algebra ... geometry ... math in the workshop

 

above is a projection of the theoretical line profile of a hip rafter for two

 intersecting curved roofs ... the pink curve is made up of short straight lines 

connecting the projected intersecting lines so autocad did not generate a radius. 

fortunately, we were able to take the pink line drawing to our cad program 

and work with it. yesterday, i was talking with 3 former math teachers and the solution 

to this problem came up as one of those former math teachers, 

my friend mrs manley, was able to solve it for me when it came in last january.

this project happened in 2021, and i have always meant to write about it.

here goes .... click the photos to enlarge them ...

the rafter profile we were looking for is the angled one in the corners ...

and the architects response below

we had to use this formula on other, longer (12') 

hip rafters that we had to cut in two pieces

the main roof

a test in advantec

 

the two piece hip rafters

and then we had to cut a template sheet for the plywood 

****

well that is the algebra part ... next the geometry ...

 

you can see the main entry on the right side of

the elevation above, below the cupola ...

the entryway space looked like this

 

' Ensure Slope Matches Side Wall Angle for Conical Ceiling'

at 2 and 1/16th x 12

 not a lot of detail there ...

i sort of sorted out that info in my cad program

 

and then to be sure i understood what i was trying to do, i decided

                                to make a 1/8th scale model from my drawings on the cnc

looks like it all might work ...

a little harder than it looked, as theory collides with reality ...

the right hand wall was off a couple of degrees

and it all worked out in the end ..

plastered and stoned

inside ... living room ...