Dachausmittlung -- Rake Wall Geometric Roof Design

This example of Dachausmittlung, Geometric Roof Design, was too see if I could could up with any theories on the geometric roof design construction lines for the sloping/raking eave lines. The roof ground plan is square, 10.00, with equal pitched roof slopes, 40°, and with the sloping/raking eave rising 1.5.

Ground Plan.

First develop the sloping/raking construction lines that define the direction of the averaging/hip rafter intersecting lines.

In Manfred Euchner's book he uses lines that are tangent to a circle using the rise of the sloping/raking eave line, but I think it's easier to use a framing square, with the 1.5cm on the one corner and swing the framing square until it intersects with the other corner.

Framing Square intersecting at corner of ground plan with the sloping/raking eave rise to establish the averaging/hip rafter intersecting lines.

Draw the averaging/hip rafter intersecting lines and draw the hip rafter run lines through the intersecting lines.

Draw the construction lines for the Sectional Area of the Intersection of the Roof Planes. This area represents a level plane of the intersection of the roof planes.

Drawings showing the Sectional Area of the Intersection of the Roof Planes.

Theories: I'm still not sure about all the geometrical theories for developing the geometric roof design with sloping/raking eave, but this last drawing showing the eave angles, roof slope angles, hip rafter slope angles suggest that this particular ground plan can be calculated using some trigonometry.  The only real theory I can could up with is using the 1.5 rise tangent to the corner opposite of the raking eave line develops a level plane of the intersecting roof planes. That represents the eave angles to use with trigonometry to calculate the rest of the roof.  I just need a way to find plan angles without knowing the true slope angle of the roof plane on the raking eaves(44.99930°).

1. Use the sloping eave rise to establish the eave angles. In this drawing the sloping  eave line has a rise of 1.5 and the length of the ground plan is 10.00. 
2. arcsin(1.5 ÷ 10.00) = 8.62692°
3. Eave angle = 90° + 8.62692° = 98.62692°  
4. Eave angle = 90° - (2 x 8.65692°) = 72.74614°

The eave lines are all suppose to be sloping at 40°, however the sloping/raking eave lines do not. With the raking eave lines not at a 40° roof slope angle it's hard to take the trigonometry any future.  So, once again this theoretical roof design can only be calculated using geometry at this time.  

Dachausmittlung -- Complex Geometric Roof Design

This example of Dachausmittlung, Geometric Roof Design, is rather complex geometrically and is extremely complex if we were using trigonometry. After I drew out the geometric roof design I checked the plan angles with my RafterTools apps and to my dismay my RafterTools apps were not able to calculate the plan angles for the eave angles when the eave lines are sloping.

3D View of the Roof Design

Wire Frame sketch of the Roof Design with raking/sloping eave lines.

Ground Plan of Roof Design.

Two different roof pitches with two eave lines raking/sloping.

In this drawing I've labeled the eave angles that my RafterTools apps could not calculate the plan angles for.

Drawing showing the geometric construction of the roof design with some of the construction lines removed for clarity. 

Steps for drawing the geometric roof design.

This is one of those roofs where the hip rafters can only be calculated from the geometric design of the roof. I'm not sure if there are any American CAD programs that could automatically draw out the roof design like the German CAD programs do. I'll have to look into writing a new Android/iPhone app that can be used to check the roof plan angles when the eave lines are sloping. 

Dachausmittlung -- Geomtric Roof Design

This example of the geometric roof design is from the book
Basiswissen Dachausmittlung by Peter Kubler & Albert Muller

Three different roof profile slope angles, 40° - 50° - 60°, and all of the eave angles are not at 90°.

Ground Plan 

Ground Plan  & Profile Slope Angles

to develop the dimensions for the different rafter runs, g1 - g2  -g3, based on the rise h.

Drawing with the parallel lines drawn using the dimensions g1 - g2  -g3. To develop the Sectional Area of the Intersection of the Roof Planes.

Hip Rafter Run Lines

 drawn from the intersection of the parallel lines.

Cripple Hip Rafter Run Lines

drawn in to locate the cripple hip rafters.

Cripple Hip Rafter Run Lines

drawn in to locate the cripple hip rafters.

Roof Design Complete.

Profile Rafter Slopes

drawn in to locate the height of the ridges & cripple hip rafters.

3D Views of the Roof Design.

Super Zimmerer 2012 Task Model

Aufgabe 1 Dachausmittlung from the Super Zimerer website

Task Model 1 Roof Design

Here's a link to the Super Zimmerer's website with other task models.

Super Carpenters Task Models

This task model is all about roof design. Your given a ground plan and you have to draw the unequal pitched hip roof out geometrically.

 The roof profile slope angles are 50° and 40° with eave angles on 2 of the corners of the ground plan that are not at 90°. In this next drawing I drew out the roof design without the ± 1.00 , that represents raised or lowered plate lines to make sure I understood the basic roof design of the ground plan. The g1 & g2 dimensions are developed from the profile of the roof slopes using the same rise dimension h. The rise dimension h can be any dimension, but it's best to made it about 1/3 of the total rise of the roof for clarity. When your drawing parallel lines from the eave line using the g1 & g2 dimensions you want to keep them away from the ridge lines for clarity. The intersections of the  g1 & g2 dimensions locate the hip rafter run lines.

It's best to separate the different areas of the roof  to draw out the cripple hip rafters  that are developed by extending the lines of the eave lines. 

Here's the completed drawing for the roof design without using the ± 1.00 , that represents raised or lowered plate lines.

Here's the completed drawing for the roof design using the ± 1.00 , that represents raised or lowered plate lines.

3D model of the roof design showing the raised and lowered plate lines.

Here's the roof design for the Aufgabe 1 Dachausmittlung from the Super Zimerer website for 2009.

Super Zimmerer 2008 Task Model

This is a task model from the German Federal Education Center for Zimmermann's from the  2008 Super Zimmerer competition. This task model has unequal pitched roof slopes and eave angles that are not at 90°.

Here's a link to the Super Zimmerer's website with other task models.

Super Zimmerer Task Models

A list of dimensions that the carpenter has to calculate/draw out geometrically in 45 minutes using a CAD program. No calculators are allowed. However, I did check my drawing using my RafterTools Apps for Android & iPhone.

Höhe Traufe HT = ................
Höhe First HD HFHD = ................
Höhe First AB HFA = ................
UK Firstpfette HD UKFPHD = ................
Max. Rücksprung HD ger. G1 = ................
Max. Rücksprung AB/W ger. G2 = ................
Drempelhöhe AB/W HDA = ................
Länge Firstpfette HD LFP = ................
Schifterbackenschmiege HD BS = ................
Grundverlegung Breite HD XH = ................

After drawing the ground plan (Grundriss) you have to draw the profile of the roof slopes,(40°,50°) to draw out the bisecting lines that determine the plan angles for each corner of the roof design.  Here, I used a 200.00mm rise to draw out the bisecting lines for the location of the hip rafter in plan view.

Next, I drew in the Hip Rafter Shift/Offset for the location of the edges of the hip rafters for roof plane alignment. They call it the Basic Shift.

Höhe Traufe HT = 59.86mm

Höhe First HD HFHD = 461.75mm

Höhe First AB HFA = 452.2589mm

UK Firstpfette HD UKFPHD = 406.6610mm

Max. Rücksprung HD ger. G1 = 9.6339mm

Max. Rücksprung AB/W ger. G2 = 6.1530mm

Drempelhöhe AB/W HDA = 123.2060mm

Länge Firstpfette HD LFP = 502.8071mm

Schifterbackenschmiege HD BS = 244.2788mm

Grundverlegung Breite HD XH = 11.4472mm