In Fig. 730 is shown the elevation and plan of an elliptical window head in a circular wall. The outer curve of head is represented by A B C in elevation and by A' B' C in plan. The inner curve is represented by F E D in elevation and F' E' D' in plan. A B C D E F therefore represents the splayed or beveled portion in elevation for which the pattern is required, and A' B' C D' E F' the plan of the same Divide A B of elevation into any convenient number of parts, in the present instance five. For convenience number the points thus obtained, as shown by the small figures. Drop perpendiculars from the points in A B, cutting A' B' of plan, as shown. Also divide F E of elevation into the same number of parts as was A B, and drop similar perpendiculars to F' E' of plan. Connect opposite points in A' B' with those in F' E'. as shown by the solid lines, as 2 11, 3 10, etc. Also divide the four-sided figures thus produced into triangles by means of the dotted lines, as shown from 1 to 11, 2 to 10, etc. To ascertain the true distances across the face of the arch which these several solid and dotted lines of the plan represent, it will be necessary to construct vertical sections through the arch upon each one of these lines as a base. The lines dropped from A B to A G of elevation give the hight of sections on A'B' of plan, as the lines dropped from F E to F G give the hight of sections on F' E' of plan.
Fig. 730. - Elevation and Plan of Splayed Elliptical Arch.
To construct the sections shown in Fig, 731, represented in plan by the solid lines, proceed as follows: Draw the right angle a a' 1, making n a' equal to E' B' of plan, and a' 1 equal to G B(a 1) of elevation. Draw a 12 parallel to a' 1, making its length equal to G E (a 12) of elevation, and connect 12 with 1. The distance 12 1 of this section represents the actual distance between the points 1 and 12 in the elevation or plan. The second section is constructed in a similar manner; b c represents the distance 2 11 of plan; b 11 is equal to b 1 1 of elevation and c 2 to c 2 of elevation. Connect 11 with 2 of section, which will give the actual distance between points 11 and 2 of elevation or plan. The remaining sections are constructed in a similar manner, each of the sections representing a vertical section through the head on the lines of corresponding numbers in the plan. The sections based upon the dotted lines of the plan, shown in Fig. 732, arc constructed in exactly the same manner. Draw b a. in length equal to 1 11 of plan, and erect the two perpendiculars, as shown. Make a 1 of section equal to n 1 of elevation, and also make b 11 of section equal to b
11 of elevation, and connect 11 with 1. The remaining sections are constructed in the same manner.
Before the pattern can be obtained it will be necessary to develop extended sections of the inner and outer curves, as shown to the left and right of the elevation. This is done for the purpose of obtaining the actual distance between points shown in elevation. For convenience, on G A extended, as H K, lay off a stretchout of A' B' of plan, and from the points therein contained erect the perpendiculars, as shown. From the points in A B of elevation draw lines parallel with H G, cutting perpendiculars of similar number erected from H K. A line drawn through these points of intersection, as shown by H J, will show the shape of A B of elevation as laid out on a flat surface. The development of the inner curve is shown to the right of the elevation. On L N is laid out the stretchout of F' E' of plan, and on the perpendiculars erected from the points in the line are set off the same distances as on lines of similar number in F E G of elevation. A line traced through these points, as shown by L M, also slows the shape of F E, as laid out on a flat surface, and gives the distance between points as if measured on the finished article.
Fig, 731. - Sections Based Upon the Solid Lines of the Plan, Fig. 730.
Fig. 732. - Sections Based Upon the Dotted Lines of the Plan, Fig. 730.
To obtain the pattern, using the distances between points in H J and L M of Fig. 730, and the diagram.-: in Figs. 731 and 732, proceed as follows: Draw any line, as B E in Fig. 733, in length equal to 1 12 of the first section in Fig. 731. With E as center, and M 11 of inner curve as radius, describe a small arc, 11, which intersect with one struck from B as center, and 1 11 of Fig. 732 as radius, thus establishing the point 11 of pattern. With 11 of pattern as center, and 11 2 of the second section in Fig. 731 as radius, describe another small arc, 2, which intersect with one struck from point B of pattern as center, and J 2 in J H of outer curve as radius, thus establishing the point 2 of pattern. Continue in this way, using the tops of the sections in Figs. 731 and 732 for the measurements across the pattern, the spaces in the inner curve L M and in the outer curve H J for the distances about the edges of the pattern, establishing the several points, through which draw the lines shown. Then B A F E is the half pattern of splayed head, shown in elevation by A B E F. The other half can be obtained by any convenient means of duplication.
Fig. 733. - Pattern of Splayed Arch in Fig. 730.
A semicircular splayed arch can be developed in the same manner as above described.
The pattern for a blank for a curved molding, either semicircular or semi-elliptical, for an arch in a circular wall comprises really the same relations of parts as are shown in Fig. 730, and could be obtained as above described.