## Saturday, February 23, 2013

### WorldSkills 2011 Carpentry Competition Model Geometry

The WorldSkills 2011 Carpentry Competition Model - Project was based on a pentagon ground plan with a sloping ridge. The Model - Project also has valley rafters rotated into the roof surface plane supporting a dormer.
 Ground Plan of Model

 Ground Plan showing post and roof beam location.

 Roof Plan

The sidewall length of the pentagon was given as 1000 mm. There are a number of different ways to layout the pentagon. However, I suggest you familiarize yourself with the use of using the tan of the angle and multiplying the tan of the angle by 10 and taking 10" on the other end of the framing square.

To find the circumscribed radius, that is also the hip rafter run dimension, you can use
sidewall  ÷ (sin(180° ÷ number sides) x 2) = sidewall multiplier.

sin(180° ÷ 5) x 2 = 1.175571
1000mm  ÷ 1.175571 = 850.6504 mm circumscribed radius
or
39.3701" = 1000mm
39.3701 ÷ 1.175571 = 33.49019" circumscribed radius

The roof framing geometry should start off by drawing the common rafter slope angle of the pentagon. You could use an calculator to find the rise, line BC, or draw out the line AC at an 35° angle using a metric framing square or possibly a large protractor. The ridge of the model is slopping, so we need to find the height at H. Line BE is parallel to eave line / gutter line, the height at F is the same as the height at C. By drawing a line from D thru F it will locate the point H. Which is the total height of the slopping ridge. Triangle CFH gives an slope angle of 12.20919°.

Next, we need to lay out the  real roof surfaces. The line A1 - A1' is equal in length to the line AC. True Common Rafter Length. The line HR-A1' is equal in length to the True Length of  the Hip Rafter. From A1' draw a perpendicular  towards F' the length of the line BE. You should swing an arc from center point D with the radius equal to DF, so that the line A1'-F' intersect with the arch. Draw a line from D thru F' towards H'. Then swing an arc from center point D using the radius equal to DH.

In this next drawing there are two examples of drawing the hip rafter backing angles. For all hip rafter backing  triangles the line at D is perpendicular to the hip rafter run line and the line at E is always drawn perpendicular to the hip rafter length line. Point G is located from the radius ED, with center point D.

Next develop the devers de pas for the Valley Rafters Crossing each other. These valley rafters are rotated into the roof surface plane. First develop the hip rafter right triangle BGH in the drawing below.  Next draw the line LD perpendicular to line AB that intersects line BG at D. Then draw the line DF perpendicular to line BG. Line DK is equal in length to DF and is perpendicular to line LD. Draw the line LK. Next draw a line that is perpendicular to line LK.Continue line LD to intersect the line KM . The line KM is the TC line. From E, draw a line to M. The line EM is the DP line, that will establish the rafter's miter and bevel angle.

In this next drawing the point P is the intersection of line BG and EM. From point P draw a line to F. Transfer the lines between point F,P,E and D to the side of the drawing to establish the miter angle of the rafter that's rotated into the roof surface plane. We need to establish the point Q and V for the miter angle.

Draw the line DF' perpendicular to line ED, then draw the line EF'. Next strike an arc from center point D the length of DF . Strike an arc from center point E the length of EF'. Where the two arcs intersect , point Q, draw the line QP and EQ. Draw another perpendicular line to EQ that intersects at point P. This will form the line VP. The angle VPQ is the miter angle of the valley rafter rotated into the roof surface plane.

Rafter Tools Devers De Pas Calculations

Main Plan Angle = 54.00000
Main Pitch Angle = 35.00000
Skewed Plan Angle = 54.00000

Main hip Rafter Angle = 29.53068
Main Hip Rafter Backing Angle = 19.70271
Main Jack rafter Side Cut Angle = 30.75894

Skewed Hip Angle = 29.53068
Skewed Jack Rafter Side Cut Angle = 30.75894
Skewed Roof Sheathing Angle = 59.24106

k2 = 61.51788
k9 = 70.29729

k1 Valley Rafter Peak Miter Angle = 22.16679
k2 Valley Rafter Peak Bevel Angle = 61.51788
k3 Valley Rafter Peak Saw Blade Bevel Angle = 26.67730
k4 Valley Rafter Horizontal Plane Rotation Angle = 10.00996
k8 Valley Rafter Vertical Plane Tilt Angle = 19.16497
R1 Valley Rafter Slope Angle = 29.53068
k5 Valley Rafter Rotated Slope Angle = 31.03562
k6 Valley Rafter Vertical Plane Tilt = 19.16497
k7 Hip Rafter Housing Angle = 10.36571

Valley Rafter Foot Miter Angle = 39.17428
Valley Rafter Bevel Angle = 59.24106
Valley Rafter Saw Blade Bevel Angle = 24.76747

Valley Rafter Ridge Miter Angle = 39.17428
Valley Rafter Ridge bevel Angle = 59.24106
Valley Rafter Ridge Saw Blade Bevel Angle = 24.76747

Valley Rafter Foot Level Cut Miter Angle = 31.03562
Valley Rafter Foot Level Cut Bevel Angle = 59.24106
Valley Rafter Foot Level Cut Saw Blade Bevel Angle = 17.05818

Valley Rafter Cross Cut Miter Angle = 0.00000
Valley Rafter Cross Cut Bevel Angle = 61.51788
Valley Rafter Cross Cut Saw Blade Bevel Angle = 28.48212