Piping
Eccentric reducer layout calculator
In short
A concentric reducer is a right cone frustum: half angle β = atan((D1 − D2) / 2L), generator g = √(L² + (r1 − r2)²). Its flat pattern is a sector of radii Rg = g × r1 / (r1 − r2) and Rg − g, with angle θ = 360° × r1 / Rg; the eccentric one is laid out by triangulation.
Calculation
Example calculated with the tool’s default values.
Inputs
- Large end
- DN100 · 114.3 × 3.6 mm
- Small end
- DN50 · 60.3 × 2.9 mm
- Type
- Concentric
- Length
- Entered
- End-to-end length
- 150 mm
- Pattern diameters
- Mean line (OD − wall)
- Marks around
- 16
Results
- Half cone angle
- 10.20°
Worked example
Every value in this section belongs to the example, calculated with the tool’s default values.
Other results of the example
- Taper
- 18.0%
- End-to-end length
- 150.0 mm
- Shortest generator (seam)
- 152.3 mm
- Longest generator
- 152.3 mm
- Large arc layout radius
- 316.4 mm
- Small arc layout radius
- 164.1 mm
- Sector angle
- 62.97°
- Pattern on the mean line (Ø 110.7 / 57.4), no weld allowance.
Step-by-step calculation
Half angle
β = atan((D1 − D2) / 2L)
atan(27.0 / 150.0) = 10.20°
Generator
g = √(L² + (r1 − r2)²)
√(150.0² + 26.7²) = 152.3 mm
Large arc radius
Rg = g × r1 / (r1 − r2)
152.3 × 55.4 / 26.7 = 316.4 mm
Sector
θ = 360° × r1 / Rg
360 × 55.4 / 316.4 = 62.97°
Pattern generators
| No. | Angle (°) | Arc on the large end (mm) | Arc on the small end (mm) | Generator (mm) |
|---|---|---|---|---|
| 1 | 0.0 | 0.0 | 0.0 | 152.3 |
| 2 | 22.5 | 21.7 | 11.3 | 152.3 |
| 3 | 45.0 | 43.5 | 22.5 | 152.3 |
| 4 | 67.5 | 65.2 | 33.8 | 152.3 |
| 5 | 90.0 | 86.9 | 45.1 | 152.3 |
| 6 | 112.5 | 108.7 | 56.4 | 152.3 |
| 7 | 135.0 | 130.4 | 67.6 | 152.3 |
| 8 | 157.5 | 152.2 | 78.9 | 152.3 |
| 9 | 180.0 | 173.9 | 90.2 | 152.3 |
| 10 | 202.5 | 195.6 | 101.4 | 152.3 |
| 11 | 225.0 | 217.4 | 112.7 | 152.3 |
| 12 | 247.5 | 239.1 | 124.0 | 152.3 |
| 13 | 270.0 | 260.8 | 135.2 | 152.3 |
| 14 | 292.5 | 282.6 | 146.5 | 152.3 |
| 15 | 315.0 | 304.3 | 157.8 | 152.3 |
| 16 | 337.5 | 326.0 | 169.1 | 152.3 |
How to use it
- Pick the large end and small end pipes: outside diameter and wall thickness.
- Pick the type: concentric, or eccentric (one flat side).
- Pick the end-to-end length: entered, or EN 10253-2 or ASME B16.9 standard from the large end.
- Pick the pattern diameters (mean line or outside diameters) and the number of marks around (8, 12, 16, 24 or 32).
- Read the half cone angle (for an eccentric reducer: the sloped side angle).
Frequently asked questions
How do I lay out a concentric reducer?
Work out the generator g = √(L² + (r1 − r2)²), then the large arc radius Rg = g × r1 / (r1 − r2) and the small arc radius Rg − g. The sector to mark has the angle θ = 360° × r1 / Rg. The radii r1 and r2 are taken on the mean line (OD − wall) or on the outside diameters, as you choose.
What pattern for a 114.3 to 60.3 reducer?
Concentric reducer 114.3 × 3.6 to 60.3 × 2.9, 150 mm long, on the mean line (Ø 110.7 / 57.4): half angle atan(27.0 / 150.0) = 10.20°, taper 18 %, generator √(150.0² + 26.7²) = 152.3 mm, large arc 152.3 × 55.4 / 26.7 = 316.4 mm, small arc Rg − g, sector 360 × 55.4 / 316.4 = 62.97°.
How do I make an eccentric reducer layout and template?
An eccentric reducer keeps one flat side: its sloped side makes atan(2Δr / L) with the axis, and the axes are offset by Δr = (D1 − D2) / 2. This oblique frustum is laid out by triangulating the generators, with the seam on the shortest generator: mark the arcs on the large and small ends and the length of each generator.
What is the largest reducer angle?
Above 30°, the calculation warns that EN 13480-3 and ASME B31.3 call for a specific check (knuckle). The small end must be smaller than the large end.
Limits
Indicative results. Pattern with no weld allowance. The standard length comes from the EN 10253-2 or ASME B16.9 tables for the large end: check that this size pair exists in the catalogue, as bought fittings have short straight ends.
Sources
- Développé d’un tronc de cône : Géométrie : triangulation des génératrices (cône droit ou oblique), joint sur la génératrice la plus courte