FabLayout

Y branch pipe calculator (equal diameter)

Enter the pipe diameter, the main and branch lengths and the branch angle. You get the three cylinder patterns of an equal-diameter Y branch, cut on bisecting planes.

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2,900.7 mm546.7 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

4,664.5mm

Exact geometry

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.

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How to lay it out

  1. Draw three stretch-outs

    For the main pipe and each branch, draw a base line as long as πD and divide it into a number of equal parts that is a multiple of 4.

  2. Erect the ordinates

    At each division, draw a line square to the base line.

  3. Mark the main pipe cut

    On the main pipe lines, set off the top cut L1 − kT × |cos φ|, where φ is the girth angle of that line from the seam. The cut peaks at the quarter points where the two branch cuts meet.

  4. Mark the branch cuts

    On each branch, set off the bottom cut: kC × cos φ on the crotch half, −kT × cos φ on the outer half. Both halves meet at zero on the quarter points.

  5. Join, cut and assemble

    Join the marks with smooth curves, cut the three pieces and roll them. The two branch patterns are the same; fit them mirror-wise on the main pipe.

Good to know

  • FabLayout runs the same code as Trueflat; the result is exact geometry.
  • Source: Derived from first principles: three equal cylinders cut by the bisecting planes and the plane of symmetry between the branches, developed by ordinates in closed form on the middle of the sheet. Checked against an independent reference implementation in Trueflat.

Method and formula

All three pipes have the same diameter D. Each branch leaves the main pipe at the branch angle θ, so the branches are 2θ apart. Three planes do the cutting: between the main pipe and each branch, the plane that bisects their axes, and between the two branches, the plane of symmetry.

With r = D ÷ 2, two lengths set the whole pattern:

  • kT = r × tan(θ ÷ 2), the step on the bisecting planes;
  • kC = r × cot θ, the depth of the crotch between the branches.

Measured round the pipe by the girth angle φ from the seam (φ = 0 on the crotch side of each branch):

  • main pipe top: y = L1 − kT × |cos φ|;
  • branch bottom: y = kC × cos φ where cos φ ≥ 0, and −kT × cos φ where cos φ is negative.

The cut lines have corners at the quarter points, so the number of divisions must be a multiple of 4; then every corner falls on a line and the pattern is exact. Inside or outside diameters are converted to the sheet middle. The branch angle is limited to 15°–75°: below 15° the crotch becomes a long thin wedge, and above 75° the part is a tee, not a Y.

Worked example

D = 100 mm, L1 = L2 = 200 mm, θ = 30°: kT = 50 × tan 15° = 13.40 mm and kC = 50 × √3 = 86.60 mm. The shortest branch generator is 200 − 86.60 = 113.40 mm. The main pipe area is 60 152.36 mm² and each branch 52 831.85 mm².

Questions

How is this different from a trouser piece?

In a Y branch all three pipes have the same diameter and each part is a mitered cylinder, so the pattern is exact. In a trouser piece the main pipe divides into two smaller legs, each a slanting cone. Use the Y branch when the branches stay at full pipe size.

What does the branch angle measure?

The angle of each branch from the main pipe axis. The angle between the two branches is twice that, so 30° gives branches 60° apart.

Why must the divisions be a multiple of 4?

The branch cut has a corner at the quarter points, where the crotch plane meets the main pipe plane. A multiple of 4 puts a line exactly on those corners, so the drawn curve has no error.

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