How to Precisely Layout an Irregular Pitch Hip Rafter

How to Precisely Layout an Irregular Pitch Hip Roof Rafter using Rafter Tools+ for iPhone
or
How to Precisely Layout an Split Pitch Hip Roof Rafter using Rafter Tools+ for iPhone

or
How to Precisely Layout an Bastard Pitch Hip Roof Rafter using Rafter Tools+ for iPhone

Using the default settings in Rafter Tools+ for iPhone

90° Eave angle

8:12 main roof pitch

10:12 adjacent roof pitch

3 ½” for the width of the hip rafter

Press the calculate button

Then Scroll down the page, the calculated results should look like the following:

Main Slope Angle

33.69007

Adjacent Slope Angle

39.80557

Main Plan Angle

51.34019

Adjacent Plan Angle

38.65981

Hip Rafter Layout
@ Foot of Hip Rafter

Hip Rafter Slope Angle

27.50055°

Main HR Backing Angle

20.27452°

Adjacent HR Backing Angle

29.99339°

Hip Rafter Width

3 1/2''in

Hip Rafter Backing Depth Dimension

13/16''in

Hip Rafter Plumb Line Shift Dimension

1 11/16''in

Main HR Shift Dimension Perpendicular to HR Run Line

2 1/8''in

Adjacent HR Shift Dimension Perpendicular to HR Run Line

1 3/8''in

Main HR Saw Blade Bevel Angle @ foot of HR

 38.65981°

Adjacent HR Saw Blade Bevel Angle @ foot of HR

51.34019°


Hip Rafter Layout
@ Peak of Hip Rafter

Main HR Bevel Angle

 35.35971°

Adjacent HR Bevel Angle

47.95238°

Main HR Saw Blade Bevel Angle @ peak of HR

51.34019°

Adjacent HR Saw Blade Bevel Angle @ peak of HR

38.65981°

Main HR Plumb Line Shift Dimension

2 11/16''in

Adjacent HR Plumb Line Shift Dimension

1 1/16''in

Hip Rafter Square Tail Fascia Layout
Hexenschnitt The Witches Cut

Main HR Miter Angle

77.01151°

Adjacent HR Miter Angle

64.35702°

90° - Main HR Miter Angle

12.98849°

90° - Adjacent HR Miter Angle

25.64298°

Main HR Back Bevel Angle

58.01937°

Adjacent HR Back Bevel Angle

50.25040°

Main HR Saw Blade Bevel Angle

31.31734°

Adjacent HR Saw Blade Bevel Angle

36.86131°

Main HR Miter Line Shift Dimension @ tail of HR

1 5/16''in

Adjacent HR Miter Line Shift Dimension @ tail of HR

1 ''in

Next press the Lengths button

Enter

Main Rafter Run = 22

Ridge Width = 3.5

Material Depth = 3.5

SeatCut Length = 1.5

Main Overhang Run = 6

Make sure the Unequal button is selected, then press the calculate button, it will calculate the roof rafter lengths for an unequal overhang roof.

Then Scroll down the page, the calculated results should look like the following:

Main Rafter Run

22  ''in

Main Rafter TL

26 7/16''in

Main Rafter Length to Ridge

24 5/16''in

Main Rafter OverHang Run

6  ''in

Main Rafter OverHang Rafter Length

7 3/16''in

Main Rafter Seatcut Length

1 1/2''in

Main Rafter HAP

3 3/16''in

Main Rafter Plumb Height

4 3/16''in

Plate Height Difference

0

Hip Rafter Offset From Corner

0

Adjacent Rafter Run

17 5/8''in

Adjacent King Rafter TL

22 15/16''in

Adjacent King Rafter Length to Ridge

21 1/16''in

Adjacent Rafter OverHang Run

4 13/16''in

Adjacent Rafter OverHang Rafter Length

6 1/4''in

Adjacent Rafter Seatcut Length

1 5/8''in

Adjacent Rafter HAP

3 3/16''in

Adjacent Rafter Plumb Height

4 9/16''in

Hip Rafter Run

28 3/16''in

Hip Rafter TL

31 3/4''in

Hip Rafter Length to Ridge

29 1/4''in

Hip Rafter Length to Long Point

31 3/16''in

Hip Rafter OverHang Run

7 11/16''in

Hip Rafter OverHang Rafter Length

8 11/16''in

Ridge Height

16 11/16''in

We’ll layout the hip rafter using the Hip Rafter Length to Ridge, 29 1/4''in, and the Hip Rafter OverHang Rafter Length, 8 11/16''in.

Mark 3 perpendicular lines on the top edge of the hip rafter using these dimensions.

Next click on the Hip Angles button and then click on the Hip/Valley Rafter Slope Angle text. It will display the Framing Square Usage for the Slope Angle of the Hip Rafter, 27.50055°, 6 ¼ / 12. We’ll use the 12” as the rotation point on the framing square and move the other end of the framing square to the edge of the hip rafter material using the 6 ¼” rotation dimension.

 Draw the Hip Rafter Level Plane Line

Draw the hip rafter backing depth line on both sides of the hip rafter using the Hip Rafter Backing Depth Dimension of 13/16''in.

Draw a hip rafter plumb line using the Hip Rafter Plumb Line Shift Dimension of 1 11/16''in.

The Hip Rafter Plumb Line Shift Line & the Hip Rafter Level Plane Line must intersect at the hip rafter backing depth line. These 3 lines must intersect at the Roof Plane Alignment Point.

Draw a line on the top edge of the hip rafter using Main HR Shift Dimension Perpendicular to HR Run Line

2 1/8''in

Draw the Hip Rafter Back Bevel Lines at the hip rafter seat. It will result in the Main HR Bevel Angle of  47.95238° and the Adjacent HR Bevel Angle 35.35971° .

Draw the hip rafter seat cut line at the dimension for the Main Rafter HAP of  3 3/16''in.

At the peak of the hip rafter draw the Main HR Plumb Line Shift Dimension @ 2 11/16''in

and the

Adjacent HR Plumb Line Shift Dimension  @1 1/16''in

On the main screen of Rafter tool+ for iPhone the miter angles for square tail fascia are displayed as

Main HR Miter Angle

77.01151°

Adjacent HR Miter Angle

64.35702°

90° - Main HR Miter Angle

12.98849°

90° - Adjacent HR Miter Angle

25.64298°

An  easy  way to use these miter angles is to  click on the Hip Angles button and then click on the Main Side Hip Rafter Purlin Housing Angle, Square Tail Fascia Hip Rafter, or Witches Cut, Miter Angle  text. It will display the Framing Square Usage for the Square Tail Fascia Hip Rafter Miter Angle of , 12.98849°, 2 3/4 / 12. We’ll use the 12” as the rotation point on the framing square and move the other end of the framing square to the edge of the hip rafter material using the 2 3/4” rotation dimension.

Layout the Square Tail Fascia miter angle as shown in this next drawing using 2 3/4 & 12 on the framing square.

Repeat the process on the adjacent pitch side of the hip rafter using   5 3/4 & 12 on the framing square, for a miter angle of 25.64298°.

Use the Main HR Miter Line Shift Dimension @ tail of HR 1 5/16''in to draw a line parallel with the HR Miter Line. Repeat the process on the adjacent pitch side of the hip rafter using, Adjacent HR Miter Line Shift Dimension @ tail of HR 1 ''in.

Draw the Square Tail Fascia Back Bevel Angle Lines on the top & bottom edges of the hip rafter.

The Hip Rafter Square Tail Fascia Miter Line Shift Line & the Hip Rafter Level Plane Line must also intersect at the hip rafter backing depth line. These 3 lines intersect at the Roof Plane Alignment Point.

Set your saw to the Main HR Saw Blade Bevel Angle 31.31734° and Adjacent HR Saw Blade Bevel Angle 36.86131° and cut along the miter lines of the hip rafter square tail.

Hip Rafter Backing Angles for Edge Bevel

I've written an a couple of articles on how to draw the dihedral angle triangle for the hip/valley rafter backing angles, but after reading an JLC article it needs to be clarified again. So no one makes the mistake of using the hip rafter plumb backing angle instead of the hip rafter backing angle to edge bevel the hip/valley rafter.

Here's a wire frame sketch showing the location of the hip/valley rafter backing angle and the hip/valley rafter plumb backing angle.

The hip/valley rafter plumb backing angle is plumb to the earth, or plumb to the ground plan.

The dihedral angle triangle for the hip/valley rafter backing angles is perpendicular to the hip/valley rafter in elevation. You only use the hip rafter backing angle to edge bevel hip/valley rafters. 

Hip/Valley Rafters are backed out to align with the roof planes.

How to draw the hip/valley rafter backing angle in plan view.

How to draw the hip/valley rafter backing angle in section view.

For equal pitched roofs .

Here are all the hip/valley rafter backing angle formulas(C5) by Joe Bartok.

• Hip Rafter Backing Angle  = arccos (sin Plan Angle ÷ cos Jack Rafter Side Cut Angle)
• Hip Rafter Backing Angle  = arccos (sin Plan Angle ÷ sin Sheathing Angle)
• Hip Rafter Backing Angle  = arccos (cos Common Rafter Pitch Angle ÷ cos Hip-Valley Pitch Angle)
• Hip Rafter Backing Angle  = arcsin (sin Common Rafter Pitch Angle x cos Plan Angle)
• Hip Rafter Backing Angle  = arctan (tan Common Rafter Pitch Angle x sin Jack Rafter Side Cut Angle)
• Hip Rafter Backing Angle  = arctan (tan Common Rafter Pitch Angle x cos Sheathing Angle)
• Hip Rafter Backing Angle  = arcsin (tan Jack Rafter Side Cut Angle x tan Hip-Valley Pitch Angle)
• Hip Rafter Backing Angle  = arcsin (tan Hip-Valley Pitch Angle ÷ tan Sheathing Angle)
• Hip Rafter Backing Angle  = arctan (sin Hip-Valley Pitch Angle ÷ tan Plan Angle)
• Hip Rafter Backing Angle  = arctan (sin Hip-Valley Pitch Angle x tan Adjacent Plan Angle)

Here are some the hip/valley rafter plumb backing angle formulas (A7) by Joe Bartok.

• Hip Rafter Plumb Backing Angle = arctan (tan(Hip Rafter Slope Angle) x sin(Hip Rafter Slope Angle))
• Hip Rafter Plumb Backing Angle = arctan( tan( Common Rafter Slope Angle ) * cos( Plan Angle ))

I only know of 2 types of roof framing that you would use the hip rafter plumb backing angle to cut material related to a roof. 

1. Hip Rafter Post rotated perpendicular to the hip rafter run line.
2. Hip Rafter Rake Wall Studs.

Here's an study by Joe Bartok on the angle A7, when the Hip Rafter Post is rotated perpendicular to the hip rafter run line.

Here's a study I did on the angle A7, when the Hip Rafter Post is rotated perpendicular to the hip rafter run line.

You can also use the hip rafter plumb backing angle for hip rafter rake walls rotated into the roof surface plane. The rake stud is cut using the hip rafter plumb backing angle as the miter angle and the formula to calculate the saw blade bevel angle to cut the compound cut of the hip rafter rake wall stud uses A7.

Saw blade bevel angle = P5BV = arctan(sin A7 x tan DD)