Just a warning, I doubt this post will be that interesting to many of you since it doesn’t have that much to do with my TH but I wanted to share this information since I couldn’t find an answer already on the web.
I started refining my SketchUp model over the weekend and ran into an old problem; determining the correct angles and lengths for rafters. There is a lot of information on the web on making this calculation if you know the slope of your roof, however, when the exact slope is unknown, this can be a difficult calculation. When would the slope be unknown since I’m designing the roof you ask? In my case it was the portion of the roof above the dormers. When I designed my model, I created my walls, determined the slope that I wanted, and then drew the rafters and ridge beam in where it all lined up. But above the dormer walls the ridge beam was already in place, so I had to draw the rafters at exactly the right angles.
What prevents this from being a simple geometry (Pythagorean theorem) problem is that at the peak of the roof I know where I want the TOP of the rafter board to be (lined up with the ridge beam – B), and at the bottom I know where I want the BOTTOM of the ridge board to be (lined up with the inside edge of the wall – A). But these two lines (the top and bottom of the rafter) are not the same but instead parallel lines.
(Please excuse my not-so-great drawings)
The first time I ran into this I just approximated the angles since I didn’t want it to hold me up from starting my build (which in all honesty worked just fine). But now that the pressure is off, my perfectionism got the better of me. So with a lot of thinking and a little help from an online math forum here is what I came up with.
the angle at A = arctan(u/t) + arcsin(v/sqrt(t^2 + u^2))
You can use the scientific calculator included with Windows, but I have found the one at http://web2.0calc.com/ much easier to use.
I warned you!
Update: While this can be very exact, it’s a lot easier to use standard roofing angles (e.g. 12/12, 2/12, etc). We’ve since switched all our plans to standard angles.