Rafter Lengths Of Octagonal And Other Polygonal Hips And Valleys. First Method: Knowing the run of a hip or valley for the polygon under consideration (17" for the square, 13" for the octagon, etc.), by assuming the respective rises for the various pitches and solving c'2 = a'2 + b'2, Fig. 76, data pertaining to hip or valley unit rafter lengths, such as that for the octagon in Fig. 73, is obtained.

To determine a rafter length, having available such a table, multiply the hip or valley length per foot of run of common rafter as given in the table by the run of the common rafter of that roof.

Reduce to feet. Such lengths will be laid off by measurement from the side or cheek cut, which will have been laid off, down the top edge of the rafter.

Lengths of hip or valley tails will be determined in a similar manner from the same table.

Second Method: This consists in successive placings of the square, using the same numbers on tongue and blade as will be used in laying out the plumb cut for this particular roof. The successive advances will be determined, as in the hip or valley of a square cornered building, by the number of feet in the run of the common rafter of this roof. A fractional part of a foot in run will be treated in a manner similar to that described for the square cornered building. Suitable allowance must be made for the fact that the length of rafter is along the middle of the top edge of the rafter, when this latter method is used.

Example:

An octagonal roof of ¼ pitch has a span of 25'.

The run of common rafter = 12' 6".

Taking 13" on the tongue and 6" on the blade lay off successively 12 measurements. Take 6/12 or ½ of 13" or 6½" on the tongue and 6/12 or ½ of 6" or 3" on the blade for the fractional foot of run.

Fig. 76. King-Post.