Figure 1A

So you’re now finished developing the pattern for a transition that you haven’t done in a really long time or perhaps you’ve never made it before. And only after an honest attempt of bending it up did you realize that something was out of whack or perhaps missing all together?

Was the problem that the true length of the many needed lines is just not there? And because many people don’t do this everyday, you sit and scratch your head. If you could just remember where to start to establish lines you could get it done the right way, the first time.

When explaining how patterns are made using triangulation, many like to include two views of the transition, the elevation and plan view. These two views together can be used to help you better understand the layout of the most difficult patterns. These two views also contain much-needed information, especially when using triangulation as the method of developing the pattern.

But are both these views really needed? How much information is redundant or unnecessary? It would be to your advantage in mastering the technique of triangulation to understand which views are necessary and which are not. When you begin to lay out these fittings, you should be looking for only the information that is absolutely necessary to get the job done. Why would you want to complicate it with more drawing?

The views necessary for the pattern using triangulation are best described as four “rules” in a supplementary reference sheet by Frank O’Rourke in Sheet-Metal Pattern Drafting, published in 1949.

When using triangulation to lay out any particular fitting, there are rules you can follow and when you understand and apply them, you will be able to save time developing the pattern. Here is a breakdown of the four rules and how we can apply them to our square-to-round transitions.


1. “When the halves of a symmetrical figure are symmetrical in the plan and the elevation, and when the planes in the elevation are parallel, the true lines may be formed by using either view.”

The best example for Rule No. 1 is shown in Figure 1A, a common square-to-round transition where the center of the square is also the center of the round.

The plan view would be the most practical, since all you will need is the height of the fitting shown in elevation and one corner of the transition to develop a true-length diagram. The elevation method would also work; however, you would need an additional drawing as you will have to develop and extend the profile of the round Figure 1B separately to develop your true-length diagram.

Either way, you would only need to solve this problem for one section, as it will be similar for all four sections of the fitting. Take this one step further and all you really need is one section of the transition as shown in the shaded area of Figure 1B. See how easy this can be?

Take a look at Figure 1B as you establish the true-length lines from the elevation view. Once the profile is drawn and divided into equal sections, reference these as points 1 through 4.

Figure 1B

Now draw a line, perpendicular to the top plane, to each division on the profile view establishing points 1, 2”, 3” and 4” on the top plane. Create a true-length diagram by drawing two lines perpendicular to each other and marking off half the distance of the plan A to B, as shown: A’ to B.

Using your dividers, transfer the lengths of lines A-1, A-2”, A-3” and A-4” to the base of the true-length diagram. And using Point A’ as center, draw a reference mark to these mentioned lengths as shown along the base by the distance of A’ to 1’, 2’, 3’ and 4’. Perpendicular to each one of these lengths on the base is a line drawn to points 2x, 3x and 4x. You get the distance from the profile in the elevation view in points 2 to 2”, 3 to 3” and 4 to 4”.

If you did this correctly and all is truly symmetrical, the true-length lines from B to 1’ and B to 4x will be the same length as well as B to 2x and B to 3x. The other true-length lines necessary for the pattern are already shown in true length in the elevation as the distance of A to B, being half of the length of the base, but it’s all you need to develop the quarter pattern.

Figure 2

No. 2

2. “When the halves are not symmetrical in the plan view and the planes are parallel in the elevation, the plan should be used without the aid of the elevation. This is because only one height is required and if this is known we really have no other use for the remainder of the elevation, so it is eliminated all together.”

A good example of rule No. 2 would be a square- or rectangular-to-round fitting where the round is offset two ways from center, as shown in Figure 2. See the plan drawing in Figure 2. Sides one and two cannot be duplicated by laying out one side and using it as a template for the other, so you’re having to develop the true-length lines from the plan.

The only useful information in Figure 2B would be the height of the fitting and you don’t need to draw an elevation for it.

This rule could apply to a number of transitions, including tapered round with an offset as long as the top and bottom round are parallel.

3. “When the halves are not symmetrical in the plan view and the planes are not parallel in the elevation, both views are necessary to produce the surface lines. If the heights of the elevation and the base lines of the plan are known, a diagram of triangles can be drawn.”

Figure 3

In Figure 3, you use the drawing from Figure 2 but add a slant to the base. In Figure 2 (rule No. 2), you learned that you had no use for the elevation. In Figure 3, rule No. 3, you were told you need both the elevation and the plan to develop the pattern. All this because of one change and that would be that plane No. 1 and plane No. 2 are no longer parallel to one another in Figure 3B as they were in Figure 2B.

Figure 3C

Figure 3

You can see by the drawing in Figure 3A that there are no symmetrical sides in the plan as well as plane Nos. 1 and 2 are not parallel to each other in the elevation shown in Figure 3B. This particular fitting looks a little more complicated because it’s elevated and you need to solve for each true-length line individually, as briefly described in Figure 3C.

Together with the aid of both the elevation and plan view, you’re going to solve for each true-length line. You need to establish the height of each line (elevation view) and the base length of each line (plan view). The hypotenuse of the two corresponding lines is the true length of that line.

In this particular fitting, to establish the height of the true-length diagram, extend two horizontal lines, one each from Point A and Point B to the right, as shown in the elevation view.

To the right of the elevation view, referenced as B1, draw a line perpendicular to reference X as the height of the diagrams. With your dividers or trammel points, transfer the distances from plan view A’ to 1’, 2’, 3’ and 4’ to the line extended from Point A in the elevation view as shown.

Now using Point A as center, draw reference marks as shown: 2”, 3”, 1” and 4”. Connecting these to Point X will establish several of the true-length lines necessary for this part (side No. 1) of the transition. The other lines that must be established are from Point 4 to Point F from the elevation view.

Again, the base line is drawn - shown in the elevation - and the true length is established. The plan shows the true length of lines F to A’ and A’ to e. In the plan view, the true length line of Point 1’ to e can be taken from the elevation - shown as Line 1-A - as would be the same reference mark for e.

4. “Symmetrical fittings having planes that are not parallel in the elevation should be developed by using the elevation without the plan.”

We can discuss Rule No. 4 next time around or stop by for all your sheet metal layout questions.

Visit Wisconsin contractor Bud Goodman’s Web site,, for free worksheets that you can use to brush up on your pattern-development skills.