How long a blank does a rolled cylinder need?

1. Find the mean diameter

The line that keeps its length when plate is rolled lies at the middle of the thickness (Atkins, pp. 350–352). From an inside diameter, add one thickness; from an outside diameter, subtract one (Neubecker, pp. 116–117). A shell 1000 mm inside in 10 mm plate has a mean diameter of 1010.0 mm; one 1000 mm outside has 990.0 mm.

2. Take its circumference

Blank length = π × mean diameter = π × 1010.0 = 3173.0 mm, and the blank is as wide as the shell is high, here 1500.0 mm.

3. Take off any seam gap

If the seam is welded with a root gap, the blank is shorter by the gap: with a 3 mm gap, 3173.0 − 3 = 3170.0 mm. For a lap seam, add the lap width as extra material instead. Separately, where courses of a stack telescope — one lapping outside the next — the outer course is about 2π × the thickness longer than the inner one (Atkins, pp. 356–358): here about 62.8 mm. That is a difference between two courses, not an allowance for one seam.

The 31 mm mistake

Using the inside diameter gives π × 1000 = 3141.6 mm — 31.4 mm short, which is π × the thickness. The seam will not close; forced shut, the shell comes out one thickness (10.0 mm) small in diameter. With the outside diameter the error is the same size the other way.

Rings from flat bar

The same rule cuts a ring from bar. Rolled flat, the bar’s thickness lies across the ring; rolled edgewise, its width does: “it is the thickness of the bar measured radially that is to be taken into consideration” (Bourne, p. 152). Moore works a 3 ft ring of 3 × 2 in bar bent edgewise: on 36 + 3 = 39 in, π × 39 = 122.52 in, his 10 ft 2½ in before an allowance for upsetting (pp. 153–154). Bent flat, the same rule gives 36 + 2 = 38 in, and the tool works out π × 38 = 119.38 in. Rings of angle are another matter: the old books give different rules for them, so the tool does not work them out.

Common mistakes

• Using the inside or outside diameter instead of the mean.
• Adding twice the thickness to an inside diameter: the mean is one thickness bigger, not two.
• Forgetting the seam gap, or a lap allowance, when the drawing gives the finished size.

How this matches the tool

The rolled cylinder blank calculator takes an inside, outside or mean diameter, the thickness, height and seam gap, and exports the blank as DXF. The worked numbers on this page were produced by its code when the page was built.

Sources

1. E. A. Atkins, Practical Sheet and Plate Metal Work, 2nd ed. (Pitman, undated), Ch. XXXII “Plater’s Work, Tanks, Shells, etc.”, section “Allowance for Metal Thickness”, pp. 350–352: the neutral line at the middle of the thickness, with a worked example; pp. 356–358: lapped courses about 2π × thickness longer
2. W. Neubecker, Sheet-Metal Work (1920), pp. 116–117: add the thickness to an inside diameter, subtract it from an outside one; theoretically correct, he says, but in practice add seven times the thickness to the circumference, as material is lost in forming
3. J. Bourne, A Catechism of the Steam Engine (1850), p. 152: a bar bent edgewise adds its breadth to the diameter
4. T. Moore, Engineers’ and General Smiths’ Work (1906), pp. 153–154: a 3 ft ring of 3 × 2 in bar bent edgewise, 10 ft 2½ in before the upsetting allowance