FabLayout

Tapered branch on pipe calculator

For a conical branch that narrows away from a round main pipe, such as a reducing take-off: enter the main diameter, the branch root and mouth diameters, length and angle. You get the branch sector and the hole.

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Enter your measurements

Your dimensions are measured to the

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1:1 PDF and DXF files of this flat pattern are made in Trueflat, ready for print, plasma, laser or waterjet. It works offline on site.

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1,208.9 mm600.0 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

2,312.5mm

Exact geometry

Cut length
In the app
Cut curve length
In the app
Sheet size
In the app

Every result is in Trueflat

The free web version shows the main result and the drawing. Trueflat gives you every mark and measurement, and exports a cut sheet. It is free to download.

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How to lay it out

  1. Find the branch apex

    Set a centre point for the apex of the branch cone. All branch lines run out from this point.

  2. Swing the mouth arc

    Swing the mouth arc at the mouth radius from the drawing and step the branch sector angle along it, divided into equal parts.

  3. Mark the cut on each radial line

    Draw a line from the apex through each division and mark the cut point at its distance from the apex, then join the points.

  4. Lay out the main pipe and hole

    Draw the main pipe rectangle, then mark each hole point by its distance along the pipe and its arc from the top line.

Good to know

  • FabLayout runs the same code as Trueflat; the result is exact geometry.
  • Source: No published source. Method: each straight line of the branch is intersected with the main surface and both parts are unrolled, developed on the sheet middle; checked by two independent implementations in Trueflat.

Method and formula

The branch is a truncated cone that stands on a round main pipe and narrows toward its mouth. Its lines all run to one apex, so the branch unrolls into a sector, as a cone does.

  • Root diameter d1 is the diameter of the branch cone at the main pipe axis, where the branch axis meets it. The mouth diameter d2 is at the branch length.
  • Cut: each branch line meets the main pipe at the outer root of a quadratic equation.
  • Branch pattern: a point at branch radius ρ lies ρ × s ÷ (rb1 − rb2) from the apex, where s is the slant length of the branch, and the sector angle is 360° × (rb1 − rb2) ÷ s.

The mouth must be smaller than the root; a branch that widens toward its mouth is not covered in this version. The pattern is exact. Enter measurements to the middle of the sheet. Which face of the branch seats on the main depends on how you fit and weld it, so this shape is developed on the sheet middle only.

Worked example

Main 300 mm, 600 mm long, foot at 300 mm, branch 150 mm at the root and 100 mm at the mouth, 300 mm long, 90°: the lines in line with the main pipe meet it at its top, 150 mm from the main axis; the lines at the sides at 135.81 mm. On the branch pattern the mouth arc has a radius of 602.08 mm and the cut point on the seam line is 752.60 mm from the apex.

Questions

Where is the root diameter measured?

At the main pipe axis, where the branch axis meets it, not where the branch touches the pipe wall. The branch is narrower than that where it actually meets the wall.

When do I use this page instead of the pipe tee or pipe on cone?

Use it when the branch itself is tapered and the main is a straight pipe. For a straight branch on a pipe use the pipe tee; for a straight branch on a cone use pipe on cone; if both are cones use cone on cone.

Why does the pattern need such a long radius?

The branch is developed from its apex. When the root and mouth diameters are close, the apex is far away and the radii grow quickly.

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