Sunday, March 9, 2014

Saw Blade Bevel Angle

Formulas for the Saw Blade Bevel Angle, depending on what angles you know or what the direction of saw travel is.

Saw Blade Bevel Angle From Miter Line Side = arctan(cos(Miter Angle) ÷ tan(Bevel Angle on Stick)
Saw Blade Bevel Angle From Miter Line Side = arctan(cos(33.69007°) ÷ tan(39.76216°) = 45.00°

Saw Blade Bevel Angle From Miter Line Side = arctan(sin(Miter Angle on Stick) ÷ tan(Bevel Angle on Stick)
Saw Blade Bevel Angle From Miter Line Side = arctan(sin(56.30993°) ÷ tan(39.76216°) = 45.00°

Saw Blade Bevel Angle From Bevel Line Side =arctan(sin(Bevel Angle on Stick) ÷ tan(Miter Angle on Stick)
Saw Blade Bevel Angle From Miter Line Side = arctan(sin(39.76216°) ÷ tan(56.30993°) = 23.09347°

Saw Blade Bevel Angle From Bevel Line Side =arctan(cos(Bevel Angle) ÷ tan(Miter Angle on Stick)
Saw Blade Bevel Angle From Miter Line Side = arctan(cos(50.23784°) ÷ tan(56.30993°) = 23.09347°

Online Saw Blade Bevel Angle Calculator





Intersection of vertical plumb plane following the eave line and the vertical plumb plane of the hip rafter . The saw blade bevel angle is the intersection of these two planes for jack rafters head cuts and hip rafter head cuts.


Roof Eave Angle = 90.00000
SS = Main Rafter Slope Angle = 36.86990
S = Adjacent Rafter Slope Angle = 45.00000

DD = Main Plan Angle = 53.13010
D = Adjacent Plan Angle = 36.86990

Saw Blade Bevel Angle = arctan(sin(45.00°) ÷ tan(43.31386°) = 36.8699° = Plan Angle for Plumb Hip Rafters




Rake Crown Molding Saw Blade Bevel Angle Problem




I still need to calculate the saw blade bevel angles. I can calculate the dihedral angle, but not the saw blade bevel angles.

Face angle a = 52.07865
Face angle b = 86.60217
Face angle c = 90
Dihedral angle = arccos((cos(c) - cos(a) * cos(b))/ (sin(a)*sin(b)) = C = 92.65123°
Dihedral angle = arccos((cos(a) - cos(b) * cos(c))/ (sin(c)*sin(b))=A = 52°
Dihedral angle = arccos((cos(b) - cos(a) * cos(c))/ (sin(a)*sin(c))=B =85.69117°

Dihedral angle = arccos((cos(90) - cos(52.07865) * cos(86.60217))/ (sin(52.07865)*sin(86.60217))= 92.65123°

Eave side
Miter Angle on Stick  = 52.07865°
Saw Blade Bevel Angle = 37.01689

Rake side
Miter Angle on Stick =86.60217°
Saw Blade Bevel Angle = 50.33188



Now, it looks like the Saw Blade Bevel angles are
Eave side
Miter Angle on Stick  = 52.07865°
Saw Blade Bevel Angle =38.18968°

Rake side
Miter Angle on Stick =86.60217°
Saw Blade Bevel Angle = 49.15886°


Roof Eave Angle = 54.53879
SS = Main Rafter Slope Angle = 46.62978
S = Adjacent Rafter Slope Angle = 55.15376

DD = Main Plan Angle = 31.73219
D = Adjacent Plan Angle = 22.80660

R1 = Hip Rafter Slope Angle = 29.10711.... This the only variable we know.
C5m Main Hip Rafter Backing Angle = 38.18968
C5a Adjacent Hip Rafter Backing Angle = 49.15886
Valley Sleeper Saw Blade Bevel Angle = 90° - (C5m + C5a) = 2.65146
Dihedral = 92.65146

P2m = Main Jack Rafter Side Cut Angle = 47.99665
90° - P2m = Main Roof Sheathing Angle = 42.00335
P2a = Adjacent Jack Rafter Side Cut Angle = 53.64927
90° - P2a = Adjacent Roof Sheathing Angle = 36.35073




Joseph Fusco at Fine HomeBuilding on exterior Crown Miter Angles

The American House-carpenter

The American house-carpenter
a treatise upon architecture, cornices and mouldings, framing, doors, windows, and stairs. Together with the most important principles of practical geometry.
5th ed., with additions. Illustrated by more than three hundred engravings.
By R. G. Hatfield.

Published  


4 comments:

  1. Sim, A suggestion - this article would be improved if you added some illustrated definitions of the terms used (miter line, miter line side, etc) to show how they apply to a real "stick".
    I have always thought (one) really useful question is "given the results one of from Sim's calculator for e.g. major common rafter pitch and and major pitch jack rafter side cut angle, how do I set up my portable circular saw to cut this e.g. jack rafter cheek (?) compound cut?"
    Rob

    ReplyDelete
    Replies
    1. Added a couple of drawings. hope they help.

      Delete
  2. Plan angle is saw bevel angle when cutting plumb ,as long as hip or valley is plumb as well

    ReplyDelete
    Replies
    1. Added a drawing to visualize your statement. I guess we should call it the Plumb & Plumb Saw Blade Bevel Angle.

      Delete