Add to the diagonal ribs further ribs (tiercerons) that rise from the same springers to points on the ridge rib, so that each springer sends up a sheaf of ribs and the vault reads as a palm.
England took rib vaulting in its own direction. At Lincoln the nave vault adds tiercerons and a continuous longitudinal ridge rib; at Exeter as many as eleven ribs spring from each support, running the length of the church like an avenue of palms. Structurally the extra ribs stiffen the webs and let them be built in shorter spans; visually they dissolve the bay divisions.
In the model all the ribs lie on conoids (surfaces of revolution about each springer), so every rib of the sheaf has the same curvature, a simplification that let masons cut many ribs from one template.
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.
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.
Load the top of a buttress pier with a heavy pinnacle: the added weight steepens the resultant of the flyer’s thrust and the pier’s own weight, keeping it well inside the base of the pier.
Draw a square the width of the pinnacle; inscribe a second square on the mid-points of its sides, and a third on the mid-points of the second. Turned back into line, the squares give the widths of the body, its panels and the spire; every height is a multiple of the first side.
widths: s, s⁄√2, s⁄2, s⁄(2√2) … · heights: n × s
Instead of cutting separate openings through a plate of wall, fill the whole window arch with glass and divide it by slender stone bars (mullions below, and circles, foils and sub-arches above) set out with compasses from the centres of the window’s own arches.
Cite this page Chris Paton, “Tiercerons: more ribs from each springer”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/tierceron-vault. Text, drawings and models licensed under CC BY-NC 4.0.