Raise the crown of each bay well above the tops of its boundary arches, so that the vault becomes a shallow dome on ribs whose thrust falls more steeply onto the walls.
crown ≈ half-diagonal above the springing; boundary arches ≈ half-span
In Anjou and Poitou (at Angers Cathedral in the mid-twelfth century and at Saint-Serge nearby) builders covered wide aisleless naves with domed rib vaults, heirs to the domes of Aquitaine. Seen from below the ribs radiate from a boss high above the arches; the later Angevin vaults add ridge ribs and many slender liernes.
A round arch must rise half its span, so arches of different spans on one springing line have crowns at different heights. A pointed arch can be given any rise at least half its span, so arches of different widths can all be made to reach the same height.
round: f = s⁄2 (fixed) · pointed: r = (s²⁄4 + f²) ⁄ s for any f ≥ s⁄2
An arch cannot support itself until it is complete. Build it on a timber centring shaped to the intrados, strike the centring only when the keystone is set and the mortar has taken, and reuse it from bay to bay, which is one reason to keep the spans of an arcade equal.
Throw an arch diagonally across each upper corner of the square, backed by a small conch or cone; the four squinches and the four walls between them make an octagon, on which a round dome can sit.
octagon side = S (√2 − 1) ≈ 0.414 S; squinch span = octagon side
Carry the outward thrust of a high vault across the aisle roof by a half-arch of stone (the flyer) that leans against the clerestory wall at the level of the vault’s haunches and springs from a massive buttress pier outside the aisle, which takes the thrust down to the ground.
Draw the curve of a pointed dome with arcs whose radius is four-fifths of the span, their centres standing on the springing line one-fifth of the span in from the opposite side.
r = ⅘ S; centre at ⅕ S from the far springing; rise ≈ 0.74 S
Strengthen a barrel-vaulted nave with transverse arches at every bay, springing from shafts on the piers; they stiffen the vault, mark the bays and serve as ribs on which the vault can be built bay by bay.
Cite this page Chris Paton, “The Angevin vault: a dome with ribs”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/domical-vault. Text, drawings and models licensed under CC BY-NC 4.0.