Rules · Structure · Site · Cities
Lay the channel of an aqueduct with a steady fall of not less than a quarter of an inch in every hundred feet, cover it with a vault against the sun, and carry it through hills in tunnels and across valleys on arches.
minimum fall ≈ 1 : 4,800 (Morgan’s reading); Nîmes aqueduct: ≈ 12.6 m in ≈ 50 km ≈ 1 : 4,000
Roman aqueducts ran by gravity alone, so the fall had to be enough to keep the water moving but not so steep that it scoured the channel. The whole Nîmes aqueduct, of which the Pont du Gard is the most famous part, descends only about 12.6 m over some 50 km. Surveyors set out such slopes with the chorobates, a long levelling table that Vitruvius describes in the preceding chapter.
The manuscripts’ figure for the minimum gradient is uncertain, and editors read it differently; the formula follows Morgan’s translation. Vitruvius also asks for access shafts in tunnels at regular intervals and a distribution tank at the city with separate outlets for public fountains, baths and private houses.
In a bonded masonry wall the courses above an opening corbel over it of their own accord, so the lintel carries roughly the triangle of wall with sides rising at 60° from its ends; everything above that triangle arches onto the jambs.
load ≈ equilateral triangle on the span: W ≈ 0.43 · L² · t · ρ g
Build an arch of wedge-shaped stones (voussoirs) whose joints all point towards the centre of the curve: each stone can then fall only by forcing its neighbours apart, and so the ring holds itself up once the last stone, the keystone, is in place.
joints ⟂ intrados (radial to the centre)
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)
Trace the path of the resultant force through the stones from crown to foundations. If a line can be found that stays everywhere within the masonry, the arch will stand; where it touches an edge, a hinge will open, and four hinges make it collapse.
An arch cannot support itself until it is complete. Build it on a timber centring shaped to the intrados, strike the centring only when the keystone is set and the mortar has taken, and reuse it from bay to bay, which is one reason to keep the spans of an arcade equal.
In a row of arches the thrusts of neighbouring arches cancel over each intermediate pier, which may therefore be slender; at the ends of the row nothing balances them, so the outermost piers must be made wider or buttressed.
Cite this page Chris Paton, “The fall of an aqueduct”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/aqueduct-gradient. Text, drawings and models licensed under CC BY-NC 4.0.