Nozzle on a Sphere: flat pattern
A round nozzle on a sphere made in zones, radial or upright: the nozzle unrolled with its cut, and the zone it stands on with the hole marked. A round nozzle set onto a sphere made in zones, square to its surface or upright: the nozzle unrolled with its saddle cut, and the zone it stands on with its hole marked.
Open the nozzle on a sphere in SheetMorphConfigurations
- Radial. The axis of the nozzle passes through the centre of the sphere, at a latitude: the nozzle is cut square.
- Upright. The nozzle is parallel to the axis of the sphere, at an offset from it, on the upper half: the nozzle is cut to a saddle.
A worked example
The radial configuration with the sizes SheetMorph opens with, in mm. Two plates: the nozzle, and zone 3 of the sphere with the hole marked: 2 parts, 3 seams.
| Blank of P1 | 944.1 mm × 407.6 mm |
| Blank of P2 | 8060.1 mm × 2601.7 mm |
| Length of cut, every outline and hole | 21619.7 mm |
| Diameter of the sphere | 3001.00 mm |
| Diameter of the nozzle | 301.00 mm |
| Number of zones | 4 |
| Latitude of the edge of the caps | 70.53 ° |
| Latitude each zone spans | 35.26 ° |
| Latitude of its axis | 20.00 ° |
| Length along its axis | 400.00 mm |
| Girth of the plate | 945.62 mm |
| Length of its shortest line | 407.57 mm |
| Length of its longest line | 407.57 mm |
| Lowest latitude of the hole | 14.24 ° |
| Highest latitude of the hole | 25.76 ° |
| Across the hole, round the sphere | 301.51 mm |
| P1 Nozzle, long | 944.10 mm |
| P1 Nozzle, wide | 407.57 mm |
| P2 Zone 3, long | 8060.07 mm |
| P2 Zone 3, wide | 2601.69 mm |
| Plates | 2 |
| Triangular facets | 128 |
| Pattern extent X | 11019.19 mm |
| Pattern extent Y | 2601.69 mm |
| Area of the blanks | 8,152,694 mm² |
| Area cut out | 66,704 mm² |
| Net area | 8,085,990 mm² |
| Total cut length | 22536.13 mm |
| Longitudinal seam length | 1316.59 mm |
How it is developed
Parallel-line development (nozzle) and zone (polyconic) development (sphere). This is a triangulated approximation: the curved surface is divided into small flat triangles, each laid out at its true size. The finer the division, the closer the pattern is to the surface; SheetMorph states the deviation it found.
- Radial, the nozzle meets the sphere in a circle square to its axis: every line of the nozzle is the same length and its end is cut square.
- The hole is on zone 3 of 4. It is marked on the zone as the zone lies flat, each point at its own angle round the sphere and as far up the zone as its latitude is, and cut before the zone is pressed: pressing stretches the zone to the sphere, and the hole with it. The fewer the zones, the more it is stretched.
- The other zones and the caps are made as in the sphere module.
Checked before it can be exported
Every pattern SheetMorph draws is checked against the 3D part it comes from. For this example:
- Surface connectivity (passed): 128 facets form a nozzle and the zone of the sphere it is set onto: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 0).
- Developed edges equal true 3D lengths (passed): 384 facet edges compared between the 3D surface and the flat pattern (max deviation 1.46e-12).
- Shared edges and seam closure (passed): 126 internal edges are shared vertex-for-vertex between adjacent facets; 2 seam(s) have mating edges of equal true length (max deviation 7.96e-13).
- Developed facets consistently oriented (passed): All developed facets are counter-clockwise (outside face up); none is mirrored or degenerate.
- Developed area equals surface area (passed): Facet area in 3D and in the flat pattern agree (difference 4.66e-9).
- Cut outlines closed and non-overlapping (passed): 2 closed outline(s); no outline crosses itself or another outline.
- HOLE-N lies within its plate (passed): 48 points of the hole compared with the edges of the plate; its developed area is 66704.2729.
Assumptions
- The pattern is developed on the mid-thickness surface; inside or outside sizes are converted to it by the thickness.
- Curves are chains of chords between division points.
- No seam, lap, weld-preparation or pressing allowance is added.
Limits of this module
- A sphere cannot be laid flat: the zone is a plate cut flat and then pressed, and the hole is marked on it before pressing.
- The nozzle is radial or parallel to the axis of the sphere; a nozzle inclined any other way is not modelled.
- Where the hole falls on a cap, the cap is not drawn: the place and size of the hole on the cap blank are listed.
- The nozzle is set onto the sphere, not through it, and the saddle is taken on the mid-thickness surfaces of both.
- Curves are chains of straight chords between division points.
- No seam, lap, weld-preparation or pressing allowance is added, and plates are not nested onto stock sheets.
Conventions
Coordinate system. The part stands on the Z axis with End A at Z = 0. Angles round the axis are measured from +X toward +Y, counter-clockwise seen from +Z.
Divisions and thickness. A circle is divided into 4N equal chords. Sizes are inside, mid-thickness or outside sizes; the pattern is developed on the mid-thickness surface and the views show the sizes as entered.
Sphere. The centre of the sphere is at the origin and its axis is the Z axis. As in the sphere module it is made of equal zones between two round caps, each zone the band of a cone through two circles of latitude. Only the zone the nozzle stands on is drawn.
Nozzle. Radial, the axis of the nozzle passes through the centre of the sphere toward +X, at its latitude above the equator (negative below). Upright, it is parallel to the Z axis on the upper half, its axis moved along +X by the offset. The length is measured along the axis of the nozzle from where that axis meets the sphere. End A is the saddle and End B the end of the nozzle.
Hole. The hole is where the nozzle meets the sphere, marked on the zone as it lies flat. It must fall wholly on one zone, or on one cap; a hole across the joint between two plates is refused, and moving the nozzle or changing the zones or the caps clears it.
Seams. The zone is cut on the -X side, away from the nozzle, so the hole is near the middle of its plate. The nozzle is cut on its line nearest the pole below it (radial) or nearest the axis of the sphere (upright).
Change the sizes to your own in SheetMorph, check the drawing, add seam and flange allowances, and export DXF, PDF, SVG, CSV or G-code. Check every pattern against your own standards before cutting.
Open the nozzle on a sphereOther pipe ends and nozzles
- Angled Cut: A length of round pipe with one or both ends cut at an angle: mitered ends, wedges and oblique lengths.
- Pipe on Plate: A round pipe standing on a flat or sloping plate, such as a roof: the pipe cut to the slope, and the plate with its hole.
- Nozzle on Head: A round nozzle set onto a dished or hemispherical head, on its centre or off it: the nozzle unrolled with its saddle cut.
- Pipe on Elbow: A round branch set onto a segmented bend, on its outside or on its side: the branch unrolled with the saddle that fits the gores.
- Bellmouth: A flared inlet to a round duct or a fan, with a straight spigot: made in rings, each part of a cone, or in petals pressed to the curve.
- Roof Flashing: The flashing where a flue or vent passes through a pitched roof: the base plate on the slope with its hole, and the sleeve cut to the pitch.