The optimum spanning catenary cable

Abstract

A heavy cable spans two points in space. There exists an optimum cable length such that the maximum tension is minimized. If the two end points are at the same level, the optimum length is 1.258 times the distance between the ends. The optimum lengths for end points of different heights are also found.

Optimization and Form-finding of the Heavy Cable Suspending a Deck

“…Table 2 shows the optimum cable length for various deck relative weights and height ratios h. The optimum length (for minimum tension) increases with both deck weight and height difference. The = 0 (cable without a deck) values agree, to 1%, with the results of the free catenary studied by Wang [23]. Fig.…”

“…The third class of optimization considers the uniform cable with minimal maximum tension. Such an optimum was found by Wang [23] but only for the uniform catenary (without a load) and Wang [24] for the catenary with a single concentrated load. Minimizing total weight is different from minimizing tension.…”

Errata and Addenda to Mathematical Constants

“…. Also, sinh(µ) = 1.5088795615... occurs in asymptotic combinatorics and as an extreme result in complex analysis [538,539,540,541]; sinh(µ)/µ = 1.2577364561... occurs when minimizing the maximum tension of a heavy cable spanning two points of equal height [542].…”

Calculation of Optimal Length for Skyline

“…Technical means of skyline system are widely used in many branches of engineering [1], [15,16], in particular in the logging and timber industries. At present, in the process of forestry, especially in difficult terrain, soil, and hydrological conditions, cable logging systems and snubbing have been widely used [2], [7], [11], [13,14].…”