Transition Pieces

Transition Pieces

A transition piece joins two different shapes — most commonly a square duct to a round one. Its surface is not a simple prism, cylinder, pyramid or cone, so it is developed by triangulation: the surface is divided into triangles, each triangle's true shape is found, and they are laid out side by side.

Why triangulation works. A triangle is rigid: if you know all three side lengths you can construct it exactly. So any surface split into triangles can be developed, provided every side length is a true length.

The procedure:

1. Divide the round end into equal parts, and join each division to the nearest corner of the square end. The surface is now a set of triangles.
2. Find the true length of every sloping line — the plan shows their horizontal run and the elevation their rise, so each is the hypotenuse of a right triangle. A true-length diagram is the efficient way to get them all.
3. Build the triangles one at a time, side by side, using true lengths only.

Worked example. A square-to-round transition has four flat triangular faces (one per side of the square) and four conical corner sections. The conical parts are where the round end's divisions matter — take too few and the corners come out faceted rather than round.

Core checkpoint: Every line used in triangulation must be a true length. The plan and elevation give you the two components; the true length is the hypotenuse.