AH!!! I remember long ago, my mathematics professor gave a lecture on this very topic! Suppose you have a cable suspended between two towers (such as a powerline). What kind of function would best model the curvature of that suspended cable, with the forces of gravity applied to it? The answer of course, is a Hyperbola! As far as specific equations go, you’re on your own. This is just the direction I’d go in with your engineering problem.