An arch pushes outward on its supports as well as down. For the same load and span the horizontal push grows as the rise falls: halve the rise and you roughly double the thrust.
H ≈ w·s² ⁄ 8f (uniform load w per metre, span s, rise f)
Rules · Proportion · Plans
Linked rooms in a plan
Let the rooms of a house share dimensions, so that the length of one is the breadth of the next and each stands to its neighbours in the ratios of the scale; the whole plan then forms one proportional system.
e.g. rooms of 12 × 12, 12 × 18 and 18 × 30 feet, sharing 12 and 18
Palladio wrote the dimensions of the rooms onto the woodcut plans of his villas in Book II, and in 1949 Rudolf Wittkower showed that many of them form sequences in which dimensions are shared and ratios are musical. The analysis was enormously influential among post-war architects. Later scholars measured the buildings and found that as built they often differ from the book, and that Palladio adjusted his published figures to make the numbers neater: evidence of his ideal rather than of his practice. Both are worth knowing.
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 unify a façade of two or more storeys, run a single order of pilasters or columns through all of them, from the base to the main cornice.
Give the villa garden porticoes for sun and for shade, grottoes made in imitation of nature with tufa and shells, evergreens planted in straight rows at equal distances, and hedges of box; set vines on columns over the walks.
Lay the ideal garden out on a circular plan in concentric rings, woods outside, then meadows and orchards, then gardens of knots and clipped evergreens divided by walks, with water and the fountain of the goddess at the centre.
Take the plan, the orders and the details from the builders’ pattern books, simplified for timber and for the carpenter: a symmetrical front, a central hall and stair with rooms either side, a doorway under a pediment or fanlight, and mouldings drawn to be made with the plane.
Cite this page Chris Paton, “Linked rooms in a plan”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/harmonic-room-sequence. Text, drawings and models licensed under CC BY-NC 4.0.