W :
Angle viewed in plan between Hip eaves or Valley ridges; any value greater than zero up to 180°.
SS :
Main or Major side
Common Rafter Pitch Angle
or
Common Rafter Plumb Cut Angle
S :
Adjacent or Minor side
Common Rafter Pitch Angle
or
Common Rafter Plumb Cut Angle
Angle = arctan (Pitch) or
arctan (Rise ÷ Run)
Rise = 12 × tan Common Pitch Angle or
12 × Rise ÷ Run
The initial values of the Common Rafter Pitches are generally given as Over 12
DD :
Main or Major side
Cheek Cut Angle
or Saw Blade Bevel Angle to cut along the plumb lines on a Jack Rafter, at the Hip peak or the Valley foot.
Angle in Plan
or
Deck Angle
measured between the Main or Major side Hip eave and the Hip run, or the Main or Major side ridge viewed in plan and the Valley run.
D :
Adjacent or Minor side
Cheek Cut Angle
or Saw Blade Bevel Angle to cut along the plumb lines on a Jack Rafter, at the Hip peak or the Valley foot.
Angle in Plan
or
Deck Angle
measured between the Adjacent or Minor side Hip eave and the Hip run, or the Adjacent or Minor side ridge viewed in plan and the Valley run.
Major Side Plan Angle = arctan [sin W ÷ (Major Pitch / Minor Pitch + cos W)]
Major Side Plan Rise = 12 × sin W ÷ (Major Pitch / Minor Pitch + cos W)
Minor Side Plan Angle = arctan [sin W ÷ (Minor Pitch / Major Pitch + cos W)]
Minor Side Plan Rise = 12 × sin W ÷ (Minor Pitch / Major Pitch + cos W)
R1 :
HipValley Rafter Pitch Angle
or
HipValley Rafter Plumb Cut Angle.
The intercept of the Jack Rafter with the HipValley Rafter creates the footprint angles 90° ± R1 on the side (plumb) face of the HipValley Rafter.
Angle = arctan (tan Common Rafter Pitch Angle × sin Plan Angle)
Rise = 12 × tan Common Rafter Pitch Angle × sin Plan Angle
P2 :
Jack Rafter Side Cut Angle,
located on the Jack Rafter face set in the plane of the roof.
Angle = arctan (cos Common Rafter Pitch Angle ÷ tan Plan Angle)
Rise = 12 × cos Common Rafter Pitch Angle ÷ tan Plan Angle
90° – P2 :
Sheathing Angle,
also the angle on a
Jack Purlin
on the face set in the plane of the roof. Complementary to the Jack Rafter Side Cut Angle.
Angle = arctan (tan Plan Angle ÷ cos Common Rafter Pitch Angle)
Rise = 12 × tan Plan Angle ÷ cos Common Rafter Pitch Angle
C5 :
Backing Angle, the Saw Blade Bevel Angle to cut a ridge on a Hip Rafter or trough on a Valley Rafter.
Also the Saw Blade Bevel Angle when cutting along the Sheathing Angle, the angle on the face of the Purlin set in the plane of the roof (the Sheathing Angle) or the complementary Jack Rafter Side Cut Angle.
Angle = arctan (sin HipValley Rafter Pitch Angle ÷ tan Plan Angle)
Rise = 12 × sin HipValley Rafter Pitch Angle ÷ tan Plan Angle
A7 :
Plumb Backing Angle.
Backing Angle C5 projected to or viewed along the HipValley Rafter Plumb Cut.
Angle = arctan (tan HipValley Rafter Pitch Angle ÷ tan Plan Angle)
Rise = 12 × tan HipValley Rafter Pitch Angle ÷ tan Plan Angle
R4B :
HipValley Rafter Side Cut Angle
at the Hip Rafter foot or Valley Rafter peak.
Angle on the stick created on the upper/lower shoulders of the HipValley Rafter as the rafter intercepts a plumb plane following the Hip eave or Valley ridge line.
This angle may occur at the Valley Rafter foot if the plumb plane intercepted follows the eave line.
Angle = arctan (cos HipValley Rafter Pitch Angle × tan Plan Angle)
Rise = 12 × cos HipValley Rafter Pitch Angle × tan Plan Angle
R4P :
HipValley Rafter Side Cut Angle
at the Hip Rafter peak or Valley Rafter foot.
Angle on the stick created on the upper/lower shoulders of the HipValley Rafter as the rafter intercepts a plumb plane at right angles the Hip or Valley eave line.
Angle = arctan (cos HipValley Rafter Pitch Angle ÷ tan Plan Angle)
Rise = 12 × cos HipValley Rafter Pitch Angle ÷ tan Plan Angle
A5B :
Saw Blade Bevel Angle
to make the cut along the HipValley Rafter Side Cut Angle R4B at the Hip Rafter foot or Valley Rafter peak.
A5P :
Saw Blade Bevel Angle
to make the cut along the HipValley Rafter Side Cut Angle R4P at the Hip Rafter peak or Valley Rafter foot.
Angle = arctan (sin HipValley Rafter Side Cut Angle × tan HipValley Rafter Pitch Angle)
Rise = 12 × sin HipValley Rafter Side Cut Angle × tan HipValley Rafter Pitch Angle
R5B :
HipValley Rafter Footprint Angle
90° ± R5B is created by cutting the Compound Angle defined by R4B and 90° – R1 at the intercept of the HipValley Rafter and a plumb plane following the Hip eave or Valley ridge line.
Angle = arctan (cos Plan Angle × tan HipValley Rafter Pitch Angle)
Rise = 12 × cos Plan Angle × tan HipValley Rafter Pitch Angle
R5P :
HipValley Rafter Footprint Angle
90° ± R5P is created by cutting the Compound Angle defined by R4P and 90° – R1 at the intercept of the HipValley Rafter and a plumb plane at right angles to the eave line.
Angle = arctan (sin Plan Angle × tan HipValley Rafter Pitch Angle)
Rise = 12 × sin Plan Angle × tan HipValley Rafter Pitch Angle
P1 :
Purlin Saw Miter Angle
on the faces of Purlins or BirdBlock set perpendicular to the plane of the roof, at the intercept of this face with the side or plumb face of the HipValley Rafter.
Angle = arctan (sin Common Rafter Pitch Angle ÷ tan Plan Angle)
Rise = 12 × sin Common Rafter Pitch Angle ÷ tan Plan Angle
R2 :
Square Tail Fascia Saw Miter Angle on the HipValley Rafter.
Purlins or BirdBlock intercepting the side or plumb face of a HipValley Rafter create the footprint angles 90° ± R2 on the HipValley Rafter.
Angle = arctan (sin Backing Angle × tan Jack Rafter Side Cut Angle)
Rise = 12 × sin Backing Angle × tan Jack Rafter Side Cut Angle
C1 :
Purlin Saw Blade Bevel Angle
to make the cut along 90° – P1 on the faces of Purlins or BirdBlock set perpendicular to the plane of the roof, at the intercept of this face with the side or plumb face of the HipValley Rafter.
Also the
Saw Blade Bevel Angle
along the miter line of angle R2 on the HipValley Rafter to accommodate Square Tail Fascia.
Angle = arctan (sin Purlin Saw Miter Angle ÷ tan Common Rafter Pitch Angle)
Rise = 12 × sin Purlin Saw Miter Angle ÷ tan Common Rafter Pitch Angle
Miter Angle for Square Tail Fascia :
Major Side Angle = arctan (sin Main Common Pitch Angle ÷ tan Adjacent Plan Angle)
Major Side Rise = 12 × sin Main Common Pitch Angle ÷ tan Adjacent Plan Angle
Minor Side Angle = arctan (sin Adjacent Common Pitch Angle ÷ tan Main Plan Angle)
Minor Side Rise = 12 × sin Adjacent Common Pitch Angle ÷ tan Main Plan Angle
Saw Blade Bevel Angle for Square Tail Fascia :
Angle = arctan (cos Square Tail Fascia Miter Angle × tan Jack Rafter Side Cut Angle)
Rise = 12 × cos Square Tail Fascia Miter Angle × tan Jack Rafter Side Cut Angle
90° – R3 :
Angle on the stick, located on the upper/lower shoulders of a HipValley Rafter.
90° – R3 is the
Hip Rafter Square Tail Fascia Side Cut Angle
at the foot of the Hip Rafter, or the
Valley Rafter intercepts Main Purlin Side Cut Angle
at the peak of the Valley Rafter.
Angle = arctan (tan Sheathing Angle ÷ cos Backing Angle)
Rise = 12 × tan Sheathing Angle ÷ cos Backing Angle
C2 :
Saw Blade Bevel Angle
to make the cut along the miter line of angle 90° – R3 on the upper/lower shoulders of the HipValley Rafter.
Angle = arctan (cos Hip Rafter Square Tail Fascia Side Cut Angle × tan Backing Angle)
Rise = 12 × cos Hip Rafter Square Tail Fascia Side Cut Angle × tan Backing Angle
