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)
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.
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.