Irregular Roof: Sections through Hip Rafters
Irregular Roof: Shifting and Dropping the Hip Rafters
Back to Irregular Hip Roof Dimensions
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Irregular Roof: Plan detailing Sections through Hip Rafters

Irregular Roof: Cross Sections through Hip Rafters bevelled about Centerlines detailing Backing Angles
Development of Backing Angles

Irregular Roof: Plumb Sections through Hip Rafters bevelled about Centerlines detailing Plumb Backing Angles

Irregular Roof: Plumb Sections through Hip Rafters bevelled about Centerlines

Irregular Roof: Plumb Sections through Hip Rafters bevelled according to Plan Angle Ratios
Development of Proportioned Plumb Backing Angles

Hip Shift Unit Ratios
The unit ratios are factored by the actual rafter widths to determine the offsets detailed in the diagram above.

615/16/12 Hip Rafter, 8/12 Side
tan 60.25512° ÷ (tan 60.25512° + tan 29.74488°) = .75385

615/16/12 Hip Rafter, 14/12 Side
tan 29.74488° ÷ (tan 60.25512° + tan 29.74488°) = .24615

915/16/12 Hip Rafter, 14/12 Side
tan 45.19422° ÷ (tan 45.19422° + tan 89.80578°) = .00340

915/16/12 Hip Rafter, 915/16/12 Side
tan 89.80578° ÷ (tan 45.19422° + tan 89.80578°) = .99660

715/16/12 Hip Rafter, 915/16/12 Side
tan 52.91319° ÷ (tan 52.91319° + tan 82.08681°) = .15532

715/16/12 Hip Rafter, 8/12 Side
tan 82.08681° ÷ (tan 52.91319° + tan 82.08681°) = .84468

Irregular Roof: Hip Drops and Shifts about the Framing Lines

The Hip Rafters are shifted and dropped as per the drawing above. The lengths conform to the theoretical framing lines with the following exception.

Length reduction for 915/16/12 Hip Rafter
This Hip rafter has been positioned to act as a Common (Jack) Rafter.
The 89.85038° angle at the corner is rounded to 90°.
Width on adjoining 715/16/12 Hip Rafter in plan = .23298" (see Section View)
Angle in plan = 90° - 52.91319° = 37.08681°
Hip Rafter Run = .23298" ÷ sin 37.08681° = .38635"
Reduction of Hip Rafter Length = .38635" ÷ cos 39.61624° = .50153" (approx. 1/2")
Hip Rafter Length = 19.34208' - (.50153" ÷ 12) = 19.30029' = 19' - 3 5/8"

Irregular Roof: Rafter Side Cut Angles at Peaks and Blade Bevels along Plumb Lines

Example Side Cut Calculation for 615/16/12 Hip Rafter, 8/12 Side
The Side Cut Angle at the Hip Rafter peak on the 8/12 side is 26.31492°
The width on the 8/12 side of the Hip Rafter is 1.13078" (see Section View)
1.13078" ÷ sin 26.31492° = 2.55080"
We want a closer match to the .75" of the Ridge Board.
Angle in plan between Ridge Board and Hip Run = 180° - 60.25512° = 119.74488°
90° - 60.25512° = 29.74488° is covered by the Hip Rafter
(The projection of the 29.74488° Plan Angle to the Hip Rafter produces the 26.31492° Side Cut Angle at the Hip Rafter peak)
The remaining 90° will be divided equally between the Ridge Board and Hip Rafter.
Plan Angle at Hip Rafter = 45° + 29.74488° = 74.74488°
Blade Bevel Angle along Plumb Cut = 90° - 74.74488° = 15.25512°
Hip Rafter Side Cut Angle
= arctan (cos Hip-Valley Pitch Angle ÷ tan Blade Bevel along Plumb Line)
= arctan (cos 30.06349° ÷ tan 15.25512°) = 72.50931°
The edges are approximately:
Ridge Board = .75" ÷ sin 45° = 1.06066
Hip Rafter = 1.13078" ÷ 72.50931° = 1.18560"
Since the Hip Rafter edge actually slopes away from level; the current 1/8" difference will be about 1/32" as viewed in plan.

Blade Bevel Angles along Rafter Plumb Lines

615/16/12 Hip Rafter, 14/12 Side
arctan (cos 30.06349° ÷ tan 56.56514°) = 29.74488°

715/16/12 Hip Rafter, 8/12 Side
(NOTE: The "natural" Side Cut Angle value of 6.61620° has been changed to 64.06753° for a better match with the edge of the Ridge Board)
arctan (cos 33.43752° ÷ tan 64.06753°) = 22.08681°

715/16/12 Hip Rafter, 915/16/12 Side
arctan (cos 33.43752° ÷ tan 32.24437°) = 52.91319°

915/16/12 Hip Rafter (= Common Rafter)
arctan (cos 39.61624° ÷ tan 30.21300°) = 52.91326°

14/12 Common Rafter
arctan (cos 49.39871° ÷ tan 32.87839°) = 45.19422°


Joe Bartok
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