OK. I'm giving a talk in a few months to a group of non-carpenters about traditional french layout (Trait de Charpente). As a part of it, I'd like to include a comparison with other (probably mostly European) techniques for the layout of "complex" joinery such as those found in hip and valley timbers. I would distinguish these joins from the "simple" truss which represents one plane. (A hip being the intersection of two planes, it cannot simply be laid out using the roof pitch directly).

Were hip rafters simply calculated (application of trigonometry)? Or measured in situ as the roof was assembled? Or did historic builders limit themselves to certain pitches for which the ratio of rafter to hip rafter lengths was known? How were the cut angles established for the rafters that meet the hip rafter (Sorry about the lack of terminology here... I actually only know these terms in French)?

Above all... can anyone cite a reference source (book / website) that discusses some of this? I've looked through my original edition Audels, and the various timberframing books in my collection but no light has been shed!

Thanks in advance and hoping that all of this makes sense without the handwaving that I would normally employ to explain this stuff!

Jon