Irregular Valley Roof

Valley Pitch Angle = 29.01714°

12/12 Main Span Angles
Common Rafter Pitch Angle = 45.00000°
Plan Angle = 33.69007°
Sheathing Angle = 43.31386°
Jack Rafter Side Cut Angle = 46.68614°
Backing Angle = 36.03989°
Valley Rafter Side Cut Angle (Peak) = 30.24146°
Valley Rafter Side Cut Angle (Foot) = 52.67946°

8/12 Dormer Angles
Common Rafter Pitch Angle = 33.69007°
Plan Angle = 56.30993°
Sheathing Angle = 60.98286°
Jack Rafter Side Cut Angle = 29.01714°
Backing Angle = 17.92021°
Valley Rafter Side Cut Angle (Peak) = 52.67946°
Valley Rafter Side Cut Angle (Foot) = 30.24146°

Irregular Valley Definitions of Angles
Saw Blade Bevels for the Valley Rafter cheek cuts are complementary to the Plan Angles.
The Saw Blade Bevel for the Jack Rafter cheek cut is the same as for the cheek cut at the Valley Rafter foot.
The Jack Rafter Side Cut Angle and Sheathing Angle are complementary.
Irregular Valley Plan Angles
If the Valley Roof ridges (or Hip Roof eaves) intercept at 90° in plan:
Irregular Valley Plan Angle Formulas
Irregular Valley Main Side Jack Rafter Compound Angle
Irregular Valley Dormer Side Jack Rafter Compound Angle
Calculation of Jack Rafter Compound Angles

Irregular Valley Rafter Side Cut and Cheek Cut Angles
Irregular Valley Sheathing Angle and Sheathing Layout
Jack Rafter Difference in Length = Spacing on Centers × tan Sheathing Angle
12/12 Main Span Jack Rafter Difference in Length
If spacing on centers along Valley ridge line = 16"
Difference in Length = 16" × tan 43.31386° = 15.08495" = 15 1/16"
8/12 Dormer Jack Rafter Difference in Length
If spacing on centers along Valley ridge line = 16"
Difference in Length = 16" × tan 60.98286° = 28.84441" = 28 7/8"

Irregular Valley Rafter Backing Angles
Over 12 Ratios

Valley Pitch Angle = 12 × tan 29.01714° = 6.65640 = 6 11/16

12/12 Main Span
Plan Angle = 12 × tan 33.69007° = 8.00000 = 8
Sheathing Angle = 12 × tan 43.31386° = 11.31371 = 11 5/16
Jack Rafter Side Cut Angle = 12 × tan 46.68614° = 12.72792 = 12 3/4
Backing Angle = 12 × tan 36.03989° = 8.73128 = 8 3/4
Valley Rafter Side Cut Angle (Peak) = 12 × tan 30.24146° = 6.99580 = 7
Valley Rafter Side Cut Angle (Foot) = 12 × tan 52.67946° = 15.74054 = 15 3/4

8/12 Dormer
Plan Angle = 12 × tan 56.30993° = 18.00000 = 18
Sheathing Angle = 12 × tan 60.98286° = 21.63331 = 21 5/8
Jack Rafter Side Cut Angle = 12 × tan 29.01714° = 6.65640 = 6 11/16
Backing Angle = 12 × tan 17.92021° = 3.88057 = 3 7/8
Valley Rafter Side Cut Angle (Peak) = 12 × tan 52.67946° = 15.74054 = 15 3/4
Valley Rafter Side Cut Angle (Foot) = 12 × tan 30.24146° = 6.99580 = 7


Joe Bartok