SBE Builders

Strong Built Establishments Builders

SBE Builders is a commercial and residential framing contractor located in Discovery Bay California. Our Systematic Construction Logic produces Strong Built Establishments. E-Defense stands for Earthquake-Defense.

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

RFI | structural | framing | online tools | company | site map
safety | building resource links | build it green | photo gallery | Octagon | crown molding angles | home
WindsorOne Protected Trim
Remodel & Insurance Work
Commercial Tenant Improvements (TI)
  
  

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


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...

Carpenters Of Steel

Canadian & American Geometric Roof Framing Development
using a Steel Framing Square

Geometric Roof Framing Development for Irregular Hip Roof Calculations
using a Steel Framing Square

Geometric Development of Tetrahedron
using a Steel Framing Square

Hip Rafter Backing Bevel Angles from 1830 to 2009

Applied Geometry and Euclidean GeometryA lesson in Applied Geometry and Euclidean Geometry

This Is Carpentry

Website Usage Legal Policy