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.
Hidden buttressing arches under aisle roofs had been used for a long time; the flyer that rises into the open air, designed as part of the building rather than added to save it, is usually dated to the nave of Notre-Dame de Paris around 1180. By 1200 flyers were being built in two or three tiers, the upper resisting the vault, the lower perhaps the wind on the high roof.
A flyer works only in compression; its top is often a channel carrying rainwater from the high roof out to a gargoyle on the buttress. Its curve is a compromise between the straight strut that would carry the thrust most directly and the arch that keeps it from sagging under its own weight.
Build an arch of wedge-shaped stones (voussoirs) whose joints all point towards the centre of the curve: each stone can then fall only by forcing its neighbours apart, and so the ring holds itself up once the last stone, the keystone, is in place.
joints ⟂ intrados (radial to the centre)
An arch pushes outward on its supports as well as down. For the same load and span the horizontal push grows as the rise falls: halve the rise and you roughly double the thrust.
H ≈ w·s² ⁄ 8f (uniform load w per metre, span s, rise f)
A chain hanging freely takes the one shape in which it is in pure tension; turn that shape upside down and it is the shape of an arch in pure compression for the same loads.
free-hanging chain (catenary) ↔ ideal arch under its own weight
Trace the path of the resultant force through the stones from crown to foundations. If a line can be found that stays everywhere within the masonry, the arch will stand; where it touches an edge, a hinge will open, and four hinges make it collapse.
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
To find how thick the pier of an arch must be, divide the intrados into three equal parts; draw a line from the springing through the first division, and produce it beyond the springing by its own length. A vertical through the end of that line marks the outer face of the pier.
pier ≈ ¼ span (semicircle) · ≈ 0.23 span (equilateral) · less for a lancet
Cite this page Chris Paton, “The flying buttress”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/flying-buttress-thrust. Text, drawings and models licensed under CC BY-NC 4.0.