FabLayout

Helical segmented elbow calculator

Enter the pipe diameter, helix radius, pitch, sweep and number of pieces. You get one segment pattern that you cut several times to build a pipe that climbs in a helix.

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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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2,053.4 mm186.0 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

4,897.8mm

Exact geometry

Cut length
In the app
Axis 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. Draw the stretch-out

    Draw a base line as long as the pipe circumference πD and divide it into equal parts.

  2. Erect the ordinates

    At each division, draw a line square to the base line.

  3. Set off both miters

    On each line, mark the bottom and top miter heights from the calculated pattern. All middle pieces share the same pattern.

  4. Cut the pieces

    Join the marks with smooth curves and cut one piece per segment; the two end pieces are cut square on their outer end.

  5. Assemble towards the axis

    Roll each piece with its seam facing the helix axis and weld them in order. Keeping every seam on the inner side sets the twist between pieces.

Good to know

  • FabLayout runs the same code as Trueflat; the result is exact geometry.
  • Source: No published source. Miter planes bisect the angle between neighbouring piece axes and each piece is developed in closed form on the middle of the sheet; checked against an independent 3D reference implementation in Trueflat.

Method and formula

A smooth helical pipe cannot be unrolled from flat sheet: its surface is curved in two directions. In the shop the helix is built from straight cylinder pieces instead, and that version is exact.

Trueflat places m + 1 corner points on the helix at equal steps of the sweep Φ: radius Rh, rising p per full turn. Each piece is a straight cylinder along the chord c between two neighbouring corners, so all pieces are the same length. Neighbouring pieces meet on the plane that bisects the angle between their axes, and the miter half-angle is

  • β = asin(2 Rh sin²(Φ ÷ 2m) ÷ c).

With no pitch (p = 0) the helix flattens to a plane bend and β = Φ ÷ (2m). The seam of every piece is on the side that faces the helix axis. Inside or outside diameters are converted to the sheet middle.

Limits: Rh between D and 100D, so the coil does not cut through its own axis; β no more than 67.5°; and the two open ends at least one diameter apart, so a coil close to a full turn does not run into itself.

Worked example

D = 100 mm, Rh = 300 mm, p = 400 mm, Φ = 180°, 6 pieces: chord c = 158.83 mm and β = 14.66°. The shortest generator is 132.71 mm and the two ends of the coil are 632.46 mm apart.

Flat check: D = 80, Rh = 250, p = 0, Φ = 90°, 3 pieces gives c = 2 × 250 × sin 15° = 129.41 mm and β = 15°.

Questions

Is this a true helix?

It is a segmented helix: straight pieces whose corners sit on the helix. A smooth helical tube cannot be unrolled flat, which is why fabricators build it from miter-cut pieces. More pieces follow the helix more closely.

How is this different from a segmented elbow?

A segmented elbow turns in one plane. A helical elbow also climbs by the pitch as it turns, so it suits stair rails, coils and chutes that wrap round a column.

Why is my helix radius rejected?

Rh must be at least the pipe diameter, or the coil cuts through its own axis. It must also leave the two pipe ends at least one diameter apart, which rules out some tight near-full turns with little pitch.

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