Trying to figure out some problems here and hoping someone can help out, or point me to the correct information. I'll divide the problem into three parts

Part 1

Suppose you have a fixed cylinder, such as a column, and wrapped around the cylinder is some string. To keep things simple, the thickness of the string is negligible. Let's label the radius of the column as 'r'. Now suppose that you unwrap a portion of the string, take the loose end and pull it until it is taught. We will label the length of the loose part from where you are standing to where it makes contact to the column as 's'. Now I want to calculate the distance 'd' from where you are standing to the center of the column.

I believe I have the answer, but am not sure. The line segments s, r, d form a right triangle where the angle between s and r are 90 degrees. So d should be calculated as Sqr(s*s + r*r). is this correct?

Part 2

Suppose I start to walk around the column so that the string unwinds itself. Say the angle I walk around is 'a'. How much string will now be unwound and what is now the current distance?

I believe you would need to divide the circumference by 360/a. So c = 2*pi*r then s = s + c/(360/a)

Part 3, the part I am heading to and most confused by

Suppose that the string is wrapped around two or more columns? How would it affect the calculations above?

Answer: no idea!