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ondaries of transformers of different sizes, being half loaded on the average. The primaries are supplied by two No. 2 wires from the generator two miles distant, the wires being 18 inches apart, and the frequency of 125 periods per second. The voltage of the lamps is 100, and the ratio of transformation is 10. In Fig. 181 the horizontal lines represent energy components, and the vertical lines inductive components of E.M.F. For the sake of uniformity the lamp voltage is multiplied by 10, the ratio of transformation making 1000 volts, which is represented by the horizontal line AB, since incandescent lamps are practically non-inductive. Assuming the secondary wiring to have an energy loss of 3 per cent, BC is laid off as 30 volts, and an inductance component CD, of the same amount. (Both of these are rather high values.) Take the resistance in the transformers at 1 per cent, and the inductance loss at

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Fig. 181. Graphical Calculation of Alternating Current Circuit.

one-half load as 12.5 per cent of AD, or about 13 per cent. Hence we lay off DF = 10 volts to represent resistance, and FG = 130 volts to represent inductive loss in the transformers. If there were no losses in the transformers, the current received by them would be 28.75 amperes, but with 5 per cent iron loss at half-load this becomes 30.19 amperes. The resistance of four miles of No. 2 wire from the table on page 8 is .156 x 5.28 x 4 = 3.3 ohms, and the reactance at 125 cycles is . 249 x 5.28 x 4 = 5.25 ohms. To this we add 15 per cent for distortion of current waves, making 6.04 ohms. The resistance drop is 30.19 .33 = 99 volts, and the reactance drop is 30.19 x 6.04 = 1.82 volts, which are laid off as GH and HK. Hence the line A K represents the E.M.F. required at the generator terminals, being 1188 volts. Extending KH to J, we have AJ the total energy component of 1139 volts, therefore the real power in the circuit is 11.39 x 30.19 = 34,300

watts, while the volt-amperes at the generator are 35,800, so that an alternator of 36 k.w. capacity will be required; but the power to drive it, assuming its efficiency at 90 per cent, will be 34.3 • .90 = 38 k.w., or 51 h.p. The generator should be overcompounded about 19 per cent to be self-regulating.

Arithmetical Determination. — The same result that has been obtained graphically may be found arithmetically, as follows :

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1139 342 Taking the square root of the sum of the squares of 1139 and 312, we find 1188 volts to be the E.M.F. pressure at the generator terminals, being the same as obtained by measurement in Fig. 181.

CHAPTER XII.

OVERHEAD CONDUCTORS.

The term overhead conductors is applied to aerial electrical wires or cables carried on poles or upon brackets or other supports attached to buildings. The same general construction is used for telegraph and telephone, as well as for electric light and power lines; but the parts are usually heavier, and the insulation higher, in the case of the two latter, because of the larger size of the conductors and the more powerful character of the currents.

Materials for Overhead Conductors. — For electric light and power purposes copper is generally employed, and has now largely supplanted iron wire even for telegraph and telephone lines. The fact that hard-drawn copper has a tensile strength of 60,000 to 70,000 lbs. per square inch, compared with 25,000 to 35,000 for soft or annealed copper, makes it especially suitable for overhead construction. On the other hand, the specific resistance of hard copper is from 2 to 4 per cent greater, and it is much more brittle, so that it is not used for underground conductors or interior wiring where its greater tensile strength is not of much advantage. The fact that it is far less flexible makes it awkward to handle ; consequently, hard copper is not convenient even for overhead conductors when they are of large size, or are covered with insulation. The resistances, weights, and other data of copper wires are given on pages 8 and 15, and in Chapter XI.

Aluminum has a specific resistance about .6 that of copper, both being of pure commercial quality, therefore the sectional area of equivalent conductors would be about 1.67 times and the diameter 1.3 times greater for aluminum. The specific gravity of aluminum is about 2.7, and of copper 8.89 (page 8), so that an equal volume of the latter weighs 3.3 times as much. A copper wire would be (3.3 + 1.67 = 2) about twice as heavy as an aluminum wire of the same length and resistance. This is a great advantage for overhead conductors, since it reduces the weight on poles, cross-arms, insulators, etc., by one-half.

The tensile strength of aluminum wires is about 20,000 to 30,000 lbs. per square inch ; but the addition of a small percentage of copper increases this considerably, and alloyed with 24 per cent of copper it becomes nearly 40,000 lbs. per square inch. On the other hand, the resistance is increased about 20 per cent, so that the advantage is doubtful. Furthermore, it has been found in practice that wires made of these alloys are likely to break, even when the tests of a sample show an ample tensile strength. This is due to the difficulty of making perfect alloys of aluminum, because the light metal does not readily form a thorough and homogeneous mixture with the copper, which has a density 3.3 times greater. The result is that flaws seem to exist at certain points on the wire, and a break may occur without excessive strain. In a case cited by Mr. P. N. Nunn * an average of one break per span occurred on a long transmission line composed of aluminum alloy.

The following data for commercially pure aluminum wire are taken from the paper itself, and agree closely with those already given :

Diameter of aluminum wire . . . . . . 293.9 mils.
Wt. per mile . . . . . . . . . . . . 419.4 lbs.
Resistance per mil foot ....... 17.6 ohms at 25° C.
Resistance per mile at 25° C. ... ... 1.00773 ohms.
Conductivity compared with copper ... 59.9% by dimension.
Tensile strength of wire . . . . . . . 1549 lbs.
No. of twists in six inches for fracture.17.9.
Tensile strength per square inch . . . . 32898.

Comparing this with copper, it is seen that this wire is approximately the same as copper in the following sizes :

Size of aluminum wire = No. 1 B. & S. copper.
Resistance of “ “ = No. 3 “ “
Tensile strength “ “ = No. 5 " "
Weight of “ “ = No. 6 " "

Therefore on the basis of the same conductivity the aluminum compares with copper as follows:

* Discussion of a paper “On the Use of Aluminum Line Wire," by Perrine and Bauin, Trans. Amer. Inst. Elec. Eng. May, 1900.

Diameter for the same conductivity 1.27 times copper.
Area

1.64 "
Tensile strength "

.629 " Weight

.501 « «

The number of twists necessary for fracture varies considerably, although the ductility test of wrapping six times around its own diameter, unwrapping and wrapping again, is well sustained. This irregularity in the twisting-test is generally a mark of impurity in wire; but we know so little as yet of the exact characteristics of aluminum in particular, and the twisting-test is in general so unreliable, that it is unsafe to base any exact statement on this one test, particularly as the wire after erection proved reliable. In carefully performing the test for tensile strength, no exact point could be assigned for the elastic limit, as the metal seemed to take a permanent set almost from the first; but at a stress of from 14,500 lbs. to 17,000 lbs. per square inch, there is a marked increase in the permanent set which indicates that the safe working-load lies somewhere in this region. In this the characteristics of aluminum do not differ materially from those of copper or other similar metals; and while this is a disadvantage, it is not a singularity.

The fact that the wire will permanently elongate if seriously strained makes it necessary to use the utmost care in the erection of lines, and also the known high coefficient of expansion with temperature changes taken in conjunction with this property renders care in line-stringing especially important and difficult. The greatest care must be taken against kinking or scarring the wire; wherever the wire is accidentally kinked or scarred, it must be cut and spliced.

One of the most serious problems in connection with the use of aluminum is in the choice of a proper joint. This metal is so highly electro-positive that it is unsafe to expose it to the elements in contact with any other material, as electrolytic corrosion is almost sure to follow such construction. Many of the failures which have been reported of this metal have been due to a neglect of this fact. Whenever this metal is soldered, or used in contact with any other metal, the joint should be thoroughly waterproofed to prevent such action. Without such protection the joints may be made by slipping the ends of the wire into an oval aluminum tube about nine inches long, which is then twisted about two and

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