47. Pitches of roofs. There are three terms used in describing the dimensions of roof pitches: the "run"

(ab, Fig. 67) is the horizontal distance between the plate, b, and the point a, directly under the apex of the roof, c; the "rise" is the vertical distance between a and the apex of the roof, c; the "pitch" or "line of the rafter," is the angle or line between b and c.

Then are three pitches in common use in the construction of pitch roofs, the half, third, and quarter pitches (Fig. 68). The angles at b and c (Fig. 67) of any one of these pitches are always the same, no matter what the dimensions of the run and rise or the plan of the house may be.

The run of a pitch roof house is half of its width at the outside of the plate. The rise of any of the above pitches may be found by dividing the width of the house, or the distance between the outsides of the opposite plates, by 2, 3, or 4, as a half, third, or quarter pitch may be desired. This will give the height of the roof to its apex, measuring from the base line, or the line of the outside of the plate, upon the top of the rafters, as shown at k, Fig. 71. The rafter will be discussed later.

Fig. G7. - Roof Dimensions.

Fig. 68. - Roof Pitches.

The following, formulas illustrate the mathematical method of finding the lengths of the run and of the rise of a roof.

W = width of the house.

R = run.

A = rise of the roof, or altitude of the triangle.

Formula 6. R = W / 2

Rise of the half pitch roof.

Formula 7. A=W / 2

Rise of the third pitch roof.

Formula 8. A = W / 3

Rise of the quarter pitch roof.

Formula 9. A = W/4

Thus, the dimensions of a third pitch roof, of a house 28' wide, would be found as follows: -

R = W / 2 = 28' / 2 = 14'

A = W / 3 = 28' / 3 = 9' 4"

48. The different forms of roofs are illustrated in Fig. 69. The lean-to, or shed roof, a; the pitch or gable roof, b; the hip roof, c; the gambrel roof, d; the French roof, e; the a, shed or lean-to; b, pitch or gable; c, hip; d, gambrel; e. French; f, mansard; g, ogee; h, dome mansard roof, f; the ogee roof, g, used in turret and tower construction; and the dome roof, h. The hip roof here illustrated is also a pitch roof, but the term "hip" applies to any one form of roof pitch which has hipped corners. Its general application is, however, to the roof illustrated. The roofs d, e, and f are known also as curb roofs, since a curb plate is used in their construction, at k.

Fig. 69. - Different Forms of Roofs.