Ancient Vitruvian Catenary vs. Parabolic Arch Geometry

45 mins Ages 10-14 Indoor

A challenging, hands-on discovery and STEM project designed for curious young minds aged 10 to 14.

Materials Needed

  • • Metal link chain (small steel jack chain, 1 meter long) (1 meter)
  • • Cardboard or cork backer board (large, A3 size) (1 board)
  • • Pushpins (4 units)
  • • Marker and metric ruler (1 set)

Pro Tips

  • → Suspend a heavy metal link chain by its two ends from a vertical board: it naturally hangs in a pure catenary curve with tension alone.
  • → Trace the chain with a pencil, flip the board 180 degrees upside down: the curve is now a freestanding catenary arch under pure compression with zero shear force.
  • → Architect Antoni Gaudí used inverted hanging chain models to engineer the arches of the Sagrada Família in Barcelona.

Safety First

Fasten pushpins securely into a cork board or cardboard backplate to prevent them popping loose.

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Step-by-Step Instructions

1

Step 1

Pin the two ends of a 1-meter steel link chain to the top corners of a vertical cardboard sheet, letting the chain loop hang freely.

2

Step 2

Carefully trace the path of the hanging chain onto the cardboard with a fine marker.

3

Step 3

Plot a standard quadratic parabola (y = ax²) with matching apex and base points on the same sheet.

4

Step 4

Flip the board upside-down to analyze how the catenary arch profile directs compressive loads straight into the ground without lateral bowing.

What they are learning

The catenary curve (y = a*cosh(x/a)) vs. parabola Antoni Gaudí’s hanging chain architectural models Pure compressive structural equilibrium