A Roof Cutter's Secrets

Introduction
Laying the Groundwork

Before you dive into this book, we need to discuss a few definitions and general roof framing principles. Throughout the country, different names may be given to various parts of a rafter, so I'll quickly review the ones I use.

Rafter parts. There are three main parts of a rafter that concern us: the head-cut, the birdsmouth notch, and the tail (Figure 0-1). For regular roofs the head-cut can be a plumb-line cut square, as in the case of a common rafter or a valley jack that butt to the ridge (often referred to as a ridge-cut); it can be a single 45-degrees cheek-cut, as in the case of a regular hip jack; or it can be a double 45-degrees cheek-cut as in the case of a hip or valley.

The birdsmouth notch consists of two cuts: one in the vertical plane called The heel-cut; the other in the horizontal plane called the seat-cut. The plumb distance above the plate at the outside wall line is called the heel- stand. The heel-stand measurement is needed when setting the height of any ridge boards or beams so they will flush with the top of the rafters.

The tail is simply put - the part of the rafter that sticks out of the building.

Horizontal standards. In Figure 0-2, the roof span is the total building width from outside wall to outside wall; the run (or theoretical run) is half the span; and the effective run is the run less half the thickness of the ridge.

I use the effective run when calculating most rafter lengths, as this eliminates having to shorten for the ridge thickness later. Sometimes when there is no ridge involved, the run and the effective run are the same and can be used interchangeably. Think of the effective run as an actual distance a rafter travels. Only on irregular roofs radiating from a centerpoint (bay roofs, polygons, etc.) is it more practical to calculate some rafters to the theoretical roof center and then shorten for a top connection.

In this book, the run and the effective run for hips and valleys are the same as the run and the effective run for commons. In other words, run always refers to half the span of a regular gable or hip roof. This may be a departure from traditional mainstream roof framing methods that teach that a hip or valley has a unit "run' of 17 in., but I believe it is confusing to give more than one meaning to the word. Therefore, when I use the word "run," it means only one thing: the horizontal side of a right triangle formed by the pitch of the roof. (This is also the way most rafter table books are set up.) I use the words diagonal travel or hip travel when referring to the horizontal distance directly under the hip or valley.

LL/RR method. There are many different methods to calculate rafter lengths: from the cave man cut-and-fit method, to stepping off using a framing square, to rafter table books, to specialized roof framing calculators like the Construction Master, to computer programs. The method I use to find rafter lengths and various wall and beam heights requires only a regular low-budget handheld calculator and a few simple ratios. I call this system the LL/RR method. Each specific roof pitch has its own unique ratios which you will find listed in Charts 2 and 4 in Appendix A at the back of this book. These ratios are quite simple to calculate, and I will explain how they are computed.

With the right triangle formed by the pitch of the roof (6/12 in Figure 0-3), use the Pythagorean theorem to solve for the hypotenuse (a2 + b2 = C2).

If we take the roof's unit of rise (6) and divide by the unit of run (12), we arrive at a ratio of .5000. I call this ratio the roof-rise ratio or the RR ratio. I use this ratio to calculate the change or "step" in gable stud lengths and to help determine the height of any tall walls, purlin beams, or ridges. In trigonometric terms, the RR ratio is the tangent of the roof-pitch angle (opposite side -- adjacent side).

If we take the hypotenuse of this same triangle (13.4164) and divide it by the unit of run (12), we arrive at a ratio of 1.1180. I call this ratio the common rafter line-length ratio (COM LL ratio). I use this ratio to change any horizontal dimension into a rake measurement. Some examples would include the top plates for a rake wall, common rafter lengths, and jack-step lengths. In trigonometric terms, the COM LL ratio is the secant of the roof- pitch angle (hypotenuse/adjacent side).

If a roof has any regular hips or valleys, we'll need one more ratio - what I call the hip/valley line-length ratio (H/V LL ratio). It's a little more complicated to find since it requires two separate sets of calculations (Figure 0-4). First, in the plan view, solve for the hypotenuse (unit of travel) on the equilateral right triangle created by the hip/valley traversing at 45 degrees across the building through one unit of run. Then with the unit of travel (16.9706) as the base leg for a section-view right triangle and the unit rise (6) as the vertical leg, calculate the hypotenuse (18). Divide this number by the unit of run (12) to find the H/V LL ratio of 1.5000. I use this ratio to help find the lengths of any hips or valleys.

These three ratios (RR ratio, COM LL ratio, and H/V LL ratio) express a relationship as a percentage to a known horizontal run distance. For a 6/12 pitch roof, the rise is 50% of the run value, the common rafter lengths are 11 1.8% of the run value, and the hip/valley rafter lengths are 150% of the run value. Since we can always find the horizontal dimensions off the prints or actual field measurements, determining the rise, rake, and diagonal rake involves simple multiplication.

In addition to the ratios, it is necessary to know the roof-pitch angle in degrees for cutting gable studs, rake walls, California valley jacks, etc. The degree for each common roof pitch is listed in the back of this book (Chart 3, Appendix A), or you can simply read them right off a rafter square.
(When I use the term rafter square, I am referring to the triangular layout square such as the Speed Square from Swanson Tool Co. or the Quick Square from Stanley Tool Co. This is not to be confused with the age-old framing square that is shaped like a large "L'.)

Throughout the book I have used 6/12 as the standard roof pitch with rafters spaced at 16 in. on center; 2x material is figured as 11/2 in. thick; 4x material is figured at 31/2 in. thick; and 6x material at 51/2 in. thick. All exceptions are noted. Also, anytime I mention a Skilsaw, I'm referring to a wormdrive cir