Façade Wall Issues
The tower enlargement raises an issue with the façade wall thickness and its geometric definition.
The wall thickness is the same for the façade and tower walls in the concept design. The objective with the tower enlargement is to find a way to increase the tower size while keeping the overall forms and dimensions relatively unchanged from the concept design. The measures for the façade wall thickness, the tower wall thickness, and the room width had to remain exactly as defined in the concept design.
There were no geometric issues in drawing the indoor face of the tower wall given the premise that the wall had to have the width defined in the concept design, a. It is a simple matter of drawing an octagon concentric and inside to the tower octagon, separated by the distance a.
There is however a problem with the façade wall. The indoor face of the façade wall is anchored to the innermost footing corner, AA, in the concept design. The position of this corner has not changed with the tower enlargement, although it is relabeled AA' in the modified design. Accordingly, the position of the indoor face of the façade wall has not changed with the tower enlargement.
The outdoor face of the façade wall is set at the distance a from the indoor face, but this face does not intersect the tower at a corner, but somewhere on a side of the tower, because corners B' and H' have moved away from the positions of corners B and H, which are the anchor points for the outdoor face of the façade wall in the concept design, folio 112:01.
This leaves a small gap, an open air corner between the new tower corners B' and H' and the façade wall, folio 112:02.
Such a gap is at variance with the architect’s architectural thinking of clean geometric forms; it would be an eyesore in the edifice were built in this manner.
A solution is to fill in the corner triangle with masonry, thus defining a new corner M, folio 112:02.
This is indeed the solution that the architect adopted in the final design. However, it is premature to pursue this modification before resolving another related issue, the cross vault intersection and the associated room width. The base octagon minor diagonal lines do not cross from the façade wall to the tower at the new critical corner M, and embrace a smaller portion of the tower masonry, folio 112:02.
Moving the new plant minor diagonals to cross at the new corner M might be the next logical modification, folio 112:03.
Minor diagonals that cross at corners M are geometrically anchored at suitable points Z along the plant major diagonals a short measure z inside from the new tower octagon outermost corner E', folio 112:03.
This, however, does not solve the cross vault location, which is to remain unchanged with respect to the indoor face of the façade wall as established in the concept design, folio 112:03.
It is a puzzling quest.
If the minor diagonals cross at the critical corners M, their intersection that define the cross vault location and room size changes from the layout defined in the concept design.
On the other hand, if the minor diagonal are chosen so that their intersection restores the cross vault location and room size defined in the concept design, then the crossing point from façade wall to tower moves inside, away from the critical crossing point M, involving a seemingly smaller portion of the tower masonry for abutting the lateral thrusts.
It is a conflicting situation that led the medieval architect to search for a different answer. The solution is addressed later, in the final design phase, after untangling and resolving the façade wall width first. The façade wall resolution is thus detached from the problem of the minor diagonals and is addressed in a heuristic approach.