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
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.
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.