FabLayout

Diagonal duct offset calculator (rolling offset)

Enter duct width and depth, the offset in two directions, the run length and the end piece length. You get the three straight pieces of a rectangular duct offset that moves both ways.

Get TrueflatRead the steps

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.

App StoreGoogle Play
3,134.7 mm652.9 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

5,461.9mm

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.

App StoreGoogle Play

How to lay it out

  1. Draw the girth line

    Draw a base line as long as the duct girth 2A + 2B and mark the fold points at B, A + B and A + 2B.

  2. Erect the corner lines

    At the start, the three fold points and the end, draw lines square to the base line.

  3. Set off the miter heights

    On each of the five lines, mark the height of the miter cut for that piece from the calculated pattern.

  4. Join with straight lines

    Join the marks with straight lines; every face is flat. The middle piece has two parallel miter edges.

  5. Fold and assemble

    Fold each piece on its corner lines, close the seam and fit the three pieces miter to miter.

Good to know

  • FabLayout runs the same code as Trueflat; the result is exact geometry.
  • Source: No published source. Three straight duct pieces meet on two parallel miter planes that bisect the run and the sloping direction; each flat face is developed in closed form on the middle of the sheet. Checked against an independent reference implementation in Trueflat.

Method and formula

A diagonal offset (rolling offset) moves a rectangular duct by dx and dy at the same time over a run L. It is made of three straight pieces: an end piece Lu long, a sloping middle piece, and a second end piece Lu long. The duct comes out parallel to where it went in.

The middle piece runs between the axis points V1 = (0, 0, Lu) and V2 = (dx, dy, L − Lu). Its length is L_mid = |V2 − V1| and its slope from the run is φ = acos(d_z), where d is the unit direction from V1 to V2. The result labelled sector angle is this slope. Both miter planes have the same normal n, which bisects the run direction and d, so the two miters are parallel.

  • Corner shift q = (e · n) ÷ n_z for each duct corner e. This is how far the miter moves that corner along the duct.
  • End piece: corner heights Lu − q.
  • Middle piece: from q up to L_mid + q.

Each face is a flat trapezoid or parallelogram, so the pattern is exact, with fold lines at the four duct corners. Inside or outside sizes are converted to the sheet middle.

Worked example

A = 300 mm, B = 200 mm, dx = 300 mm, dy = 400 mm, L = 1400 mm, Lu = 100 mm. V2 − V1 = (300, 400, 1200), so L_mid = 1300 mm and φ = 22.62°. The corner shifts are 2, 34, −2 and −34 mm, so the first end piece has corner heights 98, 66, 102 and 134 mm. The middle piece faces are parallelograms 1300 mm long.

Questions

How is this different from the duct offset?

The duct offset moves the duct one way, with two bends and an optional straight run. The diagonal offset moves it in two directions at once and uses only straight pieces and two miters. Choose it for a rolling offset round a beam or another duct.

What is the end piece length?

The length of each straight piece before and after the slope, measured along the duct axis. The run must leave at least 5 mm for the sloping piece, and no corner of an end piece may come out shorter than 5 mm.

Similar calculators

More in TrueflatConeTruncated coneCone by triangulationSee what the app does