Divers Hip Rafter # 2

I was redrawing the Divers Hip Rafter files to scale them down for a task model and found a way to eliminate one of the arc's that's drawn to define the divers hip rafter profile.  With a perpendicular line to the DP - Shadow Line through the center point of the hip rafters in plan view and an Arc with the radius equal to the length of the plumb hip rafter profile length, the intersection of the single Arc and perpendicular line defines the divers hip rafter profile. A lot easier than using two Arcs to define the diverse hip rafter profile.

Divers Hip Rafter

Developing the diverse hip rafter in profile.

 I wanted to develop the divers hip rafter (canted hip rafter, hip rafter rotated into the roof surface) without using the bevel square method (grasshopper -"la sauterelle") or using the roof surface ( draw-down or fold out method). Michel Verdon at , French Timber Framing Traditional Scribing , helped me and now it's pretty easy to draw out the divers hip rafter fully developed in the profile elevation only.

Retobois Charpente Couverture Ramonage
on Facebook posted this dormer with the diverse hip rafters rotated into two different roof surface planes and said it was quite common in France.  The hip rafter on the right side of the dormer is rotated into the roof surface on the front of the dormer and the hip rafter on the left side of the dormer is rotated into the roof surface of  the left side of the dormer.

Retobois Charpente Couverture Ramonage Diverse Hip Rafter on Facebook

Both divers hip rafters are cut exactly the same. The foot and head cuts on the diverse hip rafters only need to be developed one time. Layout and cut both divers hip rafters exactly the same and rotate them into place.

One of the reasons I didn't want to draw out the geometry for the divers hip rafter using  the bevel square method (grasshopper -"la sauterelle") , because I could just as easily use my RafterTools+ app on my iPhone. The divers hip rafter is the same length as a plumb hip rafter. So, you only need to know the angles to cut the divers hip rafter. In fact, to draw out the geometry of the diverse hip rafter in profile you need to know how to draw out the plumb hip rafter in profile.


RafterTools+ on iPhone

Main Slope Angle = 30°
Adjacent Slope Angle = 30°
Main Plan Angle = 45°
Adjacent Plan Angle = 45 = °
Hip Rafter Slope Angle = 22.20765°
Hip Rafter Run = 60 ÷ cos(45°) = 84.85281
Hip Rafter Length = 84.85281 ÷ cos(22.20765°) = 91.65

Treteaux Angles
R8-DP = 23.57818
PSBa-DP = 19.10661
R11m-DP = 52.62876
P11m-DP = 40.89339
P15a-DP = 49.10661

The only math - trigonometry you need to use is to calculate the saw blade bevel angle for face cut #1.
Face Cut #1
Angular Dimension (52.62876°)
Miter Angle 52.62876°
Saw Blade Bevel Angle = arctan(sin(52.62876°) ÷ tan(49.10661°)) = 34.53757°

 To draw out the geometry for the diverse hip rafter in profile I'm using the shadow line technique from Bernd Kuppers book to locate the DP-Shadow line of the canted hip rafter. After the DP - Shadow line is drawn, draw out the plumb hip rafter profile. Then draw out the plane tilt of the diverse - canted hip rafter and use the intersection of the two arc's to finish the diverse hip rafter profile.

 Here's a drawing showing how to lay the timber on top of the profile drawing of the divers hip rafter and transfer lines from the drawing to the timber for the layout on the foot cut of the divers hip rafter.

 Drawing with the diverse hip rafter head cut developed by using lines perpendicular to the DP-Shadow line.

Both sides of the diverse hip rafter head cuts developed in plan view.

After developing the geometry for the dormer I wanted to see what the head cuts on the divers hip rafter would look like when it intersects a king post.  The angles are the same at the foot and head cut of the diverse hip rafter.

After drawing the geometry for the divers hip rafter intersecting the king post, I drew out the geometry for a jack rafter on each side of the diverse hip rafter.

The geometry in this drawing makes it pretty easy to draw the head cuts of the two jack rafters. Including the upper and lower claws.

Unequal Pitched Valley Rafter Tail

I've installed 100 of false valley tails on unequal pitched roofs, but this house presented a unique framing problem. All of the other houses with the unequal pitched valley tails had rafter tails on each side of the valley tail and you could easily plane in the unequal pitched valley tail. In this house there were rafter tails only on one side of the valley tail.

Scott, a student in our Ancient Knowledge Tour class on roof framing geometry, asked where you would use the unequal pitched roof framing geometry on a job site. This would be an easy example of using geometry on the jobsite.

The main roof pitch was 4:12 and the roof dormer pitch was a 6:12 pitch. So I draw out an L on the drawing board and marked off 4" & 6" on each side of the L. Then I drew perpendicular lines from those marks. From the intersection of the perpendicular lines I drew in the hip-valley run line. Next I drew in the hip rafter basic shift to establish the location of the sides of the hip-valley in plan view. I placed the jack rafter tail at 9" from the intersection of the two roof pitches. With the jack rafter tail in plan view I picked up the exact length of the jack rafter tail on the horizontal plane placed at 9" from the intersection of the two roof pitches. I also able to draw out the jack rafter tail plumb line shift to layout the cut on the jack rafter tail.

Then I drew the hip-valley rafter in profile to determined the length of the valley rafter tail. As well as the valley rafter tail plumb line shift for the cut at the peak of the valley rafter tail and the "V" notch at the foot of the valley rafter tail.

Here are some drawings with the different steps to draw out the geometry for the unequal pitched valley rafter tail.