Fig. 88. Plan Line of Rail Projected into
Oblique Plane Inclined to One Side Only.
In [Fig. 89] is shown the geometrical solution—the one necessary to find the angle between the tangents as required on the face-mould to square the joints of the wreath. The figure is shown to be similar to [Fig. 87], except that it has an additional portion marked “Section.” This section is the true shape of the oblique plane whereon the wreath ascends, a view of which is given in [Fig. 88]. It will be observed that one side of it is the developed tangent m; another side, the developed tangent a″ (= a). The angle between the two as here presented is the one required on the face-mould to square the joints.
In this example, [Fig. 89], owing to the plane being oblique in one direction only, the shape of the section is found by merely drawing the tangent a″ at right angles to the tangent m, making it equal in length to the level tangent a in the plan. By drawing lines parallel to a″ and m respectively, the form of the section will be found, its outlines being the projections of the plan lines; and the angle between the two tangents, as already said, is the angle required on the face-mould to square the joints of the wreath.
The solution here presented will enable the student to find the correct direction of the tangents as required on the face-mould to square joints, in all cases of practical work where one tangent of a wreath is level and the other tangent is inclined, a condition usually met with in level-landing stairways.
[Fig. 90] exhibits a condition of tangents where the two are equally inclined. The plan here also is taken from [Fig. 86]. The inclination of the tangents is made equal to the inclination of tangent b in [Fig.86], as shown at m in [Figs. 87], [88], and [89].
Fig. 89. Finding Angle between Tangents.