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Sheet Metal Patterns by the Numbers
Developing flat patterns for pipes, elbows, branches, cones and transitions, with the allowances that make them fit
Develop sheet metal patterns with numbers: girth, slant cuts, segmented elbows, branches, cones, triangulation, rectangle-to-round transitions, seams, wired edges and nesting.
Start readingAbout this book
A sheet metal fitting starts as a flat shape on a sheet. Cut it out, roll or fold it, close the seam, and it becomes a pipe end cut to sit on a sloping roof, an elbow made of five short pieces, a branch that meets its main without a gap, a reducer, a hood or a transition from a fan’s rectangular outlet to a round duct. The flat shape is the pattern, and setting it out is the skill that sits underneath all of that work. Get the pattern right and the fitting goes together with a mallet and a few rivets. Get it wrong and no amount of hammering will close the gap.
This book sets out patterns with numbers. Every chapter shows the geometry by the traditional drawing method and then calculates the same lines, so that a pattern can be set out on the bench, in a spreadsheet or checked against a CAD unfold. It works through the three methods of development, parallel line, radial line and triangulation, in the order they are usually learned, then adds the seam, edge and flange allowances that turn a net pattern into one that can be made, and finishes with checking, nesting and keeping patterns.
It is for sheet metal workers and apprentices, fabrication drafters, and engineers who order or check ductwork, hoods and fittings. It assumes school algebra and trigonometry. Each chapter is worked through with one running case, includes one plausible mistake and how it was found, and ends with an exercise and its worked answer.
The running case
Every chapter follows one fictional job. This is an illustration. A joinery workshop is extending its dust extraction system and has asked a local sheet metal shop to make a new branch line. The fittings are made from 0.8 mm galvanised steel sheet. Duct sizes are inside diameters, because each piece must slip over the spigot of the next, and patterns are developed on the mean line of the metal.
- A transition from the fan’s 300 × 200 mm rectangular outlet to a Ø250 round duct, 350 mm long.
- A Ø250 main duct passing through a roof pitched at 20°, with its end cut to match.
- A 90° segmented elbow in Ø250, five pieces on a 375 mm centreline radius.
- A Ø150 branch meeting the Ø250 main square, and a second Ø150 branch meeting it at 45°.
- A concentric reducer from Ø250 to Ø200, 200 mm long, and an eccentric reducer from Ø200 to Ø150, 250 mm long, flat along one side.
- A conical hood for a sander, Ø450 at the mouth and Ø150 at the neck, with its mouth cut on a 20° slant to sit against the machine’s guard.
The workshop, the shop, the mistakes and the dimensions are invented. None describes KEVOS® work or a real business.
How to use the book
Read Chapters 1 and 2 first: they set the conventions used everywhere else, including what a girth is, why patterns are developed on the mean line and how cut lines are numbered. After that, the chapters on each kind of fitting can be read in any order, although triangulation in Chapter 7 is easier after radial line development in Chapter 5. Chapter 9 on allowances applies to every pattern in the book.
Calculated values are given to 0.1 mm, more precision than a scriber can mark, so that a reader checking the arithmetic can see where each number came from. On the bench, a pattern marked to within about 0.5 mm is good work for 0.8 mm sheet.
Source limits and professional responsibility
The geometry of development is exact, and every calculation in this book was checked by running it. Seam widths, wire sizes and other allowances are illustrations: the right values depend on the machines, the sheet and the specification for the job, and the book shows how to calibrate them with trial strips.
Ductwork for dust extraction is part of a system that controls a health hazard, and in some cases a fire or explosion hazard. Its design, airflow, materials and installation are matters for a competent designer and for Australian work health and safety requirements, including Safe Work Australia’s guidance on wood dust and the specification for the job. This book teaches the geometry of patterns. It is not a design for any duct system.
Who this book is for
Sheet metal workers, fabrication drafters, apprentices and engineers who set out flat patterns for ducts, hoods, hoppers and fittings, by hand or by checking what a CAD unfold produces.
What you will learn
- Recognise which solid a fitting is made from and choose parallel line, radial line or triangulation development.
- Calculate girths, cut ordinates and true lengths, and develop elbows, branches, cones and transitions with real numbers.
- Add seam, edge, flange and notch allowances to a net pattern, and calibrate them with trial strips.
- Find the mistakes that make patterns fail, such as chord girths, wrong joint counts and missing allowances.
- Check, nest and record patterns so that the next batch fits as well as the first.
Inside this book
Chapters
- 01Every pattern starts with a solidRead a fitting as cylinders, prisms, cones and planes, choose parallel line, radial line or triangulation, and set the conventions the rest of the book uses.
- 02Girth, thickness and the pipe cut on a slantFind a pipe's girth on the mean line, see why stepping it off with dividers falls short, and develop a pipe cut on a slant as a sine curve with 12 calculated ordinates.
- 03Elbows: mitres and segmented bendsDevelop a two-piece mitre and a five-piece segmented elbow, find joint angles, throat and heel lengths, cut all segments from one strip, and catch an elbow that turns only 72°.
- 04Tees and branches: where two pipes meetDevelop a Ø150 branch meeting a Ø250 main square and at 45°, find the hole in the main as it lies on the flat, and see why a round hole cut before rolling comes out 9 mm narrow.
- 05Cones and reducers by radial linesDevelop a concentric reducer as part of a cone's sector: slant height, apex distance, sector angle and chords, what to do when the apex is out of reach, and an apex found from diameters.
- 06Cones cut on a slant: the sander hoodDevelop a conical hood whose mouth is cut on a 20° slant: true lengths of each generator by rotation and by calculation, the elliptical mouth, and lengths measured where they appear foreshortened.
- 07Triangulation and true lengths: the eccentric reducerDevelop an eccentric reducer by triangulation: divide both ends, find every side and diagonal's true length from plan and height, build the pattern triangle by triangle, and step arcs, not chords.
- 08Rectangle-to-round transitionsTriangulate the fan transition from a 300 × 200 outlet to Ø250 round: flat triangles, part-cone corners, six true lengths, a seam on a long side, and a pattern built with every line set at 350 mm.
- 09Seams, edges and notches: the allowancesTurn net patterns into patterns that can be made: grooved seam, lap and slip joint allowances, wired edges by rule and by geometry, flange stretch on round ends, notches, and trial strips.
- 10Checking, nesting and keeping patternsCheck every fitting with independent numbers, compare a CAD unfold, nest the blanks on 2,400 × 1,200 sheets, and keep a pattern register that stops a good pattern being used for the wrong job.
Apply This in Practice
Use these KEVOS® tools to try the method from this reading with your own numbers.
Applies this method
Surface and Volume of Revolution (Pappus–Guldinus)
Gives the area of a surface of revolution from the generating outline and its centroid, an independent check.
Applies this method
Triangle Solver
Solves any triangle, including the true-length triangles that patterns rely on.
Related Tools and Examples
Useful alongside
Sheet Nesting Yield Check (Parts per Sheet, Material Utilisation, Sheets and Cost per Part)
Counts rectangular blanks per standard sheet and the yield, the nesting step this chapter adds to the pattern checks.
Related to Checking, nesting and keeping patterns
References and source notes
The manuscript and worked examples are original KEVOS® writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 26 October 2026.
- Evan A. Atkins, Sir Isaac Pitman & Sons, London. Practical Sheet and Plate Metal Work (second edition) (1912). Supplied source, read as a subject map of traditional pattern development for sheet and plate. Its wiring allowance rule is restated and tested in Chapter 9 with attribution. No text, figures, examples or exercises are reproduced, and all numbers, cases and methods of checking in this book are its own.
- Sheet Metal and Air Conditioning Contractors' National Association (SMACNA). HVAC Duct Construction Standards: Metal and Flexible (edition as called up). Named by title and scope as a widely used industry standard for duct seams, joints and gauges. No values are quoted from it; the seam sizes in this book are illustrations to be confirmed against the specification that governs a job.
- Standards Australia. AS 1397 Continuous hot-dip metallic coated steel sheet and strip (edition as called up). Named by number and scope as the Australian product standard for galvanised sheet of the kind used in the running case. No values are quoted from it.
- Standards Australia. AS 4254.2 Ductwork for air-handling systems in buildings, Part 2: Rigid duct (edition as called up). Named by number and scope as the Australian standard for rigid ductwork in buildings. The running case is an industrial extraction duct, and nothing in this book claims compliance with it.
- Wolfram MathWorld, E. W. Weisstein. Developable surface (2026). Reference for the definition of a developable surface used in Chapter 1: a surface that can be flattened onto a plane without stretching.