Laying Out a Split-Pitch Hip, continued

Creating an Equal Fascia Line

To equalize the height of the differently pitched rafter tails at the fascia line, the plate under the steeper roof pitch must be raised for each foot of overhang by the difference between the two pitches. In this case, the plate rise unit is 2 inches (10 minus 8). To calculate the plate rise for an 18-inch (1 1/2-foot) overhang, multiply 2 x 1.5 = 3 inches.

Creating Equal Overhangs

Although the differently pitched rafter tails now meet at a common fascia line, the overhangs will be unequal because the two roofs have different slopes; therefore, the steeper pitch resolves closer to the building line than the shallower main pitch. The solution is to shift the entire plane of the steeper roof off the plate by the difference between the two unit runs. As a result, the hip moves off the building corner, onto the plate of the steeper roof (red triangle). And the location of the birdsmouth shifts back onto the plate.

To figure all this out, return to triangle A and extend the 10-pitch unit run line to 12 inches. Draw a line perpendicular to the endpoint of the 12-inch line, then extend the hypotenuse to meet this line.

Each side of the resulting, smaller triangle D gives an important unit dimension. Since the entire plane of the steeper roof has shifted, the difference between the common unit run and the 10-pitch ratio unit run (2 3/8 inches) must be added to the ridge endpoint. The length of the opposing side gives the hip offset distance from the building corner onto the steeper roof's plate. And the hypotenuse gives the distance to shift the birdsmouth back onto the plate. These dimensions are all factors per 12 inches of overhang.

Backing the Hip

The hip rafter shares the same height above the plate as the common rafters, but its corners project above the planes of both roofs. Backing angles on an irregular hip are unique to each side but can be found by redrawing triangle A in two perspectives: one with an 8-inch baseline and a 10-inch opposing angle, and the other with a 10-inch baseline and an 8-inch opposing angle. In both triangles, extend the baseline to a common unit length of 12 inches. Next, draw the hip angle on top of each base angle as it relates to the opposite side of the hip. So, for the 8-inch baseline triangle, the hip rise line is 10 inches; for the 10-inch baseline triangle, the hip rise is 8 inches. If you check the angles on these two secondary triangles, you'll find that they match perfectly -- the hip angle is constant.

Finally, draw a third triangle on top of the respective hip angles, with a rise line equal to that for its side of the hip. For the 8-pitch side, draw an 8-inch line perpendicular to the hip angle hypotenuse (triangle F). For the 10-pitch side, draw a 10-inch line (triangle E). Complete both triangles with a hypotenuse. The resulting angles, at the long points of the triangles, are the backing angles for each side of the hip. To determine the drop amount for each side, superimpose the angles on the plumb cut of the hip, working from the center of the hip stock out. Remember, drop is measured in plumb, not parallel, and don't get your sides confused.

Cutting Plywood Angles

The easy way to cut roof ply is on the ground. You can't cut the plywood at the plan angle to fit the hip -- it's not the same at pitch. To find the two angles needed, draw two separate rise/run triangles: a common 8-over-12 triangle for the main side of the hip, and 8-over-9 5/8 inches for the 10-pitch side.

On each of these triangles, draw the opposing unit run -- 9 5/8 inches over the 12-inch run (triangle G) and 12 inches over the 9 5/8-inch run (triangle H) -- perpendicular to the hypotenuse and draw a second hypotenuse from the run line back to the baseline. Notice that the length of each secondary hypotenuse is equal to the hip unit length.

The plywood cut angle is adjacent to the run line. The more acute angle at the opposite end is the angle of cut across the top of the jack rafter, useful for marking cheek cuts steeper than a circular saw can accommodate.

Finding the Jack Rafter Common Difference

Jack rafter lengths, and the common difference between them, are easily developed from the plywood angle drawings. Extend the respective baselines to equal common rafter spacing -- we'll assume 16 inches -- then draw a perpendicular line at the endpoint to intersect the hypotenuse. The point of intersection is the length of the first jack rafter as well as the length of the common difference.

Jack rafter cheek cuts can exceed the angle setting of conventioinal circular saws, and the cut may have to be completed with a handsaw or saber saw. To guide the cut, lift the appropriate angle from the drawing with a bevel gauge and trace it across the top of the jack rafter. Don't make the mistake of using the plan angle for this purpose -- it's not the same and can be used only as a saw setting for making 45-degree or shallower compound plumb cuts.