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In stricter senses, the term wire rope refers to a diameter larger than 9.5 mm (3 ⁄ 8 in), with smaller gauges designated cable or cords. [1] Initially wrought iron wires were used, but today steel is the main material used for wire ropes. Historically, wire rope evolved from wrought iron chains, which had a record of mechanical failure.
Consider a long, thin wire of charge and length .To calculate the average linear charge density, ¯, of this one dimensional object, we can simply divide the total charge, , by the total length, : ¯ = If we describe the wire as having a varying charge (one that varies as a function of position along the length of the wire, ), we can write: = Each infinitesimal unit of charge, , is equal to ...
A cable in this usage cable is a thick rope or by transference a chain cable. [1] The OED gives quotations from c. 1400 onwards. A cable's length (often "cable length" or just "cable") is simply the standard length in which cables came, which by 1555 had settled to around 100 fathoms (600 ft; 180 m) or 1 ⁄ 10 nautical mile (0.19 km; 0.12 mi). [1]
A typical 11 mm (0.43 in) UHMWPE rope of 30 m (98 ft) can weigh around 2 kg (4.4 lb), the equivalent steel wire rope would weigh around 13 kg (29 lb). One notable drawback of UHMWPE rope is its susceptibility to UV damage, so many users will fit winch covers in order to protect the cable when not in use.
If the weight of the roadway per unit length is w and the weight of the cable and the wire supporting the bridge is negligible in comparison, then the weight on the cable (see the figure in Catenary#Model of chains and arches) from c to r is wx where x is the horizontal distance between c and r. Proceeding as before gives the differential equation
In the metric system of measurement, the nominal diameter is given in millimetres. The current preferred international standard for rope sizes is to give the mass per unit length, in kilograms per metre. However, even sources otherwise using metric units may still give a "rope number" for large ropes, which is the circumference in inches. [6]