Cone with Parallel-Axis Nozzle Hole flat pattern

What it is

The cone with the upright nozzle's hole already marked — the mate of the parallel-axis nozzle. Marking a hole on a cone by hand is far worse than on a cylinder, because the surface does not open into a rectangle and no tape will do.

Where it is used

The other half of the upright-nozzle job — hoppers, silos, cyclones, conical tank roofs.

Measurements the calculation needs

• D1 Diameter of the smaller mouth (bottom)
• D2 Diameter of the larger mouth (top)
• H Height of the cone
• D Outside diameter of the nozzle
• V Offset from the nozzle axis to the cone axis
• 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

Diameter of the smaller mouth (bottom) D1 (in)

Diameter of the larger mouth (top) D2 (in)

Height of the cone H (in)

Outside diameter of the nozzle D (in)

Offset from the nozzle axis to the cone axis V (in)

Divisions DV

Plate thickness THK (in)

Calculate free

Worked example

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

Diameter of the smaller mouth (bottom)	15-3/4" (15.748)
Diameter of the larger mouth (top)	118-1/8" (118.1102)
Height of the cone	19-11/16" (19.685)
Outside diameter of the nozzle	11-13/16" (11.811)
Offset from the nozzle axis to the cone axis	47-1/4" (47.2441)
Divisions	32
Plate thickness	1/4" (0.2362)
The flat pattern fits a plate of	10' 6-7/16" × 10' 5-1/16"

Result of the example

Plate	10' 6-7/16" × 10' 5-1/16"
Area and weight	79.2 ft² · ≈ 763.6 lb in 1/4" steel
Arc radii	8-3/8" · 63-1/4"
Sector angle	336°

Frequently asked questions

Why do I need this part and not just the nozzle?

Because the hole on the cone is neither a circle nor an ellipse on the flat pattern. It comes from the same intersection as the nozzle, mapped into the sector, and there is no way to mark it without the drawing.

Is the hole worked out the same way as the nozzle's mouth?

It is the same calculation, in the same place in the code. Both parts ask Base::BranchHole where one meets the other, and the spec checks it point by point — if they disagreed the hole would not match the mouth and no pattern would save it.

Where does the cone's seam go?

Diametrically opposite the hole. A longitudinal weld does not run through a cut-out.

Why is the hole larger than the nozzle's diameter?

Because the nozzle meets the cone obliquely, and the shallower the cone the more oblique the meeting. The hole is the cylinder projected onto the sloping surface, and it stretches along the slope.