Tréteaux Dit Cadet Saw Blade Bevel Angle

I thought I was pretty good with prisms, but the foot of the Sawhorse has a prism footprint that's an parallelogram on the base as well as one of the sides. This SawHorse Leg -- Hip Rafter is rotated into the hip rafter backing angle.
tréteau à devers


Here's the development of the Sawhorse footprint.






The prism on the bottom of the SawHorse Leg.

Prism Unfolded

Top view of Prism.



Timber Framing Angles are meant to be used with Right Angled prisms, so these don't work.

Timber Framing Angle: R5B 
R5B = Hip-Valley Rafter ridge or plumb header miter housing angle following the bottom of the hip-valley rafter.
    HawkinDale Formula
  • none
    Hip-Valley Roof Ratios Angle Formulas
  • R5B = arctan( tan( R1 ) x cos (D))
  • R5B = arctan( tan( hip rafter slope angle ) x cos (plan angle))
Test angles for R5B
Hip Slope Angle  70.16263
plan angles without footprint rotation
42.04769°
47.95231°
plan angles with footprint rotation
43.13036°
43.36857°

  • R5B = arctan( tan( 9.39285 ) x cos (43.13036)) = 6.883666
  • R5B = arctan( tan( 70.16263 ) x cos (43.13036)) = 63.6956

Timber Framing Angle: A5B 
A5B = Saw Blade Bevel Angle for R5B.
    HawkinDale Formula
  • none
    Hip-Valley Roof Ratios Angle Formulas
  • A5B = arctan( sin( R5B ) x tan (D))
  • A5B =arctan( sin( R5B ) x tan (D))
Timber Framing Angle: R5P
R5P = Hip-Valley Rafter ridge or plumb header miter housing angle following the bottom of the hip-valley rafter.
    HawkinDale Formula
  • none
    Hip-Valley Roof Ratios Angle Formulas
  • R5P = arctan(sin D x tan R1)
  • R5P = arctan(sin(plan angle) x tan( hip rafter slope angle ))
Timber Framing Angle: A5P
A5P = Saw Blade Bevel Angle for R5P.
    HawkinDale Formula
  • none
    Hip-Valley Roof Ratios Angle Formulas
  • A5P = arctan( sin( R5P ) ÷ tan (D))
  • A5P = arctan( sin( P6 ) ÷ tan (P2))
  • A5P =arctan( sin( R5P ) ÷ tan (D))
  • A5P = arctan( sin(Clip angle on the bottom of the Jack Rafter ) ÷ tan (Jack Rafter Side Cut Angle))


Time for some head scratching to find the saw blade bevel angle for the foot of the sawhorse leg.

Since the hip rafter is rotated into the hip rafter backing angle the miter angle for the foot of the hip rafter should be the roof sheathing angle. 
Main Slope Angle 76.41401°
Adjacent Slope Angle 75°

Main Plan Angle = arctan (tan Adjacent Slope Angle ÷ tan Main Slope Angle)
Hip Rafter Slope Angle = arctan( tan( Common Rafter Slope Angle ) * sin( Plan Angle ))
Hip Rafter Backing Angle  = arccos (cos Common Rafter Slope Angle ÷ cos Hip Rafter Slope Angle)
Roof Sheathing Angle = 90 - P2 = arctan (tan Hip Rafter Slope Angle ÷ sin Hip Rafter Backing Angle)

Main Plan Angle = arctan (tan 75° ÷ tan 76.41401°) = 42.04769°
Hip Rafter Slope Angle = arctan( tan( 76.41401° ) * sin( 42.04769° )) = 70.15895°
Hip Rafter Backing Angle  = arccos (cos 76.41401° ÷ cos 70.15895°) = 46.20403°
Roof Sheathing Angle = 90 - P2 = arctan (tan 70.15895° ÷ sin 46.20403°) = 75.40155°


Main Roof Sheathing Angle 75.40155°
Hip Rafter Miter Angle at Foot of Hip Rafter = 75.40155°

Now for the hard part, the Saw Blade Bevel Angle.


Komentar

Posting Komentar

Postingan populer dari blog ini

Layover Valley Rafter Basics

Gambar
Before I get into the Hexenschnitt for the Layover Valley Rafter I needed to review the basic geometry that defines the layover valley rafter. I needed to make sure I could draw the layover valley rafter correctly in plan view (ground plan). Here's one method of a basic drawing using the layover valley rafter backing triangle to position the layover valley rafter material on the roof surface that defines the  layover valley rafter in plan view. The  layover valley rafter top bevel is easily defined by extending the  layover valley rafter backing triangle to the top of the  layover valley rafter. The other  layover valley rafter line in plan view is defined by the bottom edge of the  layover valley rafter material sitting on the  layover valley rafter backing triangle. (Roof Surface). The  layover valley rafter plan view lines at the intersection of the two roofs. I tried this method for drawing the  layover valley rafter, but this method...
Baca selengkapnya

Hip Rafter Edge Bevel and Backing Angle

Gambar
In complex roof framing there are 7 main roof framing angles. Hip Rafter Backing Angle Valley Sleeper Bevel Angle Plain Titl (DP) Main Plan Angle Adjacent Plan Angle  Main Profile Rafter Slope Angle Adjacent Profile Rafter Slope Angle In this article I will discuss the hip rafter backing angle and the valley sleeper bevel angle. These two angles determine the miter angle and and saw blade bevel angles for jack rafters and purlin rafters that are plumb to the earth and for jack rafters and purlin rafters that are skewed from the eave line. A thorough knowledge of these two angles is critical in complex roof framing using geometry or trigonometry. The hip rafter edge bevel was avoided in the 12th century on some roof structures by rotating the hip rafter into the roof surface plane. However, by avoiding the hip rafter edge bevel, the carpenters-builders had to have a knowledge of the Valley Sleeper Bevel Angle. They didn't call it the Valley Sleeper Bevel Angle, but it's the same...
Baca selengkapnya

Layover Valley Rafter Hexenschnitt #3

Gambar
In the book Das neue Buch vom alten Wissen der Schiftung The new book on the ancient knowledge Schiftung The new book on the ancient knowledge Roof Framing The new book on the ancient knowledge Roof Framing Geometry by Bernd Küppers I'm stuck on page 23. The geometry in the book, just doesn't return the correct miter angle for the Layover Valley Rafter Witches Cut (Hexenschnitt). I don't know if I'm drawing it incorrectly, or the BE (Bottom Edge Plane of the Layover Valley Rafter) should be drawn differently. Similar drawing at File: Kehlbohle mit Hexenschnitt.jpg There's 3 canted planes that define the Layover Valley Rafter Witches Cut Miter Angle. The main roof surface, the square tail fascia plane of the main roof and the the square tail fascia plane of the adjacent roof.  I think the problem with my geometric drawings is defining the intersection of the roof surface with the adjacent  square tail fascia plane.
Baca selengkapnya