Tension adjustment

this is going to sound like a dumb question but I'm having trouble figuring out the practical solution to the following problem:

I have a stressed cable fixed at one end and attached to a crank at the other. The cable has a linear density L, is at tension T, is length K and I want to increase tension to rT. The cable passes through a fixed node as it exits the crank. Can I calculate how many radians I need to crank based on radius (assume fixed)? My missing link here is how to calculate in advance, rather than "tighten until tension reaches rT," e.g.