The Hanging Chain

Catenary, not parabola

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A hanging chain forms a catenary, $y = a\cosh(x/a)$, not a parabola.
• Suspension-bridge cables carrying a level deck form parabolas.
• Inverted catenary arches stand in pure compression.

Steps

1. Chain or parabola?
2. Set the sag
3. Angle at the post
4. Square wheels
5. Riding on square wheels
6. How much sag?
7. Arches