FabLayout

Eccentric reducer flat pattern calculator

For a reducer whose small end is off-centre but parallel to the large end. Enter both diameters, the height and the offset; you get the pattern laid out around the apex.

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590.6 mm519.0 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

500.9mm

Approximate, within ±0.1 mm

Slant length
In the app
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. Find the apex

    Extend the sides in the elevation until they meet. The apex lies at height H × R ÷ (R − r), offset X × R ÷ (R − r) from the large-end centre.

  2. Find each element's true length

    Divide the large-end circle into equal parts. For each point, take the plan distance to the apex and the apex height as the two legs of a right triangle; the hypotenuse is the element's true length.

  3. Lay out from the apex

    Draw the shortest element from a centre point. Swing the next element length from the centre and the large-end chord from the last point; the crossing is the next point. Repeat around the circle.

  4. Mark the small end

    On each element, mark the small end at r ÷ R of its length from the apex.

  5. Draw both edges

    Bend a batten through the large-end and small-end points, close with the seam on the shortest element and add your 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 167, Figs. 540–541, p. 312; same principle in Problem 163, p. 307

Method and formula

When both ends are round and parallel, an eccentric reducer is part of a scalene (oblique) cone: every element still runs to one apex. The pattern is exact, but unlike a concentric reducer its edges are not circular arcs, because the elements have different lengths.

  • Apex at height h = H × R ÷ (R − r), offset a = X × R ÷ (R − r).
  • Element length to the large end at plan angle θ: √((R − a)² + h² + 4Ra sin²(θ ÷ 2)), shortest on the side the small end leans toward.
  • Small end at r ÷ R of each element length.

The angle each element turns through on the pattern has no closed formula. Trueflat integrates it numerically instead of stepping chords, so the unrolled large edge is exactly π × D long. Thickness is taken to the middle of the sheet only.

Worked example

One side vertical: large end 60 mm, small 30 mm, height 20 mm, offset 15 mm. The apex is 40 mm above the large end, directly over the rim. The shortest element is the vertical side, 40 mm to the apex; the longest is √(60² + 40²) = 72.11 mm. The pattern spans 181.69°, and its large edge is 188.50 mm, which is π × 60.

Questions

How is this different from a concentric reducer?

In a concentric reducer the small end sits on the centre line, every element has the same length and the pattern is a ring between two arcs. Here the small end is offset, so each element has its own length and both edges are irregular curves. With an offset of 0 this page gives the concentric pattern.

What if the ends are not parallel?

Then the surface is no longer a single cone. Use the eccentric reducer with an angled top, which triangulates between the two ends.

Is the pattern exact?

The reducer is part of one cone, so it unrolls without stretching. The angles have no closed formula; Trueflat integrates them numerically and draws the edges as straight chords through the curve samples. More samples bring the drawn edges closer to the true curves.

Why only middle-of-sheet thickness?

Offsetting an oblique cone by half the sheet thickness does not give another cone with the same apex, so there is no exact inside or outside version. Enter your diameters to the middle of the sheet.

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