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 · Plans · Domes · Geometry
The oval plan
To combine the unity of a central plan with the direction a church needs, plan the space as an oval, set across the axis to widen the view of the altar, or along it to lead the eye towards it.
Serlio had published an oval plan in 1547; Vignola covered Sant’Andrea in Via Flaminia (1550s) with an oval dome and designed Sant’Anna dei Palafrenieri (begun 1565) on a fully oval plan. The Baroque made the oval its signature. Bernini’s Sant’Andrea al Quirinale is a transverse oval: one enters on the short axis and faces the altar across it, so that the whole curving wall seems to open towards the visitor. Borromini’s San Carlo is a longitudinal oval generated from a geometry of triangles and circles, drawing the eye along the axis. In Germany and Austria in the eighteenth century, Balthasar Neumann combined several intersecting ovals into a single flowing interior at Vierzehnheiligen.
Related rules
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
Divide the inside of a dome into coffers that shrink in step with the meridians as they rise, so that their perspective deepens the dome and draws the eye to the light of the lantern.
Let the wall of a façade curve in plan (concave, convex, concave) so that the front answers the street, the light and the space within, and the order bends with it.
Light the climax of a Baroque interior (the altar or the dome) from windows the visitor cannot see, so that it seems to glow of itself.
Make the stair of a palace a processional space: one broad flight rising to a landing, then turning back in two flights either side to arrive at the principal floor beneath a single great vault.
Cite this page Chris Paton, “The oval plan”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/oval-plan. Text, drawings and models licensed under CC BY-NC 4.0.