Draw the Common and Hip Rises and Lengths
Next I draw the rise — 12 inches — of one of the common rafters by extending one end of the rectangle. So, for example, I extend line CD 12 inches to point E; this represents the rise of the 5/12 common rafter. Line AE represents the 5/12 common length.
The next step is to "develop" the lengths of the commons (top, center) by drawing right triangles along the sides of the rectangle. The base of each triangle is the common run, the adjacent side is the 12-inch rise, and the hypotenuse is the common length. The hip length (bottom) is developed from the diagonal through the rectangle. Using a compass to swing a 12-inch arc saves time measuring.
Here's where the compass comes in handy. I set its points at D and E, then swing an arc around the end of the rectangle so I don't have to measure the rise three times. Next I draw the 10/12 common in exactly the same way as the 5/12, then the hip, using the framing square to draw its rise (DG) perpendicular to its run (BD).
You've now got the plumb cuts as well as the seat cuts for both commons and the hip.
Draw the Hip Backing Angle
Figuring the backing angles for an irregular hip is usually tricky, but not with this method. Start by drawing a line perpendicular to the hip length, anywhere along its length. Extend the line to the hip run; this is line JK in the drawing.
To develop the hip backing angle (angle LNM), first draw a line perpendicular to the hip length extending to the base of the hip — from point J to point K. Next, draw a line from point K perpendicular to the hip run extending in both directions until it crosses the plate lines (LM). Then, using K as the pivot point, swing an arc from point J to the hip run — to point N in the example.
Finally, draw lines from N to L and M; the resulting angle, illustrated in the cardboard model, represents the top of the hip rafter.
Next, starting at point K, draw a line perpendicular to the hip run and extend it far enough in both directions that it crosses the plate lines (LM). You may have to extend one or both of the plate lines, as in the drawing, in order to intersect this new line.
Now I set the point of the compass on K and swing an arc from J to the hip run; the intersection is point N.
Finally, drawing lines from this point — N — to points L and M gives you the backing angle for the hip rafter.
Draw the Roof Surface
You can also easily figure out the angled cuts for the roof sheathing. Put the point of your compass at point A and the pencil end at E — the distance along the 5/12 common length. Then swing this arc in the opposite direction, make a mark, and extend the 5/12 run line (AD) until it intersects at point O. Draw a line from O to B; the triangle you've drawn represents the roof surface on the 5/12 side of the hip rafter.
Repeat these steps for the other side (triangle BCP).
To draw the sheathing cuts at the hip corner, first extend both common runs well beyond the plate lines, then draw arcs from the tops of the common lengths to these new line extensions (arcs EO and FP).
The cardboard model shows how rotating triangle OAB creates a perfectly fitted roof surface.
Pulling cut angles off the developed drawing is a matter of setting the bevel square and transferring the angles to the stock. Here, the author transfers the plumb cut for the 10/12 common.
He sets the bevel angle for the 5/12 hip backing.
At this point, you can transfer the cut angles to the stock for cutting.
William Dillon is a job supervisor with South Mountain Co., an employee-owned design-build firm on Martha's Vineyard, Mass.