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

http://www.bswals.at/wrl-z1/grat/hex/hex.htm

Hexenschnitt.pdf

R5 = 16.10211°

P2 = 40.89339°

P2 + R5 = 56.9955

Dormer Square Tail Saw Bevel Angle = 25.65891

Math for the Witches Cut

http://www.sbebuilders.com/tools/geometry/treatise/Pyramidal-Roof-Rectangle.pdf

Joe Bartok's Online Math Notes

http://geocities.ws/xpf51/SQUARE_CUT_FASCIA/square_fascia_hip_notes.html

http://www.geocities.ws/web_sketches/compound_angle_developments/square_fascia_meets_hip_developments/square_fascia_meets_hip_developments.htm

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.