While some mechanics understand thoroughly the methods of laying the various kinds of roofing, there are some, however, who do not understand how to figure from architects' or scale drawings the amount of material required to cover a given surface in a flat, irregular shaped, or hipped roof. The modern house with its gables and various intersecting roofs, forming hips and valleys, render it necessary to give a short chapter on roof measurement. In Figs. 196 to 198 inclusive are shown respectively the plans with full size measurements for a flat, irregular, and intersected hipped roof, showing how the length of the hips and valleys are obtained direct from the architects' scale drawings.

Roof Mensuration 0900215

Fig. 195.

The illustrations shown herewith are not drawn to a scale as architects' drawings will be, but the measurements on the diagrams are assumed, which will clearly show the principles which must be applied when figuring from scale drawings. Assuming that the plans from which we are figuring are drawn to a quarter-inch scale, then when measurements are taken, every quarter inch represents one foot. 1/8 inch = 6 inches, 1/16 inch = 3 inches, etc. If the drawings were drawn to a half-inch scale, then 1/2 inch =12 inches, 1/4 inch = 6 inches, 1/8 inch = 3 inches, 1/16 inch = 1 1/2 inches, etc.

A B C D in Fig. 196 represents a flat roof with a shaft at one side as shown by a b c d. In a roof of this kind we will figure it as if there was no air shaft at all. Thus 64 feet X 42 feet = 2,688 square feet. The shaft is 12.5 X 6 feet = 75 square feet; then 2,688 feet - 75 feet -

Roof Mensuration 0900216

Fig. 196.

2,613 square feet of roofing, to which must be added an allowance for the flashing turning up against and into the walls at the sides.

In Fig. 197 is shown a flat roof with a shaft at each side, one shaft being irregular, forming an irregular shaped roof. The rule for obtaining the area is similar to that used for Fig. 196 with the exception that the area of the irregular shaft x x x x in Fig. 197 is determined differently to that of shaft b c d e. Thus A B C D - 108 feet X 45 feet = 4,860 square feet. Find the area of b c d e which is 9.25 X 39.5 = 365.375 or 365 3/8 square feet. To find the area of the irregular shaft, bisect xx and xx and obtain a a, measure the length of a a which is 48 feet, and multiply by 9. Thus 48 X 9 = 412, and 412 + 365375 = 777.375. The entire roof minus the shafts = 4,860 square feet - 777.375 = 4,082.625 square feet of surface in Fig. 197.

In Fig 198 is shown the plan, front, and side elevations of an intersected hipped roof. A B C D represents the plan of the main building intersected by the wing E F G H. We will figure the main roof as if there were no wing attached and then deduct the space taken up by the intersection of the wing. While it may appear difficult to some to figure the quantities in a hipped roof, it is very simple, if the rule is understood. As the pitch of the roof is equal on four sides the length of the rafter shown from O to N in front elevation represents the true length of the pitch on each side. The length of the building at the eave is 90 feet and the length of the ridge 48 feet. Take 90 - 48 = 42, and 42/ 2 = 21. Now either add 21 to the length of the edge or deduct 21 from the length of the eave, which gives 69 feet as shown from S to T. The length of the eave at the end is 42 feet and it runs to an apex at J. Then take 42 feet/ 2 = 21, as shown from T to U. If desired the hip lines A I, J B and J C can be bisected, obtaining respectively the points S, T, and U, which when measured will be of similar sizes; 69 feet and 21 feet. As the length of the rafter O N is 30 feet, then multiply as follows: 69 X 30 = 2070. 21 X 30 = 630. Then 630 + 2,070 = 2,700, and multiplying by 2 (for opposite sides) gives 5,400 square feet or 54 squares of roofing for the main building. From this amount deduct the intersection E L F in the plan as follows:

Roof Mensuration 0900217

Fig. 197.

Roof Mensuration 0900218

Fig. 108.

The width of the wing is 24 feet 6 inches and it intersects the main roof as shown at E L F. Bisect E L and L F and obtain points W and V, which when measured will be 12 feet 3 inches or one half of HG, 24 feet 6 inches. The wing intersects the main roof from Y to F1 in the side elevation, a distance of 18 feet. Then take 18 X 12.25 = 220.5. Deduct 220.5 from 5400 = 5,179.5. The wing measures 33 feet 6 inches at the ridge L M, and 21 feet 6 inches at the eave F G, thus making the distance from V to X = 27 feet 6 inches. The length of the rafter of the wing is shown in front elevation by P R, and is 18 feet. Then 18 X 27.5 = 495, and multiplying by 2 (for opposite side), gives 995 sq. ft. in the wing. We then have a roofing area of 5,179.5 square feet in the main roof and 995 square feet in the wing, making a total of 6,174.5 square feet in the plan shown in Fig. 198.

If it is desired to know the quantity of ridge, hips, and valleys in the roof, the following method is used. The ridge can be taken from the plans by adding 48' + 33'6" = 81' - 6". For the true length of the hip I D in the plan, drop a vertical line from I1 in the front elevation until it intersects the eave line 1°. On the eave line extended, place the distance I D in the plan as shown from 1° to D° and draw a line from Do to I1 which will be the true length of the hip I D in the plan. Multiply this length by 4, which will give the amount of ridge capping required. This length of hip can also be obtained from the plan by taking the vertical height of the roof Io I1 in the elevation and placing it at right angles to I D in the plan, as shown, from I to I2, and draw a line from I2 to D which is the desired length.

For the length of the valley L F in the plan,k drop a vertical line from F1 in the side elevation until it intersects the eave line at Fo.