Figs. 830 and 831.—Symmetrical and unsymmetrical distribution. When a main is supplied by a feeder, the junction of the two, if practicable, is located at the electrical center of the main, as indicated in fig. 830, so that the distribution is symmetrical, that is, the ampere feet each way from the junction are the same. This is nearly always practicable in surface wiring, and when it is practiced it is only necessary to calculate the wire size for one-half of the main, as the other half is identical. In fig. 830 there are four lamps on each side of the junction, J; the center of each group is at a distance, M, so that the lamp feet in each half of the main are 5 × M. The lamp feet of the feeder would be 10 × N, N being the distance from the feeder fuse block to the junction, J. In concealed work, however, it does not always happen that a feeder can be made to join a main at its electrical center; when this is not practicable, each end of the main should be figured separately. In fig. 831, for instance, the main has five lamps on one side and two on the other, and the distances from the junction to the centers of the two groups are at unequal distances S and S'. If the distance S be 14 feet, and the lamps, 16 c. p., the lamp feet in the left hand main equals 5 × 14 = 70, while in the main to the right, taking S' at 10 feet, there are only 2 × 10 = 20 lamp feet. Hence what appears to be one continuous main in this case would have to be treated as two mains, and each part figured separately.

circular mils = I × feet × 21.6 E = amperes × feet × 21.6 "drop" . . . . (5)

The following practical example is given to illustrate the application of the formula just obtained:

EXAMPLE.—What size wire should be used on a 250 volt circuit to transmit a current of 200 amperes a distance of 350 feet to a center of distribution with a loss of three per cent. under full load?

The volts lost or drop is equal to 250 × .03 = 7.5 volts.

PROPERTIES OF COPPER WIRE
Number
of gauge
B. & S.		 Diameter
in
mils		 Area in
circular
mils		 Weight in pounds Resistance at 68° Fahr.
1,000 feet mile Feet per
pound		 1,000 Feet mile
0000 460 211,600 640.5 3,381 1.561 .04893 .2583
000 409.6 167,800 508 2,682 1.969 .06170 .3258
00 364.8 133,100 402.8 2,127 2.482 .07780 .4108
0 324.9 105,500 319.5 1,687 3.130 .09811 .5180
1 289.3 83,690 253.3 1,337 3.947 .12370 .6531
2 257.6 66,370 200.9 1,062 4.977 .1560 .8237
3 229.4 52,630 159.3 841.1 6.276 .1967 1.0386
4 204.3 41,740 126.4 667.4 7.914 .2480 1.3094
5 181.9 33,100 100.2 529.0 9.980 .3128 1.6516
6 162.0 26,250 79.46 419.5 12.580 .3944 2.0824
7 144.3 20,820 63.02 332.7 15.87 .4973 2.6257
8 128.5 16,510 49.98 263.9 20.01 .6271 3.3111
9 114.4 13,090 39.63 209.2 25.23 .7908 4.1754
10 101.9 10,380 31.13 166.0 31.82 .9972 5.2652
11 90.74 8,234 24.93 131.6 40.12 1.257 6.6370
12 80.81 6,530 19.77 104.4 50.59 1.586 8.374
13 71.96 5,178 15.68 82.79 63.79 2.000 10.560
14 64.08 4,107 12.43 65.63 80.44 2.521 13.311
15 57.07 3,257 9.858 52.05 101.4 3.179 16.785
16 50.82 2,583 7.818 41.28 127.9 4.009 21.168
17 45.26 2,048 6.200 32.74 161.3 5.055 26.690
18 40.30 1,624 4.917 25.96 203.4 6.374 33.655
19 35.89 1,288 3.899 20.59 256.5 8.038 42.440
20 31.96 1,022 3.092 16.33 323.4 10.14 15.340

Substituting the given value in formula (5)

circular mils = 350 × 200 × 21.6 7.5 = 201,600.

Diameter = 2 √201,600 = 449 circular mils or .449 in.

From the table (on page 731 or on page 742) the nearest (larger) size of wire is 0000 B. & S. gauge.4

WIRING TABLE FOR LIGHT AND POWER CIRCUITS
VOLTS PERCENTAGE OF LOSS
2000 1.7 1.5 1.4 1.2 1.1 1.0 0.75 0.5
1000 3.4 2.9 2.7 2.4 2.2 2.0 1.5 1.0
500 6.5 5.7 6.2 4.8 4.3 3.9 2.9 2.0
220 13.7 12.0 11.0 10.3 9.3 8.3 6.5 4.4
110 — — 20.0 18.5 17.0 15.4 12.0 8.4
52 — — — — — — 22.4 16.1
VOLTS PERCENTAGE OF LOSS (continued)
2000 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05
1000 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
500 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2
220 3.9 3.5 3.1 2.7 2.2 1.8 1.4 0.9 0.45
110 7.6 6.8 6.0 5.2 4.4 3.5 2.7 1.8 0.9
52 14.7 13.3 11.8 10.3 8.8 7.1 5.5 3.7 1.9
ACTUAL VOLTS LOST
Carrying
Capacity
Amperes.		 Size
B. & S.		 35 30 27.5 25 22.5 20 15 10
300 0000 345800 296400 271700 247000 222300 197600 148200 98800
245 000 274400 235200 215600 196000 176400 156800 117600 78400
215 00 217525 186450 170912 155375 139837 124300 93225 62150
190 0 172550 147900 135575 123250 110925 98600 73950 49300
160 1 136850 117300 107525 97750 87975 78200 58650 39100
135 2 108500 93000 85250 77500 69750 62000 46500 31000
115 3 86100 73800 67650 61500 55350 49200 36900 24600
100 4 68250 58500 53625 48750 43875 39000 29250 19500
90 5 54250 46500 42625 38750 34875 31000 23250 15500
80 6 43050 36900 33825 30750 27675 24600 18450 12300
60 8 26965 23130 21202 19275 17347 15420 11565 7710
40 10 16975 14550 13337 12125 10912 9700 7275 4850
30 12 10675 9150 8388 7625 6862 6100 4575 3050
22 14 6720 5760 5280 4800 4320 3840 2880 1920
55 16 4235 3630 3328 3025 2723 2420 1815 1210
ACTUAL VOLTS LOST (continued)
Carrying
Capacity
Amperes.		 Size
B. & S.		 9 8 7 6 5 4 3 2 1
300 0000 88920 79040 69160 59280 49400 39520 29640 19760 9880
245 000 70560 62720 54880 47040 39200 31360 23520 15680 7840
215 00 55935 49720 43505 37290 31075 24860 18645 12430 6215
190 0 44370 39440 34510 29580 24650 19720 14790 9860 4930
160 1 35190 31280 27370 23460 19550 15640 11730 7820 3910
135 2 27900 24800 21700 18600 15500 12400 9300 6200 3100
115 3 22140 19680 17220 14760 12300 9840 7380 4920 2460
100 4 17550 15600 13650 11700 9750 7800 5850 3900 1950
90 5 13950 12400 10850 9300 7750 6200 4650 3100 1550
80 6 11070 9840 8610 7380 6150 4920 3690 2460 1230
60 8 6939 6168 5397 4626 3855 3084 2313 1542 771
40 10 4365 3880 3395 2910 2425 1940 1455 970 486
30 12 2745 2440 2135 1830 1525 1220 915 610 305
22 14 1728 1536 1344 1152 960 768 576 384 192
55 16 1089 968 847 726 605 484 363 242 121

RULE.—Multiply current in amperes by single distance and refer to the nearest corresponding number under column of actual volts lost, to find size of wire. It should also be noted that the underwriters prohibit the use of wire smaller than No. 14 B. & S. gauge, except as allowed for fixture work and pendant cord.

TABLE OF WIRE EQUIVALENTS
GAUGE
B. & S.		 NUMBER OF WIRES
2 4 8 1
6		 3
2		 6
4		 1
2
8		 2
5
6		 5
1
2		 1
0
2
4		 2
0
4
8		 4
0
9
6		 8
1
9
2		 1
6
3
8
4
0000 0 3 6 9 12 15 18 21 24 27 30 33 36 39
000 1 4 7 10 13 16 19 22 25 28 31 34 37 40
00 2 5 8 11 14 17 20 23 26 29 32 35 38 0+6
0 3 6 9 12 15 18 21 24 27 30 33 36 39 1+7
1 4 7 10 13 16 19 22 25 28 31 34 37 40 2+8
2 5 8 11 14 17 20 23 26 29 32 35 38 3+9 4+6
3 6 9 12 15 18 21 24 27 30 33 36 39 4+10 5+7
4 7 10 13 16 19 22 25 28 31 34 37 40 5+11 6+8
5 8 11 14 17 20 23 26 29 32 35 38 6+12 7+9
6 9 12 15 18 21 24 27 30 33 36 39 7+13 8+10
7 10 13 16 19 22 25 28 31 34 37 40 8+14 9+11
8 11 14 17 20 23 26 29 32 35 38 9+15 10+12
9 12 15 18 21 24 27 30 33 36 39 10+16 11+13
10 13 16 19 22 25 28 31 34 37 40 11+17 12+14
11 14 17 20 23 26 29 32 35 38 12+18 13+15
12 15 18 21 24 27 30 33 36 39 13+19 14+16
13 16 19 22 25 28 31 34 37 40 14+20 15+17
14 17 20 23 26 29 32 35 38 15+21 16+18
15 18 21 24 27 30 33 36 39 16+22 17+19
16 19 22 25 28 31 34 37 40 17+23 18+20
17 20 23 26 29 32 35 38 18+24 19+21
18 21 24 27 30 33 36 39 19+25 20+22
19 22 25 28 31 34 37 40 20+26 21+23
20 23 26 29 32 35 38 21+27 22+24
21 24 27 30 33 36 39 22+28 23+25
22 25 28 31 34 37 40 23+29 24+26
23 26 29 32 35 38 24+30 25+27
24 27 30 33 36 39 25+31 26+28
25 28 31 34 37 40 26+32 27+29
26 29 32 35 38 27+33 28+30
27 30 33 36 39 28+34 29+31
28 31 34 37 40 29+35 30+32
29 32 35 38 30+36 31+33
30 33 36 39 31+37 32+34
31 34 37 40 32+38 33+35
32 35 38 33+39 34+36
33 36 39 34+40 35+37
34 37 40 36+39
35 38 37+39
36 39 38+40
37 40

Ques. If the calculated size of wire be larger than any in the table how is the required area obtained?

Ans. By using two or more smaller wires in parallel, whose combined area is equal to the required area.

To facilitate finding the equivalent sizes the above table of wire equivalents has been prepared.

Ques. How is the table of wire equivalents used?

Ans. To use the table, find in the vertical column at left the size of conductor desired; then follow along horizontally until the size of wire that is desired to use for the strands, and the corresponding number at top of column will give the number of strands of that size wire required.

Fig. 832.—Break down switch for use on three wire circuit, enabling it to be operated break down fashion with the two outers connected together and the neutral wire serving as one side of the resultant two wire circuit. Such circuits must be figured as two wire installations of one half the three wire voltage. The size of the neutral wire of a three wire circuit depends on conditions of operation. Three wire circuits for occasional two wire working, must have a neutral wire whose cross section is equal to the combined cross sections of the two outer wires. This plan is useful for buildings supplied from a central station, as it will be satisfactory for two wire operation in emergencies, and for three wire, two phase or three phase distribution should the central station ultimately be changed over to either of those alternating current systems. The expense for the extra copper in the beginning will not be nearly so great as that entailed by a change in the wiring later on should developments require it. It is permissible, however, to make the cross section of the neutral wire smaller than that of each outer wire, if one be reasonably sure that there will never be any changes such as those just mentioned, and if the drop in the two outer wires do not exceed 1½ per cent. Under such conditions, it will be found a very good rule to calculate the neutral wire of a principal feeder for a maximum unbalancing of 25 per cent, that is, a condition under which the current in one outer wire will be 75 per cent of the current in the other one, the current in the neutral being 25 per cent of that in the heavier loaded outer wire.

Ques. What is the significance of the zig-zag line?

Ans. The figures below this line give the gauge numbers of two wires which will have the same conductivity as the corresponding conductor in left hand column.

TABLE OF CABLE CAPACITIES

Fig. 833.—Diagram showing capacities of cables for both open and concealed work as allowed by the underwriters.

Incandescent Lamps on 660 Watt Circuits.—The standard incandescent lamp is rated as equivalent to the light given by 16 candles, and may consume, according to type and make, from 50 to 56 watts, or from 3.1 to 3.5 watts per candle power. Therefore, a 660 watt circuit will carry thirteen 16 candle power 49.6 watt lamps, or eleven 56 watt lamps.

Fig. 834.—Diagram showing symmetrical and unsymmetrical distribution. The two 5 lamp centers are located at equal distances from the distributing pocket or cabinet, P, so that the sub-feeders, A and A', have equal values of lamp feet. The sub-feeders, B, B', have equal lengths, but as one supplies 10 lamps, and the other 16, the lamp feet are different, and each sub-feeder must therefore be figured separately. The main, G, should be considered as a part of the sub-feeder, B, in order to avoid the necessity for a fuse at the junction of the two. As it is symmetrically divided, only one-half of it would be considered. Thus, if the sub-feeder, B, were 50 feet long, and the main, G, 30 feet long, B would have 16 × 50 = 800 lamp feet and one-half of the main would have 8 × 15 = 120 lamp feet (assuming all 16 c. p. lamps). Hence 800 + 120 = 920 lamp feet should be taken as the load length and the proper size wire used for that figure, making the sub-feeder, B, of the same size as the main, G. The same procedure applies to the sub-feeder B' and main G'; also to the sub-feeder, E, and the main, F. The proper sizes of wire for the different circuits is easily found from the lamp feet table, after having calculated the lamp feet assigned the drop.

Figs. 835 and 836.—The "tree" and "modified tree" systems of wiring. The tree system consists of a feeder reducing in size and supplying mains for each floor, the general arrangement resembling the trunk and branches of a tree. Since fuses must be inserted on each floor where the size of the feeder is reduced, the system requires a large number of joints, and in the event of a fuse blowing it could not be quickly located. The tree system is not to be recommended, as it results in considerable drop, and at full load the lamps nearest the point of supply will either burn too brightly or those more remote will not give the rated candle power. In the modified tree system, fig. 836, the size of the feeder is not reduced. With this arrangement the losses are considerably reduced owing to the much smaller losses on the feeder between those centers farthest away from the point of supply.

The proper size of wire for a 660 watt circuit will depend upon the voltage for which the lamps are made. For example: a 16 candle power lamp which consumes 56 watts on 110 volt circuit will take, 56 ÷ 110 = .5 or ½ ampere of current, while the same lamp, if made for 220 volts, will take only 55 ÷ 220 = .25 or ¼ ampere. Therefore, eleven 16 candle power 56 watt lamps will require a current of 5½ amperes at 110 volts, or 2¾ amperes at 220 volts.

According to the laws of resistance, the resistance of a round wire is inversely proportional to the square of the diameter, and if the circuit be taken at 100 feet, and the allowable percentage of drop at 1 volt, then according to formula, (5) on page 748, the wire required for a circuit carrying eleven 16 candle power 56 watt 110 volt lamps, will have a cross sectional area of,

5.5 × 100 × 21.6 1 = 11,880 circular mils.

while the same number of lamps on a 220 volt circuit will require wire having a cross sectional area of,

2.75 × 100 × 21.6 1 = 5,940 circular mils.

In order to conform to the underwriters' requirements, No. 8. B. & S. gauge, wire must be used for the circuit carrying the 110 volt lamps, while No. 12, B. & S. wire, would be sufficient for the 220 volt circuit.

In the case shown in fig. 829, the branch circuits A and B are identical, each supplying four 16 candle power lamps requiring 3.5 watts per candle power at 110 volts or carrying a load of 4 × 16 × 3.5 = 224 watts, = 224 ÷ 110 = 2 amperes.

Fig. 837.—Distribution with sub-feeders (multi-center distribution). The feeder connects at a central point, A, with several sub-feeders which run to distributing centers, as at B, C, D, and E. With this arrangement, compound wound dynamos may be so designed that the pressure at A will remain nearly uniform for all loads. If, for instance, the wiring be proportioned for 2% drop, the dynamos may be over compounded to that extent, and the even illumination will compensate for the extra cost in the installation.

The distance from the feeder junction or cut out to the electrical center of each branch circuit is 12.5 feet. The compact area of distribution permits the reduction of the loss of volts to 1 per cent, or 110 × .01 = 1.1 volts "drop." Then substituting in formula (5) on page 748 the values for amperes, feet and drop as obtained above

2 × 25 × 21.6 1.1 = 981 circular mils,

or a value far below that of even No. 18 wire, B. & S. gauge (see table on page 731), but the smallest wire allowed by the underwriters for the mains A and B is No. 14, B. & S. gauge.

In calculating the size of wire for the feeders the total load must be considered. This is equal to eight 16 candle power lamps, requiring 3.5 watts per candle power at 110 volts = 8×16×3.5 = 448 watts = 4 amperes.

The distance from the entrance cut out to the feeder cut out is 200 feet. The drop should not be greater than 1.5 per cent. or 110×1.5 = 1.6 volts. Then,

4×200×21.6 1.6 = 10,800 circular mils

a value which indicates that No. 8 wire, B. & S. gauge, must be used for the feeders in order to keep the drop within the limit of predetermined value.

TABLE FOR TAPS, BRIDGES OR OTHER WIRES AT NEGLIGIBLE DROP
Wire Nos. 0 1 2 3 4 5 6 7 8 9 10 12 14 16 18
Lamp 52 v. 300 260 200 160 130 100 80 65 50 38 24 15 9 6
Feet 110v. 1,280 1,085 860 680 560 435 345 280 220 160 100 60 40 25

NOTE.—In using this table, it is only necessary to calculate the lamp feet of the tap and take the size of wire corresponding to the nearest greater number of lamp feet in the table. The lamp feet specified by this table should not be exceeded by more than 10 per cent. Thus, if a tap measure 108 lamp feet, in 110 volt lamps, No. 12 wire would be used. But if it measure 115 lamp feet, it would be advisable to use No, 10 wire.

Constant Voltage Arc Lamp Circuits.—The branch conductor should have a carrying capacity about fifty per cent. greater than the normal current required by the lamp, so as to provide for the heavy current required when the lamp is started. The underwriters prohibit the use of any size wire under No. 12 for parallel connected arc light circuits.

Constant Current Series Arc Lamp Circuits.—The wiring for series connected arc lamps should never be concealed nor encased unless requested by the electrical inspector.

For all interior wiring of this class, approved rubber covered wire should be used, and the wire should always be rigidly supported on porcelain or glass insulators which will hold the wires at a distance of at least one inch from the surface wired over. The wires on all circuits up to 750 volts, should be kept at least 4 inches from each other, and 8 inches apart on circuits of over 750 volts. No wires carrying a current having a pressure exceeding 3,500 volts should be carried into or over any building except central stations and sub-stations.

Fig. 838.—Diagram showing "bridge wiring." This method is used in the case of two parallel mains where one feeder is ample for both. The feeder is run to a central point as shown and connected to the two mains by a so called "bridge." The arrangement clearly gives good distribution and effects a saving in copper and labor, for if the bridge were omitted, two feeders would be necessary.

Wire Calculations for Motors.—The proper size of wire for a motor may be readily determined by means of the following formula:

circular mils = H.P. × 746 × D × 21.6 E × L × K . . . . (6)

in which

H.P. = horse power of motor;
746 = watts per H.P.;
D = length of motor circuit from fuse block to motor;

21.6 = ohms per foot run in circuit where wires are one mil in diameter;
E = voltage at the motor;
L = drop in percentage of the voltage at the motor;
K = efficiency of the motor expressed as a decimal.

The average values for K are about as follows: 1 H.P., .75; 3 H.P., .80; 5 H.P., .80; 10 H.P. and over, 90 per cent.