Unequal Pitch Roof Trigonometry Calculating unequal pitched roofs is easy if you know what trigonometry functions to use. The formulas below use the law of sines to calculate the unknown length or angle. Known Variables: Major Pitch Angle & Minor Pitch Angle & Span & Plate Line Difference Calculate Major & Minor Runs & Theoretical Plate Line Span Theoretical Span = Span - (Plate Line Difference ÷ tan(Minor Pitch Angle)) Plate Line Difference Run = Span - Theoretical Span Major Run = ((Theoretical Span × sin(Minor Pitch Angle)) ÷ sin (180 - Major Pitch Angle - Minor Pitch Angle)) × cos( Major Pitch Angle ) Theoretical Minor Run = ((Theoretical Span * sin(Major Pitch Angle)) ÷ sin (180 - Major Pitch Angle - Minor Pitch Angle)) × cos( Minor Pitch Angle ) Minor Run = Theoretical Minor Run + Plate Line Difference Run Major Rafter = Major Run ÷ cos (Major Pitch Angle) Theoretical Minor Rafter = Theoretical Minor Run ÷ cos (Minor Pitch Angle) Plate Line Difference Minor Rafter = Plate Line Difference Run ÷ cos (Minor Pitch Angle) Minor Rafter = Minor Run ÷ cos (Minor Pitch Angle) Roof Rise = Major Run × tan (Major Pitch Angle) Total Minor Roof Rise = Minor Run × tan (Minor Pitch Angle) Law Of Sines C = 180° - (A + B) a = ( c × sin( A) ) ÷ sin( C) a = ( b × sin( A ) ) ÷ sin( B) a = ( b ÷ sin( B ) ) × sin( A) b = ( c × sin( B ) ) ÷ sin( C) b = ( a × sin( B ) ) ÷ sin( A) b = ( a ÷ sin( A ) ) × sin( B) h = b × sin( A ) h = a × sin( B ) c = ( a × sin( C ) ) ÷ sin( A) c = ( b × sin( C ) ) ÷ sin( B)
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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.
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+ is a rafter calculator for complex roof framing angles that other roof framing calculators don't offer.
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.
Crown Molding Tools
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