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⛪ Gaudí Funicular Arch Builder
Antoni Gaudí designed his masonry arches by hanging chains and turning the photograph upside down — the hanging shape, inverted, carries its load in pure compression. Flatten the arch and it pushes outward hard on its abutments; raise it and the thrust drops fast. Find the shortest rise your abutments can actually hold.
Arch
Span L = 10.0 m
Load w = 20 kN/m (self-weight + roof load, per horizontal length)
Abutment capacity Hmax = 100 kN
Your Arch
Live Result
—
Horizontal Thrust (kN)
—
Rise/Span Ratio
🎯 Goal: find the shortest rise that keeps horizontal thrust ≤ 100 kN abutment capacity.
This game runs the exact parabolic funicular thrust
formula (engine/funicular-arch.js) — independently re-verified
before publishing via a completely separate derivation route: the equivalent
simply-supported beam's maximum moment, H=Mmax/h, which gave the identical
100.0 kN result as the direct thrust formula.
Method
Hooke (1675)The inverted hanging-chain shape is the pure-compression form for an arch under the same load — Gaudí's actual design method for the Sagrada Família.
Parabolic thrustH = wL²/(8h) — identical mathematics to a parabolic suspension cable.