Divers Hip Rafters with Saint Andrews Cross

From geometrical theory to task model to the jobsite.

When I started studying  L'Art du Trait  4 years ago the terms divers and trait carre seemed hard to comprehend. Now the divers hip rafters are as easy to cut as a plumb hip rafters.
dévers de pas  = DP line, shadow line
dévers hip rafter  =  canted hip rafter, top edge of hip rafter rotated into the roof surface plane.
trait carré  = perpendicular , 90° angle


The divers 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

18.43495

Adjacent Slope Angle

18.43495

Main Plan Angle

45.00000

Adjacent Plan Angle

45.00000

Hip Rafter Slope Angle

13.26268

R8-DP -- Diverse Hip Rafter slope angle, used at the foot cut

13.59458

R9-DP

3.01279

D-DP

41.98721

R10-DP

12.58747

PSBm-DP

71.56505

PSBa-DP

12.57063

SR4Bm-DP

48.01279

SR4Ba-DP

131.98721

R11m-DP Diverse Hip Rafter Miter Angle 

65.32272

P7m-DP

133.49152

P8m-DP

90.00000

P9m-DP

0.00000

P10m-DP

90.00000

P11m-DP

43.49152

P12m-DP

43.49152

P13a-DP

19.35965

P14a-DP

56.27325

P15a-DP  Bevel angle on the top of the Diverse Hip Rafter

46.50848

P16a-DP

18.43495

P17a-DP

54.86581

P18a-DP

43.49152

Skewed Purlin Rafter Rotation Angle

20.12000

Purlin Rafter Depth

9 1/2''in

Hip Rafter Depth

11 1/2''in

Hip Rafter Width

3 1/2''in

P19a-DP

112.37693

P20a-DP

24.12533

P21a-DP

62.35618

P22a-DP

25.39390

P23a-DP

11.73330

P24a-DP

41.52301

Seat Line Profile - Purlin Rafter Plan

30 1/16''in

Seat Line Profile - Purlin Rafter Roof

28 1/2''in

Seat Line Hip Rafter

36 3/8''in

Roof Sheathing Angle

46.50848

Claw Line 1

0

Claw Line #2

26 3/8''in

Claw Line 3 -- Seat lined used on the draw down roof surface

4 5/8''in

Claw Line 4

6 3/4''in

Sent from my iPhone

Secret Carpenters Circle for Canted Hip Rafters when you don't have an iPhone