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The round tool hanging from the rope close to the person to the left is perhaps a stone helping the ropemakers to gauge that sufficient tensile stress is present. Classical ropes appear with an easy discernible geometrical structure, even though they have been fabricated in different human cultures from a large variety of fibrous materials with diverse physical properties.

Relatively recently, Zhang et al. Why does the resulting geometry of rope appear so similar, as if it depends little on the material used, and why are ropes inextensible? Here we show, that these properties of rope are due to a universal behavior of helical structures which depends on geometry. One consequence is that a tightly laid rope, where each of the strands are rotated to their maximum in one direction while being helically laid with the maximum number of rotations in the opposite direction will be interlocked, unable to unwind, and hence a functional rope.

We notice that this structure must be maximally rotated. If it were not maximally rotated another structure would have more repeats per unit length of tube. Recently, we have determined the close-packed helices from a calculation of the volume fraction for a helix as a function of the pitch angle. It is surprisingly simple to see that there is a geometrical limit to the number of rotations on a helix, and that helical structures can be maximally rotated. A helical curve in three-dimensional space is uniquely described by two independent variables; in differential geometry it is common to use curvature and torsion.

For a description applicable to ropes formed from tubular strands, we will use n r , L r as parameters, where n r is the number of turns the helical strands makes on the imaginary cylinder of the rope, and L r is the length of the rope. Not all combinations of n r , L r are allowed and some are forbidden because of tubular interactions.

Red thread of fate

The helical tubes are assumed to have hard walls and are therefore not allowed to intercept each other. The allowed values of n r , L r are gray shaded in fig. The solid line is the boundary case where the helical tubes are in contact with each other, i. Hence the solid line in fig. If a rope is laid under tensile stress one obtains the structures that correspond to the upper part of the solid curve. This follows from considering a point n r , L r within the shaded area of fig.

In this case the point will move vertically until it reaches a point on the upper curve. The lower part corresponds to strands that are laid out flat on top of each other and then twisted around following the imaginary cylinder, which radius becomes smaller and smaller as one progresses along the curve towards the tip.

Anberlin - The Unwinding Cable Car

At the tip of the curve the radius of the imaginary cylinder is larger than the radius of the strands, i. The curve shown is for a two-, three- and four-stranded rope from left to right, respectively. The shape of these curves is universal for ropes with a given number of strands, while the specific number of rotations depend on the diameter and the length of the rope. Now we discuss in more details how fig. The length of the fabricated rope, L r , is These equations contain the radius, a , of the imaginary cylinder hosting the helical lines.

The reduced pitch, h , is given as The requirement that the minimum distance between two strands is equal to the strand diameter is solved in two steps. Then, the radius a is found by the requirement that the nearest distance equals the strand diameter, D. The peculiar point on the curve in fig.

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At this point it is impossible for the strand to be further twisted. These maximally rotated N -helices have the property that stretching will neither make the individual strands rotate in one direction, nor in the other. Henceforth, we therefore denote these helices as being zero-twist structures.

Generally, we will denote any structure that has a vanishing strain-twist coupling as being a zero-twist structure. An ideal representation of a two-, three- and four-stranded rope laid with a pitch angle corresponding to the maximally rotated zero-twist structures with the respective pitch angles of With these pitch angles, the strands will neither rotate in one or the other direction under vertical strain. Pitch angle, v ZT , for the zero-twist structures given as a function of the number of strands.

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For the zero-twist structure there is no coupling from strain to rotation. Further, to these helical structures one cannot add additional rotations. Such a rope would therefore be infinitely rigid when taken as an ideal tubular idealization with hard walls, i. In practice even a tightly laid rope will have some flexibility. One typical type of a classical rope has three strands where the individual strands each have two substrands. When flexibility is introduced by laying the rope close to, but not exactly at the zero-twist configuration, the rope will self-lock at the equilibrium given by Here n r is the number of turns the helical strands makes on the imaginary cylinder of the rope, and n s quantify the counter-rotation from the pre-twisting of the strands.

Discussion A consequence of the presented analysis is that it is a geometrical property of the rope, and not a material property, that is responsible for the nature of the equilibrium given by eq.

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This geometrical equilibrium of rope is what accounts for the unyielding nature of ropes their ability to maintain a constant length. On the long ropes fig. Look out for scorch marks on electrical fixtures such as sockets and switches or for damaged or frayed cables. If in doubt, a competent electrician should inspect and test the installation to ensure its safety. Ensure the cable reel, and all circuits fed via cable reels, are protected at source by a functioning residual current device RCD.

These RCDs are generally located in your electrical distribution board and should be tested frequently at least twice per year by pressing the test button. In addition they should be marked with a CE mark indicating compliance with the European Low Voltage Directive of and any other applicable European directives. Compliance with the standard ensures that the reel is adequately constructed and is fitted with a thermal cut-out or weak link which will trip the supply from the reel in the event of an overload.

In addition the overall electrical installation must be safe and adequately earthed with the cable reel and anything fed through the reel protected by a residual current device RCD. Healthy, Safe and Productive Lives. Managing Safety and Health in Schools. Teacher Support and Classroom Resources.

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Damage to Cables or Reels Other issues arise when the insulation on the cable becomes frayed and exposed. Precautions To avoid the risks associated with this hazard, the following precautions should be in place.

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Earthing Ensure your electrical installation is adequately installed and earthed.