Saturday, April 13, 2013

Hexenschnitt -- The Witches Cut

What is the Hexenschnitt -- The Witches Cut?
The cuts on the end of the hip rafter for square tail fascia, when there are two different roof slopes on each side of the hip rafter.

The Witches section got its name probably several hundred years ago, as Schiftkenntnisse still secret knowledge of the carpenter were. For the work on the profile of the master took as helpers often an inexperienced employee, in which he could be sure that he gave him nothing of his abschaute Schifttechnik  For journeymen and apprentices ge like the skill of the master have time borders on witchcraft.



The witches cut got its name, believing only a person of witchcraft cut make this triple canted tail cut.

Berechnung der Hexenschnittschmiegen
Calculation of the witches cut bevels

Hexenschnitt Gratsparren 
Hexen geschnitten Gratsparren
Witches Cut Hip Rafter

R5 = 16.10211°
P2 = 40.89339°
P2 + R5 = 56.9955
Dormer Square Tail Saw Bevel Angle = 25.65891









Math for the Witches Cut


Joe Bartok's Online Math Notes



Traditional Layout  to draw out the Hexenschnitt -- The Witches Cut.


This drawing shows how to develop the hip rafter miter cut angles on each side of the hip rafter.


This drawing shows how to develop the hip rafter side cut angles on each side of the hip rafter. Pretty messy,  with all the construction lines.





Witches Cut for Timber Framing
Major Pitch 8
Minor Pitch 10
Deck Angle  120
Plan Angle = 70.89339
Plan Angle = 49.10661


90  -  R2  =  Hip Rafter Miter Angle On Side Of Hip Rafter
90  -  2.99577  = 87.00427 =  Hip Rafter Miter Angle On Side Of Hip Rafter
90 - P1 = Hip Rafter Housing Angle On Side Of Hip Rafter
90 - 10.87702 = 79.12298

Witches Cut Miter Angle = arctan(sin(plan angle) x tan(tail angle - roof slope angle) + hip slope angle
Witches Cut Miter Angle = arctan(sin(70.89339) x tan(90 - 33.69007) + 32.2085
Witches Cut Miter Angle = arctan(sin(70.89339) x tan(90 - 33.69007) + 32.2085 = 87.004239









Witches Cut Miter Angle = arctan(sin(plan angle) x tan(tail angle - roof slope angle) + hip slope angle
Pitch 8
Deck Angle  90
Plan Angle = 45

71.92506° = arctan(sin(45°) x tan(90° - 33.69007°) + 25.23919°
71.92506° = arctan(0.7071 x 1.499999) + 25.23919°
71.92506° = arctan(1.0607) + 25.23919°
71.92506° = 46.68587° + 25.23919°

Here's an example of using an 80° tail angle.


Witches Cut Miter Angle = arctan(sin(plan angle) x tan(tail angle - roof slope angle) + hip slope angle
Pitch 8
Deck Angle  90
Plan Angle = 45
Witches Cut Miter Angle = arctan(sin(plan angle) x tan(tail angle - roof slope angle) + hip slope angle
61.74784° = arctan(sin(45°) x tan(80° - 33.69007°) + 25.23919°
61.74784° = arctan(0.7071 x 1.04680) + 25.23919°
61.74784° = arctan(0.740194) + 25.23919°
61.74784° = 36.50864° + 25.23919°




CopyRight 2013 by Sim Ayers (Rafter Tools, SBE Builders)
Witches Cut Miter Angle = arctan(sin(plan angle) x tan(tail angle - roof slope angle) + hip slope angle
I don't want to see my trigonometric solution in any French or German books. 

Witches cut model layout.








4 comments:

  1. Sim , another way is to consider the level line as the run and the angled lines projecting down to the building as the rise . This alternate is taught in
    Gurndwissen Des Zimmerers

    ReplyDelete
    Replies
    1. I just ordered the book, Gurndwissen Des Zimmerers, this morning after seeing your comment and reading online that the German apprentice carpenters are taught the witches geometry cut layout in their third year. Boy, the American apprentice carpentry system sucks. I should have learned this 40 years ago.

      I added a couple more drawings this morning. They use the line projected down from the profile level line to find the hip rafter side cut angles. I, also added the trigonometric solution for finding the witch cut angles when the rafter tail angle is sloped at any angle. As Americans we only use 90° square tail rafters, but the trigonometric solution will work with 80°, 70° ...etc.

      Now I need to find the correct way to draw out the bevel angles on the top edges of the un-backed hip rafter using traditional layout. If the hip rafter is backed out first, then the bevel angles on the top edge of the hip rafter are the roof sheathing angles.

      Geometry is suppose to be an unspoken language, but it still sucks not being able to read my French and German books word for word.

      Delete
    2. Sim , There is one chapter just for the witch cut ,If I remember correctly there are three ways that each German Carpenter has to demonstrate the witch cut

      Delete
  2. This comment has been removed by a blog administrator.

    ReplyDelete