Machinery's Handbook offers some guidelines for minimum sheave diamters for long life. See "wire rope".

Regards,

Mike

It depends on the construction of the cable.

See this URL too.

"Art without engineering is dreaming; Engineering without art is calculating."

Have you read FAQ731-376 to make the best use of Eng-Tips Forums?

I'm sure of the strand specification yet, but it will be stainless steel material.

A lot of hoisting and rigging handbooks will tell you the strength reductions of various cables on different radius pins or sheaves.  
Cheers

The manufacturer is the best choice, especially if you're pushing the limit.  Machinery's just doesn't cover all of the variations in this day and age.  The age and condition of the cable makes a difference, as does oiled or dry, marine or land-based, dirty environment or clean, etc, etc.

MacWhite's Catalog G-18 suggests a minimum diameter ratio (drum diameter/cable diameter) of 40 for 7x19 stainless cable.  Worst case, they say, should be at least 30.  We use a 12:1 ratio around here for 7 x 19 galvanized aircraft cable and the life is not good (measured in hours, not 100s of hours).  There are more flexible cables made that allow the use of smaller ratios.

I work with smaller diameter steel rope typically from Ø2,5mm to Ø5,0mm as used in parking brake designs etc, and generally we apply 10 times outer diameter, this is with 7*19 cable construction and achieve 1 million cycles / actuations.
Cable routing is also key, i,e, too many bends will increase hysteresis and reduce efficiency.
I thought this website was quite good, at least demonstrates the cable construction:-
http://www.tecni-cable.co.uk/s.nl