FabLayout

Multi-stage cone flat pattern calculator

A run of concentric cones and straight sections on one axis. Enter each diameter and stage height; you get a separate pattern for every stage, with the joints corrected for sheet thickness.

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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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1,901.7 mm558.3 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

806.8mm

Exact geometry

Cut 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. Split the run into stages

    List the diameters from bottom to top and the height of each stage. Each stage starts at the diameter where the last one ended.

  2. Lay out the cone stages

    For a stage whose diameter changes, swing two arcs from one centre at the pattern radii L = s × r ÷ (R − r), using its own slant length s, and mark its sector angle 360° × (R − r) ÷ s.

  3. Lay out the straight stages

    For a stage with equal diameters, draw a rectangle one circumference long and one stage height high.

  4. Label and allow

    Mark each piece with its stage number and which edge joins which, and add seam allowances before cutting.

Good to know

  • FabLayout runs the same code as Trueflat; the result is exact geometry.
  • Source: Kittredge, The New Metal Worker Pattern Book (1917), Problem 124, Figs. 452–458, p. 252 (development of each conical band and the straight band). The chain of stages and the thickness rule at the joints are Trueflat's own, checked by an independent profile-distance test

Method and formula

Each stage is either a truncated cone or a cylinder, and each unrolls exactly on its own. A cone stage gives a ring segment between two arcs; a straight stage gives a rectangle. Neighbouring pieces share a joint circle, so the edges that meet have the same length.

Without thickness, the joints sit at the heights you enter. With thickness, each stage is developed on the middle of its own sheet. Where two stages with different slopes meet, their middle surfaces cross a little above or below the drawn joint, and Trueflat moves the joint there. The two end planes stay fixed.

Worked example

Diameters 60, 30 and 30 mm, stage heights 20 and 25 mm, thin sheet. Stage 1 is a cone: slant 25 mm, pattern radii 50 and 25 mm, sector angle 216°. Stage 2 is a cylinder: a 94.25 × 25 mm rectangle.

The same part measured inside with 4 mm sheet: the joint moves up to 20.67 mm, where both middle surfaces have a radius of 17 mm. Stage 1 then has radii 54.17 and 28.33 mm and the same 216°. Stage 2 becomes 106.81 × 24.33 mm.

Questions

Why does the joint height change with thickness?

Each stage is laid out on the middle of its own sheet. When a cone meets a cylinder, or two different cones meet, those middle surfaces cross slightly off the joint you drew. Using that crossing keeps neighbouring edges the same length, so the pieces fit.

How many stages can I enter?

From 2 to 12. A single stage is a plain truncated cone, which has its own page. Every cone stage must slope between 1° and 89°.

Can a stage widen upward?

Yes. A stage that gets wider toward the top is laid out the same way; its top edge is then the outer arc of the pattern.

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