Prow Peak: Miter and Saw Blade Bevel Angles



Over 12 Values of Angles

Common Pitch Angle = 36.86990 = 9"
90 - Common Pitch Angle = 53.13010 = 16"
Deck Angle = 65.00000 = 25 23/32"
90 - Deck Angle = 25.00000 = 5 19/32"
Prow Pitch Angle = 34.20516 = 8 5/32"
90 - Prow Pitch Angle = 55.79484 = 17 21/32"
Angle between "Ridge" and "Valley Trough" = 69.54216 = 32 5/32"
90 - Angle between "Ridge" and "Valley Trough" = 20.45784 = 4 15/32"
Backing Angle = 14.68892 = 3 5/32"



Prow Rafter Compound Angles

If the cuts at the peak and foot of the unbacked prow rafter are parallel:
Upper shoulder miter at peak and foot = 60.58422 = 21 9/32"
Blade Angle upper shoulder at peak and foot = 30.62973 = 7 3/32"
Blade Angle = 25.00000 along plumb line (34.20516 Miter angle on saw) or :
Blade Angle = 30.62973 along 60.58422 angle on upper shoulder (29.41578 Miter angle on saw)
The supplementary angles on the face created by cutting the compound angle:
90 - 16.02759 = 73.97241 and 90 + 16.02759 = 106.02759
Over 12 : 16.02759 = 3 7/16"

If the compound angle as seen in plan at the prow rafter foot is at right angles rather than parallel to the cut at the peak:
The cuts at the foot on the unbacked prow rafter are:
Upper shoulder miter at foot = 21.08915 = 4 5/8"
Blade Angle upper shoulder at foot = 13.74364 = 2 15/16"
Blade Angle = 65.00000 along plumb line (34.20516 Miter angle on saw) or :
Blade Angle = 13.74364 along 21.08915 angle on upper shoulder (68.91085 Miter angle on saw)
The supplementary angles on the face created by cutting the compound angle:
90 - 31.63495 = 58.36505 and 90 + 31.63495 = 121.63495
Over 12 : 31.63495 = 7 13/32"



Related Angles and Formulas

Differences in Length

Jack Rafters
Spacing O.C. along Prow Ridge tan 69.54216
Jack Purlins
Spacing O.C. along Common Rafter tan 20.45784

Spacing along Prow Rafter

Jack Rafters
Spacing O.C. along Prow Ridge cos 69.54216
Jack Purlins
Spacing O.C. along Common Rafter cos 20.45784

Sample Purlin Calculations
Purlins are spaced 3' - 9" (3.75' or 45") as viewed in plan

Calculating Difference in Length using the Deck Angle :
90 - Deck Angle = 25.00000
Difference in Length
= Spacing O.C. in Plan tan 25.00000
= 45" tan 25.00000
= 20.98384" = 1' - 8 31/32"
Check : 4 20.98384" = 83.93536" = 83 15/16" = Prow Ridge

Calculations using the Angle on the Plane of the Roof (Angle between "Ridge" and "Valley Trough") :
90 - Angle between "Ridge" and "Valley Trough" = 20.45784
Projection of Length in Plan to the Common Rafter
= 45" cos 36.86990 = 56.25"
Difference in Length
= Spacing O.C. on Common Rafter tan 20.45784
= 56.25" tan 20.45784
= 20.98385" = 1' - 8 31/32"
Spacing along Prow Rafter
= Spacing O.C. along Common Rafter cos 20.45784
= 56.25" cos 20.45784
= 60.03653" = 5' - 0 1/32"
Check : 4 60.03653" = 240.14612" = 240 5/32" = Prow Length


Compound Angles

Jack Rafters
65.00000 Blade Angle along Plumb Line (36.86990 Miter angle on saw) or :
14.68892 Blade Angle (Backing Angle) along 20.45784 angle on face set in the plane of the roof (69.54216 Miter angle on saw)
Either of these cuts produces supplementary angles:
90 - 34.20516 = 55.79484 and 90 + 34.20516 = 124.20516 on the Jack rafter face matching the side (plumb) face of the backed Prow Rafter.
Check : arccos (cos 53.13010 cos 20.45784) = 55.79484


Jack Purlins
19.76083 Blade Angle along angle 74.36920 on the face of the Purlin perpendicular to the plane of the roof (15.63080 Miter angle on saw) or :
14.68892 Blade Angle (Backing Angle) along 69.54216 angle on face set in the plane of the roof (20.45784 Miter angle on saw)
Either of these cuts produces supplementary angles:
90 - 5.40374 = 84.59626 and 90 + 5.40374 = 95.40374 on the Jack purlin face matching the side (plumb) face of the backed Prow Rafter.
Check : arccos (cos 74.36920 cos 69.54216) = 84.59626



Joe Bartok 1