FabLayout

Dished head petal calculator (torispherical and 2:1)

Choose an ellipsoidal 2:1, torispherical F&D or Klöpper head, enter the diameter, crown disc size and number of petals. You get the crown disc, one petal and the flange strip. Pressed parts.

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Enter your measurements

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1:1 PDF and DXF files of this flat pattern are made in Trueflat, ready for print, plasma, laser or waterjet. It works offline on site.

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1,555.8 mm1,012.2 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

5,400.1mm

Approximate, within ±22.3 mm

Petal length
In the app
Petal edge
In the app
Sheet size
In the app

Every result is in Trueflat

The free web version shows the main result and the drawing. Trueflat gives you every mark and measurement, and exports a cut sheet. It is free to download.

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How to lay it out

  1. Draw the crown disc

    Swing a circle at the calculated crown disc radius. Divide its edge into as many equal parts as there are petals.

  2. Draw the petal centre line

    Draw a straight line as long as the petal length and divide it at the meridian stations.

  3. Set off the petal widths

    At each station, set off half the petal width square to the centre line on both sides, from the calculated widths.

  4. Join the petal edges

    Join the points on each side with a smooth curve. Cut as many petals as the head needs.

  5. Add the flange strip

    If the head has a straight flange, cut a strip as long as the head circumference and as high as the flange.

  6. Press and weld

    Press the crown disc and each petal to the head shape in a die, then weld petals to each other, to the disc and to the flange.

Good to know

  • This pattern is approximate; the result card shows how close it is.
  • Source: Kittredge, The New Metal Worker Pattern Book (1917), Problem 30 (sphere gores), Fig. 309, p. 124, for the gore method; its extension to ellipsoidal and torispherical heads (knuckle petals included) is Trueflat's own derivation, checked against an independent reference implementation.

Method and formula

A dished head cannot be unrolled from flat sheet. Trueflat breaks it into a crown disc, N petals and a straight flange strip, and lays each one out so that its edges and area match the head. The parts are pressed in a die before welding, so the pattern is approximate and needs a forming allowance.

  • Ellipsoidal 2:1: depth D ÷ 4.
  • Torispherical F&D: crown radius D, knuckle radius 0.06D.
  • Klöpper: crown radius D, knuckle radius 0.1D.

Petal. Its centre line is the true length of the meridian from the crown disc to the tangent line. At each station the petal is 2πρ ÷ N wide: the true arc of that circle of the head, divided by N. The centre line, every width and the petal area are exact. The side edges come out a little longer than the meridian, by at most π² × Lp × ρ′² ÷ (2N²), where Lp is the petal length and ρ′ how fast the radius grows along the meridian at the crown seam. The petals stretch to absorb that when pressed, and more petals shrink it.

Crown disc. Its radius is the meridian length from the top, so its rim shrinks slightly in the die; the calculation gives that shrink as a percentage. Flange: a plain strip πD × flange height, exact.

Measurements are to the sheet middle. This is a cutting layout, not a pressure calculation. Pressure vessel heads to ASME VIII or EN 13445 are pressed by an approved maker, and the knuckle cannot be formed by hand.

Worked example

2:1 head, D = 2000 mm, 12 petals, crown 0.5: depth 500 mm. The petal is 261.80 mm wide at the top, 523.60 mm at the bottom and 704.96 mm long. Its edge is 718.57 mm, 13.60 mm longer than the centre line, within the 22.30 mm bound. The crown disc radius is 506.09 mm and its rim shrinks 1.20 %.

Questions

Is the pattern exact?

No. A head is curved in two directions and cannot be flattened. The petal centre line, its widths and its area are exact; its side edges are longer than the meridian by up to the calculated bound (22.30 mm for a 2 m 2:1 head with 12 petals). The crown disc rim shrinks slightly. Allow for both in the die.

Which head type should I pick?

Use the type on your drawing. 2:1 is the deepest at D ÷ 4. F&D has a crown radius of D and a knuckle of 0.06D, the shallowest of the three. Klöpper, to DIN 28011, has a crown radius of D and a knuckle of 0.1D.

Can I use this for a pressure vessel?

Only as a cutting layout. It does not check pressure, thickness or thinning in the knuckle. Code heads to ASME VIII or EN 13445 are made and certified by an approved head maker.

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