Developing Cylinders and Truncated Cylinders

Developing Cylinders and Truncated Cylinders

A full cylinder develops into a rectangle. Its width is the circumference, π × diameter, and its height is the cylinder's height. That is the whole construction.

A truncated cylinder — one cut at an angle — is where the real work is, and it is done with generators:

1. Divide the plan circle into twelve equal parts and number them.
2. Project each generator up into the elevation and mark where the cut crosses it.
3. Draw the stretch-out line: a straight line of length π × D, divided into the same twelve equal parts.
4. At each division, set off the height of the corresponding generator, taken from the elevation.
5. Join the tops with a smooth curve.

The developed top edge is a sine curve, not a straight line and not an arc.

Worked example. The stretch-out length can be stepped off with dividers using the twelve chords instead of calculating π × D. That is slightly short — a chord is marginally less than its arc — so for accurate work calculate the circumference instead of stepping it.

Core checkpoint: The heights come from the elevation, one generator at a time. The widths come from the stretch-out. Never mix the two up.