Roof Planes with Unequal Pitched Roofs

To check all of the Rafter Tools App results I draw geometric roof framing layouts in Google Sketchup. To make sure it's constructable and the java mathematical results are correct. Here's a situation where you have an 8:12 main roof slope angle and an adjacent 12:12 roof slope angle. To calculate the main roof common rafter lengths you just deduct 1/2 the thickness of the ridge for the main common rafter length. However, you can't deduct 1/2 the thickness of the ridge for the adjacent 12:12 king common rafter length. You will have to chamfer the end of the ridge on a unequal pitched roof to keep the ridge in the roof plane alignment.  The Rafter Tools App Irregular Hip rafter function calculates the correct king common rafter length for unequal pitched hip rafter roofs.

The correct way to calculate the minor pitch king common rafter, keeping all of the roof framing members in the roof planes,  is to use the major and minor plan angles.

 minor ridge deduction run  = (ridge width * 0.5) ÷ tan(major plan angle)

Calculate Irregular Hip Rafter Angles

Here's a couple of screen shots of the Rafter Tools for Anfroid App showing the Calculate Irregular Hip Rafters function. Hopefully, it's Erik proof.

Input variables

1. Roof Eave Angle
2. Major Pitch Angle
3. Minor Pitch Angle
4. Input Length
5. Overhang Run
6. Jack Rafter Spacing
7. Hip Rafter Width
8. Hip Rafter Depth
9. Jack Rafter Width -- Common Rafter Width
10. Major Rafter Depth
11. Seat Cut Level Cut Length
12. Ridge Width

For Input Length use any part of the hip rafter geometry as input to find the rest of the angles.

• Common Rafter Run
• Common Rafter Span
• Common Rafter Rise
• Common Rafter Length
• Hip Rafter Run
• Hip Rafter Length
• Eave Wall Length -- Minor Run

Calculated Results for the Irregular Hip Rafters function. 

1. Major Plan Angle
2. Major Roof Pitch Angle
3. Major Roof Pitch
4. Minor Plan Angle
5. Minor Roof Pitch Angle
6. Minor Roof Pitch
7. Major Rafter Run
8. Major Theoretical Rafter Length
9. Major Rafter Length To Ridge
10. Major Rafter Seatcut Length
11. Major Overhang Rafter Length
12. Minor Rafter Run
13. Minor Theoretical Rafter Length
14. Minor Rafter Length To Ridge
15. Minor Rafter Seatcut Length
16. Minor Overhang Rafter Length
17. Hip Rafter Angle
18. Hip Rafter Pitch
19. Hip Rafter Run
20. Hip Rafter Theoretical Rafter Length
21. Hip Rafter Length plumb to plumb along the center line to the ridge.
22. Hip Rafter Long Point Length to Ridge -- long point of hip rafter sidecut
23. Saw Blade Bevel Angle to cut the hip rafter sidecut angle along the hip rafter peak plumb line.
24. Hip Rafter Overhang Length
25. Major Hip Rafter Plumb Backing Mark Height
26. Minor Hip Rafter Plumb Backing Mark Height
27. Major Hip Rafter Perpendicular Backing Mark Height
28. Minor Hip Rafter Perpendicular Backing Mark Height
29. Major Pitch First Jack Rafter Length To Long point of miter cut.
30. Major Pitch Jack Rafter Length Difference @ jack rafter spacing
31. Major Pitch Jack Rafter Saw Blade Bevel Angle
32. Minor Pitch First Jack Rafter Length To Long point of miter cut.
33. Minor Pitch Jack Rafter Length Difference @ jack rafter spacing
34. Minor Pitch Jack Rafter Saw Blade Bevel Angle
35. Theoretical Common Rafte Rise
36. Rise To Top Of Ridge
37. HAP -- Height Above Plate (Heel Height)
38. Major Rafter Plumb Cut Height
39. Minor Rafter Plumb Cut Height
40. Hip Rafter Plumb Cut Height
41. Hip Rafter Drop For Roof Plane Alignment
42. Hip Rafter Backing Offset Main Perpendicular to hip rafter run line.
43. Hip Rafter Backing Offset Adjacent Perpendicular to hip rafter run line.
44. Hip Rafter Backing Offset Main along eave line.
45. Hip Rafter Backing Offset Adjacent along eave line.
46. Hip Rafter Backing Angles
47. Hip Rafter Plumb Backing Angle
48. Hip Rafter Side Cut Angles
49. Jack Rafter Side Cut Angles
50. Roof Sheathing Angles
51. Hip Rafter Purlin Housing Angles
52. Hip Rafter Diamond Post Miter & Saw Blade Bevel Angles
53. Plywood Roof Sheathing Offset Cut Line
54. Valley Sleeper Miter & Saw Blade Bevel Angles
55. Dormer Square Tail Miter & Saw Blade Bevel Angles
56. Purlin Rafter Miter & Saw Blade Bevel Angles
57. Purlin Layover cut perpendicular to roof surface plane

Saillies De Toit

I thought this might be a good book.


La CHARPENTE en bois de Gilbert Emery ( RELI - 1 avril 2005)

I draw out page 148, .Saillies De Toit.

Roof projections
With regular projection,  = equal overhang

The ground plan is a trapezoidal ground plan with equal overhang. The book does not explain how to calculate the hip offset from the corner of the ground plan. Disappointing!!!
Back to the drawing board to see how to draw or calculate the hip offset for roof eave angles that are not at 90° and have unequal roof slope angles.

This drawing was generated by my Google SketchUp plugin using the Trapezoidal Ground Plan function.

Irregular Hip Rafter Ground Plan With Equal Overhang

It easy to draw out the tetrahedrons at the hip overhang when the roof eave angle is 90°.

It's also, just a simple math equation to find the hip offset from the corner of the fascia line.

Major Pitch Overhang Run / tan(minor plan angle) = Offset Run on fascia line

24 ÷ tan(36.8699) = 32

Here's a drawing with the math for the trapezoidal ground plan with equal overhang to find the hip rafter offset from the corner of the building plate line.

Unconstructable Irregular Roof Framing and My Android App

This is an example of an unconstructable irregular roof with an 135° eave angle. There aren't very many roofs in construction that have this set of angles, but I see a lot of carpenters trying to calculate roof framing angles that are unconstructable.

The common rafter pitch on the right side is an 4:12 pitched roof with roof angle of 18.43495°. The common rafter pitch on the left side was suppose to be an 8:12 pitched roof with an roof angle of 33.69007°. However, the 8:12 pitch on the right side has to be at 90° to the eave line. Which is impossible with an 135° eave angle. In order to make the 135° eave angle work with the major 4:12 roof pitch the minor roof pitch needs to be changed to some where around an 5:12 pitch.

Here's a screen shot of my Android Frieze Block Miter Angle & Saw Blade Bevel Angle app showing  Minor Tetra Angle = 22.99236°. This is another good example of the different math functions on different platforms and different devices calculating different angles when the roof is unconstructable to begin with. The Minor Tetra Angle is from an function that I wrote that tries to draw the 2 tetrahedrons for the 2 different pitches. If the 2 tetrahedrons don't align with the hip rafter than the roof is unconstructable.

This image shows an screen shot of the Android Frieze Block Miter Angle & Saw Blade Bevel Angle app where I've changed the minor pitch to an 5:12 pitch, so we can view the results for the Frieze Block Miter Angle & Saw Blade Bevel Angle for both the major roof pitch and minor roof pitch.

This image shows an screen shot of the Android Frieze Block Miter Angle & Saw Blade Bevel Angle app when the View Hip Rafter Angles button is pressed. The hip rafter or valley angles are not needed to cut the frieze blocks, but are shown for reference. 

In this screen shot of the Android Frieze Block Miter Angle & Saw Blade Bevel Angle app you can see that the Major & Minor plan angles are set to 0.00 when you enter an Roof Eave Angle of 1356°, which is an unconstructable roof.

Note: the screen shots of my Android Frieze Block Miter Angle & Saw Blade Bevel Angle app are just about the same size of my Google Nexus 7 tablet.