Winding Stairs Spindles

[Westy 1971]

Happy Weekend to all you woodworkers out there.

I’m fitting turned timber spindles and handrails on an approximately 1000 Diameter winding staircase. I’ve fitted the inside spindles and nearly got the angles correct using measurements from an existing replica. However due to some height differences and cutting errors, I’m seeing lumps where the handrail passes over the spindles instead of a nice smooth curve.

Does anyone know how to calculate the angle from the outside to the inside of the inner-spindle that allows a decent handrail join?

My centring is good but I think I’ve used the wrong angle to set the outside edge of the spindle.
Thanks a million!

[Job and Knock]

I seem to recall that when seeing this sort of job was done years ago the spindles were inserted into holes drilled into the underside of the handrail then fixed using pins driven in at an angle from the "uphill" side to keep the height more or less constant above the treads (except in the areas of the wreath at the bottom an the transition at the top) in order to forestall this very issue. In a real world scenario I cannot see that any formula would be of assistance in dealing with the issue.