Rain Cap: flat pattern

A conical cap that runs to a point, as over a flue or a vent, with or without a skirt round its rim: the sector it is rolled from. A conical cap that runs to a point, as over a flue or a vent, with or without an upright skirt round its rim: the sector it is rolled from, and the skirt.

Configurations

• Cone only. A cone from its rim to its apex, cut from one sector.
• Cone with a skirt. The cone carries an upright band round its rim, as a drip edge or a storm collar.

A worked example

The cone only configuration with the sizes SheetMorph opens with, in mm. One plate: the cone as a sector of a circle: 1 part, 2 seams.

How it is developed

Radial-line development of a right cone. 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.

• A cone that runs to its apex is a sector of a circle whose radius is the slant height. Its arc is as long as the rim is round, which fixes its angle.
• Mark a disc of 721.9425 diameter and cut out a wedge of 60.3086 degrees; the two straight edges are brought together to make the seam.

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 a cone closed at its apex: 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 3.06e-13).
• Shared edges and seam closure (passed): 31 internal edges are shared vertex-for-vertex between adjacent facets; 1 seam(s) have mating edges of equal true length (max deviation 1.71e-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 2.91e-10).
• 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 cone runs to a sharp point. For a cone with an opening at the top use the cone, and for a cap of flat plates the pyramid hopper.
• No lap is added along the seam and none at the rim; add them under Fabrication.
• The straps or legs that hold a cap above its flue are not drawn.
• 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.

Cap. The cap stands on the Z axis with its apex uppermost. A plain cap has its rim at Z = 0; a skirted one has the foot of its skirt at Z = 0 and its rim at the top of the skirt. End A is the open edge it stands on, and End B is the apex, which is a point.

Seam. The cone is cut along the line from the apex to the rim on the -X side, and the skirt along the line below it. The sector is drawn outside face up, with the wedge that is left out between its two straight edges.

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.

Other cones

• Round to Round: Reducers and cones between two round ends: concentric, eccentric, offset or inclined.
• Round to Ellipse: A cone from a round end to an elliptical end, or from an ellipse to a round: concentric, offset, eccentric or with angled faces.
• Cut by a Plane: A right cone with its top, or both ends, cut by an inclined plane.
• Multi-Section: A large cone made of several plates: equal segments round it and courses up it.