This is Part II of a two-part series on equal-tapering elbows. Part I appeared in August.

Last month, in Part I, it was explained how to start to develop the equal-tapering elbow with a center radius. The article went as far as completing the profile/elevation view that you will use to develop the actual patterns of each of the five gores. The next step is developing the patterns.

In the July issue of Snips, we covered making a tapered cone using triangulation and a short method to developing the pattern. The actual method was in reference to the fourth rule by Frank O’Rourke, which again states: “Symmetrical fittings having planes that are not parallel should be developed by using the elevation view without the plan view.”

If you take a look at each tapered gore, it’s really similar to the tapered cone covered in August - and that’s a skill anyone doing these layouts can have with a little understanding and breakdown of the few different methods that are best applied to any particular fitting.

Gores A and E (shown in Figure 6) will be developed using parallel-line method. Gores B, C and D will be developed using triangulation, aka the short method.


FIgure 6
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With our focus on gore B, in determining the true-length lines necessary for the pattern you need to use the information from profile No. 1, 2”-14”; and profile 3, 1”-13” (profile No. 3 was also previously shown in Part I). You already have in place profile No. 1, 2”-14” in Figure 6a.

This next step can be done on the elevation view, but only for clarity this drawing is brought to the side in 6b. What needs to be done here is create two sides of each triangle, the base and the right side. The third side, or the hypotenuse, will be the true length line(s) for the pattern.

As illustrated in Figure 6b, draw a straight line from Point a to Point b. This represents Line a-b in Figure 6a. Locate near the center a point and reference it as 7a”. Use the distance of Point 1” to 7” from Figure 6a. Then on Line a to b and with point 7a” in Figure 6b as center, draw an arc from 1” to 13” as shown.

Divide the arc from 1” to 13” equally into six sections and extend a line to each section perpendicular to Line a-b as shown in Figure 6b.

To find the length of the base for each necessary triangle that you’ll need when determining each true-length line, you must first determine and reference the difference between the top profile No. 3 (Figure 6b) and the bottom profile No. 1 (Figure 6a). This includes all the sectional lines of the top profile and the respective sectional lines in the bottom profile. An example here is to find the difference between the distance of Point 3” to Point 3a of the top profile No. 3, and 4 to 4a of the bottom profile No. 1.



Figure 7
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Using your dividers, transfer the distance of 4 to 4a of the bottom profile No. 1 to the respective Line 3”-3a of the top profile No. 3 by placing one end of the dividers on 3” and striking a mark. Reference accordingly, as shown in profile No. 3, Figure 6b as 3”- 4’.

Anyone can tell you where to place the dividers or trammels through to the end of any fitting. It will benefit you more to learn about certain areas such as the distance of 4 to 4a in profile No. 1. When this line is projected upward to the edge of the B gore 4’, you’ll see that the difference of the two profiles will not only be the base of 4’ to 3”, but also the base for 4’ to 5”.

So with the dividers still set to 4 to 4a, place one end on Point 5” (Figure 6b) and strike a reference mark as shown with Line 5”-4”. Resetting your dividers to 6-6a of profile No. 1, this will be used for both Line 6’-5” and 6’-7”. Using the dividers set to 6-6a (profile No. 1), this setting must be transferred to both 5”-5a and 7”-7a and referenced as shown.

Continue this with 8-8a, 10-10a and 12-12a, and reference all marks as shown on profile No. 3 in Figure 6b.

Up to this point, you determined the difference between the two profiles and established the base of each triangle needed for all the true-length lines for the pattern. The next step in Figure 6c will be to transfer from Figure 6a and establish the second side of the triangle at a right angle to each baseline that was completed in 6b. This is done by setting the dividers to the lengths shown with the dashed lines on gore B of Figure 6a.


Figure 8
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Line 1”-2’ of 6a is shown in it’s true-length form and will be used when developing the pattern. Set your dividers to the length of 2’ to 3”. Transfer this distance to Line a-b of 6c by setting one end of the dividers on Point 3a and striking an arc also on Line a-b, shown as 2”-3”.

The distance between 2’-3” and 3” (shown in Figure 6c) is the true-length line for the distance of Point 2’ to Point 3”.

Reset your dividers to the distance from Point 3” to Point 4’ from Figure 6a. Transfer this distance to Line a-b from Figure 6c by setting one end of the dividers on Point 3a and striking a reference mark on Line a-b, shown as Line 3”-4’. The distance between 3”-4’ on Line a-b and 3”-4’ (marked in red) in Figure 6c is the true-length line for 3” to 4’ for the pattern.

Continue these steps in establishing the true-length lines of 4’ to 5”, 5” to 6’, 6’ to 7”, 7” to 8’, 8’ to 9”, 9” to 10’, 10’ to 11”, 11” to 12’ and 12’ to 13” of Figure 6a. 13” to 14’ is already shown in its true-length form in Figure 6a.

Figure 7 illustrates the pattern using all the true-length lines from Figure 6c. The true-length line of Line 1”-2’ is true length in the elevation view (Figure 6a), a partial arc drawn from 1” to 3” using 1” as center, and 2’ to 4’ using 2’ as center. These lengths are established in each of the profiles. It would be to your advantage to have a couple extra dividers and set then accordingly and have them ready for these two areas that will be consistent throughout developing the pattern.



Using the true length Point 2’ to Point 3” and with Point 2’ as center, draw an arc that intersects the first arc drawn from Point 1” to establish Point 3”. Continue this method with Point 3” to 4’, etc.

Using your dividers, you’ll go through this painstaking process of transferring all the true-length lines to develop this pattern. To save time, you can develop the half pattern as shown in the top image of Figure 7 and trace that pattern to the opposite side. Being this is an equal reducing tapered fitting, you’ll have to do this step with the two other gores, C and D.

The two end patterns for this fitting are not tapered, so you can develop these patterns using parallel lines, as gore A is shown in Figure 8. The two end patterns, A and E, are of different diameters and you’ll have to develop these separately.

Using parallel-line development for the two end gores, you’ll project out from each height the distance from Point 2’ to Point 14’ of the elevation or side view of the fitting, the distance between 2 and 4, 4 and 6. These are established from the profile where they are shown in true length and not the elevation view as shown in Figure 8. There has been no allowance included in these drawings for any seam or material thickness.

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