Square Tail Fascia Hip Rafter Dimensioning Notes
Angles at bevelled Hip Rafter Foot created by cutting Compound Angles
Formulas for angles on faces at Hip Rafter Foot created by cutting Compound Angles
Formulas for Skewed Line at Hip Rafter Foot created by cutting Compound Angles
Wedges (Terahedra) modelling angles about Skewed Line at Hip Rafter Foot
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
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 (ab |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.
Vector Formula for Angle between abutting ends of Fascia
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.
Co-Ordinates and Angles on the Fascia
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Joe Bartok
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