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 · Geometry
Raise the ridge by a third of the depth
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
This is the jǔ, the raising. The rise is fixed as a simple fraction of the depth of the building: steeper for the highest-ranking halls (dian), lower for halls of the ting-tang class, whose rise is a quarter of the depth increased by a few hundredths depending on the tiles. A Song hall therefore has a roof pitch of roughly 34° measured on the straight line from eave to ridge, but the finished roof is not straight at all: the zhé that follows bends it.
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
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.
Give the hipped roof (wudian) to the highest halls, the hip-and-gable (xieshan) to the next, and the gabled roofs, overhanging (xuanshan) and flush (yingshan), to lesser buildings and houses; double the eaves for the very highest.
double wudian > double xieshan > wudian > xieshan > xuanshan > yingshan
Cite this page Chris Paton, “Raise the ridge by a third of the depth”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/juzhe-rise. Text, drawings and models licensed under CC BY-NC 4.0.