This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
Fig. 96 shows how to find the angle between the tangents of the face-mould for the bottom wreath, which, as shown in Fig. 95, is to span over the first plan quadrant a b. The elevation tangents a" and b", as shown, will be the tangents of the mould. To find the angle between the tangents, draw the line a h in Fig. 96; and from a, measure to 2 the length of the bottom tangent a" in Fig. 95; the length from 2 to h, Fig 96, will equal the length of the upper tangent b", Fig. 95.
From 2 to 1, measure a distance equal to 2-1 in Fig. 95, the latter being found by dropping a perpendicular from w to meet the tangent b" extended. Upon 1, erect a perpendicular line; and placing the dividers on 2, extend to a; turn over to the perpendicular at a"; connect this point with 2, and the line will be the bottom tangent as required on the face-mould. The upper tangent will be the line 2-h, and the angle between the two lines is shown at 2. Make the joint at h square to 2-h, and at a" square to a"-2.
The mould as it appears in Fig. 96 is complete, except the curve, which is comparatively a small matter to put on, as will be shown further on. The main thing is to find the angle between the tangents, which is shown at 2, to give them the direction to square the joints.
In Fig. 97 is shown how to find the angle between the tangents c" and d" shown in Fig. 95, as required on the face-mould. On the line h-5, make /i-4 equal to the length of the bottom tangent of the wreath, as shown at h"-4 in Fig. 95; and 4-5 equal to the length of the upper tangent d". Measure from 4 the distance shown at 4-6 in Fig 95, and place it from 4 to 6 as shown in Fig. 97; upon 6 erect a perpendicular line. Now place the dividers on 4; extend to h; turn over to cut the perpendicular in h"; connect this point with 4, and the angle shown at 4 will be the angle required to square the joints of the wreath as shown at h" and 5, where the joint at 5 is shown drawn square to the line 4-5, and the joint at h" square to the line 4 h".
Fig. 100. Plan of Curved Steps and Stringer at Bottom of Stair.
Fig. 98 is a diagram of tangents and face-mould for a stairway having a well-hole at the top landing. The tangents in this example will be two equally inclined tangents for the bottom wreath; and for the top wreath, one inclined and one level, the latter aligning with the level rail of the landing. The face-mould, as here presented, will further help toward an understanding of the layout of face-moulds as shown in Figs. 96 and 97. It will be observed that the pitch of the bottom rail is continued from a" to b", a condition caused by the necessity of jointing the wreath to the end of the straight rail at a", the joint being made square to both the straight rail and the bottom tangent a". From b" a line is drawn to d", which is a fixed point determined by the number of risers in the well-hole. From point d", the level tangent d" 5 is drawn in line with the level rail of the landing; thus the pitch-line of the tangents over the well-hole is found, and, as was shown in the explanation of Fig. 95, the tangents as here presented will be those required on the face-mould to square the joints of the wreath.
In Fig. 9S the tangents of the face-mould for the bottom wreath are shown to be a" and b". To place tangent a" in position on the face-mould, it is revolved, as shown by the arc, to m, cutting a line previously drawn from w square to the tangent b" extended. Then, by connecting m to b", the bottom tangent is placed in position on the face-mould. The joint at m is to be made square to it; and the joint at c, the other end of the mould, is to be made square to the tangent b".
Fig. 101. Finding Angle between Tangents for Squaring Joints of Ramped Wreath.
The upper piece of wreath in this example is shown to have tangent c" inclining, the inclination being the same as that of the upper tangent b" of the bottom wreath, so that the joint at c", when made square to both tangents, will butt square when put together. The tangent d" is shown to be level, so that the joint at 5, when squared with it, will butt square with the square end of the level-landing rail. The level tangent is shown revolved to its position on the face-mould, as from 5 to 2. In this last position, it will be observed that its angle with the inclined tangent c" is a right angle; and it should be remembered that in every similar case where one tangent inclines and one is level over a square-angle plan tangent, the angle between the two tangents will be a right angle on the face-mould. A knowledge of this principle will enable the student to draw the mould for this wreath, as shown in Fig. 99, by merely drawing two lines perpendicular to each other, as d" 5 and d" c", equal respectively to the level tangent d" 5 and the inclined tangent c" in Fig. 98. The joint at 5 is to be made square to d" 5; and that at c", to d" c". Comparing this figure with the face-mould as shown for the upper wreath in Fig. 98, it will be observed that both are alike.
In practical work the stair-builder is often called upon to deal with cases in which the conditions of tangents differ from all the examples thus far given. An instance of this sort is shown in Fig. 100, in which the angles between the tangents on the plan are acute.