Tube Notching Calculator

Method

The two tube axes intersect with no lateral offset. Use the angle between the branch and main axes, from 5° to 90°. Let +z follow the branch axis and +x point toward the positive projection of the main axis onto the branch cross-section. Circumference angle φ = 0° lies along +x in the plane of the axes and gives the highest selected axial position. The template starts there at zero depth. Wrap distance increases to the right until the repeated seam at 360°; positive cut depth runs downward from that starting end plane. The tool samples the intersection at equal angular intervals.

R = main outside radius; r = branch outside radius; α = angle between tube axes; φ = branch circumference angle. The intersection satisfies (z × sin α − r × cos φ × cos α)² + (r × sin φ)² = R². The selected surface root is z = [r × cos φ × cos α + √(R² − r² × sin²φ)] ÷ sin α. Wrap distance = r × φ. The profile depth is measured from the highest axial station of the selected intersection.

Worked example

For a 2 in outside-diameter branch meeting a 4 in outside-diameter main at 90°, the wrap width is 2π in, about 6.2832 in. At circumference angles 0° and 180°, the selected intersection is 2 in from the axes' crossing plane. At 90° and 270°, it is √3 in, about 1.7321 in. The resulting depth range is about 0.2679 in.

Limits

This template describes ideal outside surfaces, not a wall-aware bevel or weld fit. Branch diameter must not exceed main diameter. It excludes offset axes, wall thickness, weld gap, bevel, ovality, kerf, fixtures, and structural checks. Increasing the sample count improves the polyline resolution but does not add those allowances. Confirm the wrap direction and seam against the actual joint, and verify import or print scale before cutting.

References

• MathWorld: cylinder–cylinder intersection geometry
• Blocklayer: pipe notching and wrap-template workflow