When calculating the rise of a curved handrail would you use the length of the arc or the chord length?

Question

Im looking to write a script that will generate handrail from 2D geometry. One element would be the radius of the arc & the other would be a line that would represent the rise. However, Im not sure whether the length of this rise would be the length of the arc or the chord length. I know what the drop is from the top to btm of handrail.

Answer 1

Think you need the angle through which the handrail turns from top to bottom too

3D model/picture I'm getting of how to model things is as follows. A large fixed s***w thread running vertically, and an arm (with a nut) holds the CSA of the handrail, a fixed distance away from the s***w. When the arm rotates around the s***w thread, the arm goes up a certain amount per revolution, and the CSA of the handrail traces out the "volume" of the handrail. The total distance the arm is raised is the rise, and it relates to the angle through which the helix turns (per 360 degrees, it's called the pitch or advance),rather than the length of the arc .

Hope the link I provided is of some help with the mathematics involved. It's got a formula which relates arc length to radius and pitch (ie 1 complete 360 deg rotation)

Answer 2

It sounds like you are talking about a spiral rail.  The only way to describe it in two dimensions is with a circular radius in plan and a difference in elevation from start to end.  From this you should be able to calculate length and all the details of the spiral.  Just don't ask me how to do it.

Answer 3

Arc length, the Rise is generally tip to tip, since the cord Length is center of the handrail you will not have accurate results.