Tapered Segmented Bend flat pattern

What it is

The mitred bend that also reduces: it goes in at one diameter and comes out at another, along the same arc. It is the part nobody wants to mark out by hand, because here the gores are ALL DIFFERENT — s + 1 patterns instead of the two a constant-diameter bend takes.

Where it is used

Flues and extraction ducts that taper as they rise, curved transitions in process piping, dust collection, fan outlets that change size through the bend.

Measurements the calculation needs

• D1 Diameter 1
• D2 Diameter 2
• H Height
• ANG Angle
• S Sections
• DV Divisions
• THK Thickness

Worked example

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

Diameter 1	300 mm
Diameter 2	500 mm
Height	800 mm
Angle	90°
Sections	4
Divisions	32
Thickness	6 mm
The flat pattern fits a plate of	941 × 358 mm
Flat patterns produced	5

Frequently asked questions

Why is every gore a different pattern?

Because the diameter grows along the bend. On a constant-diameter bend the middle gores are all alike and come on one sheet cut s − 1 times; here each has its own size. That is why the gore count is capped at twelve — twelve gores is already thirteen sheets.

Does the assembly order matter?

Very much. The gores go in the order they come out, smallest to largest. Assembled out of order the bend does not close — and there is no telling from the patterns, because each one closes on its own. The printed sheet carries that warning.

How is the part built geometrically?

By inscribed spheres: one sphere at each joint, on the same tangent polygon the ordinary bend uses, with growing radii. Each gore is the frustum of the cone circumscribed about two neighbouring spheres — and it is that construction which makes the joints plane ellipses, which is what lets the mitre close.

Are the two diameters given the openings?

They are — circles perpendicular to the axis, which is what you measure and what meets the next pipe. Worth saying because it changes the arithmetic: with that definition the taper enters through the tangent of the cone's angle, not the sine, which is what you get if the diameters are taken at the joints.