Shortcuts don't always work when laying out miters

"Since almost anyone can cut a square miter, the question at once arises, in view of this statement, why is it he cannot cut a raking miter, or pinnacle miter, or any other equally hard form? The answer is, because he does not understand how he cuts a square miter. He may perform the operation just as he has seen someone else do it, or as laid down in some book or paper. He may produce results entirely satisfactory from a mechanical standpoint, but after all is finished he is not intelligent as to what he has done, he does not comprehend the why and the wherefore of the steps taken."

- From The Metal Worker Pattern Book by A.O. Kittredge, 1881.

A miter, shown in Figure 1, represents the intersection of two like profiles at a given angle with the proper shape to fit against any surface at any angle or combined angles. A square miter is made of two like profiles that, when placed together, form a right (90-degree) angle.

Drawing the miter line is usually the last step of projection used before many sheet-metal articles are developed. Understanding projection (projecting lines) is a skill sheet-metal workers should be familiar with.

Learning shortcuts in pattern development sometimes costs you later: You don't know the techniques needed for more challenging miters. If you learn the long methods, you will have the necessary skills for when shortcuts will not work.

The following rules will help you lay out perfect miters every time.

To obtain a miter line there must be a plan, elevation or other view of the shape, in line with its profile, showing the line the surface against which it miters. Reference all points in the elevation view as shown in Figure 2, points 1 through 8. Once the profile and the miter line have been drawn at the desired angles, create lines from the reference points labeled on the profile to the miter line, shown as 1A, 2-3B, 4-5C, 6-7D and 8E in Figure 2.

Now look at Figure 3. From the points where the projection lines meet the miter line BACD and E, extend lines parallel to the elevation view as shown by BB', AA', CC', DD', and EE'.

Using E as your stretch-out line, as shown in Figure 4, mark off the distance from 1' to 2', 2' to 3', 3' to 4', etc., until all points, including 8', are laid out. These distances are obtained from the profile (elevation view) by setting the dividers to each distance and transferring them to the stretch-out line.

From points 1' to 8' on the stretch-out line in Figure 4, draw right-angle lines to intersect the lines drawn or dropped from the profile (elevation view) and carried over to the right from the miter line. Follow the line drawn from Point 1 in the elevation view to A, where it meets the miter line. From A on the miter line, draw a line parallel to the elevation drawing, as shown. From the stretch-out line, beginning at 1', drop a right-angle line until it intersects with the line drawn from Point A on the miter line.

Do the same with all similar reference points on the elevation view and stretch-out lines, 1 to 1', 2 to 2', 3 to 3, etc., until all the points are defined. Complete the pattern by connecting the points as shown in Figure 4. This completes one side of the miter. To complete the second half of the miter (if needed), you can create a mirror image by carefully tracing the pattern and making bends opposite of the original. You can also develop the full second pattern of the miter as shown in Figure 5, using the same miter line.

Figure 6 is a comparison between two different miter degrees. The top of Figure 6 shows the 45-degree miter line which we used in this article. The lower part of Figure 6 is a 22.5-degree miter line, using the same steps, demonstrating that any miter line can be solved with this method. Note that all points were chosen for clarity and that any profile will work. However, a curved profile would need to be clearly defined with more projection lines extended to the miter line and carried over to the pattern.

Printable worksheets for this and similar projects are available at www.thesheetmetalshop.com.