Appendix 2
Finding the Centerline
Before the reference planes and the center quarter of the arch can be defined, the arch’s centerline must be found (see "The Elevation Drawing", in Appendix 1). This is complicated because both the inside and outside boundary of the arch are irregular curves and these are not concentric.
To locate the centerline, pairs of lines are drawn between the upper and lower perimeter of the arch at a number of arbitrarily-selected locations. One line of each pair (for example, line a-b in Figure 19) is perpendicular to the lower boundary. The second line (c-d) is perpendicular to the upper boundary. The lines are located to meet somewhere near the middle of the arch. The exact location of the intersection is not critical, the angles not the location are the important factor.
A third line (e-f) is added, bisecting the angle formed by the first two and extending the full distance across the arch. A curve plotted through the center points of these bisecting lines is a good approximation of the centerline of the arch.
Due to the irregular profile of the arch, the intersections of the first two lines may not fall on the arch’s centerline. The center points of bisector lines e-f are determined by measuring the line and may not coincide with the intersections.