Length of a catenary in terms of sag and span?
August 3, 2008 6:43 AM Subscribe
I am building a zip line. The supports are 70m apart and one is 7m higher than the other. I want the lowest point of the zip line to be 2m lower than the lower support. How long is the wire?
posted by unSane to Science & Nature (17 answers total) 2 users marked this as a favorite
Obviously the curve is a catenary but everything online is expressed in terms of the wire tension and mass per unit length, which I want to eliminate from consideration.
To be a bit clearer about the parameters, assume one support is at (0,0) and the second is at (70, -7). I want the lowest point of the zip line to be at y= -9. I'm trying to calculate the arc length along the catenary from one support to the other.
Alternatively, assuming the supports are at (0,0) and (0,L) and that the sag is S, is there a function f(L,S) which gives the arc length of the catenary in terms of the span L and sag S?