Laying Out a Split-Pitch Hip, continued
Creating an Equal Fascia
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
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
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.
Joe Fuscois a carpenter and cabinetmaker in Staten
Holbrookis an associate editor at