Rectangular duct breeches calculator (duct Y split)
Enter the main duct size, both branch sizes, the height and the gap between branch outlets. You get the two four-sided branch patterns of a rectangular duct split.
Enter your measurements
Seam
2,245.6mm
Approximate, within ±0.0 mm
- Cut 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
Mark the split line
On the main duct mouth, mark the split line at the calculated distance x_s; it divides the mouth between the two branches.
Find the true lengths
For each branch, take the four corner lines from the main mouth to the branch outlet and the diagonals of its four faces, and find their true lengths.
Lay out the triangles
Starting at the corner seam, lay out each face as two triangles from those true lengths, side by side.
Draw the edges and fold lines
Join the outer points with straight lines. The lines between faces are fold lines; the crotch face edge is seamed to the other branch.
Fold and assemble
Fold both branches, close their corner seams and join them along the split line.
Good to know
- This pattern is approximate; the result card shows how close it is.
- Source: No published source. Each branch is a planar four-sided transition developed by triangulation from true lengths, in closed form on the middle of the sheet; checked against an independent reference implementation in Trueflat.
Method and formula
A rectangular duct breeches splits one duct A × B into two branch outlets, A1 × B1 and A2 × B2, at height H. The outlets sit side by side with a gap g between them.
The main mouth is divided where the two flows have equal velocity:
- Split line x_s = −A ÷ 2 + A × A1B1 ÷ (A1B1 + A2B2), measured from the duct centre.
Each branch is a four-sided transition from its part of the main mouth to its outlet. All four faces are flat trapezoids, so each branch is developed by triangulation from true lengths, and the result is exact. The face that runs up from the split line is the crotch face. The two crotch faces touch only along the split line and open apart above it.
The calculator rejects branches that are too flat: each side edge must rise at least about 5.7° from the horizontal, and H must be at least a tenth of the largest duct size. Each part of the main mouth must be at least 10 mm.
The pattern itself is exact on the middle of the sheet. If you enter inside or outside sizes, the conversion to the middle is approximate: the outlet can deviate by a small calculated amount, and above 1 mm the calculator asks for middle-of-sheet sizes instead. The gap between outlets changes by the same conversion.
Worked example
A = 600 mm, B = 300 mm, both branches 200 × 300 mm, H = 400 mm, g = 100 mm. The split falls on the centre (x_s = 0). The crotch face and the outer face of each branch are 300 × 403.11 mm, the side faces are trapezoids of 100 000 mm², and each branch has an area of 441 867.73 mm².
Questions
How is this different from a round trouser piece?
A round trouser piece splits a pipe into two round legs and needs curved patterns. This page splits a rectangular duct into two rectangular branches; every face is flat, so the branches fold up from straight lines.
Is the pattern exact?
Yes, on the middle of the sheet: every face is flat and is laid out from true lengths. Only the conversion from inside or outside sizes is approximate, and the calculator rejects it when an outlet would deviate by more than 1 mm.
Why is the split line not in the middle?
The main duct is shared in proportion to the two outlet areas, so air keeps the same speed into both branches. With equal outlets the split is on the centre.
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