Enter pitches and Total Deck Angle in the Framing Angle Calculator
fields as usual. Open a Framing Angle Calculator in another window and make the following entries: |
DD =
HSDD
90° – P2m = HSCm C5m = See example below * R1 = HSR1 |
D =
HSD
90° – P2a = HSCa C5a = See example below * R1 = HSR1 |
First Iteration : The Dihedral Angle measured between
the fascia equals 180° – (SFBm + SFBa) Second Iteration : The Dihedral Angle measured between the planes about the skewed line at the foot of the Hip Rafter equals 180° – (C5m + C5a) * The values of both calculated Dihedral Angles are equal. |
Note and solve the following values from the First Iteration :
xa = sin R3m ya = cos R3m za = 0 |
Note and solve the following values from the Second Iteration :
xb = cos HSDD yb = sin HSDD zb = – tan HSR1 |
Substituting in the formula to solve the angle between two vectors
θ = arccos ± (a·b ÷ |a| |b| ) returns the First Iteration value for the angle between the abutting ends of the fascia. Trig functions of angles from the Adjoining side of the roof yield the same value. |
The results of the formulas above may be checked using trig functions
of First Iteration of angles measured with respect to level. Trig functions of angles from the Adjoining side of the roof return the same value. The same results are produced substituting the Angles on the Fascia or Saw Miter Angles in the standard Compound Angle Formula. |