Vaults

A vault is an arch that has become a ceiling. Its virtues are those of the arch (it spans with stone in compression, and it does not burn), and so are its problems: it is heavy, it must be built on centring, and it pushes outward on whatever holds it up. For two thousand years European builders refined a small number of vault forms, each a different answer to the same three questions: where the weight goes, where the thrust goes, and where the light can come in.

The models in this chapter build every vault from its geometry. The barrel and the groin and cloister vaults are surfaces generated by circles; the rib vaults are built cell by cell, each thin web spanning between two ribs and a boundary arch; and the English tierceron, lierne and fan vaults are laid on conoids (surfaces turned about each springer), which is why all their ribs share one curve.

The barrel

Slide an arch along its axis and it sweeps out a barrel, or tunnel, vault. It is the simplest vault to set out and to build, and the Romans used it for everything from sewers and substructures to the corridors of the Colosseum. But it has two great disadvantages. Its weight and thrust are spread uniformly along both side walls, which must therefore be continuous and thick; and any window cut into its sides below the springing weakens the very wall that holds it up, while a window above the springing must break into the vault itself.

Romanesque builders who wanted stone over their naves reached first for the barrel, and lived with its consequences. At Saint-Savin-sur-Gartempe the painted barrel springs straight from the arcade and the nave has no clerestory at all; in the pilgrimage churches of Conques, Toulouse and Santiago the barrel is braced by half-barrels over galleries (Galleries that buttress the nave); in Burgundy it was pointed to reduce its thrust, and at Cluny III it rose to about thirty metres. They also learned to run transverse arches under the vault at every bay. These arches were built first, the barrel was laid on them, and they divide the tunnel into a rhythm of compartments.

℟A barrel vault needs a continuous wall

A barrel (tunnel) vault is an arch extruded along its axis. It thrusts outward all along both sides, so it must rest on continuous thick walls, which can be pierced only sparingly, and only below its springing.

thrust per metre of wall ≈ constant along the whole length

Groin and cloister

Cross two barrels of the same height at right angles, and you get one of the two most important vaults in history. Where the barrels intersect, their surfaces meet in four curved edges, the groins, which run diagonally from the corners to the crown. Seen from below, the space of both barrels is united: the vault is open on all four sides, each side framed by the arched end of a barrel. The weight and the thrust, which in a single barrel spread along the whole wall, are gathered by the groins and delivered to the four corners. The walls between the corners carry little; they can be opened into arcades or pierced by great lunette windows.

The Romans built groin vaults in concrete over the great halls of their baths and over the nave of the Basilica of Maxentius (308–12), three colossal bays in a row on eight piers. Romanesque builders used them everywhere over aisles, and over naves too once they dared: at Speyer, around 1080–1106, the nave was covered with great square groin vaults, each spanning two bays of the arcade.

℟Two barrels crossed gather their thrust at the corners

Intersect two barrel vaults of equal height at right angles: the result is a groin vault, whose weight and thrust are gathered along the diagonal groins to the four corners, leaving the sides free for openings.

surface = max(barrel₁, barrel₂) · groins on the diagonals

Take the intersection of the two barrels instead of their union, and the result is the cloister vault: four curved cells rising from all four walls and meeting in valleys along the diagonals. Where the groin vault is open on every side, the cloister vault is closed on every side, and it needs walls all round. It is the natural vault for a tower or a square room, and on an octagon it becomes a ribbed dome, the form of Brunelleschi’s dome at Florence.

℟The cloister vault: the groin turned inside out

Where the groin vault is the union of two barrels, the cloister (domical) vault is their intersection: four curved cells rise from all four walls and meet in valleys along the diagonals. It needs walls on every side.

surface = min(barrel₁, barrel₂) · valleys on the diagonals

The problem of the oblong bay

The groin vault has a hidden condition: the two barrels must reach the same height, so that their crowns meet. With semicircular barrels, that means they must have the same span: the bay must be square. This single geometric fact shaped Romanesque planning. It is why Speyer vaults its nave in square double bays, why each nave bay there corresponds to two square aisle bays, and why the piers alternate strong and weak (The crossing square as module).

Builders increasingly wanted oblong bays, narrower along the nave than across it, to give the nave a quicker and more even rhythm of supports. In such a bay the narrow barrel, if it is a semicircle, rises too low. The builder must stilt it, flatten it into an ellipse, or accept groins that wander in and out of plane and are nearly impossible to set out true. The model shows the flattened compromise.

℟The problem of the oblong bay

Two semicircular barrels of different spans rise to different heights. To groin-vault an oblong bay the narrower barrel must be stilted or flattened, and the groins then wander out of plane: the difficulty that pushed builders towards ribs and pointed arches.

The rib vault

The solution came from changing the order of construction. Instead of building the vault as a continuous shell on full centring, the builder first erects the arches that bound and divide each bay: the transverse arches across the vessel, the wall ribs along the sides, and the two diagonal ribs that cross at the centre, where a carved boss locks them. These ribs are narrow arches that need only light centring. Once they are up, the triangular cells between them are filled with thin webs of stone, laid course by course from rib to rib with little or no further support.

The first high rib vaults in Europe were built at Durham Cathedral from the 1090s. By the 1140s the masons of Saint-Denis had found how to vault even the awkward trapezoidal bays of an ambulatory with ribs. The advantages were practical and visual together. The ribs fixed the lines of the groins exactly; the webs could be made thin and light, reducing the thrust; the loads came down at points, on shafts that could be carried visibly to the floor; and, with the pointed arch, the builder was no longer bound to the square.

℟Ribs first, webs after

Build the arches of the vault first (transverse, wall and diagonal ribs) on light centring, then fill the triangular cells between them with thin webs of stone laid course by course from rib to rib.

For the vault over an oblong bay has arches of three different spans: the long diagonals, the transverse arches nearly as wide, and the short wall ribs. Draw the diagonals as semicircles and they set the height of the central boss. Then strike the transverse arches as slightly pointed arches, and the wall ribs as steep lancets, so that their crowns rise to nearly the same level (Pointed arches reach any height on any span). The whole bay closes cleanly, and the wall rib frames a tall clerestory window beneath it. This is the quadripartite vault of Chartres, Reims and Amiens, the standard vault of the High Gothic cathedral.

℟Level crowns over an oblong bay

Over an oblong bay, make the diagonal ribs semicircular and strike the transverse and wall arches as pointed arches of the heights needed to bring every crown nearly level with the central boss.

diagonal: r = ½ diagonal · transverse & wall: pointed, rise ≈ half-diagonal

Before the quadripartite vault on oblong bays became standard, Early Gothic builders kept the square double bay and added a rib to it. The sexpartite vault of Sens, Laon and Notre-Dame de Paris spans two bays of the arcade with one square vault divided into six cells by its diagonals and an intermediate transverse rib. The main piers carry three ribs, the intermediate piers one, and so the Romanesque alternation of strong and weak supports survived into Gothic.

In Anjou builders went another way. The domical vaults of Angers Cathedral, from the middle of the twelfth century, raise the crown of each bay well above its boundary arches, so that each bay is a shallow dome on ribs, a descendant of the domed churches of Aquitaine, whose steeper thrust suited the wide aisleless naves of the region.

Tiercerons, liernes and fans

Once ribs existed, masons multiplied them. In England, from the nave of Lincoln Cathedral in the 1230s–40s, builders added tiercerons (ribs that rise from the same springer as the diagonals but run to points on a ridge rib along the crown), so that each support sends up a sheaf of ribs like a palm. At Exeter the sheaves are so dense that the nave vault reads as one continuous avenue.

The fourteenth century added liernes, short ribs that spring from neither the springers nor the central boss but connect one rib to another. Their role is almost purely geometric and decorative: they turn the vault into stars and nets, as over the choir of Gloucester or the Lady Chapel at Ely, and in Central Europe into the net and looping vaults of Peter Parler’s Prague and the late Gothic of Saxony. Seen from below, the webs almost disappear behind the pattern.

All the ribs in these English vaults can be given the same curvature, a simplification that let one template serve for many stones. Carry the idea to its end and every rib from a springer becomes identical, spaced evenly around a vertical axis: the ribs then lie on a surface of revolution, an inverted half-cone, or conoid. That is the fan vault, England’s last and most original vault. It appeared in the cloister of Gloucester in the 1350s and culminated in the vaults of King’s College Chapel, Cambridge, and Henry VII’s Chapel at Westminster in the early sixteenth century. Where the conoids stop, the centre of the bay is filled with flat panels; the ribs are no longer separate arches but tracery carved onto the surface of the blocks.

℟The fan vault: identical cones of tracery

Make each springer the foot of an inverted half-cone (a conoid) whose ribs all have the same curve and are cut across by horizontal rings; where the conoids stop, fill the centre with flat panels.

Vaults compared

Each of these forms was an answer to the thrust. The barrel spreads it; the groin gathers it; the rib vault gathers it more precisely and makes it lighter; and once it is gathered onto a few points, those points can be propped from outside. That is where the next development, and the Gothic cathedral, begins: with the flying buttress, which carries the thrust of the vault across the aisle roofs through the open air (The flying buttress). It is the subject of the chapter on Romanesque and Gothic.