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
Rules · Doors & windows · Geometry · Ornament · Light
The rose: a window turned about its centre
Design a rose by dividing the circle into equal sectors; fill each with the same traceried unit (a light with a cusped pointed head, an oculus above) radiating from a central hub, so that the whole is generated from one sector by rotation.
n petals · each sector 360° ⁄ n
Romanesque wheel windows were ringed with small round arches on colonnettes like the spokes of a wheel. Gothic roses grew with the rest of the window: the west rose of Chartres (c. 1215) is still a plate of stone pierced with circles; the transept roses of Notre-Dame de Paris (c. 1250–60) are almost all glass, their tracery a web of radiating bars. Villard drew both the Chartres and the Lausanne roses, not quite accurately, which suggests that he was more interested in the scheme than in the particulars.
Related rules
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.
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
Over a doorway or window spanned by a lintel, turn an arch in the wall above so that the weight of the masonry is carried round the opening onto the jambs, leaving the lintel to carry only the small triangle of wall beneath the arch.
Cite this page Chris Paton, “The rose: a window turned about its centre”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/rose-window-geometry. Text, drawings and models licensed under CC BY-NC 4.0.