Ogee pipe offset calculator (S offset)
Enter the pipe diameter, offset, axis length, bend radius and pieces per bend. You get every piece of a segmented S offset, with the bend angle and straight run worked out from your sizes.
Enter your measurements
Seam
5,456.2mm
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
For each piece, draw a base line as long as the pipe circumference πD and divide it into equal parts.
Erect the ordinates
At each division, draw a line square to the base line. These are the pipe's generators.
Set off the miter heights
On each line, mark the bottom and top miter heights of that piece from the calculated pattern.
Join the curves
Connect the marks with smooth curves. End pieces have one miter; the long middle piece has two parallel miters.
Roll and fit
Roll each piece with its seam on the inside of its bend and weld the pieces in order, end piece to end piece.
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
An ogee offset is two equal segmented bends turning in opposite directions, with a straight run between them. In the shop the bend radius R is usually fixed by the standard elbow, and the offset δ and axis length L come from site. So Trueflat takes R as an input and works out the bend angle.
- Bend factor t = δ ÷ (L + √(L² + δ² − 4Rδ)).
- Bend angle α = 2 × atan t.
- Straight run g = (L − 2R sin α) ÷ cos α.
- Largest radius R_max = (L² + δ²) ÷ (4δ). At R_max the straight run is zero.
With m pieces per bend, N = m − 1 and the miter half-angle is β = α ÷ (2N). The offset has 2m − 1 pieces: end pieces Rτ long, inner pieces 2Rτ, and one middle piece 2Rτ + g that joins both bends and has two parallel miters. Each piece is a cylinder cut by planes, so the pattern is exact. Inside or outside diameters are converted to the sheet middle.
Worked example
D = 100 mm, δ = 200 mm, L = 400 mm, R = 250 mm, 2 pieces per bend. Here R equals R_max, so t = 0.5, α = 53.13°, β = 26.57°, τ = 0.5 and g = 0. The three pieces are 125, 250 and 125 mm along the axis, 500 mm in total, and the end of the offset lands at exactly 200 mm across and 400 mm up.
With the default sizes (150, 300, 800, 225, 3 pieces) the bend angle is 22.94° and the straight run is 678.23 mm.
Questions
Why does my bend radius get rejected?
The two bends must fit inside the offset box. If R is larger than (L² + δ²) ÷ (4δ), there is no straight run left and no solution exists. Shorten R or lengthen L. R must also be at least D, and the bend angle must stay between 1° and 90°.
How is this different from the duct offset?
This page is for round pipe: each piece is a cylinder developed by ordinates. The duct offset uses the same bend-angle solution for rectangular duct, with flat cheeks and wrapper strips.
Why are there two axis lengths?
The axis length you enter is the run L, measured parallel to the pipes from one end to the other; the offset is the sideways distance between the two centre lines. The axis length in the results is the total centre-line length of all pieces, which is longer because the middle runs at an angle: 500 mm for L = 400 mm in the example.
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