The speed square was specifically designed for roofers, but it has proved useful to many regular woodworkers. Here, I will show how you can use a speed square to do miter cuts on your table saw sled. I'll also explain what the "common" markings mean, and how an average DIY'er can put that to use.
Step 1: What Is a Speed Square?
When I bought this thing, I had no clue what it was. But I could immediately see that it is useful for marking 45 and 90 degree angles. For squaring things during construction. For use as a straight edge. And there is also a 12" ruler on one edge. So for a long time, that's all I used mine for. Turns out, "Speed Square" is actually a registered trademark of the Swanson Tool Company. According to Wikipedia, the Speed Square was invented by Albert Swanson in 1925, and it is a tool made specifically for roofers. When I finally googled it, I found out I was missing out on some useful properties. There are at least a dozen ways to use a speed square, but here I'll show you two of the more unique ways I use mine.
Step 2: Miter Gauge
I don't have a table saw sled, yet. So this is actually my bandsaw sled. BTW, I'm completely unqualified, so don't take any suggestion I make as expert advice. Anyway, I digress. As you can see, all you have to do is clamp the speed square to the side of your saw sled to make 45 degree miter cuts. Speed squares come in 7" and 12" sizes. If your sled is too big for one of these sizes, then you won't be able to support smaller work pieces, directly.
Step 3: Squaring the Sled
But first, you have to square your sled, of course. The easiest way to do that is with a hand plane. Use your speed square to roughly square the edge of your sled to the front fence. Then as you continue planing, you can sight along the edge until you're close enough for government work. If you're especially meticulous, you can measure the distance from the saw slot to the edge at various locations.
Step 4: Odd Angles
The "protractor" on the speed square is actually kinda special. With a regular protractor, you mark two points to set the angle. Then you have to connect the marks to get a line. The speed square is made to pivot on the workpiece using the built in fence on its edge as a pivot point. You simply swing the speed square on the pivot point until the edge of the workpiece lines up with the desired angle. In this pic, the square is set to 25 degrees. So you can simply draw the cut line, directly. Or in this case, I'm using it as a miter gauge, so there's no need for any marking, at all. Note, a table saw sled usually has a back fence. So you will not be able to cut a particularly acute angle on the average table saw sled, because longer stock material will run into the back fence.
Step 5: Common Rafter Markings
There are a couple of cryptic markings on a speed square, to non-roofers. Besides the angle markings on the outer edge of the hypotenuse, there are also two other rulers. One is marked "common." And another set marked "hip" and/or "valley." The markings are actually a measure of slope. Common denotes "common rafters," and the numbers show the slope in inches per foot. In other words, if a rafter must span X feet, horizontally, and it's cut to an angle that coincides with the "3" on the common gauge, it will rise to a height of 3 inches times X. Or 3 inches per foot. (This coincides with an angle of about 14 degrees, FYI). So to boil it down, empirically, the common gauge is a measure of mathematical slope x 12. I have dubbed this "roofer's slope," for want of a better term. The hip/val markings are for measuring the slope of hip and valley rafters. These have compound mitered cuts, and I really don't know how or what I'd use those for...
Step 6: How to Use "roofer's Slope"
For us regular joes, here's an instance where we might find roofer's slope handy: odd angle support brackets for a shelf. I drew up a mock shelf on a piece of paper and will figure out the miter angles without a calculator. The dotted line is the support beam that I desire . First, you physically measure the depth of the shelf, and the height of the support. If you divide the depth by the height, you get the slope. If you multiply this by 12, you get the roofer's slope. In this case, the height was 8 1/16". If you don't have a calculator handy, you can just round this down to 8. So the slope is ~5.25/8. The roofer's slope is 5.25 x 12/8, or 5.25x1.5. That's ~7.8-7.9ish. So now you can go back to your sled and set your speed square-cum-miter gauge to around 7.8. Actually, you want to set your square to the nearest corresponding angle marking. In this case, 7.8 on the common gauge is closest an angle of 33 degrees. So cut it to exactly 33 degrees, because when you cut the other end of the bracket, you will use the complementary angle, which is 90-33=57 degrees. After you have cut one end, you can hold it against the wall and mark the length of the beam with a pencil. Or you can use a tape measure. Or you can use pythagorean's theorem. In this case, the length is a shade over 9 1/2". Either way you measure, once you know the length, you should subtract a bit, because you've been fugding the numbers on your miter angles. You don't want the bracket to extend past the front of the shelf. So maybe cut to a length of 9" (measuring from tip to tip of the outer length of the beam). Mark off 9", then cut to that mark at a 57 degree angle. And you're done!
Step 7: Using a Scientific Calculator
If you have a scientific calculator handy, the more exacting way to do this is with trigonometry. Once you have measured the actual slope (not roofer's slope), all you have to do is punch up the inverse tangent of the slope. The calculator will show you the exact angle of the miter cut. In this case, it would have been tan-1 (5.25/8.0625) = 33.07 degrees. In this case, the speed square method was pretty much spot on!