Rules · Domes · Light · Structure
Pierce the base of the dome with a close ring of windows between buttressing ribs, so that the shell seems to float on light rather than to rest on the arches.
Hagia Sophia: 40 windows and 40 ribs; dome ≈ 31 m across, crown 55.6 m above the floor
Justinian’s historian Procopius wrote that the dome seemed not to be founded on masonry but to hang from heaven on a golden chain. This is the effect of the forty windows, whose light dissolves the line where dome meets support. Structurally the ring is a row of short piers, each continuing one of the forty ribs of the dome down to the cornice, and each backed outside by a small buttress.
The windows occupy exactly the zone of the dome where hoop tension would otherwise crack it: the ribs are, in effect, the arches into which a dome naturally divides, and the buttresses restrain their feet.
To set a round dome on a square bay, imagine a sphere passing through the four corners of the square; cut it by the four vertical planes of the sides and by the horizontal plane of their crowns. The four spherical triangles left in the corners are the pendentives; the circle at their top carries the dome.
sphere radius R = S⁄√2; arches = sphere ∩ side planes (radius S⁄2); ring at h₀ + S⁄2 with radius S⁄2
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
If the sphere that forms the pendentives is simply continued above the ring, the bay is covered by a single shallow dome, the sail vault or pendentive dome, which springs directly from the four corners.
crown = h₀ + S⁄√2 (lower than a hemisphere on the ring, h₀ + S)
Lift the dome on a cylindrical or polygonal drum pierced with windows between the ring of the pendentives and the springing of the dome, to light the centre of the church and to make the dome visible from afar.
drum height ≈ ⅓–1 × its radius (Byzantine); much taller in Russian churches
To turn a domed square into a long church, open two of its great arches into semidomes of the same radius, and open the semidomes in turn into smaller exedrae, so that the space expands by stages from the central dome.
Hagia Sophia: central square 31 m; two semidomes of radius ≈ 15.5 m; four exedrae; interior ≈ 31 × 70 m
Where no semidome takes the thrust of the dome, on the north and south, carry it across the aisles to massive buttress piers that rise above the roofs, and fill the great arches with thin walls pierced by windows.
Cite this page Chris Paton, “A ring of windows at the foot of the dome”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/forty-windows. Text, drawings and models licensed under CC BY-NC 4.0.