Rolling Spirals for Staircases

The size of a staircase is usually indicated by 4 dimensions; The Horizontal Diameter or Radius of the railing, the Total Height of the staircase, the Total Arc (in degrees) of the staircase and last but certainly not least, the Direction of Rise (clockwise or counterclockwise).

The height of the staircase will be 120” and its radius at the rail will be 48”. The railing will be going up in a counter-clockwise direction. In order to make a spiral, all this information is needed although it may come in different forms. For instance, the rise and run of a step, the number of steps, might replace the total height and the total arc of the staircase, but this is less desirable.

The first step in determining a rolling radius to find the horizontal circumference of the portion of a circle being used by the staircase, in this case 270deg.. NOTE: A triangle will best illustrate each of the following steps. The horizontal circumference is represented by the Base Line of the triangle.

Step #1 – Base Line of Triangle

48” x ∏(3.14159) = 150.8”. Now x 270 = then ÷ 180 = 226.2”. This is the base of our triangle. With a total height of 120” we will now figure the length of the hypotenuse of our triangle, which will represent the Arc Length of your work-piece.

Step #2 – Figuring the Arc Length.

120 ² + 226.2 ² = 65566.44, now (square-root), you get 256.05”.

This number represents the amount of material (Arc Length) required to do the project.

Step #3 – Figuring the Rolling Radius.

256.05” ÷ 226.2” = 1.132. Now 1.132², you get 1.2814 now x 48” = 61.508”. Your rolling radius is 61.5”.

In short:

Step #1: Radius x ∏(3.14)=___ x Arc of staircase =___ ÷ 180 = Base line.
Step #2: Height² + Base line² =___ √(square-root) =Arc Length.
Step #3: Arc length ÷ Base line =___² x Radius = Rolling Radius.

Note:Any size spiral can be figured using the above method.