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 · Plans · Modules · Proportion
The crossing square as module
Let the square of the crossing set the measure of the whole church: the nave and transept arms are multiples of it, each nave bay is a square of the same size, and each aisle bay a square one quarter its area.
nave bay = crossing square; aisle bay = ¼ of it; nave length = n squares
German historians call this the gebundenes System, the bound system. At Hildesheim the transepts and the crossing are three equal squares and the nave is three more; at Speyer, when the nave was vaulted, every nave bay became a square groin vault matched by two square aisle bays. The system grew naturally out of groin vaulting, which works best on squares.
Related rules
Order the church as a single path: a colonnaded atrium, a narthex, the long nave drawn toward the altar, and the apse framed by a triumphal arch at the end of the axis.
End the choir in a semicircle of piers; wrap an aisle (the ambulatory) around it, and open a ring of chapels off the ambulatory, each with its own altar and windows, so that the east end steps down in tiers of roofs and buttresses.
Lay out the church as an Early Christian basilica (a tall nave lit from above, lower aisles on either side, a sanctuary ending in an apse to the east) and cross it with a transept, so that the plan becomes a Latin cross with a tower over the crossing.
Multiply altars at the east end by opening apses off the transept arms and the choir, stepped back from the main apse in echelon, each with its own small semidome and roof.
Mark the west end with a massive, towered block containing an entrance hall below and a chapel or gallery above, rising higher than the nave: a church in front of the church.
Cite this page Chris Paton, “The crossing square as module”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/rom-square-schematism. Text, drawings and models licensed under CC BY-NC 4.0.