Cone Branch flat pattern
What it is
The branch entering a conical hopper, horizontally. The pipe branch handles a branch entering a PIPE; this one handles a branch entering a CONE, and the cut curve is different: there the branch meets a surface of constant radius and the mouth comes out nearly symmetric; here it meets a surface whose radius changes with height, and the mouth comes out deeper at the top than at the bottom.
Where it is used
Hopper and conical silo nozzles, cyclone inlets, take-offs in conical vessel bottoms, side discharges on bins.
Measurements the calculation needs
- D1 Smaller diameter, at the bottom
- D2 Larger diameter, at the top
- H Height of the cone
- D Diameter of the nozzle
- Y Height of the nozzle axis (from the bottom)
- C Length of the branch (from 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
Worked example
The values the form comes pre-filled with, run through the tool itself:
| Smaller diameter, at the bottom | 11-13/16" (11.811) |
|---|---|
| Larger diameter, at the top | 35-7/16" (35.4331) |
| Height of the cone | 31-1/2" (31.4961) |
| Diameter of the nozzle | 7-7/8" (7.874) |
| Height of the nozzle axis (from the bottom) | 19-11/16" (19.685) |
| Length of the branch (from the cone axis) | 27-9/16" (27.5591) |
| Divisions | 16 |
| Plate thickness | 1/4" (0.2362) |
| The flat pattern fits a plate of | 24" × 15-11/16" |
Result of the example
| Plate | 24" × 15-11/16" |
|---|---|
| Area and weight | 2.4 ft² · ≈ 23.4 lb in 1/4" steel |
Ordinate table
| # | Position on the plate | Element height |
|---|---|---|
| 1 | 0" | 12-13/16" |
| 2 | 1-1/2" | 13" |
| 3 | 3" | 13-1/2" |
| 4 | 4-1/2" | 14-3/16" |
| 5 | 6" | 14-13/16" |
| 6 | 7-1/2" | 15-5/16" |
| 7 | 9" | 15-9/16" |
| 8 | 10-1/2" | 15-11/16" |
| 9 | 12" | 15-11/16" |
| 10 | 13-1/2" | 15-11/16" |
| 11 | 15" | 15-9/16" |
| 12 | 16-1/2" | 15-5/16" |
| 13 | 18" | 14-13/16" |
| 14 | 19-1/2" | 14-3/16" |
| 15 | 21" | 13-1/2" |
| 16 | 22-1/2" | 13" |
| 17 | 24" | 12-13/16" |
Frequently asked questions
- Is the mouth symmetric?
- No, and that is what sets this part apart from the pipe branch. At the top the branch meets the cone where it is wider, and the mouth is deeper there; at the bottom the cone is narrower and the mouth is shallower. The pattern comes out with one asymmetric wave, not two equal troughs.
- Does the branch enter perpendicular to the cone's axis or to its surface?
- To the AXIS — the nozzle runs horizontally, which is the usual case for a side discharge. A nozzle perpendicular to the sloping surface is a different part, with a different cut curve.
- Where do I measure the branch length from?
- From the AXIS of the cone to the end of the branch — the centre-to-face dimension, the same convention as the pipe branch. Measuring from the cone's surface would give a different number depending on the height.
- What size of nozzle fits?
- The branch's radius must be less than the distance from its axis to the cone's surface measured PERPENDICULAR to that surface. The guard falls out of the arithmetic: it is where the intersection's radicand stops being positive. And the whole mouth has to sit between the base and the top of the frustum.
You can work out the figures right here, with no account. PDF, DXF, 3D and history take an account — free, with unlimited calculations.