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Midnight math: hip-valley layout and developed drawing

by on 13 Jun 2011

Late Sunday evening, my eyes glazed from photo editing, I headed downstairs in the Dom for a break. It was pretty quiet in the hotel lobby, with most of the crew off to bed in anticipation of an early day Monday. But in the dining room, I found Adam and Gerry facing each other across a table, Jackson on one side between them, with a number of empty beer glasses, a couple of pencils and a spread of napkins covered with lines. A few seconds of study made it obvious that I had happened upon a roof geometry session and the looks on their faces testified that all was not going smoothly.

The story unfolded as follows: A contingent of framers had spent the day at the eco-fair at the school in Arek’s home town, chopping, pitsawing and otherwise demonstrating the craft. Adam and Jacob had collaborated over a compound roof layout demo, learning in the process that the Japanese and Danish traditions were very similar in this regard.

The Fair

Jacob and Adam begin the roof layout.

Laying out the hip in plan

They get some help

and do some head scratching

But now later, in the dark, here were the bulk of our classically trained framers representing three national schools on two continents, fetched up against the rock of backing angle layout. Perhaps Jacob, with his young and agile mind fresh from apprenticeship, might have been able to cut through the fog, but he was probably in bed across the river at Sosenki. So I joined the circle round the table to see if I could help.

Classic napkin layout

Adam and I went through the napkins and tried to suss out the problem, I was struck with a strong sense of déjà vu. Here I was, with a North American trained in Japan, engaged in late night hip and valley layout. Almost thirty years earlier at the first or second Timber Framers Guild Western Conference at Timberline Lodge high on Mt. Hood in Oregon, having closed the bar, Len Brackett and I had ransacked a janitor’s closet for a large cardboard box, laid it flat and began drawing out a Japanese hip layout.

Adam and I walked through the Guild standard for developed drawing, extracting the essential core roof element (sometimes called the kernel), developing it by unfolding the surfaces and laying it flat. Then we proceeded with step by step backing angle layout. The principal difference between this session in Poland and that other up on the mountain in Oregon a generation and half before is that instead of going for large drawing surface, straightedges, dividers and pencils, Adam and I trotted upstairs to get our computers.

At some risk of alienating readers, we here append a series of these drawings. If roof geometry is not your thing, skip ahead to the next item or post.

A hip roof with regular pitch and plan

We slice out a 3D section with all the information needed to develop the hip.

This kernel is extracted from the roof,

and developed, that is unfolded and laid flat.

Here is the  developed kernel

And here we see that development, with parts and areas labeled.

Finally, here is the classic backing angle derivation,  as follows:

1. From the right angle corner in plan where eave and common run meet, strike a perpendicular to the run of the hip.  This line represents the run of the backing.

2. Continue on perpendicular to the length of the hip. This line represents the rise of the backing.

3. With the point of compass or dividers at the intersection of backing run and rise, set the dividers to the length of the backing rise and arc back down to the hip run.

4. Connect the dots. This last line represents the surface of the backing, that is the top of the hip rafter.

Tonight Adam and Jacob will return to their hip layout to see if they can get it done. Stay tuned for further developments.

*     *     *

Cailigh rescues frogs from the road

Josh turn 23

Professor Brown reads from Anne Lamott’s Bird by Bird

Log wall team captain John Nininger takes down a thirty foot timber with a block plane

Cupola invades the office

Mez at rest (well deserved)

  1. Laurie permalink

    That’s my boy…sieizing the moment. 😉

  2. sam permalink

    way to go cuz. good to see u in action.

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