Hi folks,

Call me geometrically challenged, but I can make no sense of the rafter tables on an old square. More precisely a picture of an old square. The picture is of part of an octagon rafter table on an Eagle square that was probably made at the turn of the last century. Eagle was absorbed by Stanley around 1915.

The table includes rows labelled with:

- Length of Octagon Hip Rafters per Foot Run
- Length of Octagon Jacks Spaced One Foot
- Side Cut of Octagon Hip Rafters
- Side Cut of Octagon Jack Rafters

From what I understand of Eagle squares all the angle cuts are made by using the 12" mark on the tongue and the table value on the blade, then cutting along the tongue.

In my world, simple octagon roofs are framed with eight common rafters centred on each side of the octagon and eight hip rafters rising from the octagon's corners. Jack rafters leave the wall at 90 degrees in plan view and meet the hips at 22.5 degrees. The hips and common rafters also meet at 22.5 degrees in plan view. In other words, if the roof was flat the hip and jack side cuts would both be 22.5 degrees.

If this is correct, hip and jack rafters on a roof with any pitch at all would require a side cut at something less than 22.5 degrees. To my surprise the octagon rafter table value for hip rafter side cuts for a 1/12 pitch roof is 16, producing an angle of over 53 degrees! The jack rafter side cut value for the same roof is given as 6-7/12, which translates into a side cut of 28.75 degrees!

I'm confused.

What were these old tool makers thinking? Did they frame octagons differently a hundred years ago? How did they do it> Or better: How did they use squares such as this to do it?

Anyone out there willing to throw me a bone? I'd appreciate it. Thanks.

--
Terry