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
The horseshoe arch existed before Islam, in Visigothic Spain and in Syria, but it was the Umayyads of al-Andalus and their successors in North Africa who made it a signature. Structurally the extra curve below the centre does little; it is carried by the jambs as corbelling. Visually it makes the arch seem to swell, to enclose the space beneath it rather than merely span it.
In Córdoban work the extrados is often drawn from a slightly higher centre than the intrados, so the voussoirs grow deeper towards the crown, and the arch is framed by a rectangular moulding, the alfiz. Later Maghrebi builders produced a pointed horseshoe, in which two arcs meet at the crown.
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
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
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.
Frame an important arch with a rectangular moulding or band rising from its springing, so that the curved opening is set within a square field.
Cite this page Chris Paton, “The horseshoe arch”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/horseshoe-arch. Text, drawings and models licensed under CC BY-NC 4.0.