The Tower Locus
The next step in the design is to draw the towers. This is at variance from other scholars, like H. Götze, who theorize a design sequence that starts at the courtyard and moves progressively to the perimeter, ending at the towers.
The actual design progression is from the perimetric forms, the towers, and moving inward toward the center; the courtyard is the last element to be defined. This progression is logical because, as shown later, the architect saw the towers as abutments to the cross vaults lateral trusts. Abutments like foundations are initial considerations in the design of a building.
A prominent feature at the castle is the Gothic cross vault, repeated in each of the castle 16 majestic rooms, eight on each floor. A design concern for cross vaults is the lateral thrusts, specifically how to “terminate” them with proper abutments. In the geometric design of Castel del Monte these lateral forces flow along the minor diagonals of the base octagon and terminate at the corners of the base octagon where the towers are located. An initial step is therefore to define the abutments, which were imagined as octagonal masonry masses in the creative process of the architect.
The quest is to find a way to geometrically locate the towers in the plant octagon and geometrically define their dimension. The solution is remarkably simple, it is provided by the square two natural circles: the inscribed and the circumscribed circles.
The base square, folio 106:01, has an inscribed circle, folio 106:02, and a circumscribed circle, folio 106:03. The intersection of the inscribed circle with the base octagon major diagonals define another natural octagon inscribed in the base square, folio 106:04.
The space between the circumscribed and inscribed circles is a circular ring, folio 106:05. A similar octagonal ring is formed between the base octagon and the octagon inscribed in the base square, folio 106:06. These two rings overlap each other; they serve interchangeably to locate the towers.
The rings define the field zone for the tower.
The radius of the geometrically defined inscribed circle is l, half of the base square side, folio 106:07.
The radius of the geometrically defined circumscribed circle is r, half of the base square diagonal, folio 106:07.
The width of the circular ring is t, the difference between r and l, folio 106:07.