inveniam viam

So, I was thinking about my cabin, and I had this idea.

I'm going to be building a stackwood cabin, about 48'X32' or so. (yes, this is a *big* cabin) It'll face south, and that south face will be an arc, a curved wall to take in the sun.

One of the things stackwood/cordwood walls are famous for is the ability to set colored glass into the wall:


I was thinking that it'd be cool to have the equinoxes marked, setting colored glass into the wall where the sun would shine in on those days. The latitude of the cabin will be about 46.5°N

Reading about the equinoxes on wikipedia, I figure from the discussion of day arc, that on the equinoxes the sun would rise due east and at noon would sit at about 43.5°:



I'm wondering if I could mark the sun's path along the arc of that south wall, where it rises in the east to where it sets, due west.

Geometry! The wall would be more of a semi-circle than just a rounded wall, from due east to due west, and it'd have to be... I'd need a skylight to capture the noon equinoctial sunlight. Or maybe just a cathedral ceiling? hmm. Still, it's a cool idea. I'll have to think about it.

Edit: so, finding length of the sides when you know one side and two angles... If my house is 32' wide, with side A being from the south wall to the north wall along the floor, side B being up the wall, and side C being from where the sun comes in to the north wall, then angle AC would be 46.5°; angle BC would be 43.5° and angle AB would be 90°.

Finding the length of the sides: 32/sin(43.5°) = B/sin(46.5°)
Which gets me: 32/0.68835458=B/0.72537437
so, 32(0.72537437)/0.68835458=B no need to be that exact! 32(.725)/.688=B
height sun would come in= 33.72', or 33'8.64"

*sigh* That's a pretty tall wall, even for a cathedral ceiling! But ... it would really work for a Great Hall. Hmm.