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10 Five possible methods of resolving the misalignments in keystones
and springing points caused by the Prinzipalbogen. In all cases, the curvature
of all ribs is assumed to be based on a regular circular arc with a
radius equal to that of the principal arc. The radius of the principal arc is
defined by the longest rib path from a springing point to the vault apex
without backtracking (1-2-3). Elevations (above) are derived from the
plan (below). In elevation, A B
should be read as ‘point A, where its height
is derived from that of point B.’
The diagrams are based on those in: Palacios Gonzalo, José Carlos, and
Rafael Martín Talaverano, “Technological Development in Spanish Gothic
Vaults Design,” International Journal of Architectural Heritage 7, no. 2
(January 2013): 192.
Where the length of one rib path from a springing point
to the highest point in the vault is different to another, a
misalignment at rib intersections or at the springing point
results.
Figure 10 illustrates five ways of negotiating this design
problem. In this case, the radius of the principal arc is defined
by the longest rib path to the top of the vault (1-
2-3). Methods A1 to A3 involve finding the form of ribs
along paths other than that which defined the radius of
the principal arc by moving the centre of the arc defining
their curvature. In A1, an arc with the principal arc radius
which passes through points 1 and 3 defines the form of
the ribs along path 1-4-3, after which point 4 is located
along it. In A2, the same ribs are derived from the highest
keystone (3) downwards, where an arc with the principal
arc’s radius is thrown down from point 3 to point 4,
Byera Hadley Travelling Scholarships Journal Series