Tuesday, July 14, 2020

Alastair Knows All the Angles

When you have two boards that meet to form a 90° angle, you can cut each one at 45° to make a miter. Likewise, if the boards form a 45° angle, you cut each at 22.5° and there's your miter. The circular saw has an angle guide that goes up to 45 and has 22.5 specially marked.

So, when the plans call for a 33° and a 21° angle on the "prow," and you're cutting the rim joists on either end, we just split the angle, right? I cut one at 16.5° and the other at 10.5° and I was horribly wrong.

I still don't quite get it. If the prow was 45° on both sides, wouldn't we miter at 22.5°? If not, when do you use 22.5? (Answer: When you're cutting baseboard facets around rounded-corner drywall.)

So, I went back to the drawing board. I simply drafted the 33° corner at large scale. The non-rim joists that hit the prow would be cut at 33°--that much was clear, at least. And that means setting the circular saw to 33°.

But the miter not so much. On my drawing, I confirmed that the angle of the two rim joists was 123° on the inside and 237° on the outside (which makes 360°). So, just split 123 and set the circular saw to 61.5°, right?

First of all, no, because the circular saw only goes to 45. I need a Spinal Tap circular saw. I drew the "perfect" miter on my large scale drawing and I could see that neither board required more than a 45° cut. So, we're looking at the right angle inverse of 61.5, which is 28.5°. Just to be clear: When you're mitering a 33° break like this, just cut both boards at 28.5° and you're good. What the hell?

Furthermore, while that might work, I drew the perfect miter--the line that bisects the intersection of two 1.5" boards at 33°--and the angles were not equal. It measured out at 33° for the straight rim joist and 24° for the angled prow rim joist. They add up to 57°, which is the right angle inverse of...wait for it...33°.

I unscrewed the rim joist and recut the end that had been 16.5° and made it 33°. Then I recut my first attempt at the prow rim joist because I had measured to the cantilevered joist, not the tip of the prow that wasn't there yet. But when I put it together, it worked. Yay for drawings at large scale. Not so much for my conceptual math skills.
Framing as of Monday evening


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