Tallon: Structure in Gothic, page 1

Structure in Gothic

Andrew Tallon

The Cambridge History of Religious Architecture, ed. Richard Etlin and Stephen Murray. Cambridge: Cambridge University Press, in press.

This essay might well have been called Structure is Gothic—or rather Gothic is Structure. For from the very beginnings of its modern reception, Gothic has been an architecture appreciated primarily (and often solely) for its structural audacity. The astonishing conquest of space and clearly-apparent structural brinksmanship of the Gothic masters, whose lissome buildings bent and twisted as they adapted themselves to ever-evolving load distributions, dazzled the architects and aesthetes of the French Enlightenment, who were as impressed with this manifest intrepidity as they were anxious to reject that which seemed to obscure it (a profusion of ornament).1 The heritors of the nascent esteem accorded to the Gothic, in particular the great architect and theorist Eugene-Emmanuel Viollet-le-Duc and his apologists, dissected and categorized the inner workings of the Gothic frame and elevated them into a credo of structural rationalism based on knowledge acquired on hundreds of post-Revolutionary restoration chantiers. Widely diffused through means such as Viollet-le-Duc’s ten-volume Dictionnaire raisonné de l’architecture française du XIe au XVIe siècle or Auguste Choisy’s Histoire de l’architecture, the ideas were elucidated through novel means of representation.2 The most important among these, in terms of structure was the transverse section (Fig. 1). Because of their construction in a series of nearly-identical bays, Gothic buildings were assumed to function as a succession of lateral frames, through which thrust moved from vaults to walls to flying buttresses to buttress-uprights (culées) to the ground. The overwhelmingly complex three-dimensional assembly of stones, mortar and iron could thus be profitably reduced into a single, representative section that allowed the restorers but also—through their publication in the Annales archéologiques, Bulletin monumental, Congrès archéologique and a host of regional journals— generations of amateur archeologists, who could not hope (or did not wish) to participate in the “scaffold culture,” to ponder the means of support and its successful deployment by builders

1 See Robin Middleton, “The Abbé de Cordemoy and the Graeco-Gothic Ideal: a Prelude to Romantic Classicism (Part I),” Journal of the Warburg and Courtauld Institutes 25 (1962): 278-320.

2 Eugène-Emmanuel Viollet-le-Duc, Dictionnaire raisonné de l’architecture française du XIe au XVIe siècle, 10 vols. (: B. Bance and A. Morel, 1854-68); Auguste Choisy, Histoire de l’architecture, 2 vols. (Paris: Gauthier- Villars, 1899). See Arnaud Timbert, “Les illustrations du Dictionnaire raisonné: le cas de la cathédrale de Noyon et des églises de l’Oise,” in Viollet-le-Duc à Pierrefonds et dans l’Oise, ed. Dominique Seridji, 98-108 (Paris: Editions du patrimoine, 2008), accessed 15 August 2010, http://www.monuments-nationaux.fr/fichier/editions_livre/664/ livre_pdf_fr_violletleduc.pdf. Tallon: Structure in Gothic, page 2

without access to the things that seem indispensable on a modern worksite, such as reliable means for calculating stresses and equilibrium.3 However, once this intuitively resonant, privileged view was in the hands of a new class of “armchair” scholars, interpretations of Gothic structure proliferated. The structural fortunes of countless Gothic buildings were arbitrated based often on little more than a strong hunch, with a concomitant growth in the number of paradoxical contradictions in the literature. Alain Erlande- Brandenburg, the author of the most recent monograph on Notre-Dame of Paris, for example, said of the high vaults that they thrust but little, while Marcel Aubert, responsible for the penultimate monograph, said quite the opposite.4 Unlike a conventional archeological puzzle, in which a range of dates might be assigned to a portion of a building, for which at least the material elements can be known with some certainty, to attempt to understand Gothic structure is ever to grapple with the invisible—the forces that move through the building. To be sure, the section drawing reveals positive structural connections among vault, wall and buttress. But it cannot indicate what they actually do. The Gothic builder seems to offer some assistance: he supplies us with a representation of the structure in a language of support which suggests the presence and movement of forces along ribs and colonnettes adossed to walls—yet it is but a feint, in a grammar never meant to be taken literally. Piers, ribs and flying buttresses are the dicta that tell us that the building is doing work, but there can be no certainty, in the absence of documents supplied by the medieval builder, that the element in question is primarily designed to do the work or to seem to do the work. The prolonged debate over the structural-constructional-decorative role of the rib, what Henri

3 Andrew Tallon, “The transverse section and the creation of Gothic,” in preparation.

4 Alain Erlande-Brandenburg and A.-B. Merel-Brandenburg, Histoire de l’architecture française du Moyen Age à la Renaissance (Paris: Mengès, 1995), 274; Marcel Aubert, “Les plus anciennes croisées d’ogives: leur rôle dans la construction,” Bulletin Monumental 93 (1934): 1-67, 137-237, esp. 86. See also Alain Erlande-Brandenburg, Notre- Dame de Paris (Paris: Nathan/CNMHS, 1991), 74 and 90. Tallon: Structure in Gothic, page 3

Focillon called “the most delicate, the most bitterly contested point in the history of architecture,” is testament to this.5 The flying buttress is similarly multilingual. Architect and historian Anne Coste has ventured, based on the results of a computer model, that the traceried flyers in the choir of the cathedral of Auxerre are not structurally essential (Fig. 2).6 Similar observations were made of the flyers at the cathedral of Sens and the abbey church of Saint-Remi in Reims by engineers Robert Mark and Leonard Van Gulick.7 These experimental results suggest that flying buttresses may have been assessed as much for their ability to provide structural support as for their look, as instruments by which the decorative and spatial treatment hitherto proper to the interior might equally be extended to the exterior—transforming what was before an unrelieved envelope into an ever-changing and indistinct zone of shadow and light. Confirmation of this mode of reception is found in a number of early thirteenth-century manuscript illuminations and windows in which the flying buttress has been transformed into a symbol of structure (f. 50 v of the Bible moralisée Codex Vindobonensis 2554 or window 8 of the cathedral of Auxerre, for example).8 Perhaps the flying buttress was intended to prop not only according to structural rules, but to comfort the intuitions of the canons and bishop standing below. A Gothic builder like William of Sens, who began his tenure at Canterbury Cathedral as a “handler” of monks frightened by the destruction by fire of their choir in 1174, had to convince his clients—and perhaps himself—that what he was attempting was safe. Clearly-visible arches such as William

5 Henri Focillon, The art of the West in the Middle Ages, ed. Jean Bony, trans. Donald King, 2 vols. (London, 1963), I, 54. The key statements in the discussion, in chronological order, are as follows: Roger Gilman, “The Theory of and the Effect of Shellfire at Rheims and Soissons,” American Journal of Archaeology 24, no. 1 (1920): 37-72; Victor Sabouret, “Les voûtes d’arêtes nervurées: rôle simplement décoratif des nervures,” Le génie civil 92, no. 3 (1928): 205-09; Pol Abraham, “Nouvelle explication de l’architecture religieuse gothique,” Gazette des Beaux-Arts 6th series, no. 9 (1934): 257-71; Pol Abraham, “Viollet-le-Duc et le rationalisme médiéval,” Bulletin Monumental 93 (1934), 69-88; Aubert, “Les plus anciennes croisées d’ogives,” 1-67, 137-237; Henri Masson, “Le rationalisme dans l’architecture du Moyen Age,” Bulletin Monumental 94 (1935): 29-50; Henri Focillon, “Le problème de l’ogive,” Recherche 1 (1939): 5-28; George Kubler, “A Late Gothic Computation of Rib Vault Thrusts,” Gazette des Beaux-Arts 6th series 26 (1944): 135-48; Paul Frankl, The Gothic: Literary Sources and Interpretations Through Eight Centuries (Princeton: Press, 1960), 563-578; John Fitchen, The Construction of Gothic Cathedrals (Chicago: University of Chicago Press, 1961), 68-173; Jacques Heyman, “On the rubber vaults of the Middle Ages and other matters,” Gazette des Beaux-Arts 6th series 71 (1968): 177-188, esp. 183-184; and Robert Mark, K. D. Alexander, and J. F. Abel, “The Structural Behavior of Medieval Ribbed Vaulting,” Journal of the Society of Architectural Historians 36 (1977): 241-51. For a recent discussion see Santiago Huerta, “The Debate about the Structural Behaviour of Gothic Vaults: From Viollet-le-Duc to Heyman,” in Proceedings of the Third International Congress on Construction History, 20th-24th May 2009, ed. Werner Lorenz, 837-844, Cottbus, Germany, 2009.

6 Anne Coste, L’architecture gothique: lectures et interprétations d’un modèle (Saint-Etienne: Publications de l’université de Saint-Etienne, 1997), 115 and 188-197.

7 These unpublished studies were made in 1987; I am grateful to the authors for having allowed me to make use of the analyses.

8 See Claudine Lautier, “Les édifices réligieux et leur construction dans les vitraux narratifs de la première moitié du XIIIe siècle en ,” in Actes du XXIe colloque international du Corpus Vitrearum: Représentations architecturales dans les vitraux, Bruxelles, 22-27 août 2002, ed. Robert Tollet, 43-51 (Liège: Commission royale des Monuments, Sites et Fouilles de la Région wallonne, 2002). Tallon: Structure in Gothic, page 4

and his successor, William the Englishman, erected at Canterbury may have served just such a function.9 It is equally possible that flying buttresses were intended to have the opposite effect: to heighten the viewer’s sense of the awesome fragility of the cage of glass which they held in place.10 If the building, at least on the surface, tells an ambiguous story, surely a more obvious source, such as construction records authored by the builder, should be more instructive. Yet the search for medieval documents which can precisely elucidate Gothic structural method has been, alas, a rather fruitless one. Suger at Saint-Denis, Gervase of Canterbury, Villard de Honnecourt, or later, architects like Jehançon Garnache, all speak of construction in his own way—but their words can do but little to assist in the formulation of a comprehensive idea of Gothic statics.11 Modern documents, particularly those created by the architects charged with the repair of the buildings, are more forthcoming. For while they call tell us but little of the medieval structural imagination, they supply something equally important for decrypting the Gothic structural puzzle: in many cases they preserve states of the buildings which are today lost because of remodeling, restoration or destruction. The cathedral of Notre-Dame in Paris is a case in point. The clerestory walls were heavily remodeled in the first two decades of the thirteenth century (and then rather capriciously returned in part to their supposed earlier state by Viollet-le- Duc in the mid-nineteenth century); the tribune vaults and exterior walls, especially in the choir, were remade by Viollet-le-Duc and Lassus; and the flying buttresses were overhauled several times (such is the fate of elements constantly exposed to the weather), rebuilt most recently by Viollet-le-Duc and Jean-Baptiste Lassus beginning in 1845—to cite but three examples.12 To accurately recover the twelfth-century state one must turn to a host of sources: the archeological discoveries made by early restorers, especially Viollet-le-Duc and Lassus (some published, but the majority preserved in worksite drawings and their accompanying texts); early photographs (a fortuitous coincidence of nascent photographic techniques with a well-lighted subject newly visible from the left bank of the Seine after the sack of the archbishop’s palace in 1830 and again in 1831), engravings and manuscript illuminations; a plaster scale model made in 1843; and finally, the evidence supplied by contemporary buildings which preserve architectural citations

9 On the flying buttresses at Canterbury see Yoshio Kusaba, “Some observations on the early flying buttress and choir triforium of Canterbury Cathedral,” Gesta 28, no. 2 (1989): 175-189.

10 It was this aspect of the flying buttress which impressed (or rather, distressed) early modern observers most. Marc-Antoine Laugier, for example, said of the typical Gothic “forest of flyers and buttresses” that “the meticulously arranged decorative elements do nothing to counter the impression that the building is propped up throughout and threatens to collapse.” Laugier, Observations sur l’architecture (La Haye: Desaint, 1765), 298.

11 See Victor Mortet, Recueil de textes relatifs à l’histoire de l’architecture et à la condition des architectes en France, au Moyen âge I (Paris: A. Picard, 1909); II, with Paul Deschamps (Paris: A. Picard, 1929); Frankl, The Gothic, 1-234; and Stephen Murray, “Master Jehancon Garnache (1485-1501) and the Construction of the High Vaults and Flying Buttresses of the Nave of Troyes Cathedral,” Gesta 19, no. 1 (1980): 37-49.

12 The flying buttresses they built are now due for replacement which will take place, pending budget approval, over the next several years. Tallon: Structure in Gothic, page 5

made of Notre-Dame in the twelfth century. These include, to name but the most important examples, the south flank of the nave of the cathedral of Saint-Mammès in Langres (today replaced but with original form preserved in nineteenth-century restoration documents); the nave of Saint-Martin in Champeaux; the choir of the Cluniac priory of Saint-Leu-d’Esserent; the westernmost nave bay of the cathedral of Senlis; and finally, the nave of the abbey church of Saint-Martin at Tours (now destroyed, but preserved in various media).13 Photographs and observations made after bombing raids in both world wars are as useful as they are disheartening—peering into partially-demolished nave of the cathedral of Soissons, for example, with vaults and flying buttresses in various states of suspension, honed the structural intuitions of the collective art historical establishment far more than simple section drawings had been able to do.14 Yet the greatest advance in the understanding of Gothic statics was made through the application of structural modeling techniques in the mid-twentieth century. Though procedures for the calculation of equilibrium had been sporadically applied to Gothic buildings by engineers and restoration architects since the mid-nineteenth century, only in 1966 did Cambridge University professor Jacques Heyman, using an approach called limit analysis, begin to systematically address the structural questions that art historians had long posed.15 Limit analysis is an approach to understanding equilibrium in which a masonry structure is assumed to be composed of a series of rigid (non-deformable) blocks with sufficient frictional resistance to prevent them from sliding in relation to one another, but which together cannot resist tension. The state of equilibrium is thus considered independent of the material properties of the constituent elements and becomes a question of stability. The force that will just maintain equilibrium among the stones of an arch, for example—that will keep the arch from collapsing under its own weight—is called the lower limit. The greatest possible force that does not cause the arch to collapse (or fold) under compression is the upper limit. Between these two limits lies a range of working loads that the arch—or the structure—can handle. These loads can be determined graphically: force can be represented as an intuitively comprehensible “thrust line” (one among the range of forces determined by the limits) on a two-dimensional scaled section drawing of the structure being tested. The structure is assumed to be in a state of equilibrium when this thrust line, determined graphically using Robert Hooke’s “hanging chain” law (force travels according to an inverted catenary), falls within the boundaries of the architectural members in the section drawing.16

13 See Andrew Tallon, “Experiments in Early Gothic Structure: the Flying Buttress” (Ph.D. diss., , 2007), 145-206.

14 Gilman, “The Theory of Gothic Architecture and the Effect of Shellfire at Rheims and Soissons.”

15 See Jacques Heyman, The stone skeleton: structural engineering of masonry architecture (Cambridge: Cambridge University Press, 1995).

16 See Maria-Katerina Nikolinakou, Andrew Tallon and John Ochsendorf, “Structure and form of early Gothic flying buttresses,” Revue Européenne de Génie Civil 9, no. 9-10 (2005): 1191-1217. Tallon: Structure in Gothic, page 6

At the same time Princeton University professor Robert Mark began to address similar problems using scale models made of epoxy plastic (Fig. 3).17 Mark reasoned that a building could be represented as a monolithic two-dimensional section uniformly subject to the material properties of stone—an elastic substance for which deformation (strain) is directly (or linearly) proportional to the load applied (stress). He was thus able to use epoxy plastic, which had a linear elastic response similar to that of stone, to make small-scale section models. When heated and subjected to scaled loads applied according to their presumed distribution in the actual building, the epoxy models revealed patterns of strain under polarized light. These regions of strain were assumed to be directly proportional to the tensile and compressive forces in the model, and, when appropriately scaled, to the actual building. Computer-based linear elastic finite element modeling was used by Mark beginning in the 1980s; here the structure was represented as a mesh of blocks (elements) of small enough size to resolve local perturbations in stresses and for which equilibrium and material properties could be readily described. Mark’s work served to raise interest as never before in the structural workings of great Gothic buildings; it breathed fresh air into a discipline hampered by the limitations of intuition starved for facts. At last, it seemed, “real” structural information about the buildings could be had. But structural modeling is not without problems. With certain techniques accuracy depends on a precise understanding of the materials being modeled, such as type and thickness of mortar beds, position of cracks, the geometry, density and frictional characteristics of stonework, and the regular but often-neglected presence of iron ties or cramps.18 When these details are hidden within walls or vaults and cannot be quantified, the modeler is obliged to simplify—with a concomitant decrease in accuracy. In all cases precision depends directly on the exactitude with which the building geometry is represented—and, in terms of both limit analysis, the technique used by Heyman, and photoelasticity, that used initially by Mark, the degree to which a complex three-dimensional structure can tolerate abstraction into a two-dimensional section. It is one thing to engage in this reductive process as an intuitive aid, as happens when creating a section drawing; it is another to make the assumption that a building actually behaves this way. Finally, we must, as art historian Robert Branner wrote presciently, “make a distinction between structural realities as they are now understood, and what Gothic masters thought they

17 See especially Robert Mark, Experiments in Gothic Structure (Cambridge, Mass.: MIT Press, 1982). For a discussion of the relative merits of the different approaches to the modeling of masonry structures see Thomas E. Boothby, “Analysis of masonry arches and vaults,” Progress in Structural Engineering Materials 3 (2001): 246-256; Santiago Huerta, “Mechanics of masonry vaults: the equilibrium approach,” in Historical Constructions, ed. P. B. Lourenço and P. Roca, 47-69 (Guimarães: University of Minho Press, 2001); and Rowland Mainstone, “Structural Analysis, Structural Insights, and Historical Interpretation,” Journal of the Society of Architectural Historians 56, no. 3 (1997): 316-340.

18 See Arnaud Timbert, ed., L’homme et la matière: l’emploi du plomb et du fer dans l’architecture gothique. Actes du colloque de Noyon, 16-17 novembre 2006 (Paris: Picard, 2008); Marc Ferauge and Pascal Mignerey, “L’utilisation du fer dans l’architecture gothique: l’exemple de la cathédrale de Bourges,” Bulletin Monumental 154 (1996): 129-148. Tallon: Structure in Gothic, page 7

were doing.”19 Creating an accurate model is a challenge to which engineers and architects have long aspired, and great strides have been made in the past few years particularly in three- dimensional modeling techniques.20 Yet asking the most useful questions of these models is a challenge of equal importance. To know the specific value of thrust of a vault or the putative mode of failure of a structure in a state of equilibrium is ultimately of rather limited utility— especially given the degree to which the assumptions made must call into question the precision of model results. For these reasons a very old approach to understanding structural behavior—that used by the builders themselves—has recently been given new life, and a new name: spatial archeology.21 If we assume that a Gothic building was constructed more or less in plumb, then the degree to which it is no longer so can be “read” as the result of the action of forces: the direct feedback supplied by the building to its creator, anxious to confirm his assumptions about its stability—today supplied also to the art historian or restoration architect, anxious to understand why the building stands as it does. Gothic buildings, as Viollet-le-Duc and Choisy made clear, constantly reconfigure themselves in response to their environments, to the shifting loads of wind and wear—and did so with unusual abandon during the first few years after the completion of construction, when the mortar was still in a plastic state.22 Cracking in mortar (and exceptionally, in the stone itself) and concomitant deformation are the primary manifestations of this plasticity. Today, with the help of laser technology, these movements, now essentially locked in stone and mortar, can be resolved with astonishing detail. Even if the means of support have since changed, as was the case at Notre-Dame; even if the upper windows and wall panels were reworked, the piers and responds —the framework—were unaltered and thus preserve the evidence of the first great moment of structural truth, the de-centering of the vaults.23

19 Robert Branner, Gothic Architecture (New York: George Braziller, 1961), 20.

20 For example, Philippe Block and John Ochsendorf, “Thrust Network Analysis: A New Methodology for Three- Dimensional Equilibrium,” Journal of the International Association for Shell and Spatial Structures 48, no. 3 (2007): 167-173.

21 Andrew Tallon, “Archéologie spatiale: le bâtiment gothique relevé (et révélé) par laser,” in Architecture et sculpture gothiques: renouvellement des méthodes et des regards, ed. Arnaud Timbert and Stéphanie Daussy, in press.

22 “It is certain,” wrote restoration architect Jean-Pierre Paquet, “that lime mortars remained in a plastic state for several months and sometimes even several years after their initial use. They hardened slowly, and, for a certain time after the centering was removed, deformations took place; later, temporary displacements due to shifting loads and other incidents sustained over the centuries accentuated this evolution.” Jean-Pierre Paquet, “Structures des monuments anciens et leur consolidation,” Monuments Historiques de la France, no. 1 (1957), 168-169.

23 Note that it is impossible to rectify a deformed masonry structure after the fact without rebuilding it. Such an operation was in fact attempted in the nave at Saint-Leu-d’Esserent by Daniel Ramée, ca. 1848. Threaded iron tie rods were stretched across the main vessel but as the bolts were tightened pieces of the transverse arches were crushed and fell; the rectification was abandoned. The details are preserved in a letter by the entrepreneur, Charles Puissant. Puissant, “Rapport,” Paris: Médiathèque du Patrimoine 0081/060/159, ca. 1850. Tallon: Structure in Gothic, page 8

The data is acquired as follows: a computer-controlled laser measures the distance between itself and every surface that it can “see” at up to fifty thousand times per second. The resultant measurements, assembled into a document called a point cloud, can then be linked to additional point clouds acquired in different areas to create a highly accurate three-dimensional map of the building, in this case Notre-Dame in Paris, scanned in January of 2010 with a resolution of over one billion data points (Fig. 4).24 The data set can be framed to view particular aspects more clearly; a section through one of the westermost bays of the nave, for example, reveals interesting details about the building’s response to its loading (Fig. 5). The wall has assumed the characteristic, unilateral curvature of the structurally-minimalist Gothic building: the thrust of the aisle vaults has generated a rotation of the pier into the space of the main vessel, despite the vertical load supplied by the superstructure, which tends to resist this overturning force. It is not a particularly egregious case (the capital has been displaced outward by four cm); one has only to visit the collegiate church of Saint-Quentin (Fig. 6), or, on a smaller scale, the church of Saint-Pierre in Bar-sur-Aube to realize the extent to which the geometry of a Gothic building can adapt (and sometimes fail to adapt, as is the case at Notre-Dame in Louviers) to unanticipated loading conditions. Such deformation seems to have been considered a fundamental structural and aesthetic problem by Gothic builders. The architects of the cathedral of Bourges, for example, whose conception of the spatial matrix depended on perfect rectilinearity, installed a series of iron chains and ties to prevent the onset of vault-thrust deformation; the cathedral of Amiens was similarly fitted with a series of massive iron chains, which gird the building at triforium level, after the building exhibited alarming bowing in the crossing piers.25 The upper walls of Gothic buildings typically present some outward deformation as well because of the greater size and thrust of the vaults—particularly where there were no flying buttresses present initially, as was long believed to be the case in the choir of Notre-Dame (Fig. 7).26 Yet the laser scan presents what in the context of a typical Gothic building constitutes an astonishing fact: each straight-bay main-vault respond of the choir, measured at a point just below the high capital, has remained almost perfectly in plumb (within several centimeters) with respect to a similar point just above the main arcade capital. Had the flying buttresses been absent during the critical first few years before complete mortar hardening, the outward thrust of the vaults would very likely have pushed apart these tall, thin walls. The presence of the flying

24 The scanning campaign, undertaken by the author with assistance from Paul Blaer and Antoine Billault, was funded by PBS/Nova and Arte.

25 Andrew Tallon, “La cathédrale de Bourges à la lumière du laser,” in La cathédrale de Bourges, ed. Olivier Nauleau and Marie-Reine Renon (Rennes: Presses universitaires de Rennes), in press; Stephen Murray, Notre-Dame, Cathedral of Amiens: the Power of Change in Gothic (Cambridge: Cambridge University Press, 1996), 164; Emiline Lefebvre, “Le chaînage du triforium de la cathédrale Notre-Dame d’Amiens,” in L’homme et la matière, 141-147.

26 See Stephen Murray, “Notre-Dame of Paris and the Anticipation of Gothic,” Art Bulletin 80, no. 2 (1998), 234-42; Paul Crossley, in Paul Frankl, Gothic Architecture, revised ed. Paul Crossley (New Haven: Press, 2000), 315 n. 37a and 38; and Tallon, “Experiments in Early Gothic Structure,” 145-181. Tallon: Structure in Gothic, page 9

buttress in the choir of Notre-Dame (the form of which, quite similar to that of those currently present, is preserved in the documents cited earlier) is thus incontrovertible, and they did their job well. Despite the seemingly high placement of the flying buttress with respect to the transverse arch, it is more or less centered on the mass of the vault, and the slope of the flyer follows that of the lateral vault webs. Such flyer placement may reflect a conception of bracing that included wind loading—an average position on the upper wall designed to handle a variety of thrusts. The laser scan further indicates that in certain bays the wall is displaced inward; we thus have reason to suspect that the flying buttresses, which, given their prodigious length, would have thrust considerably against the main vessel due to their dead weight, were put in place before the vaults could supply a counter-thrust of greater magnitude. It is important to note that the builders of the choir at Notre-Dame had other structural tools at their disposition, which surely contributed to the unusual rectilinearity of the clerestory. The upper wall, only sixty-eight cm thick (not including the responds or wall buttress on the exterior), is composed of ashlar blocks consolidated from above by the considerable weight of a large wooden roof covered with lead. The top of this wall originally terminated in a set of three bands of billet molding which were corbelled outwards to provide broader footing for the roof, and whose courses were interlocked with iron cramps. The choir was thus encircled with what Viollet-le-Duc called “a powerful chain”: the flying buttresses were not the only means of upper wall support.27 Perhaps the key advantage of spatial archeology is one of representation, which is half the battle when it comes to understanding structure. Like Choisy’s famous axonometric drawings (Fig. 8), a three-dimensional point cloud allows us to peer into the building—but also to displace it, move through it, measure it, and, most importantly, immerse ourselves in the spatial and structural matrix in a way impossible in the actual building.28 Until modern modeling techniques are sufficiently able to account for the myriad conditions of the actual building and able to elucidate these conditions to engineer and art historian alike, close observation by laser, which invites the building to ‘speak’ its structural state directly, is the most promising approach to understanding of Gothic structure.29 The Gothic structural dare—which in an era of intense correlation of sacred and mundane must have been especially powerful—is still tangible in a present weary of tall buildings and architectural stunts. Gothic builders wedded a keen sense of monumental stability, developed

27 Eugène-Emmanuel Viollet-le-Duc, “Chaînage,” Dictionnaire raisonné de l’architecture française du XIe au XVIe siècle, vol. 2 (Paris: B. Bance, 1856), 400.

28 On Choisy’s axonometric views see Thierry Mandoul, Entre raison et utopie: l’Histoire de l’Architecture d’Auguste Choisy (Wavre: Mardaga, 2008), 111-162; and Hilary Bryon, “Revolutions in space: parallel projections in the early modern era,” Architectural Research Quarterly 12, no. 3/4 (2008): 337-346. Jean Bony proposed a similar mode of representation in his magisterial “Essai sur la spiritualité de deux cathédrales: Notre-Dame de Paris et Saint-Etienne de Bourges,” in Chercher Dieu, 150-167 (Lyon: Editions de l’abeille, 1943).

29 See Andrew Tallon, “Rethinking Medieval Structure,” in New Approaches to Medieval Architecture, ed. Robert Bork and Abby McGehee (Farnham: Ashgate), in press. Tallon: Structure in Gothic, page 10 through close observation of edifices in equilibrium as well as incipient failure, with an equally refined command of the illusionistic language of structure in which visible and invisible, effort and effortless were deftly apportioned. Their primary motive was not to push ever higher, with ever more slender members, driven by ego, desire or faith, until arrested suddenly in 1284 when the vaults of the cathedral of Saint-Pierre in Beauvais came crashing down, as familiar and attractive (though ill-informed) as this evolutionist take might be: it was rather to create an empyrean space radically freed of the means of support, in which light was the primary medium of creation. Gothic is indeed structure, but not only structure: structure can only be a means— however compelling and essential—to an end. Tallon: Structure in Gothic, page 11

Figures

Figure 1. Laon, cathedral of Notre-Dame, section through the nave before restoration, after a drawing by Emile Boeswillwald, 1847. Anatole de Baudot and Anatole Perrault-Dabot, Archives de la Commission des Monuments Historiques, série 1, Paris, 1855-1872, vol. 1. Tallon: Structure in Gothic, page 12

Figure 2. Auxerre, cathedral of Saint-Etienne, choir flying buttress. Photo: Andrew Tallon. Tallon: Structure in Gothic, page 13

Figure 3. Sens, cathedral of Saint-Etienne, Photoelastic section through the choir. Photo: Robert Mark (used by permission). Tallon: Structure in Gothic, page 14

Figure 4. Paris, cathedral of Notre-Dame, laser scan data produced in January 2010. Tallon: Structure in Gothic, page 15

Figure 5. Paris, cathedral of Notre-Dame, section through laser scan data of the nave. Tallon: Structure in Gothic, page 16

Figure 6. Saint-Quentin, collegiate church of Saint-Quentin, view of the main vessel from the chevet triforium. Photo: Andrew Tallon. Tallon: Structure in Gothic, page 17

Figure 7. Paris, cathedral of Notre-Dame, section through laser scan data of the choir. Tallon: Structure in Gothic, page 18

Figure 8. Paris, cathedral of Notre-Dame, reconstruction axonometric view of the nave. Auguste Choisy, Histoire de l’architecture, 2 vols., Paris, 1899, vol. 1, 428.