"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.
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.
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.
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.