Rules · Cities · Light · Geometry
Run housing slabs in parallel rows, north to south so that the flats have morning and evening sun, and space them by a fixed angle of light: then the taller the rows, the more dwellings the same ground holds, or the more ground is left free for the same number.
gap = H ÷ tan α (α the chosen angle of light, e.g. 30°: gap ≈ 1.7 H)
Gropius’s diagrams took a site of fixed size and a fixed angle of light and compared rows of two, three, five and ten storeys. With the angle held constant, the gap grows in proportion to the height, but the number of storeys grows faster than the land they take, so high slabs win: they give more flats, or more park. The low rows of Gropius’s Dammerstock estate at Karlsruhe (1928–29) and the ten-storey slabs he advocated sit side by side in this town to make the comparison.
A saddle surface in which two opposite corners are raised and two lowered is a hyperbolic paraboloid; it contains two families of straight lines, so it can be formed with straight boards and yet has double curvature.
y = k·x·z (or any bilinear patch through four points not in one plane)
Raise the main storey on slender columns so that the ground beneath flows under the building (for circulation, cars, gardens or public space) and the rooms are lifted into light, air and view.
Run the windows in a continuous horizontal band from one end of the façade to the other, lighting the room evenly across its whole depth.
Check the proportions of a façade with a few geometric lines (diagonals of similar rectangles, the golden section) so that its parts share one order and nothing is arbitrary.
Size everything from a single scale: a red series in which each measure is φ times the one before, anchored on a man 183 cm tall, and a blue series of its doubles, anchored on his raised hand at 226 cm.
red: … 27, 43, 70, 113, 183, 296 … (×1.618) · blue: … 53, 86, 140, 226, 366 … (= 2 × red)
House a whole community in one tall slab: stack duplex flats that run through the block with light on both sides, put shops and services on an interior street half-way up, and give the roof to everyone.
Cite this page Chris Paton, “Rows spaced by the angle of light”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/zeilenbau-spacing. Text, drawings and models licensed under CC BY-NC 4.0.