FabLayout

Oval to round transition calculator

For an elliptical duct going into a round one: enter both axes of the ellipse, the round diameter and the height. The pattern joins points with parallel tangents, so the sheet does not stretch.

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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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848.4 mm1,147.2 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

602.1mm

Approximate, within ±10.8 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. Divide both ends by tangent direction

    Mark points on the ellipse and on the circle at the same tangent directions, in steps of 90° ÷ n, starting at the end of the B axis.

  2. Join matching points

    Join each ellipse point to the circle point with the same tangent direction; these lines are straight on the finished part.

  3. Find the true lengths

    Work out the true length of every joining line and of the outward diagonal of each four-sided piece from the plan distance and H.

  4. Lay out the strip

    Start from the seam at the end of the B axis and build the pieces one after another from their true lengths.

  5. Close

    Finish on the second seam line, draw smooth curves through both edges 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 ellipse and the circle, points joined at parallel tangents, triangulated; checked against a separate reference implementation in Trueflat.

Method and formula

The bottom is an ellipse with full axes A and B, the top a circle of diameter D, both centred. Older layouts divide both curves into equal parts and join them, which gives a warped surface that has to be stretched into place. Trueflat joins points whose tangents are parallel instead. Along each such line the surface has a single tangent plane, so it unrolls without stretching; it is the outer envelope of the two openings.

  • Ellipse point for tangent direction θ: (a² cos θ, b² sin θ) ÷ √(a² cos² θ + b² sin² θ), with a = A/2, b = B/2.
  • The ellipse may be at most 4:1.
  • Each four-sided piece is split along its outward diagonal.
  • Accuracy: both curves are drawn as 4n chords. Each edge is short by at most π³R ÷ (48 n²), with R = (larger semi-axis)² ÷ smaller semi-axis.

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

A = 600, B = 300, D = 350, H = 300 mm, six sections per quarter. The seam line from the end of the B axis to the circle is √(300² + 25²) = 301.04 mm, both edges 602.08 mm. The ellipse is 1453.27 mm round and its chords are 4.09 mm short; the circle is 1099.56 mm and its chords are 3.14 mm short, both inside the 10.77 mm bound.

Questions

What is the difference between oval to round and flat oval to round?

Oval to round is for a true ellipse. A flat oval has straight sides and half-circle ends; it has its own calculator because its pattern contains flat triangles.

Why not divide both curves into equal parts?

Equal division joins points whose tangents point different ways. The surface between them is warped and has to be stretched into shape. Joining points with parallel tangents gives a surface that bends without stretching, so the pattern fits.

Is the pattern exact?

The surface itself unrolls exactly; the only error is drawing the curves with chords. Each edge is short by at most π³R ÷ (48 n²), where R is the largest radius of curvature of the ellipse. Thickness conversion for inside or outside dimensions is approximate and the deviation is shown.

How is this different from the ventilation neck?

The ventilation neck has the round end at the bottom and the ellipse on top, and its elliptical mouth can be tilted up to 45°. Here the ellipse is the bottom and both ends are level.

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