By Mia Sherman
Introduction
The iconic domes of the Renaissance pushed the boundaries at the balance of grandeur and structural stability. It was the first time in centuries that people had even approached the size of the Pantheon when creating new domes, and it was a feat of engineering to successfully construct a heavy stone or brick dome of this size. As Attilio Pizzigoni described it, “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”. I can agree with this statement, after having seen said dome. The Florentine dome in particular is astounding, and the thorough understanding of engineering, space, and geometry required to create such a structure makes it all that much more impressive. That dome, by Brunelleschi, was the first of multiple massive Renaissance domes, all of which incorporated impressive engineering techniques into their design.
This report will compare the dome of Santa Maria del Fiore in Florence with the domes in Saint Peter’s Basilica in Rome, which can be seen in the map in Figure 1. For each, I will briefly describe the history behind it, including what the structures were before and what led up to the design and construction of the domes themselves. Then, I will go into some of the major engineering aspects of the domes, the primary ones being the double vault and the loxodromic curve and its accompanying herringbone pattern. These techniques were most famously used by Brunelleschi in the Duomo in Florence, which had massive influence on the domes that came after it, including the ones in Saint Peter’s Basilica.
Santa Maria del Fiore
The dome over Santa Maria del Fiore was the biggest dome built at the time of its construction and included groundbreaking technical innovation by Filippo Brunelleschi that helped to raise a dome of that size (Foraboschi, 2016). The history behind it includes a long stretch of time before the dome was built, when there simply was not a roof on the cathedral, and a competition held by the city to solve the question of how to construct that large of a dome. Brunelleschi won said competition and the design for the dome. His engineering was innovative for the time, proposing a double vault and a loxodrome, among other techniques, which made the impossible construction possible. Figure 2 shows the iconic dome in the Florence skyline.
History
Before Brunelleschi
In 1294 the officials of Florence made the decision to enlarge a small church called Santa Reparata, which would become Santa Maria del Fiore (Scaglia, 1991). They intended it to be a grand symbol of Florence, so when they built the rest of the church before finalizing a plan for the dome, architects of the time enlarged the octagonal tribune of the church to the point where in 1418 they were unsure of how to continue (Scaglia, 1991). The 182.5-foot diameter dome would have required so much formwork to make a traditional arch/dome that there was not enough wood in Tuscany for it, and it would have been near impossible and very expensive to acquire the wood for the project (Foraboschi, 2016). Thus until 1418, the church sat dome-less for near 140 years until the competition was announced on August 19, 1418 (Slavinsky, 2006).
The Competition
In 1418 the Guild of Wool Merchants, who were presiding over the project at the time, announced the competition for the best scale-model of the dome (Foraboschi, 2016). The competition required only that no formwork was used, no buttresses were added, the lantern had to be great, and that it was coherent with the project of the past century, which was conducted in the gothic style (Foraboschi, 2016). For this, the guild offered 200 florins (Slavinsky, 2006).
Brunelleschi (see Figure 3) at the time had just returned from a trip to Rome after losing to Ghiberti in the previous competition for the doors of the baptistry (Slavinsky, 2006). He was sculptor and a goldsmith and had been studying buildings such as the Pantheon in Rome (Scaglia, 1991; Slavinsky, 2006). Brunelleschi had taken a special interest in the Pantheon, some of whose elements may have inspired elements of his dome in Florence (Slavinsky, 2006). See the article by Kae Ransom for further analysis of the Pantheon in relation to Brunelleschi’s Duomo.
When he returned from Rome, Brunelleschi entered the competition to design the dome. Figure 4 shows Brunelleschi’s scale model. In the end, the competition was again between Brunelleschi and Ghiberti. Brunelleschi’s design won the commission, but despite Brunelleschi’s wishes, the guild appointed both artists to oversee the project (Foraboschi, 2016). Eventually Ghiberti was dismissed, and Brunelleschi oversaw the project alone (Foroboschi, 2016).
Engineering
Brunelleschi’s model was chosen because of his thorough, innovative engineering. According to Foraboschi, “no one else could have accomplished the mission”. The main features proposed consisted of a double vault and a loxodromic curve, which in combination with other supports and considerations made it possible to construct a dome of this scale.
Double Vault
One of the primary mechanisms he used to support a dome so large was a double vault. When studying the Pantheon, Brunelleschi could see that the material got lighter and thinner the closer to the top of the dome you got (Slavinsky, 2006). He knew that a lighter dome lowered the springing thrust, while a thicker dome also lowered the springing thrust (Foraboschi, 2016). Thus, Brunelleschi designed a double vault, in which most of the volume of the dome was actually empty space (Foraboschi, 2016). Figures 5-7 show this empty space within the dome. The spaces themselves, when walking in them, do not feel all that big, but that is only a result of the extensive system of connections between the two. Ribs often divide the space, as well as additional supports, all of which contributes to an impressively sturdy dome as a whole.
Both shells of the double vault taper in thickness as you get higher, and they are connected strongly enough, using a rib and ring system, to where the dome behaves like a monolith structure (Foroboschi, 2016). Figures 8 and 9 show the frequent and strong connections between the two vaults. Furthermore, the outer dome protects the inner, stronger dome from the elements, and the space between them serves as a route for repairs and maintenance to be done (Scaglia, 1991). Thus, the double vault allowed the dome to be lighter while maintaining its thickness, making it possible for a dome of this size to remain standing.
Loxodromic Curves
The pattern of the stone/brickwork in the dome is what allowed Brunelleschi to design a dome that used no formwork during its construction. The dome was created in rings, building the bricks on top of one another until they reached the peak (Foraboschi, 2016). This way, no formwork was necessary, as each ring was supported by the ones below it. But it was the special herringbone pattern of bricks used in the construction of the dome, laid into a loxodromic curve, which was the key for the dome to be self-supporting (Foraboschi, 2016). Figure 10 shows a loxodromic curve, as would be created within the dome.
This loxodromic curve is made of a herringbone brick pattern made to be self-supporting, although only when created a full ring at a time (Paris et al., 2017). Herringbone patterns had been used in other domes of the time, but never to this scale, as shown in Figure 11. The bricks themselves create three dimensional partial cubes, made of three irregularly sized bricks forming three sides of said cube, which can be fit together within one another to create the self-supporting structure (Paris et al., 2017; Pizzigoni, 2015). This structure can then be tilted to form the loxodrome by using precise, uneven amounts of mortar between the partial cubes so as to curve the overall shape of the structure. This concept can be seen in Figure 12, as shown in the study by Paris, Pizzigoni, and Ruscica in 2017.
This herringbone-patterned loxodromic curve was the integral piece of Brunelleschi’s design which allowed the dome to support itself both during construction and for the last centuries.
Additional Supports
Brunelleschi considered some other very critical aspects in his design of the dome as well. The dome is gothic, more pointed than other Roman-inspired semicircular arches of the time. This is not only because of the strict adherence to the original design as given by the competition, but also because the more pointed design created less horizontal thrust and required less springing thrust than a rounder dome would have (Foraboschi, 2016; Slavinsky, 2006). The pointed dome also carries the heavy lantern desired by Florentines better than a round dome otherwise would have (Foraboschi, 2016).
Brunelleschi also designed a stone chain system by joining the stones at the ribs of the vaults and reinforcing those connections using metal cross pins. This greatly strengthens the cupola and the ribs especially, preventing them from pushing outward. A wooden chain also supplemented this, and the entire system was embedded into the masonry (Foraboschi, 2016). These systems ran within the circumference of the lower portion of the dome to reduce the springing thrust, although they can no longer be considered, as they failed shortly after completion of the dome (Foraboschi, 2016).
To control the placement of any cracks forming in the dome, Brunelleschi made sure that the ribs of the dome were significantly stronger, especially in tension, than the webs (Foraboschi, 2016). The brick patterns were laid so as to be continuous through the ribs and have no angular discontinuity as they passed them (Foraboschi, 2016). This allowed the ribs to be able to withstand more tensile stress and thus any cracking of the dome occurred at the webs, giving the dome more stability (Foraboschi, 2016).
In addition to everything else, the dome includes a plethora of additional features. Openings in the outer dome help dissipate forces from wind, iron bars support scaffolding for artists, and rainwater spouts are included in the exterior (Scaglia, 1991). A seraglio, or circular stone enclosure for the oculus, includes windows to let in light and air, and to support scaffolding that supports the lantern during construction, which in turn becomes the keystone of the dome (Scaglia, 1991). In the end, Brunelleschi once again won the competition to build the lantern of the dome, knowing that the dome could handle the heavy weight and designing it to increase the rise of the already tall and pointed dome (Foraboschi, 2016).
Saint Peter’s Basilica
Saint Peter’s Basilica is yet another iconic dome of Renaissance Italy, constructed next to the Vatican in Rome. The Basilica itself has an extensive history, as it was born out of an older basilica, created by Constantine. It was a part of the new project for a grander church and to create an equally grand central dome. This dome, though, unlike the one in Florence, went through several well-known architects throughout its design before it was finally constructed. In the end, these architects created many engineering innovations to complete such a dome, taking inspiration from both Santa Maria del Fiore and the Pantheon. They once again used a double vault and loxodromic curves, as Brunelleschi did in Florence, among other mechanisms to ensure the dome’s stability. The dome can be seen below in Figure 13.
History
History of the Basilica
The Basilica as it had been built by Emperor Constantine had become a major pilgrimage point during the Middle Ages (Frommel, 1994). The papal ceremonies and masses took place there, while altars were beginning to take over the space, which itself was struggling to support its own weight (Frommel, 1994). Extra supports and additions to the cathedral were crowding the church and disturbing the façade (Frommel, 1994). Thus, Pope Nicholas V, reigning permanently in Rome, considered altering the church to make the building and the neighboring papal buildings not only more functional but grander, to convey the authority of the church to its followers (Frommel, 1994). The Pope confirmed these plans on his deathbed, spurring the thorough renovation of the old Constantine basilica (Frommel, 1994). After this, the plans and renovations were pursued by a long line of other popes and with them a long line of architects. Unlike the dome in Santa Maria del Fiore, the Saint Peter’s dome did not stump architects for quite so long, and the building was actually completed after the completion of the dome.
Contributing Architects
Over the course of its design and the many issues of engineering approached in designing the massive dome, a handful of relatively famous architects all worked in succession to design Saint Peter’s dome. The first notable architect working on the dome’s design was Bramante, from 1505-1514 (Frommel, 1994; Mainstone, 1999). The dome was intended to be a grand marker over the location of Saint Peter’s tomb, so Bramante designed a grand dome to match, with a similar diameter to Santa Maria del Fiore (Mainstone, 1999). Bramante, though, did not have Florentine connections and so based his designs primarily on the Pantheon, making the dome solid and not taking into account the very strong drum of the Pantheon in comparison to Saint Peter’s significantly weaker drum made up of rings of columns (Mainstone, 1999). Next were Giuliano da Sangallo, Raphael, and Peruzzi, from 1514-1521, whose only particularly notable alterations to the plans were a reinforcement of the piers and arches made under Bramante (Mainstone, 1999). Antonio da Sangallo then worked from 1521-1546 (Mainstone, 1999). He strengthened the piers further and took a taller shape which would be able to support a heavier lantern, possibly a result of his more Florentine background, although his design still included a solid dome and rather weak supports (Mainstone, 1999). Michelangelo, once again with more Florentine connections, worked on the dome from 1546-1564 (Mainstone, 1999). He further strengthened the drum and adopted a double-shell approach, although the shells were rather thin and the shape of the dome likely still not pointed enough to have stood (Mainstone, 1999). Finally, Giacomo Della Porta saw the construction of the dome and worked from 1588-1591 (Mainstone, 1999). His final design included much of what the other architects had contributed, but made the dome slightly more pointed, gave it a double shell, and added ribs and ties for additional support (Mainstone, 1999). On May 12, 1590, construction of the dome finished up to the base of the lantern (Mainstone, 1999).
Engineering
The dome in Saint Peter’s Basilica takes inspiration primarily from the Pantheon and Brunelleschi’s Duomo, incorporating some of the same engineering to hold up the dome. The main feature of the large dome of Saint Peter’s is in fact the double vault, which is created to be slightly pointed rather than hemispherical, like in Florence (Mainstone, 1999). The loxodromic curve used by Brunelleschi was elaborated upon as well in Saint Peter’s Basilica by Antonio da Sangallo, although it does not appear in the main dome but in the smaller Simon Mago dome (Roberti et al., 2021).
Double Vault
In the design of the main dome of Saint Peter’s, Michelangelo was the first architect on the project to adopt the double-shell structure (Mainstone, 1999). The previous architects on the project had designed a solid dome, which would have been far too heavy to be supported by the drum of columns in the cathedral (Mainstone, 1999). Their designs had been more influenced by the Pantheon, but the Pantheon possessed an incredibly thick and strong drum which supported its dome, and even then, there was cracking and strain on it (Mainstone, 1999). Michelangelo’s dome design included shells so thin that some doubted if they would even be stable, and it had ribs which only went a small portion of the way up the dome (Mainstone, 1999). Della Porta was the one to oversee the final design, with a double vault that had a more thorough connection between the two shells; ribs traveled the full height of the dome, diminishing in width on the way up and providing a strong connection between the two domes (Mainstone, 1999). When walking between the domes, I was surprised even by how many connections between the two shells had been added. Both designs are shown in Figure 14, as used in Mainstone’s report in 1999. The space between the two shells can be seen in Figures 15-17, while the extensive connections between the shells and the frequency of ribs can be seen in Figures 18-20.
This design once again diminished the weight of the dome while maintaining its thickness, as Brunelleschi had done in Florence. This strategy made it much easier for the dome to stand by reducing springing thrust and placing less weight on the ring of columns supporting it.
Loxodromic Curves
Saint Peter’s main dome itself did not in fact use the loxodromic curve and herringbone combination used by Brunelleschi in Florence, as the larger dome was known to have used formwork in its construction, which would not have been necessary when using Brunelleschi’s technique (Mainstone, 1999). The dome of Santa Maria del Fiore still contributed its loxodromic curve technique to the basilica though, in the smaller dome of Simon Mago located near the large dome (Paris et al., 2020). Figure 21 shows a scan of the dome of Simon Mago as used in the Princeton study.
Sangallo also further pushed the technology by changing it from Brunelleschi’s single helix to a double helix, also called a cross-herringbone structure (Paris et al., 2020). This structure maintains Brunelleschi’s original feat: the construction of a dome without any major formwork required (Paris et al., 2020; Roberti et al., 2021). Studies have shown that this cross-herringbone structure works by causing the horizontal bricks between the helixes to push outwards onto the herringbone bricks, forming straight arches, also known as plate-bandes, whose thrust outward keeps the bricks in place during construction (Paris et al., 2020). Figure 22 shows these components in the context of a dome shape. This structure not only works during construction, but has added benefits after construction, contributing stiffness and stability to the structure (Roberti et al., 2021).
Additional Supports
The main dome of Saint Peter’s primary assisting support is simply in the evolution of its shape. In earlier plans, the dome was intended to be more hemispherical than pointed (Mainstone, 1999). In the end, though, the dome was somewhere between hemispherical and the pointed shape of Brunelleschi’s dome, which decreased the thrust, carried the lantern better, and allowed for easier construction near the end, all with the added bonus of making the dome stand taller and grander in the Roman skyline (Mainstone, 1999).
In addition, circumferential ties were incorporated into construction, one just above the drum and one just above where the shells divide (Mainstone, 1999). These theoretically act to contain thrusts around the entire circumference rather well, and to assist thus in keeping the dome standing.
Summary
Both domes – Santa Maria del Fiore and Saint Peter’s – have an extensive history behind them and were converted from smaller churches during the Renaissance to add grandeur and glory to their cities. The real feat though was in the engineering. Brunelleschi’s designs in Florence heavily influenced all those Renaissance domes which came after it, including those built in Saint Peter’s Basilica. He most notably implemented a double vault and a herringbone patterned brick shape in a loxodromic curve. These innovations helped to decrease thrust by the dome into its supports and keep such a large dome structurally sound while also allowing it to be built without using any formwork. These two major pieces, in addition to the pointed shape, the system of chains, and the controlling of crack locations allowed the dome to decrease any unwanted thrust and maintain its integrity for so long. Saint Peters’ main dome borrowed Brunelleschi’s idea of a double shell as well, and in conjunction to a slightly more pointed (Florentine) shape and circumferential ties this allowed the architects of the time to create yet another enormous, structurally stable dome. As for the loxodrome, it was not used in the primary dome of the basilica, but in a smaller dome there, where Renaissance architects furthered Brunelleschi’s herringbone and loxodrome technology into a cross-herringbone pattern which offered even more stiffness and stability to the dome when completed and when under construction.
Out of the two, I would say that because of its infamy and how groundbreaking it was for the time, Brunelleschi’s dome would be my pick. It was the largest dome built in so long, and Brunelleschi’s genius alone designed not just some of the engineering methods that kept the dome standing, but all of them. He utilized the double vault while using a loxodromic curve and beautifully mixed form and function, using the necessary geometry for the engineering to create a visual design just as impressive. This dome influenced so many other domes of the Renaissance and could surely lend more insight even today.
Roberti, Ruscica, Paris, Pizzigoni, and Adriaenssens in their studies in 2021 and 2020 pointed out the possible usefulness of Brunelleschi and his contemporaries’ ideas even in modern construction. In particular, the cross-herringbone pattern could potentially be used in autonomous construction, such as when using drones and tailoring the shape of a surface, as it is self-supporting and needs no formwork (Paris et al., 2020). The pattern could be used in other structures as well, and the lack of formwork would allow for a huge decrease in the traditional construction materials used in formwork (Roberti et al., 2021). Some buildings already incorporate similar geometry as the domes, using the loxodromic curve to create a large vault as in the “Tij” bird observatory by Geometria Architecture Ltd and the Orvieto Airplane Hangar by Pier Luigi Nervi (Roberti et al., 2021). Further, the ideas behind the Renaissance architects’ approach could be useful today, using knowledge of geometry and principles to create seemingly simple solutions and using the engineering needs of the structure to shape its final appearance. The Renaissance masters created structures that we still marvel at today; I believe that we can still take some inspiration from them in the future.
References
Foraboschi, P. (2016). The central role played by structural design in enabling the construction of buildings that advanced and revolutionized architecture. Construction and Building Materials, 114. https://doi.org/10.1016/j.conbuildmat.2016.03.092
Frommel, C. L. (1994). St. Peter’s: The Early History.
Herb, A. (2020, May 21). Double helix of masonry — researchers uncover the secret of Italian Renaissance domes. Princeton University. https://www.princeton.edu/news/2020/05/21/double-helix-masonry-researchers-uncover-secret-italian-renaissance-domes
Mainstone, R. J. (1999). The Dome of St Peter’s: Structural Aspects of its Design and Construction, and Inquiries into its Stability. Architectural Association School of Architecture, AA Files(39).
Paris, V., Pizzigoni, A., & Adriaenssens, S. (2020). Statics of self-balancing masonry domes constructed with a cross-herringbone spiraling pattern. Engineering Structures, 215. https://doi.org/10.1016/j.engstruct.2020.110440
Paris, V., PIZZIGONI, A., & RUSCICA, G. (2017). Brunelleschi’s herringbone hidden reciprocal structure and the form finding of its self-supporting bricks. International Association for Shell and Spatial Structures.
Pizzigoni, A. (2015). Brunelleschi’s bricks. Journal of the International Association for Shell and Spatial Structures, 56(2).
Rhumb Line. (2024). Dr. Bernd Frassek. https://www.frassek.org/3d-mathe/orthodrome-gro%C3%9Fkreis-und-loxodrome/loxodrome/
Roberti, G. M., Ruscica, G., & Paris, V. (2021). From the herringbone dome by Sangallo to the Serlio floor of Emy (and beyond). Curved and Layered Structures, 8(1). https://doi.org/10.1515/cls-2021-0023
Scaglia, G. (1991). Building the Cathedral in Florence. Scientific American, 264(1). https://doi.org/10.1038/scientificamerican0191-66
Slavinsky, R. (2006). Filippo Brunelleschi and the Creation of Il Duomo . The University of Tampa, 1.
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