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Two diameters and a height. Out comes the flat pattern — the two radii to swing, the angle to step round, and the size of plate you need. Wall thickness is handled properly, which is where most cones go wrong.
0 for a full pointed cone.
Those diameters are the…
| Outer radius (big end) | — |
| Inner radius (small end) | — |
| Included angle | — |
| Chord across it (outer corners) | — |
| Slant height | — |
| Big end girth | — |
| Small end girth | — |
| Blank size | — |
| Area | — |
| Step on the outer arc | — |
| Step on the inner arc | — |
1. Mark a centre and strike two arcs from it — one at the outer radius, one at the inner radius. A beam compass or a bar with two scribers; on a big cone that centre lands well off the plate, so work off a straightedge run out from it.
2. Draw one radial line from the centre across both arcs. That is your first seam edge.
3. Use the chord, not the angle. Hook a tape on the outer corner of that seam line and swing it until it crosses the outer arc at the chord figure — that is the other corner. Join it back to the centre and you have the sector. Nobody can protract 138 degrees and a bit across a metre of plate; everyone can pull a tape.
4. If you would rather walk it round, set dividers to the step figure and take that many bites along each arc. Both chords advance the same angle, so the stations pair up across the two arcs — join station 6 to station 6 and that is a true radial, no centre required. Handy on a big cone where the centre is three metres off the plate. Add the seam lap outside the two radial edges, not inside them.
Rolled metal stretches on the outside of the curve and squashes on the inside. The line that does neither runs up the middle of the material, and that is the line the flat pattern has to be developed on. So the girth is π × the mean diameter, whatever the drawing happened to quote.
Most calculators — and a fair bit of software — quietly assume the number you typed was already the mean. No drawing says mean diameter. It says 300 NB, or 300 ID, or 300 OD. Get it wrong and you are out by π × the thickness:
| Cone end | Inside | Mean | Outside | Out by |
|---|---|---|---|---|
| 300 dia × 1.2 mm | 946.2 | 942.5 | 938.7 | 7.5 mm |
| 600 dia × 3 mm | 1894.4 | 1885.0 | 1875.5 | 18.8 mm |
| 900 dia × 6 mm | 2846.3 | 2827.4 | 2808.6 | 37.7 mm |
Girth in millimetres. On thin duct the lap swallows it. On 6 mm plate it is a scrapped cylinder — and it is the same error every time, so it never looks like a mistake, just like the roll being out.
With R and r the big and small neutral radii and H the vertical height:
slant s = √(H² + (R − r)²)
outer radius = s × R ÷ (R − r)
inner radius = outer radius − s
included angle = 360 × (R − r) ÷ s
The neutral radius is the quoted one plus half the thickness for an inside diameter, minus half for an outside one. A small diameter of zero stays zero — a pointed cone has no top, and adding a wall to something that is not there is how you end up with a negative inner radius.
One shape of twenty-four
Sheet.Developments does the ones that are not: oblique cones, lobster-back bends that reduce as they turn, branches into cones, dished vessel heads, wyes, transitions. Same care over the wall thickness on every one of them, plus a DXF, a marking-out sheet and a full-size printable template.