Antoni Gaudí revolutionized architectural design not through standard blueprints, but through physical analog computation. To design structural arches that experienced pure compression without shearing forces, Gaudí utilized the physics of the catenary curve. A catenary is the natural curve a flexible chain or cable forms when suspended from its ends under its own weight.
Mathematically defined by the hyperbolic cosine function, a hanging catenary cable experiences pure tension. Gaudí realized that if you invert this curve upside down, the tension forces flip symmetrically into pure compression forces, eliminating internal bending moments. To design structures like the Colonia Güell Church and elements of the Sagrada Família, Gaudí constructed massive, multi-story stereostatic hanging models using hemp strings and small canvas bags filled with lead shot.
Each bag was meticulously weighted to represent proportional loads of proposed building components, such as masonry walls, vaults, and roofs. As strings pulled on adjacent strings, the entire network dynamically resolved into an interconnected web of funicular curves. Gaudí placed mirrors underneath the models or photographed them, then flipped the images right-side up to reveal the precise organic shapes required for stable stone construction.
By allowing gravity to calculate the ideal load paths, Gaudí created soaring, tree-like column structures that required far less masonry mass and eliminated the need for traditional external flying buttresses.