Piping
Pipe saddle cut calculator
In short
A branch is the intersection of two cylinders. Each branch generator φ meets the header at s(φ) = [√(Rc² − (e + r sin φ)²) − r cos φ cos β] / sin β; its length from the square end is g(φ) = L − s(φ), laid out on a development π × d wide.
Calculation
Example calculated with the tool’s default values.
Inputs
- Header (run pipe)
- DN100 · 114.3 × 3.6 mm
- Branch
- DN50 · 60.3 × 2.9 mm
- Angle between axes
- 90°
- Axis offset
- 0 mm
- Fit-up
- Set-on
- Branch height from header axis
- 150 mm
- Layout surface
- Branch outside
- Generators
- 16 (every 22.5°)
- Template to print
- Branch cut
Results
- Longest generator
- 101.5 mm
Worked example
Every value in this section belongs to the example, calculated with the tool’s default values.
Other results of the example
- Shortest generator
- 92.8 mm
- Saddle depth
- 8.6 mm
- Generator 1 (0°) heel
- 92.8 mmfrom the square end
- Generator 2 (22.5°)
- 94.0 mmfrom the square end
- Generator 3 (45°)
- 97.0 mmfrom the square end
- Generator 4 (67.5°)
- 100.1 mmfrom the square end
- Generator 5 (90°)
- 101.5 mmfrom the square end
- Generator 6 (112.5°)
- 100.1 mmfrom the square end
- Generator 7 (135°)
- 97.0 mmfrom the square end
- Generator 8 (157.5°)
- 94.0 mmfrom the square end
- Generator 9 (180°) crotch
- 92.8 mmfrom the square end
- Generator 10 (202.5°)
- 94.0 mmfrom the square end
- Generator 11 (225°)
- 97.0 mmfrom the square end
- Generator 12 (247.5°)
- 100.1 mmfrom the square end
- Generator 13 (270°)
- 101.5 mmfrom the square end
- Generator 14 (292.5°)
- 100.1 mmfrom the square end
- Generator 15 (315°)
- 97.0 mmfrom the square end
- Generator 16 (337.5°)
- 94.0 mmfrom the square end
- Template width (π × OD)
- 189.4 mm
- Hole: length along header
- 54.5 mm
- Hole: wrapped width
- 56.8 mm
- Template drawn on the branch OD: bevel afterwards to the welding procedure.
Step-by-step calculation
Radii used
r = d / 2 ; Rc = D / 2 (posé)
r = 30.15 mm ; Rc = 57.15 mm
Contact of generator φ
s(φ) = [√(Rc² − (e + r sin φ)²) − r cos φ cos β] / sin β
s(0°) = 57.15 mm ; s(90°) = 48.55 mm
Generator length
g(φ) = L − s(φ)
150.0 − 57.15 = 92.8 mm (φ = 0°)
Depth
p = s max − s min
57.15 − 48.55 = 8.6 mm
Developed width
l = π × d
π × 60.3 = 189.4 mm
Template ordinates, point by point
| No. | Angle (°) | Position around (mm) | Ordinate (from the high point) (mm) | Length from the square end (mm) |
|---|---|---|---|---|
| 1 | 0.00 | 0.0 | 0.0 | 92.8 |
| 2 | 22.50 | 11.8 | 1.2 | 94.0 |
| 3 | 45.00 | 23.7 | 4.1 | 97.0 |
| 4 | 67.50 | 35.5 | 7.2 | 100.1 |
| 5 | 90.00 | 47.4 | 8.6 | 101.5 |
| 6 | 112.50 | 59.2 | 7.2 | 100.1 |
| 7 | 135.00 | 71.0 | 4.1 | 97.0 |
| 8 | 157.50 | 82.9 | 1.2 | 94.0 |
| 9 | 180.00 | 94.7 | 0.0 | 92.8 |
| 10 | 202.50 | 106.6 | 1.2 | 94.0 |
| 11 | 225.00 | 118.4 | 4.1 | 97.0 |
| 12 | 247.50 | 130.2 | 7.2 | 100.1 |
| 13 | 270.00 | 142.1 | 8.6 | 101.5 |
| 14 | 292.50 | 153.9 | 7.2 | 100.1 |
| 15 | 315.00 | 165.8 | 4.1 | 97.0 |
| 16 | 337.50 | 177.6 | 1.2 | 94.0 |
How to use it
- Pick the header (run pipe) and the branch: outside diameter and wall thickness.
- Enter the angle between axes (30° to 90°), the axis offset (0 = axes intersect) and the fit-up: set-on or set-in.
- Enter the branch height, measured along its axis from the header axis to the square-cut end.
- Pick the layout surface (branch outside, mid-wall or inside) and the number of generators (8, 12, 16, 24 or 32).
- Read the longest generator.
Frequently asked questions
How does a pipe saddle cut calculator work?
With r the branch radius, Rc the header radius, β the angle between axes and e the axis offset, generator φ meets the header at s(φ) = [√(Rc² − (e + r sin φ)²) − r cos φ cos β] / sin β. Its length from the square end is g(φ) = L − s(φ), and the saddle depth p = s max − s min. Set-on: Rc is the header outside radius; set-in: its inside radius.
What does a pipe notching calculation give for a 60.3 branch on a 114.3 header?
Set-on 60.3 × 2.9 branch at 90° on a 114.3 × 3.6 header, 150 mm high: r = 30.15 mm, Rc = 57.15 mm. At the heel, s(0°) = 57.15 mm, so the generator is 150 − 57.15 = 92.8 mm; at the flank, s(90°) = 48.55 mm. Depth: 57.15 − 48.55 = 8.6 mm. The hole in the header is 54.5 mm long along its axis.
How do I make a pipe saddle template?
The template is the development of the intersection curve on the branch outside: width l = π × d (189.4 mm for a 60.3 OD), with one ordinate per generator. It wraps around the branch, generator 1 at the heel. With 16 generators, one point every 22.5°; you can also pick 8, 12, 24 or 32.
Does the pipe coping calculator handle angled branches?
Yes: enter the angle between axes, from 30° to 90°. Generator 1 (0°) is the heel, on the obtuse side; the generator at 180° is the crotch, on the acute side. Below 45°, the calculation warns that the weld on the crotch side is hard to reach.
Should I lay out on the branch outside or inside?
The layout surface is the branch surface that meets the header: outside by default, mid-wall or inside. The curve is computed on that diameter, then carried onto the outside circumference, where the template always wraps. Laid out on the outside for a set-on branch, bevel afterwards to the welding procedure.
Limits
Indicative results. The branch cannot be larger than the header; the axis offset is limited so the branch stays on the header; a set-in branch must fit in the header bore. With nearly equal diameters, the cut turns vertical at the flanks and fit-up is tricky. Set-on and set-in fit-ups: ASME B31.3, § 328.5.4.
Sources
- Intersection de deux cylindres : Géométrie : développé de la courbe d’intersection sur la circonférence extérieure du piquage
- Piquage posé / pénétrant : ASME B31.3, § 328.5.4 et fig. 328.5.4D (raccordements de piquage soudés)