Elevator compensating cable having a selected loop radius and associated system and method

A compensating cable adapted to be operably engaged with an elevator car, the compensating cable comprising:

• a core layer;
• a first sheath layer disposed about the core layer and comprising a first polymeric material having a first hardness;
• a second sheath layer disposed about the first sheath layer and comprising a second polymeric material having a second hardness;
• and a third sheath layer having a substantially circular outer cross-section and disposed about the second sheath layer, the third sheath layer comprising a third polymeric material having a third hardness, such that the relative first, second, and third polymeric materials of the compensating cable cause the compensating cable to form a substantially catenary arcuate portion having a radius no greater than a selected maximum loop radius;
• wherein the first, second, and third hardnesses are substantially equivalent;
• and wherein the first, second, and third polymeric materials comprise PVC and the first, second, and third hard nesses are about 84 Shore A.