The one thing to keep in mind is the one diameter should always be of equal area as the two combined branch diameters.

Also remember that the larger pipe should equal the square root of the sum of the squares of the diameters of the others. For example if we needed to supply two 6-inch branches, we would use this formula:

6 x 6 x 2 = 72

The large diameter (lower profile) would be the square root of 72 or an 8.49-inch diameter.

Begin by drawing the elevation view and establishing the angle of the two branches, including the spread between the two in relationship from center. Draw a line the length of the base diameter, as shown in Figure 2, Line 1-2 and bisect Line 1-2 as shown by Point 3.

Draw a line perpendicular to Line 1-2 as shown by Line 3-4. This represents the center of the Y branch. Points 5 and 5' mark the distance of the offset from center line, 3-4. The length of the upper diameter of each branch is marked off from Line 5-6 and Line 5'-6'.

## Equal spread

To establish the location and height of the fitting's "crotch," draw a line from Point 5 to Point 1, shown in Figure 2, and from Point 5' to Point 2. The crotch is marked by the No. 7 in Figure 2. Since the fitting is symmetrical, you only need to create one side, which you can then use as a pattern for the second side.## The next step

The next step is to develop the necessary profile views as shown in the shaded areas Figure 3, and divide the arc into any number of equal spaces. Divide the upper and lower profile into equal spaces, as shown in Figure 3. For clarity, we chose to use 12 equal spaces on our profile, six per half and three per quarter.To establish points 3, 5, 9 and 11 in Figure 4, start by drawing a profile for the base. Using 7 as center and the dividers set to the radius of the base, draw an arc from Point 1 to Point 7'". Divide this profile into six equal parts as shown in points 1 to 3', 3' to 5', 5' to 7', 7 to A, A to B and B to 7'".

Extend vertical lines perpendicular to Line 1-7 from points 5' and 3' to establish Point 5 and Point 3 on Line 1-7, which is the base of the branch. This takes care of the right side of the lower profile, the region from Point 1 to Point 7'.

## Fixing potential problems

The left side of the lower profile, the distance from 7' to A to B to 7'" fixes two potential problems with this pattern. It gives us the needed information of the base of triangles to complete developing the true-length lines for these points. It also helps us determine the true shape of the crotch by projecting vertical lines perpendicular to Line 7-7" from both Point A and Point B, as shown in Figure 4.
The height of the crotch, shown Line 7-13 in Figure 4, is higher than the radius of the base. You can see this by placing your dividers on points 7 and 13 and making an arc using Point 7 as center. Make the arc from Point 13 to Point 7".

## Adjustments

You need to make some proportional adjustments in the actual profile of the crotch. Before doing this, divide the arc from Point 7" to Point 13 into three equal parts, as shown by 7" to 9" and 11" to 13. From points 9" and 11", project lines horizontally to establish Point 9 and Point 11 as shown.Where the vertical lines from points A and B intersect the horizontal lines 9" and 11" establishes the new profile for the crotch as seen from 7'" to 9'" to 11'" to 13. Be careful when drawing the pattern that when you use these points in creating your triangles that you also use the distance between each as needed: points 7'" to 9'", 9'" to 11'" and 11'" to 13.

As shown in the shaded area of the elevation view in Figure 5, and for a clearer understanding of the layout, connect Line 2 to 3, 3 to 4, 4 to 5, 5 to 6, 6 to 7, 7 to 8 until you connect 12 to 13.

There are two separate sets of true-length triangles; the first set includes all the lines from points 1, 3, 5 and 7 to 2, 4, 6 and 8. To establish the true-length lines, draw a line from A to B as shown in Figure 5. Then draw a second line perpendicular to Line AB, the same height of the fitting, as shown. This shows the height of each triangle within that particular group of numbers.

Line AB represents the base of each triangle, as labeled. To know the distance of each base line, you must look at it from the top view. By projecting the upper profile down to the lower one and using the center horizontal line, you can create a top view and then mark it accordingly, as shown in first profile.

Connect points 1 to 2 (as shown in red), 2 to 3, 3 to 4, etc., until 7 to 8 is drawn in. Using the dividers or trammel points, transfer and label all these distances to the base of the true-length triangle, using A as center. By connecting all these points to the top of the true-length triangle, you have created all the true-length lines for the base to the top of fitting.

## True lengths

Creating the second true-length triangle is completed the same way with the exception of the different heights that form the crotch-plane surface. How to draw the lines that need to be transferred to connect points 8 to 9, 9 to 10, 10 to 11, etc., is shown in the second profile of Figure 5. Transfer and label all lines from the second profile, for clarity purposes, to the top of the true-length triangle marked Line CD. Connect these lines as shown to establish their true lengths. Now you can take these true lengths and begin to develop the pattern.Take all the true-length lines from Figure 5 and put them together in the form of triangulation to develop the pattern. This would be a good place to have multiple sets of dividers. The distance between the top, even numbers, 2 to 4 to 6 to 8, etc., are all the same distance. This distance is taken from the upper profile and the length of each division that you have divided the profile into. For example if you were to divide the 6-inch diameter pipe opening into 12 equal parts, the distance between each part would be 1.57- or 1 9/16 inches The second set of dividers would be set to one-twelfth of the circumference of the base and used for connecting points 1 to 3, 3 to 5 and 5 to 7.

Now points 7 to 9, 9 to 11 and 11 to 13 are all going to be a different length and taken from the crotch's profile. This is shown in the elevation view as points 7'", 9'", 11'" and 13.

One set of dividers will be changed as needed for the long legs of the triangle, such as from Point 1 to Point 2. Point 1 to Point 2 was chosen as a center because it is the longest point of the branch. Point 13 to Pont 14 is the shortest and a good location on the inside of the fitting.

## Triangulation

If you were to use Line 1-2 as the seam, your seam would be not only longer but also exposed on the outside of the fitting. Triangulation starts by drawing Line 1-2, make an arc from Point 1 to Point 3, using Point 3 as center. Now from your true-length triangle, set your dividers at the distance from Point 2 to Point 3 and using Point 2 as center, create a mark that intersects the arc made from Point 1. This becomes Point 3.Now with the dividers set the distance from Point 2 to Point 4, make a mark using Point 2 as center. Then take the distance from Point 3 to Point 4 from your true-length triangle and draw an arc that intersects with the arc struck from Point 2. This intersection becomes Point 4.

Continue back and forth as shown in Figure 6, remembering that you have to reset the dividers individually for each crotch section. Figure 7 shows the finished flat pattern with only a half inch added to the short side for seaming. No more seam allowances are given due to the many different ways that it can be seamed. Two branches are required.

There are many different ways to lay out the branches. They won't always be symmetrical. The spread may not be equal or centered. Practice with light-colored construction paper to get a feel for the task. The next time you're approached to tackle one, hopefully you will be able do so with confidence.