Pipe on a Plate: flat pattern

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. A round pipe standing on a flat or sloping plate, such as a roof or a hopper side: the pipe cut to the plate, and the plate with its hole.

Configurations

• Flat plate. The plate is square to the pipe: a plain length of pipe and a plate with a round hole.
• Sloping plate. The plate slopes. The pipe is cut to the slope and the hole in the plate is an ellipse.

A worked example

The sloping plate configuration with the sizes SheetMorph opens with, in mm. 2 plates: the pipe, unrolled with 32 divisions, and the plate with its hole: 2 parts, 2 seams.

How it is developed

Parallel-line development (unrolled cylinder); the plate in true shape. 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 plate slopes, so it cuts the pipe in an ellipse: the foot of the pipe plate is a sine-shaped curve, and the hole in the plate is an ellipse D / cos(slope) long and D wide.
• The pipe is a cylinder, which is developable: its plate is as wide as the developed circumference and as high, at each division, as the pipe is there.
• The plate is flat, so it is drawn in its true shape, with the hole marked from the feet of the pipe. The 3D view shows the plate without its hole; the weight is for the plates with the hole cut out.
• Division points lie on the true circle, so the plate width of the pipe (a sum of chords) is slightly less than pi x D, and the hole is the polygon through the same points.
• The pipe's seam is on its low side (-X).

Checked before it can be exported

Every pattern SheetMorph draws is checked against the 3D part it comes from. For this example:

• Top square, foot on the plate (passed): All 64 points of the pipe's two ends lie at radius 100.5: the top in its square plane, the foot in the plane of the plate (max deviation 1.42e-14).
• Plate flat, at the slope, centred on the pipe (passed): The plate is a flat 500 x 400 rectangle at 30 deg, centred on the pipe axis (max deviation 0).
• The pipe is a cylinder (passed): Every generator is parallel to the pipe axis and runs up from the plate (max deviation 0).
• Surface connectivity (passed): 66 facets form a pipe and the plate it stands on: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 1).
• Developed edges equal true 3D lengths (passed): 198 facet edges compared between the 3D surface and the flat pattern (max deviation 1.24e-12).
• Shared edges and seam closure (passed): 64 internal edges are shared vertex-for-vertex between adjacent facets; 1 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 1.22e-9).
• Cut outlines closed and non-overlapping (passed): 2 closed outline(s); no outline crosses itself or another outline.
• Pipe plates are true unrolled cylinders (passed): Every generator and seam of every pipe plate is perpendicular to the plate's baseline, as on an unrolled cylinder (max deviation 4.73e-12).
• Hole in the plate matches the foot of the pipe (passed): The hole lies inside the plate and its edge has the length of the foot of the pipe (max deviation 0).
• Symmetric about the plane of the slope (passed): Every point of the pipe has its mirror image across the XZ plane (max deviation 8.02e-14).

Assumptions

• The pipe pattern is developed on its mid-thickness surface. An inside or outside diameter is converted to it by one thickness; the height, the slope and the plate size are not changed.
• The pipe stands on the plate and does not pass through it; the hole is the size of the mid-thickness pipe.
• The plate is a rectangle centred on the pipe axis, sloping about the Y axis.
• The top of the pipe is cut square.
• No rolling allowance, and no seam, lap, flange, weld or trimming allowance, is added to any outline.
• Plates are drawn outside (upper) face up.

Limits of this module

• The pipe is set onto the plate; a pipe passing through with a collar or flashing is not covered.
• The plate is a plain rectangle sloping one way; a plate sloping two ways (a hip or valley) is not covered.
• The hole is drawn at the mid-thickness size of the pipe, with no clearance.
• The 3D view and the orthographic views show the plate without its hole.
• Plate edges and the hole are straight between divisions, not smooth curves.
• No rolling allowance, and no seam, lap, flange, weld or trim allowances.

Conventions

Coordinate system. Right-handed, Z vertical in the views. The pipe stands on the Z axis and its square top, End B, is at Z = height. The plate passes through the origin, where the pipe axis meets it, and rises toward +X. The Front view shows the slope as a straight line.

Height. The height is measured on the axis of the pipe, from the plate to the square top. On a sloping plate the pipe is shorter on the high side (+X) and longer on the low side, by half the diameter times the tangent of the slope.

Slope. The slope is the angle of the plate from square to the pipe, from 0 to 75 degrees: a roof pitch when the pipe is upright. The plate rises toward +X.

Plate. The plate is a rectangle centred on the pipe axis. Its length is measured up the slope and its width across it (along Y). It must be larger than the hole, which is D / cos(slope) long and D wide.

Numbering. The circumference of the pipe is divided into 4N equal parts, N per quarter: division 0 is toward +X (the high side), N toward +Y, 2N toward -X (the low side). J<k> is the foot of division k on the plate and B<k> its top. P0 to P3 are the corners of the plate. Plate S1 is the pipe and S2 the plate.

Development method. The pipe is cut along its seam and unrolled: its plate is as wide as the circumference, straight along the top, and follows the slope along the foot. The plate is flat already; the hole is marked on it through the feet of the pipe.

Material thickness. The pipe plate has the length of the sheet's neutral surface, taken as mid-thickness. Say whether your diameter is an inside, mid-thickness or outside size. The hole is the size of the mid-thickness pipe; open it out or leave it tight to suit the joint. The 3D view and the views show the diameter as entered.

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 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.
• 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.
• Nozzle on Sphere: 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.
• 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.