Layout and Pattern Development
Three development methods
- Parallel line development for cylinders and prisms: project the true-length elements, then step the circumference along a stretch-out line.
- Radial line development for cones and pyramids: find the true length of the slant element and swing it from an apex point.
- Triangulation for transitions and warped surfaces - square-to-round, eccentric cones, mitred intersections - dividing the surface into triangles whose three sides are each found as true lengths.
True length is the whole game
A line shows true length only when it is parallel to the plane of projection. Rotate the view until the element is parallel, then read the length. In triangulation every triangle side must come from such a view before the pattern can be laid out.
Stretch-out arithmetic
Circumference C = πD. If the pattern is divided into n equal parts, dividers are set to the chord distance, not the arc distance: chord = 2R sin(180°/n). The difference per division is small, but it accumulates to the seam.
Worked example: 12-division stretch-out for a 600 mm pipe
R = 300 mm, n = 12. C = π × 600 = 1885 mm. Arc division = 1885 ÷ 12 = 157.1 mm. Chord = 2 × 300 × sin(180°/12) = 600 × 0.2588 = 155.3 mm. Set dividers to 155.3 mm and step off twelve times: the seam closes within a millimetre or two. Step 157.1 mm twelve times and you drift about 21 mm past the start point, and the closing seam will not fit.
Thickness, seam and kerf allowances
- Rolled shells develop on the mean diameter: D_mean = D_outside − t.
- Add seam or lap allowance and cutting kerf to the developed length; add edge trim to the width.
- Mark from a single datum line, punch the divisions rather than relying on ink, and wrap the template in the direction the plate will roll.
Traps
- Developing on outside or inside diameter instead of the neutral axis.
- Forgetting that both halves of a mitred elbow come from one pattern developed on the mean radius.
- Trusting a scaled drawing instead of projecting true lengths.