Apprentice Carpentry Roof Framing Geometry Part 2

In part 2 of  Apprentice Carpentry Roof Framing Geometry we'll discuss the hip rafter backing angle and the dihedral angle. The hip rafter backing angle aligns the top of the hip rafter with the roof surface and the plan angle.


This picture of an 8:12 & 10:12 irregular hip roof model shows how the hip rafter backing angle aligns the hip rafter with the square tail fascia.

This picture shows how the hip rafter backing angle aligns the hip with the roof surface.

This picture shows the valley rafter backing angle aligning with the plan angle.

This picture shows how the hip rafter backing angle aligns the hip rafter with the plan angle.

Valley rafters backed out to keep the top of the valley rafters aligned with the roof surface.

The hip rafter backing angle is developed from the dihedral angle triangle. The dihedral angle is the angle between two planes. In roof framing geometry the dihedral angle is the angle between the two roof surfaces on each side of the hip rafter.  


This drawing shows the dihedral angle drawn in plan view as well as a 3D view of the dihedral angle.

In this drawing , in plan view, the dihedral angle triangle is drawn from the eave line (AB) to the opposing eave line (AF). Note, the eave line is also referenced as the gutter line. To draw the dihedral angle triangle start with a line at point W. The point W can be located anywhere on the eave line. The line WX is always drawn perpendicular to the hip rafter run line AE. At point X draw a line to point Y that is perpendicular to the hip rafter length line AG. Then swing an arc from point X with the radius equal to the line length XY until it intersects the hip rafter run line AE. Angle XWZ is the hip rafter backing angle and angle XFZ is the hip rafter backing angle for the other side of the hip rafter. For an equal pitched roof these angles will be the same. For irregular pitched roofs the hip rafter backing angle will not be the same angle.

The dihedral angle is angle WZF. The angle between the roof planes.

Here are a couple more drawings showing the dihedral angle in 3D.

Here's a link to the Google SketchUp files showing the Basic Roof Framing Kernel with the hip rafter backing angle and the location of the dihedral angle.


Hip Rafter Backing Angle-1.skp

Hip Rafter Backing Angle-3.skp

Hip Rafter Backing Angle-4.skp

Hip Rafter Backing Angle-6.skp

Apprentice Carpentry Roof Framing Geometry Part 1

Tony McGartland,  who teaches carpentry at a college in N.Ireland and who is also responsible for training the better apprentices for carpentry competitions in the UK, sent me a couple of Google SketchUp models the other day. From past carpentry competitions in the UK. These Google SketchUp roof framing models made me realize how poor the American Union Apprentice program is compared to the apprentice programs in Europe. France?,Switzerland, Austria and Germany have specialized training for their apprentices for these apprentice competitions and are light years ahead of the United States of America apprentice program in roof framing construction and geometry. If we sent American apprentices to these carpentry compensation, not only would they not medal they would most likely embarrass themselves. By the time I completed my 4 years of the Union Carpentry apprenticeship program I had already cut and stacked (framed) about 100+ track home roofs, but I didn't know anything about roof framing geometry. Yes, I used a framing square to mark and layout the rafters, but if anyone had asked me to draw out the roof framing geometry of the roofs I was cutting, I would have said no I can't draw out the roof framing geometry to the roofs that I've cut.


This is part 1 in Apprentice Carpentry Roof Framing Geometry for the Americans and maybe the Canadians. 


Roof framing geometry is empirical-type knowledge.
Information gained by means of observation, experience, or experiment.

It will take more than just reading to understand roof framing geometry. You'll need to draw out the roof framing geometry. Preferably on 4x8 sheets of plywood or mdf  to gain the experience you will need to compete in the apprentice carpentry competition. You'll need a compass, straight edge and framing square. Yes, you can use your calculator in the apprentice carpentry competition, but you'll also have to draw out the roof framing geometry as well. Just like they did 100+ years ago.

I suggest getting a 6" and 16" compass like these compasses from Lee Valley.

http://www.leevalley.com/US/wood/page.aspx?p=32625&cat=1,42936,42937

While your at Lee Valley you might as well order a Chappell Framing Square

http://www.leevalley.com/US/wood/page.aspx?p=69569&cat=1,42936

First up, The Basic Roof Framing Kernel

This is a plan view of a roof framing kernel with the section view drawn above the plan view.The plan view is also referenced as the ground plan. The real roof surface angles and lengths are located by drawing an arc (radius=common rafter length) at the apex of the common rafter run (point D) in plan view. The common rafter is also called the principal rafter.


F-E = Common Rafter Plan View Run
A-E = Hip Rafter Plan View Run
P-R = Jack Rafter Run
E-H = Common Rafter Real Surface Rise 
F-H = Common Rafter Real Surface Length
A-G = Hip Rafter Real Surface Length
R-S = Jack Rafter Length


Angle FAB = Eave Angle
Angle EAB = Plan Angle
Angle EFH = Common Rafter Slope Angle
Angle GAE = Hip Rafter Slope Angle
Angle NCD = Roof Sheathing Angle
Angle DNC = Jack Rafter Side Cut Angle

The next 2 drawings are  the basic roof framing kernel drawn in Google SketchUp. The basic roof framing kernel is drawn unfolded and folded up into 3D roof surfaces of the roof framing kernel. This is also a good example of swing an arc to establish the points of the real roof surfaces.

Here's a link to the Google SketchUp file Basic Roof Framing Kernel.

Basic Roof Framing Kernel.skp

In part two of Apprentice Carpentry Roof Framing Geometry we'll add the hip rafter backing angle to the basic roof framing kernel.