Ray, how do you dimension and lay out your rafters?
I use a compter or calculator program to generate a list of angles similar to the Hawkindale Angles. Each angle is rigidly defined in terms of its location on the roof. Since angles are ratios they describe the geometry of the intersecting components of a hip/valley roof on any scale.
Beginning with the angles and gable spans the rafters and joints may be dimensioned using trigonometry. I generally work with log builders, sometimes there’s the odd timber frame or some stick framing. Given the irregularities of logs and variations in dressed timber up to half an inch it’s best to work from the theoretical centerlines of the roof members. Lengths, mortises and tenons are solved on-site.
Dimensioning is generally done with a programmable calculator for speed and accuracy but any calculator with trig functions will suffice. The lengths (inches) and angles (degrees) are expressed to five decimal places. Final results are rounded of to the nearest 1/32 inch. Tenons are cut “outside” the line leaving them a hair long, mortises are made a bit shallow by cutting “outside” the line.
This has always worked well in my little corner of the world. The calculations can be done quickly, the results are deadly accurate, layout and cutting takes place on the safety of the ground. An entire complex hip or valley roof can be produced in the shop. We usually end up touching up on-site to remove a bit of excess wood and the assembly generally requires a little help with a sledge. No gaps.
