Here’s an awesome pic of a stair railing idea. This stair is part of an ellipse; see how one side of the handrail rises faster than the other. That’s because each side of that stair is describing a different arc. Since they cover the same distance, the inside railing has to rise faster than the outside. This presents an extreme challenge for the stair builder and an even greater one for the trim carpenter.
The stair builder generally will make some sort of template to copy the shape of each arc. This must then be translated into three dimensions. The trim carpenter deals with the same issues but with much smaller tolerances: ZERO. Good trim carpentry requires joints that are flawless and this railing is exemplary.
