There are different ways of laying out an offset to maintain the correct width. Figure 2 illustrates the use of miters; they're good for applications such as downspouts, as well as ductwork.

To find the proper miter as shown in Figure 2, mark off your offset as shown. If you're working in a new home or business, this can be done on a scrap of plywood, on the back of a piece of drywall lying around, or even lightly on the wood floor before the finished floor goes in.

The first step is to lay out the offset as shown (points 1 to 2, 2 to 3, and 3 to 4) Set the dividers approximately 3 to 4 inches apart, and using Point 3 as center, make an arc as shown from Point a to Point b in Figure 2. Reset the dividers approximately 7 to 8 inches apart and using Point a as center, draw an arc near Point c. Using Point b again as center, make an arc that intersects with the previous arc at Point c. Using a steel rule, or similar straight edge, draw a line from Point c to Point 3, continue this line through to Point d. This establishes the miter line. Use a sliding T bevel to transfer this miter line to your work.

## Equal sides

Figure 3 illustrates an offset of equal sides with a straight throat and back. Once you have marked the height of the offset and the length of the fitting as shown, set your dividers to the width of the ductwork from Point A to Point B. Then using Point A as center, create an arc from Point B to Point B' as shown; repeat this for both ends. From Point A, draw a line tangent to the arc as shown. At Point B, draw a line perpendicular to Line AB to intersect with the previous line drawn from Point A tangent to the arc. This intersection becomes Point C. By doing this you will have maintained a constant width throughout the offset. Figure 3(a) shows a close-up of the corner and the intersection at C.Now using Point A as center, create an arc from Point B to Point B'. Reset the dividers from Point A to Point C. Again using Point A as a center point, strike an arc from Point C to Point C'. Repeat these steps for the other end of the fitting.

With a straight edge, draw a line tangent to both arcs (D to E) for the top and bottom of the fitting as shown in the second drawing in Figure 4.

## The developed cheek

The third drawing in Figure 4 shows the developed cheek of the offset fitting without the layout marks. The allowance necessary for the lock has been added. The quickest way to determine the length of the throat and back is to use a flexible rule or piece of metal. Measure from Point A to Point B and add the necessary dimensions for the S-slip and drive.Figure 5 illustrates a plain offset with curved back and throat. Looks complicated to some, but a few standard steps make creating these offset cheeks easier.

As previously done, mark the offset as shown. The height of the offset is marked from Point B to Point D. Most of these cheeks can be developed with your dividers or trammel points. Lines AC and DE should be the same dimensions. Use points 6 and 7 as a center for the necessary arcs. Extend line AC to Point C' (to be used for reference only). Do this again with Line ED, and extend it to Point B.

Draw a line perpendicular at center (midpoint) of Line 1-3. Set your dividers at a distance greater than half the distance from Point 1 to Point 3. Using points 1 and 3 as centers, strike two arcs. Draw a line from the intersection of both arcs as shown from Point 4 to Point 5. Extend this perpendicular line from Point 4 to Point 5 until it intersects the plane of line CC'. This intersection becomes Point 6.

Set the dividers the distance from Point 6 to Point 1. Then using Point 2 as center, draw an arc at Point 7.

Draw a line from Point 6 to Point 7 that passes through the center of Line 1-2 at Point 3. If it does not pass through the center at Point 3, check your work and make corrections. The line from Point 6 to Point 7 also serves as a guide on how to draw your arcs, as shown by Point 8.

To draw your arcs, set the dividers at the distance from Point 6 to Point C. Using Point 6 as center, make an arc from Point C to Point 8.

Using the same settings, with Point 7 as center, now make an arc from Point D to the line drawn from Point 6 to Point 7. Reset the dividers to the distance of Point 7 to Point E. With Point 7 as center, strike an arc from Point E to Point 8.

Move the dividers over to points 6 and A. Using Point 6 as the center, make an arc from Point A to the line drawn from Point 6 to Point 7. This will meet with the previously drawn arc and complete the curve. Using points 6 and 7 as centers, add and subtract a quarter inch to the completed arcs and strike new arcs needed to create seams. The stretch-out for the back and throat are measured as previously explained with the use of a flexible steel rule. A two-inch strip of light gauge steel would also work.