Computer assisted research
A computer program was written which could exactly calculate X and Y coordinates on the iso-line, together with the Z (vertical) coordinate. The baseline, the longitudinal arch and the transverse arches were all described as parts of a circular arc. It was easy to adapt the program for different baseline layouts and the longitudinal arch shape in order to obtain a quick solution to the various properties of the shell, as made clear by the isolines. Then the baseline and the longitudinal arc in the centerline were manipulated, still as parts of a circular arc, in order to increase the size of the fan sector, and to accomodate the dual element property covering half the shell. In my initial experiments I constructed the baseline using six different arc sizes, approximately following the outline near the deepest point in the scoop and close to the Sacconi arc-shaped baseline. To find the Sacconi base line I had to calculate a number of points which occur when the extended circular arc of a transverse cross section intersect the zero level. The solution to this problem with a fan shaped shell containing dual elements between "upper" and "lower" quadrants was much easier than expected. This concept of baseline consists of three identical circular arcs connected at angles of 60 degrees. The computer program then produced isolines as shown in the belly. If the "upper" and "lower" widths of the outline (model) are equal, which means that the baseline is parallel to the longitudinal axis, four equal quadrants arise. The "upper" quadrants become physically exact duplicates of the "lower" quadrants. The partially rotated baseline causes a difference in width but only a slight dissimilarity in the layout of the isolines. This difference, however, is surprisingly limited to a small local area, when the single isoline is checked against its own mirror-image in the proportionally rotated transverse axis. The dually identical elements in the "upper" and "lower" quadrants are still present.