I am not sure about Ray's math - I just did the numbers myself, and here is what I got:
1) The diameter of an octagon is D = Sqrt[2 (2 + Sqrt[2])] a, where a is the length of a single side. a = 8' D = Sqrt[2 (2 + Sqrt[2])] a = Sqrt[2 (2 + Sqrt[2])] 8 = 20.905' R = radius = 1/2 D = 10.453 2) The angle of the roof can be modeled like so: http://i.imgur.com/FdqIF.png This assumes a 12' long roof panel. The general formula for calculating the angle P is ArcCos[10.45/L], where L is the length of a roof panel. Given the angle, the length of a roof panel is calculated as 10.45/Cos[P Degree]. I don't know the angle of the roof for a default hexayurt off-hand, but this should get you where you need to be. All of the formulas in this message can be copied to Wolfram Alpha for use/verification. Also, hello hexayurters (first message on board). ~Adam On Wed, Jan 4, 2012 at 1:55 PM, ken winston caine < [email protected]> wrote: > Joshua, if I extend the length of the roof diagonals enough, I actually > increase the roof pitch -- even though I've gone all octo. But there is a > point of diminishing returns because of the flex in the foam board. (The > longer the reach, the less rigid it is.) > > I'm trying to figure out what the shortest length is that will give me a > greater pitch than the traditional hexayurt has. > > Anyone have numbers? > > (Sure wish I'd paid more attention in Geometry. Or had understood how and > when I would NEED to know this stuff in the real world. That would have > gotten me to pay more attention to it then.) > > -- kwc > > > On Wed, Jan 4, 2012 at 2:41 PM, Joshua Keroes <[email protected]> wrote: > >> The more sides you add, the flatter the roof becomes. If you're worried >> about snow load, I think you'd want the steeper roof of a pentayurt or >> quadyurt than the rather flat roof of an octoyurt. >> >> >> On Wed, Jan 4, 2012 at 1:34 PM, kenwinston caine < >> [email protected]> wrote: >> >>> Thanks, Jason. Not suggesting that you're wrong. Just want to >>> understand why the standard 6 - side version would be both simpler and >>> stronger? >>> Stronger simply because it's smaller and would thus have more >>> rigidity? Or something else? Something in the math? >>> >>> I'm wanting to do the octagon to retain the essential structural >>> integrity of the hexayurt design and the hogan-like appearance--which >>> I like, and to gain significant floor area. The octagon gives 309 >>> square feet of floor space vs. the 166 for the hexagon. And, if I've >>> successfully increased the roof pitch enough, it also provides room >>> for a sizeable, comfortably usable loft. >>> Thanks,ken >>> >>> >>> On Wed, Jan 4, 2012 at 1:30 AM, jason chinn <[email protected]> >>> wrote:How come you don't do the standard 6 side version? Doing so >>> makes the design / math / production a lot more simple, and stronger. >>> I have only made one hexayurt, it was made with 8' tall vertical sides >>> that I then chopped down to 6' tall on the outside. >>> I suggest making a smaller model to work things out. Good Luck, jason >>> >>> -- >>> You received this message because you are subscribed to the Google >>> Groups "hexayurt" group. >>> To post to this group, send email to [email protected]. >>> To unsubscribe from this group, send email to >>> [email protected]. >>> For more options, visit this group at >>> http://groups.google.com/group/hexayurt?hl=en. >>> >>> >> -- >> You received this message because you are subscribed to the Google Groups >> "hexayurt" group. >> To post to this group, send email to [email protected]. >> To unsubscribe from this group, send email to >> [email protected]. >> For more options, visit this group at >> http://groups.google.com/group/hexayurt?hl=en. >> > > -- > You received this message because you are subscribed to the Google Groups > "hexayurt" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/hexayurt?hl=en. > -- You received this message because you are subscribed to the Google Groups "hexayurt" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/hexayurt?hl=en.
