Branch & Run Geometry

Tube Notcher & Coping Calculator

Calculation Results & Fishmouth Blueprints

Full-scale unrolled fishmouth wrap template blueprint, saddle cross-section elevation, and station ordinates:

📐 Tube Notch — Unrolled Fishmouth Wrap Template
Tube Notch Fishmouth Wrap Pattern Blueprint Scaled unrolled wrap template showing station ordinate lines, seam alignment marks, and saddle cut contour.

Print template at 100% scale without page scaling — wrap branch tube, trace contour line, and grind saddle notch.

⭕ Cylinder Joint Elevation & Saddle Geometry

Branch Tube Saddling Main Run Elevation Side elevation diagram showing branch tube intersecting main run cylinder at joint angle β.
Max Saddle Coping Depth
0.268 in
y(90°) = Rr − √(Rr² − rb²)
Joint Angle (β)
90.00°
Perpendicular T-Joint
Branch Wrap Circumference
6.283 in
Circumference = π · ODb
Joint Configuration
2" onto 4" Tube
✓ Full Penetration Saddle

🔨 Fishmouth Template Station Ordinate Table

Sequential tape-measure mark points around branch tube circumference:

Station # Angle (φ°) Arc Distance around Tube Cut Height Ordinate y(φ)

📦 Required Material & Notching Checklist

Select Item Description Est. Quantity Fabrication Notes

Related Development Flat-Pattern Templates

⚠️ Structural & Roll Cage Safety Disclaimer: Templates are provided for layout and coping guidance. Structural roll cages, handrails, and chassis tubing must be fully fit-up with zero gap before welding, and must comply with SFI / FIA / AWS D1.1 structural codes.

🧮 Step-by-Step Worked Example: 90° T-Joint Tube Notch

Consider notching a 2.000 inch OD branch tube (r_b = 1.000") to saddle perpendicularly (β = 90.0°) onto a 4.000 inch OD main run tube (R_r = 2.000") with 0.120 inch wall thickness.

Mathematical Derivation Steps:

  1. Branch Wrap Circumference (L):
    L = π × OD_b = 3.14159 × 2.000 in = 6.283 inches (159.59 mm)
  2. Maximum Saddle Coping Depth (y at 90° valley):
    y(90°) = R_r - √(R_r² - r_b²) = 2.000 - √(2.000² - 1.000²) = 2.000 - √3.000 = 2.000 - 1.7321 = 0.268 inches (6.81 mm)
  3. Sinusoidal Station Contour Heights (y at 12 stations):
    y(φ) = R_r - √(R_r² - (r_b × sin(φ))²)
    Station 1 (0°, Top Peak): y = 2.000 - √(4.000 - 0.000) = 0.000 inches
    Station 4 (90°, Side Valley): y = 2.000 - √(4.000 - 1.000) = 0.268 inches
    Station 7 (180°, Bottom Peak): y = 2.000 - √(4.000 - 0.000) = 0.000 inches
    Station 10 (270°, Opposite Valley): y = 2.000 - √(4.000 - 1.000) = 0.268 inches

🛠️ Tube Coping Equipment, Safety (PPE) & Notching Pitfalls

Notching & Fit-Up Tools

  • Hole saw tube notcher jig & bi-metal hole saws
  • Die grinder with carbide rotary burrs
  • Contour gauge / paper wrap template
  • Digital angle finder & V-blocks
  • Deburring tool & half-round needle files

Required Personal Safety (PPE)

  • ANSI Z87.1 impact safety glasses + clear face shield
  • Heavy-duty leather work gloves (metal chip protection)
  • Ear protection (NRR 25+ during die grinding)
  • Leather shop apron / long sleeves
  • Steel-toe boots (ASTM F2413)

Critical Tube Notching Failure Pitfalls

  1. Opposite Notch Phase Rotation Error: Notching the second end of a tube brace out-of-phase relative to the first notch causes twisted alignment on the roll cage.
  2. Over-Feeding Dull Hole Saws: Forcing an un-lubricated dull hole saw bends the notcher arbor, causing oversized "egged" fishmouths.
  3. Excessive Joint Gap (>1/16"): Leaving loose gaps between coped branch and main run creates weak welds and requires heavy filler wire bridging.
  4. Forgetting Internal Edge Bevel: Failing to bevel the inside fishmouth edge on thick tubing restricts internal fluid flow and prevents 100% root penetration.

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Frequently Asked Questions (FAQ) — Tube Notching & Fishmouth Coping

What is a fishmouth notch in tube fabrication?

A fishmouth (or saddle) notch is a curved crescent cut at the end of a branch tube that conforms exactly to the outside cylindrical surface of a mating main run tube.

How is maximum saddle coping depth calculated for a 90° joint?

For a 90° T-joint, maximum coping depth at the side valleys is y = R_run - √(R_run² - r_branch²), where R_run is main pipe radius and r_branch is branch tube radius.

How does joint angle (β) affect notch depth on angled intersections?

On angled joints (β < 90°), the fishmouth becomes asymmetric. The cut extends further on the acute side due to y_angled(φ) = y_saddle(φ) / sin(β) + r_branch × (1 - cos(φ)) / tan(β).

What is the unrolled wrap template length for tube coping?

The flat unrolled template length equals the exact outside circumference of the branch tube: Circumference = π × Branch OD.

What tools are commonly used to cut fishmouth notches in a metal shop?

Fabricators use hole-saw tube notchers, 5-axis CNC plasma/laser cutters, end mills on a vertical milling machine, or manual die grinders with carbide burrs.

Why is zero gap fit-up critical for welding roll cages and chassis tubing?

Tight zero-gap joints prevent weld burn-through, minimize joint shrinkage distortion, and ensure 100% full-penetration weld strength required by SFI, FIA, and AWS D1.1 codes.

How do you align opposite-end notches on a single tube brace?

Scribe a continuous longitudinal reference line down the tube length before notching. Use an angle finder on the notcher arbor to align the second notch relative to the first.

What hole saw diameter should be selected for tube notching?

The hole saw outside diameter must exactly match the outside diameter (OD) of the main run tube that the branch will saddle against.

How does wall thickness affect internal beveling of notched joints?

For branch tubing thicker than 1/8" (3.2 mm), the inside edge of the fishmouth must be beveled or feathered to allow full-penetration root welds without internal flow restriction.

What cutting fluid is best when using bi-metal hole saws for steel tubing?

High-viscosity cutting wax or heavy cutting oil extends hole saw tooth life and prevents chatter when notching chromoly (4130) or mild steel tubing.

How do 1:1 printable paper templates simplify hand-grinding notches?

Printing a 1:1 wrap template allows fabricators to tape the pattern onto raw tubing, trace the fishmouth contour with a scribe, and rough-cut with an angle grinder.

What station spacing is recommended for tube notch template accuracy?

12 stations (30° increments) provide smooth contour accuracy for standard 1.5" to 2" tubing; 24 stations (15° increments) are used for large diameter tubes over 3" OD.

What is the difference between pipe coping and tube notching?

Pipe coping refers to structural steel pipe or handrail joint preparation, while tube notching refers to precision thin-wall round or square tubing for chassis and roll cages.

How do you cope square or rectangular tubing into round pipe?

Square tubing requires a straight 90° end cut with two opposing semi-circular side notches matching the radius of the mating round pipe.

Why should hole saw spindle RPM be reduced when notching hard steel?

Running hole saws at high RPM burns saw teeth. Recommended cutting speed for 1.75" tubing in chromoly is 150 to 250 RPM with steady feed pressure.

How do offset (non-centered) branch notches differ from inline notches?

Offset notches occur when the branch tube centerline does not intersect the main run tube centerline, requiring asymmetric 3D contour equations.

What AWS welding standard applies to structural tubing joints?

AWS D1.1 Structural Welding Code — Steel (Section 9 Tubular Structures) governs design, fit-up tolerances, and welding procedures for coped tubular connections.

What safety precautions are necessary when operating a drill-press tube notcher?

Clamp raw stock rigidly in the vise, ensure hole saw arbor is tight, wear ANSI safety glasses, and keep hands clear of rotating hole saw teeth.

Sources & Fabrication Standards

  1. Industrial Press Machinery's Handbook: Cylinder Intersection & Coping Formulae View Reference
  2. AWS D1.1 / D1.2 Structural Welding Code: Tubular Connection & Fit-Up Standard View Standard
  3. WBDG UFGS 07 62 00 Sheet Metal Specification: WBDG UFGS Specification View Standard