FabLayout

Cone to cone intersection calculator

For a conical branch on a conical main, such as a tapered take-off on a reducer: enter both cones, the branch length, angle and offset. You get both sector patterns, the branch cut and the hole.

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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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1,106.9 mm828.0 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

1,960.8mm

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 main cone

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

  2. Lay out the branch cone

    From a second apex, swing the branch mouth arc and step the branch sector angle along it in equal parts.

  3. Mark the branch cut

    Draw a line from the branch apex through each division and mark the cut point at its distance from the apex.

  4. Mark the hole

    On the main cone, place each hole point by its distance from the main apex and its angle from the centre line of the sector.

  5. Join and cut

    Join the points into smooth curves on both patterns, check each matching pair and cut.

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

This is the most general round intersection in Trueflat: both the main and the branch are truncated cones, and the branch can be tilted and offset. The pipe tee, pipe on cone and tapered branch pages are special cases of it.

  • Cut: each branch line meets the main cone at the outer root of a quadratic equation. The same root gives the point on the branch and the point in the hole.
  • Patterns: each cone unrolls into a sector from its own apex. A point at radius ρ lies ρ × s ÷ (r1 − r2) from the apex, and its angle around the cone is multiplied by sin β, the half-angle of that cone.
  • Checks: if a branch line is flatter than the side of the main cone, it would cut the main twice; if the two roots are closer than 2 mm, the branch is almost tangent. Both are rejected.

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 cone 400 to 200 mm over 400 mm, foot at 200 mm, branch 150 to 100 mm, 300 mm long, angle 75°, offset 20 mm. Along the branch axis the cut lies 145.04, 118.10, 143.23 and 138.89 mm from the foot on the lines at 0°, 90°, 180° and 270°. The shortest branch line is 153.45 mm, and the hole stays 101.67 mm from the nearer end of the main cone.

Questions

Should I use this page if only one part is a cone?

You can, but the simpler pages ask for fewer inputs: pipe on cone when only the main is a cone, tapered branch when only the branch is. With a straight pipe on a straight pipe, use the pipe tee.

Why does it say the branch is too shallow?

A branch line is flatter than the side of the main cone, so it would pass through the cone wall twice. Increase the branch angle.

Why does it say the branch is almost tangent?

The branch only grazes the main cone at some line, so the cut point cannot be placed reliably. Change the offset, the angle or the branch size.

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