Analysis of the formation and elimination of loops in twisted cable

Serious failures of ocean cable have resulted from the phenomenon known as hockling. When a cable is under tension, helical windings can cause the cable to twist. With relaxation of the tension, loops can form. Reapplication of tension tightens the loop, and at some point the loop in the cable may be eliminated or pop out. If it does not but hockles instead, serious damage will result. An analysis is made of the conditions for loop formation and pop-out. The force versus displacement at the ends of a twisted cable and the point at which the cable flips into a loop are derived in closed form from the basic differential equations of an elastica. From this, the maximum allowable cable slack is derived as a function of the cable's twist per unit length. For a cable in the looped configuration, the cable tension at which the loop pops out and the maximum curvature in the loop at the instant of pop-out are found as functions of the cable diameter, torque, and mechanical properties.