The term geometrical is applied to stairways having any kind of curve for a plan. The rails over the steps are made continuous from one story to another. The resulting winding or twisting pieces are called wreaths.

Wreaths

The construction of wreaths is based on a few geometrical problems - namely, the projection of straight and curved lines into an oblique plane; and the finding of the angle of inclination of the plane into which the lines and curves are projected. This angle is called the bevel, and by its use the wreath is made to twist.

Fig. 82. Geometrical Stair with Winders all Around Cylinder.

Fig. 83. Plan and Elevation of Stairs Turning around a Central Post.

In Fig. 84 is shown an obtuse-angle plan; in Fig. 85, an acute-angle plan; and in Fig. 86, a semicircle enclosed within straight lines.

Projection

A knowledge of how to project the lines and curves in each of these plans into an oblique plane, and to find the angle of inclination of the plane, will enable the student to construct any and all kinds of wreaths.

The straight lines a, b, c, d in the plan, Fig. 86, are known as tangents; and the curve, the central line of the plan wreath.

The straight line across from n to n is the diameter; and the perpendicular line from it to the lines c and b is the radius.

A tangent line may be defined as a line touching a curve without cutting it, and is made use of in handrailing to square the joints of the wreaths.