Axel, I thought you read the forum points on pulleys?
Any triaxial stress analysis program (Prestress v3.0; ANSYS, et al) will tell you that the arc angle can cause varying degrees of buckling stress when the shell contact angle is in the 60 degree neighborhood verses 180 wrap. Below 20 degrees it again becomes less critical.
Lyle's second reference leads to some earlier corrections of the hoop stress sensitivity by degrees of wrap. This is a so-so substitute for a proper analysis.
Make-em fat and sassy, the iron ore industry will love you.
Contact stress vs pulley diameter is another matter. Now you get into twist wind-up on wires et al.
Since contact pressure or normal force is proportional to Fn = Tension/Radius, you can do the sums with respect to any reduction in diameter that will not exceed your shell theory of the moment.
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