Electric Transmission of Water Power

by Alton D. Adams

Soft copper shows a tensile strength between 32,000 and 36,000 pounds per square inch, and hard-drawn copper between 45,000 and 70,000 pounds, depending on the degree of hardness. Silicon-bronze wires vary in strength from less than 60,000 to more than 100,000 pounds per square inch, and phosphor-bronze has a tensile strength of about 100,000 pounds. Bronze wires, like those of most alloys, show a much wider range of strength than those of iron or copper.

In silicon-bronze wire the electrical conductivity decreases as the tensile strength increases. The tensile strength of aluminum wire is lower than that of any other used in transmission lines, being only about 30,000 pounds per square inch. Solid aluminum wires of large size have given trouble by breaking under strains well within their nominal strength, due probably to imperfections or twists. This trouble is now generally avoided by the use of aluminum cables.

In that most necessary property of a transmission line—conductivity—copper excels all other metals except silver. Taking the conductivity of soft copper wire at 100, the conductivity of hard-drawn copper is 98; that of silicon-bronze ranges from 46 to 98; that of aluminum is 60; of phosphor-bronze, 26; of annealed iron wire, 14; and of steel wire of 100,000 pounds tensile strength per square inch, 11. Copper wire, both soft and hard, as regularly made, does not vary more than one per cent from the standard, and aluminum and annealed iron wires also show high uniformity as to resistance. Silicon-bronze and steel wires, on the other hand, fluctuate much in electrical conductivity. For any particular transmission line the resistance is usually determined by considerations apart from the metal to be used as a conductor, so that a line of given resistance or conductivity must be constructed of that material which best conforms to the requirements as to size of wire, weight, strength, and cost.

Allowing the weight of any definite mass of copper to represent unity, the weight of an equal mass of wrought iron is 0.87; of steel, 0.89; of aluminum, 0.30; while that of bronze is very nearly equal to that of the copper. The smallest line wire that can be used for a given length and resistance is one of pure, soft copper. Next in cross-sectional area come hard-drawn copper and some silicon-bronze, either of which need be only two per cent larger than the soft copper for an equal resistance. Some other silicon-bronze wire of greater tensile strength per square inch would require a sectional area of 2.17 times that of the soft copper.

Aluminum wire with 60 per cent of the conductivity of copper requires 1.66 of its section for wires of equal resistance. As phosphor-bronze has only 26 per cent of the conductivity of copper, the section of the bronze must be 3.84 times that of the copper wire if their lengths and resistance are to be equal. An annealed iron wire is equal in resistance to a copper wire of the same length when the iron has 7.14 times the section of the copper. Steel, with 11 per cent of the conductivity of copper, must have 9.09 times the copper section in order that wires of the same length may have equal resistances.

It is not desirable to use a copper wire smaller than No. 4 B. & S. gauge for transmission lines, because of the lack of tensile strength in smaller sizes. When the conductivity of a copper wire smaller than No. 4 is ample, an iron wire will give the required conductivity, with a strength far greater than that of the copper. For a line of given length and conductivity of any other metal the weight compared with that of a copper line is represented by the product of the figures for relative section of the two lines and of the weight of unit mass of the metal in question compared with that of copper.

Thus, for the same conductivity the weight of a certain length of iron wire is 0.87 × 7.14 = 6.21 times the weight of a copper wire. For the steel wire above named the weight is 0.89 × 9.09 = 8.09 times that of a copper line of equal conductivity. Phosphor-bronze in a line of given length and resistance has 3.84 times the weight of soft copper. Silicon-bronze for a transmission line must weigh from 1.02 to 2.17 times as much as soft copper for a given length and conductivity. Aluminum for a line of fixed length and conductivity will weigh 1.66 × 0.3 = 0.5 times as much as copper. For a line of fixed length and resistance, hard-drawn copper will weigh about two per cent more than soft copper.

Taking the tensile strength of soft copper at 34,000 pounds per square inch, hard-drawn copper at 45,000 to 70,000, silicon-bronze at 60,000 to 100,000, phosphor-bronze at 100,000, iron at 55,000, steel at 100,000, and aluminum at 30,000 pounds, the relative strengths of wires with equal sectional areas compared with the soft copper are, for hard-drawn copper, 1.32 to 2.06; silicon-bronze, 1.76 to 2.94; phosphor-bronze, 2.94; iron, 1.62; steel, 2.94; and for aluminum, 0.88.

Comparing wires on the basis of equal resistances for equal lengths, with soft copper again the standard, the tensile strength of each as to it is as follows: A hard-drawn copper line has 1.02 × 1.32 = 1.34 to 1.02 × 2.06 = 2.10 times the strength of a line of soft copper. With silicon-bronze the strength of line wire would range between 1.02 × 1.76 = 1.79 and 2.17 × 2.94 = 6.38 times that of copper. Iron would give the line a strength as to soft copper represented by 7.14 × 1.62 = 11.56. Steel of 100,000 pounds tensile strength per square inch will give a line 9.09 × 2.94 = 26.70 times as strong as it would be if composed of soft copper. With aluminum the strength of the line would be 1.66 × 0.88 = 1.46 times that of copper. For phosphor-bronze the figures are 3.84 × 2.94 = 11.29.

From the foregoing it may be shown how many times the price of soft copper per pound may be paid for each of the other metals to form a line of given length and resistance at a cost equal to that of a soft copper line. These prices per pound for the several metals relative to that of soft copper are as follows: Taking the price of soft copper as one, the price for hard-drawn copper must be 1 ÷ 1.02 = 0.98. For silicon-bronze the price may be as high as 1 ÷ 1.02 = 0.98, or as low as 1 ÷ 2.17 = 0.46 of the price of soft copper wire. Phosphor-bronze may have a price represented by only 1 ÷ 3.84 = 0.26 that of copper. The price of iron wire should be 1 ÷ 6.21 = 0.16 of that of copper, and for steel wire of the quality stated the price can only be 1 ÷ 8.01 = 0.12. Aluminum wire alone may have a higher price per pound than soft copper for the same resistance and cost of line, the figure for the relative cost of this metal being 1 ÷ 0.5 = 2.