Square Tail Fascia Hip Rafter Dimensioning Notes

Using the Framing Angle Calculators
 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:
Second Iteration Entries
 Rise/Run Degrees 5 Decimals 2 Decimals 3 Decimals 4 Decimals 6 Decimals 7 Decimals 8 Decimals 9 Decimals
 Main Rise = Main Run = Adjoining Rise = Adjoining Run = Total Deck Angle =
Second Iteration Returns
 DD = HSDD 90° – P2m = HSCm C5m = See example below * R1 = HSR1
Second Iteration Returns
 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.

Vector Product Calculation of
Angle between abutting ends of Fascia

Terminal Point of Vector following Hip Rafter Ridge Line
 Note and solve the following values from the First Iteration : xa = sin R3m ya = cos R3m za = 0
Terminal Point of Vector following Skewed Line at Hip Rafter Foot
 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.

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