Die Gewölbe vom Dorpater Dom



This is the very long story about how I spent two nice days (Dec 28 and 29), sitting quietly at a desk and drawing (Day One) and then building a model (Days One and Two) about a small section of the possible former vaults in the mediaeval cathedral of Tartu (location link; Google Street View from outside is also available). It was a remarkedly large building for its city, and since catching fire from a nearby bonfire in the 17th century, it has been more or less crumbling ruins. Half of it was recycled in the 19th c. to the university library which now is a museum.

Background

A cathedral is headed by a bishop. In the Middle Ages (1208/1227 to 1561), what is now Estonia was a patchwork of two dioceses (Dorpat and Oesel-Wiek; which functioned as political entities) and territories belonging to the Livonian Order (and up to 1346 also to Denmark). There were three bishops: the bishop of Reval (Tallinn) had little secular power; the successive bishops of Oesel-Wiek used to reside in different locations; and only the bishop of Dorpat (Tartu) had both, his diocese functioning as a largely independent political entity and having a single residence.

Three dioceses means that theoretically there were three cathedrals.

The cathedral of Tallinn (Reval) is a modest affair (link), its construction having started as for the church of a Dominican monastery. It is three aisles wide and four bays long, with a narrow chancel, and got a west tower only in the 17th c.

 

The absense of a capital in Oesel-Wiek means that there was no splendid cathedral either. Closest of it is in the castle of Haapsalu (link) which has a single aisle and three bays (and it is still referred as a cathedral, as most of the Oesel-Wiek bishops resided there). But some also resided in Pärnu (Pernau) which older part probably had a similar one-aisle three-bay church which was typical for the area in the 13th c., and which new part had (until it was was blown up in 1954) a city church of slightly more ample dimensions, but it hardly was a cathedral and the new part of the city was not in the bishop's lands. The third residence in Lihula (Leal) had not much else than a modest castle chapel (unless the bishop needed to use the nearby nunnery), and the fourth residence in Kuressaare (Arensburg; link) had also only a castle chapel (though this is not that modest, as it rises through two stories and has richer decorations than the rest of the castle) and possibly the town church which was near the castle but which plan is unknown.

 

Now the cathedral of Tartu (Dorpat; dedicated to St. Peter and St. Paul, if I remember correctly) is slightly gigantomanic (certainly for a mediaeval city which population was only 5,000) and different from everything that was built in what is now Estonia up to that time. Its interior length is a whooping 85 metres – the longest church in Tallinn was the St. Catherine with 67 m. It is three aisles wide (or five with the chapels) and its nave is eight bays long; its chancel had three bays plus an ambulatory (there were only three mediaeval chancels in Estonia with an ambulatory). Its chancel was a massive edifice and could have enclosed the entire cathedral of Tallinn inside (which at the time had no tower). It was the only church in what is now Estonia and Northern Latvia which had two massive towers; the next twin towers were erected in Estonia only in the Revival style in the 19th c. By surface area (measured along the mediaeval outer perimeter of the main body, with chancel, but without vestry), it was on par with (but not larger than, as it is sometimes claimed) the main body of the Riga cathedral (2,700 m² without the latter’s cloister and chapter rooms) and was easily the largest church in what is now Estonia – the largest surviving mediaeval churches in Estonia are in Tallinn and they are all smaller: St. Olai is 2,100 m², St. Nicholas 2,000 m², St. Bridget 1,500 m², St. Catherine 1,400 m², St. Mary (Tallinn cathedral) is 1,300 m², the two St. Michaels are 1,000 and 600 m², and the Holy Ghost is 700 m²; the only completely surviving mediaeval church in Tartu, St. John, is 1,100 m², and the cathedral of Haapsalu is 700 m². It also had the most numerous pillars – 23 (two lines of 11 each, plus a central one in the apse), the second most numerous were St. Bridget and St. Catherine with 14, St. Nicholas and St. Olai have 12, and the Tallinn cathedral has just 6 pillars.

 

Wars and fires have erased much of the documents and most of its construction history is speculative. Stylistically, it is assumed that the chancel may have been built by a master from the Parler school, maybe from Bohemia. The sequence of different construction stages of the nave relies on the digs in the 1930s; some small archaelogical digs have been made during the ongoing renovation. The chancel has been built over and since receiving a concrete floor in the 1980s future digs will be improbable for a long time. The state of the ruins before building the university library in the 1800s is known from engravings and a detailed plaster model. The ruins have been stabilised in the 1930s; then a little in the 1960s; then a little in the 1980s (the library part was completely overhauled then, converting it to a museum); and renovation has been under work since the early 2000s, thanks to the availability of custom-made tiles.

 

Late 19th c. reconstruction by Wilhelm Neumann, along the lines of the St. Mary of Lübeck, in a book of the history of mediaeval art in Estonia (Eesti kunsti ajalugu I: Keskaeg, by A. Waga, 1926). W. Neumann (1849–1919) was an architect, a productive art historian and founder of the art museum of Riga.

 

Paper model by yours truly (1/500, 1989), mangled by a lack of references and having seen just a glimpse of Neumann’s reconstruction several years before.

The plaster model of the ruins in 1804 which, I guess, is one of the oldest architectural models of a single building in Estonia. The western wall of the chancel appears a little too high and the openings in the towers are a little imaginative (compare to the cross section or photos below), but otherwise it is excellent.

Elevation and plan of the ruins in 1804. The plan may be somewhat idealised (some chancel buttresses have irregular alignment – which suggests the chancel was built around an existing structure), but the height of the chancel gable appears to be more realistic than in the plaster model.
Curiously the elevation view shows the large vertical crack through the southern celestory wall of Bay 1 already there; the 1959 conservation document says it may be mediaeval (may have appeared soon after the massive towers had been built and settled).
Note that by1804 the western towers had been incorporated in the city defences (traces of the curtain wall were visible on the tower walls until the current renovation).

Longitudinal section (1959)

Section though the westernmost bay in the 1959 conservation document

Plan in 1959

The ruins before the current renovation, in 1996, from the northern side-aisle, with pillars S-2, S-1, N-3, N-2 and N-1 in the view. Note the octagonal shape of the pillars, the vertical shafts in their corners, and how the shafts extend upwards and become arcade and vault ribs.



The nave in 1996. If you look closely, you can see the remains of the transverse rib on the western wall of the nave: it starts from the springing above the triforium and arcs inwards on the tower wall, terminating at the upper edge of the wall where the stucture has crumbled.

Southern end of the triumphal arch in 2004, with an earlier spiral staircase.

The nave from the triforium height westwards in 2004, with the last renovation underway

The pillar N-1 of the nave in 2004. Several elements discussed below can be seen here: the vertical shafts at the corners of the pillar; how the pillar protrudes from the celestory wall; the [pseudo]triforium (which in Bay 2 has exceptionally only 3 niches on the northern side); remains of the ribs and their position and curvature at the springing; and traces of the vaults along the celestory wall. Bay 1 has a large vertical crack also in its northern wall.

 

 

Glossary

DD: Dorpater Dom

 

Aisle: a lengthwise space, separated by pillars or a wall on its side. The cental aisle is nave (in the narrow sense of the term).
Ambulatory: a walkway along the inner perimeter of the chancel, continuation of the side aisles of the nave. In DD, its s height exceeded that of the side aisles about twice.

Basilica: design where the nave of a multi-aisle building raises clear of the other aisles.
Boss: the decorated keystone of a vault

Celestory: the top part of the nave; in true basilica, it raises over the roof of the lower aisles. Absent in hall church.

Bay: a rectangle formed by a vault in plan; handy in measuring vaults along the length of the nave. Diagonal ribs run along the diagonals of this rectangle.

Chancel: in narrow sense, the space around the main altar in the eastern end; in wider sense, the entire part of a church containing the chancel, with ambulatory (if present). Is separated from the nave by the triumphal arch which in DD is the only surviving major arch (it’s inside the museum building, 3rd floor, in the hallway, and it has been hewn into the existing wall between the nave and the chancel).

Course: a row of ashlars or tiles that make up a vault web. Its ends rest on ribs or the wall; if facing downwards, it generally is curved upwards (i.e. the upper parts of webs are somewhat bulging upwards).

Drop arch: a slightly squat-looking Gothic arch which defining radius is shorter than span. (In the sharp lancet arch the radius is longer, in equilateral arch it is equal, in the 16th c. Tudor arch there are two pairs of different radii etc.) In what is now Estonia, the predominant Gothic arch in 14th to 16th centuries was the 3/4 drop arch which defining radii were 3/4 of the span, and the origin points of the radii were at the same height as the springing, exactly between the midline and the springing. A 1/2 drop arch would be semicircular, and below that the arc would look like a letter B sideways that won’t stand structurally.

Groin: downward-projecting edges of vault; in quadripartite vault, each bay has four groins. Rib vaults have ribs under the groins.

Hall church: multiaisle design where there is no celestory. This implies that usually the nave has the same height as the other aisles, but sometimes it is higher. DD’s chancel had a hall church design, but its nave had the same height than the nave in the rest of the church.

Nave: both the part of the church between the chancel and the western towers (de: Langhaus) and its central aisle (de: Mittelschiff).

Quadripartite vault: a vault which in its simplest form has four webs, four groins and four diagonal ribs. In plan it can be quadratic (length = width), or elongated (length along the nave < width across the nave).

Springing: lowest point of the vault (where the ribs spring from the walls or pillars).

Stilted vaults in Ste-Chapelle, the gold standard of mediaeval vaulting (late 13th c.). See how the webs immediately next to the windows are twisted and how the springing of the arches over windows is higher than that of the transversal arches.

Stilted vault: a quadripartite vault where the transverse (narrow) web starts much higher than the longitudinal (wide) web. The result is that the web forms a vertical line on the celestory wall some distance from the springing upwards, and the resulting web itself is twisted along vertical axis, because its other edge along the diagonal rib moves inwards with progressing height. This feature appeared in the late 13th c. and is absent from DD.

Tracing: ornamental window “frames” of stone or brick.

Triumphal arch: the arch between the chancel and the nave.

Vault ribs: decorative load-bearing elements of the vault that transfer the weight to the pillars and walls. The actual ribs may seem fragile for such task, but most of the load was carried by the hidden structure inside the vault along vault groins. There are fancy names for different ribs in English, but I call the main ones simply diagonal and transverse ribs. In what is now Estonia, it was normal to use transverse arches which had much different cross-section than that of the vault ribs.

Web: a sheet of vault between ribs or wall.

 

What I wanted to know

• What was the shape and height of the nave vaults?
• Is it possible to triangulate downwards from the vaults and find the original height of the floor?
• How long was the foot used in the construction?
 

What I knew

• The octagonal pillars carrying the celestory wall have a shaft on each corner which all grow upwards into arch and vault ribs. Three ribs become side aisle ribs (diagonal, transverse, diagonal), two go under the arcade arches, and three continue upwards and become the nave ribs.
• The nave bays are elongated, being about twice as wide as long. The side aisle bays are quadratic.
• Lowest parts of the nave vaults (about one metre at the springing) have survived. Parts of the westernmost transversal arch have survived on the eastern sides of the towers. Contours of the vaults on the celestory walls have survived.
• The surving parts of the nave vault ribs (diagonal, transverse) have all more or less the same curvature.

 

The puzzle

• The eight shafts around a pillar are separated by 45°. While this works beautifully for the side aisles (which have quadratic bays and diagonal ribs at 45° to the wall), it won’t for the nave. Diagonal ribs at 45° to the wall would suggest that the ribs continued through two bays, but that would have required a complex design (reticulated vault) and would have made the transverse rib redundant.
• The same curvature would imply that ribs with larger spans would be also higher. That contradicts with the diagonal ribs at 45°, because otherwise the transversal ribs would pass under than the diagonal ribs.

The solution

1. Drawing
 

About a month ago I randomly discovered (while searching something else) the so-called “architectural heritage passports” from the 1980s, digitized in the Estonian registry of cultural heritage (these were compact standardised documents summarizing the information and state of building monuments). Then I discovered that it also holds the documentation for the restoration projects of listed buildings, together with their plans, historic overviews and often photos. What a treasure trove! I spent much of the holidays pouring over those, as I know many of the buildings well, many projects involved an art historian who was my schooltime’s best friend’s grandfather, and several were designed by an architect whose restoration projects (e.g. the Kuressaare castle) I very much appreciated at the time and who was a friend of a relative. I hadn’t seen nearly nothing of this material before! Several questions why something was restored one or other way were answered at once!

Form a conservation document of 1959 documenting the state of DD’s ruins I found a neat cross-section of the ruins (see above). This was the first detailed and accurate elevation plan I had ever seen of DD, and certain perspective distortions near its top suggest it has been drawn from actual photos of the ruins.

The cross-section shows the remains of a decorative transverse arch on the western wall of the nave. It can be assumed it had the same shape and height as the transverse ribs of the nave vaults. I tried to construct its original height with compasses – the plan shows traces of someone having attempted the same. Its shape turned out to be a 3/4 drop arch, typical for the region. Only after I had found its height, I browsed the photos of the 1804 plaster model and recalled that the triumphal arch (which is still in place) should have the same height; with the help of the side elevation in a 1804 plan by Krause (see above) I estimated its height in respect of the celestory windows, and the result was within 20 cm of the constructed height.

However, this didn't say much about the total height of the vaults, i.e. the height of the boss and the diagonal ribs. Typical German-style vaults had their bosses slightly higher than the tops of the transverse arches (in British- and often also French-style vaults the top line was straight and level), but this could be not estimated without a model.

The true scales of the cross-section and the plan slightly differ (the width of the nave between the celestory walls is 10.54 m on the section, 10.22 m on the plan). It was customary at the time to use an integral number of units for dimensions (preferrably round numbers, and in the Middle Ages counting was done by dozens), and the section shows that the widths of the different aisles of the nave had the proportions of 32 to 16 to 9 (feet), while the length of the foot was 0.328 m. (More specifically: the nave proper 10.54 m, northern side aisle 5.17 m, southern side aisle 5.24 m, northern chapel aisle 2.99 m). This is similar to the so-called Greek foot (0.33 m) used in some 14th c. buildings in Tallinn. However, according to the plan, the average length of the foot was 0.316 m which is similar to the Rhineland foot used in Tallinn slightly later. According to the plan, some measurements are: width of the nave 10.22 m, length of the second bay 5.65 m (18 ft.), inner length of the nave (8 bays) 45.36 m (144 ft.), width of the northern side aisle 5.16 m, width of the southern side aisle 5.00 m, width of the northern chapel aisle 2.58 m (8 ft.), width of the southern chapel aisle 2.42 m. According to the plan, the sides ratio of the nave bays (between celestory walls) is not the assumed 2 to 1, but 32 to 18 or 16 to 9.

Plan (1959) with measurement notes, transversal and diagonal rib shapes, and a drawing to see how much the shafts in pillar corners protrude from the celestory wall

2. Triangulation attempts

There are niches on the tower walls facing the nave of which only tops show above the current ground level; the original floor is covered with rubble. An article about the digs in 2001 (Archaeological Fieldwork in Estonia 2001, pp. 110–120) in the westernmost bay had a profile through the southern walls (p. 113), and this shows the elevations as follows: prehistoric ground at 65.00 m above sea leval, lowest excavated point of the foundations of the original southern wall at 64,00, original floor level in the sourthern aisle at 65.4 m, original planned ground outside the cathedral at 64.3 m, modern ground in the southern aisle at 66.50 m, modern ground outside at 66.00 m. This would mean the modern ground in the southern aisle is 1.1 m above the mediaeval level.

Also, this archaeology MA thesis describes two burials from the westernmost bay of the nave: one (p. 20) at 60 cm depth from the modern ground in the nave proper, from ca. 1700, in the rubble, and the other (p. 44) at 185 cm depth from the modern ground in the southern aisle, mediaeval (p. 67: perhaps from ca. 1400), ca. 80 cm under the mediaeval floor level. This would mean that the modern ground is about 1 metre above the mediaeval level.

The St. Bridget in Tallinn had also tile vaults, and its ruins had a 1½ m thick layer of rubble and earth on its floor (it was removed from there in the late 1970s, and archaeologists still wince imaging how much archaeological material might have simply gone to the landfill, only the arcade and transverse arch blocks having been recovered). Lowering the ground to the original floor level was suggested in 1959, but it appears that only some of the ground outside the church perimeter has been lowered, to help draining rainwater.

There were no spectacular results of triangulation. Some springings and keystones align, but only two lines cut the original outer wall (inside the later chapel aisle) under ground level. This results in two possible depths of the original floor:

 

Various heights vs. the 1959 ground level, and triangulation attempts

 

• The line through the underside of the keystone of the transversal arch and the highest point of the celestory wall arcade (green line above) intersects the outer surface of the supposed original outer wall about 0.9 m below the 1959 ground level. This line is inclined 62° which is neither the 60° of the equilateral triangle nor the 63.4° of the h = a isosceles triangle which was popular in Estonian mediaeval architecture. (The height of an h = a isosceles triangle equals its base; its sides are inclined arctan 0.5 = 26.6° from the vertical and 90° – 26.6° = 63.4° from the horizontal. I suspect the claims that DD’s towers were 66 m high are also based on the h = a isosceles triangle, as the western side with the two towers is approximately 33 m wide.)
• Approximately the same depth is achieved when considering that the height of the vaults in the nave from springing to the boss was double the height from floor to their springing (dotted triangles in the nave above).
• If the triangulation was based on the h = a isosceles triangle and we lower a line (blue line above) at 63.4° from the horizontal from the vault bosses (keystone of the transversal arch + 1 ft.) to the original external wall, it cuts it at about 1.6 m below the 1959 ground. This seems more realistic, considering the analogy to the rubble layer in the ruins of the Pirita convent.
• If the original floor was 0.9 m lower than the 1959 ground, and if the triangulation was based on the h = a isosceles triangle, a line inclined at 63.4° from the horizontal rising from the intersection of the outer surface of the chapel aisle wall with the original floor level to the middle line at the height of 30.12 m in respect to the 1959 ground. This would be the roof top line and its height from the original floor would be 31 m or ca. 95 ft., close to the round number (if counted by dozens) 96 ft. With the height of the celestory walls as in the 1804 elevation plan this means that the minimum angle of the roof was 52° (fine dotted line above) which is still realistic for a tile roof. (My late dad claimed that the minimum inclination of tile roof where snow falls off was 54°. I do not know the source of this claim, but a profile of street fascades from 1825 shows most mediaeval tile roofs of the houses in Tallinn being between 50° and 60°, and the St. Bridget's convent had exactly 54°. Flatter roofs could be covered with copper or lead sheeting.)

3. Model

For the floor plan I used another 1959 plan (see above) that was more detailed than the 1804 plan and showed the misalignment of the chancel buttresses realistically. This and the section had each a linear scale bar which I measured and calculated their numeric scales. However, by measurements of the shown features I later saw the linear scales disagreed by about 3%; I assumed it was the floor plan which scale was more inaccurate, and adjusted it accordingly.

The scale of the model is 1/100, and I measured the distance how much the pillar shafts would protrude from the celestory wall from an 1/50 drawing of my own, taking the celestory wall thickness from the cross-section and the thickness of the ribs from photos and memory. The shafts and ribs are about 15…20 cm thick, in the model the ribs are imitated with 1 mm binding wire.

Height of my vault reconstruction and position of the two bays of the model. The dotted line shows the height of the celestory walls as on the 1804 elevation plan; this height has survived in the two easternmost bays of the nave that were built over in the 1800s (at the left). The human figure stands 1.60 m tall on the 1959 ground level (the original floor was deeper).

The model shows two bays of the nave (let’s say Bays 3 and 4 from the west).

At one time I thought of extending the model downwards to the floor level and sideways to the full width of DD through all five aisles (when it would have become fairly large, but it would have been necessary to do also the six windows (the windows of the chapel aisle were in pairs) – too much work. Then briefly thought to expand it lengthwise, or at least doing four bays so that with a mirror the full eight bays of the nave could be seen – but what to do with the chancel which interior must have been well visible from the nave?

As materials, I briefly considered papier maché, but this is water-based and cannot be used in contact with regular cardboard (which supply is ample and usually bears the logo of Amazon). Then considered plaster gauze, but this would be too coarse (needing filler afterwards) and I was not sure how to do the necessary upwards bulge of the vaults – perhaps hanging the model upside down while the plaster sets?

Finally I decided to do only the vaults and perhaps the celestory walls with their external supports (no mediaeval church had flying buttresses in what is now Estonia; usually the lateral stress of nave vaults were taken by triangular supporting walls under the side aisle roof). This then shrunk to just the vaults and the inner surface of the celestory walls under the vaults, without the windows, without the rest of the walls, without the external supports.

The final material is layers of tissue paper bonded with contact glue. More construction details of the model are listed below.

4. Analogy

Clustered pillars looking as if consisting of a bundle of shafts was one of the five elements that defined the Gothic style (the others being: the pointed arch, the ribbed vault, the ambulatory, and the flying buttresses; all five met for the first time in the abbey of St-Denis under Abbot Suger who effectively created a new architectural style that dominated in Europe for three centuries), and even with modest decoration, it was common to have a shaft raising from floor to the springing under each bay corner (i.e. in the 45° position), and that beautifully grew into a diagonal rib at a steeper angle than 45° (see e.g. the photo of the Ste-Chapelle above).

 

 

Conclusions and speculations:

• The nave of DD had simple quadripartite vaults.
• The transversal arc on the western wall of the nave had the same height as the triumphal arch.
• The unit of measurement used for the nave was a 32.8 cm foot (according to the section) or a 31.6 cm foot (according to the plan).
• The width and length of the nave bays are about 16:9 (or what appears to be 32 by 18 feet). The rib spans are somewhat shorter, as they start from the pillars which protrude a little from the walls.
• The elongated bays mean that the span of the diagonal is not much longer than of the transverse arch, largely eliminating the second puzzle.
• The diagonal ribs are about 60° to the celestory wall in plan and have nearly the same curvature as the transversal ribs (the defining radius is 7.5 m vs. 7.2 m). The shape of the archs is different: the transversal arch is sharper, a 3/4 drop arch, and the diagonal arch is flatter, a 2/3 drop arch, about a foot higher. The span (between pillars) of the transversal arch is 9.6 m and of the diagonal arch 11.3 m.
• The vault remains on the celestory walls indicate that the vaults were not stilted: the line next to the windows is not vertical. Though it is nearly linear, it at ca. 75° to the horizontal. Possible simple explanation: the masons couldn’t do the twisted part of the stilted vaults.
• The simple vaults makes me think that perhaps the nave vaults were copied from those of the chancel. The latter had more complex shape in the ambulatory (as the external wall was slightly irregular and built to an earlier, different plan). Maybe the Parler-inspired masons built the chancel and the nave vaults were copied from that?
• It has been suggested (assuming that the entire DD was built under the same masters, and while the St. John has similar details, but simpler form) that the St. John was built by the masters who had previously built the DD. It would be interesting to speculate that maybe things happened the other way around.

The model

• Ribs are from 1 mm binding wire, with the necessary curvature bent on cardboard templates. Ends of the wires are punched into and glued to the board, considering how the pillar was protruding from the wall. One of the two diagonal arches in each bay is continuous, the other is from two pieces leaning against the continuous one at the top.
• Webs are layered from tissue paper (cut from a 4-ply paper hankerchief (Tempo Cotton Feel), then each ply separated, cut to shape and applied one by one with some overlap and slack). Each ply is about 0.015 mm thick (about 8 times thinner than regular office paper).

The celestory wall template

• The celestory walls are from cardboard, cut after a template. The window openings present the shape of the windows at the inner surface of the walls. The walls show also the tops of the pseudotriforium.
• The glue is contact glue which could be used in two ways: two-sided contact method for fixing cardboard and wire, one-sided method for fixing tissue paper. Contact glue does not wet the tissue as white water-based glue does; this could lead to some sloppy mess and the webs would later straighten with such force that it bends the wire. Disadvantages: 1) slightly dried glue residues on tweezers, the outside of the glue tube nozzle and fingers instantly bonded to any other slightly dried glue residues on the model which would tear the hair-thin tissue; 2) solvent fumes. The model dried overnight in the hall. After all the webs were in place, I heated the webs with warm air from air-dryer blowing to the underside of the webs. The solvent smell disappeared in some days.
• Laying the tissue paper strips for the webs followed the general method of laying the courses of ashlars or bricks: from bottom to top, strips perpendicular to the force paths in the web. Some slack was needed for the upwards bulge.
• The “right-hand” halves of the transverse webs of the model use six strips from springing to bottom, the left-hand halves use four (I had seen that wider strips will do, too).
• Most of the tissue pieces in the first layer are trapezoidal: the angle of the ends was cut to eye and the piece was placed so that its edges were on the top of the ribs (which were covered with glue from the top), then gently rubbed down along the ribs and the bulge pushed from the underside.
• Later extra paper was trimmed from the free edges and two or three reinforcing layers were added to the top.
• As a matter of fact, the webs of the model used only about 2/3 of a single hankerchief.

 

End view of the possible vaults. In reality, there was a 14–15-metre drop below this “floor” here (though there must have been a temporary floor approximately at this height during vault construction, supported at the pseudotriforium), each bay had a keystone at the top, and the ribs were about twice thicker and straighter, and the webs were thicker. Wobblyness of the ribs is unintended, the green wire had been wrapped tightly on a square-section stick.



A closer view, with a 1.60 m human added for scale (people were much shorter in the Middle Ages than now, partly from having a chronic heavy metal poisoning from eating from tin plates). The window openings show the shape of the windows at the inner surface of the celestory wall; the true opening tapered towards outside, and then there was the window tracing, of course.

Top view of the vaults. Note the complex curvature of the webs.