Length of a Hanging Cable

Citation data:

Undergraduate Journal of Mathematical Modeling: One + Two, Vol: 4, Issue: 1

Publication Year:
2011
Usage 23692
Downloads 23294
Abstract Views 398
Repository URL:
http://scholarcommons.usf.edu/ujmm/vol4/iss1/4
DOI:
10.5038/2326-3652.4.1.4
Author(s):
Costello, Eric
Publisher(s):
University of South Florida Libraries
Tags:
Hanging Cable; Newton’s Method; Catenary; Mathematics
article description
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. Both of these values are unknown for this problem. Newton's method was used to approximate the scaling factor and the arc length function to determine the length of the cable. A script was written using the Python programming language in order to quickly perform several iterations of Newton's method to get a good approximation for the scaling factor.