SBE Builders

Strong Built Establishments Builders

SBE Builders is a commercial and residential framing contractor located in Discovery Bay California. Dedicated to the art of Carpentery & Roof Framing. We are the professionals for the future of the craft of carpentry.

Hopper Miter Angle and Saw Blade Bevel Angle Settings Development

Hopper with 52° slope angle


Hopper Miter and Saw Bevel Angles Calculator

Hopper angles are the same angles that are use for cutting roof sheathing. The hopper miter angle is the same as the jack rafter side cut angle and the hopper saw blade bevel angle is the same as the hip rafter backing angle. The crown spring angle is measured on a vertical plane. The hopper slope angle is measured on a horizontal plane.

Hopper Slope Angle


Roof Pitch Angle = Hopper Slope Angle

Use any of these formulas to find the Hopper Miter Angle
Hopper Miter Angle = arccos( sin ( Plan Angle ) ÷ cos ( Hip Rafter Backing Angle ))
Hopper Miter Angle = arccos( sin ( Hip Rafter Angle ) ÷ sin ( Roof Pitch Angle ))
Hopper Miter Angle = arcsin ( cos ( Plan Angle ) × cos ( Hip Rafter Angle ))
Hopper Miter Angle = arcsin ( tan ( Hip Rafter Backing Angle ) ÷ tan ( Roof Pitch Angle ))
Hopper Miter Angle = arctan( cos ( Roof Pitch Angle ) ÷ tan ( Plan Angle ))
Hopper Miter Angle = arctan( sin ( Hip Rafter Backing Angle ) ÷ tan ( Hip Rafter Angle ))

Use any of these formulas to find the Hopper Saw Blade Bevel Angle
Hopper Saw Blade Bevel Angle = arccos( sin ( Plan Angle ) ÷ cos ( Jack Rafter Side Cut Angle ))
Hopper Saw Blade Bevel Angle = arccos( cos ( Roof Pitch Angle ) ÷ cos ( Hip Rafter Angle ))
Hopper Saw Blade Bevel Angle = arcsin ( sin ( Roof Pitch Angle ) × cos ( Plan Angle ))
Hopper Saw Blade Bevel Angle = arcsin ( tan ( Jack Rafter Side Cut Angle ) × tan ( Hip Rafter Angle ))
Hopper Saw Blade Bevel Angle = arctan( tan ( Roof Pitch Angle ) × sin ( Jack Rafter Side Cut Angle ))
Hopper Saw Blade Bevel Angle = arctan( sin ( Hip Rafter Angle ) ÷ tan ( Plan Angle ))


Hopper Miter Angle = arctan (cos(Roof Pitch Angle) ÷ tan (Plan Angle))
Hopper Saw Blade Bevel Angle = arctan( sin ( Hip Rafter Angle ) ÷ tan ( Plan Angle ))
example:
Roof Pitch Angle = 38°
Wall Angle = 90°
Plan Angle = 45°
Hip Rafter Angle = arctan( tan ( 38° ) × sin ( 45 )) = 28.91856°

Hopper Miter Angle = arctan (cos( 38° ) ÷ tan( 45° )) = 38.23849°
Hopper Saw Blade Bevel Angle = arctan( sin( 28.91856° ) ÷ tan( 45° )) = 25.80683°

or
Hopper Miter Angle = arctan (cos(Roof Pitch Angle) ÷ tan (Plan Angle))
Hopper Saw Blade Bevel Angle = arccos( sin ( Plan Angle ) ÷ cos ( Hopper Miter Angle ))
Hopper Miter Angle = arctan (cos( 38° ) ÷ tan( 45° )) = 38.23849°
Hopper Saw Blade Bevel Angle = arccos( sin( 45° ) ÷ cos( 38.23849° )) = 25.80683°


Polygon table with hopper base and IPE decking table top. All of the lumber used for this table were left overs from different jobs.

Polygon Hopper Table


Martindale's Bin and Hopper Angles Case Study 3
Bevel angles for three dimensional connections: Tapered bin, hopper & tower corner angles : hip and valley roof framing connections : analytic proof of ... of hip & valley bevel connection angles


Martindale's Bin and Hopper Angles Case Study PDF file

Side A

Side D

 


 

SIDE D
PITCH S = 8:12
S = 33.69007°
D1 = arctan(tan(S) ÷ tan(S)) = 45°
R1 = arctan(tan(S) * sin(D1)) = 25.23940°
P2 = arctan(cos(S) ÷ tan(D1)) = 39.76216°
C5 = arctan(sin(R1) ÷ tan(D1)) = 23.09347°

S = 33.69007°
D2 = arctan(tan(SS) ÷ tan(S)) = 64.98310°
R1 = arctan(tan(S) * sin(D2)) = 31.13710°
P2 = arctan(cos(S) ÷ tan(D2)) = 21.22071°
C5 = arctan(sin(R1) ÷ tan(D2)) = 13.56656°

 

SIDE A
Run = 3.5
Rise = tan(33.69007) * 7.5 = 5
SS = arctan( 5 / 3.5) = 55.00798°
D2 = arctan(tan(SS) ÷ tan(S)) = 64.9831°
D22 = arctan(tan(S) ÷ tan(SS)) = 25.0169°
R1 = arctan(tan(SS) * sin(D22)) = 31.13711°
P2 = arctan(cos(SS) ÷ tan(D22)) = 50.86232°
C5 = arctan(sin(R1) ÷ tan(D22)) = 47.93405°

 
SIDE C
PITCH S = 8:12
S = 33.69007°
DD1 = arctan(tan(S) ÷ tan(S)) = 45°
R1 = arctan(tan(S) * sin(DD1)) = 25.23940°
P2 = arctan(cos(S) ÷ tan(DD1)) = 39.76216°
C5 = arctan(sin(R1) ÷ tan(DD1)) = 23.09347°
 

SIDE B
SS = 55.00798°
D22 = arctan(tan(S) ÷ tan(SS)) = 25.0169°
R1 = arctan(tan(SS) * sin(D22)) = 31.13711°
P2 = arctan(cos(SS) ÷ tan(D22)) = 50.86232°
C5 = arctan(sin(R1) ÷ tan(D22)) = 47.93405°

SS = 55.00798°
D1 = arctan(tan(sS) ÷ tan(SS)) = 45.00°
R1 = arctan(tan(SS) * sin(D1)) = 45.28938°
P2 = arctan(cos(SS) ÷ tan(D1)) =29.83265°
C5 = arctan(sin(R1) ÷ tan(D1)) = 35.40023°

 




Hopper Miter and Saw Bevel Angles Calculator

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SBE Builders
SBE Builders
5305 Laguna Ct.
Discovery Bay, California 94505
(925) 634-6022 • Fax: (925) 634-6022
Commercial & Residential Framing Contractor
American Carpenter and Builder
California Licensed General Building Contractor
CA LIC.#  546126


Roof Framing Geometry

  • Roof framing geometry is empirical-type knowledge.
  • Information gained by means of observation, experience, or experiment.
  • From ground Line 0: Z1, Z2, Z3 etc...
  • To Roof Axis 0: A1, A2, A3 etc...
  • To the bring back line 0 for scribing: B1, B2, B3 etc...

Roof Framing Geometry Blog

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American College of the Building Arts, carpentry and timber framing programs.

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