Monday, October 7, 2013

Basiswissen Dachausmittlung #3 Averaging

Basiswissen Dachausmittlung

Dachfläche --roof surface

Ausmittlung -- averaging -- design

Basiswissen Dachfläche Ausmittlung

Base Knowledge of Roof Surface Design/Geometry

Now I think it means
Base Knowledge of Roof Surface Averaging

In this drawing the eave angles are A & B = 77.66091° and C & D = 102.33909°. The ground plan has two roof slopes that are 35° & 55° and the ridge is sloping and not parallel to any of the eave lines. In this drawing I'm using the average rise of 2.1422cm in each profile view of the roof slope triangles that are perpendicular to the eave line to establish the averaging lines, that develop the averaging intersecting points that define the hip rafter run lines in plan view. When the roof pitch is equal on each side of the hip rafter the eave angle is bisected to form to equal plan angles.



Using trigonometry for the king common runs.

Plan Angles
A = 77.66091 ÷ 2 = 38.83046°

RafterTools 
77.66091° Eave Angle
Plan Angles
23.43872° & 54.22219° 


Plan Angles 
C = 102.33909° ÷ 2 = 51.16954°

RafterTools 
102.33909° Eave Angle
Plan Angles
74.19138° & 28.14771° 

Law of Sines for the king common rafter runs.
a = ( c × sin( A) ) ÷ sin( C)
a = 3.1457 = ( 7 × sin(23.43897) ) ÷ sin( 117.73058)
b = ( c × sin( B) ) ÷ sin( C)
b = 4.9586 = ( 7 × sin(38.83046) ) ÷ sin( 117.73058)
h = a × sin( B )
King Common Run = 1.9724 = 3.1457 × sin( 38.83046 )

Law of Sines
a = ( c × sin( A) ) ÷ sin( C)
a = 3.3433 = (3.5 × sin(51.16954) ) ÷ sin(54.63943)
b = ( c × sin( B) ) ÷ sin( C)
b = 4.1294 = (3.5 × sin(74.19102) ) ÷ sin(54.63943)
h = a × sin( B )
King Common Run = 3.2168 = 3.3433 × sin(74.19102 )

For the angle of the sloping ridge ???
Why too much trigonometry, it's easier to use geometry to calculate the angle of the sloping ridge.








1 comment:

  1. Most of the time I don’t make comments on websites, but I'd like to say that this article really forced me to do so. Really nice post!
    Certified Precision Roofing

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