Tapered Y branch calculator
A Y whose legs taper from the main pipe down to a smaller branch diameter. Enter the main and branch diameter, height and branch angle; you get the leg pattern for both legs.
Enter your measurements
Seam
2,432.6mm
Approximate, within ±1.7 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
Find the mouth spacing
Work out c = 2H tan θ and place the two branch mouths at ±c ÷ 2 on the centre line, at height H.
Divide main pipe and mouth
Divide the leg's half of the main pipe circle and the crotch half each into equal parts, and the branch mouth at the same angles.
Mark the crotch points
Join matching points with generators. Mark where each crotch-side generator crosses the centre plane between the legs.
Triangulate
Find the true lengths of the generators and diagonals and lay out the triangles from the outer seam line.
Cut two legs
Join the edges with smooth curves and cut the pattern twice, the second one turned over as a mirror image.
Good to know
- This pattern is approximate; the result card shows how close it is.
- Source: Derived from first principles: each leg is the oblique cone between the main-pipe circle and the leg mouth, the crotch lies in a plane, so every facet is flat and the leg is laid out by triangulation on the middle of the sheet. Checked against an independent reference implementation in Trueflat.
Method and formula
A tapered Y takes a main pipe D1 into two branches of a smaller diameter D2, each leaning θ from the main axis. The legs taper over the height H: each is a slanting cone from the main pipe circle to its branch mouth. The mouths sit at
- c = 2H tan θ apart, centre to centre.
This is the same part as the equal-leg trouser piece, entered by angle instead of by mouth spacing. With the same sizes the two pages give the same pattern. Use this one when your drawing gives a branch angle.
The two cones meet on the centre plane between them, so the crotch is flat and every facet between two generators is flat too. Each leg is laid out by triangulation from true lengths. The only error is the chord used for each curve segment: the branch mouth is short by at most π³r ÷ (48n²), with r = D2 ÷ 2.
The branch diameter must be between D1 ÷ 10 and D1. A Y that widens into its branches is not covered. θ runs from 5° to 60°. Inside or outside sizes are converted approximately and rejected above 1 mm of mouth deviation.
Worked example
D1 = 400 mm, D2 = 160 mm, H = 300 mm, θ = 30°, n = 6. The mouth spacing is c = 346.41 mm. The middle crotch point sits 204.63 mm up, the mouths clear the crotch plane by 93.21 mm and the shortest generator is 133.35 mm. Each leg has an area of 202 525.15 mm².
Questions
How is this different from a Y branch?
The Y branch keeps the branches at the main pipe diameter and is made of mitered cylinders. A tapered Y reduces to a smaller branch diameter, so each leg is a slanting cone laid out by triangulation.
Is this the same as the trouser piece?
Yes, the geometry is the same. The trouser piece page takes the spacing between leg mouths; this page takes the branch angle and works out c = 2H tan θ. Pick whichever matches the dimensions on your drawing.
Is the pattern exact?
The flat facets are laid out exactly; only the curves are drawn with chords. The branch mouth is short by at most π³r ÷ (48n²) with r = D2 ÷ 2. Doubling the curve samples cuts it to a quarter.
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