How many ordinate lines should I use for marking a pipe template?

For small pipes (NPS 2 inches to 4 inches), 8 or 12 ordinate divisions are usually sufficient. For medium pipes (NPS 6 inches to 12 inches), 16 divisions are recommended for smooth contours. For large-bore industrial piping (NPS 14 inches and above), 24 or 32 ordinate lines provide maximum contour fidelity.

How do you calculate fishmouth saddle cuts for 90° pipe tees?

For an equal diameter tee where branch radius r equals header radius R, the saddle drop height at ordinate angle θ is y(θ) = R - √(R² - (r × sin θ)²). At θ = 90° and 270°, the curve reaches its maximum depth equal to the radius.

Can I export and print the generated template at 1:1 scale?

Yes, you can export the flat pattern as an exact SVG vector file or use the printable coordinate table to lay out the ordinate points directly on sheet metal, roofing felt, or cardboard with a steel rule.

Cylindrical Wrap-Around Layout Generator

Pipe Flat Pattern Calculator Online

Generate printable 1:1 scale wrap-around templates and precise ordinate coordinate points for pipe miter cuts, 90° saddle branch tees, and angled lateral wyes. Designed for industrial pipefitters, welders, and sheet metal fabricators.

Fast Presets:

Template Geometry

16 Ordinates

Number of Circumference DivisionsΔX = 0.884 in

Pipe Size (NPS)

Pipe Outside Diameter (OD)Standard

Miter Cut Angle (α)45°

11.25°22.5°30°45° (Standard)60°

Baseline Sleeve Margin Height

Extra cylindrical collar length to wrap and secure around the pipe spool.

Unrolled Wrap-Around Template Visualizer

Vector 2D Flat Pattern

Circumference

14.137 in

Ordinate Spacing

0.884 in

Cut-Back / Drop

4.5 in

Total Cut Height

7.5 in

Wrap-Around Ordinate Coordinates (16 Points)

Seam to Seam (0° to 360°)

Line #	Angle (deg)	Distance X (in)	Cut Height Y (in)	ΔY Offset
Ord 0	0°	0	3	+0
Ord 1	22.5°	0.884	3.171	+0.171
Ord 2	45°	1.767	3.659	+0.488
Ord 3	67.5°	2.651	4.389	+0.73
Ord 4	90°	3.534	5.25	+0.861
Ord 5	112.5°	4.418	6.111	+0.861
Ord 6	135°	5.301	6.841	+0.73
Ord 7	157.5°	6.185	7.329	+0.488
Ord 8	180°	7.069	7.5	+0.171
Ord 9	202.5°	7.952	7.329	-0.171
Ord 10	225°	8.836	6.841	-0.488
Ord 11	247.5°	9.719	6.111	-0.73
Ord 12	270°	10.603	5.25	-0.861
Ord 13	292.5°	11.486	4.389	-0.861
Ord 14	315°	12.37	3.659	-0.73
Ord 15	337.5°	13.254	3.171	-0.488
Ord 16	360°	14.137	3	-0.171

What is a Pipe Flat Pattern Wrap-Around Template?

A pipe flat pattern (also known in boilermaking as a cylindrical surface development) is a 2D planar unrolling of a 3D intersection curve. When pipes meet at an angle—whether for an oblique miter bend, a 90° saddle tee, or a 45° lateral wye—the resulting weld line is not a simple flat circle, but a 3D space curve (such as an ellipse or hyperbolic cylinder intersection).

When unrolled onto a flat sheet of gasket paper, roofing felt, or thin sheet metal, that 3D curve unfolds into a sinusoidal wave. By calculating discrete ordinate height points along the pipe circumference, fabricators can wrap the template around raw steel pipe, trace the exact cut line with soapstone, and torch-cut a fishmouth joint that fits without gaps.

How to Create & Apply a Wrap-Around Template in 4 Steps

Follow this workshop-tested procedure to lay out and flame-cut accurate pipe joints.

Select Joint Type & Sizes

Pick Miter Cut, 90° Saddle Branch, or Lateral Wye, then input outside diameters for the branch pipe and main header run.

Choose Ordinate Resolution

Choose 8, 12, 16, 24, or 32 ordinates depending on pipe diameter. Larger pipes (over 6 inches) benefit from 16 to 24 lines for smooth contours.

Mark Layout Paper or Export SVG

Export the 1:1 SVG pattern or use a steel rule to transfer ordinate height points onto craft paper at pitch distance intervals.

Wrap, Trace & Bevel Cut

Wrap the cut paper snugly around the pipe, align the baseline squarely, trace with soapstone, and cut with oxy-fuel or plasma torch.

Professional Flat Pattern Layout Features

Engineered for accuracy in pipe shops, structural fabrication, and field installations.

Miter Bend Templates

Unrolled sine curve coordinates for single or multi-segment miter turns at any user-defined angle from 5° to 80°.

90° Saddle Tees (Fishmouth)

Exact branch fishmouth profile for equal and unequal header/branch combinations with automatic crotch drop depth.

Lateral Wye Branches

Rigorous trigonometric intersection for 45° and 60° wye saddles with asymmetric heel and toe depth calculations.

Header Hole Cutout Profile

Computes the mating hole cutout boundary along the curved surface of the main run pipe to eliminate flow restrictions.

1:1 Scalable SVG Vector Export

Download standalone vector SVG templates ready for plotters, vinyl cutters, or CNC plasma and laser cutting tables.

Up to 32 Ordinate Divisions

Select 8, 12, 16, 24, or 32 ordinate lines with cumulative X circumference distances and Y height markers.

Mathematical Derivations & Cylinder Intersection Trigonometry

When two cylinders intersect in three dimensions, their interpenetration curve is derived by solving their orthogonal Cartesian equations simultaneously:

Miter Cut Development Formula

For a cylinder of radius r sliced by a plane angled at α to the perpendicular:

y(θ) = r × tan(α) × (1 - cos(θ))

As the circumferential angle θ traverses 0° to 360°, the flat pattern traces a cosine wave. The maximum cut-back amplitude occurs at θ = 180°:
Cut-Back = 2r × tan(α) = OD × tan(α).

90° Saddle Fishmouth Equation

A branch of radius r saddled perpendicularly onto a header of radius R:

y(θ) = R - √(R² - (r × sin(θ))²)

- At θ = 0° and 180° (crotch): sin(θ) = 0, so y = 0.
- At θ = 90° and 270° (sides): sin(θ) = 1, so y reaches maximum penetration depth = R - √(R² - r²).

Angled Lateral Wye Equation

When a branch intersects a header at an inclined angle φ (e.g. 45°):

y(θ) = (-r × cos(θ) × cos(φ) + √(R² - (r × sin(θ))²)) / sin(φ)

The inclination creates an asymmetric profile: the heel (θ = 0°) has a long tapering toe, while the throat (θ = 180°) has a sharp return angle.

Header Hole Cutout Geometry

The flat layout opening required in the header pipe shell:

x_h(θ) = R × arcsin((r × sin(θ)) / R)
y_h(θ) = (r × cos(θ)) / sin(φ)

This non-circular oval cutout prevents the branch pipe from protruding into the flow stream, maintaining laminar flow and minimizing cavitation in slurry or steam.

Field Fabrication & Torch Beveling Best Practices

1. Template Material Selection

For one-off cuts, heavy craft paper or builder's rosin paper works best. For repeat production spools, transfer the unrolled coordinate points onto 18-gauge sheet steel, 1/16-inch fiberglass wrap, or linoleum gasket material. These durable templates can be clamped around pipes dozens of times without tearing.

2. Maintaining Baseline Alignment

Always establish a square circumferential reference line on the pipe before wrapping the template. Ensure both ends of the wrap-around band overlap exactly on the circumference seam; any spiral skew will twist the saddle profile and cause misalignment during final tack welding.

3. Torch Angle & Weld Bevel

When cutting a fishmouth with an oxy-acetylene or plasma torch, do not hold the torch tip perpendicular to the pipe surface at all points. To achieve a 37.5° weld bevel compliant with ASME B16.25, angle the torch blade outward along the crotch and heel to maintain uniform root-face clearance when saddled onto the header.

4. Quarter-Mark Alignment Checks

Always mark four 90-degree quadrant lines (Top Dead Center, Bottom Dead Center, 3 o'clock, and 9 o'clock) along the pipe spool. Align the template's 0°, 90°, 180°, and 270° ordinate marks with these quadrants to prevent axial roll errors before making the final cut.

Frequently Asked Questions (FAQ)

Answers to common questions regarding wrap-around template layout, ordinate spacing, and branch saddling.

Dividing a 360-degree cylinder into equal ordinate divisions creates known circumferential distance steps: X = Circumference / N. Pipefitters can measure these linear distances easily with a flexible tape along the baseline, then mark the calculated height (Y) at each ordinate point and connect the dots with a flexible band.

In an equal saddle (where branch diameter equals header diameter), the fishmouth drops deeply to the center plane of the header (90-degree saddle depth equals the pipe radius). In an unequal saddle (where the branch is smaller than the header), the branch only sits on the upper curvature of the header, resulting in a much shallower drop.

The exported SVG contains a closed vector path representing the flat unrolled development. You can import this vector directly into CAM software such as SheetCAM, Fusion 360, or AutoCAD to generate G-code for flat sheet cutting, or wrap it around a 4th-axis rotary pipe cutter.

This specific tool is designed for cylindrical round pipes because the development relies on circular trigonometric equations. For square or rectangular tubes, miter cuts are straight line angles across each flat face rather than sinusoidal curves.

When marking the outside surface of a pipe, you should use the Outside Diameter (OD). If you are fabricating an inside hole or internal sleeve, use the Inside Diameter (ID). For thick-walled pipe (Schedule 80 or heavier), beveling the cut face with an angle grinder after rough cutting ensures full-penetration butt welding.

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