Engineers and tourists alike have long marveled at the impressive domes of the Italian Renaissance, including Filippo Brunelleschi’s famed red-brick addition to Florence Cathedral and the gargantuan rotunda of St. Peter’s Basilica.
These domes were built as self-supporting structures, meaning they did not require additional supports or shoring to keep their bricks from tumbling down during construction. Until recently, however, researchers’ understanding of these engineering marvels was largely limited to speculation, reports artnet News.
Now, a new study published in the journal Engineering Structures provides insight on the physics behind these domes’ structure and construction. Per a statement from Princeton University, researchers used complex computer analysis to answer two overarching questions: How can builders construct such large structures without supporting framework, and what can we can learn from Renaissance techniques?
Princeton’s Sigrid Adriaenssens and Vittorio Paris and Attilio Pizzigoni of the University of Bergamo analyzed domes designed by Antonio Sangallo the Younger and his family of architects, who created many such structures in 15th- and 16th-century Italy.
“Nothing is more moving than reading the lightness of the heavens in stone, in an absolute and simple form such as that of the Florentine cupola,” says Pizzigoni in the statement. “With these studies, we aim to approach moments in history when the sole form of technology available to man was the abstract rationality of geometry. What we as designers, architects, and builders can learn from the past is the knowledge of a structural equilibrium of form based on the geometry of materials and of their reciprocal measurements in three-dimensional space.”
For the study, the researchers examined the physics behind the double loxodrome technique that the Sangallo architects employed in their designs. In the dome’s inner shell, bricks were laid in a “cross-herringbone spiraling pattern” that enabled lines of vertical bricks to extend diagonally across the curved structure, creating a diamond-shaped pattern, reports Mark Bridge for the Times. This “double-helix” of support “distribute[d] and equalize[d] weight and thrust within the structure,” according to the statement.
The researchers used a technique called discrete element modeling (DEM), as well as a limit state analysis, to study the forces acting on each individual brick in a double-loxodrome dome. They found that at each stage of construction, the structure was stable and able to stand on its own, eliminating the need for costly scaffolding.
Goldsmith-turned-architect Filippo Brunelleschi employed a single helix of vertical bricks in the famous red-brick dome of Florence Cathedral, which was constructed more than a century before the Sangallo architects built their domes. This timeline led the researchers to suspect that the Sangallo double loxodrome technique was based on Brunelleschi’s pioneering work. They argue that the same principles at work in the Sangallo domes apply to Brunelleschi’s dome, reports the Times.
The team behind the new study hopes to apply the lessons learned from the research to modern architectural practices. Without the need for scaffolding, architects could build domes more easily—perhaps with drones, the researchers suggest.
“The study of the cross-herringbone spiraling pattern does not merely serve historical or conservation purposes,” the trio writes. “It has practical applications for the development of dry self-balanced robotic masonry construction technologies, particularly suited for unmanned aerial vehicles.”