The laying out of the roof plan for a building is a problem which requires some little thought and skill and it may be well to give a little space to a consideration of the best way in which to approach this problem. Suppose that we have a frame building whose general outline in plan is as shown in Fig.

175, and on which we wish to plan a hip and valley roof. There are, we will say, two projections or wings on the front of the building, at A A, another wing on the right-hand side of the building at B, and another wing on the back of the building at C.

The first thing to do is to draw the rectangle A B C D, in Fig.

176, enclosing the main portion of the building, and leaving out the wings or projections. From each corner of the rectangle A B C D, may be drawn a line at forty-five degrees, with the side of the rectangle, each pair of which will meet at the points R R, and these points R R may be connected by a line parallel to the long sides of the rectangle. This is a plan of a simple hip roof covering the main portion of the building, E being the ridge and G G G G being the hip lines. The projecting portions or wings are, however, not yet covered and in order to take care of them some further planning is necessary. Let us consider the two wings on the front of the building, marked A A, in Fig. 175. We will decide to cover these with a simple gable roof and for this the first step is to draw in the ridges. These ridges will, of course, come exactly in the center of the wings and will be shown on the plan by a line in the center of the plan of the wings, perpendicular to the line of the front. These lines should be drawn in as shown in Fig. 177, where they are marked E E. The lines E E intersect the hip lines marked G G, in Fig. 176, at a point about half way between the corners D and C, and the peaks R R. In order to look well the slope or pitch of the sides of the pitch roof which covers the wings A A, must be the same as the slope or pitch of the end of the hip roof shown in Fig. 176 and there marked S S, and thus the roof of the wing A will on that side become a part of the roof over the main portion of the building, and the lower portion of the hip line G may be erased, leaving only the upper portion showing as a hip, as indicated in Fig. 177. The other side of the pitch roof over the wing A will, however, not correspond with any slope in the roof over the main portion of the building and must intersect it in some line. Since the ridge E is at the top of this roof surface and the wall line of the wing A is at the bottom of the roof surface, a line drawn from the corner in which the wall line of the wing intersects the wall line of the main portion of the building, to the point in which the ridge line intersects the hip line of the main roof, will be the line of intersection of the two roofs. This line is shown in Fig. 177, where it is marked F. The line F in the plan, Fig. 177, will represent a valley. Thus we have the two wings, A A, Fig. 175, completely roofed over, and the small roofs connected to the large main roof.

Fig. 175. Ground Plan of Building on Which Rafter Must Be Placed.

Fig. 176. Plan of Roof Covering Main Portions of the Building.

Fig. 177. Added Development of Roof Plan Covering Wings A, B, and C of Fig. 175.

Suppose that we wish to cover the wing on the right-hand side of the building also with a simple gable roof. This wing is marked B in Fig. 175. We proceed in the same way as explained for the wings A A, drawing the ridge line E, in Fig. 177, until it intersects the hip line of the main roof G and then drawing the valley line F. The slope on the back side of the roof over the wing B should have the same slope as the back side of the main hip roof and, therefore, the lower part of the hip line G, starting at the point B, can be erased, leaving only the three lines, E, F, and G, shown in Fig. 177. Thus the wing B is completely roofed over and shown in plan. The line F in this case also represents a valley. Suppose that we wish to cover the wing on the back of the building, marked C in Fig. 175, with a hip roof instead of a gable roof.

We will start at the outside corners, and from these points draw lines G G in Fig. 177 at forty-five degrees with the front and side wall lines of the wing, until they meet. The lines must meet exactly in the center of the wing between the two side wall lines, and from this point a line should be drawn at right angles to the front wall line of the wing, but away from this wall line instead of towards it. This line is marked E in Fig. 177. It will intersect the hip line G of the main roof and from this point of intersection a line F should be drawn at forty-five degrees, which will meet the side wall line of the wing in the point in which this side wall line meets the main wall of the building. One slope of the roof over the wing C, Fig. 175, will be the same as the slope of the end of the main hip roof, and so the lower part of the line G, starting at the point A, may be erased and the upper part only left to show as a hip line. The line F in this case also will be a valley line. Thus the wing C, Fig. 175, will be completely roofed over and shown on the plan. Our roof plan is now complete in outline, all the lines marked E being ridges, all the lines marked G being hip lines, and all the lines marked F being valley lines. The same method of procedure may be followed out in the case of any roof plan, and the final complete plan obtained by successive steps as explained above. The first step is always to lay out the roof over the main portion of the building and then to proceed with the roofing of the projecting portions or wings.