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Oval Sheet Metal Work by the Numbers

Four-centre ovals, ellipses and flat ovals in sheet metal: girths, capacities, flared ovals developed as part cones, seams, nesting and checks

Lay out and make oval sheet metal work with numbers: four-centre ovals, perimeters, capacities, flared ovals as part cones, patterns, seams, flat ovals, material and checks.

10 chapters · About 100 minutes · Free to read · Intermediate sheet metal layout and fabrication

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KEVOS® LibraryMANUFACTURINGOval Sheet MetalWork by theNumbersKEVOS® ORIGINAL BOOK10 CHAPTERS

About this book

An oval is the shape a round vessel takes when it must be longer than it is wide: a trough that fits along a fence, a bath that fits a person lying down, a duct that fits a shallow ceiling, a hood over a long machine. Ovals look like ellipses, and on a drawing they are often called ellipses, but most oval sheet metal work is not elliptical at all. It is a four-centre oval: two tight arcs at the ends and two flat arcs along the sides, each struck from its own centre and meeting its neighbours smoothly. That construction is what makes ovals practical in sheet metal, because every part of it is a circle, and every part of a flared oval is part of a cone.

This book works through oval work with numbers. It starts with the shapes and how to construct a four-centre oval exactly, then calculates girths, areas and capacities, develops a flared oval vessel as a set of part cones, places its seams and makes its bottom and rim, deals with flat ovals, and finishes with material, nesting and checks. Each chapter calculates with one running case, includes a plausible mistake and how it was found, and ends with an exercise and its worked answer.

It is for sheet metal workers, fabricators, apprentices and drafters, and for engineers who check oval vessels and ducts. It assumes school algebra and trigonometry and some familiarity with round pattern development; the Library’s Sheet Metal Patterns by the Numbers covers radial line development of cones, which this book builds on.

The running case

Every chapter follows one fictional job. This is an illustration. A rural fabricator has been asked for galvanised steel stock-water troughs, oval in plan so that cattle can drink along both sides and the trough sits along a fence line. Each trough is 1,800 × 900 mm across the top and 450 mm deep, measured on the mean line of 1.6 mm galvanised sheet, with walls flaring outward by 75 mm all round, so the bottom is 1,650 × 750 mm. The oval is a four-centre oval with an end radius of 300 mm at the top. The walls are made in four pieces, two ends and two sides, joined by vertical seams; the bottom is a flat oval plate; the rim is rolled over a steel rod.

The fabricator, the dimensions, the prices and the mistakes are invented. None describes KEVOS® work or a real business.

How to use the book

Read Chapters 1 and 2 first: they set out the four-centre oval and its construction, which every later chapter uses. Chapters 3 and 4 deal with lengths and volumes, Chapters 5 to 7 with the flared vessel’s patterns and joints, and Chapters 8 to 10 with flat ovals, material and checks. Values are given to 0.1 mm so that the arithmetic can be followed; oval work is usually marked to the nearest half millimetre.

Source limits and professional responsibility

The geometry in this book is exact, and every calculation was checked by running it. Seam, rim and bottom allowances are illustrations, to be calibrated with trial pieces. A trough full of water is heavy: the running case’s holds about 440 kg of water to its fill line, and a vessel of that kind must be designed and supported for its full load and for the animals or people around it. Drinking-water and stock-water vessels also have material and coating requirements that depend on their use. This book teaches layout and fabrication geometry. It is not a design for any vessel, and qualified review governs real work.

Who this book is for

Sheet metal workers, fabricators, apprentices and drafters who set out oval or flat-oval vessels, troughs, hoods and ducts, and engineers who check their capacities and patterns.

What you will learn

  • Construct a four-centre oval from its length, width and end radius, and know how it differs from an ellipse.
  • Calculate an oval's perimeter, area and a flared oval vessel's capacity to any level.
  • Develop a flared oval as a set of part cones, including patterns whose apex is metres away.
  • Place seams where the parts meet smoothly, and make bottoms, rims and flat-oval variants.
  • Nest, weigh and check an oval job so that the finished vessel matches its numbers.

Inside this book

Chapters

  1. 01Ovals, ellipses and flat ovalsThree shapes that all get called 1,800 × 900 oval: the ellipse, the four-centre oval and the flat oval, how their girths differ by up to 268 mm, why sheet metal prefers arcs, and the running case.
  2. 02Constructing a four-centre ovalFind a four-centre oval's side radius, centres and tangent points from its length, width and end radius, choose the end radius, mark it out with a trammel, and catch a radius worked from full sizes.
  3. 03Perimeter and girth of an ovalAdd up an oval's four arcs for its girth, see why every offset oval's girth differs by 2π times the offset, compare the ellipse, measure the made vessel, and find a rim rod cut 24 mm short.
  4. 04Area and capacity of oval vesselsThe exact area of a four-centre oval, the offset rule for areas, capacity to any level by integration, 1.24 L per mm at the fill line, and a capacity claimed from the top area.
  5. 05Flared ovals as part conesWhy each wall of a flared oval is part of a right cone, the four cones share one half-angle of 9.46°, their apexes lie 1.8 m and 9.45 m below the rim, and a pattern radius taken as the apex depth.
  6. 06Developing the wall patternsDraw the trough's end patterns from their apex and its side patterns by chord offsets, with radial division lines, rim and seam allowances, and a side pattern cut straight because it looked straight.
  7. 07Seams, bottom and rimJoin the trough's four wall pieces on their shared generators, flange the bottom plate up into the wall with 8.4% shrink at the ends, roll the rim over its rod, and find an end flange that leaked.
  8. 08Flat ovals and flared flat ovalsThe flat-oval version of the trough: half-cone ends, flat rectangular sides, 575 L brim-full, the same offset rules, flat-oval duct sizes, and side panels wrongly shortened for the flare.
  9. 09Material, nesting and massTurn the trough's patterns into rectangles on 2,400 × 1,200 mm sheets: two sheets per trough at 54% yield, the finished mass of about 42 kg, the material cost with GST, and sheets ordered by area.
  10. 10Checking the finished ovalProve a finished oval trough by templates, girth tape, axes, flare, level rim, capacity fill and leak test, and catch a side piece rolled flat on a trough checked only across its axes.

Apply This in Practice

Use these KEVOS® tools to try the method from this reading with your own numbers.

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.

  • William Neubecker, American School of Correspondence, Chicago. Tinsmithing (instruction paper) (1903). Supplied source, read as a subject map, in particular its oval foot bath and wash boiler cover, where a flaring oval is struck from several centres and developed as parts of cones. No text, figures, constructions, tables or exercises are reproduced; the analytic construction, numbers, cases and checks in this book are its own.
  • Wolfram MathWorld, E. W. Weisstein. Ellipse (perimeter approximations) (2026). Reference for the ellipse's area and for Ramanujan's approximation to its perimeter, used in Chapters 3 and 4 to compare an ellipse with a four-centre oval.
  • Standards Australia. AS 1397 Continuous hot-dip metallic coated steel sheet and strip (edition as called up). Named by number and scope as the product standard for galvanised sheet of the kind used in the running case. No values are quoted from it.

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