# Tension of Power Transmission (High Tension) Lines

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Farr, Holland H. Transmissions line design manual: a guide for the investigation, development, and design of power transmission lines. Denver: US Dept. of Interior, Water and Power Resources Services; US Government Print. Off., 1980. 9. "For example, if we string a 242 mm2, ACSR, 24/7 conductor on a 213.4-m ruling span, the initial sag at minus 18 °C with no ice and no wind will be 2,549mm, and the tension will be 19,700N. THe limiting condition, as determined by the Bureau, for this conductor under NESC heavy loading conditions is 33-1/3 percent of the ultimate strength at minus 40 °C initial, no load. THe NESC heavy loading conditions are 13mm radial ice, 0.19 kPa transverse wind, and a constant of 4.3782 N/m. After loading the conductor to a full load tension of 33,362 N, the immediate sag at minus 18 °C with no ice and no wind is 2906 mm, and the tension is 17,580." 19,700 N
17,580 N

Power transmission lines are used to transport electrical energy over long distances. They are often found in communication system, such as in telephone networks, broadcasting, and TV transmission lines.

When a cable is hung between two supports it forms a curve or arc called a catenary. The term catenary applies to a flexible cable that has uniform mass through out its length and is being acted upon by a gravitational force. The basic mathematical equation of a catenary is y = a cosh(x/a). Where a is the distance between the lowest point of the cable's arc to the ground, cosh signifies that the catenary is an hyperbolic function, and x is the effective span-the horizontal distance of the portion of the cable that a support holds. This distance is usually between the lowest point of the arc of the support.

The gravitational force, weight, acting on a hanging cable causes tension to exist. The tension has a vertical and horizontal component, and is tangent to the catenary. Minimum tension is found at the lowest point of the arc where the tension is equal to zero. Maximum tension is found at the supports. The tension of a cable can be determined by using the diagram and equations below.

Elizabeth Eng -- 2004