FabLayout

Double offset boot calculator

For a boot whose round end is offset both ways, even past the edge of the rectangle: enter the diameter, rectangle, both offsets and height. One-piece triangulated 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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841.3 mm924.3 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

702.8mm

Approximate, within ±2.9 mm

Cut length
In the app
Top edge (chords)
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 both openings in plan

    Draw the rectangle and the circle with its centre moved by dx and dy; in plan the two may just touch.

  2. Mark the tangent points

    On each side of the rectangle, mark the circle point whose tangent runs parallel to that side; these are the tops of the flat triangles.

  3. Take the true lengths per corner

    Split each corner arc into the chosen sections and work out √(plan distance² + H²) from the corner to every point.

  4. Lay out from the seam

    Draw the seam line from the middle of an A side, then add the corner fans and flat triangles one after another.

  5. Check and close

    The second seam line must match the first. Curve the round edge, keep the rectangle edges straight and add your allowances.

Good to know

  • This pattern is approximate; the result card shows how close it is.
  • Source: No published source checked for this shape. Method: outer envelope of the two openings (flat triangles and oblique cone corners), triangulated; checked against a separate reference implementation in Trueflat.

Method and formula

A double-offset boot joins a rectangular opening to a round one whose centre is moved along both the width and the depth, often so far that the round end overhangs the rectangle in plan. It is built like a square to round: four flat triangles and four oblique cone corners, the outer envelope of the two openings. With the circle this far out, the lines on one side get long and shallow.

  • Offset limits: |dx| ≤ (A + D)/2 and |dy| ≤ (B + D)/2, so the two openings at least touch in plan.
  • Slope: no line may run more than 10 × H horizontally, about 5.7° from flat.
  • Accuracy: the round edge is drawn as n chords per corner, shorter than πD by at most π³D ÷ (96 n²).

It does not matter whether the round end is drawn above or below: turning the part over gives the same pattern.

With sheet thickness and inside or outside dimensions, each opening is moved by one amount to the middle of the sheet. This is approximate: the calculator shows how far the opening can be off, and asks for middle-of-sheet dimensions if that is more than 1 mm.

Worked example

D = 250, A = 400, B = 300 mm, dx = 250, dy = 120 mm, H = 200 mm, two sections per corner. The round end overhangs the rectangle. Each seam edge is 351.46 mm (702.92 mm together). The lines from the middle of the other sides to their tangent points are 291.59, 333.95 and 400.03 mm. The round edge in chords is 765.37 mm, 20.03 mm short of πD and inside the 20.19 mm bound.

Questions

When do I need a boot instead of an eccentric square to round?

When the round end has to sit so far over that its centre is no longer above the rectangle. The eccentric square to round keeps the circle centre over the base; the boot lets the openings move apart until they only touch in plan.

Is the pattern exact?

The flat triangles are exact. The cone corners are drawn with chords, so the round edge is short of πD by at most π³D ÷ (96 n²). Thickness conversion for inside or outside dimensions is approximate, and the page shows the deviation.

Why is my offset refused?

Either the openings no longer meet in plan (|dx| above (A + D)/2 or |dy| above (B + D)/2), or a line would run more than ten times the height sideways. Reduce the offset or increase the height.

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