This space-saving transition will be developed by the method of triangulation, concentrating on locating the true-length lines needed for the development of two half-patterns. It will use two offsets and will be pitched at a 30-degree angle.

Because pitch has been added on the round end of the transition, you will need to draw both the elevation view and top view, as shown in Figure 1.

When a square-to-round transition has the square and the round parallel to one another, it is only necessary to draw the top view. However, when the top and bottom are not parallel, such as the transition in Figure 1, two views are necessary. The reason is that in any square-to-round, where the top plane is parallel to the bottom plane, you're looking at the round plane in its true shape. You can divide the circumference of the circle into equal spaces as necessary in developing the true-length triangle.

## Taking shape

When the top of the transition (the round) is required to be at an angle, you cannot see the true shape from the top view. Instead, you see an elliptical shape. However, you still need the reference points on this ellipse to develop the true-length triangle. The only way to accomplish this is to use the elevation view to construct a profile view of the circle and project the points from this view to the top view, as shown in Figure 2.Another reason the two views are necessary: when the base and the top of the square-to- round are parallel, the height needed for the true-length triangle is the height of the actual transition. When you have the top at an angle as previously described, you now have several heights to help determine the length of lines necessary for the pattern. These lines are individually projected, horizontally, to the true-length triangle as shown in Figure 3.

From the elevation view, you now can project lines (shown in red) and determine the minor axis of the elliptical shape in the top view, F to F1. The major axis, E to E1, shown in the top view is already known to be 12 inches. The true length of the minor axis is shown in the elevation view.

It is very important you're accurate in developing the ellipse in the top view.

Once you have completely developed the elliptical shape in the top view, which represents the round part of the fitting, the circumference of this circle must be divided into equal spaces, as shown in Figure 2. Because you are not looking at the circumference of the circle perpendicular to its plane, you cannot equally divide the circumference of circle in the top view.

The elevation view in Figure 2 also does not show the true plane of the circle, but does show the true length of the circle's diameter. With this information, you can easily draw an auxiliary view, called a "profile view," of the circle and show it in its true shape.

Now that you're looking at the circle perpendicular to its plane surface, you should divide the profile view, the circumference of the circle, into equal parts.

## Divide and conquer

Divide each half into 12 equal parts, or six parts per quarter, and number them one through 13. Draw a line from each point perpendicular to Line AB, as shown in red in the elevation view of Figure 2. Where each line meets AB, it represents the equal divisions in the circle's elevation view.You need to know where these points are to be able to project each one to the elliptical shape, shown in the top view. Reference all points as they intersect the circumference of the ellipse in the top view with the same number as the profile view. This has established points 1 through 13 in the top view. To establish points 2' through 12' on the top of the ellipse, extend the projection lines from the first reference points established, points 2 through 12.

To finish the top view: From each point on the ellipse, draw a line to the corner of the square base. Keep in mind that the circle and the base are split into four sections. All lines drawn are to stay within their same section. Connect lines 1 through 7 to C, lines 7 through 13 to D, lines 1 through 7' to C', and 7' through 13' to D'. Lines 13A and 1B are the seams that divide the two half-patterns. All lines that are drawn from the corner to the circle are used in creating the true-length triangles.

Figure 3 illustrates the development of the true-length triangles. There are two sets shown in Figure 3, one for each side of the transition. The explanation is the same for both.

## The vertical bar

Typically, the vertical bar in the true-length triangle is the same height as the transition, if the top and the bottom of the transition are parallel. The top of the transition is at a 30-degree angle, which means several heights need to be marked along the vertical bar of the true-length triangle.In fact, every bend line shown in the elevation drawing is a different height and needs to be projected over to the vertical bar. Now take the distances of C1 through C7 from the top view in Figure 2 and transfer them to the base line, as shown in Figure 3. Use the point where the vertical line meets the base line as the edge for each length being transferred.

Now transfer the distance of D7 through D13 from the top view in Figure 2 to the base line, also shown in Figure 3. The distance of Point 13 to Point A and Point 1 to Point B should also be placed on the base of the true-length triangle. Connect these points on the base line, one through 13, with the like number on the vertical bar. These become the true-length lines for the half pattern.

The first step in developing this pattern is draw a straight line by taking the distance of Line BC from the top view in Figure 2. This is shown in Figure 4. Next, determine Point 7, which is the center of the half pattern. Take the true-length distance from Point 7C on the base (true-length triangle DC) in Figure 3 to Point 7 on the vertical bar, as shown. Place one end of the dividers on Point C and using it as center, create an arc near Point 7, as shown.

## Arcs

Now take the true-length distance from Point 7D on the base (true-length triangle DC) to Point 7 on the vertical bar. Using Point D as center, draw a line that would intersect with the previously created arc. This intersection becomes Point 7.Save time by using two sets of dividers. Set one at the distance that was used to divide the circumference of the circle in the profile shown in Figure 2. With the other, place one end on Point 7 and create a slight arc near both sides of Point 7. To the right of Point 7 will be Point 6 and to the left, Point 8.

Locate the true-length distance of Point 8 from the true-length triangle and using D as center, make an arc that intersects with the arc drawn from 7. This becomes Point 8. Repeat similar steps with Line 6. Now using Point C as center, make an arc that intersects from the arc drawn from Point 7. This becomes Point 6.

From Point 6, create an arc near Point 5. Take the true-length distance of Line 5 from the true-length triangle and use Point C as center to make an arc that intersects with the arc drawn from Point 6.

Continue to do these steps until you reach points 1 and 13. Take the distance from Point A to Point D in the top view of Figure 2 and use Point D as center to make an arc near Point A, as shown in Figure 4a. Repeat this with the distance of Point C to Point B, using Point C as center.

To establish points A and B on D and C's partial arcs, take the true-length line of 13A from the true-length bar in Figure 3 and use Point 13 as center to make an arc that intersects with the arc drawn from Point D. This will establish the exact position of Point A. Repeat this with the true-length line 1B from the true-length triangle in Figure 3 and use Point 1 as center to make an arc to intersect with the arc drawn from Point C.

This becomes one half-pattern. The other half is developed the same way; however, you would use the true-length triangle D'C' in Figure 3. The pattern is shown complete in Figure 4b. No allowance was given for seams or flanges, which would be added parallel to Line 13A and 1 B.

(For more information on manual sheet metal layout, write to The Sheet Metal Shop Resource Center, 516 Chicago Ave., Waukesha, WI 53188, or visit www.thesheetmetalshop.com.)