Cone and reducer development
The cone is the transition between two diameters: concentric and eccentric reducers, oblique cone, conical cap and hopper. They open into an annular sector or by triangulation, and the holed cones carry the nozzle mouth already marked on the plate.
Cone
Cone (frustum) development: formula for the slant height, both radii and the sector angle, on the neutral axis. Free calculator, no account needed.
Oblique Cone
An offset transition where the two diameters share no axis, so the symmetry is gone and the pattern is solved by triangulation, strip by strip.
Offset Cone
The reducer whose mouths are parallel but not coaxial: you give the offset. At zero it is concentric; at tangency it is the eccentric reducer, one side plumb.
Chinese Hat
The conical cap is a full cone with no smaller mouth: a disc with a wedge taken out. The sector angle comes only from the diameter and the height.
Angle Cut Cone
A conical shell with its top opening on a tilted plane. Still a sector, but the cut edge is no longer an arc — it is an ellipse projected onto the cone.
Cone with Branch Hole
The cone with the nozzle hole already marked. A cone does not open into a rectangle — it opens into a sector, and the hole curve has to be carried in.
Cone with Parallel-Axis Nozzle Hole
The cone with the upright nozzle hole already marked. A cone does not open into a rectangle, and no tape will carry that hole onto the plate.
Cone with Rectangular Hole
The name misleads: the hole is bounded by two circular arcs and two hyperbolas, and on the opened sector it comes out wider at the bottom.
Cone with Conical Tap Hole
The hopper, silo or cyclone wall that takes a conical nozzle, marked out before rolling. Enter the same tap in both parts and both templates agree.
Which cone to use
- Concentric reducer, both diameters on one axis: Cone. It opens into a sector of an annulus, with two radii and one angle.
- Eccentric reducer, one straight side so the pipe can run flat against something: Offset Cone.
- The two openings parallel, offset until one side is plumb: Oblique Cone. Developed by triangulation.
- A conical cap for a stack or a silo, small end closed: Chinese Hat.
- A cone meeting a wall or a tilted shell: Angle Cut Cone.
- A hopper with a nozzle in the wall: Cone with Branch Hole for a nozzle square to the wall, Cone with Parallel-Axis Nozzle Hole for an upright nozzle, Cone with Conical Tap Hole for a conical one.
- A grille mouth or damper in the cone wall: Cone with Rectangular Hole.
What they all share
The concentric cone opens into a sector of an annulus: inner radius Ri = g × r1 / (r2 − r1), outer radius Re = Ri + g and angle θ = 360° × (r2 − r1) / g, with g the slant height and r1 and r2 the mean-surface radii of the openings. The thickness on a cone is taken along the normal to the surface, (t/2) × cos α on the radius; the shop usually takes t/2, as on a rolled shell, and the difference between the two conventions is tenths on an ordinary reducer and grows on a shallow cone.
Oblique and offset cones are developed by triangulation: the surface is divided into lines, the true length of each is calculated, and the plate is built triangle by triangle. Holed cones open into a sector, like the cone, with the hole carried into it. Every page in this family gives the ordinates for marking out, the PDF template at 1:1, the DXF and the 3D view.
Frequently asked questions
- How do I develop a cone?
- With the slant height g = √(h² + ((D2 − D1)/2)²), the sector radii Ri = g × r1 / (r2 − r1) and Re = Ri + g, and the angle θ = 360° × (r2 − r1) / g. For 800/1200/800 in 3 mm plate: 1643 and 2468 mm, 87.3°. The cone development guide shows the whole calculation.
- What is the difference between a concentric and an eccentric reducer?
- In the concentric one both openings share an axis and the part opens into a sector. In the eccentric one a single side is straight and vertical, so the pipe can run against a wall or a floor, and the part is developed by triangulation.
- Can a cone with a nozzle hole be developed?
- Yes. The holed cones in this family deliver the cone plate with the nozzle mouth already marked, to cut before rolling. The nozzle plate itself is under Branches and nozzles.