When I started studying L'Art du Trait 4 years ago the terms diverse and trait carre seemed hard to comprehend. Now the diverse hip rafters are as easy to cut as a plumb hip rafters.
dévers de pas = DP line, shadow line
déverse hip rafter = canted hip rafter, top edge of hip rafter rotated into the roof surface plane.
trait carré = perpendicular , 90° angle
The diverse hip rafter can be cut the same way you cut plumb hip rafters, once you have the angles. The Saint Andrew Cross purlin rafters need to be laid out using the draw down roof surface method.
Draw down roof surface. The 2 blue lines represent the top edge of the hip rafter and the bottom edge of the profile rafter. These lines allow you to scribe the miter angle on the sides of the rafters. The draw down roof surface works for any rafter that has it top edge set in the roof surface.
Steps for laying out the diverse hip rafter:
First I used the Diverse Hip Rafter Boucher drawing method developed by Olivier Phojo. You can draw it out on a piece of plywood or a CAD drawing program. This gives you the miter angle on the side of the hip rafter and the edge bevel angle on the top of the hip rafter.
First I laid out the miter angle on the foot of the diverse hip rafter . Then I cut the compound cut with a saw blade bevel angle of 40.76275°
Saw Blade Bevel Angle
arctan(sin 65.32268 ÷ tan 46.50849) = 40.76275
Then I laid out an trait carré = perpendicular , 90° angle and made the cut using
Saw Blade Bevel Angle
90° - Roof Sheathing Angle
90°- 46.50849 = 43.49151
Next I marked off the 8 3/4" plumb height that I'm using on my profile-common rafters for the HAP. Then from that mark draw perpendicular lines for the seat cut line. Then finish laying out the rest of the seat cut line using the diverse hip rafter slope angle.
The Hip Rafter Length is developed from the profile-common rafter run to the ridge and marked on the one inside edge of the hip rafter material. The Hip Rafter Head Cut, is cut using the same miter and saw blade bevel angle as the first cut
on the foot of the rafter.
Drawings to develop the draw down roof surface.
You can also use my Treteaux Angles calculator on iPhone to calculate the angles and check the dimension for the seat-claw #3 line on the draw down roof surface.
Main Slope Angle
Adjacent Slope Angle
Main Plan Angle
Adjacent Plan Angle
Hip Rafter Slope Angle
R8-DP -- Diverse Hip Rafter slope angle, used at the foot cut
R11m-DP Diverse Hip Rafter Miter Angle
P15a-DP Bevel angle on the top of the Diverse Hip Rafter
Skewed Purlin Rafter Rotation Angle
Purlin Rafter Depth
Hip Rafter Depth
Hip Rafter Width
Seat Line Profile - Purlin Rafter Plan
Seat Line Profile - Purlin Rafter Roof
Seat Line Hip Rafter
Roof Sheathing Angle
Claw Line 1
Claw Line #2
Claw Line 3 -- Seat lined used on the draw down roof surface
Claw Line 4
Sent from my iPhone
Secret Carpenters Circle for Canted Hip Rafters when you don't have an iPhone