Contenido

Las obras del actual edificio de la catedral de Santa María del Fiore se iniciaron entre los años 1294 y 1295 para sustituir a la antigua iglesia de Santa Reparata, de dimensiones más pequeñas.[14]​ Entre 1410 y 1413 se construyó el tambor "Tambor (arquitectura)"),[1]​ quedando finalizada su base superior entre 1414 y 1415. Sin embargo, a principios del siglo todavía no se había planteado en profundidad el problema de la cubierta, cuya edificación preocupaba a los miembros de la Opera del Duomo "Museo dell'Opera del Duomo (Florencia)") desde hacía tiempo.[nota 1]​No era una tarea fácil construir y ubicar el punto donde se tenían que apoyar las enormes cimbras de madera que debían sostener la cúpula hasta su cierre final con la clave "Clave (arquitectura)").[21]​ Más aún, resultaba inviable que una obra de tales dimensiones pudiera ser sujetada mediante los andamiajes tradicionales, puesto que ninguna variedad de madera habría podido soportar provisionalmente un peso tan grande.[1]​.

Arnolfo di Cambio, el arquitecto que proyectó la nueva catedral, probablemente había previsto este contratiempo, puesto que había imaginado la conclusión de su edificio con una cúpula, un elemento muy distinto y de mayores dimensiones que el tradicional cimborrio de las catedrales medievales. Su idea de emplear un tipo de cubrición de apariencia más convencional se puede apreciar en un conocido fresco de Andrea di Bonaiuto ubicado en la Capilla de los Españoles de Santa María Novella en Florencia.[22]​ La pintura, datada de 1355 aproximadamente, muestra en segundo plano una iglesia claramente reconocible como Santa María del Fiore, en la que se representa una cúpula desprovista de tambor y con forma semiesférica, aunque de lados muy curvados.[23]​ Sin embargo, una cúpula de medio punto, aunque fuese de menor tamaño y no tuviera tambor, hubiese tenido grandes problemas para soportar el peso de la linterna "Linterna (arquitectura)") de la imagen sin la ayuda de refuerzos. De todas formas, es posible que Bonaiuto hubiese dado al dibujo una forma más redondeada que la que pretendía di Cambio para su proyecto.[24]​.

El 19 de agosto de 1418, la Opera del Duomo convocó un concurso público para la construcción de la cúpula.[nota 2]​Además de resolver los problemas técnicos de ingeniería, debía rematar el edificio de forma armónica, resaltando el valor simbólico e imponiéndose sobre el espacio urbano y el entorno.[25]​ De los diecisiete participantes pasaron a una segunda fase Filippo Brunelleschi, quien había fabricado una maqueta de madera para la ocasión, y Lorenzo Ghiberti.[26]​ Brunelleschi perfeccionó su modelo, «grande como un horno», aportando una mayor información para demostrar la viabilidad de una cúpula sin armazón. A finales de 1419, con la ayuda de Nanni di Banco y de Donatello, organizó una demostración en la plaza del Duomo "Piazza del Duomo (Florencia)"), entre la catedral y el campanile, con una maqueta realizada con ladrillo y argamasa y sin armazón. Esta representación impresionó positivamente a los miembros de la Opera del Duomo.[26]​ El 20 de marzo de 1420, la obra fue asignada definitivamente a Brunelleschi y a Ghiberti, quienes fueron nombrados Superintendentes de la Cúpula.[nota 3]​[28]​.

The Document of 1420

On July 30, 1420, the so-called Document of 1420 was drafted, attributed to Brunelleschi himself, in which the construction program of the dome was determined. It was one of the first contracts in which a master builder assumed responsibility for the project towards the client.[29] This agreement explained how the drum should be closed and specified the most important aspects of the construction. In essence, it was a new "work program" that synthesized in a few lines the structure, form and dimensions of the construction, although rather than exposing a programmatic intention, Brunelleschi enunciated the project by giving executive provisions. The twelve points listed contained not only the finished work, but even indicated the variations, incidents and additions that had to be made. For example, the insertion into the walls of the dome of several iron rings was planned to hold the scaffolding on which the authors of the frescoes had to work.[30]​.

The works officially began on August 7, 1420 with an inauguration banquet.[31]​ Before and during the course of the works, Brunelleschi and Ghiberti always maintained a great rivalry, collected and documented in the chronicles of the time.[32]​ In 1425 and after numerous confrontations, Ghiberti was finally removed from the work due to various technical errors.[27]​ The works became entirely directed by Brunelleschi,[33]​ who continued his work without appreciable interruptions until the completion of the base of the lantern on August 1, 1436. On March 25, 1436, the first day of the year in the Florentine calendar, the end of the works was officially celebrated with the solemn blessing of Pope Eugene IV, although the dome was not completed until August 31 with the ceremony of laying the last stone.[34]​ The Consecration was commemorated with the premiere of Guillaume Dufay's isorhythmic motet Nuper rosarum flores, with references to the shield "Shield (heraldry)") of Florence and the dedication of the basilica to Saint Mary of the Flower.[35]​.

Once the construction of the dome was completed, another public competition was called for the lantern, won again by Brunelleschi.[16] Work began in 1446, a few months before the architect's death.[35] They were resumed under the direction of his friend and disciple Michelozzo di Bartolomeo, to be finally completed on April 23, 1461.[16]

The lantern suffered various mishaps throughout history due to lightning strikes. The most important were recorded in 1492 and 1601, the last of which caused the collapse of the sphere and the coronation cross, which were restored in 1602.[36] The structure has also suffered various earthquakes, the most notable being those that occurred in 1453, 1542 and 1695.[16]

In 1639, various cracks were recorded in the dome that ran vertically from the top of the arches in the blind panels, crossing the oculi until reaching the lantern. It was observed that these cracks experienced alternating seasonal cycles of expansion and contraction depending on the temperature.[37]​ In 1757, Leonardo Ximenes already noted the existence of several angular cracks on the inner face of the eight intersecting edges of the panels, located in the lower third of the dome.[38]​ These cracks have been developing slowly over the centuries.[39]​ In recent years, numerous investigations and studies have been carried out, as well as a monitoring of the structural behavior of the dome since the 1980s.[40]​.

La cúpula de Santa María del Fiore está constituida en líneas generales por tres grandes elementos: el tambor, la cúpula propiamente dicha y la linterna de coronación.

La cúpula está compuesta por ocho grandes paños "Paño (arquitectura)") de ladrillo rojo llamados también gajos "Gajo (textil)") o «gallones». Interiormente, la base o primer tramo es macizo hasta una altura de 3.50 metros desde el nivel de arranque, y está formado por seis hileras de bloques de piedra arenisca unidas con piezas de hierro estañado.[41]​ A partir de esa altura, la cúpula se divide en dos hojas, una interior y otra exterior, realizadas en ladrillo y separadas por un espacio vacío intermedio. La exterior tiene una misión de conservación y protección frente a los agentes externos,[42]​ mientras que la interior desempeña una función estructural.[43]​ El casquete interior tiene un espesor de dos metros, y el exterior mide unos sesenta centímetros.[44]​ El espacio intermedio tiene una anchura de aproximadamente 1.20 metros y a través de su recorrido se disponen cuatro pasillos internos y varias escaleras que llegan hasta la linterna.[45]​ Parece ser que Brunelleschi decidió emplear este diseño con un hueco entre ambas hojas para aligerar la estructura, que de otra forma habría sido demasiado pesada para poder ser sujetada por los cuatro grandes pilares sobre los que apoya toda la cúpula.[44]​.

Los ocho paños están separados y ribeteados por ocho costillas de piedra,[nota 4]​ que parten desde las aristas del tambor y llegan hasta la linterna de coronación. Abarcan todo el espesor de las dos cúpulas, la interior y la exterior, uniéndolas. En cada paño, entre dos de estas costillas principales se disponen verticalmente otras dos menores embebidas en el hueco intermedio, haciendo un total de 16 costillas menores y 24 verticales incluyendo las principales. Nueve arcos de mampostería se distribuyen horizontalmente en planos paralelos a cada paño, uniendo las costillas principales con las menores. Un entramado de madera de roble, formado por 24 vigas conectadas entre sí con placas de hierro, ata toda la estructura en su parte inferior, macizando la base de la cúpula. A la solidez del conjunto también contribuyen las seis hiladas de bloques de piedra de la base antes mencionadas, así como una cadena de hierro situada sobre ellas. En el documento de Brunelleschi también se menciona otra cadena de hierro situada sobre el encadenado de madera, aunque esta última no es visible o está oculta en la mampostería.[47]​ Las costillas de piedra y todos los estribos están realizados con piedra de macigno[nota 5]​ y con pietra forte.[42]​.

Los expertos han discutido mucho sobre la eficacia de este sistema de refuerzo. En principio, una cúpula es más estable cuanto más robustos son su tambor y la base de la imposta; por tanto, un sistema adecuado de zunchado favorece la estabilidad.[nota 6]​Estos anillos tendrían la función de «ceñir» la estructura en su base, con el objetivo de contrarrestar las fuerzas que empujan hacia el exterior. En lo que respecta a las cadenas de madera y de piedra, su utilidad es dudosa, debido a la elasticidad de la madera y a la incapacidad de la piedra para trabajar a tracción.[50]​.

Cuatro grupos de escaleras conducen desde el suelo hasta la parte superior del tambor, alojadas en el interior de los cuatro grandes pilares sobre los que descansa la cúpula. Durante la construcción de la misma, dos de ellas se emplearon para ascender y las otras dos para descender, facilitando así la circulación de los operarios.[51]​ Estas escaleras terminan en un primer balcón interior que rodea la base de la cúpula. Desde este balcón se accede al espacio entre los dos casquetes a través de una pequeña puerta, que a su vez dirige hacia otro grupo de escaleras de ascenso al segundo y tercer pasillo interior.[52]​ Finalmente, un último tramo de escalones tallados en el casquete interior desemboca en el cuarto pasillo interno, situado en la base de la linterna.[53]​.

En cada paño exterior se abren nueve aberturas circulares para la ventilación, distribuidas en tres hileras de tres huecos cada una. Además de estas, se realizaron otros pequeños agujeros rectangulares para iluminar y ventilar el hueco existente entre los dos casquetes.[54]​ La hoja interior presenta dieciséis pequeños óculos a la altura del segundo y tercer pasillo, dos en cada paño, que permitían la visión del templo y el montaje de los andamios para la realización del revestimiento interior de la cúpula.[55]​.

Geometry and proportion

The composition of the dome follows the golden proportions, as was the custom of the time, seeking a feeling of balance and harmony between its parts.[56]​ The base of the imposts is about 55 meters from the ground, the lantern is 21 meters high, the drum measures 13 meters and the average height of the dome is 34 meters. The total height of the structure, including the golden ball and the cross raised above it, is 116.50 meters. It should be taken into account, however, that the actual measurements of the dome were calculated in Florentine arms[note 7]​and not according to the decimal metric system. Therefore, any theory referring to the famous Fibonacci sequence, that is, to the numbers 13, 21, 34, 55..., is totally erroneous and meaningless. When the dome was consecrated in 1436, the composition of the Flemish musician Guillaume Dufay, the motet Nuper rosarum flores, reproduced in music the relationships of the construction.[56]​.

The apparent contour of the dome also follows very precise rules. The outer profile is an acute quarter arc, while the interior has a curvature of an acute fifth arc. The layout of these arches is made from the diagonal of the interior octagon, 54 meters long, which is subdivided respectively into four and five equal parts.[note 8]​In this way, the resulting pointed profile is a circular segment whose radius is one fifth greater than the span of the vault.[58]​ Theoretically, Brunelleschi was confident that this pointed Gothic form would provide greater stability,[59]​ as well as greater height than a hemispherical dome.[note 9]​

[61]​ In order to materialize the acute fifth arch in the work, wooden templates were used with the curvature of the arch, which were fixed in the interior corners of the octagon and slid upwards as the panels were being built.[62]​ The layout of the dome according to the acute fifth appears reflected in the parchment of Giovanni di Gherardo da Prato") 1426.[63]​.

This profile also closely resembles an upside-down catenary, a type of curve that is highly effective in terms of stability. This shape physically represents the curvature generated by a chain "Chain (object)") or rope suspended from its two ends. According to the century's mathematician Leonardo Ximenes, Brunelleschi would have intuitively drawn a catenary curve, the geometry of which would have given the dome great resistance.[60]​ As Leibniz, Huygens and Bernoulli would later demonstrate at the end of the century, this is the most stable way to design a self-supporting dome, that is, one that is supported by its own weight.[64]​.

For the construction of his great work, Brunelleschi surrounded himself with a large team of experts in various subjects, among whom were the mathematicians Paolo dal Pozzo Toscanelli, whose calculations were essential for the success of the project,[2]​ and Giovanni dell'Abaco. Brunelleschi himself was also a mathematician and was the creator of the geometric rules of perspective.[56][65]​.

the drum

The drum on which the dome sits is an octagonal prism, located between the top of the four large angular pillars and the line of imposts or starting level of the dome. Its height is 13 meters from the roof of the main nave "Nave (architecture)") of the cathedral, it has an approximate width of 42 meters and the thickness of its walls is four meters.[1] It is located 54 meters from the ground. In its upper part, eight large oculi open up to illuminate the interior of the triconcha of the apse, whose diameter is about 4.65 meters on the inside and about seven meters on the outside. The entire weight of the dome and the lantern unloads on the drum, which is subjected to great stress and which in turn must be transmitted to the four corner pillars.[66]​ The interior is delimited by two balconies with cantilevered balustrades. The first balcony is accessed by four stairs housed inside the pillars, which join in the southeast area forming a single staircase located between the two caps of the dome.[67]​.

Brunelleschi had inherited as a starting premise the construction of a dome on a large drum.[68]​ The size of the dome was notably larger than initially planned, surpassing that of the Pantheon in Rome, which until then was considered the largest in the world, while legend attributed it to a "work of the devil."[2]​ The reasons for this dimensional increase were due not so much to a desire for superiority over the Roman dome, but to the need to reinforce the drum as much as possible. In fact, this had been raised compared to the original model with an additional body in which the eight large oculi had been opened for illumination. This strategy also raised the plane of the dome's imposts above all the vaults built to date.[note 10]​The reduced thickness of the drum further increased the problem, since the resistance against the lateral thrusts transmitted from the dome was reduced.[22]​.

However, the main obstacle to the construction of the dome was the irregularity of the drum, since its diagonals did not converge on a single reference center, so the vertical central axis of the dome was not unique.[note 11]​On the contrary, the union of the opposite angles of the octagon produced four different centers, which could lead to errors since they served as a reference to measure distances during the construction of the dome. This irregularity could have been solved by working with pairs of opposite sides, as pointed out in one of the construction hypotheses mentioned later.[70]​.

The type of dome

A hemispherical, parabolic "Parabola (mathematics)") or ellipsoidal dome is a figure or place of points generated from an arc "Arch (geometry)") that rotates around a vertical axis, called in this case dome of revolution.[note 12]​It is made up of pieces called voussoirs that are arranged in the shape of an arc up to the upper voussoir or key "Key (architecture)"), which It balances the efforts in a manner analogous to an arch or vault but in three dimensions. To allow light to enter the interior of the dome, a zenithal oculus can be opened, accompanied or not by a lantern "Lantern (architecture)"). To do this, the key is replaced by an upper ring of pieces that resist compression efforts, sometimes made of bronze for greater stability and durability.[note 13]​ Theoretically, it is always possible to build a dome of revolution, since it is made up of infinite rings that hold themselves together once completed. The construction technique is quite simple: the bricks are arranged in overlapping concentric circular rings, whose diameter decreases as it rises towards the top. In this way the structure is self-supporting, that is, capable of supporting itself.[72]​.

Those in charge who were in charge of the works on the duomo were concerned that the project envisaged an octagonal dome with flat faces, a figure very different from a solid of revolution. The dome of the Cathedral of Florence, rather than a "dome" itself, is an octagonal cloister vault,[44]​ described as the 45° intersection of two ribbed vaults, very similar to those of the naves of the cathedral itself. Unlike a dome of revolution, a vault is not self-supporting, so in this case the use of falsework or wooden scaffolding would have been essential to hold the walls under construction until the mortar "Mortar (construction)" sets. As it is a structure with an octagonal base, it presents a discontinuity at the vertices of said octagon, where the stresses are concentrated.[72] On the other hand, in Italy it was not possible to obtain the large beams available in northern Europe, and even if it had been possible, the enormous beams used in the cathedrals of France and England would not have been sufficient to support a vault like the one that was intended to be built. According to some hypotheses, this difficulty would have been resolved by the continuous horizontal factory rings, contained within the perimeter of the structure, which would make it behave similarly to a true dome despite being a vault, and therefore would be self-supporting.[44]​.

The scaffolding

One of the initial drawbacks in the construction of the dome was the impossibility of using traditional construction techniques. An entablature system supported from side to side of the drum would not have been feasible, due to the great distance it had to cover and the enormous weights to which it would be subjected. The enormous height at which the works were carried out also did not allow a structure supported from the ground.[1] Although the decision not to use fixed falsework was not taken from the beginning, in the construction program of July 30, 1420, the architect had already foreseen a construction without the use of frameworks or falsework, with the exception of service scaffolding. For this purpose, he devised an aerial scaffold arranged on a circular wooden platform mounted at the height of the interior of the drum, supported by large crossbars[note 14]​ inserted in the needles,[note 15]​ still visible at the level of the balcony floor,[76]​ and which was gradually raised.[77]​ Eight wooden forms were placed on this scaffolding, anchored to the wall with hooks, which moved upwards at as the construction evolved.[31]​ This arrangement had to be followed up to a height of 30 arms, leaving open the possibility of using other construction solutions later.[note 16]​The project to construct the dome without traditional falsework was an innovative idea that caught the attention of the Opera del Duomo.[22]​.

At the beginning of the works, when the dome wall was almost vertical, the scaffolding was supported with beams inserted into the wall, while in the last section, when the dome curved to converge towards the center, Brunelleschi designed another scaffolding suspended from the central hole, perhaps supported with long beams on a platform supported on a lower level, where the materials and construction machinery would also be deposited.[77]​.

La obra se organizaba principalmente en el área del presbiterio "Presbiterio (arquitectura)"), donde se hacía el acopio de materiales, máquinas y herramientas, así como en las cuatro zonas donde se emplazan los absidiolos. Al nivel del arranque de la cúpula se construyó el gran andamio interno anular donde se organizaban los trabajos. En otras ubicaciones alrededor de la catedral se almacenaba la madera y el mármol, las herramientas de trabajo, una forja, un tejar para la fabricación de ladrillos y un espacio reservado para los artistas, donde Brunelleschi construyó un modelo a escala de la cúpula.[78]​[nota 17]​.

La mayoría de los operarios trabajaba en los andamios, mientras que en el suelo lo hacían los que manejaban la maquinaria y los funcionarios que controlaban la recepción de los materiales. A medida que la obra progresaba en altura, se hizo obligatorio tomar mayores medidas de seguridad. Se colocaron parapetos en los andamios, se prohibió el consumo de vino puro durante la jornada y a los obreros se les permitió aceptar o rechazar las actividades más arriesgadas (con una evidente diferencia de salario). Para que el ritmo de la obra no tuviese tiempos muertos, los obreros solo bajaban del andamio una vez al día, siéndoles suministrado directamente el material de trabajo y la comida.[80]​ La organización de los trabajos de construcción pudo llevarse a cabo gracias a una mano de obra experta y de confianza, un eficaz sistema de distribución de las distintas labores y un aprovisionamiento eficiente de los materiales. La plantilla de obreros se renovaba cada año, aunque el personal más experto aseguraba su continuidad. Los operarios debían comprometerse a seguir unas reglas de comportamiento precisas, y los salarios eran asignados según la calidad del trabajo realizado.[81]​.

Las labores de construcción se organizaban en ocho sectores paralelos que trabajaban a la vez, uno por cada paño, lo cual permitía levantarlos uniformemente, ya que estos se iban autosustentando a medida que el mortero fraguaba. El aparejo "Aparejo (construcción)") dispuesto a cuerda floja[nota 18]​y en espina de pez[nota 19]​permitía la continuidad de las superficies y la correcta trabazón de los ladrillos, incluso cuando el mortero estaba fresco. Así, estas dos técnicas fueron esenciales para la construcción de la cúpula sin cimbras fijas.[84]​ Brunelleschi calculó con gran precisión cada detalle, desde la inclinación de los muros hasta la disposición de los ladrillos en espina de pez para que la cúpula fuese capaz de mantenerse en pie por sí misma a medida que crecía progresivamente, sin necesidad de apoyar sobre los tradicionales y enormes andamiajes de madera levantados desde el suelo.[85]​.

Brunelleschi's machines

The lifting of large quantities of material was not possible through the spiral stairs, used by the bricklayers to access the base of the scaffolding. Therefore, Brunelleschi had to devise and build new machines and tools, which would later inspire other Renaissance engineers such as Leonardo da Vinci.[note 20]​The main lifting machine was the reversible ground winch, located at ground level, which allowed large loads to be raised and lowered without having to reverse the direction of rotation, thereby saving time. Furthermore, it was capable of lifting a wide range of weights, from the lightest to the heaviest, with equal traction power, which meant that no more animals or several lifting operations were necessary. The reversible winch operated for ten years without substantial modifications or repairs.[86]​.

In addition to the reversible winch, cranes and machinery were used in the construction to precisely lift heavy loads, located on the internal scaffolding or on the walls of the dome. A large crane 20 meters high was used to close the key and to lift the lantern materials. Another of them, probably drawn by Bonaccorso Ghiberti"), was mounted on the oculus for the construction of the keystone. Many other mechanisms and devices used, such as light winches or wired rotating hoists, are also attributed to Brunelleschi.[87]

These mechanisms used to lift materials during construction mark in themselves a great milestone in building technology.[88]​ Most experts, from Giorgio Vasari to Ross King"), consider them as an application of the techniques devised by Brunelleschi for his famous clocks,[89]​ of which only the one on the tower of the Palazzo dei Vicari" in Scarperia is preserved.[90]​ None of the lifting machines have survived to the present day. Brunelleschi, although numerous copies remain in different drawings made by Mariano di Jacopo, Francesco di Giorgio, Bonaccorso Ghiberti and Leonardo da Vinci.[91]​[92]​.

Filippo Brunelleschi era famoso en Florencia, además de como artista polifacético, como poseedor de un carácter un tanto irascible y de un sentido del humor bastante mordaz.[nota 21]​Era además un maestro en el arte de la manipulación;[94]​ de hecho es considerado como el padre de la perspectiva, que es una representación imaginaria de una realidad tridimensional mediante un sistema bidimensional.[95]​[96]​[97]​.

En lo que respecta a la construcción de la cúpula, parece ser que Brunelleschi también jugó al despiste, puesto que tras años de debate sobre cual debía ser el «mágico artificio» que habría permitido su edificación, no se llegó a ninguna conclusión definitiva. La cúpula octogonal de caras planas, construida sin cimbras y con mortero de fraguado lento de la época teóricamente no podía sostenerse. El arquitecto fue muy celoso del modo en que fue edificada y trató de desvelar lo menos posible de su técnica constructiva.[2]​ La disposición de los ladrillos con un aparejo en espina de pez, visibles en el corredor hueco existente entre las dos cúpulas, se indicaba normalmente como una parte del «secreto» aunque sin que se entendiese la función real. Sin embargo, según algunos expertos estas superficies de albañilería no se corresponderían con una función estructural real y serían únicamente un engaño deliberado,[98]​ tal vez con el propósito de evitar las críticas que malograran su proyecto o el robo de su idea.[99]​.

Los detalles de la estructura de la cúpula, así como el proceso constructivo empleado por Brunelleschi permanecen todavía ocultos en su interior. Las especificaciones del documento de 1420 se ajustan al resultado final, pero proporcionan poca información sobre la metodología constructiva empleada.[11]​ Se han propuesto diversas teorías sobre el sistema de construcción y la forma en que funciona estructuralmente, sin que ninguna de ellas sea concluyente:[100]​.

A dome of revolution contained in the octagonal dome

One of the best-known theories is the one mentioned separately by professors Rowland J. Mainstone and Salvatore Di Pasquale,[101]​[102][11]​ and which had already been pointed out in ancient times by Alberti.[103]​[104]​ In 1977, during the process of removing the tiles in one of the sectors for restoration, it was discovered that the brick laying lines were not horizontal but rather They followed an open upward curve, called tightrope. This fact, which had never been noticed before, led us to examine the arrangement of the bricks in more detail.[note 22] It was also observed that the faces of the bricks were not horizontal but were inclined in rows that converged at a point located in the center of the octagon at the base of the dome. It was as if the flat-faced dome had been made by taking parts from walls built like a classical dome. The conclusion reached by the researchers was that the bricks were arranged as if a dome of revolution was going to be built. In this way and to guarantee that the structure was self-supporting, it would be enough if a dome of revolution of adequate thickness for its stability could be inscribed in the thickness of the walls.[105]​.

However, since he could not build the dome with a thickness large enough to contain a revolution inside, Brunelleschi would have created a dome with a double cap and horizontal intermediate connecting ribs. These are not of constant section, but rather have greater thickness at the junction with the eight large main ribs, while their thickness is reduced in the center of the panel. The profile of these arches, together with the profile of the intrados of the exterior cap of the dome, generate an almost circular shape,[106]​ so that between both caps it would be possible to inscribe a complete circular ring of lesser thickness, which would be tangent to the angles of the interior octagon and to the midpoints of the exterior. Thus, the real octagonal dome would be assimilated to an equivalent virtual dome of revolution.[103]​[11]​.

This system requires that the mortar courses describe the shape of a cone of revolution "Cone (geometry)") inscribed within a circular dome, with a common vertical axis coinciding with the vertical axis of the dome and its vertex "Vertex (geometry)") pointing downward.[11]​ At the place where this virtual cone intersects with the octagonal shape of the dome, a tightrope conical line is produced.[107]​ In Essentially, this theory proposes that the dome would be composed of a series of horizontal conical sections, whose inclination would increase as greater height is reached, and whose mortar courses would also increase their curvature with height.[108]​.

As for the function of the bricks arranged in herringbone, according to Paolo Rossi[109]​ this would have been to support the structure until it was closed with the key "Key (architecture)"), thus avoiding the use of large trusses.[110]​ In this way, Brunelleschi would have managed to build the octagonal masonry dome without the help of formwork and in a somewhat intuitive way.[103]​.

However, this theory was questioned by some experts in the 1980s, since a virtual dome of revolution of small thickness, contained within another enormous octagonal dome of greater thickness and weight, would have produced a large amount of "dead weight" without great benefits in return. Furthermore, this hypothesis did not give any importance or structural function to the eight great main nerves and, in essence, did not consider the dome as an integrated structure in all its parts.[110]​.

A radial dome drawn with guide ropes

Another of the most famous theories is the one formulated and published by Professor Massimo Ricci.[111]​[112]​[113]​ According to this hypothesis, the construction technique of the dome would not respond at all to a dome of revolution, not even in its internal structure. The method used for its construction would be through a system of radial ropes that would intersect on a central axis and that would be attached to a fixed reference frame.[114]​ This procedure would determine the position and inclination of the bricks during the construction process,[110]​ which would not have been placed according to a circular arrangement, but rather concave with respect to the opposite side of the octagon.[115]​.

After carrying out various checks on the intrados of the faces of the dome, it was deduced that the structure of the dome could have been developed in a vertical radial direction and not horizontally, as suggested by the hypothesis of the dome of revolution. According to this new assumption, the structure of the dome would have been generated as a succession of inclined radial rows.[110] Brunelleschi would have used a "pseudocircular" curve,[note 23]​drawn from the circular scaffolding located at the base of the imposts, and centered on the vertical of the building. This curved shape would have been materialized through a system of ropes crossed with each other and measured with a plumb line on the diagonals of the base, fixed at the interior angles of the octagon.[114]​.

In this way it would have been possible to define the angles of the dome using small mobile forms. The "pseudocircular" curve would trace the contour of each panel by means of a mobile rope fixed on one side on the curve itself and which would also pass through the center on the vertical. This rope would describe a curve in each panel following this scheme in the shape of a lobed flower, which would move upward as the construction progressed in height.[117]​ Through this system, the bricklayers would have a reference at each point of the construction to arrange the course of bricks.[118]​ These would be placed in courses inclined towards the center of the dome, with the herringbone rig rising with a spiral arrangement.[119]​ This would be, according to Ricci, the true function of the herringbone arrangement: to fix the exact radial position of each brick (following the direction marked by the rope) during its placement so that it performs its specific function.[120]​ In addition, this technique would make it possible to construct the eight panels independently and without interruptions, which would have avoided the difficulty of constructing the eight faces at the same time.[110]​ According to this hypothesis, the tightrope arrangement would not have any structural function, but would be a consequence of the construction method used using the flower-shaped template.[121]​.

In the program of 1426, reference was made for the first time to the lantern, when the dome was almost finished and closed with the upper compression ring that joined both caps. strong, light, luminous and better waterproofed.[16]​ On April 15, 1446, shortly after the laying of the first stone, Brunelleschi died.[35]​ After his death, various artists continued its construction following his design, among them his friend and disciple Michelozzo di Bartolomeo, Antonio Ciaccheri"), Bernardo del Borra (Bernardo Rossellino) and Tommaso Succhielli, who finished it on April 23, 1461.[16] Various machines and inventions devised by Brunelleschi himself were used for its construction, including a rotating crane and a wooden frame.[125]​.

The lantern design continues the polygonal shape of the dome. It is made up of a central octagonal prism "Prism (geometry)") six meters in diameter and sixteen meters high. It sits on a marble platform held by the stone chain that closes the dome at the top. Its edges are surrounded by eight buttresses finished in the shape of a volute "Volute (architecture)") and supported on eight pilasters crowned by Corinthian capitals. Eight stylized windows nine meters high open on its faces.[126] Above the prism is a conical piece "Cone (geometry)"), grooved like a needle, adorned with semicircular arches on its faces. On May 30, 1471, a bronze finishing sphere, designed by Andrea Verrocchio[35] and crowned with a cross, was installed at the top. In order to lift it, Brunelleschi's machines were also necessary, an operation carried out by the assistants of the Verrocchio workshop, among whom was a young Leonardo da Vinci.[92]​.

In 1475, the mathematician Paolo dal Pozzo Toscanelli installed the gnomon of a sundial at the base of the lantern, which allowed him to calculate with great precision the orbit of the Earth around the Sun.[127]​.

Formally, the lantern represents the visual axis of the cathedral and serves as a finishing touch to the ascending lines of the eight large vertical ribs. It is believed that Brunelleschi may have been inspired by religious metalwork for his design, such as the censers or the "Custody (liturgy)" monstrances, enlarged to a monumental scale. The lantern that was finally built may have undergone modifications with respect to the original project, with a more elegant and refined ornamentation in accordance with the taste of the middle of the century, dominated by the figure of León Battista Alberti.[128]​.

The lantern has a very important function in the overall statics, since it stabilizes the compression ring of the dome.[129]​[130]​ The eight vertical ribs converge towards its base and continue in the buttresses, so that the weight of the lantern is unloaded on them and transmitted through the ribs.[35]​ On the other hand, the forces acting on the structure are so great that the ribs themselves tend to bend inwards due to the effect of the loads and their own weight. The enormous weight of the lantern, about 750 tons, counteracts the inward thrust of the base of the dome.[131]​.

The lantern has suffered numerous vicissitudes throughout history. On the night of April 5, 1492, lightning struck it, destroying almost half of it, although without causing significant damage.[36] During the night of January 26 to 27, 1601, around 5 in the morning, the sphere collapsed due to another lightning strike. The dome was affected in different places,[note 25]​ and the ball had to be replaced in 1602. Behind the plaza under the dome, a marble disc still marks the exact point at which it crashed to the ground.[2]​ In 1859 a lightning rod was installed to protect the lantern and the sphere.[36]​.

Once the construction of the dome was completed, only the outer part of the octagonal "Drum (architecture)") remained to be decorated. A first note, regarding the dimensions, had already been sketched by Brunelleschi in the wooden model attributed to the architect himself and preserved in the Museum of the Opera del Duomo "Museo dell'Opera del Duomo (Florence)"). Brunelleschi.[134]​ Among these first projects of the century was also a model attributed to Giuliano da Maiano.[135]​.

The problem remained unresolved until the beginning of the century, when a competition was called for the completion of the drum. Various architects participated in it, each of them with their own wooden model. Andrea Sansovino proposed a coronation with a baluster surrounded by Ionic columns; However, Giuliano and Antonio da Sangallo the Elder proposed a model without a balustrade.[17] Another project was presented by Simone del Pollaiolo, together with Giuliano da Sangallo and Baccio d'Agnolo.[136]

In the summer of 1507, the Opera of Santa Maria del Fiore commissioned Michelangelo to make a drawing or model for the drum competition before the end of August. According to the author Giuseppe Marchini, the artist would have sent some sketches to a carpenter in Florence for the construction of the model.[note 26]​The project broadly proposed maintaining a certain continuity with the pre-existence, by inserting a series of rectangular pieces in green Prato marble aligned with the capitals of the corner pilasters. Another entablature was planned, closed by a cornice, analogous to that of the Strozzi Palace. The design would be completed with a series of eight statues placed at the top, corresponding to the eight ribs of the dome. However, this project was not chosen by the jury.[134]​.

In 1512 the decision was made to begin work on the completion of the drum according to the project designed by Baccio d'Agnolo together with Pollaiolo and Giuliano da Sangallo, the winners of the competition. The regulations imposed that they had to work as a team and respect the proposal partially built to date, in order to avoid unnecessary cost overruns.[134] D'Agnolo himself, in charge of the Santa María del Fiore Opera at that time, was responsible for continuing the work after Pollaiolo's death and Sangallo's abandonment.[17] The project included a frieze of classical inspiration and two pilasters on the sides of the oculi. It also provided for the incorporation of a solid continuous balcony at the top of the drum, supported by white marble columns, with nine arcades on each side divided by lesenas.[134] The balcony was composed of three parts: a central corridor and two balustrades, one lower and one upper. The central one was accessed through the doors opened by Brunelleschi in the drum.[138]​ This solution through a continuous balcony had already been foreseen by the architect in the document of 1420.[17]​.

During the construction phase some modifications were made. The balusters were replaced with more robust ones, two arches were added on each side and grooves were made in the lesenas.[134] However, the works were interrupted in 1515, with the balustrade completed only on the side of the dome facing the Via del Proconsolo. The reasons for the paralysis may have been due to the lack of success obtained among the Florentines or to the criticism expressed by the citizens and especially by Michelangelo.[139]​[note 27]​.

Around 1516, Michelangelo made some drawings for the completion of the drum, preserved in the Buonarroti house.[134] He probably had a new wooden model built,[note 28]​where the balustrade was again suppressed in favor of greater relief of the supporting elements. Specifically, one of the drawings shows the addition of paired columns, located at the corners of the octagon and crowned by several projecting cornices.[17] It is thought that this scheme could have later been used for the dome of St. Peter's Basilica in the Vatican. However, Michelangelo's ideas remained only a project and the drum ultimately ended up incomplete on seven of its eight sides.[134]

In 1694 the architects Gherardo and Pier Francesco Silvani" advised reinforcing the continuous balcony, since it had experienced various movements despite having been strengthened on previous occasions.[134] It is thought that probably the enormous weight of the entire finished balustrade would have created stability problems in the dome.[142]

Eight wooden models presented in competition representing one side of the drum are preserved in the Duomo Opera Museum. Numbers 136 and 137 belong to the century, while those cataloged with numbers 139 to 144 are from the century. The oldest of all, number 136, is attributed to Ciaccheri, while in the other seven there are doubts about its authorship.[143]​.

Brunelleschi carecía de referencias tecnológicas a la hora de resolver el problema de construir una cúpula gallonada, es decir, una bóveda de cañón apuntada de planta octogonal, por lo que tuvo que inventar literalmente el procedimiento constructivo empleado en todo su proceso. Todas las cúpulas que se han intentado proponer como modelos para la de Florencia eran de revolución (autoportantes) o bien realizadas con cimbras y armaduras, mientras que la de Santa María del Fiore no estaba basada estos sistemas. A pesar de la novedad de la técnica finalmente utilizada, se han formulado diversas hipótesis sobre las posibles fuentes que podrían haber inspirado al arquitecto: por una parte, los precedentes florentinos; por otra, las estructuras abovedadas de época romana y por último, la tradición constructiva de Persia.

Varios autores coinciden en que Brunelleschi tenía presente la geometría y la técnica constructiva de la cubierta del baptisterio de San Juan "Baptisterio de San Juan (Florencia)"), realizada mediante una cúpula de perfil apuntado sobre una planta octogonal.[144]​[145]​ Esta cúpula arranca desde un nivel inferior a la línea de coronación de los muros exteriores y está recubierta por un techo piramidal octogonal de piedra. Entre la parte interior y los muros perimetrales de cierre hay un hueco de 1.25 metros de anchura.[144]​ Sin embargo, para su construcción no se empleó la técnica del aparejo en espina de pez.[146]​.

En lo que respecta a la segunda fuente de inspiración, el biógrafo Antonio di Tuccio Manetti relata que Brunelleschi pasó en Roma varios años de estudio,[147]​ atraído quizás por el hallazgo de objetos y esculturas propios de aquellos años. A principios del siglo , la ciudad eterna era un inmenso yacimiento arqueológico.[148]​ Durante su estancia se habría inspirado en la arquitectura clásica y habría conocido las teorías de Vitruvio, según las cuales toda arquitectura estaba basada en un módulo y en una retícula geométrica.[149]​ Asimismo, podría también haber conocido la disposición en espina de pez tras haberla observado en diversos edificios romanos.[150]​.

La cúpula más famosa de la romanidad, el Panteón de Agripa, es una cúpula de revolución semiesférica de dimensiones similares a Santa María del Fiore.[151]​ Su diámetro de 43 metros y su óculo superior de 8 metros pudieron haber inspirado a Brunelleschi en su diseño.[22]​ Sin embargo, la de Roma tiene un único casquete y está realizada en hormigón con casetones,[152]​ una técnica de construcción que no era reproducible e incluso debía ser del todo incomprensible en la Italia del primer Renacimiento, que había perdido la tradición romana del hormigón.[153]​ Del estudio del exterior, Brunelleschi como máximo habría podido apreciar que la forma escalonada se levantaba a partir de una forma circular y que, por lo tanto, las cúpulas romanas generalmente contenían siempre un anillo circular completo en cada nivel de su espesor. Quizás Brunelleschi conoció la cúpula de la Domus Aurea, levantada sobre un pabellón octogonal y construida con hormigón fresco, que requirió cimbras durante el fraguado.[154]​ Durante su construcción, su forma poligonal inicial se fue transformando en una circular a medida que se elevaba y estrechaba, una técnica empleada en diversos edificios romanos.[150]​.

La hipótesis del viaje romano de Brunelleschi está generalmente aceptada por toda la crítica,[155]​ aunque recientemente se ha apuntado que, si se descarta que el origen de la cúpula del duomo fuese el Panteón, nada en la obra del gran arquitecto debería por fuerza relacionarse con elementos arquitectónicos que eran visibles únicamente en Roma. El viaje a Roma por lo tanto fue posible, pero no indispensable para la formación de los cánones arquitectónicos brunellesquianos.[156]​.

Respecto a la inspiración en Persia, se ha querido conjeturar que el arquitecto hubiese conocido las técnicas constructivas de los mausoleos orientales, dados los importantes intercambios comerciales existentes con el Medio Oriente, aunque la influencia no está clara.[152]​ La doble cúpula levantada sin cimbras del mausoleo de Soltaniyeh en Irán, construido entre 1302 y 1312,[157]​ la construcción de los muros en espina de pez de los antiguos edificios selyúcidas del siglo , o las mezquitas posteriores de Isfahán y Ardistán") son comparables al lenguaje estructural y a la técnica de Brunelleschi,[146]​ aunque diferenciándose sustancialmente en los materiales, en el aparejo murario y en las dimensiones.[158]​.

Later influences

The dome of Santa María del Fiore also served as inspiration for later constructions. Giuliano da Sangallo took it as a model for the dome of the Sanctuary of the Holy House of Loreto "Loreto (Italy)") in 1500, although with a single cap. The lantern also resembles that of Brunelleschi and was made by Giuseppe Sacconi in 1889.[159]​Antonio da Sangallo the Younger studied the dome for his lantern project for Saint Peter's in Rome.[160]​.

In 1546, Michelangelo analyzed the structure of the dome and reinterpreted it in his project for the dome of Saint Peter,[note 29]​where he adopted a similar double-cap solution.[note 30]​Likewise, he introduced a system of sixteen ribs that converged towards the crown, joining both caps and supporting the lantern.[162]​[163]​Giorgio Vasari took it as an example. for the basilica of the Virgin of Humility") in Pistoia and in the temple of Saint Stephen of Victory") in Foiano della Chiana. In his book Le Vite he dedicated a large part of his writings to the biography of Brunelleschi and to the narration of the construction process of the dome. Santi di Tito in 1597.[164]​.

Although it was built with innovative techniques, the dome always had a direct inspiration from that of the baptistery, from which it took its development and its octagonal shape. Initially, an interior decoration with mosaic had been planned, another element in common with the Romanesque dome. Brunelleschi made various sketches that the workers could have used in the ornamentation of the immense interior surface of the dome, of more than 3,600 square meters. poem from the early 1470s could refer to this project.[17]​.

However, the mosaic technique was already very little used at that time and was considered extremely expensive. Additionally, there were also concerns that the binder used to secure the tiles could increase the overall weight. This problem does not seem very important today, knowing the enormous weight of the dome and its resistance, but at the time it was considered an essential reason to abandon the project in favor of decoration using the fresco technique.[18]​.

The work did not begin until 1572, in the midst of Mannerism, a century after the completion of the masonry works. Grand Duke Cosimo I de' Medici chose the theme of the Last Judgment to decorate the enormous dome, and entrusted the task to Giorgio Vasari, with the collaboration of Vincenzo Borghini in choosing the iconographic theme. At Vasari's death, only the first of the planned concentric stripes had been completed, the smallest of them, located at the top around the octagonal oculus covered by the lantern "Lantern (architecture)").[165]

He was succeeded by Federico Zuccari, who in a few years and according to his own words, almost single-handedly, completed with tempera painting the immense figurative cycle, one of the largest in the world in surface area, and one of the masterpieces of mannerism. monsters, 23 children and 12 animals.[166] The painter himself, in his will, proudly recalled having conceived and completed the work, of which he especially mentioned the great Lucifer, thirteen Florentine arms high (about 8.5 meters). Obviously, he used many assistants, among whom was a young Domenico Cresti. The work was completed in 1579, just three years after the beginning of the work.[18]​.

The contents of the cycle were those adopted at the Council of Trent, which had reviewed medieval Catholic doctrine, ordering it in a clear way.[18] The dome was divided into six concentric rings and eight vertical stripes. At the top, the central lantern is surrounded by the 24 prophets of the Apocalypse, located in groups of three characters in each strip. Starting from the top, each vertical stripe comprises four scenes represented in each of the rings, which are organized from top to bottom with the following scheme:

• - a choir of angels with instruments of the Passion (second ring);

• - a category of Saints and Elect (third ring);.

• - a triad of characters representing a gift of the Holy Spirit, the seven virtues "Seven Virtues (catechism)") and the seven Beatitudes;.

• - a region of Hell dominated by a capital sin.[167]​.

In the eastern strip, in front of the central nave, the four rings become three to make room for the great Christ in Majesty, in contrast to the image of Lucifer, located in the opposite strip. Christ the Judge, represented with great hieraticism, is located between the Virgin Mary and Saint John the Baptist. Below them are placed the three theological virtues: Faith, Hope "Hope (virtue)") and Charity "Charity (virtue)"), followed below by allegorical figures that represent Time[note 31]​ and the Triumphal church.[167]​ Among the Elect, the painter represented a wide gallery of contemporary figures, such as the patrons of the Medici family, the emperor, the king of France, Vasari, Borghini, Giambologna and other artists, including himself and many of his relatives and friends.[18] Zuccari also added his signature and the date.

In 1980, a long process of restoration of the frescoes in the dome of Santa María del Fiore began, which lasted until 1995.[18]​.

• - History of Italian Renaissance domes.

Additional bibliography

• - n.10, 1972; n.12, 1972; n.2-3, 1977; n.12, 1977; n.7-8.

• - ; appendix:.

• - (with the collaboration of Massimo Ricci).

• - Cathedral of Santa Maria del Fiore.

• - Filippo Brunelleschi.

• - Dome.

• - Museo dell'Opera del Duomo (Florence) "Museo dell'Opera del Duomo (Florence)").

• - Piazza del Duomo (Florence) "Piazza del Duomo (Florence)").

• - Renaissance Architecture.

• - Italian Renaissance.

• - Republic of Florence.

• - Wikimedia Commons hosts a multimedia category on Dome of Santa Maria del Fiore_-_Dome "commons:Category:Santa Maria del Fiore (Florence) - Dome").

• - Official website.

• - History and complementary information about the dome, Galileo Museum of the History of Science.

• - Association Filippo di Ser Brunellesco for the construction of the model of the dome.

• - Some aspects of the funicular curves. Articles on the mathematical study of the funicular curves referred to the dome of Santa María del Fiore.

• - Lecture by Professor Luca Giorgi at the Higher Polytechnic School of the University of Alicante, February 2014.

• - Documentary that explains Massimo Ricci's theory.

• - Includes an animated short film created by National Geographic (in English).

• - Article on the construction techniques of domes and vaults in ancient times.

Contenido

Las obras del actual edificio de la catedral de Santa María del Fiore se iniciaron entre los años 1294 y 1295 para sustituir a la antigua iglesia de Santa Reparata, de dimensiones más pequeñas.[14]​ Entre 1410 y 1413 se construyó el tambor "Tambor (arquitectura)"),[1]​ quedando finalizada su base superior entre 1414 y 1415. Sin embargo, a principios del siglo todavía no se había planteado en profundidad el problema de la cubierta, cuya edificación preocupaba a los miembros de la Opera del Duomo "Museo dell'Opera del Duomo (Florencia)") desde hacía tiempo.[nota 1]​No era una tarea fácil construir y ubicar el punto donde se tenían que apoyar las enormes cimbras de madera que debían sostener la cúpula hasta su cierre final con la clave "Clave (arquitectura)").[21]​ Más aún, resultaba inviable que una obra de tales dimensiones pudiera ser sujetada mediante los andamiajes tradicionales, puesto que ninguna variedad de madera habría podido soportar provisionalmente un peso tan grande.[1]​.

Arnolfo di Cambio, el arquitecto que proyectó la nueva catedral, probablemente había previsto este contratiempo, puesto que había imaginado la conclusión de su edificio con una cúpula, un elemento muy distinto y de mayores dimensiones que el tradicional cimborrio de las catedrales medievales. Su idea de emplear un tipo de cubrición de apariencia más convencional se puede apreciar en un conocido fresco de Andrea di Bonaiuto ubicado en la Capilla de los Españoles de Santa María Novella en Florencia.[22]​ La pintura, datada de 1355 aproximadamente, muestra en segundo plano una iglesia claramente reconocible como Santa María del Fiore, en la que se representa una cúpula desprovista de tambor y con forma semiesférica, aunque de lados muy curvados.[23]​ Sin embargo, una cúpula de medio punto, aunque fuese de menor tamaño y no tuviera tambor, hubiese tenido grandes problemas para soportar el peso de la linterna "Linterna (arquitectura)") de la imagen sin la ayuda de refuerzos. De todas formas, es posible que Bonaiuto hubiese dado al dibujo una forma más redondeada que la que pretendía di Cambio para su proyecto.[24]​.

El 19 de agosto de 1418, la Opera del Duomo convocó un concurso público para la construcción de la cúpula.[nota 2]​Además de resolver los problemas técnicos de ingeniería, debía rematar el edificio de forma armónica, resaltando el valor simbólico e imponiéndose sobre el espacio urbano y el entorno.[25]​ De los diecisiete participantes pasaron a una segunda fase Filippo Brunelleschi, quien había fabricado una maqueta de madera para la ocasión, y Lorenzo Ghiberti.[26]​ Brunelleschi perfeccionó su modelo, «grande como un horno», aportando una mayor información para demostrar la viabilidad de una cúpula sin armazón. A finales de 1419, con la ayuda de Nanni di Banco y de Donatello, organizó una demostración en la plaza del Duomo "Piazza del Duomo (Florencia)"), entre la catedral y el campanile, con una maqueta realizada con ladrillo y argamasa y sin armazón. Esta representación impresionó positivamente a los miembros de la Opera del Duomo.[26]​ El 20 de marzo de 1420, la obra fue asignada definitivamente a Brunelleschi y a Ghiberti, quienes fueron nombrados Superintendentes de la Cúpula.[nota 3]​[28]​.

The Document of 1420

On July 30, 1420, the so-called Document of 1420 was drafted, attributed to Brunelleschi himself, in which the construction program of the dome was determined. It was one of the first contracts in which a master builder assumed responsibility for the project towards the client.[29] This agreement explained how the drum should be closed and specified the most important aspects of the construction. In essence, it was a new "work program" that synthesized in a few lines the structure, form and dimensions of the construction, although rather than exposing a programmatic intention, Brunelleschi enunciated the project by giving executive provisions. The twelve points listed contained not only the finished work, but even indicated the variations, incidents and additions that had to be made. For example, the insertion into the walls of the dome of several iron rings was planned to hold the scaffolding on which the authors of the frescoes had to work.[30]​.

The works officially began on August 7, 1420 with an inauguration banquet.[31]​ Before and during the course of the works, Brunelleschi and Ghiberti always maintained a great rivalry, collected and documented in the chronicles of the time.[32]​ In 1425 and after numerous confrontations, Ghiberti was finally removed from the work due to various technical errors.[27]​ The works became entirely directed by Brunelleschi,[33]​ who continued his work without appreciable interruptions until the completion of the base of the lantern on August 1, 1436. On March 25, 1436, the first day of the year in the Florentine calendar, the end of the works was officially celebrated with the solemn blessing of Pope Eugene IV, although the dome was not completed until August 31 with the ceremony of laying the last stone.[34]​ The Consecration was commemorated with the premiere of Guillaume Dufay's isorhythmic motet Nuper rosarum flores, with references to the shield "Shield (heraldry)") of Florence and the dedication of the basilica to Saint Mary of the Flower.[35]​.

Once the construction of the dome was completed, another public competition was called for the lantern, won again by Brunelleschi.[16] Work began in 1446, a few months before the architect's death.[35] They were resumed under the direction of his friend and disciple Michelozzo di Bartolomeo, to be finally completed on April 23, 1461.[16]

The lantern suffered various mishaps throughout history due to lightning strikes. The most important were recorded in 1492 and 1601, the last of which caused the collapse of the sphere and the coronation cross, which were restored in 1602.[36] The structure has also suffered various earthquakes, the most notable being those that occurred in 1453, 1542 and 1695.[16]

In 1639, various cracks were recorded in the dome that ran vertically from the top of the arches in the blind panels, crossing the oculi until reaching the lantern. It was observed that these cracks experienced alternating seasonal cycles of expansion and contraction depending on the temperature.[37]​ In 1757, Leonardo Ximenes already noted the existence of several angular cracks on the inner face of the eight intersecting edges of the panels, located in the lower third of the dome.[38]​ These cracks have been developing slowly over the centuries.[39]​ In recent years, numerous investigations and studies have been carried out, as well as a monitoring of the structural behavior of the dome since the 1980s.[40]​.

La cúpula de Santa María del Fiore está constituida en líneas generales por tres grandes elementos: el tambor, la cúpula propiamente dicha y la linterna de coronación.

La cúpula está compuesta por ocho grandes paños "Paño (arquitectura)") de ladrillo rojo llamados también gajos "Gajo (textil)") o «gallones». Interiormente, la base o primer tramo es macizo hasta una altura de 3.50 metros desde el nivel de arranque, y está formado por seis hileras de bloques de piedra arenisca unidas con piezas de hierro estañado.[41]​ A partir de esa altura, la cúpula se divide en dos hojas, una interior y otra exterior, realizadas en ladrillo y separadas por un espacio vacío intermedio. La exterior tiene una misión de conservación y protección frente a los agentes externos,[42]​ mientras que la interior desempeña una función estructural.[43]​ El casquete interior tiene un espesor de dos metros, y el exterior mide unos sesenta centímetros.[44]​ El espacio intermedio tiene una anchura de aproximadamente 1.20 metros y a través de su recorrido se disponen cuatro pasillos internos y varias escaleras que llegan hasta la linterna.[45]​ Parece ser que Brunelleschi decidió emplear este diseño con un hueco entre ambas hojas para aligerar la estructura, que de otra forma habría sido demasiado pesada para poder ser sujetada por los cuatro grandes pilares sobre los que apoya toda la cúpula.[44]​.

Los ocho paños están separados y ribeteados por ocho costillas de piedra,[nota 4]​ que parten desde las aristas del tambor y llegan hasta la linterna de coronación. Abarcan todo el espesor de las dos cúpulas, la interior y la exterior, uniéndolas. En cada paño, entre dos de estas costillas principales se disponen verticalmente otras dos menores embebidas en el hueco intermedio, haciendo un total de 16 costillas menores y 24 verticales incluyendo las principales. Nueve arcos de mampostería se distribuyen horizontalmente en planos paralelos a cada paño, uniendo las costillas principales con las menores. Un entramado de madera de roble, formado por 24 vigas conectadas entre sí con placas de hierro, ata toda la estructura en su parte inferior, macizando la base de la cúpula. A la solidez del conjunto también contribuyen las seis hiladas de bloques de piedra de la base antes mencionadas, así como una cadena de hierro situada sobre ellas. En el documento de Brunelleschi también se menciona otra cadena de hierro situada sobre el encadenado de madera, aunque esta última no es visible o está oculta en la mampostería.[47]​ Las costillas de piedra y todos los estribos están realizados con piedra de macigno[nota 5]​ y con pietra forte.[42]​.

Los expertos han discutido mucho sobre la eficacia de este sistema de refuerzo. En principio, una cúpula es más estable cuanto más robustos son su tambor y la base de la imposta; por tanto, un sistema adecuado de zunchado favorece la estabilidad.[nota 6]​Estos anillos tendrían la función de «ceñir» la estructura en su base, con el objetivo de contrarrestar las fuerzas que empujan hacia el exterior. En lo que respecta a las cadenas de madera y de piedra, su utilidad es dudosa, debido a la elasticidad de la madera y a la incapacidad de la piedra para trabajar a tracción.[50]​.

Cuatro grupos de escaleras conducen desde el suelo hasta la parte superior del tambor, alojadas en el interior de los cuatro grandes pilares sobre los que descansa la cúpula. Durante la construcción de la misma, dos de ellas se emplearon para ascender y las otras dos para descender, facilitando así la circulación de los operarios.[51]​ Estas escaleras terminan en un primer balcón interior que rodea la base de la cúpula. Desde este balcón se accede al espacio entre los dos casquetes a través de una pequeña puerta, que a su vez dirige hacia otro grupo de escaleras de ascenso al segundo y tercer pasillo interior.[52]​ Finalmente, un último tramo de escalones tallados en el casquete interior desemboca en el cuarto pasillo interno, situado en la base de la linterna.[53]​.

En cada paño exterior se abren nueve aberturas circulares para la ventilación, distribuidas en tres hileras de tres huecos cada una. Además de estas, se realizaron otros pequeños agujeros rectangulares para iluminar y ventilar el hueco existente entre los dos casquetes.[54]​ La hoja interior presenta dieciséis pequeños óculos a la altura del segundo y tercer pasillo, dos en cada paño, que permitían la visión del templo y el montaje de los andamios para la realización del revestimiento interior de la cúpula.[55]​.

Geometry and proportion

The composition of the dome follows the golden proportions, as was the custom of the time, seeking a feeling of balance and harmony between its parts.[56]​ The base of the imposts is about 55 meters from the ground, the lantern is 21 meters high, the drum measures 13 meters and the average height of the dome is 34 meters. The total height of the structure, including the golden ball and the cross raised above it, is 116.50 meters. It should be taken into account, however, that the actual measurements of the dome were calculated in Florentine arms[note 7]​and not according to the decimal metric system. Therefore, any theory referring to the famous Fibonacci sequence, that is, to the numbers 13, 21, 34, 55..., is totally erroneous and meaningless. When the dome was consecrated in 1436, the composition of the Flemish musician Guillaume Dufay, the motet Nuper rosarum flores, reproduced in music the relationships of the construction.[56]​.

The apparent contour of the dome also follows very precise rules. The outer profile is an acute quarter arc, while the interior has a curvature of an acute fifth arc. The layout of these arches is made from the diagonal of the interior octagon, 54 meters long, which is subdivided respectively into four and five equal parts.[note 8]​In this way, the resulting pointed profile is a circular segment whose radius is one fifth greater than the span of the vault.[58]​ Theoretically, Brunelleschi was confident that this pointed Gothic form would provide greater stability,[59]​ as well as greater height than a hemispherical dome.[note 9]​

[61]​ In order to materialize the acute fifth arch in the work, wooden templates were used with the curvature of the arch, which were fixed in the interior corners of the octagon and slid upwards as the panels were being built.[62]​ The layout of the dome according to the acute fifth appears reflected in the parchment of Giovanni di Gherardo da Prato") 1426.[63]​.

This profile also closely resembles an upside-down catenary, a type of curve that is highly effective in terms of stability. This shape physically represents the curvature generated by a chain "Chain (object)") or rope suspended from its two ends. According to the century's mathematician Leonardo Ximenes, Brunelleschi would have intuitively drawn a catenary curve, the geometry of which would have given the dome great resistance.[60]​ As Leibniz, Huygens and Bernoulli would later demonstrate at the end of the century, this is the most stable way to design a self-supporting dome, that is, one that is supported by its own weight.[64]​.

For the construction of his great work, Brunelleschi surrounded himself with a large team of experts in various subjects, among whom were the mathematicians Paolo dal Pozzo Toscanelli, whose calculations were essential for the success of the project,[2]​ and Giovanni dell'Abaco. Brunelleschi himself was also a mathematician and was the creator of the geometric rules of perspective.[56][65]​.

the drum

The drum on which the dome sits is an octagonal prism, located between the top of the four large angular pillars and the line of imposts or starting level of the dome. Its height is 13 meters from the roof of the main nave "Nave (architecture)") of the cathedral, it has an approximate width of 42 meters and the thickness of its walls is four meters.[1] It is located 54 meters from the ground. In its upper part, eight large oculi open up to illuminate the interior of the triconcha of the apse, whose diameter is about 4.65 meters on the inside and about seven meters on the outside. The entire weight of the dome and the lantern unloads on the drum, which is subjected to great stress and which in turn must be transmitted to the four corner pillars.[66]​ The interior is delimited by two balconies with cantilevered balustrades. The first balcony is accessed by four stairs housed inside the pillars, which join in the southeast area forming a single staircase located between the two caps of the dome.[67]​.

Brunelleschi had inherited as a starting premise the construction of a dome on a large drum.[68]​ The size of the dome was notably larger than initially planned, surpassing that of the Pantheon in Rome, which until then was considered the largest in the world, while legend attributed it to a "work of the devil."[2]​ The reasons for this dimensional increase were due not so much to a desire for superiority over the Roman dome, but to the need to reinforce the drum as much as possible. In fact, this had been raised compared to the original model with an additional body in which the eight large oculi had been opened for illumination. This strategy also raised the plane of the dome's imposts above all the vaults built to date.[note 10]​The reduced thickness of the drum further increased the problem, since the resistance against the lateral thrusts transmitted from the dome was reduced.[22]​.

However, the main obstacle to the construction of the dome was the irregularity of the drum, since its diagonals did not converge on a single reference center, so the vertical central axis of the dome was not unique.[note 11]​On the contrary, the union of the opposite angles of the octagon produced four different centers, which could lead to errors since they served as a reference to measure distances during the construction of the dome. This irregularity could have been solved by working with pairs of opposite sides, as pointed out in one of the construction hypotheses mentioned later.[70]​.

The type of dome

A hemispherical, parabolic "Parabola (mathematics)") or ellipsoidal dome is a figure or place of points generated from an arc "Arch (geometry)") that rotates around a vertical axis, called in this case dome of revolution.[note 12]​It is made up of pieces called voussoirs that are arranged in the shape of an arc up to the upper voussoir or key "Key (architecture)"), which It balances the efforts in a manner analogous to an arch or vault but in three dimensions. To allow light to enter the interior of the dome, a zenithal oculus can be opened, accompanied or not by a lantern "Lantern (architecture)"). To do this, the key is replaced by an upper ring of pieces that resist compression efforts, sometimes made of bronze for greater stability and durability.[note 13]​ Theoretically, it is always possible to build a dome of revolution, since it is made up of infinite rings that hold themselves together once completed. The construction technique is quite simple: the bricks are arranged in overlapping concentric circular rings, whose diameter decreases as it rises towards the top. In this way the structure is self-supporting, that is, capable of supporting itself.[72]​.

Those in charge who were in charge of the works on the duomo were concerned that the project envisaged an octagonal dome with flat faces, a figure very different from a solid of revolution. The dome of the Cathedral of Florence, rather than a "dome" itself, is an octagonal cloister vault,[44]​ described as the 45° intersection of two ribbed vaults, very similar to those of the naves of the cathedral itself. Unlike a dome of revolution, a vault is not self-supporting, so in this case the use of falsework or wooden scaffolding would have been essential to hold the walls under construction until the mortar "Mortar (construction)" sets. As it is a structure with an octagonal base, it presents a discontinuity at the vertices of said octagon, where the stresses are concentrated.[72] On the other hand, in Italy it was not possible to obtain the large beams available in northern Europe, and even if it had been possible, the enormous beams used in the cathedrals of France and England would not have been sufficient to support a vault like the one that was intended to be built. According to some hypotheses, this difficulty would have been resolved by the continuous horizontal factory rings, contained within the perimeter of the structure, which would make it behave similarly to a true dome despite being a vault, and therefore would be self-supporting.[44]​.

The scaffolding

One of the initial drawbacks in the construction of the dome was the impossibility of using traditional construction techniques. An entablature system supported from side to side of the drum would not have been feasible, due to the great distance it had to cover and the enormous weights to which it would be subjected. The enormous height at which the works were carried out also did not allow a structure supported from the ground.[1] Although the decision not to use fixed falsework was not taken from the beginning, in the construction program of July 30, 1420, the architect had already foreseen a construction without the use of frameworks or falsework, with the exception of service scaffolding. For this purpose, he devised an aerial scaffold arranged on a circular wooden platform mounted at the height of the interior of the drum, supported by large crossbars[note 14]​ inserted in the needles,[note 15]​ still visible at the level of the balcony floor,[76]​ and which was gradually raised.[77]​ Eight wooden forms were placed on this scaffolding, anchored to the wall with hooks, which moved upwards at as the construction evolved.[31]​ This arrangement had to be followed up to a height of 30 arms, leaving open the possibility of using other construction solutions later.[note 16]​The project to construct the dome without traditional falsework was an innovative idea that caught the attention of the Opera del Duomo.[22]​.

At the beginning of the works, when the dome wall was almost vertical, the scaffolding was supported with beams inserted into the wall, while in the last section, when the dome curved to converge towards the center, Brunelleschi designed another scaffolding suspended from the central hole, perhaps supported with long beams on a platform supported on a lower level, where the materials and construction machinery would also be deposited.[77]​.

La obra se organizaba principalmente en el área del presbiterio "Presbiterio (arquitectura)"), donde se hacía el acopio de materiales, máquinas y herramientas, así como en las cuatro zonas donde se emplazan los absidiolos. Al nivel del arranque de la cúpula se construyó el gran andamio interno anular donde se organizaban los trabajos. En otras ubicaciones alrededor de la catedral se almacenaba la madera y el mármol, las herramientas de trabajo, una forja, un tejar para la fabricación de ladrillos y un espacio reservado para los artistas, donde Brunelleschi construyó un modelo a escala de la cúpula.[78]​[nota 17]​.

La mayoría de los operarios trabajaba en los andamios, mientras que en el suelo lo hacían los que manejaban la maquinaria y los funcionarios que controlaban la recepción de los materiales. A medida que la obra progresaba en altura, se hizo obligatorio tomar mayores medidas de seguridad. Se colocaron parapetos en los andamios, se prohibió el consumo de vino puro durante la jornada y a los obreros se les permitió aceptar o rechazar las actividades más arriesgadas (con una evidente diferencia de salario). Para que el ritmo de la obra no tuviese tiempos muertos, los obreros solo bajaban del andamio una vez al día, siéndoles suministrado directamente el material de trabajo y la comida.[80]​ La organización de los trabajos de construcción pudo llevarse a cabo gracias a una mano de obra experta y de confianza, un eficaz sistema de distribución de las distintas labores y un aprovisionamiento eficiente de los materiales. La plantilla de obreros se renovaba cada año, aunque el personal más experto aseguraba su continuidad. Los operarios debían comprometerse a seguir unas reglas de comportamiento precisas, y los salarios eran asignados según la calidad del trabajo realizado.[81]​.

Las labores de construcción se organizaban en ocho sectores paralelos que trabajaban a la vez, uno por cada paño, lo cual permitía levantarlos uniformemente, ya que estos se iban autosustentando a medida que el mortero fraguaba. El aparejo "Aparejo (construcción)") dispuesto a cuerda floja[nota 18]​y en espina de pez[nota 19]​permitía la continuidad de las superficies y la correcta trabazón de los ladrillos, incluso cuando el mortero estaba fresco. Así, estas dos técnicas fueron esenciales para la construcción de la cúpula sin cimbras fijas.[84]​ Brunelleschi calculó con gran precisión cada detalle, desde la inclinación de los muros hasta la disposición de los ladrillos en espina de pez para que la cúpula fuese capaz de mantenerse en pie por sí misma a medida que crecía progresivamente, sin necesidad de apoyar sobre los tradicionales y enormes andamiajes de madera levantados desde el suelo.[85]​.

Brunelleschi's machines

The lifting of large quantities of material was not possible through the spiral stairs, used by the bricklayers to access the base of the scaffolding. Therefore, Brunelleschi had to devise and build new machines and tools, which would later inspire other Renaissance engineers such as Leonardo da Vinci.[note 20]​The main lifting machine was the reversible ground winch, located at ground level, which allowed large loads to be raised and lowered without having to reverse the direction of rotation, thereby saving time. Furthermore, it was capable of lifting a wide range of weights, from the lightest to the heaviest, with equal traction power, which meant that no more animals or several lifting operations were necessary. The reversible winch operated for ten years without substantial modifications or repairs.[86]​.

In addition to the reversible winch, cranes and machinery were used in the construction to precisely lift heavy loads, located on the internal scaffolding or on the walls of the dome. A large crane 20 meters high was used to close the key and to lift the lantern materials. Another of them, probably drawn by Bonaccorso Ghiberti"), was mounted on the oculus for the construction of the keystone. Many other mechanisms and devices used, such as light winches or wired rotating hoists, are also attributed to Brunelleschi.[87]

These mechanisms used to lift materials during construction mark in themselves a great milestone in building technology.[88]​ Most experts, from Giorgio Vasari to Ross King"), consider them as an application of the techniques devised by Brunelleschi for his famous clocks,[89]​ of which only the one on the tower of the Palazzo dei Vicari" in Scarperia is preserved.[90]​ None of the lifting machines have survived to the present day. Brunelleschi, although numerous copies remain in different drawings made by Mariano di Jacopo, Francesco di Giorgio, Bonaccorso Ghiberti and Leonardo da Vinci.[91]​[92]​.

Filippo Brunelleschi era famoso en Florencia, además de como artista polifacético, como poseedor de un carácter un tanto irascible y de un sentido del humor bastante mordaz.[nota 21]​Era además un maestro en el arte de la manipulación;[94]​ de hecho es considerado como el padre de la perspectiva, que es una representación imaginaria de una realidad tridimensional mediante un sistema bidimensional.[95]​[96]​[97]​.

En lo que respecta a la construcción de la cúpula, parece ser que Brunelleschi también jugó al despiste, puesto que tras años de debate sobre cual debía ser el «mágico artificio» que habría permitido su edificación, no se llegó a ninguna conclusión definitiva. La cúpula octogonal de caras planas, construida sin cimbras y con mortero de fraguado lento de la época teóricamente no podía sostenerse. El arquitecto fue muy celoso del modo en que fue edificada y trató de desvelar lo menos posible de su técnica constructiva.[2]​ La disposición de los ladrillos con un aparejo en espina de pez, visibles en el corredor hueco existente entre las dos cúpulas, se indicaba normalmente como una parte del «secreto» aunque sin que se entendiese la función real. Sin embargo, según algunos expertos estas superficies de albañilería no se corresponderían con una función estructural real y serían únicamente un engaño deliberado,[98]​ tal vez con el propósito de evitar las críticas que malograran su proyecto o el robo de su idea.[99]​.

Los detalles de la estructura de la cúpula, así como el proceso constructivo empleado por Brunelleschi permanecen todavía ocultos en su interior. Las especificaciones del documento de 1420 se ajustan al resultado final, pero proporcionan poca información sobre la metodología constructiva empleada.[11]​ Se han propuesto diversas teorías sobre el sistema de construcción y la forma en que funciona estructuralmente, sin que ninguna de ellas sea concluyente:[100]​.

A dome of revolution contained in the octagonal dome

One of the best-known theories is the one mentioned separately by professors Rowland J. Mainstone and Salvatore Di Pasquale,[101]​[102][11]​ and which had already been pointed out in ancient times by Alberti.[103]​[104]​ In 1977, during the process of removing the tiles in one of the sectors for restoration, it was discovered that the brick laying lines were not horizontal but rather They followed an open upward curve, called tightrope. This fact, which had never been noticed before, led us to examine the arrangement of the bricks in more detail.[note 22] It was also observed that the faces of the bricks were not horizontal but were inclined in rows that converged at a point located in the center of the octagon at the base of the dome. It was as if the flat-faced dome had been made by taking parts from walls built like a classical dome. The conclusion reached by the researchers was that the bricks were arranged as if a dome of revolution was going to be built. In this way and to guarantee that the structure was self-supporting, it would be enough if a dome of revolution of adequate thickness for its stability could be inscribed in the thickness of the walls.[105]​.

However, since he could not build the dome with a thickness large enough to contain a revolution inside, Brunelleschi would have created a dome with a double cap and horizontal intermediate connecting ribs. These are not of constant section, but rather have greater thickness at the junction with the eight large main ribs, while their thickness is reduced in the center of the panel. The profile of these arches, together with the profile of the intrados of the exterior cap of the dome, generate an almost circular shape,[106]​ so that between both caps it would be possible to inscribe a complete circular ring of lesser thickness, which would be tangent to the angles of the interior octagon and to the midpoints of the exterior. Thus, the real octagonal dome would be assimilated to an equivalent virtual dome of revolution.[103]​[11]​.

This system requires that the mortar courses describe the shape of a cone of revolution "Cone (geometry)") inscribed within a circular dome, with a common vertical axis coinciding with the vertical axis of the dome and its vertex "Vertex (geometry)") pointing downward.[11]​ At the place where this virtual cone intersects with the octagonal shape of the dome, a tightrope conical line is produced.[107]​ In Essentially, this theory proposes that the dome would be composed of a series of horizontal conical sections, whose inclination would increase as greater height is reached, and whose mortar courses would also increase their curvature with height.[108]​.

As for the function of the bricks arranged in herringbone, according to Paolo Rossi[109]​ this would have been to support the structure until it was closed with the key "Key (architecture)"), thus avoiding the use of large trusses.[110]​ In this way, Brunelleschi would have managed to build the octagonal masonry dome without the help of formwork and in a somewhat intuitive way.[103]​.

However, this theory was questioned by some experts in the 1980s, since a virtual dome of revolution of small thickness, contained within another enormous octagonal dome of greater thickness and weight, would have produced a large amount of "dead weight" without great benefits in return. Furthermore, this hypothesis did not give any importance or structural function to the eight great main nerves and, in essence, did not consider the dome as an integrated structure in all its parts.[110]​.

A radial dome drawn with guide ropes

Another of the most famous theories is the one formulated and published by Professor Massimo Ricci.[111]​[112]​[113]​ According to this hypothesis, the construction technique of the dome would not respond at all to a dome of revolution, not even in its internal structure. The method used for its construction would be through a system of radial ropes that would intersect on a central axis and that would be attached to a fixed reference frame.[114]​ This procedure would determine the position and inclination of the bricks during the construction process,[110]​ which would not have been placed according to a circular arrangement, but rather concave with respect to the opposite side of the octagon.[115]​.

After carrying out various checks on the intrados of the faces of the dome, it was deduced that the structure of the dome could have been developed in a vertical radial direction and not horizontally, as suggested by the hypothesis of the dome of revolution. According to this new assumption, the structure of the dome would have been generated as a succession of inclined radial rows.[110] Brunelleschi would have used a "pseudocircular" curve,[note 23]​drawn from the circular scaffolding located at the base of the imposts, and centered on the vertical of the building. This curved shape would have been materialized through a system of ropes crossed with each other and measured with a plumb line on the diagonals of the base, fixed at the interior angles of the octagon.[114]​.

In this way it would have been possible to define the angles of the dome using small mobile forms. The "pseudocircular" curve would trace the contour of each panel by means of a mobile rope fixed on one side on the curve itself and which would also pass through the center on the vertical. This rope would describe a curve in each panel following this scheme in the shape of a lobed flower, which would move upward as the construction progressed in height.[117]​ Through this system, the bricklayers would have a reference at each point of the construction to arrange the course of bricks.[118]​ These would be placed in courses inclined towards the center of the dome, with the herringbone rig rising with a spiral arrangement.[119]​ This would be, according to Ricci, the true function of the herringbone arrangement: to fix the exact radial position of each brick (following the direction marked by the rope) during its placement so that it performs its specific function.[120]​ In addition, this technique would make it possible to construct the eight panels independently and without interruptions, which would have avoided the difficulty of constructing the eight faces at the same time.[110]​ According to this hypothesis, the tightrope arrangement would not have any structural function, but would be a consequence of the construction method used using the flower-shaped template.[121]​.

In the program of 1426, reference was made for the first time to the lantern, when the dome was almost finished and closed with the upper compression ring that joined both caps. strong, light, luminous and better waterproofed.[16]​ On April 15, 1446, shortly after the laying of the first stone, Brunelleschi died.[35]​ After his death, various artists continued its construction following his design, among them his friend and disciple Michelozzo di Bartolomeo, Antonio Ciaccheri"), Bernardo del Borra (Bernardo Rossellino) and Tommaso Succhielli, who finished it on April 23, 1461.[16] Various machines and inventions devised by Brunelleschi himself were used for its construction, including a rotating crane and a wooden frame.[125]​.

The lantern design continues the polygonal shape of the dome. It is made up of a central octagonal prism "Prism (geometry)") six meters in diameter and sixteen meters high. It sits on a marble platform held by the stone chain that closes the dome at the top. Its edges are surrounded by eight buttresses finished in the shape of a volute "Volute (architecture)") and supported on eight pilasters crowned by Corinthian capitals. Eight stylized windows nine meters high open on its faces.[126] Above the prism is a conical piece "Cone (geometry)"), grooved like a needle, adorned with semicircular arches on its faces. On May 30, 1471, a bronze finishing sphere, designed by Andrea Verrocchio[35] and crowned with a cross, was installed at the top. In order to lift it, Brunelleschi's machines were also necessary, an operation carried out by the assistants of the Verrocchio workshop, among whom was a young Leonardo da Vinci.[92]​.

In 1475, the mathematician Paolo dal Pozzo Toscanelli installed the gnomon of a sundial at the base of the lantern, which allowed him to calculate with great precision the orbit of the Earth around the Sun.[127]​.

Formally, the lantern represents the visual axis of the cathedral and serves as a finishing touch to the ascending lines of the eight large vertical ribs. It is believed that Brunelleschi may have been inspired by religious metalwork for his design, such as the censers or the "Custody (liturgy)" monstrances, enlarged to a monumental scale. The lantern that was finally built may have undergone modifications with respect to the original project, with a more elegant and refined ornamentation in accordance with the taste of the middle of the century, dominated by the figure of León Battista Alberti.[128]​.

The lantern has a very important function in the overall statics, since it stabilizes the compression ring of the dome.[129]​[130]​ The eight vertical ribs converge towards its base and continue in the buttresses, so that the weight of the lantern is unloaded on them and transmitted through the ribs.[35]​ On the other hand, the forces acting on the structure are so great that the ribs themselves tend to bend inwards due to the effect of the loads and their own weight. The enormous weight of the lantern, about 750 tons, counteracts the inward thrust of the base of the dome.[131]​.

The lantern has suffered numerous vicissitudes throughout history. On the night of April 5, 1492, lightning struck it, destroying almost half of it, although without causing significant damage.[36] During the night of January 26 to 27, 1601, around 5 in the morning, the sphere collapsed due to another lightning strike. The dome was affected in different places,[note 25]​ and the ball had to be replaced in 1602. Behind the plaza under the dome, a marble disc still marks the exact point at which it crashed to the ground.[2]​ In 1859 a lightning rod was installed to protect the lantern and the sphere.[36]​.

Once the construction of the dome was completed, only the outer part of the octagonal "Drum (architecture)") remained to be decorated. A first note, regarding the dimensions, had already been sketched by Brunelleschi in the wooden model attributed to the architect himself and preserved in the Museum of the Opera del Duomo "Museo dell'Opera del Duomo (Florence)"). Brunelleschi.[134]​ Among these first projects of the century was also a model attributed to Giuliano da Maiano.[135]​.

The problem remained unresolved until the beginning of the century, when a competition was called for the completion of the drum. Various architects participated in it, each of them with their own wooden model. Andrea Sansovino proposed a coronation with a baluster surrounded by Ionic columns; However, Giuliano and Antonio da Sangallo the Elder proposed a model without a balustrade.[17] Another project was presented by Simone del Pollaiolo, together with Giuliano da Sangallo and Baccio d'Agnolo.[136]

In the summer of 1507, the Opera of Santa Maria del Fiore commissioned Michelangelo to make a drawing or model for the drum competition before the end of August. According to the author Giuseppe Marchini, the artist would have sent some sketches to a carpenter in Florence for the construction of the model.[note 26]​The project broadly proposed maintaining a certain continuity with the pre-existence, by inserting a series of rectangular pieces in green Prato marble aligned with the capitals of the corner pilasters. Another entablature was planned, closed by a cornice, analogous to that of the Strozzi Palace. The design would be completed with a series of eight statues placed at the top, corresponding to the eight ribs of the dome. However, this project was not chosen by the jury.[134]​.

In 1512 the decision was made to begin work on the completion of the drum according to the project designed by Baccio d'Agnolo together with Pollaiolo and Giuliano da Sangallo, the winners of the competition. The regulations imposed that they had to work as a team and respect the proposal partially built to date, in order to avoid unnecessary cost overruns.[134] D'Agnolo himself, in charge of the Santa María del Fiore Opera at that time, was responsible for continuing the work after Pollaiolo's death and Sangallo's abandonment.[17] The project included a frieze of classical inspiration and two pilasters on the sides of the oculi. It also provided for the incorporation of a solid continuous balcony at the top of the drum, supported by white marble columns, with nine arcades on each side divided by lesenas.[134] The balcony was composed of three parts: a central corridor and two balustrades, one lower and one upper. The central one was accessed through the doors opened by Brunelleschi in the drum.[138]​ This solution through a continuous balcony had already been foreseen by the architect in the document of 1420.[17]​.

During the construction phase some modifications were made. The balusters were replaced with more robust ones, two arches were added on each side and grooves were made in the lesenas.[134] However, the works were interrupted in 1515, with the balustrade completed only on the side of the dome facing the Via del Proconsolo. The reasons for the paralysis may have been due to the lack of success obtained among the Florentines or to the criticism expressed by the citizens and especially by Michelangelo.[139]​[note 27]​.

Around 1516, Michelangelo made some drawings for the completion of the drum, preserved in the Buonarroti house.[134] He probably had a new wooden model built,[note 28]​where the balustrade was again suppressed in favor of greater relief of the supporting elements. Specifically, one of the drawings shows the addition of paired columns, located at the corners of the octagon and crowned by several projecting cornices.[17] It is thought that this scheme could have later been used for the dome of St. Peter's Basilica in the Vatican. However, Michelangelo's ideas remained only a project and the drum ultimately ended up incomplete on seven of its eight sides.[134]

In 1694 the architects Gherardo and Pier Francesco Silvani" advised reinforcing the continuous balcony, since it had experienced various movements despite having been strengthened on previous occasions.[134] It is thought that probably the enormous weight of the entire finished balustrade would have created stability problems in the dome.[142]

Eight wooden models presented in competition representing one side of the drum are preserved in the Duomo Opera Museum. Numbers 136 and 137 belong to the century, while those cataloged with numbers 139 to 144 are from the century. The oldest of all, number 136, is attributed to Ciaccheri, while in the other seven there are doubts about its authorship.[143]​.

Brunelleschi carecía de referencias tecnológicas a la hora de resolver el problema de construir una cúpula gallonada, es decir, una bóveda de cañón apuntada de planta octogonal, por lo que tuvo que inventar literalmente el procedimiento constructivo empleado en todo su proceso. Todas las cúpulas que se han intentado proponer como modelos para la de Florencia eran de revolución (autoportantes) o bien realizadas con cimbras y armaduras, mientras que la de Santa María del Fiore no estaba basada estos sistemas. A pesar de la novedad de la técnica finalmente utilizada, se han formulado diversas hipótesis sobre las posibles fuentes que podrían haber inspirado al arquitecto: por una parte, los precedentes florentinos; por otra, las estructuras abovedadas de época romana y por último, la tradición constructiva de Persia.

Varios autores coinciden en que Brunelleschi tenía presente la geometría y la técnica constructiva de la cubierta del baptisterio de San Juan "Baptisterio de San Juan (Florencia)"), realizada mediante una cúpula de perfil apuntado sobre una planta octogonal.[144]​[145]​ Esta cúpula arranca desde un nivel inferior a la línea de coronación de los muros exteriores y está recubierta por un techo piramidal octogonal de piedra. Entre la parte interior y los muros perimetrales de cierre hay un hueco de 1.25 metros de anchura.[144]​ Sin embargo, para su construcción no se empleó la técnica del aparejo en espina de pez.[146]​.

En lo que respecta a la segunda fuente de inspiración, el biógrafo Antonio di Tuccio Manetti relata que Brunelleschi pasó en Roma varios años de estudio,[147]​ atraído quizás por el hallazgo de objetos y esculturas propios de aquellos años. A principios del siglo , la ciudad eterna era un inmenso yacimiento arqueológico.[148]​ Durante su estancia se habría inspirado en la arquitectura clásica y habría conocido las teorías de Vitruvio, según las cuales toda arquitectura estaba basada en un módulo y en una retícula geométrica.[149]​ Asimismo, podría también haber conocido la disposición en espina de pez tras haberla observado en diversos edificios romanos.[150]​.

La cúpula más famosa de la romanidad, el Panteón de Agripa, es una cúpula de revolución semiesférica de dimensiones similares a Santa María del Fiore.[151]​ Su diámetro de 43 metros y su óculo superior de 8 metros pudieron haber inspirado a Brunelleschi en su diseño.[22]​ Sin embargo, la de Roma tiene un único casquete y está realizada en hormigón con casetones,[152]​ una técnica de construcción que no era reproducible e incluso debía ser del todo incomprensible en la Italia del primer Renacimiento, que había perdido la tradición romana del hormigón.[153]​ Del estudio del exterior, Brunelleschi como máximo habría podido apreciar que la forma escalonada se levantaba a partir de una forma circular y que, por lo tanto, las cúpulas romanas generalmente contenían siempre un anillo circular completo en cada nivel de su espesor. Quizás Brunelleschi conoció la cúpula de la Domus Aurea, levantada sobre un pabellón octogonal y construida con hormigón fresco, que requirió cimbras durante el fraguado.[154]​ Durante su construcción, su forma poligonal inicial se fue transformando en una circular a medida que se elevaba y estrechaba, una técnica empleada en diversos edificios romanos.[150]​.

La hipótesis del viaje romano de Brunelleschi está generalmente aceptada por toda la crítica,[155]​ aunque recientemente se ha apuntado que, si se descarta que el origen de la cúpula del duomo fuese el Panteón, nada en la obra del gran arquitecto debería por fuerza relacionarse con elementos arquitectónicos que eran visibles únicamente en Roma. El viaje a Roma por lo tanto fue posible, pero no indispensable para la formación de los cánones arquitectónicos brunellesquianos.[156]​.

Respecto a la inspiración en Persia, se ha querido conjeturar que el arquitecto hubiese conocido las técnicas constructivas de los mausoleos orientales, dados los importantes intercambios comerciales existentes con el Medio Oriente, aunque la influencia no está clara.[152]​ La doble cúpula levantada sin cimbras del mausoleo de Soltaniyeh en Irán, construido entre 1302 y 1312,[157]​ la construcción de los muros en espina de pez de los antiguos edificios selyúcidas del siglo , o las mezquitas posteriores de Isfahán y Ardistán") son comparables al lenguaje estructural y a la técnica de Brunelleschi,[146]​ aunque diferenciándose sustancialmente en los materiales, en el aparejo murario y en las dimensiones.[158]​.

Later influences

The dome of Santa María del Fiore also served as inspiration for later constructions. Giuliano da Sangallo took it as a model for the dome of the Sanctuary of the Holy House of Loreto "Loreto (Italy)") in 1500, although with a single cap. The lantern also resembles that of Brunelleschi and was made by Giuseppe Sacconi in 1889.[159]​Antonio da Sangallo the Younger studied the dome for his lantern project for Saint Peter's in Rome.[160]​.

In 1546, Michelangelo analyzed the structure of the dome and reinterpreted it in his project for the dome of Saint Peter,[note 29]​where he adopted a similar double-cap solution.[note 30]​Likewise, he introduced a system of sixteen ribs that converged towards the crown, joining both caps and supporting the lantern.[162]​[163]​Giorgio Vasari took it as an example. for the basilica of the Virgin of Humility") in Pistoia and in the temple of Saint Stephen of Victory") in Foiano della Chiana. In his book Le Vite he dedicated a large part of his writings to the biography of Brunelleschi and to the narration of the construction process of the dome. Santi di Tito in 1597.[164]​.

Although it was built with innovative techniques, the dome always had a direct inspiration from that of the baptistery, from which it took its development and its octagonal shape. Initially, an interior decoration with mosaic had been planned, another element in common with the Romanesque dome. Brunelleschi made various sketches that the workers could have used in the ornamentation of the immense interior surface of the dome, of more than 3,600 square meters. poem from the early 1470s could refer to this project.[17]​.

However, the mosaic technique was already very little used at that time and was considered extremely expensive. Additionally, there were also concerns that the binder used to secure the tiles could increase the overall weight. This problem does not seem very important today, knowing the enormous weight of the dome and its resistance, but at the time it was considered an essential reason to abandon the project in favor of decoration using the fresco technique.[18]​.

The work did not begin until 1572, in the midst of Mannerism, a century after the completion of the masonry works. Grand Duke Cosimo I de' Medici chose the theme of the Last Judgment to decorate the enormous dome, and entrusted the task to Giorgio Vasari, with the collaboration of Vincenzo Borghini in choosing the iconographic theme. At Vasari's death, only the first of the planned concentric stripes had been completed, the smallest of them, located at the top around the octagonal oculus covered by the lantern "Lantern (architecture)").[165]

He was succeeded by Federico Zuccari, who in a few years and according to his own words, almost single-handedly, completed with tempera painting the immense figurative cycle, one of the largest in the world in surface area, and one of the masterpieces of mannerism. monsters, 23 children and 12 animals.[166] The painter himself, in his will, proudly recalled having conceived and completed the work, of which he especially mentioned the great Lucifer, thirteen Florentine arms high (about 8.5 meters). Obviously, he used many assistants, among whom was a young Domenico Cresti. The work was completed in 1579, just three years after the beginning of the work.[18]​.

The contents of the cycle were those adopted at the Council of Trent, which had reviewed medieval Catholic doctrine, ordering it in a clear way.[18] The dome was divided into six concentric rings and eight vertical stripes. At the top, the central lantern is surrounded by the 24 prophets of the Apocalypse, located in groups of three characters in each strip. Starting from the top, each vertical stripe comprises four scenes represented in each of the rings, which are organized from top to bottom with the following scheme:

• - a choir of angels with instruments of the Passion (second ring);

• - a category of Saints and Elect (third ring);.

• - a triad of characters representing a gift of the Holy Spirit, the seven virtues "Seven Virtues (catechism)") and the seven Beatitudes;.

• - a region of Hell dominated by a capital sin.[167]​.

In the eastern strip, in front of the central nave, the four rings become three to make room for the great Christ in Majesty, in contrast to the image of Lucifer, located in the opposite strip. Christ the Judge, represented with great hieraticism, is located between the Virgin Mary and Saint John the Baptist. Below them are placed the three theological virtues: Faith, Hope "Hope (virtue)") and Charity "Charity (virtue)"), followed below by allegorical figures that represent Time[note 31]​ and the Triumphal church.[167]​ Among the Elect, the painter represented a wide gallery of contemporary figures, such as the patrons of the Medici family, the emperor, the king of France, Vasari, Borghini, Giambologna and other artists, including himself and many of his relatives and friends.[18] Zuccari also added his signature and the date.

In 1980, a long process of restoration of the frescoes in the dome of Santa María del Fiore began, which lasted until 1995.[18]​.

• - History of Italian Renaissance domes.

Additional bibliography

• - n.10, 1972; n.12, 1972; n.2-3, 1977; n.12, 1977; n.7-8.

• - ; appendix:.

• - (with the collaboration of Massimo Ricci).

• - Cathedral of Santa Maria del Fiore.

• - Filippo Brunelleschi.

• - Dome.

• - Museo dell'Opera del Duomo (Florence) "Museo dell'Opera del Duomo (Florence)").

• - Piazza del Duomo (Florence) "Piazza del Duomo (Florence)").

• - Renaissance Architecture.

• - Italian Renaissance.

• - Republic of Florence.

• - Wikimedia Commons hosts a multimedia category on Dome of Santa Maria del Fiore_-_Dome "commons:Category:Santa Maria del Fiore (Florence) - Dome").

• - Official website.

• - History and complementary information about the dome, Galileo Museum of the History of Science.

• - Association Filippo di Ser Brunellesco for the construction of the model of the dome.

• - Some aspects of the funicular curves. Articles on the mathematical study of the funicular curves referred to the dome of Santa María del Fiore.

• - Lecture by Professor Luca Giorgi at the Higher Polytechnic School of the University of Alicante, February 2014.

• - Documentary that explains Massimo Ricci's theory.

• - Includes an animated short film created by National Geographic (in English).

• - Article on the construction techniques of domes and vaults in ancient times.