Helical Chute: flat pattern
A spiral chute: a floor that winds round an axis as it falls, with or without walls on its edges. A spiral chute: a floor that winds round an axis as it falls, with or without a wall on its inner and outer edges.
Open the helical chute in SheetMorphConfigurations
- Floor only. The helical floor alone, as for a chute fitted between existing walls or a spiral stair soffit.
- Floor and walls. The floor with a wall standing on its inner edge and another on its outer edge.
A worked example
The floor only configuration with the sizes SheetMorph opens with, in mm. The floor in one plate: 1 part, 0 seams.
| Blank, the rectangle the plate is cut from | 2105.9 mm × 919.9 mm |
| Length of cut, every outline and hole | 5306.3 mm |
| Inner radius | 300.00 mm |
| Outer radius | 800.00 mm |
| Width of the floor | 500.00 mm |
| Turn angle | 180.00 ° |
| Rise | 1200.00 mm |
| Rise in one full turn | 2400.00 mm |
| Length of the inner edge | 1525.87 mm |
| Length of the outer edge | 2785.06 mm |
| Slope of the inner edge | 51.85 ° |
| Slope of the outer edge | 25.52 ° |
| Inner radius of the flat ring | 605.89 mm |
| Outer radius of the flat ring | 1105.89 mm |
| Angle the whole floor takes up on the ring | 144.29 ° |
| Lengths the floor is cut in | 1 |
| P1 Flight, long | 2105.90 mm |
| P1 Flight, wide | 919.91 mm |
| Plates | 1 |
| Triangular facets | 32 |
| Pattern extent X | 2105.90 mm |
| Pattern extent Y | 919.91 mm |
| Developed area | 1,073,165 mm² |
| Total cut length | 5306.35 mm |
| Longitudinal seam length | 0.00 mm |
How it is developed
Triangulation (true-length unfolding) of a helicoid. 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.
- The floor is divided into narrow triangles between its inner and outer edges and unfolded from their true lengths. It comes out very nearly as part of a flat ring, whose radii and angle are listed.
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): 32 facets form one open sheet: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 1).
- Developed edges equal true 3D lengths (passed): 96 facet edges compared between the 3D surface and the flat pattern (max deviation 3.41e-13).
- Shared edges and seam closure (passed): 31 internal edges are shared vertex-for-vertex between adjacent facets; 0 seam(s) have mating edges of equal true length (max deviation 0).
- 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 0).
- Cut outlines closed and non-overlapping (passed): 1 closed outline(s); no outline crosses itself or another outline.
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
- The floor is a helicoid and cannot be laid flat exactly: it is unfolded from triangles and is stretched in forming.
- The floor is level across and of constant width and slope; a dished or banked floor is not modelled.
- Walls are upright and of constant height. Sizes are those of the surface the sheet lies on: the thickness is used for the weight only.
- 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.
Chute. The floor winds round the Z axis, counter-clockwise seen from above, from the +X side at Z = 0, rising the height entered over the turn angle. It is level across: every line across it points at the axis. End A is its inner edge and End B its outer edge. For a chute that falls, read the drawing from the top down.
Walls. A wall stands upright on an edge of the floor, to the height entered. It lies on a cylinder, so it unrolls exactly, to a strip that slopes at the angle of that edge.
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 helical chuteOther rings and helicals
- Segmented Flange: A flat ring, as a flange, a stiffener or a base ring, made in equal segments so that it nests on the plate, with or without its bolt holes.
- Rolled Bar: A ring, a hoop or part of one rolled from flat bar or strip: the length to cut on the neutral line, with the gap for the weld and the flat ends.
- Screw Flight: One flight of a screw conveyor or auger, right or left hand: standard, tapered or ribbon, as the flat blank that is pulled out to one pitch.
- Stair Stringer: The stringer of a spiral or helical stair: a plate rolled to stand on a cylinder as it climbs, alone or as a pair, with a line for every tread.