Jack Rafters. The length of jack rafters may be obtained by using Formula 24, which is applicable to all pitches and angles.

R4 = run of jack rafter.

A2 = rise of jack rafter.

C = constant, which may be found by calculating the ratio of the rise of the jack rafter to its run. In a half pitch it = 1.00; in a third pitch, it = .67, and in a quarter pitch, it = .50.

D = horizontal thickness of the hip rafter at the angle of its intersection with the jack; upon a rectangular corner D would - 2.823".

H = length of the jack rafter.

Formula 24. H = rafter vertical diagram a, b, c, scaled, upon the bevel board; slide the square back from the rise, ac, of the common rafter upon the base line, ab, the distance equal to J of Formula 25. J1 will give the distance, less the length of the common rafter, which the jack rafter should be cut, and from this must be subtracted T4 of Formula 25. (See T3 of Formula 20, Fig. 78.) The result thus obtained will be the actual length of the longest jack, and the others will be shortened a distance equal to the pitch line of j, or the distance J1 of Fig. 84.

A method of using the steel square to find the lengths of the jack rafters or of roofs of any pitch or angle is illustrated by Fig. 84, which is based upon quarter pitch, common rafters spaced two feet to centers. In finding the length of the jack rafter, draw the common

Fig. 84. - Method of finding the Lengths of Jack Rafters.

In using the square to lay out the length of the jack rafters, the following formula may be applied, if the center of the common rafter is placed at the apex of the hip rafter.

J = horizontal distance between centers of jacks.

H = length of jacks.

H1= length of common rafter.

T4= pitch line of jack rafter, of the diagonal of the thickness of the hip.

j1= pitch line of J.

Formula 25. H = H1 -(T4 / 2+ J1).

The above assumes that a common rafter is located at the apex of the hip; but if the center line of its top edge is not in line with the apex of the hip rafter, as shown in the rafter plan at m, Fig. 80, the above formula may be used by changing J in the formula key to read as follows: J = distance between the apex of the hip rafter, and the center line of the longest jack, as at n, Fig. 80. This will give only the length of the longest jack; the length of the others may be found by shortening each one a distance equal to J1.

Many framers use the lower end of the hip rafter as the starting point, instead of the apex of the hip. The length of the first, or shortest jack, equals J1 - T4 of the above formula, laid off upon the base line of the roof, and each rafter is made longer than the preceding one, by a distance equal to J1.

The same principle is applied, but J1 is added instead of subtracted, as described.

In favor of this method it may be said that if the rafters are set 2' to centers, throughout the length of the house, there may be less waste of stock in cutting sheeting, and in covering boards, and, if an open finish house is being built, uniformity in the spacing of the lookouts may sometimes be obtained more easily than if the common rafters were fixed at the apex of the hip rafters.

In finding the plumb and the seat cuts of jack rafters, the same constants are used as when cutting the common rafters. The side or cheek cuts are obtained in the same way as those of a hip rafter, since the jack comes in contact with the hip at the same horizontal angle as the hip and the ridge.