Fig. 675. - Diagram of Sections Upon Dotted Lines of Fig. 67S.

PROBLEM 207. The Pattern for a Y Consisting of Two Tapering Pipes Joining a Larger Pipe at an Angle.

In Fig. 677, BC D E represents the elevation of a portion of the larger pipe and C K D' L its profile. This pipe is cut off square at its lower end, with which the branches of the Y are to be joined. A B O H J and G H O E F are the elevations of the two similar branches joining each other from H to O, and the larger pipe on the line BE. A' N J' M is the profile of one of the tapering branches at its smaller end.

Fig. 677. - Elevation and Profiles of Y with Tapering Branches.

Since the article consists of two symmetrical halves when divided from end to end on the lines A' J' or C' D' of the profiles, and since the two branches are alike, the pattern for one-half of one of the branches, as A B O H J, is all that is necessary.

The dividing surface A B O H J, lying as it were at the back of the half of the branch shown in elevation by the same letters, will then form a plane or base from which the hights or projection of all points in the surface of the branch piece can be measured.

As the branch piece A B O H J is an irregular tapering form, its surface must be divided into a series of measurable triangles before its pattern can be obtained. Therefore divide the half profile C' L D' into any convenient number of equal parts - in the present instance six. as shown by the small letters f g h j k - and from these points drop lines parallel with C B, cutting the line B B, as shown. In a similar manner divide the half profile A' N J' into the same number of equal parts as was C L D', as shown by the small letters a b c d e. From the points thus obtained carry lines parallel with J' J. cutting A J. Connect the points in A J with those in B E, as shown.

Fig. 678. - Elevation of One Branch of Y, Showing Method of Trangulation.

To avoid a confusion of lines the subsequent operations are shown in Fig. 678, in which A B O H J is a duplicate of the piece bearing the same letters in Fig. 677. The profiles B L E and A N J arc also duplicates of those shown in Fig. 677 and are for convenience here placed adjacent to the lines which they represent. B L of the upper profile then represents a section on the line B O, and A N J that upon the line A J, but the section on the line O H, the miter between the two brandies, is as yet unknown. To obtain this it will be necessary to first obtain sections upon the various lines drawn across the elevation from B E to A J in Fig. 678, or in other words, diagrams upon which the true lengths of those lines can be measured. In the diagram of sections shown in Fie. 679

Fig. 679.

Fig. 680.

Diagrams of Sections Upon Solid Lines of the Elevation.

S T represents the dividing surface or base plane alluded to above and is made equal in length to 2 2' of Fig. 678. At either extremity of this line erect the perpendiculars S band T f, as shown. Make T f equal in hight to 2' f of profile B L E, and upon S b set off from S the hight S a, equal to 2 a of the profile A N J, and draw the line a f. On S T, measuring from T, set off the distance 2' 2", and erect the perpendicular 2" f", cutting a f at f". Then will a f represent the true distance between the points 2 and 2' in Fig. 678, and a f" will represent the true distance from 2 to 2", while 2" f" will be the hight of the point 2". In a similar manner set off from S, on S T, a distance equal to 3 3' of Fig. 678 and erect the perpendicular 3' g, equal in length to 3' g of profile B L E. Make S b equal to 3 b of profile ANJ and draw b g. From S set off on S T a distance equal to 3 3" of Fig. 678 and erect the perpendicular 3" g", cutting b g at; g". Then will b a be equal to the true distance between 3 and 3' of Pig. 678, b g" will be the true distance from 3 to 3" of Fig. 678 and 3" g" will be the hight of the point 3". To construct the section on the line O H, at points 3" and 2" draw 3"g' and 2" f" at right angles to O H, making them respectively equal 3" g" and 2"f" of Fig. 679. As the profile B L E is a semicircle the hight of point 4' - that is, 4' h - is equal to O E; therefore through the points E, g' f and H draw the curve shown, which will be the true section on line O H, from which the stretchout can be taken for that portion of the pattern.

Fig. 681.

Fig. 682.

Diagrams of Sections Upon Dotted Lines of the Elevation.

The sections on the remaining lines (4 4', 5 5' and 6 6') of the elevation are shown in Fig. 680 and are constructed in exactly the same manner as those shown in Fig. 679, giving c h, dj and e k as the true lengths of those lines. Before the pattern can be developed the four-sided figures into which the surface of the branch pipe has been divided by the solid lines must be subdivided into triangular spaces, as shown by the dotted lines in the elevation. Sections upon these lines must also be constructed, in order that their true lengths can be obtained. These are shown in two groups in Figs. 681 and 682 and are constructed in a manner exactly similar to that described in connection with Fig. 679. They may be easily identified by correspondence between the figures on the base lines U V and W X and those of the elevation.

Fig. 683 - Pattern of Tapering Branch.

To describe the pattern proceed as follows: Draw-any line, as J H in Fig. 683, in length equal to J If of Fig. 678. With J of pattern as center, and J' n of smaller profile as radius, describe a small arc (a), which cut with one struck from H of pattern as center, and 1" a of Fig. 681 as radius, thus establishing the point " of pattern. With a of pattern as center, and af of

Fig. 679 as radius, describe another small are (f'), which intersect with one struck from H of pattern as center, and H f" of profile H E as radius, thus establishing the point f of pattern. In a similar manner, a b of pattern is struck with a b of profile as radius; f' b of pattern with f" b of Fig. 681 as radius: b g' of pattern with b g" of Fig. 679 as radius, and f' g' of pattern with f g' of profile H E as radius; also, b, c of pattern is struck with b c of profile as radius; g' c of pattern with g" c of Fig. 681 as radius; g' h of pattern with g' E of profile as radius, and c h of pattern with c 7t of

Fig. 680 as radius. Thus arc the points established in O H J P of pattern.

B O P A of pattern corresponds with B O P A of elevation and is obtained in the same manner. The points in O B of pattern are derived from profile L B, as are the points in P A of pattern from N A of small profile. The lengths of solid lines in pattern are obtained from the diagram of sections in Fig. 680, as are those of the dotted lines from the diagram of sections in Fig. 682. Lines drawn through the points in B O H J P A, Fig. 683, will be the half pattern for ABO H J of elevation. The other half of pattern, as shown by A J' H' O' B, can be obtained in a similar manner or by duplication.