Tutorial Advanced ⏱ 18 minutes

Pipe Notch (Saddle Cut)

Create a pipe notch (saddle cut) profile — the geometry needed when one pipe meets another at 90° and must be cut to fit.

What You Will Build

A 50mm diameter pipe notch profile for joining to a 80mm diameter main pipe at 90°. The notch is the intersection curve of two cylinders.

Operators Used

Circle/Centre,R Point/Intof,C,C Arc/Centre,R Trim/C,to,L

Understand the Pipe Notch Geometry

A pipe notch is the curve of intersection between two cylinders. In 2D, this is represented as the profile of the cut end of the branch pipe.

Branch pipe: 50mm OD  → radius 25mm
Main pipe:   80mm OD  → radius 40mm

The notch profile is an ellipse-like curve.
In XyzPilot, we approximate it using the
circle-circle intersection method.

Setup: Branch pipe axis is vertical (Y-axis)
       Main pipe axis is horizontal (X-axis)
       Branch pipe centre at (0,0)

Create the Branch Pipe Circle

Create the cross-section circle of the branch pipe.

P_branch = (0, 0)  [branch pipe centre]

Circle/Centre, P_branch, R=25, 0
→ C0: branch pipe cross-section, diameter=50mm

Create the Main Pipe Circle

Create the cross-section circle of the main pipe at the junction point.

P_main = (0, 40)  [main pipe centre — at top of branch]
   [The main pipe centre is at distance = main pipe radius from branch centre]

Circle/Centre, P_main, R=40, 0
→ C1: main pipe cross-section, diameter=80mm

The intersection of C0 and C1 gives the notch profile points.

The main pipe centre is placed at Y=40 (the main pipe radius) so that the main pipe circle passes through the branch pipe centre.

Find the Notch Profile Points

Find where the branch pipe circle intersects the main pipe circle.

Point/YLarge, Intof, C0, C1  → P0 = upper intersection
Point/YSmall, Intof, C0, C1  → P1 = lower intersection

For C0 (centre 0,0 r=25) and C1 (centre 0,40 r=40):
  dist(centres) = 40
  40 < 25 + 40 = 65  [circles intersect]

The intersection points define the deepest and shallowest
points of the notch cut.

Create the Notch Profile Arc

The notch profile is the arc of the main pipe circle that lies within the branch pipe.

The notch cut follows the surface of the main pipe.
In 2D cross-section, this is the arc of C1 between P0 and P1.

Trim/Circle, C1, Between, P0, P1, CCW
→ A0: notch profile arc (the cut surface)
   This arc represents the saddle cut on the branch pipe end.

The branch pipe end profile:
  Left side: arc of C0 from P1 to P0 (outer edge)
  Notch: arc of C1 from P0 to P1 (cut surface)

The notch arc (A0) is the profile that must be cut on the end of the branch pipe to fit against the main pipe surface.

Create the Complete Notch Profile

Combine the branch pipe edge and the notch arc to create the complete cut profile.

Complete branch pipe end profile:
  Right outer edge: arc of C0 from (25,0) to P0 [right side]
  Notch arc: A0 from P0 to P1 [saddle cut]
  Left outer edge: arc of C0 from P1 to (-25,0) [left side]
  Bottom: straight line from (-25,0) to (25,0) [pipe end]

This profile is used to set up the pipe notching operation
or to create a template for manual cutting.

Tips & Best Practices

The notch depth depends on the ratio of branch to main pipe diameters.
For a 90° intersection, the notch is symmetric about the branch pipe axis.
For angled intersections, the notch profile is asymmetric — adjust the main pipe circle position.
This 2D profile can be used to create a cutting template or set up a pipe notcher.
Verify the notch profile by checking that it matches the main pipe curvature.

Operators Used in This Tutorial

Circle/Centre,R

Pipe Notch (Saddle Cut)

Understand the Pipe Notch Geometry

Create the Branch Pipe Circle

Create the Main Pipe Circle

Find the Notch Profile Points

Create the Notch Profile Arc

Create the Complete Notch Profile

Tips & Best Practices

Operators Used in This Tutorial

Circle by Centre and Radius

Circle Circle Intersection

Trim Circle Between Two Points

Related Tutorials

Tangent Circle Chain

Intersection-Based Construction

Complete CNC Profile from Drawing