This section is from the book "The Carpenters' Guide", by Harvey Miller. Also available from Amazon: The carpenters' guide.

When there is a number of inches rise given to one base foot, the height of ridge is equal to the given rise as many times as there are base feet in the rafter. Add the height of the heel of the rafters in line with the outside of the plate. (See fig. 22.) When a certain height of ridge is given the number of inches rise to one base foot is equal to the height, reduced to inches, di-vided by the number of base feet in the rafter. The height of ridge, 5' 4", the number of base feet, 8. 5'4"=64"divided by 8, the number of base feet, gives 8" rise to one base foot.

For a hip roof the length of ridge is equal to the difference between the width and length of the building. (See fig. 23.) For a gable roof that intersects a main roof, the length of ridge is equal to half the width of the gable, plus any projection of building from main building. (See fig. 23.) The dotted lines represent an offset of 4', the ridge in line of plate is 8', making a total Length of the ridge 12'.

Fig. 23

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