Hope I can describe this without screwing up!
1" x 4" lumber can be bought in 16 foot lengths. If you choose your wood carefully, you can bend it into arches.
I want to make an arch roof for a playhouse I'm building for my grandkids. I'm assuming that when the 1 x 4 is bent to form a roof that the resulting shape is a parabola (quadratic).
I live in an area that can get quite a snow load, so the higher the arch, the better the snow will slide off. So my problem is how wide a length can the roof span and still have sufficient height to facilitate the snow sliding off when using a 16' board?
More specifically, how can I find an equation for the parabola, knowing two points on the curve (but not the vertex) with an arc length of 16 feet?
I realize I could just skip all the math and play with a 16 board, but this question is consuming me intellectually.