Vault Design Choice
The ribbed cross vault was the established structural technique for building vaults at the height of the Middle Ages.
The archetypical ribbed cross vault has a square or a rectangular base. The complication at Castel del Monte is the trapezoidal shape of the room space.
The ribbed cross vault construction technique is modular enough to be adapted to a trapezoidal base. Indeed, the ambulatory spaces in the cathedrals of central and northern Europe of the times had a trapezoidal base. The cross vaults have a corresponding trapezoidal form with cross vault ribs that reach to the corners of the trapezoidal space, folio 116:01.
The architect of Castel del Monte chose instead a perfect square for the ribbed cross vault, which he fitted in the center of the trapezoid, with two sides of the square lined respectively along the major and minor bases of the trapezoid. The remaining triangular areas, on the sides of the square to complete the trapezoidal ceiling space, are covered by barrel vaults truncated diagonally to fit the triangular space, folio 116:02.
The resulting room vault is outlined in folio 116:03 for the ground floor and folio 116:04 for the upper floor.
Designing a square cross vault involves resolving the lateral thrusts that they generate.
Resolving lateral thrusts may seem just another ordinary step in the geometric design process of Castel del Monte. In reality there is much more to it. This is most likely the kernel that gave rise to the idea of this unique building.
This key structural concept of Castel del Monte is that the lateral thrust of eight square cross vaults disposed in a circle, each within a wing of the octagon, converge at the eight corners of the base octagon. The lateral thrusts flow along the minor diagonals of the base octagon.
The question of lateral thrusts is addressed next, a necessary step to explain the determination of the room width.
The section “Ribbed Cross Vault Construction Technology” provides a brief history and a concise study on the historical provenance of cross-vaults.