My research into the knowledge of the medieval carpenter in setting out roofs and buildings without using geometry or numeric measurement came about while studying vernacular buildings in Kent and Sussex. I was interested in the different roof layouts from crown posts to clasp-purlin queen post roofs from the 13th to the 18th century. I realised that roof pitches had constant angles of 43, 48, 52, 55 and 58 degrees. I then checked vernacular roofs in the Midland England cruck and box-frame country and in East Anglia and found the same constant roof pitches. Then I took my research futher to the early medieval era and found pre-conquest Saxon churches also had similar roof pitches ,for example St Lawarence Saxon church at Bradford upon Avon had a roof pitch of 48 degrees, Odda's Chapel Gloucestershire had a roof pitch of 43 degrees, Old St. Helens church in Hastings Sussex also had a roof pitch of 43 degrees suitable for slates.
In studying these buildings I also realised that the tie beam was the longest timber in the building which supported the principal rafters in the case of a queen post roof. I knew that a 48 degree pitch roof was achieved by the rafter length being 3/4 of the span of the tie beam. So I continued to divide the tie beam from wall plate to wall plate into half, and dividing half span of the tie beam into 8 divisions which could be done by folding string 4 times. These 8 divisions would be marked on the tie beam or a rod and checked with dividers. This would then give the 5 common rafter lengths by laying the rafter timber along the full length of the tie beam and marked at 5 would give a roof pitch of 52 degrees and so on. This is all explained on my website: https://www.medievalbuildings.co.uk Where you will see a video of me setting out a new oak frame in 3 parts: Part 1 setting out the tie beam with string. Part 2 setting out the rafters and Part 3 setting out the building from the rod.