Struggling with stereotomy

[Philip Davies]

By which is meant solid geometry,
This little prism has taken me 8 hours to do, today, and it is only one quarter of what is required, at one end of a piece of wood I want to use!
About 35 years ago I saw a picture of a timber framed building under construction and what was quite intriguing was that the hip rafter was square in section, rotated so that the diagonal through was plumb. That’s not the way I’d been taught and I didn’t know how to do it then, but I had the vague ambition of investigating it one day.

This is the start. On the basis that I will learn more if it is more than usually complicated, there are two unequal planes. So the hip rafter, which is what I am working on here, is inclined to the post at 34 degrees on plan. The two sides are 36 degrees and about 26 degrees respectiveLy and meet together at the junction of the hip with the post.
There has been such a plethora of lines and points, so many elevations to rabat, that I stopped using geometry, and have been using trigonometry. The data is over a page and a quarter of A4, and that’s without some of the jottings. Projecting the points lead to creeping inconsistencies. Also, picking compasses up and putting them down , I rarely find the radius is the same when I next want it. Digital callipers and winged dividers I find are more reliable.
And with all the lines on the board, I found the best way of avoiding confusion is to make overlays. Some of them are stuck to the model, some a stuck to the boards, some are lying about on the floor and a lot are in the bin.
The only way to speed up is by practice, if I’m spared!

[nova_robotics]

I have absolutely no idea what's going on, but it looks interesting! Keep us updated.

[Toolmaker51]

Inspecting the photos, Phillip D, I know you'll arrive at solution.
After all, we both use same calculator!

[mklotz]

There are a wealth of roofing calculators on the interweb, e.g...

https://www.blocklayer.com/roof/roofeng.aspx

I don't know if they will be of help to your specific problem but they may be useful in checking the solution at which you arrive.

In my experience, solid geometry problems have always been easier to solve if expressed in vector form and then attacked with analytic geometry.

At any rate, good luck with your work.

[Philip Davies]

Thank you. Unfortunately, although I did further maths, vector analysis was not included. I have never used roofing tables, but my ambition is to master the stereography traditionally used by carpenters, most notably by the French master-carpenters, the Compagnons, although they’re not the only ones who are good at it.

[Toolmaker51]

Does this, by some measure, relate with variety of fastener-less construction we associate to Japaneses carpentry?

[Philip Davies]

The Japanese, the Koreans, and easiest to relate to, the French, are very good carpenters, but advanced carpentry is not confined to those nations.

The book you see here is probably the best on the subject, by an American, and his timber framed buildings are very complex. It is lavishly illustrated. His buildings
use sophisticated joinery, quite as good as good as the Japanese, who don’t go in for odd angles so much, but use tiers of interlocking components. As well as stereotomy, the French compagnons can lay out all their construction bevels on a single board, using only square, straightedge and compasses. This is what I aspire to, and it was how I was trained, except with this project the multiple developments are so confusing, the dimensions quite small (for a carpenter!) that I have to construct all these overlays and prisms. For example, just the two top faces of the hip need 3 prisms. I got some of my sums wrong and cut bits of card the wrong shapes, so not terribly efficient.
The book is “Advanced Timber Framing” by Steve Chappell. He uses trigonometry almost exclusively, it seems.