### Essay 2

*Complete the Pattern - Sheet Metal
Ductwork*

### Marianne Parsons

While designing ductwork, it is important for
engineers and ductwork manufacturers to geometrically construct
the three-dimensional duct from a two-dimensional piece of sheet
metal. This is especially important for projects in which standard
duct sizes are not useful, and custom sizes and custom angles
for ducts must be produced. This geometric process can be broken
into parallel line and radial line constructions depending on
the desired shape of the ductwork.

By coordinating different views of the same
object, the expanded pattern can be geometrically constructed
to represent the two-dimensional pattern of the three-dimensional
object. If we have the desired **plan** of the duct (the bottom
view) and the desired **elevation** (the side view) we can
geometrically *unfold*, or *unroll*, the shapes to generate
the two-dimensional **expanded pattern **(the surface).

Points can be identified along the base of
each shape and then through construction their corresponding locations
on the expanded pattern can be determined. Once the pattern is
complete, it can be rolled or folded to produce the three-dimensional
duct!

**Parallel Line Development**
Parallel line development uses parallel lines
to construct the expanded pattern of each three-dimensional shape.
Essentially, parallel lines project specific points from one view
to another, to determine proper heights of the shape, as shown
in the following explorations.

Rectangular
Ducts

Round
Pipes

**Radial Line Development**

Radial line development uses lines radiating
from a central point to construct the expanded pattern of each
three-dimensional shape. These shapes each form part of a cone
and lines radiating from the vertex of the cone generate the expanded
pattern of the curved surface as shown in the following explorations.

Round Taper

Round
Taper with Pitch

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