I've been trying to find a way to calculate the contact pressure between a rope under tension and a pulley (free to move, or fixed). I'm expecting to find an equation that considers the wrap angle - similar to the capstan equation - but I'm specifically looking for an expression for the contact angle. Not concerned about the mass of the rope, in my problems the force applied is far greater than the weight of the rope.
EDIT: I need this to consider friction between the rope and the pulley - just like the capstan equation. Consider a fixed pulley with a very large radius, and a very high contact friction. In this case, you would expect the region close to the centre of the contact area to have a lower contact pressure.