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
The winding stair
Where space is short, wind the stair round a newel or an open well; measure the going on the walking line, about halfway along the tread, where it should be as generous as on a straight flight.
A winding stair has tapering steps, narrow at the centre and wide at the wall. The comfortable going is found only along the line where people actually walk, a little outside the middle of the tread; nearer the newel the steps become too short to use. Palladio illustrates round and oval winding stairs, open in the middle so that light falls down the well, and the double spiral at the château of Chambord (begun 1519), whose two interlaced flights allow two people to pass without seeing each other.
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
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.
Proportion every step so that twice its height plus its depth equals the length of a natural pace on the level: two feet, or 24 pouces.
2 r + g = 24 pouces ≈ 65 cm (modern practice: 60–66 cm)
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.
Give the flight of steps before a temple an odd number, so that one who starts with the right foot will also set the right foot first on the top.
Cite this page Chris Paton, “The winding stair”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/double-spiral-stair. Text, drawings and models licensed under CC BY-NC 4.0.