Friday, September 6, 2013

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.

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.


  1. Sim,

    What an excellent presentation of my method you have created here!

    I'm glad you like it!

    Copyright! =)

    1. Your method should be included in the Swanson's Little Blue Book.

  2. An endorsement from a World Class and Renown Roof Cutter such as yourself is a good start.

    It really is the code breaker that resolves the mystery for complete understanding of typical H/V Roof Framing Geometry.

    In My Humble Opinion. =)

    It should be taught everywhere!

    1. The only think I don't like about it is... that I didn't think of it first.

  3. I think you are not alone, on both counts of that statement.

  4. It really is a brilliant concept, if I say so myself. =)

  5. Good grasp of this basic idea here...However, the German school of trades (holz bou --wood roof construction) has been doing this approach for, oh, 250 +/- years.

    What about the hip/valley backing angle?

    1. This comment has been removed by the author.

    2. Jack,

      I'm pretty sure that any roof framing layout method we come up with or figure out today, was used long before our time. This method for American use, just need a name.

      I'm not sure what you're referring to about the hip or valley rafter backing angle. The one length method on this page has nothing to do with the backing angle. It's just for lengths and side cut angles.