The Packing Problem for Twisted Pairs

Pairs of telephone wires are often packed closely together in large numbers. These wires may belong to a cable or lie together on a shelf as jumper wires of a main distribution frame. To avoid inductive coupling, which produces crosstalk, the wire pairs are always twisted. A twisted pair packing problem arose with a proposal for monitoring the accumulation of inoperative jumper pairs on a main distribution 2143 frame. Robert Graham of Western Electric has developed a technique for measuring the cross-sectional area of a bundle of jumper wires. Telephone company records determine the number of working jumper pairs in the bundle. The total number of pairs, working or inoperative, could be estimated from the measured area if the density of pairs in the bundle were known. If each wire has radius r, a twisted pair has cross-sectional area AP -- 277-r2. The number N of pairs in a bundle of area AB is then N = fAa/Ap, (1) where f is the packing fraction (or density) of the bundle, the fraction of cross-sectional area filled by wire. Graham's measurements on spools of twisted pair wire suggest a value of /"near 0.5. That is a much smaller packing fraction than could be achieved with single wires or untwisted pairs. To show that twisting the pairs reduces the packing fraction, this paper looks for packings that are as dense as possible. The problem takes several forms, depending on what regularities the packing may be assumed to have. For instance, do the pairs all twist around parallel, straight-line axes? If so, do they all twist at the same rate (in turns per foot)? The most regular packings are the "lattice" packings described in Section IV.