In Fig. 709, let A B C D represent the profile of the round pipe and E F G H I J K L the elevation of the elbow. In the plan the profile of round pipe is represented by A1B1C1 D1, the elbow by P1 M1 G1 M2

Fig. 709. - Plan and Elevation of Three-Piece Elbow, Bound at One End and Elliptical at the Other.

P2 and the shape of elliptical end of elbow by J1 M1 G1 M2. The section J G H I of elevation is without flare, and sections K F G J and E F K L arc flared, as shown in plan. Through the plan draw E1 G1 and M1 M2 and carry M1 M2 through the center of elevation, as shown by MNO P. Perpendiculars dropped from the points K O F of elevation, cutting P1 M1, E1 G1 and P2 M2, as shown by K1 O1 F1 O2 will give the shape of miter line K F in plan.

As J G H I of elevation is without flare the pattern for this part is procured in the ordinary manner as for a pieced elbow. Since J1 M1 G1 M2 is the profile of an elliptical cylinder, the section upon the oblique line J G of the elevation, cutting the same, must necessarily be an ellipse whose major axis is equal to M1 M2 and whose minor axis is equal to J G. In like manner, the section at K F of the elevation may be assumed as an ellipse whose minor axis is K F and whose major axis is equal to O1 O2

In Fig. 710, a duplicate of K F G J of elevation is shown by T R U W. Bisect T R in d and erect the perpendicular d S, and make d S equal to Q1 O1 of plan. Through the points T, S and R trace the half ellipse, as shown. In a similar manner bisect W U in l, and erect the perpendicular l V, in length equal to N1 M1 of plan. Through the points thus obtained trace the half ellipse W V U. Divide T S R into any convenient number of equal parts, and from the points thus obtained drop perpendiculars cutting T R, as shown. Also divide W V U into the same number of equal parts as was T S R, and from the points thus obtained drop perpendiculars cutting W U. Connect points in T R with those opposite in W U, as shown by the solid lines. Thus connect a with h, b withy, c with k, etc. Also connect the points in T R with those in W O, as indicated by the dotted lines. Thus connect 1 with h, a with j, b with k, etc.

The next step will be to construct a series of sections upon the several solid and dotted lines just drawn for the purpose of obtaining the true distances which they represent. The sections represented by solid lines are shown in Fig. 711. To construct these sections proceed as follows: For section a, draw the line a h, in length equal to a h of Fig. 710. From a erect a perpendicular, in length equal to a 2 in T S R, as shown by a 21, and from h erect a perpendicular, in length equal to h 11 in W V U, as shown by h 111, and connect 2' 111, as shown. For section b, draw bj, in length equal to bj of Fig. 710. From b erect the perpendicular b 31, in length equal to b 3 in T R S, and from j erect a perpendicular, in length equal to j 12 in W V U, and connect 31 121, etc. For the sections representing the dotted lines, as shown in Fig. '712, proceed in a similar manner. For section h, draw 1 h, in length equal to 1 h of Fig. 710. From h erect a perpendicular, in length equal to h 11 in W V U, and connect 1 with 112. For section j, draw a j, in length equal to a j of Fig. 710. From a erect the perpendicular a 22, in length equal to a 2 in T S R, and from j erect a perpendicular, equal in length to j 12 in W V U, and connect 22 122, etc.

Fig. 710. - Elevation of Middle Section of Elbow, Showing Method of Triangulation.

Fig. 711. - Sections on Solid Lines of Fig. 710.

Fig. 712. - Sections on Dotted Lines of Fig. 710.

To describe the pattern for part of article represented in Fig. 710 by T R U W, as shown in Fig. 713, proceed as follows: Draw any line, as R V of pattern, in length equal to R U of Fig. 710. With R of pattern as center, and 1 112 of the diagram of sections, Fig. 712, as radius, describe a small arc, which intersect with one struck from point V of pattern as center, and U 11 of Fig. 7l0 as radius, thus establishing the point 11 of pattern. With point 11 of pattern as center, and 21 111 of diagram of sections, Fig. 711, as radius, describe a small arc, which intersect with one struck from R of pattern as center, and R 2 of Fig. 710 as radius, thus establishing point 2 of pattern. Proceed in this manner, using the dotted lines in Fig. 712 for the distances in pattern represented by dotted lines; the spaces in W V U for the stretchout of V W1 of pattern; the distances between points represented by numbers in Fig. 711 for the length of solid lines in pattern, and the spaces in R S T for the stretchout of R T1 of pattern. Lines drawn through the points thus obtained, as indicated by R T1 W1 V, will be one-half of the required pattern. The other half, as shown by R T W V, can be obtained by a repetition of the same process or by duplication.

Fig. 713. - Pattern of Middle Section of Elbow.

The pattern for E F K L of elevation can be obtained in a similar manner, A B C of profile being one-half the shape on E L, and R S T of Fig. 710 being the half section on F K.