Prism Plane = Unbacked shoulder of Hip Rafter & Valley Rafter

Prism Plane = Hip Rafter & Valley Rafter diamond post

Vertical Rotation Plane = arctan(tan Vertical Plane x cos Horizontal Plane)

Horizontal Rotation Plane = arctan(cos Vertical Plane ÷ tan Horizontal Plane )

Hinge Rotation Plane = arctan( tan Horizontal Plane ÷ cos Vertical Plane)

R1 = Vertical Plane of adjoining roof planes.

Hawkindale R1 = Arctan [Tan S x Sin D]

R1 = arctan(tan SS x cos D)

R1 = arctan(tan S x cos DD)

R1 Plumb Plane = S Plumb Plane rotated by the adjacent plan angle

R2 = Purlin Housing Angle.

Hawkindale R2 = Arctan [Sin S x Cos S x Cos D / Tan D]

R2 = 90° - arctan(sin(plan angle) x tan(purlin rotation angle - roof slope angle) + hip slope angle

Purlin Rotation Angle = 90°

R2 = 90° - (arctan(sin(DD) x tan(90° - SS) + R1)

R2 = 90° - (arctan(cos(D) x tan(90° - SS) + R1)

R2 =Intersection of R1 Plane and a Perpendicular Plane to P2 Plane

R3 = Line traced on top or bottom of unbacked hip rafter following the perpendicular plane of the purlin.

Hawkindale R3 = Arctan [Sin S x Cos S x Cos D / Sin R1]

R3 = arctan( tan( Jack Rafter Side Cut Angle ) * cos ( Hip Rafter Backing Angle ))

R3 = arctan( tan( P2 ) * cos (C5))

Intersection of Prism Plane & R2 Plumb Plane

R4 = Angle of intersection of prism plane and vertical plane.

R4 = arctan (tan P2 ÷ cos C5)

R4 = arctan (tan Jack Rafter Side Cut Angle ÷ cos Hip Rafter Backing Angle)

R4 = arctan ( cos Hip Rafter Slope Angle ÷ tan Plan Angle)

Intersection of Hip Rafter Vertical Plumb Plane & Horizontal Plan Angle Plane

P1 = Purlin Miter Angle on Edge Perpendicular to Roof Surface

P1 = arctan(sin Vertical Plane ÷ tan Horizontal Plane )

P1 = arctan (sin S ÷ tan D)

P1 = arctan (sin Common Rafter Slope Angle ÷ tan Plan Angle)

Intersection of Common Rafter Plumb Plane & Horizontal Plane

P2 = Jack Rafter Side Cut Bevel Angle

P2 = arctan(cos Vertical Plane ÷ tan Horizontal Plane )

P2 = arctan (cos S ÷ tan D)

P2 = arctan (cos Common Rafter Slope Angle ÷ tan Plan Angle)

Intersection of Horizontal Plan Angle Plane & Common Rafter Plumb Plane

P2 - 90 = Roof Sheathing Angle

Hinge Rotation Plane = arctan( tan Horizontal Plane ÷ cos Vertical Plane)

P2 - 90 = arctan( tan Horizontal Plane ÷ cos Vertical Plane)

P2 - 90 = arctan( tan Plan Angle ÷ cos Common Rafter Slope Angle)

Intersection of Horizontal Plan Angle Plane & Common Rafter Plumb Plane

Steps To Draw the Roof Framing Prism Plane

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