## Saturday, April 9, 2016

### Sloping Ridges

It's been a while since I've had a sloping ridge in a roof. So, I drew it out in SketchUp to find the angles needed for this equal pitched roof. The first thing that was obvious, I would never be able to draw it out full scale on the jobsite. A sloping ridge is actually hip rafter , so we need to draw out the intersecting eave lines to find the eave angle, or point of intersection. These intersecting eave lines can often be extremely long and require a lot of drawing room on the jobsite.  So, drawing it out in a CAD program is very helpful,  but not always practical either.

The roof has one corner of the building with the typical 90° eave angle. Using any calculator we can find the standard angles for the hip rafter slope angle at an 45° angle from the corner of the building. For the next corner of the roof the eave angle is 120°. Using my RafterTools+ for iPhone we can enter the roof pitch and an eave angle of 120° to find the hip rafter slope angle off the 120° eave angle.

For the sloping ridge we can subtract 90° from the 120° , which leaves us with an Eave angle of 30° that we can use with the RafterTools+ for iPhone to find the slope angle of the sloping ridge.

Here's a drawing of the typical roofs most of us cut and stack here in American homes. The building turns at an 45° angle. The sloping ridge can be calculated using an Eave angle of 45° with the RafterTools+ for iPhone. (135° - 90° = 45°).

## Saturday, March 26, 2016

### Tracage Du Delardement

Tracage du delardement = trace the edge bevel on the hip rafter.

My drawing is based on this dormer.
Tracage du delardement

Tracing the edge bevel of a curved rafter is something that I learned when I took Billy's eyebrow dormer class in Portland. The edge bevel is always the same length along the edge of the hip rafter and the direction of the edge bevel is always in the same direction.

Drawing showing the Saint Andrews cross orthographic projection geometric development.

Drawing showing the side cut bevel for the curved jack rafter. All of these timbers are positioned in a vertical plane, so the the plumb line shift that works on hip roofs, also works on these curved timbers.

## Friday, March 25, 2016

### Guitarde Dormer Cabanie

Charpente General Theorique et Pratique - bois croche - B. Cabanié page 143

Michel Verdon helped me figure out the curve in question. Here's an updated drawing showing what I believe to be the profile curve of the guitarde and from looking at Emil Delataille's guitarde drawing I can see where the knee brace curve is developed.

Here's a couple of SketchUp drawings showing the orthographic projection (softening lines) to develop the profile curve of the guitarde.

English Translation

GUITAR RIDGE TRANSCRIPT.
PARIS. - PRINTING OF MADALIE VERNE IP-UCHARD ZUZARD STREET 1:

French OCR

GUITARDE A FAÎTAGE RELEVÉ.

On commence, premièrement (planche 86e), de tracer, du centre A, sur un plan horizontal, le plan par

terre B CD et l'épaisseur du lien-guitarde. On figure l'épaisseur des poteaux par une ligne B A'D' parallèle à

B D, on figure également une épaisseur des vitraux et les poteaux vus de bout. Ensuite, sur un plan vertical
passant par B' B", on élève B' B", E T', A' A", F                                       D' D" d'équerre à B' D'. On se met au point A' comme centre,
on décrit les vitraux E AilF. On tire E' d'un relevé quelconque, et B" D" dessus du chapeau, parallèles à 11,

on divise l'arc FA" en un certain nombre de lignes d'adoucissement, telles que 1, 2, 3, 4, 5, 6, 7, 8 ; on mène
ces lignes parallèles à B' D', •jusqu'à la rencontre de D' D", comme en                                                             2 en 2', 3 en 3', 4 en 4', 5 en 5', 6 en

6', 7 en 7', 8 en 8', et A" en A'. Sur un plan vertical passant par D C', on élève le poteau D' D"' d'équerre à D C'.
On se met au point D' comme centre, on fait tourner 1' en 1" 2' en 2", 3' en 3", 4 en 4", en 5", 6' en 6", 7' en

7', 8' en 8" , A" en Atv, le dessous et le dessus du chapeau D" en D"'; on mène le dessus du chapeau D"', le des-
-     s et les lignes d'adoucissement parallèles à D C' ou de niveau. On fixe en plan la tête du lien d'arête en G,

point voulu ; on remonte G en G', C en Cu parallèles à D' D"; on fait passer un cercle par les trois points D G'

comme il a été dit. On descend H' H, I' I, J' J, K' K, L' L, M' M, N' N, 0' 0, jonctions de la courbe et des lignes
d'adoucissement parallèles à D' D"', jusqu'à la rencontre de I H, 2 I, 3 J, 4 K, 5 L, 6 M, 7 N, 8 0 parallèles à A' A";

on joint XII I J K L M N O G par une règle flexible; de même pour l'autre arêtier. On les prolonge du point C,
comme centre, jusqu'à la face des liens-guitardes, après les avoir dévoyés, comme on le voit sur l'épure. On

y met ensuite les remplissages comme on les juge nécessaires, et de manière, autant que possible, que ces

remplissages partagent le vide en deux parties égales et qu'ils viennent se déjouter ensemble au pied des po-

teaux, comme on le voit sur l'épure.
Pour faire l'élévation du lien-guitarde B C, on tire une ligne P Q, extrémité des faces, puis on élève B B"',

P P", Q Q", C C"' d'équerre à P Q ; on tire P' Q', pour éviter la confusion des lignes, parallèle à P Q. On prend

sur la ligne D' D"' les lignes d'adoucissement, et on les porte sur P' P". On mène ces lignes parallèles à p' Q',
c'est-à-dire de niveau. On remonte d'en plan par terre R R', S S', T                                                             U U', etc., parallèles à 13 P"; on joint

avec une cerce BIV R' 1", etc., et P' S' U', etc., et on a les deux lignes du délardement, et l'élévation du lien-

guitarde est faite. On cherche donc une pièce de bois de la largeur qu'elle est figurée en élévation et de l'épais-

seur V V' en plan. On fait paraître sur ladite pièce de bois une ligne de trave presque sur le bord d'une des
faces, de manière qu'au levage elle tombe sur P Q. On met donc le lien sur son élévation de niveau et de
dévers suivant la ligne de trave ; une fois ce lien sur ligne, on y fait paraître les lignes d'adoucissement , ainsi

que les traits ramènerets. Ces lignes étant parues et rembarrées, on fait quartier à la pièce de bois, et on trace

dessus et dessous comme si le lien B V' C en plan était une courbe. Une fois le lien scié et travaillé, on fait

reparaître en dehors et en dedans les lignes d'adoucissement et les traits ramènerets. Le croisillon des lignes

d'adoucissement en dehors et en dedans, joint par une règle flexible, donne le délardement en enlevant le

bois d'une ligne courbe à l'autre. En rembarrant le trait ramèneret B' B"' du dehors par P' P" du dedans, on

a la coupe du pied dans le poteau ; en rembarrant le trait ramèneret C C'" par Q' Q", on a le déjoutement d'un
lien-guitarde contre l'autre : la hauteur hachée en plus de p" Q" est l'embrèvement dans la sablière. On peut
donc couper le lien carrément sur B"'                                       On opère de même pour l'autre lien D C.
Pour faire l'élévation du lien d'arête X G Y, on joint G X par une ligne droite; on élève X X' Y Y' d'équerre

à X G; on tire X' Y', pour éviter ta confusion des lignes, parallèle à X G. On prend sur D' D"' les lignes d'adou-

cissement, et on les porte sur X' X", on les mène parallèles à X' Y'; puis on remonte d'enplan par terre H II",
I r, J J", K K",                   M M", N N", 0", G G", de même que les lignes d'adoucissement et le joint Y Y"; on joint par

une règle flexible X' H" I" J" K" L" M" N" 0" G", etc. , Y", et on. a l'arête du lien d'aréte ou lien-tenaille ( on dit
tenaille à cause de la forme). On opère de même pour le délardement en le redescendant d'en plan sur son
élévation, comme on le voit sur l'épure. Les traits ramènerets du pied et de la tète indiquent, les deux pre-

miers, l'enfourchement dans le poteau ; les deux derniers, la coupe à plomb dans la sablière. Les quatre traits
ramènerets, dans le milieu, indiquent pour entailler les deux liens d'arête l'un dans. Vautrer; eu enlevant

entre les quatre traits ramènerets la moitié de la force du bois Ôté à l'un pour la laisser à l'autre> de manière

que les deux liens affleurent en dessous et en dessus, comme on le voit figuré. On peut établir rautre lien
d'arête sur la même épure.

Pour faire l'élévation du lien de remplissage E Z, on opère comme à l'ordinaire,                                                                    comme on le voit figuré
(figure Ire); de même pour le petit remplissage, comme on le voit (figure 2e) en se rappelant seulement que

les remplissages compris depuis l'arête des arêtiers aux liens X G P jusqu'à E se cintrent et se délardent sui-
vant la courbe E A" F, et que ceux compris depuis la même arête des liens X G P jusqu'à BC I) se cintrent et; se.
délardent suivant la courbe I) G' C".

PARIS. - IMPRIMERIE DE MADÀLIE VERNE IP,UCHARD-ZUZARD, RUE DE 1:EPERON, 5■              •  (1.),

## Sunday, March 20, 2016

### Guitarde Dormers Carpenter's Art

French Guitarde
Wall dormer or Balcony, circular or elliptical in plan view

This drawing is of two intersecting cylinders. I think I can develop the orthographic projections that will develop the correct curve of the intersecting cylinders.  I need to study this a lot more.

I started off with these two intersecting cylinders and realized that the horizontal cylinder is not rotated correctly.

The horizontal cylinder rotated correctly for the guitarde.

I'm not sure, but you might be able to build a guitarde with a cylinder and sloping plane. However, most of the guitardes look like the intersection of cylinders or cones.

Comparison of the sloping plane and horizontal cylinders intersecting the vertical cylinder.

Orthographic development for the sloping plane for a circular plan.

By Odeee (Own work) [CC BY-SA 3.0], via Wikimedia Commons

http://www.historicalcarpentry.com/guitarde---beautiful-french-dormers.html

http://www.historicalcarpentry.com/master-piece-photos.html

http://manoirs-cauchois.blogspot.com/2012_09_01_archive.html

http://www.lecompagnonnage.com/?Brive

http://compagnonnage.info/blog/blogs/blog1.php/2012/02/08/une-belle-guitarde-a-vendome-41

http://creationsculturejeuxdemeuzac.blogspot.com/2013_01_01_archive.html

http://imagesdouvrages.free.fr/compagnonnage_guitardes.htm

## Sunday, February 21, 2016

### Octagon Overlay Sleeper Math Notes

I thought I could break down the different parts to an Octagonal roof overlay, so you would only need to use some trigonometry to calculate the different dimensions to precisely frame the Octagonal Roof Overlay, California sleepers. However, I don't think it's possible. To precisely locate the sleepers on the main roof you have to geometrically draw out the main roof surface showing the location of the valleys sleepers developed from the location of the valleys sleeper in plan view.

In this drawing I developed the roof surface of the Octagonal Roof from the Octagon roof in plan view and elevation view. You can developed the valley sleepers on the octagonal roof surfaces, but it does not give the location of the sleepers on the main roof surface.

To develop the Octagonal Roof sleepers on the main roof surface you need to rotate the Octagon in plan view, so it's perpendicular to the main roof slope in the Octagon in elevation view. Dropping perpendicular from the main roof slope in elevation view develops the location of the sleepers on the main roof surface.

After you've developed  the sleepers on the main roof surface when you can get the sleeper miter angles you still need a saw blade bevel angle to miter the two sleepers together. You can use this formula for sleeper #1, Saw Blade Bevel Angle = arcsin(sin main roof slope) x cos(67.5)). For the saw blade bevel angle for the miter at sleepers #2 & #3 use  Saw Blade Bevel Angle = arcsin(sin main roof slope) x cos(22.5)). Or you can use the RafterTools+ app on the iPhone. Enter 135° eave angle and use the hip rafter backing angle for the Saw Blade Bevel Angle. Use an eave angle of 45° for the saw blade bevel angle for sleepers #2 & #3.

Use the same saw blade bevel angle to cut the miter on the bottom of the Octagonal Hip Rafters that frame into the sleepers. For the miter angle cut at the hip rafters that frame into the sleeper you could also use Layover Cut Angle = Layover Rafter Slope Angle + arctan (tan Main Roof Slope Angle x sin Layover Rotation Angle in Plan View) ....where the Rotation Angle in Plan View is  67.5° and 22.5°.

## Sunday, January 10, 2016

### 45 Plan Angle Rake Wall Plates

Yesterday, I was building the rake walls for a corner fire place. I have studied rake wall plates rotated into the roof surface plane quite extensively. However, yesterday I just couldn't remember how to calculate the rake plate miter angles. So this post is a reference for me the next time I'm on the jobsite building rake walls rotated into the roof surface plane.

Here's a drawing of the corner fire place I was building. The roof slope angle was 26.56505°, 6:12, with a 135° eave angle for the wall rake plate rotated into the roof surface.

Saw Miter Angle for Common Rafter Pitch Rake Wall = arctan ( tan (Direction Of Saw Travel ) ÷ cos (Roof Slope ))

R2 = Saw Miter Angle for Common Rafter Pitch Rake Wall = arctan ( tan (22.5° ) ÷ cos (26.56505° )) = 24.84908°

R2 = Saw Blade Bevel Angle = arcsin ( sin (26.56505° ) × cos (22.5° )) = 24.40422°

Saw Miter Angle = 180° - Real Roof Surface Angle - Saw Miter Angle for Common Rafter Pitch Rake Wall
H2 = Saw Miter Angle = 180° - 138.18969 - 24.84908= 16.96123°
H2 = Saw Blade Bevel Angle = arcsin ( sin (26.56505° ) × cos (22.5° )) = 24.40422°

A1 = Saw Miter Angle = arctan ( cos (26.56° ) ÷ tan (67.5° )) = 20.32886°

A1 = Saw Blade Bevel Angle = arcsin ( sin (26.56° ) × cos (22.5° )) = 24.3996°

Saw Miter Angle = 180° - Real Roof Surface Angle - Saw Miter Angle for Common Rafter Pitch Rake Wall

H1 = Saw Miter Angle = 180° - 131.81031 - 20.32886= 27.86083°

H1 = Saw Blade Bevel Angle = arcsin ( sin (26.56° ) × cos (67.5° )) = 9.85418°

```Hip Rake Wall Studs
Hip Rafter Pitch Angle = arctan( tan( Pitch Angle ) * sin( Plan Angle ))
Hip Rafter Backing Angle = arctan( sin( Hip Rafter Pitch Angle) ÷ tan( Plan Angle ) )
Hip Rafter Plumb Backing Angle = arctan( tan( Pitch Angle ) * cos( Plan Angle ))

Hip Rake Wall Pitch Angle = arctan( tan( Rafter Pitch Angle ) * sin( Working Angle ))
Hip Rake Wall Pitch Angle = arctan( tan( 26.56505.69 ) * sin( 45 )) = 19.47121°
Rake Stud Saw Miter Angle = Hip Rafter Plumb Backing Angle = 19.47121°
Rake Stud Saw Blade Bevel Angle = arctan(cos(Hip Rafter Plumb Backing Angle)* tan(Hip Rafter Pitch Angle))
Rake Stud Saw Blade Bevel Angle = arctan(cos(19.47121)* tan(19.47121)) = 18.4349°
```

## Saturday, January 2, 2016

### Diverse Hip Rafter Boucher

This method of drawing out the diverse hip rafter was shown to me by Olivier Phojo. He said the French compagnon-Professor J.D. Boucher (1890?), developed it. This method of drawing out the diverse hip rafter using the Sauterlle method, bevel square, is brilliant. Boucher may have developed the method, but Olivier drew it out were I could easily understand it. I looked through Boucher's book , L'art Du Trait of Charpente, yesterday and I couldn't find this method in his book.

This method of drawing out the bevel square angles for the diverse hip rafter only takes a couple of minutes. 5 minutes at most. It's something Billy and I should teach in our roof framing geometry classes.

Start off by drawing 2 perpendicular lines. You can draw this on a piece of paper 24" x 18". Then place the framing square on the vertical line and the end point of the framing square on the horizontal line. Trace the framing square for the profile rafter roof slope angle. In this task model I use and 8:12 pitch (33.69007°).

Next draw a perpendicular line to the roof slope line. This line will represent the eave line. I used 12" in this task model for an equal pitched roof. Then connect the eave line to the rise of the roof slope triangle. This line will represent the hip rafter on the roof surface.

At the intersection of the hip rafter on the roof surface with the horizontal line draw a perpendicular line equal in length to the roof slope triangle's tangent. 6 21/32", or 6 11/16" in this task model.

Then draw the diverse hip rafter bevel square lines connecting back to the roof surface triangle.

The red angle is used for the miter angle on the side of the diverse hip rafter. The blue angle is the top bevel on the diverse hip rafter.

The orange angle is used for the miter angle on the side of the diverse hip rafter and the blue angle is used for the bevel angle on top of the diverse hip rafter for the first face cut at the head of the diverse hip rafter. For the second face cut use the brown angle on top of the diverse hip rafter and the miter angle on the side of the hip rafter will be 90°.

Another drawing using a different roof slope angle. The DP line is easier to understand in this drawing. You don't need to draw the DP line, but you can check your cuts with the DP line.

Here's a picture of laying out the miter and bevel angle on the foot of the hip rafter using the red and blue angles. The cut will be a parallelogram, so you use the same angles on the top and bottom of the foot cut.

Here's a picture of the layout for first face cut at the head of the rafter.

Bottom view of the rafter layout.

The cut at the foot of the hip rafter is complete and the first face cut is complete.

Checking to make sure the foot cut aligns wit the eave line and DP line in elevation view.

Checking to make sure the first face cut is plumb to the horizontal plane.

For the second face cut you use the brown angle or 90° to the first bevel cut on top of the rafter.

Second face cut laid out.

I checked the accuracy of my drawing using a digital bevel square.

I then used a skill saw for all of the cuts. You could align the blade for the saw blade bevel angles on the timber, but using some math makes somewhat easier.

For the diverse hip rafter foot cut I used.
Miter Angle 27.1°
Saw Blade Bevel Angle  = arctan(sin(27.1) ÷ tan(50.24) = 20.7 °

For the diverse hip rafter face cut #1  I used.
Miter Angle 49.07°
Saw Blade Bevel Angle  = arctan(sin(49.07) ÷ tan(50.24) = 32.1 °

For the diverse hip rafter face cut #2  I used.
Miter Angle 90°
Saw Blade Bevel Angle  = 39.7 °

Here's a link to a PDF file that you can print out for this task model layout.
Boucher 8:12 Pitch

I can't think of an easier framing square exercise for carpenters. If your a carpenter and can't draw out this diverse hip rafter drawing, than maybe you should think about a career at McDonalds or Walmart.

Here's a wire frame drawing of the Boucher technique. Your folding the canted plane flat to the plumb plane of the hip rafter. I'm guessing you can use this same technique for just about any canted rafter.

Another example of folding the purlin rafter (frieze block, bird's block) plane flat. Pretty easy, only 3 triangles.