
V= voltage rise from where the current is zero, to
a point D feet away.
a = current increment in amperes per foot, i.e.,
total load on section divided by length of section.
r= resistance of return conductors per foot of
line.
Therefore, if one such curve be drawn with its
corresponding current diagram over it, as shown in
Fig. 23, the voltage curve for any of the schemes
shown in Fig. 20 may be traced from it.
132
ELECTRIC POWER CONDUCTORS
Thus to obtain the voltage curve shown in Fig. 22,
set off HD and DP on tracing paper to the same
scale as the general voltage curve, and select any
point ] for the booster feed point. Put P over
the point on the general curve, make HD parallel
to XX, and trace the voltage curve to M, where
it intersects the perpendicular through /. Then,
still keeping HD parallel to XX, run M along the
general voltage curve until H lies on that curve.
The intersection of OF and HD is the point 7 where
the current divides. This, having been marked, avoid
shifting the papers and trace the remainder of the
voltage curve, i.e., HNM.
Knowing I, draw the current diagrams HGI and
JKI (Fig. 21). The current in the booster and its
cable, will be the sum of JK and JC. The booster
voltage will be the sum of the drop in the booster
cables, and (DP-MP), Fig. 22. This should be
tried for various positions of /, and the best selected.
DETERMINATION OF SIZE OF CONDUCTORS 133
5. ALTERNATING-CURRENT TRANSMISSION LINE
CALCULATIONS *
(From an article by H. Fender, also published in part in the Electrical
World.}
Let E= pressure between adjacent wires at receiv-
ing end in kilovolts (thousands of volts) ;
V = pressure between adjacent wires at the gen-
erating end in kilovolts (thousands of
volts) ;
W = power delivered in megawatts (thousands
of kilowatts) ;
k= power factor of the load expressed as a
decimal fraction;
/ = tangent corresponding to k=cosa (Table
Hi);
^o= power factor at the generating end, ex-
pressed as a decimal fraction;
L =in case of a three-phase system, the length
of each wire in miles; in the case of a
single-phase system, the total length of
both wires in miles;
r = resistance of each conductor per mile;
x =x 1 +x 2 = reactance of each conductor per
mile, where %\ is the reactance per mile
of a number oooo B. and S. wire (Table I),
and #2 the difference in the reactance
per mile of a No. oooo wire and that of
the wire actually used (Table II) ;
* See Appendix IV for derivation of formulae.
134
ELECTRIC POWER CONDUCTORS
Q = power lost in transmission as a fraction of
the delivered power;
P = pressure drop as a fraction of the delivered
pressure.
(kE) 2
R = = equivalent resistance of receiver
per mile of line*
TABLE I
REACTANCE PER MILE OF A No. oooo B.
S.
Distance Apart
of Wires in
Feet.
15 Cycles.
25 Cycles.
40 Cycles.
60 Cycles.
125 Cycles
I
2
3
0.128
0.149
0.161
0.213
0.248
0.268
0.340
0.396
0.429
0.510
0-594
0.644
1.063
1.238
I-34I
4
5
6
0.170
o. 176
0.182
0.283
0.294
0.303
0.452
0.470
0.485
0.678
0.705
0.728
!-4i3
1.470
1.516
7
8
9
0.187
o. 191
0.104
0.311
0.318
0.324
0.498
0.508
0.518
0.746
0.763
o-777
i-555
1.589
1.618
10
15
20
0.197
0.210
0.218
0.329
o-35^
0.364
0.526
o-559
0.582
0.790
0.839
0.874
1.645
1.748
1.820
25
0.225
0-375
0.601
0.901
1.877
Case I. Given the delivered pressure E, the
power delivered W, the power factor of the load k,
DETERMINATION OF SIZE OF CONDUCTORS 135
the length of the line L, the frequency, the size, and
spacing of the wires. The following are exact expres-
sions * for the quantities to be determined.
Y
Powerless Q=.
/v
Pressure drop P = k V(i+Q) 2 + T 2 - 1 .
Power factor at generating end k = j^k.
Case II. Given the delivered pressure E, the
power delivered W, the power factor of the load k,
the length of the line L, the frequency and the allow-
able power loss Q. The size wire to use is determined
by the following exact formula:
Resistance of each wire per mile, r=RQ,
the corresponding size of wire being given in Table II.
The pressure drop and power factor at the generat-
ing end can then be determined by the formulae
given in Case I.
Case III. Given the delivered pressure E, the
power delivered W, the power factor of the load k,
the length of the line L, the frequency and spacing
of the wires, and the allowable pressure drop P.
An exact determination of the size of wire to use
in this case cannot be made directly, since this would
* These formulae can also be used to determine the overall efficiency,
regulation and power factor of any number of circuits in series (e.g. line and
transformers) if we let r and x represent the sum of the component resist-
ances and reactances respectively and R the total equivalent resistance of
the receiver.
136 ELECTRIC POWER CONDUCTORS
require the solution of a logarithmic equation.
However, since the reactance of commercial sizes
of wire for a given frequency and spacing differ but
slightly from one another, a close approximation
to the exact size of wire to use can be obtained by
assuming that the reactance, for a given frequency
and spacing, for any size between 1,000,000 circular
mils and a No. 6 B. and S. wire is equal to that of
a No. oooo wire. It will be found that except when
the line reactance is large compared to the line
resistance, the error due to this assumption will
not cause a change in the size of wire; that is, the
error will be less than* half the percentage difference
(26%) between successive sizes on the B. and S.
gauge. On the other hand a large error in the
approximate formula for the size of wire, indicates
immediately that the drop is due chiefly to the
line reactance, and that by allowing a very small
increase in the permissible drop, or by employing
two separate circuits instead of one, a very consid-
erable saving in copper can be effected.
Put
where %\ is the reactance of a No. oooo wire. Then to
a close approximation, resistance of each wire per
mile
r\ =
DETERMINATION OF SIZE OF CONDUCTORS 137
the corresponding size of wire being given in Table II,
as well as the difference x 2 between the reactance
corresponding to this size and the reactance of a
No. oooo wire.
TABLE II
RESISTANCE* PER MILE OF COPPER AND ALUMINUM
CABLES AND REACTANCE INCREMENT x 2 .
Size C.M.
and
B. & S.
Ohms per Mile at 20 C.
Difference in Reactance per Mile of any Size
Wire and that of No. oooo B. & S. Wire = * 2 .t
Copper.
Aluminum.
15
Cycles.
25
Cycles.
40
Cycles.
60
Cycles.
125
Cycles.
1,000,000
0.0566
0.0894
0.024
-0.039
0.063
-0.094
-0.196
900,000
0.0629
0.0993
0.022
-0.037
-0.059
-0.088
-0.183
800,000
0.0707
0.1118
O.O2O
-0.034
-0.054
-0.081
-0.168
700,000
0.0808
0.1278
O.OlS
-0.030
0.048
-0.073
0.152
6co,ooo
0.0943
0.1490
0.016
0.026
0.042
0.063
0.132
500,000
0.1131
0.1788
0.013
O.022
-0.035
0.052
0.109
450,000
0.1257
0.1987
o.on
O.OI9
0.031
0.046
-0.095
400,000
0.1414
0.224
0.005
O.OO9
0.014
O.O2I
0.044
350,000
0.1616
- 2 55
0.008
0.013
O.O20
0.031
o . 064
300,000
0.1886
0.298
-0.005
0.009
0.014
0.021
0.044
250,000
0.226
o.358
-0.003
O.OO4
O.007
o.oio
O.O2I
oooo
0.267
0.423
ooo
0-337
0-533
+ 0.004
+ O.OO6
+ O.OO9
+ 0.014
+ O.O29
00
0.425
0.672
+ 0.007
+ O.OI2
+ O.OI9
+0.028
+ 0.059
o
o-53 6
0.848
+ O.OII
+ 0.018
+ 0.028
+ 0.042
+ 0.088
I
0.676
i. 068
+ 0.014
+ 0.023
+ 0.038
+ 0.056
+ o 117
2
0.852
1-347
+0.109
+ 0.029
+ 0.047
+ 0.070
+ 0.147
4
1-355
2.14
+ 0.025
+ 0.041
+ 0.066
+ 0.098
+ O.2O5
6
2-15
3-4i
+0.032
+ 0.053
+ 0.084
+0.127
+ 0.264
* Stranded wire, copper 98%, aluminum 62% conductivity, resistance increased
i% on account of stranding, temperature coefficient 0.42% per degree C.
t The total reactance of a wire for any spacing and frequency is x = xi + xz where
xi is the reactance of a No. oooo wire under the same conditions.
138 ELECTRIC POWER CONDUCTORS
By substituting for T\ in the above formula
the value T = T\+^- the error in the value of r
K
caused by neglecting x 2 can be readily found. As
stated above, in any practical case this will, as a
rule, be negligible, but should the error in the par-
ticular problem in hand be sufficient to give a new
value for r, for which the corresponding value for
%2 differs appreciably from the first value found, r
should be again calculated, using this second value
for x 2 , and so on, until the difference in x 2 for two
successive values of r, as thus determined, becomes
negligible. In this w.ay an exact determination of
the size corresponding to the given drop can be
readily made, although, as stated above, a large
error in the first approximation immediately indi-
cates that the feasibility of increasing the permis-
sible drop, or of dividing the circuit, should be
investigated. If the formula gives a negative value
of r, it is impossible, with any amount of copper, to
transmit the assumed amount of power with the
drop and inductance assumed.
Case IV. Given the pressure at the generating
end V, the power delivered W, the power factor of
the load k, the length of the line L, the frequency
the size and spacing of the wires.
In this case R, the equivalent resistance of the
receiver per mile of line, can be expressed in terms
of the pressure at the generating end V.
*
DETERMINATION OF SIZE OF CONDUCTORS 139
Put
Then
M
2LW
M 2
Using this value for R, the exact formulae given under
Case I become immediately applicable.
TABLE III
VALUES OF /=tan CORRESPONDING TO =cos a
k.
o.oo.
O.OI.
O.O2.
O.O3.
O.O4.
0.05.
O.o6.
0.07.
0.08.
0.09.
o-5
0.6
0.7
1.732
1-333
i. 020
1.687
1.299
0.992
1.643
1.265
0.964
I. 600
1-233
0.936
1-559
I. 201
0.909
I.5I9
1.169
0.882
1.479
I.I38
0.855
1.442
1.108
0.829
1.404
1.078
0.802
1.368
1.049
0.776
0.8
0.9
0.750
0.489
0.724
0.456
0.698
O.426
0.672
0-395
0.646
0.363
0.62O
0.329
0-593
0.292
0.567
0.251
0.540
0.203
0.512
0.143
Effect of Line Capacity. A complete and accurate
treatment of transmission lines, taking into account
the capacity and leakage, is given below. In most
practical cases, however, the leakage is negligible and
the effect of line capacity can be determined with
sufficient accuracy by assuming that this effect is
the same as would be produced by two condensers,
each having a capacity equal to half that of the
line, shunted across the line at the receiving and
sending ends respectively. The effect of the con-
denser at the receiving end is to increase both the
140
ELECTRIC POWER CONDUCTORS
equivalent resistance of the load and also the load
power factor; the condenser at the sending end
has no effect on the power loss and line drop, but
merely increases the resultant power factor at the
generating end.
TABLE IV
SIZE AND WEIGHT OF STRANDED COPPER AND ALUMI-
NUM WIRES
Size B. & S.
Circ. Mils.
Diameter, Ins.
Lbs. per Mile.*
Copper.
Aluminum.
1,000,000
1.152
16,140
4,870
9OO,000
1.092
14,53
4,380
800,000
' I -3S
12,910
3,890
700,000
0.963
11,300
3,410
600,000
0.891
9,690
2,920
500,000
0.819
8,070
2,43
450,000
0.770
7,260
2,190
400,000
0.728
6,460
i,947
350,000
0.679
5^50
!,73
300,000
0.630
4,840
1,460
250,000
0.590
4,040
1,217
oooo
211,600
-53
3,420
1,030
000 ,
167,800
0.470
2,710
817
oo
133,100
0.420
2,150
648
o
105,500
0-375
i73
5i3
i
83,690
0-330
I 35 I
407
2
66,370
o. 291
1,071
3 2 3
4
41,740
0.231
674
203
6
26,250
0.183
420
128
* Increased i % over weight of solid wire on account of stranding.
DETERMINATION OF SIZE OF CONDUCTORS 141
In addition to the above symbols let
b = capacity susceptance * per mile of two parallel
wires for a frequency of one cycle per second
(Table V) ;
B =nbL for a three-phase line or - - for a single-phase
4
line, where n is the number of cycles per second,
and L as defined above is the length in miles of
each wire for a three-phase line or the length of
both wires for a single-phase line.
Then the equivalent power factor at the receiving
end is the cosine k' corresponding to the tangent t'
where
BE 2
t'=t-
W
The above formulae for power loss and pressure
drop (Case I) are then immediately applicable, sub-
stituting for k and t the values k f and t' ; the formula
for predetermining the size of wire in terms of the
pressure drop (Case III) may also be applied, assum-
ing the capacity susceptance equal to that of a
No. oooo wire, an assumption which will introduce
but a slight error, since the capacity susceptance
varies but slightly with the size of wire. The power
factor formula ko = - k', given under Case I, is
* b='LTzC where C is the capacity per mile in farads of the condenser
found by each pair of wires.
142
ELECTRIC POWER CONDUCTORS
the power factor at the generating end excluding the
second condenser, the actual power factor at the
generator is the cosine k' Q corresponding to t' where
t o = fo ~~
o'
where Wo = (i+Q)W, the total power supplied at the
generating end.
TABLE V
CAPACITY SUSCEPTANCE PER MILE OF TWO PARALLEL
STRANDED WIRES FOR FREQUENCY OF ONE CYCLE
PER SECOND
Size C.M.
Distance Apart of Wires in Feet.
ana J. & ^>.
i.
2.
3-
6.
10.
1,000,000
500,000
250,000
9-3XIQ- 8
8. 3 Xio- 8
7.6Xio~ 8
7-5Xio- 8
6. 9 Xio- 8
6.4Xio~ 8
6.8Xio- 8
6. 3 Xio- 8
5-SXio- 8
5.8Xio~ 8
5.4Xio 8 -
S.iXio- 8
5-3Xio- 8
4.gXio~ 8
4.yXio~ 8
0000
I
6
7-4Xio- 8
6.6Xio~ 8
5-8Xio- 8
6.2Xio- 8
5-7Xio- 8
5.oXio- 8
5-7Xio- 8
5.2Xio- 8
4-yXio- 8
5.oXio~ 8
4-6XIQ- 8
4.2Xio- 8
4.6Xio~ 8
4-3Xio- 8
3-9Xio- 8
NOTE. The charging current per mile of sine.le-ph.ase line (2 miles of wire^ is
equal to io 3 XbnE; for a three-phase line the charging current per wire per mile of
line (3 miles of wire) is equal to 1.16 X io 3 nbE, where n is the cycles per second, b
the capacity susceptance given in the table, and E the kilovolts between wires.
A. C. Trolley. The resistance and reactance of
various combinations of overhead trolleys and zoo-lb.
return rails are given in the Table VI. This table is
based on extended tests made by A. W. Copley on the
New York, New Haven and Hartford Railroad and
DETERMINATION OF SIZE OF CONDUCTORS 143
other single-phase roads, the results of which were
published in the Proceedings of the American Insti-
tute of Electrical Engineers for December, 1908.
Unfortunately there is no reliable data on rails of
smaller section, but as the greater part of the resist-
ance is in the trolley, and only a small percentage
of the total reactance is due to the magnetic field in
the rail, the values given for the combined resistance
and reactance respectively may also be used with
but slight error in case the rail is of smaller size. It
should be noted that the reactance for the three sizes
of wire given are constant to within 5% for any
height from 15 to 30 feet above the track.
The figures showing the division of current between
the track and the earth refer to intermediate por-
tions of long sections (over three miles) ; a greater
portion of the current flows in the track near the load
and the power house. It will be noted that if we let
p f be the percentage current in each trolley and p"
the percentage current in each rail, and the respective
resistances r' and r n ', the total resistance of any com-
bination of trolleys and rails, as measured by Mr.
Copley, is approximately p r r'+p"r"\ similarly the
total reactance is p'x' + p"x", where x f and x" are the
reactances of a single trolley and rail respectively ;
using these formulae, a closely approximate value for
the equivalent resistance and reactance for any other
combination of trolleys and rails for any division of
current between the rails and the earth can be ob-
144
ELECTRIC POWER CONDUCTORS
TABLE VI
RESISTANCE AND REACTANCE OF SINGLE-PHASE TROLLEY
WITH loo-LB. RAIL-RETURN
Percent-
Resistance Ohms per Mile.
No. of
Tracks.
No. of
Trolley
Wires.
No. of
Return
Rails.
age of
Current
Return-
ing this
oooo Trolley
ooo Trolley
Rail.
25 Cycles.
15 Cycles.
25 Cycles.
12 Cycles.
i
..
0.26*
0.26
0-33
-33
I
100
0.16*
0.13
0.16
0.13
I
i
25
0.30
0.29
o-37
0.36
I
Track i
2
40*
0.29*
0.28*
0.36
o-35
2
" 2
4
58*.
0-155*
0.15*
0.20
0.19
4
" 4
8
75*
0.086*
0.082*
O.II
O.IO
Resistance Ohms
Reactance Ohms
Percent-
per Mile.
per Mile.
No. of
Tracks.
No. of
Trolley
Wires.
No. of
Return
Rails.
age of
Current
Return-
ing this
Rail.
oo Trolley.
No. oooo, No. ooo or
No. oo Trolley.
25 Cycles.
12 Cycles.
25 Cycles.
12 Cycles.
I
..
...
0.42
0.42
0.38
0.23
I
100
0.16
0.13
0.44
0.26
I
I
25
0.46
0-45
0.49
0.30
I
Track i
2
40*
0-45
0.44
0.47*
0.282*
2
" 2
4
58*
0.24
0.23
0.269*
0.161*
4
" 4
8
75* '
0.13
0.12
0.168*
O. IOI*
NOTE. The figures marked thus (*) are taken directly from Mr. Copley's paper;
the others are derived from these. At the point where the current enters the
rail Mr. Copley found that 70% of the current starts toward the power house on
a singe track road and similarly 87% on a four track road, in each case the rail
currents falling to the values given in the table in a distance of about three miles
and from that point on remaining practically constant until near the power house.
DETERMINATION OF SIZE OF CONDUCTORS 145
tained. In case of a catenary suspension a certain
percentage of the overhead current is carried by the
messenger cable, but on account of the high effective
resistance of a steel cable to alternating currents, this
current will be quite small. (In a T V messenger
cable carrying a No. oooo wire Mr. Copley gives the
messenger current as but 3.5% of the total.)
To determine the power loss, pressure drop, etc.,
for a single-phase trolley system, the formulae given
above under Case I are directly applicable, putting L
equal to the distance in miles of the load from the
power house (or substation) and r and x equal re-
spectively to the combined resistance and reactance
of trolley and track per mile, as given in Table VI.
Similarly, the proper size of trolley for any given set
of conditions can be determined by the formulae
given under Case III, taking from Table VI the react-
ance per mile (which is constant for the three sizes
of trolley given and likely to be used in good practice),
and selecting the size of trolleys from Table VI corre-
sponding to the value of the resistance per mile r it
given by the formula
146 ELECTRIC POWER CONDUCTORS
NUMERICAL EXAMPLES
Case I. A load of 5000 kilowatts at 80% factor
is to be delivered at 40,000 volts over a three-phase
line of No. 2 B. and S. copper wire 30 miles long,
frequency 25 cycles per second, wires spaced 4 feet
apart. To find the power loss, pressure drop, and
power factor at generating end we have
=40;
=3;
r=o.8
#=0.283 + 0.029 =0.312
o
Then
08^2
Power loss Q = =0.125,
0.03
*
DETERMINATION OF SIZE OF CONDUCTORS 147
Pressure drop P =o.8v (i. 125)2 + (-796) 2 I =0.102.
Generator power factor
<,= + 0.8=0.817.
1. 102
Case II. A load of 5000 kilowatts at 80% power
factor is to be delivered at 40,000 volts over a three-
phase line of copper wire 30 miles long, allowable
power loss 12.5%. To find the size wire to use, we
have
= 40;
=3;
2 = 0.125;
^(0^x40)*
30X5
Then, using the formula r = RQ,
Resistance per mile r = 0.125 X 6. 83 =0.854,
whence from Table II we find that the proper size
is No. 2 B. and S.
Case III. A load of 5000 kilowatts at 80% power
factor is to be delivered at 40,000 volts over a three-
phase line of copper wire, 30 miles long, frequency
148 ELECTRIC POWER CONDUCTORS
25 cycles per second, wires spaced 4 feet apart, allow-
able pressure drop 10.2%. To find the size wire to use
we have
= 40;
P = o.io2 ;
xi -0.283;
(0.8X4Q)',,,
30X5
71=0.75+^^-0.791
0.53
Then
Resistance per mile
- i = 0.880,
whence from Table II we find the nearest size wire
is No. 2 B. and S. The value of x 2 corresponding to
TI =0.880 is 0.030, which makes ^ = 0.796 and gives
0.854 as the corresponding value for r, showing that
the error in the first approximation for r is only 3%.
The above example may also be used to illustrate
* *
DETERMINATION OF SIZE OF CONDUCTORS 149
an extreme case, in which the first approximation
for r may be entirely erroneous, but by successive
applications of the above formula a correct solution
can be obtained.
Keeping the other conditions the same, suppose we
change the frequency to 125 cycles per second. Then
#1 = 1.413,
First approximation
ri - 6.83 >- (-957) 2 - i -0.060,
which shows that it is impossible to deliver power
under the conditions stated over a line having a
reactance as great as that of a No. oooo wire.
As a second approximation assume a reactance
equal to that of a 500,000 c.m. wire. The resistance
per mile then works out 0.041 ohm, which is again
too small a value, because the reactance correspond-
ing to a wire having this resistance is less than that
of a 500,000 c.m. wire.
As a third approximation assume a reactance equal
to that of a 700,000 c.m. wire. The resistance per
mile then works out 0.079, the reactance of which is
about i% less than that of the 700,000 c.m. assumed.
150 ELECTRIC POWER CONDUCTORS
The nearest commercial size of wire corresponding to
a drop of 10.2% is 700,000 circ. mil.
As a matter of fact, however, the drop for any size
between a No. oooo wire and a 1,000,000 c.m. wire
would be substantially the same, as will be readily
seen by calculating the drop for these two sizes by
the exact formula of Case I, which gives a drop of
9.6% for a 1,000,000 c.m. wire and 13.0% for a
No. oooo wire, as against the 10.2% specified. There-
fore, by increasing the drop to 13.0%, say, a saving
of 70% in copper can be effected. (Were the drops
proportional to the resistance the saving in the copper
for the same increase in drop would be only 21.5%.)
Again, the use of two circuits of No. 2 wire each
would give a drop of but 9.5%, and would effect a
saving of 81.0% in copper.
Case IV. Take the example given under Case I,
but assume the pressure at the generator 44,080 volts,
the receiver pressure E being unknown. Then
2 x 3 X 5
(0.8)2(0.852 +0.312 )
-5^5-
whence
R =3-45[ I + ^i -0.044] =6.83,
which agrees with the value found in Case I. The
power loss, pressure drop (as a fraction of the de-
DETERMINATION OF SIZE OF CONDUCTORS 151
livered pressure), and power factor at generating end
then work out the same as in Case I. The pressure
drop as a fraction of the pressure at the generating
end is
P 0.102
= ---- = 0.0926.
1+P 1. 102
Effect of Capacity. Take the example given under
Case I. From Table 5
whence B = 25 X 30 X 5.0 X io~ 8 = 3 .8 X io" 5 ,
3 .8Xio- 5 X(4o) 2
and '=0.75-- - = 0.738.
'=0.805; (Table III.)
R _ (0.805 X4Q) 2
30X5
Then
Power loss Q~-r - = 0.123,
6.91
Pressure drop P = 0.805^(1. 123)2 + (0.783)2 i =0.102
o = -~X 0.805 =0.821;
1.090
*o= 0.683 (Table III);
5.02
Generator power factor '0 = 0.831 (Table III.)
152 ELECTRIC POWER CONDUCTORS
A. C. Trolley. 2000 kilowatts are to be supplied
to a locomotive at 90% power factor, and 10,000
volts at a distance of twenty miles from the power
house (or substation) ; No. oooo trolley, return cir-
cuit two 100 Ib. running rails, frequency 25 cycles.
To find the power loss, pressure drop and power
factor at power house, we have, assuming the divi-
sion of current between rails and earth, as given in
Table VI,
= 20
k = o.g
= 0.489
r = 0.29
# = 0.47
20X2
T = 0.489+ = 0.718
Then
Power loss Q= = 0.141,
2.05
Pressure drop P = o. 9 V'(i.i4 I ) 2 + (-7 l8 ) 2 ~ I =0.213.
Power factor at power house
1.141
1.213
DETERMINATION OF SIZE OF CONDUCTORS 153
Taking the reverse problem, suppose that we wish
to determine the size of trolley to use for a drop of
21.3% between power house and locomotive, the
other conditions being the same as given in the
preceding example. We then have by formula under
Case III,
^ 2 ) 2 - (0.718)2-1] =0.29,
whence, from Table IV, the proper size of trolley is
a No. oooo.
Transmission Line with Resistance, Reactance, Leak-
age, and Capacity. The following is a complete solu-
tion involving no approximations, The only assump-
tions made are that the resistance, reactance, leak-
age, and capacity are true constants and that
sufficient time has elapsed for steady conditions to
have become established.
Let E = volts between each wire and neutral at
generator end;
I = amperes per wire at generator end ;
cos $ = power factor at generator end ;
W = El cos (/> = total watts deliver edto line per
wire.
These same symbols with the subscript "o" refer
to the receiver.
r TT-S
Q E 2 cos
receiver;
= equivalent admittance of the
154 ELECTRIC POWER CONDUCTORS
r = resistance of each wire per unit length ;
x = reactance of each wire per unit length ;
z = vV 2 + x 2 = impedance of each wire per unit
length ;
T t X\
cos e =- = power factor of the line (sin =-] ;
z \ z /
g = leakage conductance between each wire and
neutral per unit length;
b= leakage susceptance * between each wire and
neutral per unit length ;
y = \/g% + b 2 = leakage admittance per unit length ;
cos 7) = = power factor of leakage circuit I sin >?=);
L = length of line in any unit.
Calculate the following quantities : J*
J
- and r =
2 2
log m = o.4343ayL cos /?;
sin ?
U =aY ',
*b=27ifC where/ is the frequency in cycles per second and C the
capacity between each wire and the neutral per unit length.
t Greek letters are used to represent angles in degrees. The logarithm is
to the base ten.
DETERMINATION OF SIZE OF CONDUCTORS 155
m , =
cos
tfo,
q= Vi + t/o 2 zU cos a ti .
2m
i-W
49
has the same sign as <7 .
D = p 2 + q 2 + 2pq cosd;
p 2 -q 2
rne > f) _ _
DQ
6 has the same sign as d. Then
Volts at generator end, E = DEo
Amperes at generator end, / =
Power factor at generator end, cos $ = cos (6 f)
Total watts delivered to line, W = EI cos
(End of H. Fender's article.)
Voltage Drop and Synchronous Apparatus. An
excessive ohmic drop in the transmission lines is
liable to cause hunting of rotary converters or
synchronous motors. The exact amount permissible
depends upon the design of the rotary converter,
those designed for normal A.C. starting requiring
less drop than those designed for D.C. starting. In
156 ELECTRIC POWER CONDUCTORS
the latter type of machine an ohmic drop of 20% is
generally permissible whether or not a simultaneous
reactive drop exists. Converters of the A.C. start-
ing type, do not, as a rule, operate satisfactorily if
the ohmic drop is so high.
6. ECONOMICAL SIZE OF CONDUCTORS. (Kelvin's
Law)
The total expenditure on a transmission system
is made up of the initial cost plus the annual expenses.
The most economical system to install for permanent use
is that in which the sum of these items is a minimum.
The annual expenses consist of maintenance, depre-
ciation, and power lost due to resistance.
It is usual to reduce the initial cost to a yearly
basis for purposes of comparison, this yearly basis
being the interest which must be paid for the use
of the money, or which is lost by withdrawing the
money from a profitable investment and putting it,
in feeder metal.
As a rule, it is necessary to work out the sum of
the expenses for various sizes of wires and select
that size which gives the minimum total cost.
When, however, the capital outlay is propor-
tional to the amount of copper in the system, the
following law, given by Lord Kelvin, is of use.
' The most economical area of conductor will be
that for which the annual interest on capital out-
lay equals the annual cost of energy wasted."
*
DETERMINATION OF SIZE OF CONDUCTORS 157
One side of this equation would be the interest,
depreciation, maintenance, and repairs; the other, the
cost of producing energy at the station bus, includ-
ing interest, depreciation, and operating expenses.
Kapp has made Kelvin's law of more universal
application by changing it to the following form:
" The most economical area of conductor is that
for which the annual cost of energy wasted is equal
to the annual interest on that portion of the capital
outlay which can be considered proportional to
the weight of metal used."
The simplest way of applying Kelvin's law is that
due to Dr. Fender. The most economical current
density per million circular mils is
A ^c
where L = increase in annual charges on transmis-
sion line resulting from increasing the weight of
feeders one ton (2000 Ibs.), and C = increase in
annual operating and capital charges on the power
station resulting from increasing the output one
kilowatt. A is a constant whose value is
i
2170^
Weight of conductors, Ibs. per cu.in.
Specific resistance, ohms per mil-foot'
For copper, A =380
Aluminum, A = 165
158 ELECTRIC POWER CONDUCTORS
Calculations of this kind are often rendered use-
less by the following circumstances:
1. The rate of interest on the capital outlay is
difficult to estimate exactly.
The discount of bonds depending on the value
below par at which they are sold cannot be pre-
dicted for the future.
2. The life of insulation is difficult to estimate.
3. The cost of copper, lead, and insulation con-
stantly fluctuates. It makes a material difference
in the depreciation whether the price of copper and
lead is assumed to rise or fall during the period it is
in use.
4. There is not always a market for power that
can be saved by additional feeder metal.
Owing to the inaccuracy of these premises, it is
advisable to make two calculations, using for one
the maximum possible value of L and the minimum
possible value of (7, and in the other the minimum
value of L and the maximum value of C.
The economical current density will then be
between the extremes thus obtained.
It is thus obvious that the size of conductors to
be used is more a matter of judgment than of mathe-
matics.
CHAPTER V
DETERMINATION OF SIZE FOR GIVEN STRESS
IN SPAN
ALGEBRAIC METHOD
(Abstracted by permission from article in Electrical World, N. Y. Jan. 12,
1907, by H. Fender, Ph.D.)
Formulae are closely approximate:*
a = coefficient of expansion of wire per degree
Fahrenheit ;
D = deflection of wire at center of span in feet, in
the direction of the resultant force at tem-
perature t;
* = length of span in feet ;
M - modulus of elasticity (pounds, square inches) ;
m = weight of wire per cubic inch in Ibs. ;
p = ratio of the resultant of weight of wire and sleet
and wind pressure to the weight of wire, at
temperature /;
Po = corresponding ratio at temperature t ;
T = tension at center of span in thousands of Ibs.
per sq.in. at temperature /;
* See Appendix V.
159
160 ELECTRIC POWER CONDUCTORS
TQ = tension at center of span in thousands of Ibs.
per sq.in. at temperature to]
K Pl -
K ~*
o
t and t described above under D, K, K , T, and
TO, and are in degrees Fahrenheit.
General Formulae for Points of Support on the same Level
D = o.ooi$mlK.
Copper wire : *
D =
Aluminum wire: f
-K 2 o) + 1965(70- T)].
Making numerical calculations, choose various val-
ues for T and plot the corresponding values of / in
the form of a curve, from which the value of the
tension for the temperature in question can be taken.
* For Copper for which 1*1 = 0.321, a = g.6Xio~ 6 , M=i2Xio.
f For Aluminum for which ^=0.0967, a=i2.8Xio- 8 , M =9X10'.
SIZE OF GIVEN STRESS IN SPAN 161
The value of K is obtained from this value of T and
used in the formula for D.
GRAPHICAL METHOD
Instead of the trial method above outlined, a
graphical method giving a direct answer was out-
lined by Dr. Fender in the Electrical World, Sept. 28,
1907.
The two charts, Figs. 24 and 25, are the essential
parts of this method. (See p. 172 for method of
constructing these charts.)
Calculation of Tension and Sag
Given: A span of length / and the points of sup-
port on the same level ; tension 7\ ; ratio of resultant
force to weight of wire, pi. To find the tension T
when the temperature rises / degrees and the ratio
of resultant force to weight of wire changes to p (for
example, sleet melts off).
1. On the line corresponding to / find the point 3
having the abscissa / on the temperature scale.
2. On the curve corresponding to p\ find the point
having the abscissa T\ and at this point lay off the
length of the ordinate of point 3, upward if / is posi-
tive or downward if t is negative.
3. Through the point 2 thus obtained draw a line
parallel to the line /.
4. The abscissa of the point 4 where this line cuts
162
ELECTRIC POWER CONDUCTORS
SIZE OF GIVEN STRESS IN SPAN
163
164
ELECTRIC POWER CONDUCTORS
the curve corresponding to p is the tension T at the
new temperature when the ratio of the resultant force
to weight of wire is p.
5. The abscissa of the point 5 where the horizontal
line through 4 cuts the parabolic curve corresponding
to / gives the corresponding deflection D at the center
of the span in feet.
Instead of actually drawing the straight line 2-4 a
pair of compasses may be used; i.e., lay off the dis-
tance 1-2, then open the compasses until the lower
FIG. 26.
point touches the straight line /; then keeping the
compasses vertical, slide the lower point along I until
the upper point intersects the curve corresponding
to p. If t is negative, i.e., if the temperature de-
creases, lay off 1-2 in the opposite direction.
The deflection under any conditions can also be
calculated from the formula
when T is known.
*
SIZE OF GIVEN STRESS IN SPAN 165
Calculation of p
Let a) = weight of wire in pounds per foot.
The weight of sleet (and hemp core, if any) in pounds
per foot of wire is
a)i =0.312 (d 2 i - d 2 ) + 0.3 2d 2 o,
where d is the diameter of the wire, and d\ the diame-
ter over sleet and do the diameter of the core, all in
inches.
The wind pressure in pounds per foot of wire is*
a>2 = 0.00021
I
where V is the actual wind velocity in miles per hour;
di=d in case of no sleet. The relation between indi-
cated wind velocity (as given by U. S. Weather
Reports) and actual velocity is as follows:
Indicated Velocity. Actual Velocity. 0.0002 iF 2 .
10 9.6 0.0194
20 17.8 0.0667
3 25.7 0.139
40 33-3 - 2 33
50 40.8 0.350
60 48.0 0.485
70 55.2 0.640
80 62.2 0.812
90 69.2 i.oi
IOO 76.2 1.22
* H. W. Buck, in Transactions International Electric Congress, 1904.
166 ELECTRIC POWER CONDUCTORS
The ratio p, when the wind is horizontal, is then
/ wA* /o> 2
= \/ I+ "~) + (-~
\\ O)/ \W
When the wind is acting vertically downward,
0)1-}- 0)2
p = i + .
0)
Calculation of Sag with Wind Blowing. In case
of no wind, or the wind blowing vertically downward,
the vertical sag 5 will be the same as the deflection
D. A horizontal wind t gives a horizontal component
to the resultant force, so that the vertical sag when
the wind is blowing horizontally is
D
Example: A No. oo stranded copper cable is to
be strung in still air at 70 F. between two points
on the same level 800 ft. apart, so that at a tem-
perature of o F., with a coating of sleet J in.
thick all around, and wind blowing horizontally
directly across the span at 65 miles an hour (actual
velocity), the tension in the cable will be 30,000 Ibs.
per sq.in. ; (i) at what tension must the cable be
strung, and (2) what will be the vertical sag at string-
*
SIZE OF GIVEN STRESS IN SPAN 167
ing temperature, i.e., 70, also (3) what will be the
sag at zero temperature when the cable is coated
with J in. of sleet and wind is blowing with a velocity
of 65 miles an hour, and (4) what will be the sag as
a temperature of 150 in the still air?
We have
to =0.406
wi =0.312(1. 418 -0.418 ) =0.574
2
W2 =0.00021 X&5 Xi.4iQ =1.26.
Therefore, at o with wind and sleet
(i) Measure off with compasses on Chart No. i the
vertical distance from t = jo on X axis to the straight
line corresponding to / = 800. Lay this distance off
vertically above the point on the curve correspond-
ing to ,0=3.93 having the abscissa 7^=30. Keep
the upper point fixed, open the compasses until the
lower point touches the line Z = 8oo; then, keeping
the compasses vertical, slide the lower point along
the line /=8oo, until the upper point intersects the
curve = i at 7^=8.35; the cable must therefore
be strung at a tension of 8350 Ibs. per sq.in. This
value of T is readily checked by finding, by the alge-
168 ELECTRIC POWER CONDUCTORS
braic method given in the preceding section, the
temperature rise corresponding to 7^ = 8.35. Thus,
3-93X800
AO = = 104.0,
30
800
I 35(3- 8 -35) =2922;
t-to =o.o644(- 1837 + 2923) = 70,
which is the temperature rise given. (2) The ab-
scissa of the point on the parabolic curve / = 8oo,
having the same ordinate as the point corresponding
to > . ////
Held taut
MIL
FIG. 48.
2. INSTALLATION OF OVERHEAD WIRES
The erection of overhead wires is performed in
various ways, depending upon local conditions and
upon the preferences of the engineer. There are,
however, two entirely different styles of construc-
tion to be considered, namely, the simple span and
the messenger wire.
The former is used where the conductors have
sufficient tensile strength to support the stresses due
to their own weight and the weight of wind and ice ;
the latter is used where the conductors are unable to
support these stresses, as, for example, in the case of
insulated cables.
INSTALLATION OF CABLES 225
Simple Spans. Starting at an anchored pole, a rope
is placed over the cross arm and the wire pulled over
the latter and drawn to the next pole, where it is
again pulled up by means of the rope and so drawn
along from pole to pole until the reel, which remains
at the starting point, is exhausted. The pulling may
be done by a gang of men, by horses, or by a loco-
motive if the pole line parallels a railroad. Care
must be taken, as the end of the reel is approached,
that the wire does not slip away and fall over the
first pole.
The next step is to place the cable on the insulators.
This may be accomplished by means of a block and
tackle if there is a cross arm above, but unless the
wire is very large there is no difficulty in doing it by
hand. Where the cable is very heavy and there
is no cross arm above, the best procedure is to rig
up a temporary cross arm or boom projecting from
the pole.
The wire, being set upon the insulators, must be
drawn up to the required tension. Starting at the
first pole after the anchorage, the wire is gripped
by a clamp attached to a rope and the rope pulled
until the wire is drawn up to the required sag. The
wire is then firmly attached to the insulator and
the process repeated at the other poles.
The foreman should be provided with a table or
curve showing the proper sag at different tem-
peratures and spans. The desired sag is obtained
226
ELECTRIC POWER CONDUCTORS
by sighting from pole to pole by means of devices
attached to the cross arm or wire, the wire being
drawn up until the point of lowest sag is tangential
to the sight line.
Messenger Construction. The messenger wire, usu-
ally a steel cable, having been erected as described
above, a " leading-up " wire is
stretched from an anchorage to the
messenger wire on the starting pole.
A rope is fastened to the end of
the cable to be suspended and
carried along the messenger wire
over the first two poles. The cable
is then slowly drawn up the inclined
wire, under the cross arm, and along
the messenger wire, carriers being
attached to the cable as it is paid
out from the reel. Men stationed
on each pole remove the carriers
from the messenger, pass them under
the cross arm, and replace them on the other side.
The cable is pulled along, in this way, until the reel
is exhausted. A common type of carrier for this
purpose is shown in Fig. 49, but wire hooks are some-
times used instead.
When the whole length of cable is suspended, a lineman
rides along the messenger wire in a ' ' carriage ' ' or trolley-
seat, and replaces the carriers by permanent clips
which firmly fasten the cable to the messenger wire.
FIG. 49.
INSTALLATION OF CABLES 227
3. SPLICING
JOINING BARE WIRES
Copper. Solid wires up to No. oo B.
and S. are almost invariably joined by
the Western Union method. To make
such a joint, bring the two ends of the
wire together so that they lap from 3 to
8 ins. Then beginning midway between
the two ends wind each overlapping end
spirally around the adjacent wire, as
illustrated in Fig. 50. With hard drawn
copper it is important to avoid giving
the wire too much twist. This is ac-
complished by making the first turn at
a small angle and then gradually bring-
ing successive turns nearer to a right
angle until they form a close spiral.
Cables are generally joined by un-
stranding them for three or four feet,
dovetailing the wires together and wrap-
ping them one by one round the unopened
part of the cable. Solder should not
be used on overhead wires lest the tensile
strength be reduced by overheating.
Numerous mechanical connectors have
met with varying success, but do not
enjoy the vogue of the ordinary line
splice described above.
228 ELECTRIC POWER CONDUCTORS
Aluminum. Aluminum cables are joined mechani-
cally without the use of solder.
Splices between wires of an area equal to No. oooo
B. and S. gauge, or anything smaller, are best made
by twisting. The two ends to be joined are inserted,
side by side, into a piece of flattened aluminum tubing,
after which the ends of the tubing are gripped by a
pair of connectors having a groove of the same
shape as the tube, and from two and one-half to four
complete twists given to the tube with its contained
wires.
Larger conductors than No. oooo B. and S. may
be joined by special connectors supplied by the
cable manufacturers or firms dealing in such special-
ties. A representative joint of this type is made
by inserting the ends of the cable into a cast aluminum
sleeve. The sleeve is then inserted between dies
in a hydraulic jack and pressure applied to the dies
until the metal of the sleeve and of the cable flow
together into a solid homogeneous mass. A modified
form of this joint has the sleeve made in two parts,
which are pressed on the cable at the factory. These
terminals are provided with internally threaded ends,
one right-handed and the other left-handed, and
cables are joined by screwing a right- and left-hand
threaded stud into the terminals. Such joints, how-
ever, are not as popular as the ordinary cable splice,
which is made by unstranding the cable for three
or four feet, dovetailing the wires together and
INSTALLATION OF CABLES 229
wrapping them one at a time round the unopened
part of the cable.
JOINING INSULATED CABLES
Preliminary. (i) Inspect cable from edge of duct
to end, looking for mechanical injury.
(2) Be certain to select the corresponding incom-
ing and outgoing sections.
(3) Place bushings in the mouths of ducts.
(4) Bend cables neatly, taking care to avoid sharp
curves, until the ends meet properly at the point of
designated for the joint. The completed joint should
lie between supports in such a way that there will
be no strain on the joint itself. In single conductor
cables, where a butt joint is used, the cables should
overlap very slightly, but in multiple conductor
cables, where the wire joints must be staggered, the
cables should overlap sufficiently to allow for the
proper distribution of wire splices.
Drying Ends of Cable. The ends of the cable should
be carefully examined for moisture, and if any is
discovered, the cable should be cut back until all
evidence of moisture disappears, care being taken
not to cut back so far as to render it too short to
make the joint. If moisture is still evident, apply
heat to the lead cover of the cable, beginning near
the duct and very slowly approaching the open end.
This heating may be effected either by pouring on
230 ELECTRIC POWER CONDUCTORS
very hot insulating compound and catching it in a
vessel held underneath, or by means of a gasoline
torch. If the dryness of the cable remains doubtful,
an insulation test should be made before jointing,
and if the insulation is abnormally low, the cable
section should be replaced. Never cut off the end of
one section until sure there is no moisture in the
other section, as it may be possible to change the
location of the splice in case the other end is defective.
Removing the Lead, (i) Mark the lead at the point
it is to be removed and make a deep cut around the
sheath, gradually increasing the depth of the cut
until the lead is cut through, taking care not to
cut the insulation in the slightest degree. A chip-
ping knife and 1 hammer or a special tool may be used
for this purpose.
(2) Cut the lead lengthwise from the circular cut
to the end, taking the precaution to hold the knife
tangent to the insulation so that it will pass between
the insulation and the sheath.
(3) Pull off the lead with a pair of pliers.
(4) When the lead is removed examine all parts of
the bared insulation and remove all loose and pre-
jecting particles of lead, especially at the edge of the
circular cut.
Preparing Cable Sleeves. (i) Scrape the ends of
the sleeve for a length of about 2 inches along the
outside, using a knife or a shave-hook and smear the
cleaned surfaces with tallow.
INSTALLATION OF CABLES 231
(2) Slip the sleeve over the more convenient end
of the cable and push it out of the way.
Removing Insulation. Cut back the insulation of
each section for a length equal to half the length of
the connector plus from J to J inch, depending on
the size of the cable.
With multiple conductor cables having an outer
insulating belt it is necessary to cut the outer insu-
lation further back than the inner insulation. In
doing this is it essential to avoid cutting the inner
insulation in the slightest degree.
Tinning the Copper. Pour molten solder over the
copper, using a tallow candle as flux.
Joining Copper by a Connector. The usual way to
join the cable ends is to use a copper sleeve, having
a cross-sectional area at least equal to that of the
cable itself. This condition is obtained by making
the outside diameter of the connector about ij times
that of the wire.
The usual length of sleeve is shown in Table II
below :
(1) Put the connector over one cable end and then
slip the other cable end in until the two ends butt
in the center of the connector.
(2) Sweat on the connector by pouring on solder
from a ladle, catching the surplus solder in a pot
below.
(3) When thoroughly saturated with molten solder,
wipe the joint with a wiping cloth, taking care to
232
ELECTRIC POWER CONDUCTORS
leave no projecting points or sharp edges. This is
extremely important in high-tension cables, as sharp
points or edges greatly increase the dielectric stress
TABLE I
DATA ABOUT CABLE SLEEVES
(Standard Underground Cable Co.)
Outside
Diameter
of Cable,
Mils.
Inside
Diameter
of Sleeve,
Inches.
Length of
Sleeve,
Inches.
Gallons of
Compound
per
Joint.
Wiping
Solder per
Joint,
Lbs.
Single Con-
Up to 550
I
8
0.05
0.9
ductor, light
551-950
x|
10
O.I
1-7
and power,
95 I -i35
2
12
O.2
2.8
up to 6600
1351-1750
i
12
o-3
4-2
volts
1751-2150
3
14
o-5
5-5
2151-2550
si
14
0.6
6.8
Single con-
Up to 550
i
10
0.05
0.9
ductor, light
55i- 95
'*i
12
O.I
i-7
and power,
95 I - I 35
2
14
0.2
2.8
above 6600
1351-1750
2*
16
0.4
4-2
volts
1751-2150
3
18
0.6
5-5
2151-2550
3i
18
0.8
6.8
Multicon-
Up to 800
*i
14
O.2
i-5
ductor, light
801-1200
2
16
0.25
2-5
and power,
1201-1600
*i
16
o-35
3-7
all voltages
1601-2000
3
18
0.6
5-o
2001-2400
3i
18
0.8
6-3
2401-2800
4
18
I.O
7-6
2801-3200
4l
20
1.4
8-3
Joining Copper without a Connector. (i) Cut the
wires alternately short and long, so that when the
two ends are butted, the long wires of one cable
will fit against the shortened wires of the other cable
and the two cables will be interlaced.
INSTALLATION OF CABLES
233
TABLE II
SIZE OF COPPER CONNECTORS
Size of Cable.
Length of
Connector.
o B. & S. to ooo B. & S.
oooo B. & S. to 1,000,000 c.m.
1,250,000 to 2,000,000 c.m.
i in. to 2 in.
2^ in. to 4 in.
5 in. to 6 in.
(2) Bind the joint with binding wire.
(3) Sweat the cables together by pouring on molten
solder.
This type of joint is superior to the connector
joint for cables larger than, say, one-half million c.m.,
because there is less danger of the cables being pulled
apart.
Insulating the Joint with Tape, (i) If the cable in-
sulation is thicker than the connector, taper it grad-
ually with a sharp knife.
(2) Then wind on insulating tape of the same
material as the cable insulation until a thickness
somewhat greater than that of the cable insulation
is obtained. The tape should be wound tightly and
evenly, running up the tapered part of the cable
insulation until well attached to it.
(3) "Boil out " the insulation by pouring over
it hot compound. The compound should be hot
enough to throw off moisture readily without being
hot enough to ignite a piece of paper dipped into
it. The surplus compound should be caught in
a pan, and when heated may be used again.
234 ELECTRIC POWER CONDUCTORS
The jointer should not take a pot of insulation
into a splicing chamber until he has taken off the
lid and assured himself that it is at the proper tem-
perature. Many accidents to men and cables are
caused by neglect of this precaution.
Insulating the Joint with Sleeves. Instead of
winding on insulating tape, an insulating sleeve may
be slipped over the wires before soldering and put
in place when the wires are joined. The internal
diameter of the sleeve must be great enough to
permit it to slip easily over the insulation.
(1) After the wires are joined, wind cotton tape
tightly over them until entirely covered up to the
level of the original insulation.
(2) Slip the insulating tube over the taped joint
and fasten it in place with a layer of cotton tape.
(3) " Boil out " the joint by pouring on insulation.
With multiple conductor cables having an outside
belt it is necessary to slip a large tube over the belt
before splicing the wires.
Tubes may be of prepared paper, varnished cloth,
or micanite.
Wiping on the Sleeve. (i) Bring the lead
sleeve into position so as to extend equally over
the lead on each cable end, and dress down the ends
close to the lead of the cable, taking care to make
the sleeve concentric with the cable.
(2) Join the sleeve and sheath by means of a
wiped solder joint. That is to say, solder is poured
INSTALLATION OF CABLES
235
on with a ladle and as quickly wiped with a cloth.
This is continued until an absolute air-tight joint
is obtained. The joint should be carefully inspected,
a small mirror being used to examine the under
ffl
FIG. 51.
side, and if any roughness or weakness is dis-
covered, should be worked over. A small blow-
hole undetected at this stage will give great trouble
later.
236 ELECTRIC POWER CONDUCTORS
Filling the Sleeve. (i) When the sleeve is
well wiped on, make two small holes in the top of
the sleeve and pour hot insulation in one hole until
it appears at the other, and then in each hole alter-
nately until the sleeve is filled. If any frothing
appears on the insulation, continue pouring it in
one hole while it escapes out the other, until the
frothing stops.
(2) Leave the joint to cool for say an hour, and
then add compound to compensate for settling
(3) Put a small piece of lead over the holes and
solder it on.
(4) Allow the joint to thoroughly cool and solidify
and then put it in its permanent place.
The following compounds are used for filling
sleeves.
Paraffin wax;
Ozite ;
G. E. Co. No. 67 compound;
Voltax, etc.
Key to Fig. 51. The various stages for a typical
joint in a single conductor cable are shown in Fig. 5 1 .
I shows the lead stripped and the wires ready
to be joined.
II shows the wires joined by a copper connector.
III shows the insulation tapered to receive the
tape.
IV shows the joint insulated with tape.
INSTALLATION OF CABLES 237
V shows the lead sleeve slipped in position.
VI shows the ends of the lead sleeve hammered
down preparatory to wiping.
VII shows the lead sleeve wiped on.
VIII shows the lead sleeve filled and the holes in
it closed by a sheet of lead.
CHAPTER IX
DEPRECIATION AND DETERIORATION
i. DEPRECIATION
DEPRECIATION is a " lessening of value " which
may be brought about by the following causes.
1. Deterioration due to the ravages of time and
the effects of the elements.
2. Wear and tear incident to use.
3. Displacement by reason of obsolescence or
supersession, resulting from developments of the
art.
The natural life of cables in ducts is estimated by
R. Hammond as thirty years.
Value of a Cable after Installation. Calling the original
cost 100, let
y = value of cable immediately after installation
expressed as percentage of the original cost.
L = life of cable, years ;
5 = scrap value at end of L, years, expressed as per
cent of original cost;
oc= value after being installed y years, expressed as
per cent of original cost. Then if the cable is
238
DEPRECIATION AND DETERIORATION 239
assumed to depreciate by a constant amount
every year,
,, v-s
If, however, the cable is assumed to depreciate at a
constant rate per annum,
V is less than the original cost for the following
reasons :
(1) Price at which cable was bought may be arti-
ficially controlled so as to be above a free market price.
(2) The cable lengths will probably be unsuitable
for other installations and will have to be reduced,
thereby wasting some cable.
(3) Cable is injured to some extent during instal-
lation.
It is important to distinguish between the value of
a cable if removed and its value as an integral part
of a transmission system, this latter depending upon
its efficacy as a revenue producer as well as upon its
cost and age.
Life and Depreciation. Equipment worth p per
cent of its original cost after y years, is said to
depreciate at the rate of P per cent, where
D (loo-p)
240 ELECTRIC POWER CONDUCTORS
If C = original cost, depreciation is offset by an
pC
annuity to redeem in y years.
100
Depreciation Calculations. The effects of deprecia-
tion may be offset by putting aside a depreciation fund
which, added to the scrap value of the old cables, will
enable new ones to be purchased.
The payment p to be made at the end of each
year, in order to possess the sum 5 at the end of n
years, is as follows.
The payment p to be made at the beginning of
each year, in order to possess the sum 5 at the end
of n years, is as follows:
r
2. DETERIORATION BY ELECTROLYSIS AND MIS-
CELLANEOUS CAUSES
Principles of Electrolysis Protection. Where a
current passes through an electrolyte, the latter is
decomposed, hydrogen, metals, and alkaline bases
appearing at the cathode or negative electrode and
oxygen and acids at the anode or positive electrode.
In other words, the corrosive agents, oxygen and
acids, travel against the current, and it is therefore
only at the anodes or places where the current
DEPRECIATION AND DETERIORATION 241
leaves the metal to enter the electrolyte that the
electrolytic corrosion occurs.
The. important condition for electrolysis preven-
tion is therefore to keep current from flowing from
any underground metal work to earth or water in
contact with it. The current flowing from the under-
ground metal work can be kept a minimum in three
ways in grounded return railway systems.
First. Keeping the potential difference between
metal and ground very low, or in other words, by
keeping down the drop in the grounded return
circuit.
(a) By thorough bonding.
(b) By frequent cross bonding between tracks.
(c) By using negative feeders to reduce the drop
in the grounded system.
(d) By using insulated negative feeders taking
current from the rails at numerous points.
(e) By negative boosters on the track rails.
Second. Keeping the metal electronegative to the
earth.
(a) By connecting to the station negative bus.
(b) By means of negative boosters connected to
the metal work.
Third. Insulating the metal work.
(a) In concrete.
(b) By paint.
Those methods requiring special comment are more
fully described below.
242 ELECTRIC POWER CONDUCTORS
Insulated Negatives. The drop in the grounded rails
may be diminished by taking the current off by
numerous insulated cables connected to the track rails.
The drop in these cables may be of any magnitude
without affecting electrolytic conditions. This system
is in use in the New York subways.
Negative Boosters Connected to Tracks. This subject
is treated under negative boosters.
Connecting Metal to Station Bus. Pipes, columns, etc.,
connected by an insulated cable to the negative bus
are immune from electrolysis. This method of pro-
tection is especially applicable in connection with the
insulated feeder system described above, as where
that is used the main insulated negative feeders are
available for this purpose and special grounding
cables are unnecessary.
Negative Boosters connected to Metal. Important
iron work, such as iron tunnels and pipes under water,
may be protected from electrolysis by using a booster
to render them negative to the surrounding water.
Such boosters are usually motor driven, and have
their negative terminal connected at intervals to the
iron work. The positive terminal should be con-
nected to a cable paralleling the tunnel and con-
nected at intervals to graphite anodes. Where
conditions permit, a single anode may be sufficiently
effective. The voltage must be sufficient to supply
a slight current after polarization has been estab-
lished
DEPREQI^TION AND DETERIORATION 243,
Electrolysis of Concrete Encased Steel. Concrete being
porous, when saturated with water permits the
passage of current. Hence if a current is estab-
lished through concrete electrolysis can take place
through it.
There is, however, a marked increase of resistance
following the application of current and consequent
tendency of the corrosive action to cease. This
increase of resistance may be from ten to fifteen fold
before it becomes constant.
Insulation of Metal Work by Paint and Asphalt. Metal
work perfectly covered with non-conducting paint is
impervious to electrolytic corrosion. Unfortunately
a slight flaw in the paint will often suffice to start
trouble. Several coats of paint ajre therefore essential
for proper protection. Asphalt paint and others of
similar nature are generally used as common paints
are acted upon by the damp ground especially if
alkalis are present.
Alternating-Current Electrolysis. (]. L. R. Hayden,
Proc. Am. Inst. Elec. Eng., 1907.) Alternating cur-
rent electrolysis is not a phenomenon like direct
current electrolysis on which quantitative general
laws can be formulated; but it is of the character of
a secondary effect; that is, the action of the positive
half wave is not quite reversed by the action of the
negative half wave leaving a small difference rarely
exceeding J% of the electrolytic action of an equal
direct current.
244 ELECTRIC POWER CONDUCTORS
A direct current about 1.5% of the alternating
current is a perfect protection against 2 5 -cycle cur-
rent. The corrosion increases with decrease of fre-
quency.
Deterioration from Miscellaneous Causes. Cable sheaths
are generally somewhat injured, during installation,
by projecting points on the surface of the ducts.
When it is remembered that a great length of cable
is pulled over each projection of this sort, the possible,
extent of the damage is seen to be very great and the
importance of thorough and conscientious examina-
tion of ducts realized. Duct inspection is often
performed by incompetent people or in a perfunctory
manner, which is encouraged by duct manufacturers.
This arises from the fact that the process of glazing
usually develops a very high percentage of defective
ducts which the manufacturer is anxious to dispose
of, bids being usually made on the assumption that
the customer will be lenient in the inspection. Engi-
neers should remember that electrolysis is a gentle
agency of destruction compared with the ripping
action of a projection in a duct.
In warm climates, lead sheathing is attacked by
beetles, caterpillars, and even wasps. The Home
Telephone Co. of Santa Barbara, CaL, has been
troubled by insect holes of an eighth of an inch
diameter in their cable sheaths.
CHAPTER X
THIRD-RAIL CIRCUITS
The design of railway feeders is so much influenced
by the systems of contact conductors to which they
are connected, that a study of the general charac-
teristics of such systems constitutes an important
phase of the feeder problem.
The first principle in the design of contact con-
ductor circuits is that, when the contact conductor
becomes grounded on account of any kind of acci-
dent, this grounding shall not be the cause of dan-
gerous or expensive damage of any kind. Such
damage may involve material on the right of way,
rolling stock, feeder conductors, power and control
equipment, and may seriously derange the schedule
by delaying trains on one or more tracks. It is there-
fore essential to sectionalize the third rail or trolley
wire in such a way as to localize this damage as
much as possible. One way of doing this imme-
diately suggests itself, namely, the use of auto-
matic circuit breakers which will open when a ground
* Abstracted from an article by the author in the Electrical World, April
22, 1905.
245
246 ELECTRIC POWER CONDUCTORS
occurs. This method, however, is not as simple
as it seems, for, although it is easy to get a circuit
breaker that will open with a certain current, it
is impossible to get one that has the power of dis-
tinguishing between a ground and an abnormal
load. This is the principal difficulty encountered
when designing a system of third-rail sectionalizing
devices. A very destructive short circuit may take
even less current than a normal load, and it will,
therefore, not open a circuit breaker set to open at an
Substation . Substation
FlG. 52. Third Rails not Interconnected but Sectionalized.
abnormal current. When, however, the circuit
breaker does open, its contacts may be so damaged
that it cannot be put back in circuit. For these
reasons it is obvious that the promiscuous use of
circuit breakers is not desirable, and that none should
be installed without a very thorough consideration
of the advantages and disadvantages which may
arise from local conditions in each case.
The designer of a sytem of third rails should
remember that it is far more important to have a
reliable system of connection between the bus and
the cars than the most complete system of auto-
THIRD-RAIL CIRCUITS 247
matic or other interrupting devices. It is obvious
that whereas the interruption of current is an inci-
dental and unusual requirement, certainty of supply
is the requirement of fundamental importance.
Hence, certainty of supply must riot in any way be
sacrificed to certainty of non-interruption. Judging
from some complicated and expensive systems now in
use, it would seem that this fundamental proposi-
tion is not universally appreciated. One corollary
to be drawn from this is that it is not desirable to
Subitalion Substation
FIG. 53. Third Rails Interconnected but not Sectionalized.
have circuit-breakers between the load and the
source of current, unless they are under constant
supervision. As a rule, this means that there should
be no circuit-breakers in series with the line except
those in the power house or substation.
It is desirable that an accident to the third rail
of one track should not in any way interfere with
the traffic on the other tracks. For this reason,
each track should be separately fed from the bus
without any other connections. Unfortunately this
system of separate feeding is very uneconomical, as
it does not utilize all the available feeder metal
248 ELECTRIC POWER CONDUCTORS
to carry the current, unless all the tracks are
always equally loaded. In order to obtain the
advantages of separately fed tracks, and to secure
maximum feeder economy, the method of connecting
together all the tracks through circuit-breakers im-
mediately suggests itself. Damage to such circuit
breakers is not liable to cause serious trouble, as
they do not interrupt the current along each third
rail, and they are therefore not essential in the
scheme of supply. Whether the tracks are to be
Substation Substation
FIG. 54. Third Rails Interconnected and Sectionalized.
permanently connected or connected through switches
or circuit-breakers, or not connected at all, will
depend upon local conditions as viewed by the en-
gineer.
In order to confine the effects of a short-circuit
to a limited portion of the track on which it occurs,
it is desirable to divide the third rail into a number
of sections. It is, however, not advantageous to
carry this division very far, as an accident at any
point on a track will affect the traffic a long way
behind. As a rule it is sufficient to break the rail
in front of the substations and at cross-overs. Breaks
THIRD-RAIL CIRCUITS 249
at cross-overs are essential in order that a train
may go around a dead section of rail by crossing to
another track. Breaks in front of the substations
are convenient because it is possible to break the
rail there without having to install switches or circuit-
breakers on the line. Breaks in the rail at cross-
overs distant from the substations involve the use
of circuit -breakers or switches to interrupt the con-
ductor which joins the sections. As circuit-breakers
in series with the line are undesirable, it only remains
FIG. 55. Knife Switches at Cross-overs.
to recommend the use of switches for this service.
It is desirable, however, to use a type of switch
which can be opened under load. It is often desirable
to locate section breaks at passenger stations on the
" far side," in order to enable trains to reach a
station in spite of trouble ahead.
The third rail may be sectionalized for another
purpose besides confinement of accidents. It some-
times occurs that the current normally carried by
the substation circuit-breakers is of such unusual
magnitude that the circuit-breakers are materially
damaged whenever they operate. It is therefore
250 ELECTRIC POWER CONDUCTORS
necessary to divide the third rail into two or more
sections, each of which is directly fed from the sub-
station by feeders, thereby dividing the current
between two or more circuit -breakers. The breaks
at substations are useful in effecting the same
purpose.
A weak point in the ordinary feeder system is
found in the cable which connects the bus to the
third rail. Should a ground occur in this cable,
it will not suffice to open the breaker between it
and the bus, for the ground will be fed through the
third rail from the other substations. It is there-
FIG. 56. Third Rails Sectionalized at Passenger Station.
fore desirable to have a switch at the third rail
between the third rail and its feeder. It should be
remembered that a ground of this kind will neces-
sitate the interruption of current from all sources
and may, therefore, seriously delay traffic.
With separately fed third rails, auxiliary copper
may have to be provided for each rail, whereas with
rails connected together, auxiliary copper may not
be required, but if it is, it will serve to feed all the
rails and may be connected to them with the same
system of switches or breaks as are used to connect
the rails.
TqiRD-RAIL CIRCUITS 251
A much-discussed subject is the advisability of
using short isolated sections of third rail at gaps
between separately fed sections. The object of these
is to prevent a car or train from spanning across a
gap between a live and a grounded rail. With the
simple multiple-unit system that is, where only
the control wiring runs from car to car an isolated
section may be used with advantage. It must be
so proportioned as to render it impossible for one
or more cars to span both gaps which isolate the
section, and the section on each track must be fed
through a separate circuit-breaker. When a bus
line connects the main wiring of all the cars a short
section of about a car length is quite useless. In
this case the section has to be of about a train
length, and in order to avoid burning out the train
bus line, the isolated section may be protected by
a circuit-breaker arranged to open when either of
the main third- rail circuit-breakers is open. A train
length section is in use on the New York Central
R. R., where it has been of considerable service
during alterations and repairs to the third rails. An
alternative scheme which has been found satisfactory
in the I. R. T. subway, New York, is a system of sig-
nals at the gaps arranged to show danger when the
rail on either side is dead.
CHAPTER XI
RAIL BONDS
CLASSIFICATION
TABLE I
RAIL BONDS
CLASSIFIED ACCORDING TO METHOD OF ADHESION
I
Chemical Adhesion
r
Soldered Bond
(may be ap-
plied to Head,
Web or Foot).
Amalgamated
or
Bond.
Plastic
I
Mechanical Adhesion
(Adhesion is obtained by expanding ter-
minal into hole in the rail. Expansion
effected by pressure applied in follow-
ing ways.)
Brazed Bond
and Welded
Bond.
Pressure from
inside. Pin Ex-
panded Bond
for Web or
Foot.
Pressure from
one end. Com-
pressed Plead
Bond.
Pressure from
both ends.
Compressed
Web or Foot
Bond.
252
RAIL BONDS
TABLE II
RAIL BONDS
CLASSIFIED ACCORDING TO TYPE OF CONDUCTOR
253
Solid
Exposed
Concealed
I
I
Cable
!
Ribbon
Solid
Cable
I
Ribbon
Classification. Rail bonds differ in the form of con-
ductors, and in the methods of securing the terminals
of the conductor to the rails. Table I shows the
classification according to the method of securing
adhesion between terminals and rail, and Table II the
classification according to type of conductor. Each
of the classes mentioned in these tables is commented
on below. t
Soldered Bond (Figs. 57, 58, and 59). Soldered
bonds are very easy to apply, but do not always last
/ FIG. 57. Soldered Bond Head Type.
well. Good performance for several months should
not be taken as a guarantee of excellence, because
failures only begin to occur after several months'
254
ELECTRIC POWER CONDUCTORS
use. Under conditions of light service soldered bonds
are quite serviceable.
When soldered bonds become loose or are taken
FIG. 58. Soldered Ribbon Foot Bond.
off for rail repairs or renewals, they can be used
again.
In order to apply a soldered bond, the rail surface
is made bright with an emery or carborundum wheel,
FIG. 59. Concealed Soldered Web Bond.
and further cleaned with hydrochloric acid before
the solder is put on. The soldering is done with a
blow torch, the bond being held in place with clamps.
Soldered bonds being short and requiring no drill-
ing, are considerably cheaper than most other kinds.
RAIL BONDS 255
*
Brazed Bond. Similar to soldered bond except that
brass is used instead of solder.
Welded Bond (Copper Welding). A mould is set
around the bond terminal and back along the rail
a little distance, and then some copper is brought to a
red heat in a crucible placed in a small furnace using
hard coal or coke and served with an air blast. A
portion of the melted copper is poured through a
small opening in the mould where the point of con-
tact is desired; sufficient is poured in to bring the
strands of the bond and the steel to the welding point,
the mould being provided with an overflow opening
for superfluous copper. When it has solidified the
mould is taken off and the overflow knocked off with
a hammer to be used again.
The heating may also be done electrically by a
process similar to that described below for moulding
rail joints, the flat copper bond head being welded to
the rail.
Plastic Bonds. The conductivity of the fish plate
is made use of by interposing between it and the rail
a copper bond brought into intimate contact with .
the iron with the aid of a soft mercury amalgam.
Another type has a copper plate which makes
electrical contact with the rail by means of a plastic
amalgam, the plate itself being held in position by
the reaction of a spring pressing against the fish
plate.
The latest type (Fig. 60) consists of a copper plug
256
ELECTRIC POWER CONDUCTORS
surrounded with amalgam, placed in a hole drilled
through the flange of a girder rail and into the fish
plate.
Bonds with Mechanical Adhesion, General. These
bonds are more generally used than any other type
owing to their greater durability. When once re-
moved they are scrap metal, the life of the bonds
FIG. 60. Plastic Bond Plug Type.
being therefore limited to the life of the rails on
which they are installed.
There are a great many different types on the
market differing principally in the method of apply-
ing the terminal to the rail. There is, however, little
ground for discrimination between types.
Drilling of the rail must be accomplished without
RAIL BONDS
257
the use of oil, the permissible lubricants being soapy
water or caustic soda solution.
Pin-expanded Bonds. The pin-expanded terminal
has a conical hole into which a steel pin is pressed
by screw or hydraulic pressure. This presses the
copper outward into firm contact with the rail and
leaves a head on the outside of the terminal which,
acting like a rivet head, helps to hold the bond firmly
in place.
The steel-core type resembles the ordinary pin-
expanded type in many respects, but the steel pin
FIG. 61. Pin Expanded Bond. G. E. Co. Type with Steel Core.
is retained in the terminal after it is installed. The
core is similar to a double-headed rivet which, when
upset by longitudinal compression, expands radially,
forcing the walls of the rail hole in the directions
shown by the arrows in Fig. 61.
Compressed Head Bonds. One or more holes are
drilled in the side of the rail head and the bond ter-
minal pressed firmly into the hole until expanded
sufficiently to hold tight. Reaming the sides of the
hole so as to produce cavities to catch the bond head
258
ELECTRIC POWER CONDUCTORS
does not add much to the security of this type of
bond.
If constructed so that rail motion will not tend to
rotate the bond terminals in their rail holes, this
type of bond is very satisfactory.
Compressed Web or Foot Bond. The bond terminal
is put in a hole drilled through the rail web or foot,
FIG. 62. Compressed Bond. Foot Type.
and pressure applied at both ends until the copper
terminal is squeezed into the shape of a rivet, its
ends being spread out to form the rivet heads (Figs.
62, 63, 64, and 65).
Exposed and Concealed Bonds. Exposed bonds are
desirable on account of the facility of inspecting,
where there is little danger of theft or external injury.
Concealed bonds, i.e., bonds under the fish plate,
are necessary where there is danger of theft or external
RAIL BONDS
259
injury. Concealed soldered bonds are not favored
for heavy work because soldered bonds require con-
stant inspection and repairs.
Head, Web and Foot Bonds. Open bonds may be
applied to the head, web, or foot of the rail.
FIG. 63. Compressed Foot Bond and Compressed Concealed Web Bond.
The only advantage of head bonds is the lower
resistance due to the fact that most of the current
in a rail is carried in the head. This type of bond
is practical for third rails only, on account of th3
wear on the heads of track rails.
Web bonds are commonly used because concealed
bonds are necessarily of that type and expanded
260 ELECTRIC POWER CONDUCTORS
terminal bonds are most conveniently applied to the
web.
Foot bonds are little used except for third-rail work.
FIG. 64. Protected Ribbon Bond with Compression Terminals.
Soldered bonds are most easily applied to the upper
surfaces of the foot, while compressed terminal bonds
are more generally applied underneath.
FIG. 65. Solid Wire Bond.
Solid, Cable, and Ribbon Bonds. Bonds of all
classes are made either of solid copper, stranded
cable, or multiple ribbons of copper.
Solid bonds, unless of great length and small
RAIL BONDS 261
X 9
cross-section, are too stiff for traction work, but
are largely used for signal and telegraph circuits.
Exposed bonds are usually of wire cable, as on
account of its flexibility in all directions this mate-
rial is well adapted to withstand vibration.
Ribbon bonds are usually used under fish plates
on account of their compactness and the ease with
which they lend themselves to tucking about the
fish-plate bolts.
Efficiency of Bonding. The efficiency of a rail
bond is the ratio of the conductivity of the bonded
joint to the conductivity of an equivalent length
of continuous rail. If a rail of length L has a sec-
tional area equivalent to A c.m. of copper, and a
bonded joint of length / has a section equivalent to
a c.m., the efficiency of the bonded joint neglecting
contact resistance is = /.
J\.
The efficiency of the bonding of a line of rail is the
ratio of the conductivity of the bonded line to the
conductivity of the line, supposing the rail to be
continuous.
The relation between the efficiency of the bond-
ing of a line and the efficiency of a bonded joint is
given by the equation,
Efficiency of the bonding of line = .
L + -(i-/)
Fig. 66 shows this equation plotted as a curve for
262
ELECTRIC POWER CONDUCTORS
L = 6o and = 3. It will be noted that the bond
efficiency may be very low without materially reduc-
ing the efficiency of the bonded line. It therefore
appears that the size of bond to be adopted depends
80 30 40 60 CO 70 80 90 10*
Per Cent
BOND OF EFFICIENCY OF JOINT.
RELATION BETWEEN BOND EFFICIENCY OF JOINT AND OF LINE.
FIG. 66.
more upon the carrying capacity than upon the
conductivity.
Carrying Capacity of Bonds. The carrying ca-
pacity of a bond cannot be calculated by the ordi-
nary rules for wires or ribbons, on account of the
great cooling effect of the rails. A soldered bond
will become loose on account of the fusion of the
solder without the copper being in any way injured.
, RAIL BONDS
263
Thus a No. oooo soldered bond will melt off in five
or ten minutes at 10,000 amperes.
It should be noted that short bonds have far
greater carrying capacity than long bonds on account
V 2 M.C.M OOB.&.S OCOOB.&S. V 2 M.C.M.
20
10
/
i
/
/
7
/
/
/
/
800
/
/
/
1
7
/
/
700
/
/
/
y
1
/
/
/
/
/
/
/
/
/
I
500
/
/
i
1
/
7
/
/
/
1
/
/ y
/
1
5
/
/
y
i
/
i
/
/
/
/
j
/ >
/
y
/
1
d
i
,
V
/
/
H
200
/
/
/
/
2
/
/
/
100
4 5 6 7 8 9 10
Thousands of Amperes
FIG. 67. 9-in. Bond with Mechanical Adhesion.
of the proportionately greater cooling effect of the
rails.
There is, at the present time, little reliable data
on the carrying capacity of the various types of bonds.
The diagram (Fig. 67) refers to a Q-in. exposed
bond with mechanical adhesion or welded. The
heavy lines should be used in connection with the
264
ELECTRIC POWER CONDUCTORS
right-hand temperature scale, and the light lines
with the left-hand temperature scale.
Importance of Cleanliness in Bonding. In order
to secure good bonding it is essential to guard against
dirty bonds, and bond holes, rough and irregular
bond holes insufficient pressure on compressed ter-
minals, unclean rails, and insufficient heat on sol-
dered bonds. The average track construction gang,
if entrusted with bonding, even under the eyes of
a vigilant inspector, usually makes joints which,
while mechanically good, are electrically imperfect.
For this reason many companies now have special
bonding forces under a foreman with sufficient
electrical training to understand the importance of
good electrical contact.
TABLE III
CIRCULAR MILS OF COPPER EQUIVALENT TO VARIOUS
WEIGHTS OF RAIL
Weight
Ratio of Resistance of Steel to Resistance of Copper!
of
Rails,
Lbs.
per
Yard.
6.
7-
8.
9-
10.
ii.
12.
5
1,061,030
99,455
795,773
707,354
636,618
578,743
53,5 I 5
60
1,273,236
1,091,346
954,928
848,825
7 6 3,942
694,491
636,618
70
1,485,442
1,273,237
1,114,083
990,296
891,266
810,239
742,721
75
1,591.545
1,364,183
1,193,660
1,061,031
954,927
868,115
795,773
80
1,697,648
1,455,127
1,273,238
1,131,766
1,018,589
925,9 8 9
848,825
90
1,909,854
1,637,018
i,432,393
1,273,237
1,145,913
1,041,735
954,9 2 8
100
2,122,060
1,818,910
1,591,546
1,414,708
1,273,236
1,157,486 1,061,030
RAIL BONDS 265
$
Single and Double Bonding. Single bonding
has the advantage of being more likely to be in
good repair, as a defective bond soon reveals itself.
Double bonding affords a factor of safety very im-
portant on busy roads.
Welded Rail Joints. Both bonding and the mechan-
ical connection of rails are replaced by various
types of welded joints, although some companies
use the welded joint for its mechanical features
only, preferring to use copper bonds to maintain
electrical continuity.
CAST WELDING
A mould is placed around the rail joint and molten
iron poured into it.
There are various ways of effecting this, differing
in the type of mould and method of applying the
iron, but in all of them thorough cleansing of the
rails at the joints and protection of the rail top
from molten metal are of prime importance.
It is claimed by some that cast welding changes
the character of the steel at the joints so that the
joints do not wear the same as the rest of the track,
and will in time hammer down. This is apparently
due to defects in workmanship, as this trouble is not
experienced by all users of cast welded joints.
It is important to use plenty of metal in order
that it may not be too rapidly chilled.
266 ELECTRIC POWER CONDUCTORS
THERMIT WELDING
A mould is placed around the rail joint, and molten
iron poured into it. The process differs from the
ordinary cast weld in the method of preparing the
molten iron.
Preparing the Rails. The rails having been
aligned properly, the ends are thoroughly cleaned
with a sand blast or wire brush a few inches each
side of the joint. The rails are then heated by a
gasoline or oil blow torch, to expel all moisture.
Some advise heating to a dull red heat.
The Moulds. The moulds consist of iron frames
lined with a mixture of sand and 10% cheap rye
flour. This mixture' is slightly moistened, so as
to retain its form when pressed in the hands, and
in this condition placed in the iron frames and
baked at about the same temperature as bread.
By adding a teaspoonful of turpentine to each pair
of moulds, the material is hardened. This, however,
is unnecessary except for special work.
The mould frames are securely clamped to the
rails, one on each side, the interstices between
moulds and rails luted with clay about the consis-
tency of putty, and common earth heaped around
the frames.
The rail head is then painted with a watery paste
of common red clay, which the heated rail imrne-
RAIL BONDS 267
- *
diately dries to a thin coating. This is to prevent
the molten steel uniting with or burning the rail
head.
The moulds and rails are then given a final warm-
ing with the torch.
The Crucible and its Use. The crucible on its tripod
is placed with its pouring hole directly over and
about two inches above the gate in the mould. After
placing the topping pin, iron disk, asbestos disk,
and refractory sand in the bottom of the crucible to
act as a plug for the opening, the thermit compound
is poured in and in the center of the top is placed
about one-third of a teaspoonful of ignition powder,
which is set off with a match.
The compound is composed of a mixture of iron
oxide and aluminum, both in granular or flake form.
The ignition powder is composed of barium peroxide
and aluminum in fine powder. When the match is
applied to the ignition powder, the aluminum ignites,
drawing the necessary oxygen from the barium per-
oxide. The heat thus developed ignites the aluminum
of the thermit compound, which draws the oxygen
from the iron oxide and liberates the iron. The
latter settles immediately to the bottom of the cru-
cible. While this is going on, the contents of the
crucible form a glowing, seething mass, and in about
thirty seconds the action is completed.
The crucible is tapped by striking the tapping pin
with a special iron spade, and the incandescent steel
268 ELECTRIC POWER CONDUCTORS
runs smoothly into the mould, the slag following.
In five minutes the mould can be removed to permit
the passage of cars.
The mould must be of generous proportions, other-
wire the rail will chill the iron and the latter will
not adhere.
It is found that if thermit welding is performed
when the temperature is rising, the expansion of the
rails is apt to cause a hump at the joints.
For this reason it is better to work on cool days or
when the temperature is falling.
ELECTRIC WELDING
An iron bar is fitted against the web of the rail
and welded thereto by heating both the bar and the
rail to a white heat by means of an electric current.
Preparing the Rails. The rails having been aligned
properly, the ends are thoroughly cleaned with a
sand blast or wire brush a few inches along both
sides of the web. The iron bars are applied one on
each side of the web and clamped to one rail.
Source and Application of Current. A small motor
generator set on a wagon is operated by power taken
from the trolley, and supplies alternating current to
a step-down transformer. The secondary of this
transformer supplies current at very low voltage but
enormous amperage which, when applied to the
clamps which hold the bars to the rails, brings both
bars and rails to a white heat and welds them into one.
RAIL BONDS
*
While still hot, the bars are clamped to the other
rail and the current applied until the welding is
effected. As the bars cool, they contract and draw
the rails firmly together.
Iri order to obtain good results the rails^must be
well abutted before welding.
TABLE IV
BONDING AREAS
INTERNAL CONTACT AREA OF HOLE IN RAIL
Diameter,
Inches.
Length
i Inch
Length
A Inch.
Length
| Inch.
Length
2\ Inch.
Length
2i Inch.
Sq.In.
Sq.In.
Sq.In.
Sq.In.
Sq.In.
1
1.964
1.105
1.232
4-419
4.918
f
2-35 6
i-3 2 4
1.471
5-298
5.890
I
2-749
i-545
1.721
6.185
6.871
I
3-*42
1.767
1.962
7.068
7-854
l
3-338
1-875
2-085
7-509
8-345
l|
3-927
2.206
2.452
7-825
9.818
I*
4.712
2.648
2.941
10.602
i i . 780
If
5-498
3.088
3-436
12.371
13-745
2
6.283
3-528
3-925
14-137
15.708
ai
7.069
3-974
4.418
15-905
17.673
a*
7-854
4.418
4-913
17.672
19-635
CROSS-SECTION OF BONDS IN C.M. AND SQ.IN.
C.M.
Sq.In.
C.M.
Sq.In. | C.M.
Sq.In.
1,000,000
0.785
400,000
0.314
200,000
- I 57
900,000
0.707
350,000
0.275
000
o. 132
800,000
0.628
300,000
0.236
00
0.104
750,000
0.489
250,000
0.196
125,000
0.098
600,000
0.472
225,000
0.177
o
0.083
500,000
0-392
0000 *
0.166
100,000
0.079
450,000
o-354
*B.&S.
CHAPTER XII
INDUCTANCE, REACTANCE, AND CAPACITY
i. TABLES OF INDUCTANCE AND REACTANCE
OF PARALLEL WIRES *
Inductance of Single Phase Lines. To find the in-
ductance in millihenrys per mile of each of two
parallel non-magnetic wires, find A corresponding to
the distance apart of the wires, and B corresponding
to the size of wire, and add together A and B. The
sum will be the required inductance.
Thus the inductance of a 1,000,000 circular mil
cable, distant 50 feet from a similar cable, will be
2.724 .363 =2.36 millihenrys per mile.
The inductance of a No. 36 wire, distant 10 inches
from a similar wire, will be
1.407 + 1.338 = 2.745.
Reactance. Express L in millihenrys. Then if
/ = cycles per second,
Reactance = 2 X io~ 3 7r/L.
* See Appendix VII.
270
INDUCTANCE, REACTANCE AND CAPACITY 271
To find the reactance in ohms per mile of each of two
parallel wires, find a corresponding to the distance
apart of the wires, and b corresponding to the size of
wire, and add together a and b. The sum will be the
reactance at 100 cycles. At other frequencies the re-
actance will be in proportion to the frequency.
TABLE I
SINGLE PHASE
VALUES OF A
d, Distance
between
Centers of
Wires, Ins.
A.
d. Distance
between
Centers of
Wires, Ins.
A.
d. Distance
between
Centers of
Wires, Ins.
A.
I
0.6654
21
-6^5
41
.861
2
0.8886
22
.660
42
.868
3
1.019
23
-675
43
.876
4
1. 112
24
.688
44
-883
5
.183
25
.701
45
.891
6
.242
26
.714
46
.898
7
.292
27
.726
47
-905
8
-335
28
-738
48
.911
9
-373
29
-749
49
.918
10
.407
30
.760
5
-925
it
-437
31
.771
Si
-93 1
12
-465
3 2
.781
52
-937
13
.491
33
.791
53
-943
14
-5i5
34
.800
54
-949
iq
-537
35
.810
55
-955
16
-558
36
.819
56
.961
17
-577
37
.828
57
.967
18
-59 6
38
.836
58
.972
19
.613
39
-845
59
.978
20
.630
40
1-853
60
-983
272
ELECTRIC POWER CONDUCTORS
TABLE II
SINGLE PHASE
VALUES or A
d. Feet.
A.
d. Feet.
A.
d, Feet.
A.
I
1.465
15
2.336
2 9
2-549
2
1.688
16
2-357
3
2.560
3
1.819
i?
2.368
35
2.609
4
1.911
18
2-395
40
2.652
5
1-983
19
2-413
45
2.690
6
2.042
20
2.428
5
2.724
7
2.091
21
2-445
60
2.783
8
2-134
22
2.460
70
2.832
9
2.172
2 3
2.474
80
2-875
10
2.206
24
2.488
90
2.913
ii
2.237
2 5
2.501
100
2.947
12
2.265
26
2-513
500
3-465
13
2.290
27
2.5 2 5
IOOO
3.688
14
2.314
28
2 -537
TABLE III
SINGLE PHASE
VALUES or B
Size of Wire
No. B.&S.
B.
Size of Wire,
No. B. & S
B.
Size of Wire,
No. B. & S.
B.
oooo
O.II2
II
0.411
24
0.896
ooo
-0.075
12
0.448
25
0-933
00
-0.037
13
0.485
26
0.970
14
0.522
27
.008
I
0.037
15
0.560
28
.044
2
0.075
16
o-597
29
.082
3
O.II2
i7
0.634
3
.120
4
0.149
18
0.672
3i
-157
5
0.187
19
0.709
32
.194
6
0.224
20
0.746
33
.232
7
o. 261
21
0.784
34
.26 9
8
0.298
22
0.822
35
. 3 06
9
-33 6
23
0.859
36
-344
TO
-373
INDUCTANCE,^ REACTANCE AND CAPACITY 273
TABLE IV
SINGLE PHASE
VALUES OF a
= 0.46565 log d+ 0.41811)
Distance between
Centers of Wires,
Inches = d.
a.
Distance between
Centers of Wires,
Inches = d.
a.
I
0.4181
21
-0338
2
0.5626
22
.0432
3
0.6413
2 3
.0522
4
0.7071
24
.0608
5
0.7436
25
.0691
6
0.7805
26
.0770
7
0.8116
27
.0846
8
0.8386
28
.0920
9
0.8625
2 9
.099!
10
0.8838
3
.1059
ii
0.9030
36
.1428
12
0.9206
42
.1740
13
0.9368
4 8
.2OIO
14
0.9518
54
.2248
15
0.9658
60
.2461
16
0.9788
66
.2654
17
0.9911
72
.2830
18
1.0026
78
.2992
19
1.0136
84
3*42
20
1.0239
90
.3281
96
.3412
Thus the reactance at 25 cycles of a mile of No.
oooo B. and S. 36 in. between wires, is as follows:
a= 1.1428
b= .0703
dividing by
1.0725
100
.2681 ohm.
274
ELECTRIC POWER CONDUCTORS
TABLE V
SINGLE PHASE
VALUES or b
(6 = 0.023443;?)
Size of "Wire.
b.
Size of Wire.
b.
1,000,000 C.M.
o. 2272
7
o. 1641
750,000 C.M.
0.1982
8
0.1876
500,000 C.M.
-0.1572
9
0.2IIO
250,000 C.M.
0.0872
10
0.2344
oooo B. & S.
0.0703
ii
0.2579
000
0.0469
12
0.2813
oo
-0-0235
J 3
0.3048
o
o
14
0.3282
I
0.0235
15
0-35*7
2
0.0469
16
o-375i
3
0.0703
17
0.3986
4
0.0938
18
0.4220
5
0.1172
i9
0-4454
6
0.1407
20
0.4689
n is the number of the wire on the B. & S. g-uge.
Impedance.
v 7 Resistance 2 + reactance 2 = impedance.
In a three phase line with wires symmetrically
arranged the reactive drop in the loop formed by
any two wires is V$ X reactance of each wire X cur-
rent in the wire.
Inductance for Parallel Iron Wires (approximate).
d = distance apart, center to center , of wires.
r = radius of wires.
L = inductance of each wire in millihenry s.
Formulae,
^ = 75 + ( 2 lg:~~) I0 ~ 6 > P er centimeter.
INDUCTANCE, REACTANCE AND CAPACITY 275
L per centimeter = .000,075 + .000,004,6 log-.
d
L per inch =.000,191 + .000,011,68 log -.
L per foot
L per 1000 feet =2.286 +.14
=.002, 286 + .000, 14 log-.
log-.
d
= 12.070 +.741 log-.
L per mile
(Permeability assumed to be 150.)
TABLE VI
APPROXIMATE OHMIC RESISTANCE AND IMPEDANCE OF
THREE CONDUCTOR CABLES
IMPEDANCE OHMS PER MILE.
Size.
ance,
Ohms
Working Voltage.
per Mile.
3000
5000
7000
JOOOO
15000
20000
2
0.850
0.858
0.859
0.863
0.867
0.872
0.884
I
0.674
0.692
0.696
0.700
0*706
0.712
0.724
o
0-535
o-545
0-547
o-552
0.558
-5 6 5
0.580
00
0.424
0.436
o-439
0.444
0.452
0.460
0.478
000
o-33 6
0-352
0-352
o-357
0.365
o-374
0.396
0000
0.267
0.280
0.283
0.288
0.296
0.306
0-332
250,000
0.227
0.245
0.245
0.252
0.261
0.272
0.299
300,000
0.188
O.2IO
0.210
0.217
0.227
0.241
O.27O
350,000
0.161
0.187
0.187
0.194
o. 204
0.217
0.250
400,000
0.141
0.166
0.166
0.174
0.185
0.199
0-234
450.000
0.127
0.148
0.148
0.156
0.167
0.182
O.22I
500,000
0-113
o 137.
0.137
0.144
0.156
0.172
O.2I2
Based on pure copper at 75 F. with an allowance of 3% for spiral path of con-
ductors, 60 cycles per second, and standard thickness of varnished cambric insu-
lation. *
Values are practically the same for other types of insulation.
NOTE. These figures are approximately correct for 98% conductivity copper at
65 F. G. E. Co. Bulletin.
276
ELECTRIC POWER CONDUCTORS
Overcoming Effects of Mutual Induction. Neighbor-
ing circuits having currents of the same frequency
affect each other so that the inductive drop in one
circuit is increased, and in the other decreased. If
the currents differ in frequency, the potential will
rise in one circuit when the waves come in step,
and will fall in the other circuit.
1 1
O
44 44
00 O
33 33
O O O
22 22
00 00
1 1
O
2 2
33 11
00 00
22 44
O O O O
11 33
00 00
4 4
O
.
.
FIG. 68.
The simplest cure for this evil is to put the" wires
of a circuit close together compared with their
distance from the other circuit. Another way is
to transpose the wires so that the induction along
one-half the line will neutralize the induction in the
other half. This is illustrated in Fig. 68, in which
each diagram shows how the wires should be arranged
for one-quarter of the entire length.
INDUCTANCE, REACTANCE AND CAPACITY 277
2. CAPACITY
General. The capacity of a transmission line is
distributed over the whole length of the conductor,
so that the circuit can be considered as shunted by
an infinite number of infinitely small condensers
scattered along its entire length. Where the capac-
ity of the line is small, however, it may, with suffi-
cient approximation, be represented by one con-
denser of the same capacity as the line, shunted
across the line, either at the generator end, the
receiver end, or at the middle.
The best approximation is to consider the line
as shunted at the generator and at the receiver end,
by two condensers of one-sixth the line capacity each,
and in the middle by a condenser of two-thirds the
line capacity. This approximation, based on Simp-
son's rule, assumes the variation of the electric
quantities in the line as parabolic.
(Abstracted from " Alternating Current Phenom-
ena," C. P. Steinmetz.)
Injurious Effects of Capacity. The principal objection
to high capacity in a line is the large charging current
which necessitates a greater generating and transform-
ing equipment. The current, being wattless, does not
give rise to much energy loss.
In case the line is supplying a low power factor load,
a high capacity in the line may be a distinct advan-
278 ELECTRIC POWER CONDUCTORS
tage, as it improves the power factor at the generat-
ing station by neutralizing the lagging current taken
by the load.
Two Parallel Wires (Bare). The capacity given by
the following formulae are for the pair of wires, such
a pair forming with the air between them, the equiva-
lent of a condenser.
,_.. f ., .038,83
Microfarads per mile, ,
Microfarads per 1000 ft.,
'-
log
. .000,02415
Microfarads per meter, -, - r)>
log
where r
r = radius of wire;
D= distance apart, center to center.
The logarithms are to the base 10.
In the above formulse it is assumed that the dis-
turbing effect of the earth and other neighboring con-
ductors, is negligible.
Charging Current.
E= potential difference between wires, volts;
K = capacity in microfarads of the condenser
formed by any two line wires;
/ = frequency in cycles per second;
I = charging current, amperes per wire;
INDUCTANCE, REACTANCE AND CAPACITY 279
*
For a single phase line,
For a three phase line,
/ =
V3 X io 6
Single Overhead Wire with Earth Return.
h = height of wire above ground,
r= radius of wire.
(These to be given in the same units.)
The capacity of such a wire is equal to that of a
pair situated a distance 2h apart. In other words, the
capacity which such a wire forms with the earth is
equal to that which it forms with its reflected image
in the earth, assuming the earth to be a perfect con-
ductor.
Microfarads per mile,
Microfarads per 1000 ft., ;
, 2h
log
r
.000,0241 c
Microfarads per meter, r^
log^
280 ELECTRIC POWER CONDUCTORS
Single-Phase Two Conductor Cable.
Let a = capacity between one conductor and the
other in parallel with the sheathing;
b = (a | capacity between the two conductors
in parallel and the sheathing) .
These two are readily measurable quantities. Then
the capacity between the two conductors equals
|.353>53-
The diameter of a No. n wire is that of a No. o
wire divided by R n , and as the diameter of a No. o
281
282 ELECTRIC, POWER CONDUCTORS
wire is that of a No. oooo, divided by -R 3 , the diameter
of a No. n wire in mils is equal to
460
^3, exactly,
32,486
or, , approximately.
I.J229 n
The area in circular mils being equal to the square
of the diameter, is equal to
211,600
R
2n+G
-, exactly,
or , approximately.
1.2605"
The number on the B. and S. gauge of a conductor
of A circular mils area is given by the following
equation, which is derived from the above equation
for area,
/ 2ii,6oo\
or n = (9.92978 log ) 3-
\ A /
,
Numbers of conductors larger than No. o are given
as negative quantities. Thus
B. and S. No. n
O O
00 I
OOO 2
oooo 3
etc.
APPENDIX I 283
*
The ratio R is approximately equal to the sixth
root of 2, which is 1.12246. This fact makes it
possible to have a group of wires having approxi-
mately the same area as any single wire, all being
regular sizes on the B. and S. gauge. This approxi-
mation gives rise to the following formulae:
Diameter, mils =' n ;
26"
105,500
Area, circ. mils. = =~
23"
Ohms, per 1000 ft. = ;
10
-220
Pounds per 1000 ft. =^-.
23"
APPENDIX II
BASIS OF SKIN EFFECT AND CARRYING-
CAPACITY FORMULAE
SKIN EFFECT
USING the same symbols as on p. 40, the exact
expression for R is as follows:
7?__i k er - />-bei'. p bei. p-ber.' p
'
where = 0.875 Z, arid 0.875 * s the square root of STT
times the number of centimeters in one foot.
Bessel's functions may be avoided by substituting
a series, but for all practical purposes the approxima-
tion given is sufficient.
CARRYING CAPACITY
A conductor heated by a current assumes a steady
temperature when the power generated in it equals
the power dissipated from it. The rate of generation
of heat is given by the well known equation
Pk
Watts = ,
a
284
APPENDIX II 285
where / = amperes ;
k = specific resistance of conductor in ohms per
circular mil-foot at the temperature corre-
sponding to the rise T;
a = cross-sectional area of conductor, circ. mils.
The rate of dissipation of heat cannot be expressed
by any exact equation because heat is dissipated by
conduction, convection and radiation, and these
methods of heat dissipation are not susceptible of
exact expression.
It is usual to assume the dissipation of heat to be
entirely effected by one method, either radiation or
conduction, the former being nearly correct for bare
conductors and the latter, for insulated cables in
ducts.
Assuming heat dissipation by radiation and using
Newton's law of cooling,
where KI is a constant depending upon the size and
style of conductor.
Assuming heat dissipation by conduction,
+aT'
where K 2 is a constant, and
i
286 ELECTRIC POWER CONDUCTORS
t being the initial temperature. This is based upon
the assumption that the thermal resistivity and
outside temperature of the heat insulator surround-
ing the conductor are constant.
The best experimental data available is that of
Fisher, Ferguson, and Kennelly, but their results
do not exactly agree with any formula available.
The author has therefore adopted the simplest
formula, namely, that based upon dissipation propor-
tional to the temperature rise, and has derived his
.constants so as to include all the best experimental
data within his knowledge.
The formula is as follows:
Let
A = cross-sectional 'area of conductor, sq.in.;
/ = amperes ;
C = circumference of conductor, inches;
W= watts dissipated per sq.in. of surface per
degree C. temperature rise;
T = temperature rise, degree C.
r = specific resistance of conductor, ohms per
inch cube at the temperature corresponding to the
rise T.
Then in an inch of conductor,
Watts generated =/ 2 -,
A.
Watts dissipated =CWT.
APPENDIX II 287
*
Hence,
or
By changing the constants to a more practical
form, the formula of p 46 is obtained.
The Short-Period Carrying Capacity of Cables. The
watts generated in a cable on account of its ohmic
resistance are partly absorbed by the cable and
partly dissipated from it.
The joules absorbed when the temperature is raised
D F., equal pD, where = 1055 [(specific heat
of conductor X its weight in pounds per foot) +
(specific heat of insulation X its weight in pounds per
foot)]. Hence, the watts absorbed equal
dD
hr
t being the time in seconds.
The watts dissipated per foot of cable when the
temperature rise is D F., are equal to
q being the watts dissipated per foot per degree tem-
perature rise,
288 ELECTRIC POWER CONDUCTORS
Then, if W = watts generated per foot of cable,
W = watts absorbed + watts dissipated
dD
The temperature of the cable rises until the watts
dissipated equal the watts generated, so that when
D = F y the final temperature rise,
or
F-E.
q
Equation (i) may then be written
. w,t+ D . F
q qdf
whence,
dt p i
dD q F-D y
*-> "
q F-D'
lo?
q 10 %F-
The F in the numerator is the constant of inte-
gration and is determined from the condition that
W
when D = o, t must be zero. As F= and W=Pr.
APPENDIX II 289
*
where r is the resistance of the cable in ohms per
foot,
'4
and
F
which is a constant and may be called G.
Substituting for -, equation (2) becomes
Zlog--- ..... (3)
Reducing to minutes, replacing p by P, which is
, and substituting common logarithms for the
I0 55
Naperian,
GP 1 / GP\ . .
2 = 40.5- log (^ i-- j. ... (4)
Writing Z for the logarithm, the equation becomes,
'=40.5 z ...... (5)
The above deduction is based on the assumption
that r is constant. As, however, r varies with the
temperature, the time t will be proportional to the
mean value of -. Hence, we write,
290 ELECTRIC POWER CONDUCTORS
where A is the cross-sectional area in circ. mils and K
is the mean of the reciprocal of the ohms per mil-
foot over the temperature range considered. Hence,
equation (5) reduces to
t = 4o.$PAKGZ ...... (6)
The equation considered above connects the vari-
ables / and /, D being constant. The same equation,
however, may be used to express the relation between
/ and D, I being maintained constant, and for this
purpose is most conveniently written
where Z =logio( i y; j and F is the final temperature
rise with / amperes applied indefinitely.
Experiments on the time element of fuses by
Schwartz and James, detailed in the Journal of the
Institution of Electrical Engineers, July, 1908, p. 71,
may be accurately represented by this equation,
although a range of 180 F. is covered. Thus, with
an enclosed fuse consisting of a No. 27 S. W. G.
copper wire surrounded by Calais sand in a J-inch
fiber tube, the temperature rise is represented by
the current being 20 amperes.
. (From an article by the author in the Electrical
World, 1908.)
APPENDIX III
THICKNESS OF RUBBER INSULATION
The thickness of insulation to be placed on a wire
is governed by three features:
1. Errors in size of wire, eccentric situation of wire
in the insulation, and similar irregularities.
2. Insulation not to be strained by application of
test voltage.
3. Insulation to be thick enough to have mechanical
strength.
ERROR THICKNESS
The thickness of insulation required to make up
for errors and irregularities of manufacture may be
termed the " Error Thickness." This quantity can be
determined in only one way and that is by observa-
tion.
The Rubber-Covered Wire Engineers' Association
have adopted the following values in which the error
thickness depends only upon the size of wire and not
upon the thickness of insulation.
The error thickness used in the N. Y. C. R. R.
specification are based partly upon the Rubber-
291
292
ELECTRIC POWER CONDUCTORS
Covered Wire Engineers' Association values and partly
upon a series of measurements, a curve being plotted
through the mean of the numerous points obtained.
TABLE I
ERROR THICKNESS USED IN SPECIFICATIONS OF RUBBER-
COVERED WIRE ENGINEERS' ASS'.N AND OKONITE CO.
Size of Conductor.
Error Thickness.
1,000,000 to 550,000 C.M.
3/128 in.
500,000 to 250,000 C.M.
2/64 in.
4/0 to i B.& S.
3/64 in.
2 to 7
4/64 in.
8 to 14
5/64 in.
TABLE II
ERROR THICKNESS USED IN N. Y. C. & H. R. R. SPECIFI-
CATIONS
Size of Conductor.
Error Thickness,
Inches.
Size of Conductor.
Error Thickness,
Inches.
14 B.&S.
0.018
250,000 C.M.
-53
12
0.020
500,000
0.063
IO
O.O22
750,000
0.070
8
0.025
1,000,000
0.075
6
0.028
1,250,000
0.080
4
0.032
1,500,000
0.083
2
0.036
1,750,000
0.086
I
0.038
2,000,000 cone.
0.089
0.040
2,000,000 rope
0.095
00
0.042
000
0.045
0000
0.047
APPENDIX III 293
Some engineers believe that the error thickness
depends upon the thickness of insulation, being
greater for heavily insulated cables than for those
lightly insulated. A series of measurements to eluci-
date this point gave uncertain results.
DIELECTRIC STRESS
When a high potential is established across the
insulation of a cable, the insulation is subjected to a
strain which depends upon the degree of concentra-
tion of electric force. When this concentration reaches
a certain value, the insulation will no longer be able
to stand the strain and will break down. It will not
necessarily be punctured, but will be disintegrated
only where the concentration of electrical force has
been excessive. For purposes of analysis, it is usual
to represent the intensity of electric force by the
density of imaginary lines of force stretching radially
from wire to sheath.
Let F = dielectric stress in kilovolts per inch ;
V = test potential, kilovolts ;
/-thickness of insulation, inches, over error
thickness.
Then
V
F= , for a uniform static field of force.
294 ELECTRIC POWER CONDUCTORS
The field of force around a cylindrical wire, how-
ever, is not uniform, the lines extending radially
from the wire to the outside of the insulation. The
density of the force lines is therefore greater at the
surface of the wire than at the outside of the insula-
tion. This explains the well-known fact that small
wires insulated for high potentials often show a dis-
integration of the inner layers of insulation without
any visible defect on the outside. In this case
77-
.434 V
!
rlog
where r is the radius of the wire, inches, and the
logarithm is to the base 10.
This gives
V = 2.3026 Fr log - .
This is not strictly true for stranded cables, the
dielectric stress being from 1.23 to 1.46 times the
value given by the above formula.
The smaller value holds for thick insulation and
the latter for very thin insulation.
(The exact formula for stranded cables, according
to Professor Levi-Civita, is given by E. Jona in the
Transactions of the International Electrical Congress
at St. Louis, 1904.)
APPENDIX III
295
For stranded cables, therefore,
.434 V .585 V
F-I.34SX
, (<+') , (t+r)
r log - r log -
(The figure 1.345 is the mean of 1.3 and 1.46.)
MECHANICAL THICKNESS
The error thickness and the electrical thickness of
insulation are often insufficient for mechanical reasons.
Table III shows the minimum thickness of insulation
which is permitted by mechanical considerations.
The thickness of the insulation on a cable should
never be less than the value given in this table, irre-
spective of what voltage it is designed for. This
table, while based on average practice, may not
meet the requirements of some engineers, and should,
therefore, be carefully examined before it is used.
TABLE III
Diameter of
Mechanical
Diameter of
Mechanical
Conductor,
Thickness,
Conductor,
Thickness.
Inches.
64th Inch.
Inches.
64th Inch.
.0
3
I .2
9
.2
4
1.4
10
4
5
1.6
ii
.6
6
1.8
12
.8
7
2.0
13
I.O
8
296 ELECTRIC POWER CONDUCTORS
INSULATION RESISTANCE
The insulation resistance of a cable is derivable
from the following formula:
where M = megohms per mile ;
5 = specific resistance in megohms per inch cube ;
T = thickness of insulation, inches;
r= radius of wire, inches;
logarithm is to base 10.
This formula is sometimes written
where AT = 58X io~ 7 xS.
The value of K varies from 870 to 23,200 for 5 = 150
and 5 = 4000, respectively. The use of K instead of
5 has the advantage of brevity and is endorsed by
the manufacturers.
In calculating insulation resistance, the total thick-
ness of insulation should be used.
EXAMPLE OF CALCULATION
It is desired to find the thickness of insulation for
a cable to be tested for 15 kilo volts (using a stress of
127 kilovolts per inch), the size being No. 4-0 B. and S.
stranded.
APPENDIX III 297
*
Using the formula
z, .585^
we obtain
Inserting the figures,
log (t + r) ='--- -flog. 23 =1.662.
I27X.23
The error thickness from Table III is .047 ; hence
the total thickness of insulation is
18 .
.2 29 + .047 =.276 = in.
64
In the above case the thickness is well above the
amount required for mechanical strength, which
would be about G / 64 inch. If the thickness had
worked out to an amount less than is required for
mechanical strength, the proper thickness would
have to be taken from Table III.
In such cases the error thickness has to be calcu-
lated and subtracted from T in order to obtain /,
for which the test voltage is calculated.
The table on p. 84 is calculated by the above
method, using a dielectric stress of 57 kilo volts per
inch for the working voltage.
The cables, therefore, normally operate with a
factor of safety of 7, assuming a breakdown stress of
400 kv. per in. The actual factor of safety is liable
298
ELECTRIC POWER CONDUCTORS
to be much below this, as some brands of rubber
compound have a very low dielectric strength.
The megohms per mile, assuming K = 4000, are
377
M = 4000 log
2 3
= 4oooX .421 = 1684.
ONE INCH IN FRACTIONS AND DECIMALS
6 4 th.
32nds.
1 6th.
8ths.
4ths.
Decimal.
6 4 th.
32nds.
1 6th.
8ths.
4ths.
Decimal.
I
o.oi <;625
33
l6J
O '?IC 1 62 C I
2
I
0.031250
74
17
o ^12^0
l
o 04687";
3^
I 7 t
O C4687^
4
2
I
0.062500
36
18
Q
O C62C-OO
c
2*
o 07812^
37
i8i
o ^7812?
6
o 0037 =co
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APPENDIX IV
BASIS OF DIRECT AND ALTERNATING
CURRENT TRANSMISSION FORMULA
BASIS OF DIRECT-CURRENT FORMULAE
Most Economical Distribution of Copper. The formula
for the most economical distribution of copper is
derived as follows:
The current decreases uniformly from the station
to the end of the line, where a drop of V volts is to
be allowed. Required to find the arrangement which
will give this drop with the minimum amount of
copper :
(i) Divide the line into a number of short pieces
of length /.
The current in the first section from the far end
= a/, in the second section 2a/, in the third, ^al, and
so on, where a = amperes taken from the line per foot
of length.
The volume of copper in the first section may be
called yj, in the second y^l, in the third y^l, and so
on, these quantities being c.m.-ft.
300 ELECTRIC POWER CONDUCTORS
The resistance of the first section is Z, of the
y\
second /, of the third - ~/, etc., where IO.E; is
y 2 y*
the ohms per mil-foot.
The drop in the first section is io.5a/ 2 , in the
yi
9 2
second io.5a/ 2 , in the third, io.5a/ 2 , etc.
The total copper = l(y\ + y2 + y$ + , etc.).
Total drop = i o. sal 2 ( + + + , etc. ).
\3 ; i y2 ys
It is required to make l(y\ +^'2+^3 + , etc.) a mini-
mum subject to the condition that/ -- 1 --- h + , etc.)
Vxi y2 y* /
shall be a constant.
Multiply the latter series by a constant P having
the dimensions of a length to the fourth power and
add the two series. The following one is obtained:
P \ /2P \ l$P \
- + y\ ) + - - + y* ) + (- + y* + , et c.
i I \y2 / \ys /
The series l(yi +^2 + ^3 + , etc.), is a minimum when
the above series is a minimum. This occurs when
the differential coefficient of each term with regard
APPENDIX IV 301
*
to its y is zero. Hence differentiating and equating
to zero,
etc. =o.
nP
Now, w/ is x, the distance from the far end, and /
is a constant.
IP
Hence, y = \Vx.
IP
The value of the constant \ must be found. The
drop in dx, which may be called dv, equals current
at distance x from the end multiplied by
10.5 -dx
c.m. at that distance'
Hence,
ax- x = io.$a--=-x = 10.50
--^=-dx = 10.50 v^^/x-dx,
P Vx
A -
2 A / /-
y=- Xio.5 VL- Vx.
302 ELECTRIC POWER CONDUCTORS
This equation gives a parabola of circular mils
that represents the most economical distribution of
copper with uniform drain of current.
This deduction is based upon a modification of the
"Method of Undetermined Multipliers" given in
Chapter XI of Williamson's "Differential Calculus."
FIG. 69,
Resistance with Infrequent Cross-Bonding. Referring
to Fig. 69, the following additional notation is used:
R= equivalent resistance of load;
D-f+g+k.
Using Maxwell's method of imaginary currents the
following four equations are obtained:
An - 3 -/u +IRi=E
Fi 2 dis gi IR = E
ci\ di 2 +Bis =o
fii gi<2 +Di 4: =o
fl - 2 =/
APPENDIX IV
303
Then, using determinants
R
A o -c -f E
F -d -g -E
-c d B o o
-f g o D o
1 i o o I
A o - c -f I
F d g I
c d Boo
-f -g o Do
1 i o o o
R having been obtained by solving the above deter-
minant, is used in the following formula, in which %
is the resistance from the load to the two stations in
multiple :
,.f-*
E
As the expression for R contains , this quantity
cancels out, leaving
DB
304 ELECTRIC POWER CONDUCTORS
By making / = o, g = o, and /* = oo,
B
x -^ ^
which is the formula given on p. 121 with somewhat
different notation.
The formulas for x and R given on p. 122 are
obtained by differentiating R with respect to x,
equating to zero and rearranging the terms.
BASIS OF ALTERNATING-CURRENT FORMULA
With the exception of the problem of determining
the size of wire to use for a given pressure drop,
the solution in each case is given directly by means
of a comparatively simple formula; in the particular
case of determining the size of a wire for a given
drop, an approximation is first obtained and then
the error involved in the approximation determined,
which error, however, will be found negligable in
most practical cases. Moreover, the use of this
particular approximate formula, followed by a deter-
mination of the error involved, has a distinct advan-
tage, since a large error immediately indicates that
the drop for any size of wire within a wide range will
differ only slightly from the permissible drop given,
APPENDIX IV 305
and that therefore, either by allowing a slight increase
in the drop, or, if this is not feasible, by employing
two separate circuits instead of one, a very consider-
able saving in copper can be effected.
The formulas given are all readily derived from the
usual diagram of two impedances in series, namely,
the impedance of the load, and the impedance of
the line, remembering that the ratio of power lost
to power delivered is equal to the ratio of line resist-
ance to load resistance, and that the ratio of the
pressure at the generating end to the pressure de-
livered is equal to the ratio of the total impedance to
the load impedance.
The reactance tables are based upon the fact that
the reactance of a wire for a given frequency can be
considered as the sum of two quantities, one varying
only with the spacing of the wires and the other only
with the size. The resistances have been calculated
for copper of 98% conductivity and for aluminum
of 62% conductivity (Matthiessen's standard, i.e.,
one meter- gram of soft-drawn copper = 0.141729 in-
ternational ohm at o C.), both at 20 C., plus an
increase of i% on account of stranding, temperature
coefficient 0.42% per degree C. The weights given
are the weights of solid wire of equal cross-section
increased i% on account of stranding.
306 ELECTRIC POWER CONDUCTORS
BASIS OF FORMULAE FOR TRANSMISSION LINE WITH RESIST-
ANCE, REACTANCE, LEAKAGE, AND CAPACITY
(H. FENDER.)
Let i = instantaneous value of current at time / ;
V = instantaneous value of difference of poten-
tials between wire and neutral at time t\
1 = distance from load to the point where current
and voltage are being considered;
C = capacity of each line wire to neutral;
L = inductance of each line wire ;
g = leakage susceptance per line wire;
r = resistance per line wire.
The formulae are derived from the following differ-
ential equations :
dV di
from which can be derived by differentiation the
following differential equations of the second order:
d 2 i . di
-=gn + (CV + Lg)-
dV
APPENDIX IV 307
*
These equations are of the form
and are satisfied by the integral relation
= Ae kx cos (wt + hx a).
The various constants can be found by substitut-
ing this integral in the differential equations.
APPENDIX V
BASIS OF FORMULA FOR STRESSES IN SPANS
THE approximate equations for a wire suspended
between two points are
2 r
r 8 /
L =
where D = deflection of wire at center of span in feet
in the direction of the resultant force at
temperature t\
L = length of wire at temperature / under ten-
sion T\
p = ratio of the resultant of weight of wire and
sleet and the wind pressure to weight of
wire ;
m= weight of conductor per cubic inch;
/ = length of span, feet;
pl
APPENDIX V 309
*
Letters with subscript zero refer to corresponding
quantities at temperature fo and tension TQ. Hence,
The relation between the length L of wire at tem-
perature / under tension T to length L r at zero tem-
perature and unstressed, is given by the equation,
Similarly,
where a is the coefficient of expansion per degree.
Combining the last four equations and neglecting
cross products of the term 6m 2 K 2 , , and at, since
these quantities are of the order of io~ 3 or less in
any practical case, we get the following expression,
The graphical method is based upon the above
formulas, the equations of the curves being given in
Chapter IV.
APPENDIX VI
EXPLANATION OF SPECIFICATIONS
i. CABLES FOR AERIAL LINES
SOLID conductors are only used for the smaller
sizes, say up to No. o B. and S., seven strands being
used up to 250,000 c.m. and a larger number for
sizes above that.
The total effective area, of copper is that of the
sum of the individual wires laid out straight and
measured at right angles to their axes, because the
current follows the spiral of the cable without appre-
ciably passing from one strand to another.
The pitch is important on account of its effect
upon the tensile strength of the cable (see p. 17).
Pounds per square inch at the elastic limit divided
by the elongation expressed as a decimal fraction gives
the modulus of elasticity.
The object of the " flexibility " test is to assure
the possibility of making Western Union joints with
solid conductors and to assure the absence of undue
stresses in strands. Theoretically, the wrapping test
should be performed at the lowest temperature to
310
APPENDIX VI 311
- *
which the wire will be exposed in practice, but the
lowest temperature conveniently attainable is 32 F.,
which is accordingly specified.
The permissible excess of area is limited in order
to prevent the manufacturer obtaining the specified
conductivity and strength by using more metal. This
is often done where, as is usually the case, the cable
is sold by the pound, and should be avoided, not only
on account of the extra expense, but also on account
of the decreased strength of the wire per square inch.
2. INSULATED CABLE
General. It is advisable to state the conditions
under which the cable is to be used in order that
the manufacturer may run no chance of misunder-
standing any part of the specifications, thereby
producing a cable unsuitable for the purpose for
which it is intended to be used. Furthermore, it
gives the manufacturer an opportunity to judge
which, of several products fulfilling the specification,
is best suited to the conditions.
Form of Cable. Soft-drawn copper is almost uni-
versally used for insulated conductors in preference
to the hard-drawn product, on account of its com-
parative cheapness and its superior flexibility and
conductivity. Hard-drawn copper is, however, used
for special work, such as long spans of insulated wire.
Solid wire may be used where flexibility is of little
312 ELECTRIC POWER CONDUCTORS
importance but for larger sizes than No. 10 B. and S.
stranded conductors are desirable if they have to be
drawn into conduits. Conductors of 2,000,000 c.m.
area and over are inconveniently stiff even in the form
of concentric cables and are therefore often rope-laid.
Two conductor cables of oval form contain less
lead and filling than round ones, and are therefore
preferred on account of their cheapness.
The lateral fillings not only serve the purpose of
making the cable mechanically solid, but also to
prevent static discharges between the insulation and
the lead; such discharges arising from the steep
potential gradient in the air spaces due to the low
specific inductive capacity of air compared with that
of the insulating compound.
Multiple conductor cables being generally com-
posed of small wires furnished with 'sufficient insu-
lation for their individual mechanical protection,
require some further protection on account of their
greater size and consequent liability of injury in
handling. For this reason a covering of tarred
rope is advised.
The object of one conductor differently colored
from the others is to facilitate the identification of
wires at the opposite ends, care being taken in splic-
ing to first join the ends of the marked wires, and
then join the others in their natural order.
A final insulating belt over the rope serves prin-
cipally to hold the wires and ropes together and
APPENDIX VI 313
to give a smooth surface to the lead or braid cover-
ing. This is very important with lead, as a pro-
jection on the inner surface of the sheath ' greatly
reduces the dielectric strength of the cable.
Conductors. While soft drawn copper of over
100% Matthiessen's standard is obtainable, the
manufacturers have difficulty ' in producing it
steadily, and therefore charge an abnormal price
for it; 98% conductivity is about the best com-
mercially obtainable.
Rubber insulation, owing to its sulphur, attacks
copper, which must therefore be protected by a
coating of metal not affected by sulphur. Var-
nished cambric also affects copper when certain
chemicals are used in the preparation of the oils,
and therefore requires a separator like rubber.
Either tin or unvulcanized rubber containing no
sulphur is used for this purpose.
In stranded conductors the major part of the
current follows the spirals of the strands. The
increase of copper area due to spiralling, therefore,
has no effect in reducing the resistance, and the
effective area of copper is the combined area of
the strands when laid out straight and measured
at right angles to their axes.
Insulation. Many engineers leave the thickness
of insulation to be determined by the manufacturers
from the specified tests. This practice has the
disadvantage of permitting the various competing
314 ELECTRIC POWER CONDUCTORS
manufacturers to present bids based on different
factors of safety with the results that all the manu-
facturers will use as little insulation as possible
and that the lowest bidder will probably be the one
who is using the lowest safety factor. If, on the
other hand, the insulation thickness is specified,
the manufacturer who produces a compound of
higher dielectric strength than his competitors is
reduced to an equality with them, and the buyer
loses an opportunity of obtaining the cheapest
product. This objection, however, is of little weight
at the present time, as little difference exists in the
dielectric strength of different makes of paper and
cambric insulation, and rubber is seldom used under
high dielectric stress.
Taping and Braiding. Rubber insulation cannot
be properly vulcanized without a covering of tape.
The majority of manufacturers vulcanize in a tape
which becomes a permanent part of the insulation,
but some vulcanize in a temporary tape of tin-foil
or other non-adhesive material and put the per-
manent tape on the cold, vulcanized insulation.
In either case, the tape serves as a mechanical
protection by giving a hard surface to the insula-
tion, but its principal function in lead-sheathed
cables is to protect the surface of the insulation
from being burned in the lead press.
Successive turns of the tape should overlap, but
the overlap should be less than half the width of
APPENDIX VI 315
*
the tape, in order to avoid ridges where turns would
be superimposed. On the other hand, the overlap
should be sufficient to insure protection when the
cable is bent to a sharp radius.
Braiding is simply a cheap sheathing for cables
to be used in dry places or where, for any other
reason, lead cannot be used. Six-lea hemp is hemp
yarn having six times 300 yards to the pound, a
lea of hemp being 300 yards.
Sheath. Pure lead is too soft for sheathing, but
alloyed with a small quantity of tin it has excellent
mechanical properties. Two per cent of tin is found to
be ample for this purpose, a greater quantity having
the effect of rendering the metal liable to crystallize.
Armor. Armor is used either as a substitute or
as a protection for sheathing.
When used as a substitute it is usually in the
form of a galvanized steel tape. It is used where
cables are exposed to vibration which would crystal-
lize the sheath metal.
Armor is used as a protection for sheathing on
submarine cables, and on cables intended to be
laid in the ground without ducts. For these pur-
poses galvanized wire is preferable to steel tape owing
to the possibility of putting on a greater thickness
without making the cable too stiff.
Tests. Cable should be immersed for a sufficient
time to enable the water to penetrate anywhere
it could penetrate after the cable is installed. In
316 ELECTRIC POWER CONDUCTORS
the case of rubber or varnished cambric insulation
this requires from twelve to twenty-four hours, but
a very short period is sufficient for paper insulation
as it is very hygroscopic.
The conditions prescribed for the megohms test
constitute a convenient standard, which is univer-
sally accepted.
Capacity Guarantee. Cables of high electrostatic
capacity should be avoided for high tension work on
account of the large charging current they take. The
proposals should therefore be scanned with the view
of eliminating cables of undesirable capacity.
It is seldom necessary to initially specify the
capacity, as the standard products of the manu-
facturers are satisfactory in that respect.
Installation. The 'responsibility for correct cable
lengths should be placed on the contractor whenever
possible, in order to avoid troubles arising from
errors in measurement. Lengths should never be
estimated from subway plans, as splicing chambers
can seldom be built exactly according to plan.
It is advisable to specify the compound to be used
in the sleeves in order to avoid the use of more than
one kind of compound, plurality of compounds giving
rise to trouble in maintenance and repair work.
APPENDIX VI 317
3. THIRTY PER CENT PARA RUBBER COMPOUND
Description of Insulation. The object of specifying
that not more than 33% of rubber, is to be assured
that only Para rubber is used. If an inferior grade of
rubber is used the compound will have to contain
more than 33% rubber to meet the test requirements.
As the permanence of these inferior grades is doubtful
their use should be guarded against. Furthermore, in
the presence of low grade rubber, it is practically im-
possible to determine how much high grade rubber
is in the compound.
The small amount of extract in the gum is the
essential quality which differentiates the finest dry
Para rubber from other kinds. The small amount
of volatile extract specified for the complete com-
pound is to assure the absence of an excess of volatile
matter which w T ould evaporate and leave the insula-
tion dry and also to prevent the over-mastication of
rubber during manufacture.
The amount of sulphur is limited in order to pro-
tect the conductors from corrosion.
Tests. There is some question about the proper
electrical properties which rubber insulation should
possess. From the operating standpoint a very low
insulation resistance should suffice, but it appears
that a high insulation resistance is some indication
of sound homogeneous structure. High insulation
318 ELECTRIC POWER CONDUCTORS
resistance may be secured, however, by artificial
means, such as by the use of paraffine wax, and is
therefore not a reliable indication of quality.
High dielectric strength is very desirable but it is
often obtained at the cost of permanence, it being
possible to greatly increase the dielectric strength
by putting more or less volatile oils in the compound.
High insulation resistance and high dielectric
strength are each strongly recommended by different
manufacturers, but their reasons for doing so are
more commercial than technical.
The remarks under the heading of tests in specifi-
cation No. 2 apply equally to this specification.
The object of making the megohms test of multiplex
cables before assembling, is to have test figures which
can be checked by theory, there being no way of
calculating the insulation resistance of a multiplex
cable. The high voltage test is made before assem-
bling in order to eliminate faulty pieces and after
assembling in order to detect faults which may have
arisen during assembling.
The temperature coefficient of insulation resistance
is specified for two reasons: first, in order to prevent
the manufacturer using a coefficient which will make
any test results agree with the specifications; and
second, because it has been found that compounds
of high temperature coefficient (i.e., over 3% per
deg. F.) generally do not contain 30% Para rubber.
The stretch tests are somewhat arbitrary, being
APPENDIX VI 319
*
founded partly upon manufacturers' recommendations
and partly upon experience with various grades of
rubber. While many excellent compounds entirely
fail to meet this test, it cannot be questioned
that, combined with the restriction in the quan-
tity of rubber, it practically bars objectionable com-
pounds.
The paragraph containing temperature limits is
intended to prevent the heating and. stretching
of rubber prior to tests, a little judicious handling
often having the effect of making a doubtful sam-
ple pass.
4. RUBBER-COVERED WIRE ENGINEERS' ASSOCIA-
TION SPECIFICATIONS FOR THIRTY PER CENT
RUBBER COMPOUND
This specification is a compromise agreed upon by the
principal manufacturers, but while doubtless prepared
in good faith, the number of different compounds
which it is intended to cover is so great that it will
practically pass anything. In other words, this
specification contains no requirement which cannot
be met by all the manufacturers, and this compre-
hensiveness is obtained at the sacrifice of that severity
which makes a specification really useful.
320 ELECTRIC POWER CONDUCTORS
5. and 6. VARNISHED CAMBRIC AND PAPER
INSULATION
These specifications need little explanation beyond
the statement that cambric and paper being staple
articles of manufacture of undoubted permanence
and excellent electrical qualities, they need no fur-
ther specification than a general description. The
insulation resistance may be left to the manufacturer,
provided that it is sufficiently high for successful
operation, but the voltage test should be severe.
APPENDIX VII
BASIS OF TABLES GIVING SELF-INDUCTION
OF PARALLEL WIRES
IT is surprising to note the errors made by technical
writers in their attempts to express the inductance
of a pair of parallel wires, especially since a very
simple and accurate formula has been available in
most of the standard mathematical treatises on elec-
tricity from J. Clerk-Maxwell to Alex. Russel.
The inductance of a circuit is a measure of the
magnetic energy associated with the current in it and
is defined by the well known equation
where E is the energy in the magnetic field inter-
linked with a circuit of inductance L, carrying an
unvarying current i.
This definition gives rise to the following equation:
321
322 ELECTRIC POWER CONDUCTORS
where d = distance apart of wires, center to center;
r = radius of wires in same unit ;
L = inductance of each wire in millihenrys.
The formulae given in Chapter XII are based upon
the above equation.
In the case of a circuit composed of two parallel
wires the size of which is negligible in comparison with
their distance apart, the inductance is approximately
equal to the total flux embraced by the circuit due to
the unit current therein.
This definition, although based upon an approxi-
mation, is often assumed to be exact and used as
the basis of various self-induction formulae.
The flux around a wire is plotted from the well-
known equations
2
B = outside the wire,
r
n AW
and B =- inside the wire,
where B is the flux density, lines per sq.cm. at dis-
tance; r cms. from the center of a long straight wire
of radius R cms. carrying a current of i absolute
units.
When two conductors carrying currents in opposite
directions are brought into proximity, the magnetic
whirls around the conductors are squeezed together
and the axes of the two whirls are pushed away
from the axes of the conductors.
APPENDIX VII 323
-
If the integration is taken between the centers of
wires, a formula containing the term log - - instead
of log - will be obtained; if taken between the
axes of the whirls a very long and complicated for-
mula is obtained.
One of these incorrect formulae is often given in
text-books as exact, and the exact formula derived
from it as an approximation, the authors of these
books neglecting the fact that their original defini-
tion involved an approximation.
It should be noted that where only a part of a
circuit is involved, there may be some magnetic
energy interlinked with it, but originated by the
current in some other part of the circuit. Such
extraneous magnetism adds to the " flux due to
unit current," but not to the magnetic energy asso-
ciated with the current in that part of the circuit
under consideration.
The tables given in Chapter XII are based upon the
fact that the equation for inductance may be resolved
into a sum of two quantities, one of which depends
upon the size of wire and the other upon the distance
apart of the wires, a simple fact first utilized by
H. Fender and published in Foster's " Electrical
Handbook."
The fundamental formula given above may be
resolved into the various forms given below.
324 ELECTRIC POWER CONDUCTORS
Let d = distance apart of wires, center to center;
r = radius of wires in same unit;
L = self-induction of each wire in millihenrys,
or thousandths of a henry.
The logarithms are common, i.e., to the base 10.
L per cm. =.000,000,5 +.000,004,605 log-.
L per in. =.000,001,27 + .000,011,68 log.
L per ft. =.ooo, 01 5, 24 + .000, 140, 3 log-.
L per 1000 ft. =.015,24 +.140,3 log-.
f
L per mile =.o8q,47 +.74111 log-.
L per kilometer = .05 + .460,5 log
For magnetic wires the first constant in each of the
above formulae should be multiplied by permeability
of the wire. An average value of the permeability for
high grade iron telegraph wire is 150, which value has
been used in the formulae given on p. 275.
INDEX
PAGE
Acetone extract 62, 67, 189, 193, 317
Air, dielectric strength 102
Alternating current transmission formulae 133, 304, 306
Alternating current railway feeder calculations 142
Aluminum cable 20
carrying capacity 2, 3, 45
coefficient of expansion . , ' i
compared with copper i
conductivity i, 22
cost 3
elastic limit i
melting-point 1,3
modulus of elasticity i
ohms per mile 137
pounds per mile 140
resistance of cable 137
resistance of wire 27
scrap value 4
specific gravity i
sleet on 3
splicing 228
tensile strength i, 3
wire resistance 27
American or B. & S. gauge 8, 281
325
326 INDEX
American Steel & Wire Co. gauge u
Ampere-feet 108
Annular cable 43
Armor 185, 315
Auxiliary feeders for railways m
Auxiliary feeders infrequently connected to contact conductors... 119
Ayrton, W. E 202, 205
Ayrton and Mather shunt 208
Barium sulphate in rubber 66
Belted triplex cable 91
Birmingham wire gauge 10, 1 1
Block and tackle for cable pulling 222
Bonds 196, 252
Booster 127
Braiding 184, 314
Branches, drop in 108
Breaking strength, see Tensile strength.
Brown & Sharpe gauge: '
approximate rules based upon 28, no
basis of 281
combination of wires of 9
compared with others 1 1
peculiarities no
ratio of 281
size of wires in 8
Brush generator for cable testing 216
Bonds, area of rail holes for 269
brazed 255
cable 260
carrying capacity 262
chemical adhesion 252
classification 252, 253
compressed 257
concealed 258
efficiency of 261
INDEX 327
PAGE
Bonds, equivalent copper area 264
exposed 258
foot 259
head 259
mechanical adhesion 252, 256
pin expanded 257
precautions in installing 264
ribbon 260
single and double 265
soldered 253
solid 260
web 259
welded 255
Buck, H. W., on wind velocity 165
Cable, aluminum, dimensions and weights 20
copper, dimensions and weights 20
definition 13
diameter 15, 20
diameter of wires in 19
effective area of 310
grip 220
length measurement 316
number of wires in 14
resistance 19, 29, 137
space wasted in 18
specifications 1 79, 181, 310
splicing 227, 229
ultimate strength 17
weight 16, 20, 140
Cambric insulation, properties 73
specification 195, 320
test voltage 90
thickness of insulation 90
Capacity, approximation for line 277
effects in transmission line 139, 153, 277
328 INDEX
PAGE
Capacity, guarantees 187, 316
injurious effects of 277
measurement 209
parallel bare wires 278
single overhead wire 279
susceptance 141
three-phase cable 280
two-conductor cable 280
Capstan, for cable drawing 221, 223
Carrying capacity, alternating current cables 43
aluminum 2, 3, 45
annular cables 43
basis of formulae 284
chart 52
effect of number of adjacent cables on 50
intermittent 53
lead-covered cables in ducts 45
multiple-conductor cables 49
short period .* 54
underwriters' rules 44
wires of various metals 50
Cast welding 265
Catenary, equations of 175
Charging current 278
Christie's bridge 200
Circuit-breaker house system 120
Circuit-breakers to protect cables 245
Circular mil 9
Cierk-Maxwell, J 321
Cloth insulation 73
Code compounds 82
Comparison of systems of distribution 105, 106
Compound for cable sleeves 232, 236
Concentric strand, definition 13
Conductivity of atmosphere 102
Conduit wiring 82
INDEX 329
*
PAGE
Connectors 228, 231, 233
Continuous current systems 105, 106
Copper cable, weights and sizes . . . 140
Copper, hard drawn 4
Copper, soft drawn, cable cores 8
mechanical properties 5
solid wire, sizes and weights 8
ultimate strength 7
Copper wire, resistance 24, 25, 26, 137
Copley, A. W 142
Cost of energy 127
Crocker, F. B ^ r
Current density, economical 157
Current value used in feeder calculations 126
Decimal and vulgar fractions 298
Depreciation 238
Deterioration of cables 240
Determinants 35
Dielectric strength of air 102
paper insulation 72
rubber insulation 7!
Dielectric stress 293
Direct current cables in service 77
Direct current short circuits 93
Dissipation of heat from conductors 286
Distribution of copper for economy 115, 299
Distribution of railway load 114
Drawing cables in ducts 220
Drop in mains and branches 108
Economical distributi2n, basis of formula for 299
Economy of conductors 156
Economy in distribution ntj
Edison, gauge I2
five-wire system 105
330 INDEX
PAGB
Edison, three-wire system 105
Electrolysis 240
Electrostatic charges 80
Energy cost 127
English legal wire gauge 1 1
Equations, solution of, by determinants 35
Error thickness 292
Examples of transmission calculations 146
Factors for correction of insulation resistance, cambric 75
paper 72
rubber 65, 192
Faults, locating 213
Feeder calculations, lighting systems 107
railways 115, 142
Feeders for railways 1 1 1
Fisher loop test 214
Flexibility tests 180, 310
Fractions 298
Fuses, carrying capacity 290
Glass insulators 95, 96
Graded cables , 60, 83
Graphical determination of stresses in spans 161
Grounding of cables 78, 80
Hammond, R., on life of cables 238
Hayden, J. L. R., on electrolysis 243
Heating of conductors, see Carrying capacity.
Hewlett insulator 98, 199
Hunting of converters 155
Hysteresis test of rubber 66
Impedance 274
Inductance, of circuits 270
formulae 324
INDEX 331
(
PAGE
Inductance, iron wires 274
parallel wires 321
Insects attacking cables 244
Installation of overhead wires 224
Installation of underground wires 220
Insulated cables underground 76
Insulated negative feeders 241
Insulating sleeves 234
Insulation, general 59
graded 60, 83
paper 71, 87
resistance calculations 296
resistance measurements 210, 212
rubber, see Rubber.
thickness of 82, 84, 87, 89, 291
underground 76
uniform structure 59
Insulators 94, 197
Inverted three-phase system 105
Isolated section of third rail 251
Joining insulated cables 229
Jona, E 294
Kapp's modification of Kelvin's law . . 157
Kelvin's law 112, 156
Kennelly and Fessenden 30
Keiley's (J. D.) circuit -breaker house system 120
Kilovolt 133
Kirschoff's laws 33
Lamp wiring calculations 107
Langan, J 85
Laying, definition 13
Lea of hemp 184, 315
Lead sheath thickness 87, 92
332 INDEX
PAGE
Leakage from railway tracks "... 143
Length of spans 1 75
Length of wire in span 175
Levi-Civita, Prof 294
Lichenstein, L 42
Life of cables in ducts 238
Line capacity, effects of 139, 153, 277
Locating crosses 215
Locating faults 213
Madison River Power Co 95
Mains, calculation of 107
Mather, T. 208
Matthiessen's standard 22
temperature coefficient 31
Maxwell's imaginary currents 33
Mechanical thickness of insulation 295
Megawatt - 133
Megohms, calculation of . 296
Megohms, value of 317
Mershon, R. D 103
Messenger cable, current in 145
Messenger wire construction 226
Missouri River Power Co 94
Modulus of elasticity i, 310
Moisture in cable 229
Most economical distribution of copper 117, 299
Multiplex cables 91, 92, 182, 312, 318
Murray loop test 213
Negative boosters 127
Networks, resistance of 33
New York, New Haven, and Hartford R. R. trolley 142
Ohms per mile, copper and. aluminum 137
Ohms per thousand feet, copper 25, 26
INDEX 333
-
PAGB
Ohms, aluminum 27
Old English wire gauge 1 1
Oval duplex cables 182, 312
Overhead circuits, inductance 270
Ozite 196, 236
Paper insulation, dielectric strength 72
general 71
hygroscopic nature of 71
in cold weather 88
installed vertically 82
resistance and time of electrification 73
specifications 196, 320
temperature coefficient of resistance 72
thickness of 87
triplex cables 91
underground 76
water in 72, 76
Para rubber 62
Paraffin wax 236
Pender, H., alternating current transmission 133, 153, 304, 306
Kelvin's law 157
slide rule method for temperature resistance calculations 32
wire spans 159, 308
Permissible potential drop in
Petticoat insulators 95
Pin, eucalyptus 102
locust 102
Long Island R. R 101
standard A. I. E. E 102
Pin shield insulators 95
Pitch, definition 13
diameter, definition 13
factor, definition 13
minimum 17
standard 16
334 INDEX
PAGE
Polyphase systems 105
Porcelain, absorption 95, 190
insulators 94
Potential drop and car lights in
Potential, importance of high 104
Potential tests, cambric 90
Paper 87
rubber 85, 87
Power factor 133, 135
Power loss calculations 133
Pressure drop calculations 107, in, 133
Protection from electrolysis 240
Quarter-phase systems 105, 106
Racks for cables 78
Rail bonds 252
Rail-bond specifications 196
Rail reactance ' 143
Railway circuits , in, 245
Railway feeders, underground 76
Reactance, circuits 270
excessive 136
increment 137
per mile of No. oooo wire 134
single-phase trolley 144
tables 273
Reeling, effects of, upon insulation 88
Resistance, aluminum wire 27
copper 23
copper wire 25, 26
increase of > due to spiralling 29
with infrequent cross-bonds 119, 302
Resistance measurements, accuracy of 205
differential galvanometer 203
substitution 204, 210
INDEX 335
PAGE
Resistance measurements, voltmeter and ammeter 202
Resistances, plug type 205
Reichsanstalt 207
standard 205
Roberts, E. P., wiring slide rule 109
Root -mean -square 126
Rope strand, definition 13
Rotary converters and line drop 155
Rubber 62
Rubber-covered wire, Engineers' Association specification,
86,87, 193, 3i9
Rubber insulation, albumin in 70
black or white 70
desirable qualities 61
dieletric strength 71
effect of light upon 69
effect of high temperature 67, 68
equilibrium of 61
for high-tension service 194
general 60
hysteresis test 66
insulation resistance 65, 86, 296
litharge in 71
megohms 65, 86, 296
over-mastication 69, 31 7
photo-sensitiveness 69
potential tests - - - 85, 87
resinous matter in 67
set after 'stretching 64
specific resistance 65, 296
specifications 189, 193, 317
stretch test 64, 191, 193, 318
submarine 81, 91
sulphur in 66
temperature coefficient of resistance 65, 192
tenacity and temperature 68
336 INDEX
PAGB
Rubber insulation, tensile strength 63
thickness of 84, 85, 291
triplex 91
U. S. Navy 63
under water 69, 91
weathering 70
Russel, A 280, 321
Ryan, H. J 102
Sag in spans 159, 161, 308
Schwartz, A 68
Self-induction 270, 321
Sheath, composition 184
melted by current 76
thickness 87, 92
Shoddy, use of 189
Short circuits 77, 79
Short circuit indiactor 93
Short period carrying capacity 54, 287
Shunts 207
Signal circuits and grounding 79
Single-phase railway feeders 142
Size of conductors 104
Size of wire for lighting 107
for transmission 133
Skin effect 40, 284
Sleeves for cable joints 230, 232
Sleeves, settlement in 188
Slide rule for wiring calculations 109
Solid system 79
Soxhlet extractor 193
Spans, calculations for 159
equations of 1 75
length of 175
stresses in 159, 308
Specifications for bare cables 179, 310
INDEX 337
PAGB
Specifications for insulated cables 181, 311
high-tension insulator 197
paper insulation 196, 320
rail bonds 196
rubber insulation 189, 193, 317, 319
varnished cloth 195, 320
Spiralling, increase of resistance due to 29
Splicing 227, 312
Splicing diagram 235
Square root of mean square 126
Static discharges in cables 80, 312
Steel taping 185
Steinmetz, C. P 106
Strand, see Cable.
definition 13
diameter of wires in 19
Stranded conductors, dielectric stress in 294
Stranding, definition 13
Stress in dielectric 293
Stresses in spans 159, 161, 308
Stretch test for rubber 191, 194, 318
Stubb's wire gauge 10, 1 1
Submarine cables 81
Sulphur in rubber insulation 66
Systems of distribution 104
Tangents and cosines 139
Tape on rubber insulation 314
Tape, width of 83
Taping 184, 314
Temperature coefficient of resistance, cambric 75
metals 30
Paper 72
rubber 65, 192, 318
Temperature resistance calculations 30, 32
Testing for capacity 209
338 INDEX
PAGE
Testing for inductance 202
insulation resistance 210, 212
resistance, see Resistance.
Tests on insulated cable 185
Tests on rubber insulation 190, 317
Thermit welding 266
Three-conductor cables 91, 92
Three-phase systems 105, 106
Three-wire system no
Thickness of insulation, calculation of 291
cambric 89, 90
paper 87
reasons for specifying 314
rubber 84, 85, 87, 291
Third rail circuits 245
sectionalizing 246
Tin in sheathing 315
Tinning copper 231
Transmission calculations, alternating currents 133
basis of 304, 306
direct current lighting 107
direct current railways in
exact method with capacity and leakage 153, 306
Triplex cable, belted and unbelted 91
diameter 92
Trolley calculations, alternating current 142
Underground cables 76
Universal shunt 208
Uplift on poles 1 70, 1 76
Value of cable after installation 238
Varley loop test 215
Varnished cloth or cambric, effect of oil upon . 74
flexibility 74
general 73
INDEX 339
*
PAGE
Varnished cloth or cambric in sunlight 82
subjected to vibration 74
temperature coefficient 75
thickness 89, 90
Vertical stresses on poles 170, 176
Volatile matter in rubber 317
Voltage drop equations 125
Voltage drop and synchronous apparatus 155
Voltages for transmission 104, 107
Voltax 196, 236
Volume unit, circular-mil-foot 1 16
Washburn and Moen gauge 1 1
Water, cables under 81
Watts lost, equations of 118, 125
Weber, C. O 67, 69, 70, 71, 193
Welded rail joints 265, 266, 268
Welding, Thermit process 266
Wheatstone's bridge 200
Winch for cable drawing 221
Wind velocity '. 165
Wiping sleeve joint 234
Wire, calculation of tables 282
gauges ii
resistance, ohms per 1000 feet 25, 26, 27
resistance, ohms per mile 137
size for lighting 107
spans, stresses in 159
Wiring of ducts 187, 220
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WADE, E. J. Secondary Batteries: Their Theory, Construction, and Use.
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WALKER, FREDERICK. Practical Dynamo-Building for Amateurs.
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WALMSLEY, R. M. Electricity in the Service of Man. A Popular and
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WATSON, A. E. Storage Batteries, their Theory, Construction and Use.
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WATT, ALEXANDER. Electroplating and Refining of Metals. New
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WEBB, H. L. A Practical Guide to the Testing of Insulated Wires and
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WEEKS, R. W. The Design of Alternate-Current Transformer.
New Edition in Press
WEYMOUTH, F. MARTEN. Drum Armatures and Commutators.
(Theory and Practice.) A complete treatise on the theory and con-
struction of drum-winding, and of commutators for closed-coil arma-
tures, together with a full resum6 of some of the principal points
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WILKINSON, H. D. Submarine Cable Laying and Repairing. Second
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YOUNG, J. ELTON. Electrical Testing for Telegraph Engineers. Illus-
trated. 8vo., cloth, 264 pp Net, $4.00
ZEIDLER, J., and LUSTGARTEN, J. Electric Arc Lamps: Their Princi-
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OCT 25 193
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