Backing Octagonal And Other Hips. The principle involved in determining the amount of backing on hip rafters for the octagon, as well as that of other polygons, is similar to that for backing hips for the square cornered building.
(1) Place the framing square upon the hip as for making the seat cut of the octagon hip rafter, Fig. 77.
(2) Referring to Fig. 78 it will be seen that the more sides a roof possesses the less will be the backing required. Fig. 78 represents the hips on square, octagon, and hexagon as they would appear upon the plan if made to stand straight up at the corners of the plates. The backing in each case is determined by the tangent of the angle whose adjacent side is ½ the rafter thickness, and whose angle is equivalent to ½ the central angle as A, A', A", Fig. 78. The fact that the hips are inclined and not vertical in their final position in a roof makes no difference in the principle of determining backing because of the fact that our measurements are made in a horizontal plane, or in the plane of the plate, Figs. 64 and 77.
The ratio of the backing of the octagon or any other polygonal hip to that of the square of equal rise will be proportional to their tangent values. For illustration, on the square roof we measured along the tongue of the square, from the top edge of the hip, Fig. 64, ½ the thickness of the rafter, for reasons made plain in Fig. 78. In laying off the octagon backing we should lay off along the tongue in the line of the octagon seat cut, 5/12 of ½ the thickness of the rafter. In the case of a 2" rafter, 5/12" will be set off, using that side of the square containing graduations in 12ths.
Fig. 77. Laying out Backing for Octagon Hip.
(3) Where backing is not desired the rafter will be dropped a plumb distance equal to the plumb distance of the backing of the rafter, Fig. 77. Consult Fig. 73.
Fig. 78. Backing for Hip of any Polygon.