One Length Method© Richard Birch

One Length Method© by Richard Birch

Richard Birch's method,One Length Method, that he developed from the Swansons Blue Book. Measure from the plumb line shifted at the foot of the hip rafter using the hip rafter length to ridge dimension A. Use the same dimension A along both sides of the hip rafter to mark off the long point of the hip rafter top back bevels. Then use the Adjacent Plan Angle as the Saw Blade Bevel Angle to cut along the long point of the hip rafter plumb. It can be used for single cheek cuts or double cheek cuts at the ridge. This method works for 90° Eave angles with equal or unequal pitched roofs.

The Hip/Valley Rafters can be marked essentially the same as you would mark the Common Rafters. But the Pitch changes (still plumb), the length increases (still contained in the same surface boundaries), and the bevels are not square (same wall, same ridge). Fast & Accurate.

One length -- lays out all of the back bevel lines.

In this picture you can see how the one length is used to layout all of the hip rafter plumb lines.

One of the interesting things about the Birch One-Length-Method is that the Hip/Valley Rafter thickness is hypothetically irrelevant. In other words, if the hip is 1-1/2" thick or 5-1/2" thick, it can still be marked using  the same length in the same way .

For equal pitched hips the only thing you need to know
1: the hip rafter length to the ridge.
2: the hip rafter backing depth line on the side of the hip rafter (optional).

For unequal pitched hips you need to know
1: the hip rafter length to the ridge.
2: the hip rafter backing depth line on the side of the hip rafter (optional).
2: center line on the top edge of the rafter (optional).

 The hip rafter backing depth line on the side of the hip/valley rafter is optional. It is only used for reference.

The center line on the top edge of the hip/valley  rafter is optional, because the geometry is automatically generated by the saw cut and it produces an apparent shift offset. (proportional)

The hip rafter backing depth line on the side of the hip rafter, the hip rafter level line on the side of the hip rafter and the hip rafter shifted plumb line must intersect at point G in the drawing below.  Use these 3 lines for reference. Only the  hip rafter shifted plumb line is necessary to use with the One Length Method© by Richard Birch.

Fast & Accurate? Give it a try.

Richard Birch explaining the  Birch /One Length Method.

The thing that really separates the "Birch /One Length Method" from the "Shiften" method.  Now let me prelude with, both processes will ultimately produce the same fitting Rafter Geometry, It is the approach and application that is simplified with the "Birch" method.  The "Second Shifted Plumb line" is Not Necessary.  This geometry is a function of the saw, as it performs the mitered cheek bevels.  The H/V Rafters are simply cut to fit, exactly like the Commons are cut to fit. (The Marking of the two different type of Rafters, Coms Vs. H/V, is applied exactly the same, Along the shoulder, and from the shoulder.)  

One of the things that is an old standard cut on H/V rafters is the square cheek cut at the Heels of the H/V rafters,  I have changed that to be a reverse diamond beveled cheek cut,  as Sim did.  This geometry, can be real or imagined, as processing the H/V Rafters goes.  If the Heel diamond is not actually performed, then extra clearance is, otherwise the Corner Wall Connection will need notching as shown in Swanson's.  (The square birdsmouth notch on the H/V rafters may be the Centuries old mistake that has hidden this geometry for so long?)

Another visual aid might be to imagine a Common being rotated and stretched to become a Hip.  (Still plumb at head and heel, still in plane with the pitched surface, still greeting, or projecting through, the same vertical planes at the wall and Ridge. (plan-view lines, separated by the Effective Run)  Parallel cheek-cut bevels at each end, Head and Heel.

The compound miter Geometry of the Hip Rafter is, as seen from Head to Heel;  Long-to-Short = Pitch angles  and  Long-to-Short = Cheek-cut miter angles

The compound miter Geometry of the Valley Rafter is, as seen from Head to Heel;  Long-to-Short = Pitch angles  and Short-to-Long = Cheek-cut miter angles (C-c miters are reversed)

Once you have the H/V length calculated, just mark it on the side (shoulder), as you would a Common, mark the HAP at the Heel, Set saw for bevel angles, cut plumb lines, swing foot to the square position, finish the Level cut of the Birds-mouth, (add tail length to process if desired), ready to install.

If the H/V rafters are to be backed, I rip the backing bevels first, then mark the HAP from the shoulders. With this method, The Shoulders are always in plane, backed or not.

Richard Birch's Hip and Valley Demo at Google 3D Warehouse

Timber Framing example using the One Length Method© Richard Birch

Unequal Pitch with unequal height backing depths to center the mortise and tenon in the framing material.

Cutting Jack Rafters on Irregular Hip Roofs

Cutting Jack Rafter Side Cut Angles on Irregular Hip Roofs

For an example of cutting the jack rafter side cut angles we'll use a roof with an 90° Eave angle and a 9:12 & 12:12 pitched roof.

Plan Angles:
9:12 -- 53.13010°
12:12 - 36.8699°

You can cut the jack rafter side cut cheek angles using the plan angle as the saw blade bevel angle along the miter/plumb line on the side of the jack rafter. In this example, the 9:12 jack rafters would use a saw blade bevel angle of 53.130100° to cut the jack rafters side cut cheek angles. Unless you have a swing table that tilts over to the  53.130100° you need to use a different approach, besides using a hand saw.

To cut the correct jack rafter side cut cheek angle you can set the saw blade bevel angle to the complementary angle of  53.130100°, which is 36.8699°.  The complementary angle, or sometimes referred to as the Bisected Foot Print Angle, is 90° minus the plan angle. For an equal sided Octagon roof the plan angle is 67.5° and the complementary angle is 22.5°.

First layout the jack rafter side cut angle using a framing square or use the shiften method.

Cut the plumb cut of the jack rafter square.

Set you saw blade bevel angle to the complementary angle and run the saw down the face of the plumb cut.

The correct jack rafter side cut angle in this example is 30.96376°

Witches Cut Layout Simplified

Hexenschnitt -- The Witches Cut Layout Simplified, Square Tail Fascia

Hopefully, these drawings will simplify the witches cut layout for Square Tail Fascia.

These drawings are for an unequal pitch roof, but the layout technique is the same for equal and unequal pitched roofs. For unequal pitched roofs, repeat these steps on the other side of the hip rafter material and use the adjacent side common roof pitch in step 4.

Step 1: Draw a Plumb Line using Hip Rafter Pitch.

Step 2: Draw the Hip Rafter Level Line. 

Step 3: Draw  the Hip Rafter Plumb Line @ the End of Hip Rafter Level Line.

Step 4: Draw a line using the Common Rafter Pitch that  intersects @ A.

Step 5:  Draw a Line Perpendicular to line A-B that intersects @ C.

Step 6: Draw a Line from D to C . The Angle ADC = Hip Rafter Miter Angle for the Witches Cut. 

Step 7: Draw the Hip Rafter Backing Depth Line on the side of the hip rafter. 

Step 8: Shift the Miter Line D-C to intersect at point G. These lines must intersect, 1: Hip Rafter Level Line, 2: Hip Rafter Backing Depth Line, and 3: Hip Rafter Miter Line for the Witches Cut. 

Step 9: Draw the Center Line of Hip Rafter on the top edge. Draw the Back Bevel Line.

Shiften or Swanson's Blue Book

Richard Birch and I are having a discussion on Shiften. He's proclaimed for years that the best method for finding the correct lengths for hip rafters and laying out the back bevel angles, hip rafter side cut angle, was in the Swanson's Blue Book that you get when you purchase their SpeedSquare. So, I went out into my garage yesterday and found the Swanson's Blue Book that came with the last Swanson's Speed® Square I purchased.

Shiften = Transfer the dimension in plan view to elevation view.
Shiften = Transfer the dimension in plan view to profile view.
elevation view = profile view


After studying the Shiften - Shiftungen roof framing geometric layout techniques I see no difference in the layout techniques between the Swanson's Blue Book and Shiften.  They never mention the word shift or shiften in the Swanson's Blue Book, but it's the same technique that's been used by the French and German carpenters for centuries.

I'm actually impressed with the Swanson's Blue Book for describing this technique no matter what it's called.

I just thumbed thru "A Roof Cutter's Secrets", by Will Holladay, and even thou Will Holladay does not use the word shiften he still uses the same technique as shiften for the location of the second plumb line on the side of the hip and jack rafter.

We've all used the second plumb line on the side of the rafters with the dimension taken from plan view and drawn each of the views separately, but by combining the the two drawings it's called  the Shiftungen layout technique like the drawing above.

Richard and my discussion on the Swanson Blue Book


Sim,

Swanson's has evolved. This is a much better explanation than the earlier versions.

Their diagrams still only refers to the Hip length applied at the outside shoulder. Fig. 11 & 13

The "Explanation of Shortening of the Hip" (p.23) is new. This is the stuff I recognized from the meager instructions of my older version. And as I remember, their earlier versions were better than the one I have too. They (cheap bastards) obviously have had some user feedback. (or maybe they read my online posts from years back?) For myself, this method is still the best, as I gather from other books or articles, on the same subject. Less confusion once you get it.


This book is still my top pick for recommended reading. The geometric principles laid out in their regular Hip explanation work for every roof I have encountered. There are additional considerations when applying it too Valleys and Broken Hip Rafters. You just need to visualize the shoulder lines breaking the plane of the effective Ridge height. (This is the real secret to understanding the side-cuts/length applications! *No Ridge, then project thru the total Height) *(rotated rafters too? Footprint geometry at Ridge plane? useful?)


*Additional Considerations;

1) Valleys are essentially upside down Hips, Cheek bevels reverse directions. (I will drop the unbacked Valley to plane away from the shoulder but short of center. An even reveal for tighter sheathing cuts. )

2) The Irregular Broken Hip rafter may need extra considerations for calculating the length, depending on the relative directions of the two ridges. If they are parallel, [Effective Run = (difference in spans /2) - ridge thickness]. If the ridges are perpendicular, then the hypothetical parallel ridge is (plan-view ratio) proportionate to the lower Ridge. Depending on which is Major or Minor, the ridge thickness deduction affected. (It will be > r/t or < r/t, but not equal to lower r/t)


*On my Hips, Reg/Irreg, I mark the Hap plumb lines on both sides of the Heel to make setting it on the corner precise. When both lines are aligned with their wall line, that's where they go. No footprint layout needed.

*yes, thicker lumber will need modified approaches. I calc the bevel short points at each shoulder, and cut to the center.


I hope you have found this exchange of information beneficial, as I have. I have taken this Swanson's concept to new levels, far beyond where they leave off. (but they're getting better.) And this is why I post the stuff I do. The H/V- drop/shift issue is not a dead horse, it's a simple-stuff Thoroughbred. =) (as concepts go . . . . )


Thanks,
Richard

Text from the Swanson's website
Speed Squard
Includes markings for Swanson's® One-Number Method™ of rafter layout, and is packaged with the Swanson® Blue Book of Rafter Length and Roof Construction. 

One-Number Method™ of rafter layout

So what does that statement mean?
of determining the angular pitch of a roof 


Swanson® History
The Swanson® Speed® Square and the One-Number Method™ of determining the angular pitch of a roof were first developed in 1925 by a carpenter named Albert J. Swanson. As his fellow tradesmen began to appreciate the ingenuity of his idea, they wanted their own Speed® Squares. Swanson began to hand-make the squares to fill requests for the tool. Demand for the work-saving tool continued to grow, and in 1930 the Swanson® Speed® Square was first sold in interstate commerce. By 1945, Swanson started Swanson® Tool Company, Inc., to manufacture and sell the Swanson® Speed® Square through recognized channels of distribution. His son, Ronald C. Swanson, assumed control of the company in 1971 and added other quality tools to the line.

Sim,

I was reviewing the page scans you posted and I got confused by the 1/4" line spaced at the ridge. (( Line A,A)   Figs. 11 and 14)  (not in my book?  missing text?)

If Figs. 14 and 15 are overlaid, there is a discrepancy.  See below.

After editing I realized:  The discrepancy is . . . not a discrepancy.  They are showing the Hip length to the center of the Ridge.  Sort of unnecessarily confuses the illustrated explanation.  I have overlaid the effective rafter length lines (plan-view).  The plane of the effective ridge height is "greeted" by the Hip at the perpendicular red "head-cut" line location.

Maybe this is not very important. (above)

One thing that is important;  Swanson's "Shiften" method shifts the effective H/V Rafter line length(s) to the shoulders of the H/V Rafters.  Performing the cuts with a modern circular saw effectively shifts them back to "Center".  Therefore, to process the H/V rafters, all that is necessary to do is to mark the length on the shoulder, mark the plumb lines *(w/Hap @ Heel),  Perform saw cuts, w/bevels, and/or Heel clearance, as required. 

Once you get it, it's like cracking the code, Snap!  Simple Stuff!

Thanks,

Richard

Richard

I was interested in that ¼” as well. They show it 2 times. One for the center line of the ridge meeting the hip in plan view. The book also said mark off a line about ¼” long of the plumb cut line and cut on that line.  The width of the teeth of the saw blade?

Sim
Richard Birch's method,One Length Method,  that he developed from the Swansons Blue Book. Measure from the plumb line shifted at the foot of the hip rafter using the hip rafter length to ridge dimension, 29 1/4", to the long point of the hip rafter. Then use the Adjacent Plan Angle as the Saw Blade Bevel Angle to cut along the long point of the hip rafter plumb line shifted forward .

One Length Method© Richard Birch

Rotated Hip Rafters with Prismatic Foot Print

Here's a study on rotated  hip rafters with the  Prismatic Foot Print of Hip Rafter  developed from the plan view of the hip rafter rotation angle. In this study the hip rafter, 3 1/2" x 3 1/2" is simply rotated 45° from the hip rafter run line in plan view.

Draw the hip rafter in elevation view and transfer perpendicular lines from the level cut of the hip rafter in elevation view. The center line that is perpendicular to the hip rafter level cut in elevation view is at the mid point of the level cut in this example.

To develop the miter Angle on the hip rafter you use 90° - Common Rafter Slope Angle.

Saw Blade Bevel Angle Development

Plan Angle = 45°

Miter Angle = 90° - Roof Slope Angle = 19.79887°

Saw Blade Bevel Angle = arctan (sin Miter Angle x tan Plan Angle) = 18.71224°

Saw Blade Bevel Angle = arctan (sin Angle of Saw Travel  ÷ tan Angle on Adjoining Face)

Saw Blade Bevel Angle = arctan (sin 70.20112°  ÷ tan 70.20112°) = 18.71224°

Prismatic Foot Print of Hip Rafter developed as a prism. 

Prismatic Foot Print of Hip Rafter unfolded developed from prism.

Tetrahedron unfolded, showing the trigonometry developed from the geometry. 

What's really interesting here is that the hip rafter backing angle 41.70594°, when the hip rafter is not rotated, is the angle on the top of the prismatic cut when the hip rafter is rotated.

Tetrahedron Angles

D Angle = 45.0000000000

A Angle = 70.2011256662

C Angle = 63.0185900000

E Angle = 18.7122394087

B Angle = 41.7059492665 .... hip rafter backing angle

90-D Angle = 45.0000000000

90-A Angle = 19.7988743338

90-C Angle = 26.9814100000

90-E Angle = 71.2877605913

90-B Angle = 48.2940507335

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Update: 02/28/2014

Drawings I developed after Study of the Tréteaux Angles. The slope angle on the side of the hip rafter is equal to the common/profile rafter slope angle.

R8-DP = Tilted Hip Rafter Slope Angle on DP Side = SS = S

In these updated drawings the DP line is developed from the TC line following the tilt of the hip rafter block in the hip rafter backing triangle.

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Devers De Pas Valley Rafters

Devers De Pas Valley Rafters:

3D model by SBE Builders

Model to study Devers De Pas with the valley/jack rafters rotated into the roof sufrace plane.