First Method: The line of measurement for length of a hip and valley rafter is along the middle of the back or top edge, as on common and jack rafters. The manner of determining the number to use on the tongue of the square as a constant for the run, in terms of the 12" constant run of the common rafter, when the rise of the hip or valley rafter per foot of common run is taken on the blade; and the manner of constructing a table of unit lengths of hip and valley rafter, per foot of run of common rafter, are illustrated in Figs. 57, 58, 59 and 60. From a study of these illustrations it will be seen that a hip or valley rafter of a square cornered building is in either case the diagonal of a square prism which has for its base dimensions the tangent and run of the roof, and for its height the rise of the roof, Fig. 57. On a square cornered building the run and tangent are always equal.

Fig. 57. Hip or Valley Rafter is Diagonal of Square Prism.

Fig. 58-a. Hip Rafter..

Fig. 58-b. Valley Rafter.

The length of the diagonal of the base of such a prism, which is the run of the hip or valley rafter, is found by the formula c12 = a'2+b'2, Fig. 58. When tangent and run are equal: and each taken as 12", the run of the hip or valley equals 16.97", which for practical purposes of carpentry is considered as 17". In laying on the square, then, in framing a hip or valley rafter of a square cornered building, 17" will be taken upon the tongue, the rise of the roof per foot of run of common rafter or per 17" of run of hip or valley rafter, being taken on the blade.

The table of hip and valley lengths per foot of run of common rafter, Fig. 60, will be formed by solving the right triangle c"2 = a"2+b"2, Fig. 59, for each of the pitches represented.

The positions to be assumed by the worker in framing a hip or valley rafter are similar to those to be assumed in framing the common rafter.

In measuring the length of a hip or valley rafter by the first method, the plumb cut may be laid off first. The upper end of the hip rafter will have to be framed with a side cut as shown in Fig. 61. The measurement for length will be made from a point along the middle of the top arris. Where the second method is employed, the end and seat cuts are laid off first.

Fig. 59. Determining Unit Length of Hip or Valley Rafter..