Laying out a Staircase
Building any kind of staircase, whether from wood, iron or concrete, requires precise calculation before even beginning construction. Even though it can be quite simple, with the wrong calculations, it could quickly turn into a nightmare. To make everyone's life a little easier, there is a calculation module which provides answers within the blink of an eye or, more appropriately, the click of a button.
The drawing below will help you understand the issues and elements you need to take into account. Simply enter the values you are going to calculate either on the location you are going to install your staircase or on the blueprints you will have at the site.
After this, it's time for some simulations. For instance, figure out the number of steps necessary for balancing comfort with space constraints. To make a comfortable staircase, it is best to have the rise between 16-17 cm (6,3" to 6,7") tall and the run (or going) about 28 to 30cm (11" to 12") long. In any case, the tread should never be smaller than 23cm, and the risers should not exceed 21 cm (8"1/4) tall.
The Step and The Pitch line
The step length can be solved using Blondel's Formula: add the tread length to the height of two risers. The step length must be between 56 and 67 cm. For the best results, aim between 62 and 64cm. To get a more comfortable staircase, it is best to have the treads around 30 cm long and the risers 15 to 20cm tall. It is highly recommended that the headroom be higher than 2 meters.
To calculate a spiral staircase, a half spiral, quarter spiral, helical or even straight with a curvature, you just need to think of it as straight and apply the formulas to the pitch line The pitch line is 50cm from the interior handrail, or in the middle, if the clearance width is less than a meter.
To find the length and the angle of the pitch line for a spiral staircase, go to page: "Calculating an Evolute Helix". This calculation module will also allow you to find the length of a handrail for this kind of staircase.
Winding
Winding is when you alternate where you place the edges of the steps in the curvature/s in a staircase.
By reducing the gap between the narrowest and widest parts of the tread, walking up the where the steps curve is easier. The staircase is better balanced, therefore much easier to walk up and down.
While drawing, make sure to keep the same distance between the treads and the pitch line. Rotate the walkline where it intersects with the pitch line (compare the axis of rotation as illustrated in the figure).
Then shift the walkline of the first and second straight steps that follow to get a harmonious effect.
For better ergonomics and aesthetics, the distance from tread to the pitch line should stay identical for every step of the staircase.
There is no formula to define the angles of rotation. To find the perfect angle for each step, draw a blueprint and modify it one paper first.
Winding is for quarter-spiral, third-spiral and half-spiral staircases, but it can't be used with a full spiral.