Shape the underside of every arm’s end in four or five facets, and reduce the upper third of a spindle column by the same method, so that no member ends in a hard corner.
Let the eaves grow out at the corners
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.
The corner beam that carries the hip is larger and set higher than the common rafters, so the eave line necessarily rises as it approaches it; the Song manual adds a deliberate outward growth (shengchu) in plan. Together with the rising corner columns (Shengqi: raise the corner columns) they give the Chinese roof its upturned corners. Later, in the south of China, the lift was exaggerated into the dramatic flying eaves of Fujian and Guangdong; in the north and in Japan it stayed restrained.
Related rules
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
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
Make each column a little taller than the one nearer the centre, so that the corner columns stand highest: by 2 cun per column outward from the central bay, giving 6 cun at the corners of a seven-bay hall and 1 chi 2 cun for thirteen bays.
corner rise = (bays − 1) cun · each step outward = 2 cun
Cite this page Chris Paton, “Let the eaves grow out at the corners”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/eave-corner-lift. Text, drawings and models licensed under CC BY-NC 4.0.