Rules · Geometry · Use · Modules
Find a granary’s capacity from its measures: multiply length, breadth and height in cubits (or, for a round bin, the square of eight-ninths of the diameter by the height), and add half as much again to turn cubic cubits into the grain measure, the khar.
1 cubic cubit = 1½ khar
The great houses of Kahun each had a block of granary rooms, and the scribes who ran them were trained on problems like these. Problem 44 of the Rhind papyrus, copied from a text of the same dynasty as Kahun, takes a square granary ten cubits on each side and ten high and finds 1000 cubic cubits, or 1500 khar; Problem 41 does the same for a round bin nine cubits across. The grain in store was the wealth of the household and the pay of its dependants.
Specify the slope of a pyramid face by its seked: the number of palms (and fingers) by which the face runs inward for every cubit of rise. The height follows from half the base divided by the seked, times seven.
seked = 7 × (½ base ⁄ height) palms · angle = arctan(7 ⁄ seked)
The Great Pyramid of Khufu was laid out 440 royal cubits square and 280 cubits high, a seked of exactly 5½ palms and a slope of about 51°50′.
½ × 440 ÷ 280 × 7 = 5½ palms → arctan(7 ⁄ 5.5) ≈ 51.84°
Lay out Egyptian buildings in royal cubits (≈ 52.4 cm) of seven palms of four fingers, so that every dimension and every slope can be stated in whole or simple fractional units.
1 royal cubit = 7 palms = 28 fingers ≈ 0.524 m
When a steep pyramid shows signs of distress, flatten the slope of the upper part: Sneferu’s pyramid at Dahshur rises at about 54° for its lower part and about 43° above.
lower seked 5 palms (≈ 54.5°) → upper ≈ 7½ palms (≈ 43°)
Arrange the temple on a single axis (pylon, open court, hypostyle hall, sanctuary) so that at each threshold the floor rises, the roof descends and the light diminishes, until the god’s shrine is reached in darkness.
Build the town for a royal pyramid in one campaign, as a walled rectangle on a grid of straight streets; wall off the quarter of the labourers’ small houses from the quarter of the officials’ mansions, and give each rank a standard house.
Cite this page Chris Paton, “Size the granary by reckoning”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/rhind-granary. Text, drawings and models licensed under CC BY-NC 4.0.