Topic: Tether Dynamics in Kite Systems
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Aug. 31, 2020, post by Dave Santos
Space Tether Supercoiling Tech Brief:

Passive supercoiling of space tethers in slack condition promises to be a major method of tether management without need for complex reeling mechanisms and controls. Not only are there biological similarity cases, like DNA supercoiling, but also common coil-cases like telephone cords and air-compressor hoses, that have long proven useful. A related method used by large kite flyers is to store and deploy loosely laid tether from a bag, which works fairly well.

Microgravity is the ideal environment for reliable passive supercoiling. As we extend space tether topologies from simple 1D lines to 3D lattices, passive supercoiling may be an enabling technology, for example, to dynamically vary the geometry of space solar arrays, thermal radiators, and shades, without rigid latticework mechanisms. The weak force of solar wind, photo-pressure, or stronger thermo-elasticity can be tuned for cybernetic response of tether motion.
Aug. 30, 2020, post by Dave Santos
Supercoiling of NASA STS-75 Space-Tether

Some investigation into Space Tether dynamics, based on Kite Tether knowledge. This is a new item, with others in the pipeline, like the Mars Gravity-Energy Cableway concept you saw beginnings of, and grand expansion of KiteShip's Solar-Sailing Kite concepts, ca. 2004]

In a famous space mishap, NASA STS-75's 20km space tether mysteriously breaks; and in the video of the aftermath various odd phenomena occur. The break itself is easily explained as corona-discharge, by later inspection of the broken half, and lab testing. The more notorious oddities are the "UFO" appearance of small debris particles, as out-of-focus telescopic and digital image artifacts in the sunlight. These have been explained, and the UFO claims debunked.

More mysterious are the beautiful tether dynamics, starting with liquid-like phonons rippling along the unreeling tether, then especially what happened when the tether parted at its base.  The tether is seen drifting away and coiling up helically at the dimension it was stored on its reel. STS-75 orbit enters darkness, and for maybe more than one orbit there is no visual contact, but then the astronauts relocate the lost satellite by video-telescope about 150km away.

What NASA then sees was not predicted, as the puzzlement of the Control Center audio feed reveals. The 20km tether has taken on a radically shortened and widened supercoiled configuration analogous to a DNA double helix supercoiled into a chromosome (photo below). As the telescopic video camera is adjusted, the supercoil is seen shimmering with phonons. Its an almost magical object, that none of the official Mishap Reports seem to explain.

The initial coiling was obviously a polymer memory-effect of the composite tether stored on its reel. The reel-drum was sufficiently large and the level-winding pattern nicely uniform for a highly coherent order of the flattened tether on its reel, as a quasi-double-helix (helical band). Braided layers themselves did not introduce helicity, as braided windings cancel-out. The copper-wires were spiral wrapped, adding-to or canceling somewhat the dominant helical plastic deformation of the Teflon insulation.

What caused the supercoiling? A hidden mathematical series in the composite tether and its storage factor? A clue in the video is how the parted tether starts recoiling into its reel-storage helix dimension. An added bit of torsional twist evident as the tether-end does a slow turning. Somewhere in the tether manufacture, its axis was rotated unnoticed, even by just how the tether was first threaded in processing machinery. This tiny bit of torsional energy could have provided steady momentum for orderly supercoiling as the tether sought equilibrium.

Supercoiling dynamics are most wonderfully revealed by space tethers in microgravity, but there are at least two traditional domains where they are long known. Experienced kite flyers use very long lines on occasion, up to about 15km historically, and when these lines break in mid-air, the effects described here happen. Commercial and sport fishermen also use long lines, that in water are effectively weightless, and complex tether dynamics occur. DNA dynamics are more recently revealed, and their formal dynamical models are emerging.

Unique Results and Lessons Learned From the TSS Missions   or  PDF

NASA STS-75 TETHER SATELLITE UFOS DEBUNKED BLACK EXPOSURE LINE ANALYSIS

The supercoiled tether, estimated at perhaps 3m wide, and 30m long (slightly oblique), with perhaps 3-5 supercoiling dimensions.

space tether
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Ed adds clip from linked article:
"The tether consisted of  five  layers.  At the center was a core of Nomex  fibers.  Around this were wrapped ten strands  of  34  AWG  copper  wire.    The  core  with  the  wrapped  copper  wires  was  then  insulated  by  an  FEP  Teflon jacket.  The Teflon  jacket was surrounded by the  strength member, a layer of  braided Kevlar 29.  Finally, an outer layer of braided Nomex was added to mitigate the corrosive effects of atomic oxygen.  This construction is shown in Fig.7.    Pertinent  to  the  discharge  problem  are  the  facts  that:  (1)  the  inner  core  of  Nomex  was  highly  porous—something  like  a  cigarette  filter,  and  (2)  the  FEP  Teflon  insulating  jacket  was  an  unbroken,  air-tight  sleeve.    As  a result of its porous core, the air-tight insulating jacket, and the fact that this complex coaxial system was assembled under ambient atmospheric conditions, a  large  volume of air at1 Atm pressure was trapped within the 21-km  long tether.    Any  flaw  or  puncture  of  the  Teflon  jacket,  once  uncovered  by  the  deployment  action  and  exposed  to  the high-vacuum environment of space, would allow the trapped gas to rapidly escape."
August 8, 2020, post by Dave Santos
"There be Monsters"; curious complications of Advanced Tether Physics

Read enough tether physics studies, and it becomes clear that something as "simple" as vibrational modes of cables (tethers) is anything but; and that scientists can only approximate the wild dynamics possible, due to theoretic and computational limitations.

Part of the science gap is true quantum-weirdness and chaos in real cable dynamics, as quantum chaos analogs. In practical kite situations, like high-wind, a tether can break far below its expected tension limit, by a freakish conjunction of energy at a single point.

One way of "observing" the weirdness on a kiteline is to its listen to the aeolian music. The prediction is that if you listen long enough, there will be noise anomaly transients way out the norm. Careful not to be taken for mad, listening long and intently for monsters :)

Here are three representative papers on dynamical harmonic modes on a cable. There is much yet to learn:
References for the paper Large Amplitde Three-Dimensional Free Vibrations of inclined Sagged Elastic Cables:

[1] P. Hagedorn, B. Schafer, On non-linear free vibrations of an elastic cables, International Journal of Non-linearMechanics 15 (1980) 333–340.

[2] A. Luongo, G. Rega, F. Vestroni, Monofrequent oscillations of a non-linear model of a suspended cable, Journal of Sound and Vibration 82 (1982) 247–259.

[3] A. Luongo, G. Rega, F. Vestroni, Planar non-linear free vibrations of an elastic cable, International Journal ofNon-linear Mechanics 19 (1984) 39–52.

[4] G. Rega, F. Vestroni, F. Benedettini, Parametric analysis of large amplitude free vibrations of a suspended cable, International Journal of Solids and Structures 20 (1984) 95–105.

[5] F. Benedettini, G. Rega, F. Vestroni, Modal coupling in the free nonplanar finite motion of an elastic cable, Meccanica 21 (1986) 38–46.

[6] F. Benedettini, G. Rega, Non-linear dynamics of an elastic cable under planar excitation, International Journal of Non-linear Mechanics 22 (1987) 497–509.

[7] G. Rega, F. Benedettini, Planar non-linear oscillations of elastic cables under subharmonic resonance conditions, Journal of Sound and Vibration 132 (1989) 367–381.

[8] G.V. Rao, R.N. Iyengar, Internal resonance and non-linear response of a cable under periodic excitation, Journal of Sound and Vibration 149 (1991) 25–41.

[9] N.C. Perkins, Modal interactions in the non-linear response of elastic cables under parametric/external excitation, International Journal of Non-linear Mechanics 27 (1992) 233–250.

[10] C.L. Lee, N.C. Perkins, Nonlinear oscillations of suspended cables containing a two-to-one internal resonance,Nonlinear Dynamics 3 (1992) 465–490.

[11] C.L. Lee, N.C. Perkins, Three-dimensional oscillations of suspended cables involving simultaneous internalresonances, Nonlinear Dynamics 8 (1995) 45–63.

[12] F. Benedettini, G. Rega, R. Alaggio, Nonlinear oscillations of a four-degree-of freedom model of a suspendedcable under multiple internal resonance conditions, Journal of Sound and Vibration 182 (1995) 775–798.

[13] G. Rega, R. Alaggio, F. Benedettini, Experimental investigation of the nonlinear response of a hanging cable Part I: Local analysis, Nonlinear Dynamics 14 (1997) 89–117.

[14] F. Benedettini, G. Rega, Experimental investigation of the nonlinear response of a hanging cable. Part II: Global analysis, Nonlinear Dynamics 14 (1997) 119–138.

[15] M. Behbahani-Nejad, N.C. Perkins, Freely propagating waves in elastic cables, Journal of Sound and Vibration196 (1996) 189–202.

[16] M. Pakdemirli, S.A. Nayfeh, H.A.H. Nayfeh, Analysis of one-to-one autoparametric resonance in cables-discretization vs. direct treatment, Nonlinear Dynamics 8 (1995) 65–83.

[17] G. Rega, W. Lacarbonara, A.H. Nayfeh, C.M. Chin, Multiple resonances in suspended cables: direct versus reduced-order models, International Journal of Non-linear Mechanics 34 (1999) 901–924.

[18] J.V. Huddleston, Computer analysis of extensible cables, Journal of Engineering Mechanics, American Society of Civil Engineers 107 (1981) 27–37.

[19] B. Shih, I.G. Tadjbakhsh, Small-amplitude vibrations of extensible cables, Journal of Engineering Mechanics, American Society of Civil Engineers 110 (1984) 569–576.

[20] J.J. Burgess, M.S. Triantafyllou, The elastic frequencies of cables, Journal of Sound and Vibration 120 (1988) 153–165.

[21] M.S. Triantafyllou, D.K.P. Yue, Damping amplification in highly extensible hysteretic cables, Journal of Sound and Vibration 186 (1995) 355–368.

[22] A.A. Tjavaras, Q. Zhu, Y. Liu, M.S. Triantafyllou, D.K.P. Yue, The mechanics of highly extensible cables, Journal of Sound and Vibration 213 (1998) 709–737.

[23] S. Chucheepsakul, S. Wongsa, Effect of axial stretching on large amplitude free vibration of a suspended cable,Structural Engineering and Mechanics 11 (2001) 185–197.

[24] S. Chucheepsakul, N. Srinil, Free vibrations of three-dimensional extensible marine cables with specified top tension via a variational method, Ocean Engineering 29 (2002) 1067–1097.

[25] W.M. Henghold, J.J. Russell, Equilibrium and natural frequencies of cable structures (a nonlinear finite element approach), Computers and Structures 6 (1976) 271–276.

[26] F. Rosenthal, Vibrations of slack cables with discrete masses, Journal of Sound and Vibration 78 (1981) 573–583.

[27] K. Takahashi, Y. Konishi, Non-linear vibrations of cables in three dimensions. Part 1: Non-linear free vibrations, Journal of Sound and Vibration 118 (1987) 69–84.

[28] A.C.J. Luo, C.D. Mote Jr., Equilibrium solutions and existence for traveling, arbitrarily sagged elastic cables, American Society of Mechanical Engineers, Journal of Applied Mechanics 67 (2000) 148–154.

[29] S. Chucheepsakul, N. Srinil, P. Petchpeart, A variational approach for three-dimensional model of extensible marine cables with specified top tension, Applied Mathematical Modelling 27 (2003) 781–803.

[30] H.M. Irvine, T.K. Caughey, The linear theory of free vibrations of a suspended cable, Proceedings of the Royal Society of London Series A 341 (1974) 229–315.

[31] W. Lacarbonara, G. Rega, Resonant nonlinear normal modes. Part II: Activation/orthogonality conditions for shallow structural systems, International Journal of Non-linear Mechanics 38 (2003) 873–887.