Spherical Head in Gores flat pattern

What it is

One gore of a spherical head, and as many as the head takes. It is the only part in this catalogue that is NOT an exact development, and the calculation says so: a sphere is not developable, no flat sheet becomes a cap without stretching. What comes out here is the shop layout — true length along the meridian, half-width from the parallel at each station — and the gore is formed afterwards, in a press or hot.

Where it is used

Tank and silo heads, vessel caps, reservoir domes, spherical equipment bottoms.

Measurements the calculation needs

• D Diameter
• H Height
• S Sections
• DV Divisions
• THK Thickness

Worked example

The values the form comes pre-filled with, run through the tool itself:

Diameter	2000 mm
Height	500 mm
Sections	8
Divisions	24
Thickness	10 mm
The flat pattern fits a plate of	1151 × 780 mm

Frequently asked questions

If a sphere is not developable, what does this pattern guarantee?

The AREA, exactly. The gore's area is the integral of the parallel divided by the number of gores, which comes to exactly one s-th of the cap's area — added up, the gores have the area of the part, with nothing over and nothing missing, so the material ordered is right. What is approximate is the SHAPE, and forming is what settles that.

How many gores?

The more the better — the shape error falls with the width of the gore. Eight to twelve is usual. Below three the flat sheet would have to stretch a large fraction of its own length, and the calculation refuses.

Can the rise exceed half the diameter?

No. At half the diameter the head is a hemisphere, and past that the mouth stops being the widest parallel: the gore starts to belly, and a layout by meridian and parallel no longer describes the part.

And the sphere's radius, where does that come from?

From the mouth and the rise, which is what you have in hand. It is (d²/4 + h²) over 2h. The calculation does the arithmetic; you give the two dimensions of the head.