Cone with Branch Hole flat pattern

What it is

The cone with the nozzle hole already marked — the mate of the cone branch, as the holed shell is the mate of the pipe branch. And here it matters more than on a pipe: marking a hole on a cone by hand is far worse than on a cylinder, because the surface does not open into a rectangle. It opens into a sector, and the hole's curve has to be carried into it.

Where it is used

Conical hoppers and silos with a nozzle, conical vessel bottoms with a take-off, cyclone inlets, bins with a side discharge.

Measurements the calculation needs

• D1 Smaller diameter (bottom mouth)
• D2 Larger diameter (top mouth)
• H Height of the cone
• D Diameter of the nozzle hole
• Y Height of the hole centre (from the bottom mouth)
• DV Divisions
• THK Plate thickness

Calculate with your own measurements

No account needed: enter the measurements in millimetres or inches and get the figures and the drawing. The scaled PDF template, the DXF for the cutting table and the 3D model take a free account.

Diameters and sides are outside measurements. The flat pattern already allows for the plate thickness, working on the mean line.

Units: mm inches

Smaller diameter (bottom mouth) D1 (in)

Larger diameter (top mouth) D2 (in)

Height of the cone H (in)

Diameter of the nozzle hole D (in)

Height of the hole centre (from the bottom mouth) Y (in)

Divisions DV

Plate thickness THK (in)

Calculate free

Worked example

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

Smaller diameter (bottom mouth)	11-13/16" (11.811)
Larger diameter (top mouth)	35-7/16" (35.4331)
Height of the cone	31-1/2" (31.4961)
Diameter of the nozzle hole	7-7/8" (7.874)
Height of the hole centre (from the bottom mouth)	19-11/16" (19.685)
Divisions	32
Plate thickness	1/4" (0.2362)
The flat pattern fits a plate of	89-1/2" × 42-11/16"

Result of the example

Plate	89-1/2" × 42-11/16"
Area and weight	16.8 ft² · ≈ 162.2 lb in 1/4" steel
Arc radii	16-1/2" · 50-1/8"
Sector angle	126.4°

Frequently asked questions

Why isn't the hole symmetric in the sector?

Because the cone flares. At the top the nozzle meets the wall where it is wider and further from the apex; at the bottom, narrower and nearer. In the sector that becomes a curve pulled outward on one side — nothing like the nearly symmetric hole on a shell.

Which diameter do I enter?

The HOLE, as on the holed shell — for a nozzle set on top of the cone it goes at the nozzle's bore, for one set in, at its outside diameter. The welder decides.

Where does the cone's seam go?

Diametrically opposite the hole. A longitudinal weld does not run through a cut-out, and on a cone it is already the most critical joint in the part.

Does this hole match the cone branch in this catalogue?

It does, and it is its mate. Enter the same cone, the same height and the same diameter in both parts and you have both patterns for the job — the branch and the cone.