circular stairway handrail roll radius

huangyhg

circular stairway handrail roll radius
how do i calculate the radius to roll the railing for a circular stairway?  i know the plan radius and stairway angle.  i know this is simple but it eludes me!
divide the horizontal radius of the handrail by the cosine squared of the slope angle, where the slope angle is the angle between horizontal and the handrail.
the actual handrail shape is a helix.  rolling a handrail to a circular arc only approximates the shape.  the handrail has to be twisted slightly as it is installed, after rolling.
the formula above is derived by taking a very short section of handrail, finding the deviation from a straight line, and then solving for the radius that will give that deviation with the actual sloped length as the arc, with small-angle approximations applied as needed.