How to lay out a pipe saddle template by hand

What you are making

The worked example is a square tee: a 114.3 branch (4-inch pipe) landing on a 168.3 header (6-inch), centrelines at 90°. The template wraps round the outside of the branch, so it is developed on the branch's outside diameter.

1. The stretch-out

Draw a straight base line as long as the branch's outside circumference: π × 114.3 = 359.08, and divide it into twelve equal spaces of 29.92 (Coey, Ch. 16; Atkins, Ch. III). Number the points 0 to 12; 0 and 12 are the same line on the pipe, here the crotch: a point in line with the header’s axis, where the cut reaches furthest back from the end of the branch.

Kittredge and Daugherty take the spaces off a drawn circle with dividers. Those are chords, and a chord is shorter than its arc (Kidder, p. 66): twelve of them make 355.00, about 4.09 short, and the template will not meet itself round the pipe. Work out the circumference and divide it, as Kidder recommends.

2. The lengths

At each point, the branch has to reach down to the header. Measured from a base line through the points of the cut — the two tips that reach furthest toward the header — the length at an angle φ round the branch from the crotch is √(R² − r² sin²φ) − √(R² − r²), with R the header radius (84.15) and r the branch radius (57.15). At the crotch that is 84.15 − √(84.15² − 57.15²) = 22.38; a quarter turn away it is zero — the tips, on the two sides of the branch that straddle the header and reach down round it.

The books find the same lengths graphically, projecting from a half-profile of the branch onto the header in elevation (Kittredge, Problem 56; Daugherty, Problem 9). The formula gives them directly.

3. Draw the curve

Square up from the base line at every point and mark its length. Join the marks with a smooth curve — a flexible spline or batten — not with straight lines. On equal-diameter pipes the curve has a sharp point at the sides; on unequal ones like this it is smooth.

How much straight lines would cost: through these twelve points they miss the true curve by up to 1.38; with twenty-four points, 0.42. The pipe template tool lists the lengths for 8 to 32 points for any pipe, with that figure stated, under “Marking by hand”.

4. Wrap and mark

Cut the template out and wrap it round the branch with the base line square to the pipe, toward the end of the branch, and the two ends meeting at a crotch; the pipe you keep is beyond the curve. The crotches line up with the header's axis — there the header's surface is highest, so the branch is cut back furthest — and the tips fall on the two sides of the branch that straddle the header. Scribe along the curve. Wrapped the other way up, the template gives a mirrored cut that will not sit on the header.

Angled branches

For a branch at an angle the method is the same, but the lengths are no longer symmetric: the branch is shortest on the side leaning over the header, where the length up from the base line is greatest, and longest on the side opening away from it. The pipe template tool handles any angle and prints the template at 1:1, which avoids the hand layout altogether.

Common mistakes

• Developing on the inside diameter for a template that wraps the outside.
• Stepping chords off a drawn circle for the stretch-out, so the template is short round the pipe.
• Joining the points with straight lines; the error is largest exactly where the curve turns fastest.
• Wrapping the template skewed, so the base line is not square to the pipe.

How this matches the tool

The pipe template tool evaluates the same intersection exactly, samples the curve to a deviation you set rather than a point count, and prints it at 1:1 or exports DXF. The lengths on this page were produced by its own code when the page was built.

Sources

1. B. Coey, Pattern Development: Sheet Metal Level 1 (BCcampus, 2021, CC BY 4.0), Ch. 16 “Unequal Diameter 90 Degree Tee — Shop Method”, pp. 49–52
2. Coey (2021), Ch. 18 “Oblique Tee”, pp. 57–59: the same at an angle
3. G. W. Kittredge, The New Metal Worker Pattern Book (1901), Problem 56, p. 153: T-joint between pipes of different diameters
4. J. S. Daugherty, Sheet-Metal Pattern Drafting and Shop Problems (1922), Problems 8–9, pp. 32–33: T-joints, same and different diameters
5. E. A. Atkins, Practical Sheet and Plate Metal Work, 2nd ed. (Pitman, undated), Ch. III “Tee-Pieces for Round Pipes”, pp. 14–17
6. F. S. Kidder, Triangulation Applied to Sheet Metal Pattern Cutting (1917), p. 66: stepped chords very likely come to something less than the circumference; divide the computed circumference instead