## Saturday, October 18, 2014

### Tilted Valley Rafters

Das neue Buch vom alten Wissen der Schiftung
The new book on the ancient knowledge Schiftung
The new book on the ancient knowledge Compound Joinery
The new book on the ancient knowledge Roof Framing
The new book on the ancient knowledge Roof Framing Geometry
by Bernd Küppers

More images and information on the book can be found at this link.
Image from Bernd's Facebook page on Shiftung.

Verkanteter Kehlsparren in German = Tilted-Canted- Rotated Valley Rafter

Looking at page 52 in his book I decided it was time to study the valley rafters rotated into the roof surface plane. The same geometric techniques used for hip rafters rotated into the roof surface plane   can also be used for the valley rafters rotated into the roof surface plane.  Some of the geometry used for valley rafters rotated into the roof surface plane is empirical-type knowledge. Information gained by means of observation, experience, or experiment. From this empirical knowledge we know the valley jack rafters miter head cut will be 90° and the bevel cut, top cut, will be the same as the jack rafter bevel angle for plumb hip-valley rafters.

We also have a language problem when we're studying Verkanteter Kehlsparren or Verkanteter Gratsparren . What do we call each side of the canted  hip or valley rafter rotated into the roof surface plane.

Looking Michel Verdon's post on
Principes du dévers: la sauterelle
or
Principles of cant: the grasshopper

he labels each side of the rotated hip rafter in plan view as A for the side of the roof the hip rafter is rotated into and the canted side as the DP side of the hip rafter.

DP = Dévers De Pas .... need a German name for this side of the canted hip rafter.
TC = Trait Carré = Perpendicular .... need a German name-word -- senkrecht ?

I purpose labeling all canted hip or valley rafters in plan view as TC, for the side the hip-valley rafter is rotated into, and DP as the side of the hip-valley rafter that's canted-Tilted from plumb.

Example for the TC side of  the hip-valley rafter is rotated into the roof surface plane:

Plumb hip-valley rafter
Jack Rafter Miter Angle = 33.69° = Roof Slope Angle
Jack Rafter Bevel Angle = 39.76°

Rotated hip-valley rafter
Jack Rafter Miter Angle = 90.00°
Jack Rafter Bevel Angle = 39.76°

For equal pitched roofs for the canted-DP side of the hip-valley rafter:

Plumb hip rafter
Jack Rafter Miter Angle = 33.69° = Roof Slope Angle
Jack Rafter Bevel Angle = 39.76°

Rotated hip rafter
Jack Rafter Lower Claw Angle = Roof Slope Angle
Jack Rafter Bevel Angle = 39.76°

So the only angle we need to draw out or calculate for the jack rafters for the rotated hip rafter  is the Jack Rafter Upper Claw Angle on the DP side of the hip rafter.

Since the canted-tilted valley rafter is just an upside down hip rafter the only angle we need to calculate is the Jack Rafter Upper Lower Angle on the DP side of the valley rafter.

Drawing from one of my studies on the hip rafter rotated into the roof surface plain using more of the French technique "l'art du Trait" rather than the German Shiftung technique. Some times the German Shiftung roof framing geometry technique for developing the geometry of a compound joint just has too many development lines.  Here in this drawing, you can use my Axiom #3 for the line that develops the Upper Claw Angle on the jack rafter on the DP side of the hip rafter. It would develop the jack rafter Lower Claw Angle for the DP side of the valley rafter.

Roof Framing Geometry Proposition – Axioms # 3:
The intersection of the DP Lines of two rafters define the line for the upper claw angle on the rafter.

In this drawing of the rotated hip rafter the Upper Claw Angle for the jack rafter on the DP side of the hip rafter is 12.11976°.
In this drawing of the rotated hip rafter the Upper Claw - Miter  Angle for the jack rafter on the TC side of the hip rafter is 90.00°.

In this drawing of the rotated valley rafter the Upper Claw Angle for the jack rafter on the DP side of the hip rafter is 52.00°, same as the roof slope angle, and the Lower Claw Angle is 12.11976°.

The Lower Claw Angle is 12.11976° for the jack rafter on the DP side of the rotated valley rafter.
Same as the Upper Claw angle for the jack rafter on the DP side of the rotated hip rafter.

You can also use my tréteaux roof framing calculator to verify these angles.
Trèteaux Angles: P16a-DP
P16a-DP = Adjacent Side Jack Rafter Miter Angle on DP Side Of Hip Rafter on Face Perpendicular To Roof Surface, Lower Claw Angle ... this would be the Upper Claw angle for the jack rafter on the DP side of the rotated valley rafter.

Trèteaux Angles: P17a-DP
P17a-DP = Adjacent Side Jack Rafter Miter Angle on DP Side Of Hip Rafter on Face Perpendicular To Roof Surface, Upper Claw Angle... this would be the Lower Claw angle for the jack rafter on the DP side of the rotated valley rafter.

Trèteaux Angles: P18a-DP
P18a-DP = Adjacent Side Jack Rafter Bevel Angle on DP Side Of Hip Rafter on Face Set in Roof Surface
This would be the back bevel, top cut, for the jack rafter on the DP side of the rotated valley rafter.

1. Sim,
interesting remark you've done about the identification of the roof.
In fact I have not met the standard, and I will change that in the other posts to come. The A roof in my post was for LP (meaning "Long Pan" that is the main roof) and the B roof should have be called C (meaning "Croupe" that is the secondary roof). Knowing that we say :"arêtier à dévers, lattis long pan" meaning: rotated hip rafter, lath main roof. I don't know if lath is the best word to say "the top of the roof, supporting the roofing". Somebody recently suggested me "batten" instead of "lath".
Regards

1. Michel,
I don't think the words lath or batten translate very well for English roof framing geometry. "arêtier à dévers for DP translates well, but "Long Plan" does not translate into something English speaking carpenters could understand easily. The problem with main roof is, when you have equal pitched roofs there isn't a main roof or main plan.

On another problem with language is the German book by Bernd Küppers. He's writing an English version of the book and I doubt he will translate the German text to English so thats it's understandable. The German language structure is completely different from English, so you can't use translating software for the English version. It needs to be completely re-written by someone who completely understands the Shiftung geometry in his book.

2. Michel, Sim,
In his program Triangle29, Pierrick Le Floc'h uses G and D (Gauche and Droite) for Michel's A and B. Just another option, which could be L and R of course !
I think the neutral, mathematical tone of A, B is good. But I would not like Rafter Tools to change from major, minor; these are clear and familiar.
No to lath or batten; in the phrase "lattis long pan", lattis is used in an abstract sense, rather as we use roof surface. It does not really represent a physical component. That's how I understand it.

3. Sim,
On the figure Verk. Grats.-9T.jpg, what value do you get for the HR Footprint angle (between DP Line and DP Side of HR). I get 20.76°; but cannot yet get the correct upper claw angle. This is for an on-the-right-road check.
Thanks.

4. Rob,

Send me an email and I'll send you the SketchUp file. The eave angle is 60° with equal slope rafters angles of 48.01278°. The D-DP = Horizontal Plane Rotation Angle for Tilted Hip Rafter on DP Line from Eave Line to Hip Rafter Footprint = 7.77987°. The upper claw angle is 7.49727° and the lower cllaw angle is 77.06738°.
Sim