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Irregular Hip Framing Formulas

Variables
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Major Pitch 
Minor Pitch 
Major Run 
Jack Rafter Spacing

Formulas
----------------------------------

Eave Angle  = 90°
Major Pitch Angle = atan( Major Pitch ÷ 12 )
Minor Pitch Angle = atan( Minor Pitch ÷ 12 )
Minor Run = ( Major Pitch ÷ Minor Pitch ) * Major Run

Major Plan Angle =  arctan( Minor Pitch ÷ Major Pitch )
Minor Plan Angle =  arctan( major_pitch ÷ Minor Pitch )

Hip Pitch Angle = arctan( tan( Major Pitch Angle ) * sin( Major Plan Angle ))
Major Pitch Hip Backing Angle = arctan( sin( Hip Pitch Angle) ÷ tan( Major Plan Angle ) )
Minor Pitch Hip Backing Angle = arctan( sin( Hip Pitch Angle) ÷ tan( Minor Plan Angle ) )

Major Plan Angle Unit Rise = tan( Major Plan Angle )
Minor Plan Angle Unit Rise = tan( Minor Plan Angle )

Major Pitch Common Unit Run = 12 / tan( Major Pitch Angle )
Minor Pitch Common Unit Run = 12 / tan( Minor Pitch Angle )

Major Pitch Common Unit Length = Major Pitch Common Unit Run ÷ cos( Major Pitch Angle )
Minor Pitch Common Unit Length = Minor Pitch Common Unit Run ÷ cos( Minor Pitch Angle )

Hip Rafter Unit Run = hypotenuse(Major Pitch Common Unit Run , Minor Pitch Common Unit Run )
Hip Rafter Unit Length = hypotenuse( 12 , Hip Rafter Unit Run )

Major Side Shift Unit Ratio = Major Plan Angle Unit Rise ÷ ( Major Plan Angle Unit Rise + Minor Plan Angle Unit Rise ) 
Minor Side Shift Unit Ratio = Minor Plan Angle Unit Rise ÷ ( Major Plan Angle Unit Rise + Minor Plan Angle Unit Rise ) 
Major Side Shift = 0.5 * ( Major Side Shift Unit Ratio - Minor Side Shift Unit Ratio) 
Minor Side Shift = 0.5 * ( Minor Side Shift Unit Ratio - Major Side Shift Unit Ratio) 
Hip Unit Rise Run = 12 ÷ sin( Major Plan Angle)
Unit Hip Drop = Major Pitch ÷ (Hip Unit Rise Run * ( Major Plan Angle Unit Rise + Minor Plan Angle Unit Rise ))
Hip Drop = Hip Width * Unit Hip Drop

Major Plumb Backing Angle = arctan( tan( Hip Pitch Angle ) ÷ tan( Major Plan Angle ))
Minor Plumb Backing Angle = arctan( tan( Hip Pitch Angle ) ÷ tan( Minor Plan Angle ))

Major Plumb Backing Angle Rise = (( Hip_Width * 0.5 ) * tan( Major Pitch Hip Backing Angle )) ÷ cos( Hip Pitch Angle )
Minor Plumb_Backing_Angle_Rise = (( Hip_Width * 0.5 ) * tan( Minor Pitch Hip Backing Angle )) ÷ cos( Hip Pitch Angle )
Major Plumb Backing Angle Run = Major Plumb Backing Angle Rise ÷ tan( Major Plumb Backing Angle )
Minor Plumb Backing Angle Run = Minor Plumb Backing Angle Rise ÷ tan( Minor Plumb Backing Angle )

Major Plan Angle Hip Rafter Side Cut Angle  = arctan( cos( Hip Pitch Angle ) ÷ tan( Major Plan Angle )) 
Minor Plan Angle Hip Rafter Side Cut Angle  = arctan( cos( Hip Pitch Angle ) ÷ tan( Minor Plan Angle )) 

Major Pitch Jack Rafter Side Cut = acos( sin( Major Plan Angle ) ÷ cos( Major Pitch Hip Backing Angle ))
Minor Pitch Jack Rafter Side Cut = acos( sin( Minor Plan Angle ) ÷ cos( Minor Pitch Hip Backing Angle )) 

Major Pitch Sheathing Angle = acos( cos( Major Plan Angle ) * cos( Hip Pitch Angle )) 
Minor Pitch Sheathing Angle = acos( cos( Minor Plan Angle ) * cos( Hip Pitch Angle )) 

Major Pitch Sheathing Cut Measurement =  Plywood Width ÷ tan( Major Pitch Sheathing Angle)
Minor Pitch Sheathing Cut Measurement =  Plywood Width ÷ tan( Minor Pitch Sheathing Angle )

Major Pitch Jack Difference =  tan( Major Pitch Sheathing Angle ) * Jack Rafter Spacing
Minor Pitch Jack Difference =  tan( Minor Pitch Sheathing Angle ) * Jack Rafter Spacing

Major Plan Angle Frieze Block Saw Miter Angle  = arctan( sin ( Major Rafter Pitch Angle ) ÷ tan( Major Plan Angle )) 
Major Plan Angle Frieze Block Saw Blade Bevel Angle   = arctan( sin( Major Plan Angle Frieze Block Saw Miter Angle ) ÷ tan( Major Rafter Pitch Angle )) 

Minor Plan Angle Frieze Block Saw Miter Angle  = arctan( sin(Minor Rafter Pitch Angle ) ÷ tan( Minor Plan Angle )) 
Minor Plan Angle Frieze Block Saw Blade Bevel Angle   = arctan( sin( Minor Plan Angle Frieze Block Saw Miter Angle ) ÷ tan( Minor Rafter Pitch Angle )) 

Major Common Rafter Rise = Major Run * tan( Major Pitch Angle )
Major Common Rafter Length = Major Run ÷ cos( Major Pitch Angle )
Major Common JackRafter Run = Jack Rafter Spacing * tan( Major Plan Angle )
Major Common JackRafter Length = Major Common JackRafter Runn ÷ cos( Major Pitch Angle )

Minor Common Rafter Rise = Minor Run * tan( Minor Pitch Angle )
Minor Common Rafter Length = Minor Run ÷ cos( Minor Pitch Angle )
Minor Common JackRafter Run = Jack Rafter Spacing * tan( Minor Plan Angle )
Minor Common JackRafter Length = Minor Common JackRafter Run ÷ cos( Minor Pitch Angle )

Hip Rafter Run = Major Run ÷ cos( Major Plan Angle )
Hip Rafter Length = Hip Rafter Run ÷ cos( Hip Pitch Angle )

Example Irregular Hips Geometry DXF Drawing

Example Irregular Hips Geometry Dimensions DXF Drawing

Example Irregular Hips Geometry Major Plan Angle, Minor Plan Angle, Hip Backing Angle, Sheathing Cut Angle and Jack Rafter Cheek Cut Angle DXF Drawing

Example Irregular Hips Geometry Find Jack Rafter Length Difference Drawing

Pitch Common Unit Runs at 12'' Rise
Pitch Common Unit Lengths at 12'' Rise

1/12 Pitch Common Unit Run = 144.00000
1/12 Pitch Common Unit Length = 144.49913
2/12 Pitch Common Unit Run = 72.00000
2/12 Pitch Common Unit Length = 72.99315
3/12 Pitch Common Unit Run = 48.00000
3/12 Pitch Common Unit Length = 49.47727
4/12 Pitch Common Unit Run = 36.00000
4/12 Pitch Common Unit Length = 37.94733
5/12 Pitch Common Unit Run = 28.80000
5/12 Pitch Common Unit Length = 31.20000
6/12 Pitch Common Unit Run = 24.00000
6/12 Pitch Common Unit Length = 26.83282
7/12 Pitch Common Unit Run = 20.57143
7/12 Pitch Common Unit Length = 23.81562
8/12 Pitch Common Unit Run = 18.00000
8/12 Pitch Common Unit Length = 21.63331
9/12 Pitch Common Unit Run = 16.00000
9/12 Pitch Common Unit Length = 20.00000
10/12 Pitch Common Unit Run = 14.40000
10/12 Pitch Common Unit Length = 18.74460
11/12 Pitch Common Unit Run = 13.09091
11/12 Pitch Common Unit Length = 17.75871
12/12 Pitch Common Unit Run = 12.00000
12/12 Pitch Common Unit Length = 16.97056
13/12 Pitch Common Unit Run = 11.07692
13/12 Pitch Common Unit Length = 16.33090
14/12 Pitch Common Unit Run = 10.28571
14/12 Pitch Common Unit Length = 15.80493
15/12 Pitch Common Unit Run = 9.60000
15/12 Pitch Common Unit Length = 15.36750
16/12 Pitch Common Unit Run = 9.00000
16/12 Pitch Common Unit Length = 15.00000
17/12 Pitch Common Unit Run = 8.47059
17/12 Pitch Common Unit Length = 14.68846
18/12 Pitch Common Unit Run = 8.00000
18/12 Pitch Common Unit Length = 14.42221
19/12 Pitch Common Unit Run = 7.57895
19/12 Pitch Common Unit Length = 14.19297
20/12 Pitch Common Unit Run = 7.20000
20/12 Pitch Common Unit Length = 13.99428
21/12 Pitch Common Unit Run = 6.85714
21/12 Pitch Common Unit Length = 13.82101
22/12 Pitch Common Unit Run = 6.54545
22/12 Pitch Common Unit Length = 13.66905
23/12 Pitch Common Unit Run = 6.26087
23/12 Pitch Common Unit Length = 13.53508
24/12 Pitch Common Unit Run = 6.00000
24/12 Pitch Common Unit Length = 13.41641

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