Transmission lines do not connect between their supporting towers in a straight line. The shape formed by a line strung between two supports is called a catenary. If there is too much tension, the sag will be too little and the line can snap. However, if there is too much sag, it will increase the amount of conductor used, increasing the cost more than is necessary. The more space there is between transmission towers, the more the transmission line will sag.
Measure the horizontal distance between the tower attachment points. This will be denoted by the letter L.
Determine the weight per unit length of the conductor. This is signified by the letter w.
Find the tension in the line, represented by the letter T.
Substitute these values into the equation T x y = (wx)(x/2) where T is the tension, y is the vertical distance between the attachment point and the lowest point in the parabola, and wx is the weight that acts at a horizontal distance x/2 from the attachment point.
Solve the equation for y. This yields y = wx²/(2T). Substitute L/2 for x since the center between the towers is the low spot to get y = w/(2T) x (L/2)², which simplifies to y = wL²/8T. For example, the sag for a cable with a weight equal to 1 kilogram per meter tensioned to 10,000 kg between towers 500 meters apart would have a sag equal to (1)(500²)/(8)(10,000) = 250,000/80,000 = 3.125 meters.
- transmission line image by Vladimir Kirienko from Fotolia.com