Drawing the Enlarged Tower Octagon
An octagon for the enlarged tower can be drawn in a number of ways once its overall dimension is known. An example is the concept design where the base octagon was defined from a square.
The approach taken here uses the circle circumscribing the octagon, taking advantage of some of the peculiarities in the current geometry, such as the fact that we have the size of the new tower octagon side s', folio 107:03.
The design considerations that led to this asymmetric enlargement of the tower octagon also define the first two corners of the enlarged tower octagon. These are the concept design tower corner A that now becomes corner A' and the concept design footing octagon corner EE that now becomes corner E' of the enlarged tower, folio 108:01.
The same reference nomenclature for the tower and footing corners is used in the modified design, but using the prime (') designation for differentiation.
The circumscribing circle for the enlarged tower is centered at the point O' defined in the previous page and has a radius t'/2 that passes trough corners A' and E', folio 108:02.
The circle intersects the plant minor diagonals anchored at the concept design footing corner EE, corner E' of the new tower octagon. These intersections are corners B' and H' of the enlarged tower octagon, folio 108:03.
The lines that join corner A' to B' and corner A' to H' are two side of the enlarged tower octagon, thus they provide the measure s' of the enlarged tower octagon side; folio 108:03.
The other corners of the enlarged tower octagon are at the radial distances s' from other corners already-defined along the circumscribing circle, folio 108:04.
Using a circle of radius s' and centered on corner E' leads to the definition of corners D' and F', folio 108:05.
The remaining two corners, C' and G', are defined by similar circles of radius s' centered either on corners B' and H', or on corners D' and F', folio 108:06.
All eight corners are thus defined geometrically in place for the enlarged tower octagon, folio 108:07.
The enlarged tower octagon is drawn with straight line segments joining the corners sequentially, folio 108:08.
The circumscribing circle is not needed anymore, folio 108:09.
The area covered by the enlarged tower octagon is larger than the area of the tower octagon in the concept design, folio 108:10.