The solution of the cutting angles for this type of Square Cut Fascia is related to a calculation of a Valley sleeper.
The fascia is on a 10/12 Dormer which meets a 7/12 Main Roof.
The intercept of the ridges as seen in plan is 90°.
The Square Cut Fascia Pitch is the reciprocal of the Dormer Pitch. Solution using the Online Roof Framing Angle Calculator MAIN PITCH Rise : Enter 7 (Main Roof Rise) Run : Enter 12 (Main Roof Run) ADJ. PITCH Rise : Enter 12 (Fascia Rise) Run : Enter 10 (Fascia Run) Total Deck Angle : Enter 90 (Angle between intercept of Ridges viewed in Plan) Select the desired number of decimal places: Click on to calculate Main Roof Angles C5m = Main Roof Backing Angle = 12.72599° Click on to calculate Fascia Angles P2a = Fascia Saw Miter Angle = 52.78951° 90° - P2a = Angle on the Fascia = 37.21049° C5a = Fascia Backing Angle = 43.70247° Fascia Saw Blade Bevel Angle = 90° - (C5m + C5a) = 90° - ( 12.72599° + 43.70247° ) = 90° - 56.42846° = 33.57154° |
Solution by Pythagorean Theorem and Trigonometry The term Valley and the associated Valley Pitch Angle reference the line created as the Square Cut Fascia intercepts the 7/12 Main Roof Slope as per the diagram Square Cut Fascia Model Dimensions. Plan Angles are the angles created in plan by the Main Roof Run and Fascia Run. Since any reference length or scale is acceptable; we will use: Main Roof Rise = Fascia Rise = Valley Rise = 7 Main Roof Run = 12 Fascia Run = 7 × 10 ÷ 12 = 70 ÷ 12 Main Roof Run ÷ Fascia Run = 12 ÷ ( 70 ÷ 12 ) = 144 ÷ 70 Fascia Run ÷ Main Roof Run = ( 70 ÷ 12 ) ÷ 12 = 70 ÷ 144 Valley Run ² = Fascia Run ² + Main Roof Run ² = ( 70 ÷ 12 ) ² + 12 ² = 178.02778 Taking the square root of 178.02778 Valley Run = 13.34271 Valley Length ² = Fascia Run ² + Main Roof Run ² + Valley Rise ² = ( 70 ÷ 12 ) ² + 12 ² + 7 ² = 227.02778 Taking the square root of 227.02778 Valley Length = 15.06744 Backing Angle = arctan (sin Valley Pitch Angle ÷ tan Plan Angle) sin Valley Pitch Angle = Valley Rise ÷ Valley Length = 7 ÷ 15.06744 tan Main Roof Plan Angle = Main Roof Run ÷ Fascia Run = 144 ÷ 70 tan Fascia Plan Angle = Fascia Run ÷ Main Roof Run = 70 ÷ 144 Substituting in the Backing Angle formula: Main Roof Backing Angle = arctan ( [7 ÷ 15.06744] ÷ [144 ÷ 70] ) = arctan ( [7 × 70] ÷ [15.06744 × 144] ) = 12.72599° Fascia Backing Angle = arctan ( [7 ÷ 15.06744] ÷ [70 ÷ 144] ) = arctan ( [7 × 144] ÷ [15.06744 × 70] ) = 43.70247° Fascia Saw Blade Bevel Angle = 90° - (Sum of Backing Angles) = 90° - ( 12.72599° + 43.70247° ) = 33.57154° To resolve the Fascia Saw Miter Angle we require the Fascia Length: Fascia Length ² = Fascia Run ² + Fascia Rise ² = ( 70 ÷ 12 ) ² + 7 ² = 83.02778 Taking the square root of 83.02778 Fascia Length = 9.11196 Angle on the Fascia = arctan (Fascia Length ÷ Main Roof Run) = arctan ( 9.11196 ÷ 12 ) = 37.21049° Fascia Saw Miter Angle = arctan (Main Roof Run ÷ Fascia Length) = arctan ( 12 ÷ 9.11196 ) = 52.78951° or Fascia Saw Miter Angle = 90° - Angle on the Fascia = 90° - 37.21049° = 52.78951° Trigonometric Solution of Fascia Bevel Angle |
Solution by Development Provided the lengths remain proportional the development may be constructed to any convenient scale. Valley means the line created as the Square Cut Fascia intercepts the 7/12 Main Roof Slope. Backing Angles and Saw Blade Bevel SLIDESHOW: Development of Backing Angle (1) Construct the lines of the Valley ridges viewed in plan. (2) Construct the Main Roof run (= 12) and Fascia run (= 70 ÷ 12) at right angles to the ridge lines. The intercept of the Main Roof run and Fascia run determines the length of the Valley run. (3) Mark the Valley rise (= 7) at right angles to the Valley run. (4) Construct the Valley length (= hypotenuse). (5) Produce a line through the Valley rise, intercepting the ridge lines. The line segments between the Valley run and the ridge lines form the runs of the Backing angles. (6) Draw a perpendicular from the hypotenuse of the Valley triangle to the intercept of the Valley rise and run. The length of this line segment is the rise of the Backing angles. (7) Transfer the Backing angle rise length to the line of the Valley run produced. (8) Construct the Backing angles. The angle between either Backing angle hypotenuse produced and the hypotenuse of the remaining Backing angle is the Dihedral Angle on the Square Cut Fascia where it intercepts the Main Roof. The complement of this angle is the Saw Blade Bevel for the fascia. Angle on Fascia and Saw Miter Angle (1) Construct the Fascia pitch triangle. (2) Construct a perpendicular to the Fascia length. (3) Mark the length of the Main Roof run (= Fascia ridge length). (4) Construct the triangle of the Saw Miter Angle and Angle on the Fascia. |