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Eccentric reducer with angled top flat pattern calculator

For a round-to-round piece whose top is offset and tilted, like a flaring collar. Enter both diameters, height, offset and top tilt; you get a triangulated pattern.

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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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631.5 mm569.5 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

571.3mm

Approximate, within ±4.9 mm

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. Divide both ends

    Divide the bottom circle and the tilted top circle into the same even number of equal parts, numbering both in the same direction.

  2. Draw elements and diagonals

    In plan, join each bottom point to the top point with the same number, and each bottom point to the next top point.

  3. Find the true lengths

    For each line, take its plan length and the height difference between its ends as the legs of a right triangle; the hypotenuse is the true length.

  4. Lay out the triangles

    Start with a bottom chord, then swing the diagonal and the next element to place each new point. Work around until the strip is complete.

  5. Draw the edges and seam

    Join the points on each edge, draw the closing element as the second seam line and add allowance.

Good to know

  • This pattern is approximate; the result card shows how close it is.
  • Source: Kittredge, The New Metal Worker Pattern Book (1917), Problem 194 "Flaring Collar", Figs. 632–635, p. 362

Method and formula

Two circles in non-parallel planes do not, in general, lie on one cone, so there is no single apex and no exact flat pattern. Trueflat does what the pattern books do: it divides both ends into n equal parts, splits each four-sided panel along the diagonal from bottom point k to top point k + 1, and lays the triangles down from their true lengths.

The pattern is approximate in two ways:

  • Chords instead of arcs. The two ends come out short by at most π³(R + r) ÷ (3n²) together.
  • Warped panels. The four corners of a panel do not lie quite in one plane. The largest out-of-plane distance is 0 when the top is not tilted and roughly halves when you double n.

The diagonal direction is a choice; books leave it open. Thickness is taken to the middle of the sheet only.

Worked example

Bottom 300 mm, top 200 mm, height 250 mm, offset 80 mm, tilt 20°, n = 24: the bound on the end shortfall is 4.49 mm and the largest panel warp is 3.58 mm. With n = 48 these drop to 1.12 mm and 1.78 mm. The two seam edges total 570.42 mm.

Questions

When do I use this instead of the eccentric reducer?

Use the eccentric reducer when both ends are parallel: it is exact. Use this page when the top end is tilted, for example a collar meeting a sloping surface or an offset reducer between two pipes that are not parallel.

How accurate is the pattern?

It is approximate. The ends are short by at most π³(R + r) ÷ (3n²) in total, and each panel is slightly warped. In the 300/200/250 mm example with 24 divisions the bound is 4.49 mm and the warp 3.58 mm; with 48 divisions they are 1.12 mm and 1.78 mm. Use more divisions for a closer fit.

Why are some tilts rejected?

The tilt is limited to 60° and the low side of the top must stay at least 5 mm above the base. If the strip would wrap over itself on the sheet, the calculator asks you to reduce the tilt or increase the height.

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