Octagon Rafter Framing

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

I believe that those angle you are given on the sgaure for the side cut of jack or hip are the angles you would mark on the unbacked hip or the top of the jack rafter. When you cut them, if you are using a circular saw you would set it to 22.5 for the jack rafters and since you are making a compound angle cut across the face it would follow the mark you made on the top at the 28.75 deg.

Terry Branscombe wrote:
Terry, I don't know anything about the octagon rafter tables. The side cuts on a standard framing square are for the upper shoulders of unbacked Hip rafters, where the common rafter slopes are equal and intersect in plan at 90°. Very limited, in other words.

The angles in any complex roof may be determined by development with as little as a compass and straightedge. For the sake of accuracy I prefer to calculate the angles.

Framing and Joinery Angle Calculator : There are also links to some basic diagrams and tables of formulas.

Here's what I get for the Hip rafter side cut angles using your example, two intersecting 1/12 slopes with an angle in plan between the eaves of 135°:

Side Cut Angle at Hip Rafter Foot = 67.44008°
Side Cut Angle at Hip Rafter Peak = 22.44020°

If you scroll down the page in this link you will find drawings detailing one method of Developing the Hip Rafter Side Cut Angles . The angles at the Hip rafter feet are designated R4B, those at the peak are R4P. The images show an angle in plan between eaves of 90° but this may assume any value.

Another link to some sketches of an Octagon Gazebo . The common slopes in these examples are 6/12, angle in plan between the eaves is 135°.

Hip Rafter Side Cut Angles:
Side Cut Angle at Hip Rafter Foot = 65.47409°
Side Cut Angle at Hip Rafter Peak = 20.60785°

Terry, for the same roof, two 1/12 common pitches and a plan angle of 135° measured between the eaves:

Jack Rafter Side Cut Angle = 22.42999°

O.K., I'm confused as well. I don't understand where the numbers on the Eagle square are coming from either. I thought they might be complementary to the angles generally defined as the side cut angles but that doesn't seem to be the case. Can you post a picture of the square?

PS: To summarize, Terry's assesment of the side cut angles is correct ... the framing square values posted for the side cut angles just don't add up. Does anyone else have an opinion or explanation?

Hi folks:
Terry: can we see this picture?
I have a few suspicions but need information.

Best of the holidays to you,
curtis

All:
In thinking about this I have remembered that some of the old square tables used to include both numbers for framing square use and often one number was tongue length (16). It is either stamped on or implied that 16 is 16.../16 and in plan view the side cut, perversely drawn on the top, is 45 degrees or 16/16. Remember this is the angle between hips not the hip and a common. My calculations for a 1/12 common rafter pitch octagonal roof find the square settings for the hip side cut as 13'0-5/16 (rafter length) and 12'11-5/16 tangent
(not trig term but carpenters talk long lost) length) yields 16'1-1/4 / 16. A discussion of this use of tangent can be found in the conference proceedimgs from Roanoke on the TFG homepage.

With this in mind lets think about jack numbers:
SIde cut of jack is the ratio:length of common to length of eave. For a 12 foot run, 1/12 pitch the rafter length is 12'0-1/2 and the eave is 4'11-5/8. If you solve for the similar triangle with a 16' leg the result is 6'7-1/4.

We could talk multiple decimal points and finer measurements but this, I believe, is what you are seeing.

Best regards,

curtis

Curtis: Thanks for posting. Mystery solved!
I've never seen (or heard of, for that matter) an framing square with octogon rafter tables and it never occurred to me that the measurement for the side cut for the Jack Rafter would be given in terms of Eave Length/16.
In terms of multiple decimal points:
6 × 12 + 7.25 = 79.25"
16 × 12 = 192"
arctan(79.25/192) = 22.42889741° ... O.K., that's close enough, we're not doing a moon shot.

Some of the mystery is solved. Here's what I get for the Hip rafter side cut angles expressed as "over 12" values. The 12" is measured along the long axis (length) of the rafter. The angles are laid out on the upper shoulders of unbacked Hip rafters.

At the peak where the Hip rafters meet one another:
4 15/16 over 12
Hip rafter feet intersect plumb planes at the eave lines:
28 7/8 over 12

I'm still having a hard time reconciling the "16" given for the Hip side cut in the original post with any integral base: 12, 16 or otherwise. And perhaps the definition of a "hip side cut angle" in the octogon table is different than that normally given on a framing square. ???
Yeah, a picture or some more information would be nice ... while I still have all my hair.

PS: I haven't as yet checked out the file Curtis mentioned in his post; that will likely lend some insight as to what's going on.

I went looking through all my old books and found this from ABC OF THE STEEL SQUARE AND ITS USES, By Fred T. Hodgson.




Hope this helps, Tom

My 1926 ed. Audels has a detailed section on laying out Octogon rafters using a steel framing square. Will get it out tonight.