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)
A full timber is a cai and a zhi: 21 fen
Between two stacked arms leave a spacer of 6 fen, the zhi; a cai plus a zhi, 21 fen, is a “full timber” (zucai) and the vertical step of each tier of a bracket set.
zucai = 15 + 6 = 21 fen
Each arm rests in the slot of the small block below it, whose visible part rises 6 fen above the arm beneath; so each tier of the set climbs one cai and one zhi. Members that are a full timber in height, such as some beam-ends and the column-head beams, are said to be zucai; those of a single cai are dancai. The two numbers, 15 and 21, give the vertical rhythm of the whole bracket zone.
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
Build the bracket set (puzuo) of blocks (dou) and arms (gong) crossing at right angles, each tier projecting no more than 30 fen beyond the one below; a set of n projecting tiers is called an (n + 3)-puzuo, from four to eight.
projection per tier ≤ 30 fen · rise per tier = 21 fen · puzuo = tiers + 3
Where the eaves must project far, replace the outer arms by slanting levers (ang) that run down and out beyond the bracket set and rise inward to be held down under an interior purlin.
Set the heads of the outer columns inward: on the front and back by 1 fen for every chi of height (1/100), on the ends by 8 li per chi (8/1000); the corner columns lean both ways.
lean = 1/100 of height (front) · 8/1000 (flanks)
Run a single great pillar up the centre of the pagoda to carry the spire, but do not let the storeys rest on it: each storey stands on its own frame, stacked around the pillar.
Cite this page Chris Paton, “A full timber is a cai and a zhi: 21 fen”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/zucai-zhi. Text, drawings and models licensed under CC BY-NC 4.0.