This is Part I of a two-part series on equal-tapering elbows. Part II will appear next month.

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There are several ways a reducing elbow can be developed; this article will allow you to fully understand and retain the necessary steps.

Developing this type of elbow makes for some good practice, as each gore has to be made separately. Because of the taper, no two gores can be duplicated as you can do in the regular five-gore elbow.

The five gores for this equally tapered elbow will be developed using two methods: triangulation, which will be used for the inner gores, and parallel line, which will be used for the two end gores.

What you’ll need to get started on this particular fitting is to determine the size of opening A and the size of opening B. The radius will be determined by throat A or throat B plus half the diameter of opening A or opening B. Once the radius is determined you’ll set your trammel points to that distance, as shown in Figure No. 1 in the distance from R to C.

Now using R as center, strike an arc from C to C’. All the tapered gores are worked out from this line.

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**Figure No. 2**

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For Figure No. 2 - using the established radius center line points C and C’, set your trammel points to half the diameter of opening A and using Point C as center, make an arc from A to B to establish profile 1. Reset your trammel points to half the diameter of opening B and using C’ as center, draw an arc from Point A’ to Point B’ to establish profile 2.

An elbow can be divided into as many gores as necessary. Four or five gores per elbow are typical but there can be several more gores, depending on the size or the sweep of the elbow and its application. The gores can be fixed or adjustable, but in most cases you’re going to fabricate these or any elbows in a fixed position.

Once you decide on how many gores your elbow will have, take the number of gores, multiply that number by two and then subtract two. For an example, in the pattern for a five-gore elbow, multiply five times two. That equals 10. Now subtract two from 10. That equals eight.

Divide the center line into eight equal parts. These parts are the centers of each gore as shown in Figure No. 2.

You have three complete gores: B, C and D, and two half gores shown as A and E in Figure No. 2.

Now look at Figure No. 3. Divide profile 1 and profile 2 equally into six parts and reference each point in profile 1 with even numbers, two through 14, and profile 2 with odd numbers, one through 13, as shown.

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**Perpendicular lines**

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From each reference point on profile 1 and profile 2, draw a line perpendicular to plane edge Nos. 1-13 and Nos. 2-14 until you intersect the first section’s miter lines, 1’-13’ and 2’-14’.

Reference these points along the first miter line, points 2’, 4’, 6’, 8’, 10’, 12’ and 14’. Do this also with 1 through 13’ from profile 2. Now that the two end sections A and E have been established, you can work to connect the three remaining tapered gores, B, C and D.

The first thing to do is to establish Point 7” and Point 8” - the center miter line - as the “equal taper,” which is based off the center line from Figure No. 3.

To establish the location of Point 7” on the miter line 1’-13” (see Figure No. 3), draw a line from Point 8’ tangent to the arc drawn from C to C’. Mark the intersection Point 7” as shown.

To establish the location of Point 8” on miter line 2”-14”, draw a line from Point 7” tangent to the arc drawn from Point C to Point C’, where this line intersects the miter line 2”-14”. Mark this Point 8”.

At this time, still unknown are the lengths of the two miters or what would be the end points 1” and 13” and 2” and 14”. You are reducing this equal tapering fitting with four miters, the longest miter being that of 2’ to 14’ and the shortest miter being 1’ to 13’.

To determine the lengths of the two unknown miters in between gores A and E, use the method shown in Figure No. 3. Draw a horizontal line the length of Line 2’ to 8’ as shown in Figure No. 3. Mark the ends of this line a and e.

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**Miter lines**

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From Point e, take the length of the last miter line, 1’ to 7’, and using e as Point 7’, draw a mark to establish Point 1’(d) on this line. The difference between a and d or 1’ and 2’ on this line must be divided equally for the number of gores remaining.

In Figure No. 3, you have three gores remaining - B, C and D - so that the distance between a and d will be divided in three equal sections and marked accordingly, as b and c.

The distance of e to b on this line is the distance of 7” to 1” of the miter line and also 7” to 13”. The distance of e to c is the distance of Point 8” to Point 2” of the miter line and also 8” to 14”. Connect the newly established end points of the miter lines to see the profile of the elbow and each of its gore sections.

As shown in Figure No. 4, using Point 8” as center, strike an arc from 2” to 14”, establishing profile 4. Now using 7” as center, make an arc from Point 1” to Point 13” establishing profile 3. Divide each of these two additional profiles, 3 and 4, into the same number of spaces profiles 1 and 2 were divided into.

In the same manner as in profile 1 and 2, from each reference point along profile 3, draw a line perpendicular to the miter line and reference with 3”, 5”, 7”, 9” and 11”, as shown. Repeat this with the profile 4 and all points on miter line 2” to 14”.

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Connect the points on the miter lines of the center gores, B, C and D, as shown in Figure No. 5 (2’ to 3”, 3” to 4’, 4’ to 5”, etc.). These dashed lines will be used to figure out the true-length lines needed for the pattern, which will be covered in Part II.

The lesson will finish by making the patterns for this equal tapered elbow in easy-to-understand detail.

For more information on manual sheet metal layout, including free printable worksheets, visit www.thesheetmetalshop.com.