In 1540, Michelangelo Buonarroti, amazed by the Santa Maria del Fiore’s dome proportions, confided: “I’m going to Rome to make your sister, bigger than you, but not more beautiful”. Saint Peter’s dome was indeed built by the drive, knowledge, and passion of Buonarroti and Della Porta. After more than five centuries, there is still an open debate about the most beautiful masonry dome. A more objective discussion concerns the static efficiency of such ancient domes. As the domes’ efficiency is indirectly proportional to the thrust ratio χ, i.e. the ratio between the horizontal thrust and the total weight of the dome, Como (2013) computed the thrust ratio for both Santa Maria del Fiore (Florence) and Pantheon (Rome) domes, which are equal to 0.11 and 0.08, respectively (for a unitary lantern load multiplier). The static efficiency of San Peter’s dome is characterized by a thrust ratio of 0.20. This value is clearly higher, hence indicating a lower efficiency.

Marco Francesco Funari, Luis C. Silva , Paulo Lourenço and Dr. Elham Mousavian (UniNA) developed a digital tool to perform the rapid assessment of masonry arches and domes. Such a tool may provide valuable insights into the complex behaviour of such structures. Here, they tried to address the following question: how could one change the geometry of the St. Peter’s dome aiming at the same static efficiency as the Santa Maria del Fiore’s dome. To this aim, the parameter β was defined to update the geometry and it can be described as a scaling parameter that affects only the radius of the extrados shell of Saint Peter’s dome. Other geometrical dimensions, as the thickness of the shells, thickness of the dome, dimension of the ribs, etc., were kept fixed.

The results demonstrate that the dome’s thrust ratio is decreased by increasing the height of the dome (inherent consequence due to the increase of the extrados radius). The analysis proves that the thrust ratio decreases from 0.20 to 0.135. A curious remark is that, even for a β=1.4 value, the dome assumes a thrust coefficient equal to 0.135 that still resorts to be higher than the Brunelleschi dome and the Pantheon.

More information can be found in the journal article associated: link.