Prow Peak Framing Angles
Prow Peak Stud Angle and Backing Angle
Sheathing Layout and Jack Rafter Side Cut
Prow Peak
Photo courtesy of John Devries Log Homes

Prow Peak Plan View Prow Peak: Wireframe Sketch and Dimensions
Solution of Prow Peak

Initial Values:
Main Slope = 10/12
Common Run = 186.625
Ridge Length = 48
Proportion and the Pythagorean Theorem return:
Common Rise = Prow Peak Rise = 186.625 10/12 = 155.52083
Common Length = Ö ( 186.625 ² + 155.52083 ² ) = 242.93131
Prow Peak Run = Ö ( 48 ² + 186.625 ² ) = 192.69896
Prow Peak Length = Ö ( 192.69896 ² + 155.52083 ² ) = 247.62799

The angles may be solved using trigonometric formulas or the dimensions substituted in the equations in the diagrams above.

Common Rafter Pitch Angle = arctan (10/12) = 39.80557

Plan Angle = arctan (186.625/48) = 75.57614

Prow Pitch Angle = Valley Rafter Pitch Angle
= arctan (10 sin 75.57614/12)
= arctan (155.52083/192.69896) = 38.90583

Backing Angle = arctan (sin 38.90583/ tan 75.57614)
= arctan ((155.52083 48)/(247.62799 186.625)) = 9.17588

Jack Rafter Side Cut Angle = arctan (cos 39.80557/tan 75.57614)
= arctan (48/242.93131) = 11.17692

Sheathing Angle = arctan (tan 75.57614/cos 39.80557)
= arctan (242.93131/48) = 90° – 11.17692 = 78.82308

If framing a wall the difference in stud length would change:
Spacing O.C. tan 38.90583
= Spacing O.C. 155.52083/192.69896
= Spacing O.C. .80707

For the roof the miter and bevel angles are needed to cut the purlins in order that the fascia would follow a plumb plane:
Angle on the Stick = Sheathing Angle = 78.82308
Saw Blade Bevel = Backing Angle = 9.17588
Difference in Length between Purlins on 48 centers
= 48 tan 11.17692 = 9.48416

Joe Bartok
1