How to lay out an eccentric reducer
To lay out an eccentric reducer, divide both ends into the same number of points and find the true length of every line and diagonal between them from the height and the plan distance. Starting with the flat side as the seam, swing each new point from the last two, one triangle at a time, then join the points.
Drawn by Stretchout from the worked example below. Triangulation development.
What you need
- Plate or sheet big enough for the blank
- A tape and a trammel or long dividers
- A straightedge
- A flexible batten for the curves
- Soapstone or a scribe
Worked example
We’ll lay out a 24" to 12" OD eccentric reducer, 18" high, flat on one side, in 3/16" plate, laid out on the mean line, 16 lines. The numbers:
- Mean radii, large and small
- 11 15/16" and 5 15/16"
- Height
- 18"
- Small end off center
- 6"
- Lines around
- 16
- Shortest line (the flat side)
- 18"
- Longest line
- 21 5/8"
- Blank
- 57 5/16" × 32 3/8"
Step by step
Step 1
Draw the first seam, 18" long. Its end on the large end is point 1, on the small end point a.
Step 2
From 1 swing 4 11/16" along the large end. From a swing 18 9/16". Where they cross is point 2.
Step 3
From a swing 2 5/16" along the small end. From 2 swing 18 1/8". Where they cross is point b.
Step 4
Keep going the same way, one point at a time. Each new point is where the two swings cross:
Point Swing from and swing from 3 4 11/16" 2 19 1/4" b c 2 5/16" b 18 9/16" 3 4 4 11/16" 3 20 1/16" c d 2 5/16" c 19 3/16" 4 5 4 11/16" 4 20 13/16" d e 2 5/16" d 19 7/8" 5 6 4 11/16" 5 21 1/2" e f 2 5/16" e 20 9/16" 6 7 4 11/16" 6 21 15/16" f g 2 5/16" f 21 1/8" 7 8 4 11/16" 7 22 1/8" g h 2 5/16" g 21 1/2" 8 9 4 11/16" 8 22" h i 2 5/16" h 21 5/8" 9 10 4 11/16" 9 21 5/8" i j 2 5/16" i 21 1/2" 10 11 4 11/16" 10 21 1/16" j k 2 5/16" j 21 1/8" 11 12 4 11/16" 11 20 5/16" k l 2 5/16" k 20 9/16" 12 13 4 11/16" 12 19 1/2" l m 2 5/16" l 19 7/8" 13 14 4 11/16" 13 18 3/4" m n 2 5/16" m 19 3/16" 14 15 4 11/16" 14 18 1/4" n o 2 5/16" n 18 9/16" 15 16 4 11/16" 15 18" o p 2 5/16" o 18 1/8" 16 17 4 11/16" 16 18 1/8" p q 2 5/16" p 18" 17 Step 5
Join the points on each end with a smooth curve. Cut on the curves and the seams.
Watch it laid out
Every step of the worked example. Play, or step through with Next and Back (or the arrow keys).
1.Draw the first seam, 18" long. Its end on the large end is point 1, on the small end point a.
The true lengths
An eccentric reducer isn’t a cone you can swing from one center, so every line is found on its own. Put the flat side at angle 0, with the small end shifted e = R1 − R2 toward it. The line at angle φ joins (R1·cos φ, R1·sin φ) on the large end to (e + R2·cos φ, R2·sin φ) on the small end, so its plan length is 2·(R1 − R2)·sin(φ/2) and its true length is √(H² + (2·(R1 − R2)·sin(φ/2))²). The diagonals between neighbouring points are found the same way, from their own plan distances.
On the flat side (φ = 0) the plan length is zero, so that line is exactly the height: it’s the natural seam. Opposite it (φ = 180°) the line is longest, √(H² + (2·(R1 − R2))²).
Space the points on the sheet, not on the round. The chord between points measured on the round is a little short on the flat, and it adds up: about half an inch around this example. The steps above give the spacing measured on the sheet.
Questions
What makes it eccentric?
The small end sits off center so one side runs straight, flat with the pipe. That flat side keeps the bottom of a line level, so nothing pools or traps air.
Why can’t I use the cone formula?
The cone formula swings everything from one center. With the small end off center the lines don’t meet at one point on the sheet, so the pattern is built by triangulation instead.
How many lines should I use?
16 around is a good start for most reducers. Use 24 or 32 on big or steep ones so the curve between points is short.
Where should the seam go?
On the flat side, where the line is exactly the height. It’s the easiest edge to check and the straightest weld.
Why did my pattern come out short?
Spacing taken as the chord on the round is short on the flat. Around this example the shortfall is about half an inch. Take the spacing on the sheet, as the steps give it.
Can the small end be offset some other way?
Yes. The calculator’s Offset option moves the small end anywhere, not just flat on one side, and the triangulation is the same.
Your sizes
Below is the cone calculator, opened on the worked example. Put in your own sizes and it redoes every number and every step for your fitting. It’s also at /stretchout/shapes/cone.