FabLayout

Pipe on cone template calculator

For a round pipe branch on a cone or concentric reducer: enter the cone's diameters and length, the branch size, angle and offset. You get the branch cut and the hole in the cone pattern.

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Enter your measurements

Your dimensions are measured to the

Export from the Trueflat app

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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1,190.8 mm828.0 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

1,802.7mm

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. Lay out the cone

    Swing the large and small arcs of the cone from its apex point and mark the sector angle from the drawing, with the seam on the bottom of the cone.

  2. Draw the branch stretchout

    Draw the branch mouth line as long as the branch circumference, divide it into equal parts and square a line from each point.

  3. Mark the branch cut

    On each line, mark the cut point at the distance given for that line and join the points.

  4. Mark the hole on the cone

    For each hole point, swing its distance from the apex and step its angle from the centre line of the sector, then join the points.

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 main part is a truncated cone whose radius falls in a straight line from the large end (x = 0) to the small end. The branch is a round pipe at the branch angle γ, leaning toward the small end when γ is under 90°.

  • Cut: each branch line meets the cone where a quadratic equation has its outer root; this gives the cut point on the branch.
  • Branch pattern: a strip as for a pipe tee, with each line cut at its own length.
  • Cone pattern: the cone unrolls into a sector from its apex. A hole point at radius ρ lies ρ × s ÷ (r1 − r2) from the apex, where s is the slant length, and its angle around the cone is multiplied by sin β, the half-angle of the cone.

The branch stands square to the cone side when its angle is 90° minus the cone half-angle. The cone half-angle must be between 1° and 89°. 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

Cone 400 to 200 mm over 400 mm, foot at 200 mm, branch 100 mm, 300 mm long, 90°: the cone radius at x is 200 − 0.25 × x. The seam line of the branch meets the cone at x = 250, where the radius is 137.5 mm, so the cut is 137.5 mm from the cone axis. The opposite line meets at x = 150 and 162.5 mm, and the lines at the sides at 141.42 mm. The shortest branch line is 137.5 mm.

Questions

How is this different from the tapered branch and cone on cone pages?

Here the main part is a cone and the branch is a straight pipe. On the tapered branch page the branch is a cone and the main is a pipe. Cone on cone covers both being cones.

Which way can the branch lean?

Toward the small end of the cone, from 90° down to 20°. A branch leaning toward the large end is not covered in this version.

Why is the hole not symmetrical along the cone?

The cone gets narrower toward the small end, so the wall is closer to the axis on that side and the branch reaches further down. The branch is shortest on the side toward the large end.

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