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.

Development of Rake Crown Molding Miter Angles
Using geometry

24 Sided Polygon Crown Molding Angles

Crown Molding Tools
crownmoldingtools.com

Crown Molding Tools  

Upside down and backwards in a miter box or compound miter saw has been used for the last 200+ years by the majority of carpenters to cut crown molding miter and bevel angles. Right sideup and backwards for rake crown molding cuts were developed long before our time, but even today there's still confusion about the correct crown miter and bevel angles when cutting rake crown molding laying flat in the miter box or compound miter saw. By using plane geometry for developing rake crown molding profiles you can determine the correct miter and bevel angles for rake crown molding.

24 Sided Polygon Crown Molding Angles

24 Sided Polygon Crown Molding Angles

24 Sided Polygon Crown Molding Angles

Trigonometric Relationships between Tetrahedron Angles by Joe Bartok
Joe Bartok's Trigonometric Relationships between Tetrahedron Angles web page is the most significant treatise on roof framing angles in the last 100 years. If your a roof framer print out Joe's Trigonometric Relationships between Tetrahedron Angles web page and study the trigonometric relationships between each of the triangles. If your an interior trim carpenter, then just use the crown angle formulas below.

Trigonometric Crown Angle Formulas for Horizontal Plane Crown Molding Angles
Crown Miter Angle = arctan (sin( Spring Angle) ÷ tan ( Wall Corner Angle ÷ 2 ))
Crown Miter Angle = arctan (sin( 38°) ÷ tan( 45°)) = 31.62°
 
Crown Bevel Angle = arcsin (cos( Spring Angle ) * cos( Wall Corner Angle ÷ 2 ))
Crown Bevel Angle = arcsin (cos( 38°) * cos( 45°)) = 33.86°

or you can think of the wall angle as the miter bisect angle
Crown Miter Angle = arctan (sin( Spring Angle) ÷ tan ( Wall Miter Bisect Angle ))
Crown Miter Angle = arctan (sin( 38°) ÷ tan( 45°)) = 31.62°
 
Crown Bevel Angle = arcsin (cos( Spring Angle ) * cos( Wall Miter Bisect Angle))
Crown Bevel Angle = arcsin (cos( 38°) * cos( 45°)) = 33.86°

or you use the crown slope angle instead of the crown spring angle for horizontal plane crown molding angles
Crown Miter Angle = arctan (cos(Crown Slope Angle) * tan( Wall Miter Bisect Angle ))
Crown Miter Angle = arctan (cos( 52°) * tan( 45°)) = 31.62°
 
Crown Bevel Angle = arcsin (sin( Crown Slope Angle ) * sin( Wall Miter Bisect Angle))
Crown Bevel Angle = arcsin (sin( 52° ) * sin( 45°)) = 33.86°

Trigonometric Crown Angle Formulas for Vertical Plane Crown Molding Angles (cathedral/vaulted ceilings/rake gables)
Crown Miter Angle = arctan (cos( Spring Angle) ÷ tan((180° - (Roof Pitch Angle * 2)) ÷ 2 ))
Crown Miter Angle = arctan (cos( 38°) ÷ tan((180° - (33.69° * 2)) ÷ 2)) = 27.71°
Crown Miter Angle = arctan (cos( 38°) ÷ tan(56.31) = 27.71°
 
Crown Bevel Angle = arcsin (sin( Spring Angle ) * cos((180° - (Roof Pitch Angle * 2)) ÷ 2))
Crown Bevel Angle = arcsin (sin( 38°) * cos( 56.31°)) = 19.97°


 
Development of Tetrahedron Geometry
based on Joe Bartok's Tetrahedron Developmental Geometry
Development of Tetrahedron Geometry
Development of Tetrahedron for Crown Molding Geometry Using Spring Angle and Wall Angle
Development of Tetrahedron for Crown Molding Geometry Using Slope Angle and Corner Plane Angle
Development of Tetrahedron for Crown Rake Molding Geometry
Crown Moulding Miter Angle and Bevel Angle Settings Calculators

Crown Spring Angle = 52°
Crown Spring Angle = 45°
Crown Spring Angle = 38°
Wall Angle Settings
Rake Crown Spring Angle = 38°
Rake to Horizontal Crown Spring Angle = 38°
Polygon 2 Cord Exterior Rake Gable Crown Molding Miter Angle and Bevel Angle Settings
Polygon 2 Cord Interior Rake Gable Crown Molding Miter Angle and Bevel Angle Settings
Polygon Crown Molding Angles Development & Calculator

Octagon Roof Exterior Crown Molding Angles Development Calculators
Octagon Roof Interior Crown Molding Angles Development Calculators
Corner A Crown Molding Calculator
Corner B Crown Molding Calculator
Corner C Crown Molding Calculator
Corner D Crown Molding Calculator

Crown Spring Angles

Crown Spring Angle
Polygon Crown Molding Miter Angles and Bevel Angles

12 Sided Polygon Crown Molding


  
  
SBE Builders
SBE Builders


Holy Grail of Roof Framing Geometry & Trigonometry

Book I & Book II. These roof framing books were written to make complex roof framing simple..

The Art of the Line for Carpentry

The book includes step by step instructions on developing stereotomic drawings on Art du Trait de Charpente, Trestles, Tréteau à devers, Canted Trestles, Louis Mozerolles' Joiners Table, Sawhorses, and the Saint Andrews' Cross, twisted crosses. You'll also find theories on hip rafter shift-offset, standard roof framing kernel trait drawings, German Schiften DP-Shadow Line techniques, folding net roof surface and net plane geometric development, when hip rafters collide, the Warlock Cut, and developing upper and lower claws on rafters using Axioms.

HG IV Circular Work in Carpentry

The book includes step-by-step instructions on developing stereotomic double curvature drawings for circular work in carpentry. Some of the techniques presented in this book are thousands of years in the making. As carpenters, we shouldn't have to re-invent the wheel each time we are faced with new challenges. There is a likely hood that someone, that came before us, has already refined a technique that we can use today. The tools might have changed, but the piece of wood that it is twisting and turning remains the same piece of wood.

Rafter Tools+ for iPhone

Rafter Tools+ is a rafter calculator for complex roof framing angles that other roof framing calculators don't offer.

RafterTools+

Stair Tangent for iPhone

This iPhone app is for rough frame carpenters that don't build stairs everyday, but could use an stair app calculator to check their stair building calculations.
Build a set of stairs that you are gonna be proud of.
With Stair Tangent you can elimenate cumulative math errors when building - constructing stairs.

Stair Tangent
stairtangent.com

Crown Molding Tools
crownmoldingtools.com

Crown Molding Tools  

Roof Framing Geometry Blog

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