Angle de dévers Panne

Geometry & Trigonometry from the book La Charpente En Bois by  Gilbert Emery

Angle de dévers  --> Slope Angle

Panne D'Arêtier --> Purlin Cut at Hip Rafter

Angle sur le chant -- > Angle of the edge bevel

Angle sur le plat -- > Angle of the miter angle

Cote --> dimension

French Version for calculating the purlin miter and bevel angles.

Panne D'Arêtier

L= 90
H = 105
Angle A2 = 49.39871° = Rafter Slope Angle at Seat
Angle A1 = atan(L÷H) = 40.60129° ---- At Peak of Rafter
Cote I = H x sin(40.60129°) = 68.33309
Cote V = H x cos(40.60129°) = 79.72194
Cote R = V x sin(40.60129°) =51.88235
Angle sur le chant A4 = atan(V ÷R) = 56.94426
Angle sur le plat B5 = atan(I ÷R) = 52.79217
Cote R1 = R x sin(52.79217) = 41.321559
Angle de dévers B6 = atan(V ÷ R1) = 62.60135


American Version for calculating the purlin miter and bevel angles.

Angle sur le plat B5
Purlin Miter Angle = arctan( sin ( Pitch Angle ) ÷ tan( Plan Angle ))

 Purlin Miter Angle = arctan( sin ( 49.39871 ) ÷ tan( 45 ))= 37.20783°
90° - 37.20783° = 52.79217°

Angle sur le chant A4
Jack Rafter Side Cut = arctan( cos( Pitch Angle ) ÷ tan( Plan Angle )) 

Jack Rafter Side Cut = arctan( cos( 49.39871 ) ÷ tan( 45 )) = 33.05573°
90° - 33.05573 = 56.94426°


Angle de dévers B6
Purlin Saw Blade Bevel Angle = arcsin( cos ( Pitch Angle ) * cos( Plan Angle ))
Purlin Saw Blade Bevel Angle = arcsin( cos ( 49.39871 ) * cos( 45 )) = 27.39865°
90° - 27.39865° = 62.60135°