St. Paul’s Cathedral Dome: A Synthesis of Engineering and Art

Developed with James Campbell, architectural historian at Cambridge University
Inspired by taking George Deodatis’ lectures on The Art of Structural Design
at Columbia University’s Department of Civil Engineering

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In 1872, Eugène-Emmanuel Viollet-le-Duc, the French author and architect celebrated for restoring Notre-Dame of Paris, wrote in his Lectures on Architecture that the form of the Gothic cathedral was the synthesis of the early Christian basilica and the Romanesque three-aisled church. In this analysis, Viollet-le-Duc reasoned that a thesis (Early Christian) plus an antithesis (Romanesque) produced the synthesis (Gothic).

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Animation from Stephen Murray

Although the history and origins of Gothic are likely more complex than Viollet-le-Duc’s formula, this formula provides a method to dissect the Renaissance and Enlightenment counterpart to the medieval cathedral: the Greco-Roman basilica, as embodied by St. Paul’s Cathedral, constructed from 1675 to 1711 by Christopher Wren (1632-1723). St Paul’s is a symbol of Enlightenment-era London, built to rival its medieval counterpart of Westminster Abbey.
In this essay, and in my analysis of this neoclassical cathedral, I will parallel Viollet-le-Duc’s analysis of the medieval church. The thesis is that St. Paul’s is a work of techno-scientific engineering. The antithesis is that this building is a work of art that speaks to the larger cultural moment of Enlightenment London. The synthesis is the dome of St. Paul’s that merges these two forces of engineering and art into a unified and impressive creation.

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Thesis: ENGINEERING
The engineering of this dome is more complex than meets the eye.

In this animated construction sequence, view how the dome was engineered.

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Music from the organ (William Tell’s Overture) and bells of St Paul’s (recorded 2013)

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St. Paul’s Cathedral features an innovative triple dome structure. On the circular drum, the inner dome rises and is visible from the cathedral interior. Above this inner dome, a brick cone rises to support the 850 ton lantern. This brick cone also supports the wood rafters and frame of the outer dome, which is covered in wood and lead. This three dome system allows the cathedral to support such a heavy lantern, all the while maintaining the great height needed to be a visible London landmark.
  • Inner dome – visible from inside and purely for show; height 225 ft (69m)
  • Middle brick cone – a brick cone that is invisible from below but supports the 850 ton lantern above; height 278 ft (85m)
  • Outer dome – a wood and lead-roofed structure visible from the cathedral exterior; height 278 ft (85m)
  • Lantern – an 850 ton stone lantern and cross, whose weight is carried to the ground via the middle brick cone 365ft (111m)
The inner and outer domes are decorative, while the brick cone is the true weight-bearing support. The model below is created from measured plans and is accurate to reality.

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Virtual Reality Model
(click to play)

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The cathedral in the city: Rhinebeck Panorama of London dated 1806-07

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Antithesis: ART
The cathedral’s location and design reflects its cultural-historical moment of the Enlightenment.

The 1666 Fire of London turned the thirteenth-century medieval cathedral of old St. Paul’s into a charred ruin. As masons demolished the ancient ruins, the opportunity arose to erect a new cathedral designed around new cultural reference points: neoclassical instead of medieval, Protestant instead of Catholic, and with steel and brick instead of stone alone. St. Paul’s reveals what was, for the time, novel ways of thinking about space.
There are three main ways this cathedral architecture reflected its time period.
Firstly, this cathedral embodied an emerging understanding of artist and architectural space.  The burned medieval cathedral was built over centuries by numerous masons in collaboration, whose names are largely forgotten. New St. Paul’s was built in one uninterrupted sweep by a single architect, whose name and biography are known in detail. It was only during the Renaissance and Enlightenment that society began to think of art and architecture as the product of an individual artist’s personality and ambitions. The engineer, artist, and architect were elevated above nameless masons. Historians can describe the relationship between artist and artwork with a degree of detail impossible to attribute to the architects of older, medieval cathedrals. It is to this period in the history of science and philosophy that historians also attribute the cult of personality surrounding individual artistic genius. Also central to the Enlightenment period was the organization and standardization of all human knowledge into encyclopedias and libraries, much in the way that St. Paul’s was centrally planned, designed, and coordinated with more precision than survived from the sporadic organization of medieval cathedrals and monastic libraries.

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Comparative cross sections of old (left) and new (right) St. Paul’s (link)

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The irony is that for a building that appeared modern to eighteenth-century eyes, the construction methods with scaffolding and wooden winches to lift heavy stones were mostly unchanged from centuries before. The wooden rafters inside the cathedral roof are from trees planted hundreds of years before during the High Middle Ages. Most telling of all, the vaults of the nave and choir are supported by medieval-style flying buttresses. But fearing that flying buttress – an engineering technique deeply associated medieval architecture – would be inappropriate to a classical basilica, Wren hid these buttresses behind a screen wall. Modern or medieval? The building methods and religious traditions largely descended from late medieval thought, even if the building exterior evoked very different and seemingly opposed classical traditions.
Secondly, this cathedral reflected Britain’s growing interest in European and world affairs. Merchant ships sailing up the River Thames would first see the domes of Wren’s Greenwich Hospital for the wounded and retired sailors in the British navy; around the next bend in the river, the dome of St. Paul’s came into view. With Britain competing with France for colonial power, Wren visited Les Invalides, the Paris hospital for retired sailors in the French navy. Through carefully studying Les Invalides and reviewing prints of French architecture, Wren copied and improved on classical traditions when redesigning London after the fire. St. Paul’s is also markedly similar to Michelangelo’s sixteenth-century dome at the Vatican. St. Paul’s was supposed to be a cathedral, but its dome became an act of one-upsmanship against similar and existing domes in Paris and Rome.

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The River Thames with St. Paul’s Cathedral
(painted by Canaletto c.1747-48)

London from Greenwich Park
(painted by Turner in 1809)

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Lastly, this religious architecture ironically symbolized the growing power of secular thought and finance over national governance. As capital of England, London’s architectural focal points are split geographically between Westminster to the west and central London to the east. Power in Westminster is, in turn, divided between three main architectural points of interest: Westminster Abbey (symbolizing God), Buckingham Palace (symbolizing the king), and the Houses of Parliament (whose House of Commons symbolizes the country). This maps onto the neat triad of “God, King, and Country” or the three estates of “clergy, nobility, and commoners.”
However, the location of St. Paul’s, in the center of London’s financial district and near the commercial hub of the Royal Exchange, competed with Westminster Abbey in size and height. It were as if the commercial interests of bourgeois merchants and industrialists working in central London were competing with and questioning the traditional balance of power between the king, clergy, and nobility that had excluded the merchant middle classes from power. It was as if this cathedral’s architecture asserted the growing importance of London’s businesses and financial district for the governance of a country. Fittingly, as if proof of their success, zoning laws and building height restrictions in much of London are still designed for miles around so as to preserve the visibility of St. Paul’s. Wren was no opponent to the monarchy, and the construction of St. Paul’s, in fact, benefited from royal support. Nonetheless, the architecture still speaks to the distinctly eighteenth-century tension between ancient traditions and modern technologies.

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Protected vistas radiating out from Westminster and St. Paul’s. The cathedral architecture becomes, in equal parts, the symbolic, physical, and cartographic center of urban life, as if the red lines on these maps were arrows directing our gaze to the center of power.

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Construction was funded through a tax on the coal London residents and businesses consumed. In later years, coal became a polarizing symbol of both the dirty, soot-covered injustices of urban poverty and the techno-scientific progress fueling Britain’s Industrial Revolution. Fittingly, the same dark ingredient that powered Britain’s industrial looms and colonial power also funded construction of the cathedral that came to symbolize London and the empire. St. Paul’s is a church, but its neoclassical design and secular location allow it to become much more than just a church.

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Synthesis: ENGINEERING AND ART
This dome is a synthesis of art and engineering.

In addition to St. Paul’s political and cultural symbolism, this dome also synthesized the most recent advances in building (industrially manufactured brick) with simultaneous techno-scientific discoveries. This cathedral embodied the core beliefs of European Enlightenment thought: the application of science to advance society and the synthesis of Greco-Roman aesthetic traditions with modern technologies.

Parabolic behavior of an unweighted chain

In the years St. Paul’s was under construction, Wren corresponded with his polymath, scientist, and mathematician friend Robert Hooke (1635-1703). From Hooke’s empirical experiments with springs, strings, and weights (see Hooke’s Law), he confirmed that an unweighted chain suspended between two points would form a parabolic curve. Furthermore, the quadratic formula Y = X2 mathematically expressed and modeled the chain’s behavior. Math and reality were, in one formula, linked.
There is effectively no limit to how much weight a chain can hold in tension. A suspension bridge roadway weighs hundreds of thousands of tons, but the steel cables suspending it are usually no thicker than a few centimeters. However, these cables will collapse under the slightest amount of compression.
In contrast to a chain that is strong under tension but weak under compression, stone is the opposite: strong under compression but weak under tension. Imagine the incredible compressive forces of the earth’s crust that compress ancient sand and fossils into solid limestone. When masons quarried this stone into blocks, they were challenged to design cathedrals that minimized any tension on stone. Tension in the horizontal span of the cathedral vault, for instance, caused structural collapse. In response, masons devised flying buttresses and complex structural interventions to prevent stone from cracking under tension.
The genius of Enlightenment architects like Wren stems from their ability to deduce: If a suspended chain formed a parabolic curve in pure tension as modeled by Y = X2, then the converse statement must also be true: A stone arch modeled on a parabolic curve would act in pure compression, as modeled by the reverse equation -Y = X2. Thus, by mathematical logic, the downward and tensile force of chains mirrored the upward and compressive forces of stone. Spanish architect Antoni Guadí (1852-1926) observed similar phenomena when designing his final project, the Basilica of Sagrada Familia in Barcelona (begun 1883). Without the benefit of computer models, Guadí suspended weighted strings from the ceiling and then viewed these creations in a mirror, so as to deduce the optimal geometric form for his cathedral vaults.

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One of Gaudí’s string structures

The same structure upside down
models the form of the ideal dome

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Knowing this, Wren constructed the dome as a brick cone similar in shape to a parabolic arch. Around the base of the dome, where the buckling forces of tension were greatest, Wren inserted bands of steel chain the circumference of the dome. Medieval masons intuited this, too, when they designed pointed arches whose shape was somewhat closer to a parabola than was the traditional and older Roman arch. However, while medieval masons at places like Amiens Cathedral relied on trial and error with few benefits of scientific thought, Wren relied on science and math to deduce the ideal form. Thus, the brick middle dome is only nine inches thick, but it supports a lantern above that weighs 850 tons.
Wren was more than a mathematician. He also had a keen aesthetic eye from close study of French and classical architecture. His white limestone buildings all drew inspiration from the classical traditions of Greece and Rome. However, although the brick cone was cheaper, stronger, and used fewer materials than a traditional stone dome, Wren knew that a brick architectural form was too radically modern to leave exposed, and too aesthetically different from the otherwise neoclassical church. Wren therefore hid the true, weight-bearing brick cone. Outside the brick cone, Wren added a lead and wood roof that supported no weight and was in no way connected to the lantern it only seemed to support. Inside the brick cone, which was effectively too steep and too tall to paint a convincing ceiling mural on, Wren erected a decorative arched roof within that was merely a decorative surface for James Thornhill’s paintings.
Art and engineering, religion and politics, tradition and innovation were, through the design of one dome, linked. Wren might not have intended to inject his cultural-historical moment into the design. As an architect-engineer, he was merely inventing the most stable and economic way to cover the cathedral. However, the implications of this engineering were to influence the city and society at large.

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What’s wrong with Jeremy Bentham’s Panopticon?

Postmodernist thinkers, like Michel Foucault, interpret Jeremy Bentham’s panopticon, invented c.1790, as a symbol for surveillance and the modern surveillance state.
This lecture is in two parts. I present a computer model of the panopticon, built according to Bentham’s instructions. I then identify design problems with the panopticon and with the symbolism people often give it.

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Related Projects

– Computer animation of Jeremy Bentham’s panopticon
View the panopticon in virtual reality
Explore about Eastern State Penitentiary, a building inspired by Bentham

Jeremy Bentham’s Panopticon: a Computer Model

Created at the University of Cambridge: Department of Architecture
As part of my Master’s thesis in Architecture and Urban Studies
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To say all in one word, it [the panopticon] will be found applicable, I think, without exception, to all establishments whatsoever, in which, within a space not too large to be covered or commanded by buildings, a number of persons are meant to be kept under inspection.
– Jeremy Bentham
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Since the 1790s, Jeremy Bentham’s panopticon remains an influential building and representation of power relations. Yet no structure was ever built to the exact dimensions Bentham indicates in his panopticon letters. Seeking to translate Bentham into the digital age, I followed his directions and descriptions to construct an exact model in virtual reality. What would this building have looked like if it were built? Would it have been as all-seeing and all-powerful as Bentham claims?
Explore Bentham’s panopticon in the animation above or in virtual reality below:

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c.1791 plans of panopticon, drawn by architect Willey Reveley for Jeremy Bentham

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Panopticon: Theory vs. Reality

Central to Bentham’s proposed building is a hierarchy of: (1) the principal guard and his family; (2) the assisting superintendents; and (3) the hundreds of inmates. The hierarchy between them literally maps onto the building’s design. The panopticon, quite literally, becomes a spatial and visual representation of the prison’s power relations.

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To his credit, Bentham recognizes that an inspector on the ground floor cannot possibly see all inmates on the upper floors. The angle of view was too steep and obstructed by stairs and walkways. To this end, Bentham proposes that a covered inspection gallery be erected for every two floors of cells.
By proposing these three inspection galleries, Bentham addresses the problem of inspecting all inmates. However, he creates a new problem: From no central point would it now be possible to see all activity, as the floor plans below show. The panoramic view below shows the superintendent’s actual field of view, from which he could see into no more than four complete cells at a time. The view from the center is not, in fact, all-seeing. Guards would have to walk a continuous circuit round-and-round, as if on a treadmill.

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The intervening stairwells and inspection corridors between the perimeter cells and the central tower might allow inspectors to see into the cells. Yet these same architectural features would also have impeded the inmates’ view toward the central rotunda. Bentham claims this rotunda could become a chapel, and that inmates could hear the sermon and view the religious ceremonies without ever needing to leave their cells. The blinds, normally closed, could be opened up for viewing the chapel.

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Bentham’s suggestion is problematic. The two cross sections above show that, although some of the inmates could see the chapel from their cells, most would be unable to do so.
In spite of all these obvious faults in panopticon design, Bentham still claims that all inmates and activities are immediately visible and controlled from a single central point. When the superintendent or visitor arrives, no sooner is he announced that “the whole scene opens instantaneously to his view,” Bentham writes.

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Despite Bentham’s claims to have invented a perfect and all-powerful building, the real panopticon would have been deeply flawed were it built. Although the circular form with central tower was chosen to facilitate easier surveillance, the realities and details of this design illustrate how constant surveillance was not possible. It is, therefore, no surprise that the English Parliament and public rejected Bentham’s twenty year effort to build a real panopticon.
However flawed the architecture, Bentham remained ahead of his time. He envisioned an idealistic and rational, even utopian, surveillance society. Without the necessary (digital) technology to create this society, Bentham fell back on architecture to make this society possible. The failure of this architecture and its obvious shortcomings do not invalidate Bentham’s utopian project. Instead, these flaws with architecture indicate how Bentham envisioned an institution and society that would only become possible through new technologies invented hundreds of years later.

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Related Projects

My computer model is open source and free to download here.
Read my research on Eastern State Penitentiary, a radial prison descended from Bentham’s panopticon

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Credits

Supervised by Max Sternberg
Audio narration by Tamsin Morton
Audio credits from Freesound
panopticon interior ambiance
panopticon exterior ambiance
prison door closing
low-pitched bell sound
high-pitched bell sound
The archives and publications of UCL special collections

24 Hours in the London Underground

Audio effect: Heartbeat from Freesound

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Through analyzing 25,440 data points collected from 265 stations, this animation visualizes commuting patterns in the London Underground over two weeks in 2010.
Each colored dot is one underground station. The dots pulsate larger and smaller in mathematical proportion to the number of riders passing through. Big dots for busy stations. Small dots for less busy stations.
Dot color represents the lines serving each station. White dots are for stations where three or more lines intersect. Each dot pulsates twice in a day: Once during the morning commute; and again during the evening commute.
By syncing the audio volume with the density of riders and the background color with the time of day, the animation becomes visually legible. The audio volume rises and falls to mirror the growth and contraction of each colored dot during the daily commute.

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The rhythmic pulsing of commuters is analogous to the breathing human body. The passage of red blood cells from the lungs to the organs is analogous to the movement of people to and from the city’s own heart: the downtown commercial district. This analogy of human form to city plan is a longstanding theme in urban studies.
See my film about commuting patterns in the NYC subway.

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The Data

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Method

No single data set could capture the complexity of a metropolis like London. This animation is based off of open-access data collected in November 2010. According to Transport for London: “Passenger counts collect information about passenger numbers entering and exiting London Underground stations, largely based on the Underground ticketing system gate data.” Excluding London Overground, the Docklands Light Railways, National Rail, and other transport providers, there are 265 London Underground stations surveyed. For data collection purposes, stations where two or more lines intersect are counted as a single data entry. This is to avoid double-counting a single passenger who is just transferring trains in one station en route to their final destination.

Every fifteen minutes, the numbers of passengers entering the system are tallied. This yields 96 time intervals per day (4 x 24). Multiplying the number of time intervals (96) by the number of stations (265), we get the number of data points represented in this animation: 25,440. Each station was assigned:

  • A location on the map of latitude and longitude
  • A color according to the lines extant in 2010: Bakerloo, Central, Circle, District, Hammersmith & City, Jubilee, Metropolitan, Northern, Piccadilly, Victoria, Waterloo & City.
  • A circle scaled to reflect the number of passengers moving through. Stations range in business from a few hundred passengers to over 100,000 per day.
  • A time of day: each 15-minute interval becomes one image in this film. Overlaying these 96 “snapshots” of commuter movement creates  a time-lapse animation. Thus, a single day with 25,440 data points is compressed into a mere 8 seconds.

Sources

Station Coordinates: Chris Bell. “London Stations.” doogal.co.uk (link)
Ridership Statistics: Transport for London. “Our Open Data.” (link)
Click on the section “Network Statistics” to view “London Underground passenger counts data.”

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Powered by TfL Open Data. Contains OS data© Crown copyright and database rights 2016.

Burford Church: Construction Sequence

This project is also featured on Burford Church’s official website.
Created with Cathy Oakes, medieval art historian at Oxford University

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Construction Sequence: 1175-1475

While studying history at Oxford University, I based my final research project on Burford Church near Oxford, England. With the generous help from Cathy Oakes, I visited this humble parish church and recreated its 300 year construction and evolution through a computer model. View the resulting animation above or download the digital source files for free at this link. Narration below:

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  • c.1175 – Work begins on the Norman church working from east to west.
    It is a simple structure with round Norman windows and a choir, nave, and tower.
  • c.1200 – Demolition to construct a chapel, aisle, and entrance foyer.
  • c.1250 – Addition of north and south transept. Chancel is expanded.
  • c.1400 – The crypt is added, and the tower is heightened. The architectural style changes from Norman to Gothic, from round arches to pointed. Local cloth merchants construct a separate guild chapel at a slight angle to the main church.
  • c.1475 – Guild chapel is demolished to build the Lady Chapel. Most of the remaining nave is demolished to construct two new aisles, a larger west window, and new clerestory windows. Two chapels are added to either side of the choir, as well as a three floor entrance tower (not visible from this angle).
  • This completes the construction of Burford Church.

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Visual Analysis

What is the visual language of Burford Church? What aspects of medieval social history can be deduced from the church decoration? Without written historical records, how can we tell the story of this church based on building fragments alone?
Here is my tour of the architectural fabric.

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