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
Rules · Modules · Proportion · Structure
Everything is measured in cai and fen
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)
Li Jie opens his chapter on greater carpentry with the principle that all building takes the cai as its ancestor. The cai is the section of the bracket arms, and because the arms, the beams and the column-head ties are all multiples or fractions of it, the whole frame is commensurable: the length of an arm (62 or 72 fen), the height of a beam (two or three cai), the projection of a tier of brackets (up to 30 fen) and the diameter of a column (about 42 fen in a large hall) all follow.
The ratio 3 : 2 is not arbitrary. A rectangular beam cut from a round log is strongest in bending when its depth and breadth are close to that proportion, a rule European engineers derived only in the seventeenth and eighteenth centuries. The fen system is the Chinese counterpart of the classical module (The Doric module): the whole building is measured in fen, so a larger or smaller fen rescales all of it.
Related rules
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
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.
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
Make the central bay (mingjian) the widest and let the bays diminish toward the ends; keep the eave columns no taller than the width of their bay.
Cite this page Chris Paton, “Everything is measured in cai and fen”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/cai-fen-module. Text, drawings and models licensed under CC BY-NC 4.0.