Length of a Hanging Cable

by Eric Costello

Submitted : Fall 2011

The shape of a cable hanging under its own weight and uniform horizontal tension between two power poles is a catenary. The catenary is a curve which has an equation defined by a hyperbolic cosine function and a scaling factor. The scaling factor for power cables hanging under their own weight is equal to the horizontal tension on the cable divided by the weight of the cable. For this problem both of these values are unknown. I used Newton’s Method to approximate the scaling factor and the arc length function to determine the length of the cable. Using the Python programming language, I wrote a script in order to quickly perform several iterations of Newton’s Method to get a good approximation.

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