The bend radius of the cable is known as the D:d ratio. This represents the ratio of the pulley sheave diameter (D) to the cable diameter (d). The for 7x19 stranded wire rope the recommended D:d ratio is 51:1, so the recommended sheave diameter for 3/32" diameter cable is 51 x 3/32, which equals 153/32, or about 5". The minimum ratio is 34:1, which is means that a 4" pulley is typically used as they are commonly available. Ref: American Iron and Steel Institute "Wire Rope Users Manual, 2nd Edition", Table 9.
In the picture above we have a variety of design issues:
The cable is 1/8" diameter plastic-coated wire rope. It is a bit larger diameter than the required 3/32", so it would require an even larger sheave, about 6". As you can see, the pulley is only about 1-1.5" diameter, or about 1/4th the required size. This can cause the cable to 'take a set' and get a kink in it so that it doesn't want to move freely through the sheave. I've seen wire rope as large as 1/4" diameter used with pulleys like this - and they definitely take a set after resting immobile for years on end.
The cable's plastic jacket might melt and gum-up the works should there be a fire - not good.
Although this rigging point isn't bearing a significant load, it's still jsut bad juju to use pot-metal dime-store clothes-line pulleys, twisted-link 'dog chain', and quick-links to string stuff up. Man-up and install it right with load-rated equipment - after-all, this is a Fire Curtain System, not just a trick-line for a one-act play!
Have your Fire Curtain System Inspected Annually. Ref: 2010 NFPA 80, Section 20.9.1.
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