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
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.
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 with Pitch
Return to my EMAT 6690 page