Rules · Arches · Structure · Columns
Where the available columns are too short for the height you want, stand a pier on each column and carry the roof on a second, upper tier of arches, bracing the piers with a lower tier of horseshoe arches.
height ≈ column + pier + upper arch; lower arch = brace
The builders of Córdoba reused Roman and Visigothic columns, many only about three metres tall. To raise the ceiling to a dignified height and let in light and air, they placed a rectangular pier on each capital, over a projecting impost block, and sprang semicircular arches from the tops of the piers to carry the walls on which the roof gutters ran. Between the piers, lower down, they threw horseshoe arches that act as struts, holding the tall slender supports in line. The idea may echo Roman aqueducts with their tiers of arches, such as the one at Mérida.
The result is one of the most memorable interiors in the world: rows of double arches, their voussoirs striped red and white, receding in every direction like a grove of palms.
Draw a pointed arch from two centres on the springing line. With the centres at the springings, the arch is equilateral; with centres beyond them, a lancet; with centres between them, a drop arch. Late Gothic added arches of four centres and the reversed curve of the ogee.
r = s (equilateral) · r > s (lancet) · s⁄2 < r < s (drop)
Classify arches by the geometry of the intrados: the number and position of the centres (one for round and segmental, two for pointed, three or four for basket and Tudor arches), or a single continuous curve (ellipse, parabola, catenary), and distinguish true arches, with voussoirs, from corbelled “arches” of oversailing courses.
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
Make the prayer hall of identical bays of columns and arcades, so that it can be enlarged by adding aisles or bays without changing its character.
hall = n aisles × m bays of one module
Carry the curve of the arch beyond the semicircle, so that the opening at the springing is narrower than its greatest width.
springing width = 2R cos β, where the arc continues β below the centre line
Alternate voussoirs of two colours (red brick and pale stone, or black and white stone) to make the structure of the arch legible as ornament.
Cite this page Chris Paton, “Arches on arches: height from short columns”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/superimposed-arches. Text, drawings and models licensed under CC BY-NC 4.0.