Catenary Graphs and their Uses

Extract

The curve formed by any flexible uniform chain supported at both ends, in equilibrium under the action of gravity, is the catenary

y = a cosh x/a,

where a is the distance of the lowest point of the catenary above the horizontal x-axis. If the curve is required to pass through the origin, its equation becomes

y = a (cosh x/a - 1)

and it is known that a = H/w, where H is the horizontal force applied at the ends of the catenary, and w is the weight per unit length of the chain.