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Design Hypothesis
The volta ab dotsa claus which we have studied is characterized by its axial symmetry (Fig 6): the diagonal ribs disappear and there is no central keystone, at the top of the vault there is a net of four keystones, from which the grid of ribs starts. We start the vault plan design by drawing a square defined by the four central keystones, equidistant from the centre (Fig 7), later on we draw the diagonals and the bonds which join them together. In order to determine the geometry which defines the position of the other keystones, we start to trace a line that, passing through two contiguous keys (key 3 and W), stretches out until cutting the edge of the square (T) and from this point, we trace another line that is perpendicular to the same edge. The intersection of this line with the diagonal of the square determines the position of the keystone of the diagonal (keystone 1). When drawing up a line from this keystone running parallel to the edge of the square up to the previously drawn up extension line of the central keystones, we will obtain the position of the keystone close to the bond (keystone 2). In order to complete the design of the net, it is now necessary to add the ribs which connect the two keystones just defined (keystones 1 and 2) with the middle points of the two sides of the square (keystones 5 and 6), which would become the top of the supporting arches. This way we obtain the design of a quarter of the vault which, due to its symmetry, is sufficient to determine the full plan design. As we have just seen, the distance of the four central keystones from the centre of the vault determines unambiguously the position of the other keystones; thus, when this parameter changes, the other keystones adopt another position defined geometrically by the tracing method. The design of the vault plan is subject to a geometric law which defines parametrically the position of each keystone, so any change of one of them means the change of position of the others (Fig 7).
As explained above, net vaults, unlike starred vaults, have no central keystone. They are built with a net of ribs that form a grid structure of a more or less complex geometry. This type of vaults reaches its highest expressiveness in Hall Churches, whose naves have all the same height since the design of the net connects all the sections to each other until extending to the whole temple. In Germany, this type of vaults was built with only one arch.
Nevertheless, however complex the net was, only one arch, and therefore just one voussoir, enabled them to build the whole vault. Succeeding in building the whole net with only one arch, the main arch, required certain geometric skills: it was necessary to know a typically Germanic method for vault design in order to determine the height of the keystones and to trace the curvatures of the arches. This method is known as Prinzipalbogen. Although it seems unlikely that J. Ribes would know this method, we have carried out the study of J. Ribes's vault using these geometric tools with the purpose of knowing in depth the consequences the singular design of this vault may have. The information obtained has allowed us to carry out the construction of a three meters high real model as part of the course, Workshop of Gothic Construction of the Escuela Superior de Arquitectura de Madrid.[....]
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