Oval elbow pattern calculator
Enter the oval width and height, bend radius, elbow angle and pieces. You get a segmented elbow pattern for elliptical duct, with the stations spaced along the true oval girth.
Enter your measurements
Seam
3,625.3mm
Exact geometry
- Cut length
- In the app
- Axis 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.
How to lay it out
Draw the stretch-out
Draw a base line as long as the calculated oval girth.
Mark the girth stations
Mark the stations along the base line at the calculated girth distances. They are not evenly spaced, because the oval is flatter on its long sides.
Set off the miter heights
At each station draw a line square to the base and mark the bottom and top miter heights for that piece.
Join and cut
Join the marks with smooth curves and cut. The seam is on the throat, at one end of the oval width.
Form and assemble
Form each piece to the oval and weld the pieces in order, end pieces at the ends.
Good to know
- FabLayout runs the same code as Trueflat; the result is exact geometry.
- Source: No published source. Miter planes bisect the angle between neighbouring piece axes and each piece is developed in closed form on the middle of the sheet; checked against an independent 3D reference implementation in Trueflat.
Method and formula
The oval elbow follows the same axis as a round segmented elbow: N = pieces − 1, miter half-angle β = α ÷ (2N), τ = tan β, end pieces Rτ long and inner pieces 2Rτ. Only the cross-section changes. The oval width A lies in the plane of the bend and the height B across it.
On a round pipe the girth stations are evenly spaced. On an oval they are not. A point at angle θ on the oval sits at a girth distance X(θ) = (B ÷ 2) × E(θ | 1 − A² ÷ B²), the incomplete elliptic integral of the second kind. Trueflat evaluates it directly, so the stretch-out and every station are exact, not stepped off with dividers. The miter heights on each line come from the same bisecting planes as the round elbow.
- Girth = 2B × E(1 − A² ÷ B²), the full perimeter of the oval.
- Limits: B between A ÷ 20 and 20A; R between A and 100A.
This shape takes measurements to the sheet middle only. An offset oval is no longer an exact oval, so inside and outside sizes are not converted.
Worked example
A = 200 mm, B = 100 mm, R = 300 mm, α = 90°, 4 pieces: N = 3 and β = 15°. The oval girth is 484.42 mm and the quarter-girth station sits at 121.11 mm. The throat generator of the end piece is 53.59 mm, the shortest in the elbow, and the axis length is 482.31 mm.
Questions
Which way round do width and height go?
The width A lies in the plane of the bend, so it is the dimension that runs from throat to heel. B is the height across the bend. B may be larger than A; the elbow then bends the oval on its flat side.
Why can I not enter inside or outside sizes?
Offsetting an oval by the sheet thickness gives a curve that is no longer an oval. Enter the sizes to the middle of the sheet for this shape.
How is this different from a round segmented elbow?
The miter planes and piece lengths are the same. The difference is the girth: the stations along the stretch-out follow the oval, so they bunch up where the oval turns tightly and spread out along its flatter sides.
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