Hopefully I'll have time next weekend to create a WIP post for the summerhouse I've finally designed in Sketchup and started to build (sneak preview of sketchup file here https://drive.google.com/open?id=0B23Hn ... HhMTFBaZ1k and video of layers building up here https://drive.google.com/open?id=0B23Hn ... HlxdHRnOE0).
I'm currentlly at rafter level...
and have spent the past week researching into the sawtable angles to cut the jack rafter that joins the hip rafter and got completely confused by trapeziodal diagrams etc. I have actually worked out the angle by a simple jig, a manual saw cut in the correct plane then used that to set the saw table up. However I still would like to know what the maths are that converts the plan angles into sawtable compound angles. Everything I've found has assumed a ridge angle of 90 degrees, but this being a corner summer house the pitch of the hip rafter is 15.7 degrees (3.37:12) and the common /jack rafters are 21.7 degrees (4.78:12), so the relevant ridge angle is 180-15.7-15.7 = 148.6 degrees (this is actually to keep the max height to 2.49m due to planning permission).
From sketchup the hip rafter compound angles are 42.9degrees and 68.3 degrees, yet the saw table to achieve this is approx 47 degrees and 70.7 degrees (the 47 was achieved by using a wedge as the table only tips to 45). I understand why they are different from plan and elevation angles, but would like to understand the calculation.
Heres some images from sketchup (I had to save the design in sketchup 8 format and move to an old laptop that has the roof framing geometry plugin that gives angle dimensions)
the jack rafters joining the hip rafter (kingpin also shown)
A close up of the hip rafter to kingpin (90-74.27 = 15.73 degree pitch)
and the angles of the jack rafter where they meet the hip rafter (key angles are 42.9 and 68.3 - these are the ones that 'adjust' when put on a compound angle mitre saw)
Finally the plan view that shows the jackrafter is 90 to the wallplate and the hip rafter is 45.
Any help in understanding the maths gratefully received (just in case I ever need to build another one!). i have some other rafters on the door section that are at a different pitch again (23.5) as they travel a shorter distance to get from wall plate to kingpin height.
Thanks
Dave