Segmented Bend flat pattern

What it is

A segmented bend -- a lobster back, in British shops -- is built from lengths of tube cut at an angle and welded together, approximating a radius with straight pieces. Each intermediate gore is a cylinder cut at both ends; the two end gores take a single cut. The more gores, the smoother the bend.

Where it is used

Large-diameter bends in exhaust and ventilation, boiler ducting, process pipework where no forged elbow exists in the required size.

Measurements the calculation needs

• H Bend radius (to the tube axis)
• D Outside diameter of the tube
• ANG Total angle of the bend
• S Number of gores
• DV Divisions
• THK Plate thickness

Calculate with your own measurements

No account needed: enter the measurements in millimetres or inches and get the figures and the drawing. The scaled PDF template, the DXF for the cutting table and the 3D model take a free account.

Diameters and sides are outside measurements. The flat pattern already allows for the plate thickness, working on the mean line.

Units: mm inches

Bend radius (to the tube axis) H (in)

Outside diameter of the tube D (in)

Total angle of the bend ANG (°)

Number of gores S

Divisions DV

Plate thickness THK (in)

Calculate free

How it develops: the formulas

Mean radius and plate length

r = (D − t) / 2 ; L = π × (D − t) In the example, D = 800 in 10 mm plate: r = 395 mm and L = 2481.9 mm.

Half-mitre (cut angle of each gore)

β = total angle / (2 × gores) For 80° in 5 gores: β = 8°. Each middle gore turns 2β; the two end gores turn β.

Cut height at each element

y(φ) = (R + r × cos φ) × tan β R is the bend radius at the axis and φ the angle round the tube, φ = 0 at the heel and 180° at the throat. Throat: (R − r) × tan β = 113.1 mm; heel: (R + r) × tan β = 224.2 mm in the example.

Middle gore

height = 2 × y(φ) The middle gore is cut at both ends: 448 mm at the heel and 226 mm at the throat in the example.

How many plates to cut

ends: 2 ; middles: gores − 1 With 5 gores: 2 half ends and 4 full gores. With 1 gore the bend is just the two ends: the elbow. The shop's 3 gores plus 2 half gores is gores = 4 here.

Worked example

The values the form comes pre-filled with, run through the tool itself:

Bend radius (to the tube axis)	47-1/4" (47.2441)
Outside diameter of the tube	31-1/2" (31.4961)
Total angle of the bend	80°
Number of gores	5
Divisions	16
Plate thickness	3/8" (0.3937)
The flat pattern fits a plate of	97-11/16" × 17-5/8"
Flat patterns produced	2

Result of the example

Plate 1	97-11/16" × 8-13/16", cut 2 times
Area and weight	4.5 ft² · ≈ 72.4 lb in 3/8" steel
Plate 2	97-11/16" × 17-5/8", cut 4 times
Area and weight	9.0 ft² · ≈ 144.9 lb in 3/8" steel

Ordinate table

Assembly notes

Every gore comes with its longitudinal seam on the throat, the shortest weld, and the gores go together all the same way round, heel to heel. Do not turn a cut gore half a turn to stagger the seams: its long side goes to the throat and the bend loses angle. To stagger them, mark every second gore from the heel instead — cut the paper template on its middle line and swap the two halves.

How to mark it out on the plate

1. Work out β and the heights y(φ) for the dv elements (16 in the example), or copy them from the calculator table.
2. Mark a rectangle of L by y_heel for the end gore, divide L into dv parts and mark the height of each element from the base, throat at both edges and heel in the middle, as in the drawing.
3. Join the points with a flexible rule: the edge is a sine wave of amplitude 2 × r × tan β (111 mm in the example).
4. For the middle gore mirror the same wave downwards: the rectangle is 2 × y_heel high with both edges cut.
5. Cut 2 ends and (gores − 1) middles, roll each as a shell and assemble them all the same way round, heel to heel. To stagger the longitudinal seams, mark every second gore from the heel.

Common mistakes and tolerances

Radius under half the diameter

With R < D/2 the gores cross at the throat and there is no part; the calculation refuses it. In practice R of 1 to 1.5 diameters is used.

More than 90° per gore

Each gore can turn at most 90° (β = 45°, the elbow cut). A 90° bend in 1 gore is the mitred elbow; with 2 it is already a bend.

Turning a gore half a turn

Done to stagger the seams, it puts the gore's long side on the throat and the bend loses angle. Stagger them by marking every second gore from the heel instead.

Using the outside diameter for the circumference

The rolled-shell mistake: π × t extra on every gore, 31.4 mm in the example in 10 mm plate.

Confusing the axis radius with the heel radius

R is the radius at the tube axis. The heel sits at R + D/2 and the throat at R − D/2; measuring at the throat and entering that as R gives a tighter bend.

Guides about this part

• Lobster back bend calculator (segmented 90° elbow): gore angles, cut heights and how many plates
• How to lay out a mitre-cut pipe: paper template, sine wave and ordinate table
• Pie cut calculator for exhaust and tube bends: saw angle, pie lengths and a wrap-around template

Frequently asked questions

How many gores should I use?

It is the trade between finish and work: more gores follow the radius better and reduce pressure loss, but mean more cuts and more welding. For a 90 degree exhaust bend, three to five usually does it.

What is measurement H?

The bend radius measured at the tube axis. The calculation requires it to be at least half the diameter, or the gores would intersect.

How many plates come out of a 5-gore bend?

Two different ones, six plates: the half end, cut twice, and the full gore, cut four times. In the example, 2482 × 224 mm and 2482 × 448 mm.

What is the half-mitre?

The cut angle of each gore from square: β = total angle / (2 × gores). For 80° in 5 gores, 8°. It is what goes into the cut-height formula, (R + r × cos φ) × tan β.