Case II. The Flange Fitting over the Ridge of a Roof.—Figure 179 shows an elevation and profile of a roof flange fitting over the ridge of a 90° or "square-pitch" roof. Figure 180 shows the pattern for the pipe. It will be noticed that this type of flange cannot be easily double seamed; therefore, a ½-inch edge is added to the miter cut. This edge is turned off, and riveted and soldered to the apron. Figure 181 shows the pattern of the apron. A bend of 90° must be made on line 4 in order to fit the apron over the ridge of the roof. The description for Case I will apply to this problem, the only difference being the shape of the miter cut in Fig. 176.
Case III. The Flange Fitting over the Ridge and Hips of a Roof.—An elevation is first drawn according to the dimensions given in Fig. 182. Above this elevation a half-profile is drawn and divided into equal spaces and numbered as shown. Extension lines are carried from each division down to the roof line. A plan, Fig. 183, is drawn in the following manner: Extend the center line of the elevation downward indefinitely. Construct a rectangle, Fig. 183, using this line as a center line. This rectangle will represent the top view or plan of the apron of the finished flange. Draw two lines at an angle of 45° to represent the hips of the roof. The center line becomes the ridge. With the point where the ridge and hips meet, as a center, and a radius equal to that of the half-profile. Fig. 182, draw a circle. Divide this circle into twice as many equal parts as there are in the half-profile. Number these divisions to correspond. The hips cross this circle halfway between points 2 and 3 and 5 and 6. Number these points 2½ and 5½ respectively. Carry extension lines upward from each division of the circle, to the roof line.
That part of the miter line not already shown in elevation can be developed. Points 2½ and 5½ in Fig. 182 occur where the lines from these points in Fig. 183 intersect the roof line in Fig. 182. Since this is the highest point of the miter line on the hips, point 3 must be opposite point 2, point 4 opposite point 1, and point 5 opposite point 6. This is indicated by horizontal dotted lines in Fig. 182. A curved line drawn through these points will be the developed miter line. A line of stretchout, Fig. 184, is now drawn. The exact spacing is transferred from the circle in Fig. 183 to this line, and numbered to correspond.
The measuring lines of the stretchout are drawn. Starting at
