Weighted catenary
A weighted catenary is a catenary curve, but of a special form: while a catenary is the curve formed by a chain under its own weight, a weighted catenary is the curve formed if the chain's weight is not consistent along its length. Formally, a "regular" catenary has the equation
for a given value of a. A weighted catenary has the equation
and now two constants enter: a and b.
Significance
A freestanding catenary arch has a uniform thickness. However, if- the arch is not of uniform thickness,
- the arch supports more than its own weight,
- or if gravity varies,MathOverflow:, accessdate: April 13, 2017
The aspect ratio of a weighted catenary describes a rectangular frame containing the selected fragment of the curve theoretically continuing to the infinity.
Examples
The Gateway Arch in the American city of St. Louis is the most famous example of a weighted catenary.Simple suspension bridges use weighted catenaries.