Timber Framers Guild Forums Tools Timberframe Design valley jack rafter bevels

Here's a framing square short cut for irregular roofs. I was reluctant to post this earlier as it is so limited in scope, but here goes. The following applies only to:
(1) Jack Rafter Side Cut Angles
(2) The angle of intercept of the Hip eave lines or Valley ridge lines in plan must be 90°
Say the intersecting pitches are Main pitch = 6/12 and Adjacent pitch = 10/12. To find the side cut for the 6/12 side, find value on the framing square given for 6/12 and multiply it by 6/10 (the ratio of the Main pitch/Adj. pitch ... if the runs are equal the ratio of the rises will suffice). Similarly, the side cut for the 10/12 side may be determined by multiplying the 10/12 value given on the framing square by 10/6 (Adj. pitch/Main pitch).

Chris makes a good point. Rather than relying a bunch of formulas it's vital to be able to visualize the triangles and tetrahedra which which comprise the geometry of the overall roof and the joints. Do that, and the formulas automatically follow.
With a little practice it's possible to produce an equation on the spur of the moment if faced with a situation on the job that's unfamiliar. And if your calculator ever breaks it's entirely possible to construct the angles with a child's geometry set. (I always keep one handy - just in case).
Have a good weekend everyone.