An arch pushes outward on its supports as well as down. For the same load and span the horizontal push grows as the rise falls: halve the rise and you roughly double the thrust.
H ≈ w·s² ⁄ 8f (uniform load w per metre, span s, rise f)
Rules · Façades · Proportion · Light
Arcade, triforium, clerestory
Divide the elevation of the nave into three storeys: a tall arcade opening into the aisles, a low triforium passage in the thickness of the wall against the aisle roof, and a clerestory of large windows reaching up into the vault.
Chartres: arcade ≈ clerestory, triforium a narrow band between
Early Gothic churches such as Laon and Noyon have four storeys: arcade, a vaulted gallery over the aisles, a triforium and a clerestory. At Chartres the gallery was dropped, since flying buttresses now did its structural work, and the clerestory was enlarged to equal the arcade. The three-storey elevation became standard; in the Rayonnant phase the triforium itself was glazed, as at Saint-Denis after 1231, so that the whole upper wall became light.
Related rules
To find how thick the pier of an arch must be, divide the intrados into three equal parts; draw a line from the springing through the first division, and produce it beyond the springing by its own length. A vertical through the end of that line marks the outer face of the pier.
pier ≈ ¼ span (semicircle) · ≈ 0.23 span (equilateral) · less for a lancet
Raise the central nave above the lean-to roofs of the aisles and pierce the upper walls with a row of windows, the clerestory, so that the middle of a wide hall is lit from high on both sides.
nave height ≈ 1½–2 × nave width; one window over each bay of the arcade
Gather the weight and thrust of the vaults onto a few points by ribs, carry them down piers and out across the aisles by flying buttresses to external buttress piers, and the wall between the supports carries almost nothing, so it can be opened into windows.
Draw a square the width of the pinnacle; inscribe a second square on the mid-points of its sides, and a third on the mid-points of the second. Turned back into line, the squares give the widths of the body, its panels and the spire; every height is a multiple of the first side.
widths: s, s⁄√2, s⁄2, s⁄(2√2) … · heights: n × s
To make a square of half the area of another, join the mid-points of its sides: the rotated square so drawn has exactly half the area. Repeat to halve again.
side of inscribed square = s ⁄ √2 · area = ½ s²
Cite this page Chris Paton, “Arcade, triforium, clerestory”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/gothic-three-storey. Text, drawings and models licensed under CC BY-NC 4.0.