Let L F D E K I H M of Fig. 341 represent the elevation of two pipes of the same diameter meeting at the angle M H I, for which patterns are required. Draw the profile or section A1 B1 C1 in line with the branch pipe, and the section ABC in line with the main pipe. As both pipes are of the same diameter, and the end of one piece comes against the side of the other piece, both halves of the branch pipe (dividing at the point B) will miter with one-half, B D, of the main pipe. By projecting lines through the elevations of each piece from the points B or 4 of their respective profiles the point G is obtained, which, being connected with points F and H, gives the required miter line. Space both the profiles into the same number of equal divisions, commencing at the same point in each. For the pattern of the arm proceed as follows: Lay off the stretchout O N opposite the end of the arm and draw the usual measuring lines at right angles through it, as shown. Place the T-square at right angles with the arm, or, what is the same, parallel with the stretchout line, and, bringing the blade successively against the points in the miter line F G H, cut the corresponding measuring lines. Through the points thus obtained trace the line PRST, which will form the end of the pattern required. For the pattern of the main pipe proceed as follows: Opposite one end lay off the stretchout, as shown by V Y, and opposite the other end lay off a corresponding line, as shown by U X. Connect U V and X Y. From so many of the points in the stretchout line V Y as represent points in the half of the profile BAD draw the usual measuring lines. With the T-square placed parallel to the molding D I, drop the points from the profile onto the miter line F G H; then, placing it at right angles to the molding, drop lines from the points in the miter line intersecting the corresponding measuring lines. A line traced through these points of intersection, as F1 Z H1 W, will describe the shape required. The position of the seam in both the arm and the main pipe is determined by the manner of numbering the spaces in the stretchout. In the illustration the seam in the arm is located in the shortest part, or at a point corresponding to 1 of the profile. Accordingly, in numbering the divisions of the stretchout, that number is placed first. In like manner the seam in the main pipe is located at a point opposite the arm. Therefore, in numbering the spaces in the stretchout commence at 1, which, as will be seen by the profile, represents the part named. If it were desirable to make the seam come on the opposite side of the main pipe from where it has been located - that is, come directly through the opening made to receive the arm - the numbering of the stretchout would have been begun with 7. In that case the opening F1WH1Z would appear in two halves, and the shape of the pattern would be as though the present pattern were cut in two on the line 7 and the two pieces were joined together on lines 1. By this explanation it will be seen that the seams may be located during the operation of describing the pattern wherever desired. It is not necessary, as prescribed at the outset of this problem, that both profiles should be spaced off exactly alike. Any set of spaces will answer quite as well, provided there be points in each exactly half way between A and B of either profile - that is, where points 4 are now located. They are spaced alike in this case to show that lines dropped from points of the same number in each profile arrive at the same point on the miter line, and that therefore when both pipes are the same diameter and their axes intersect, one profile may be used for the entire operation.

Fig. 341   A Joint between Two Pipes of the Same Diameter at Other than Right Angles.

Fig. 341 - A Joint between Two Pipes of the Same Diameter at Other than Right Angles.

Note. - In the nineteen problems immediately following, the conditions are such that it will be necessary to obtain the miter line from the data given by the operation of raking before the straightforward work of laying out the patterns can be begun. However, as certain parts of the work of raking the miter line and of laying out the pattern are common to both operations, the two are usually carried along together, and therefore such points and spices should be assumed upon the profiles at the outset as will be required in the final stretchout.

PROBLEM 55. To Obtain the Miter Line and Pattern for a Straight Molding Meeting a Curved Molding of Same Profile.

Fig. 342.   The Miter Line between a Curved and a Straight Molding of the Same Profile.

Fig. 342. - The Miter Line between a Curved and a Straight Molding of the Same Profile.

In Fig. 342, let F G J K represent a piece of straight molding joining a curved mold, G H I J, the profiles of the straight and curved molding being the same. To obtain the miter line or line of joint, G J, proceed as follows: Draw the profile in line with the straight molding, as shown by C D E, and divide into any convenient number of parts. From the divisions in the profile draw lines parallel to F G in the direction of the miter indefinitely, and also in the opposite direction, cutting the vertical line C E of the profile, as shown by the small figures, which correspond in number to the divisions on the profile. From B, the center from which the curved molding is struck, draw the line B A through the molding, as shown. Transfer the hights of the various points of the profile as obtained on the line C E to the line A B, placing the point E at the point o of the intersection of the lower line of the curved molding with the line A B, all as shown by X o. Then, with B as a center, draw arcs from the divisions on the line X o, intersecting lines of corresponding numbers drawn from the profile parallel to the lines of the straight molding. A line traced through these intersections, as shown by G J, will be the required miter line, and, as will be seen, is not a straight line'. To obtain the pattern for the straight molding, draw the line L N at right angles to it, upon which place the stretchout of the profile C D E, as shown by the small figures. At right angles to the stretchout line L N, and through the points in it, draw the usual measuring lines. With the T-square placed at right angles to K. J, bring it successively against the points forming the miter line G J, and cut lines of corresponding number in the stretchout. Then a line traced through these points of intersection will form the miter end of the pattern shown by L M N O. The methods employed in obtaining the patterns for the curved portions are treated in Section 2 of this chapter.