Take the section of the standard timber, the cai, as the module of the building: it is 15 fen high and 10 fen wide, and every member is dimensioned in fen.
1 cai = 15 fen (height) × 10 fen (width)
Rules · Roofs · Proportion
Eaves in proportion to the rafters
Project the eaves from the centre of the eave purlin by 3½ chi for rafters of 3 cun diameter and 4 to 4½ chi for rafters of 5 cun; beyond them add flying rafters projecting six-tenths as far again.
eave projection ≈ 3½–4½ chi · flying rafters = 0.6 × eave projection
With the reach of the bracket sets added, the eaves of a large Song hall overhang the column line by three to four metres. The flying rafters (feizi) are laid at a flatter slope than the rafters beneath them, which is one source of the upward kick at the edge of the roof. The platform stops short of the drip line, so rain falls clear of the stone.
Related rules
There are eight grades of cai, from 9 × 6 cun down to 4½ × 3 cun; use the first for great halls of nine or eleven bays and the smallest for pavilions and ceiling coffers.
grades 1–8: 9×6, 8¼×5½, 7½×5, 7.2×4.8, 6.6×4.4, 6×4, 5¼×3½, 4½×3 cun
For a great hall, measure the distance between the front and back eave purlins and raise the ridge purlin above them by one third of it; for lesser halls, by about a quarter.
rise = ⅓ × depth between eave purlins (halls); ≈ ¼ (+ a small addition) for ting-tang halls
Draw a straight line from the ridge purlin to the eave purlin and lower the first purlin below the ridge from it by one tenth of the rise; from that point draw a new line to the eave purlin and lower the next purlin by one twentieth; continue, halving each time.
drop₁ = H⁄10 · drop₂ = H⁄20 · drop₃ = H⁄40 · …
Give each rafter span a fixed slope, increasing from the eaves to the ridge: half-pitch (5 jǔ) for the eave span, then about 6½ or 7, 7½, and 9 tenths for the span below the ridge.
rise of span k = run × (0.5, 0.65, 0.75, 0.9) for four spans
From the intermediate bracket set of the second bay the rafter ends advance progressively outward, so that at the corner the eave projects further (by 4 cun for a hall of one bay, 5 for three bays, 7 for five bays) and rises with the corner beam.
Cite this page Chris Paton, “Eaves in proportion to the rafters”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/yingzao-eaves. Text, drawings and models licensed under CC BY-NC 4.0.