Progress in Aerospace Science

ce

Contents

3.1.1. The TSS-1R mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2. Practical electrodynamic tether designs and proposed system technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

The eld of space tethers has received very considerableattention in recent decades, with many specialist articles

these are reviewed in this paper, and the discussion alsocovers some of the texts and handbooks available. We startwith the excellent foundation textbook by Beletsky and

ARTICLE IN PRESSLevin [1] in which the dynamics of tethers are introducedrigorously, in a progressive and pragmatic manner. Thebook starts by setting the scene for tethers in space by

0376-0421/$ - see front matter r 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.paerosci.2007.08.002

Corresponding author. Tel.: +44 141 330 4337; fax: +44 141 330 4343.E-mail address: m.cartmell@mech.gla.ac.uk (M.P. Cartmell).4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1. Introduction available in the technical and scientic literature. Some of1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2. Momentum exchange tethers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1. Summary of operating principles and relevant orbital mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2. Tether missions, constraints, and failure modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3. Dynamics of dumb-bell systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.4. Tether models in which exural effects are introduced . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.5. Control strategies and models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.6. Practical tether designs and proposed system technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.7. Deployment scenarios and mission plans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3. Electrodynamic tethers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.1. Summary of operating principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Abstract

The review paper attempts to provide a useful contextualised source of references for the student interested in learning about space tethers,

and their potential for propulsion of payloads in Space. The two principal categories of momentum exchange and electrodynamic tethers are

discussed, with the principal aim of establishing useful sources of fundamental theory in the literature, as well as highlighting important

technology and mission development papers. The large-scale international effort that continues to be made in the area of space tether research

is evident, with major literature contributions from the world-wide scientic and technical community. The overarching theme of the paper is

to show the richness and diversity of tether modelling that has been undertaken in recent times, and to emphasise, by means of many different

examples, that dynamics and control are the two fundamentally important aspects of all tether concepts, designs, and mission architectures.

r 2007 Elsevier Ltd. All rights reserved.M.P. Cartmell , D.J. McKenzie

Department of Mechanical Engineering, University of Glasgow, James Watt Building, Glasgow G12 8QQ, Scotland, UK

Available online 7 November 2007A review of spas 44 (2008) 121

tether research

www.elsevier.com/locate/paerosci

ARTICLE IN PRESSesssummarising possible applications and also by discussingfact and ction in such a way that the reader new to tethersis soon clear about the important fundamental parameterssuch as material density, strength, and orbital location, andhow these can trade off. The book then moves on todevelop equations of motion for a exible tether with endmasses and massless and massive variations, along withperturbational and certain environmental effects. Thetether is then investigated within the Newtonian eld andthe dynamics examined in terms of stability and oscillatorybehaviour. Atmospheric probes, electrodynamic (ED)tethers, libration and rotation, deployment and retrieval,and lunar anchored and satellite ring systems serve tocomplete the coverage of the book. A very useful set ofreferences is also provided, up to the publication year of1993. A chapter on the orbital mechanics of propellantlesspropulsion systems, by McInnes and Cartmell is given inthe more general astrodynamics text [1], and this coversboth solar sails and tethers, as technologies with thepotential to overcome the constraints of propulsion basedon reaction, and in the tether application this is bymomentum balance through the system. The chapterreviews some of the more well-known missions that haveown to date and then moves on to summarise theperformance expectations of hanging, librating, and spin-ning tethers, setting them in the context of results extant inthe literature. Gravity gradient stabilisation is re-examined,and the well-known literature result for sub-span tensionfor a short hanging tether on a circular orbit is obtainedand re-cast into the notation of [1]. The motorised tetherconcept is introduced next, and the equation of motion fora simple motorised dumb-bell on a circular orbit is derived,leading into the more general non-planar case. Payloadtransfer concepts, including the use of staged tethers (cross-reference with [24]) are discussed and further usefulreferences are cited. There have been several general shortarticle expositions of tether technology during the last fewdecades appearing in widely different areas of theliterature, starting with a particularly accessible andnotable example from Bekey [5]. In this summary discus-sion Bekey gives some of the history of the subject, withgood reference to missions up to 1983 and those plannedfor a few years after. Principles of momentum exchangeand electrodynamics are outlined and useful data isprovided. This paper also discusses speculative applicationsfor cryogenic propellant storage and transfer, two-dimen-sional tethered constellations, the construction of a passivespace facility in which platforms are separated by tethersgiving a possible work volume within, payload orbit raisingand lowering, and a two-tether elevator for transfer fromLEO to GEO. In a similar vein Carrolls paper of 1985 [6]also sets out the history of space tethers with a useful,applications orientated, introduction to the theory in whichthe important Lunavator concept of Moravec [7] appears,with this further explained and applied by Forward [8], and

M.P. Cartmell, D.J. McKenzie / Progr2applied again by Cartmell and Ziegler [9], noting also themore recent summaries given in [10,11]. It is also interestingto consider tethers acting as tension members within solarsail structures, and also applied as links between high-altitude sails and lower-altitude payloads. Further work oncomplex tethered systems has led to the notion of the spaceweb, where multiple tethers are set up to comprise anintricate web-like structure, McKenzie and Cartmell [12]and McKenzie [13]. Carrolls paper [6] also highlightsaerodynamic applications where a tethered balloon couldexploit atmospheric braking to lower a higher-altitudespace plane, and altitude juggling whereby a sortie vehicleis raised and lowered by means of a local closed orbitcontrolled by a variable length-spinning tether. Carroll [6]also introduces intriguing concepts of momentum transferwith celestial bodies, which are examined a little furtherlater on. The major contribution to space tether researchmade by Robert L. Forward cannot be overestimated, anda short and digestible article by Forward and Hoyt inScientific American in 1999 [14] rst showed the ingeniousconcept behind the use of multiple, staged tethers toincrease velocity without the necessity of extreme design,for EarthMoon payload transfer; note also the latercontributions of [4,10,15]. US mission plans for tetherswere reviewed in 1999 and summarised in a short paper byJohnson et al. [16], in which the use of ED tethers forreusable upper stages was to be demonstrated during theProSEDS mission. This had been planned as a conductivetether, for electromagnetic orbital adjustment, approxi-mately 15 km in length with 10 km of it insulated and theremaining 5 km as bare conductor. The mission wasscheduled to be own along with a launch of a GlobalPositioning System satellite in spring 2003, but wasultimately cancelled, initially because of concerns aboutpotential collision with the ISS. An interesting comparativestudy of in-space propulsion performance for 1 year crewedMars mission in 2018 was reported in 2001 by Rauwolf etal. [17]. This comprehensive study undertook to examinecontender propulsion technologies: chemical, bimodalnuclear thermal rocket, high-power nuclear electric,momentum tether/chemical hybrid, solar, solar/chemical,and variable specic impulse magnetoplasma rocket(VASIMR). This paper concluded that tether-based mis-sion scenarios looked attractive in terms of performancebut the two concerns of technology immaturity andoperational complexity militated against a projected 2018application. This important conclusion certainly underlinesthe need for continued international effort in all aspects oftether science and technology. Also in 2001 a major newproposal emerged as a result of a US-based researchcollaboration led by NASA Marshall Space Flight Center,and was reported by Sorensen [18]. This paper introducedan ingenious concept in which both momentum exchangeand ED reboost could be used for propellantless orbitaltransfer. This Momentum eXchange Electrodynamic Re-boost (MXER) principle relies on the tether rotating as ittravels on an elliptical orbit, catching a payload in LEO,

in Aerospace Sciences 44 (2008) 121and then transferring this to a higher orbit after, say, oneperiod. The electrodynamics would be used to re-boost the

ARTICLE IN PRESSesstether over a period of several weeks prior to the next cycle.This has the potential for a high-performance orbitaltransfer with essentially free re-boost, and the Final Report[19] of 2003 shows that survivability and ight validationissues are of primary importance, but that the necessaryscience base and the basic contributory technologies aremore or less in place for mission development to continue.In 2006, Bonometti et al. [20] conrmed that MXERcontinues development within the NASA In-Space Propul-sion Technology (ISPT) programme; note also Ref. [21,22].Tethers and debris mitigation were brought to the fore in2001 in a useful paper by van der Heide and Kruijff [23], inwhich limitations of use are dened particularly for de-orbiting applications in terms of susceptibility to orbitaldebris. This paper also discusses the potential problem oftethertether collisions with a suggestion that whenconsidering de-orbiting missions then 40 constellation de-orbits per year corresponds to approximately 4 tethers inspace at the same time, which could feasibly be coordinatedin order to avoid tethertether collisions. Further work ontether survivability has been carried out by Draper [24] inwhich a range of statistical methodologies for life predic-tion from the literature were critically compared and arevised proposal made, with some potential for practicaluse highlighted. In addition to the environmental effects ofdebris and other degrading phenomena tethers andassociated payloads are extremely vulnerable to destabili-sation because of astrodynamic and other perturbationaleffects. Practical application of any tether system in spacerequires a high level of stability control, and the stability ofa spinning generalised satellite acted upon by the gravitygradient and constant torques is examined by Sarychev etal. [25]. Importantly, it is shown in this paper that stableequilibria can exist for many general values of the inertialparameters of the satellite. There is a large literature ontethers, and the subset of this which deals with dynamicsand control is also substantial, with many modelsproposed, together with a very large number of associatedanalyses of potential dynamic performance. Dumb-bellmodels tend to proliferate, for a range of differentmomentum exchange congurations in which the tetherand payload system is assumed to behave predominantly asa rigid body. Whilst this is a somewhat questionableassumption, and certainly not the case for all phases ofdeployment and operation, it maybe has some merit forinitial studies of new ideas, and many numerical results areobtainable in the literature for such models, some of whichare cited here. A paper by Cartmell et al. [26], dealing withapplications of the multiple scales perturbation method toweakly nonlinear dynamical systems, proposes approxi-mate analytical solutions for relatively simple dumb-bellmodels. Numerical solutions to these, and allied models,are discussed in Section 2. The remainder of the paper isdivided into two main sections, dealing with momentumexchange tethers and ED tethers, and then completing with

M.P. Cartmell, D.J. McKenzie / Progrsome conclusions and a list of 122 references. Themomentum exchange discussions in Section 2 offer asummary of operating principles and relevant orbitalmechanics, then a sub-section on tether missions, con-straints, and failure modes. After that the dynamics ofdumb-bell systems, tether models in which exural effectsare introduced, control strategies and models, practicaltether designs and proposed system technologies, andnally deployment scenarios and mission plans are allinvestigated and commentaries provided on each topic. Thethird section on ED tethers is split into two sub-sections,offering a summary of operating principles and one of theprincipal missions carried out to date, and then practicaltether designs and proposed system technologies.

2. Momentum exchange tethers

2.1. Summary of operating principles and relevant orbital

mechanics

Eiden and Cartmell [27] have summarised briey thepossible role of a European roadmap for non-conductivetethers, nominally based on momentum exchange, and alsofor conductive tethers in which electrodynamics, andpossibly momentum exchange, provide propulsion. In thecase of the former class small and large payload de-orbitare seen as near term goals, with free-ying tetheredplatforms and articial gravity systems in the mid-term,followed eventually by spinning tethers providing inter-planetary propulsion. Gravity gradient stabilisation is animportant underpinning phenomenon when consideringspacecraft stability, and this is particularly the case for longmomentum exchange tethers. The work by Cartmell et al.[26] considers dumb-bell models for momentum exchangetethers, and offshoots and developments of this work haveshown conclusively that hanging, librating, and spinningtether motions are intimately connected to this funda-mental phenomenon (refer to Section 2.7 for more on thistheme, particularly [11]). An analytical solution for planarlibrations of a gravity stabilised satellite by Hablani andShrivastava [28] shows that a perturbational type of two-term solution can be developed to predict the pitchinglibrations of an arbitrary gravity stabilised articial rigidsatellite in an eccentric orbit. This followed over a decadeof extensive international work on this type of problem andthe results in [28] show that periodic responses for libratingsystems are necessarily important and form the spines ofthe systems integral manifolds [29]. Gravity gradientstabilisation of tethers is discussed in depth in [1,10] andfeatures explicitly and implicitly in a very large number ofpublications in the eld, many of which appear here in thisreview. An important paper by Kyroudis and Conway [30]considered the propulsion advantages of using an ellipti-cally orbiting, tethered dumb-bell system for geosynchro-nous satellite transfer over the conventional non-tetheredimpulsive Hohmann transfer. This was done by formingthe planar equations for the system and solving them

in Aerospace Sciences 44 (2008) 121 3numerically, notwithstanding that the analysis neglectedthe tether mass and assumed dissimilar end masses in the

ARTICLE IN PRESSessform of the space shuttle at one end and a satellite payloadat the other. In general tether propulsion performance wasfound to improve by using a long tether and a highlyeccentric orbit, and this mode showed signicant improve-ments over a reasonably comparable Hohmann transfer.Further work on using tether-based transfers was reportedby Lorenzini et al. [2] in their landmark paper in whichstaged tethers in resonant orbits are proposed as beingmore mass efcient than single tether systems, with a massratio of 1:3 using current materials. Earlier work on stagedtethers is usefully summarised in [3] by Hoyt and Forward.Lorenzini et al. [2] briey refer to tether orbit raising resultscited by Carroll [31] for radial separation as a function oftether length, and conclude that spinning staged tetherscould provide an ideal transfer rate of ve transfers peryear. The transfer rate of a staged system is determined bythe periodic realignment of the apsidal lines of the twostages, whereas in the case of a single tether it is dependenton the time required for re-boosting the stage. Orbit raisingpredictions for tethers are discussed further in Section 2.7[11]. Continuing with the theme of propulsion of a smallpayload tethered to a large mass in the form of a spacestation or large shuttle, Pascal et al. [32] investigated thelaws of deployment and retrieval by means of a three-dimensional rigid body model of a dumb-bell tether in bothcircular and elliptical orbits. Several laws are proposed andanalytical solutions for small planar and non-planarmotions of the tether are given, showing that equilibriumtension can be stated as a function of instantaneous tetherlength and corresponding axial acceleration, for whichcontrol laws can be stipulated. It is shown that deploymentis generally stable whereas retrieval is not. Various laws areexamined for deployments and retrievals, and also forcrawler congurations in which the end payload moves outalong a pre-deployed tether and how this can mitigate theinherent instability of retrieval. The next conceptual step totake when considering deployment is to include some formof exibility within the tether, and an interesting study ofthis was published by Danilin et al. [33] in 1999, in whichthe elastic tether model of No and Cochrane Jr [34] is usedbut with different variables and derivation. The objectiveof this paper was to consider deployment of a completelyexible tether from a rigid rotating space vehicle under theinuence of a central gravitational eld. The tether ismodelled as a series of discrete masses interconnected bymassless elements and with internal viscous damping. Theauthors make the very important point that tether elementforces cannot be compressive, so conditions within thenumerical solution algorithm have to be set up toaccommodate the consequential folding effects. Twonumerical examples are summarised; one for a swingingterrestrial cable with an end mass, which starts from ahorizontal initial condition, mainly as a verication of themodel in those conditions, and the other for plane motionof a space vehicle deploying a relatively short 3 km tether,

M.P. Cartmell, D.J. McKenzie / Progr4with elemental spacing of 100m, on orbit. The deploymentis linear and conditions are set up to apply smooth brakingof the tether to a halt at the end of the deployment. It isalso possible, and potentially very useful, to considertethered vehicles within an aerobraking context. In suchcases a vehicle, or probe, and an orbiter, connectedtogether by a tether, are congured so that the vehiclepasses through a planetary atmosphere to obtain a targetvelocity change, with the orbiter passing above the atmo-spheric inuence. Longuski et al. [35] give a full account ofthis very interesting problem. Their modelling is based onthe premise that a dumb-bell tether arrives spinningretrograde to the orbit and when the lower payload entersthe atmosphere the aerodynamic effects decelerate thetether until it reaches a minimum orientation angle atwhich point the drag starts to spin the tether in theopposite direction. An optimisation scheme referred to asspin matching is used to equate the spin rates entering andleaving the atmosphere. This has the desirable effect ofminimising the forces on the tether during the manoeuvre.They consider the atmospheric y-through as an impactproblem and the analysis is congured to lead toconclusions for mass optimisation, with gas giants suchas Jupiter used for the environmental context. It is shownto work well for massive tethers interacting with the Jovianatmosphere, and the results are particularly tractable inthat they only require knowledge of four parameters formassive tethers (orbiter-to-probe mass ratio, non-dimen-sionalised clearance between minimum altitude of theorbiter and minimum altitude of the probe, non-dimensio-nalised speed, and DV). In the case of smaller tethers theDV is subsumed within a revised non-dimensionalisedspeed variable, so the parameter space is reduced to three.A major and authoritative work on the dynamic analysis oftethers using continuum modelling has been provided byAuzinger et al. [36], in which stiff equations of motionobtained by Hamilton-Ostrogradskii and balance princi-ples are solved numerically in a detailed parametric study.This sophisticated numerical investigation offers a greatdeal of useful predictive data on momentum exchangesystems.It should be pointed out that the papers cited above also

contain valuable sources of references, some of which alsofeature in this review, and the interested reader is stronglyadvised to consult widely on each sub-topic, using thereferences supplied within this review and also those whichare precluded from inclusion due to space reasons butwhich can be found from the cited papers. In addition tointroductory issues of performance, orbital contextualisa-tion, modelling strategy, deployment, and aerodynamiceffects, it is also important to appreciate that collisionprevention necessarily features within any serious applica-tions for tethers and we introduce some of the literature onthis and related matters next. An interesting introductionto calculating collision probability between a tether and asatellite is given by Patera [37,38] of the Center for Orbitaland Reentry Debris Studies in Los Angeles, based on a

in Aerospace Sciences 44 (2008) 121computational scheme for long slender tethers of prede-ned shape and a spherical collision space on the basis of

ARTICLE IN PRESSessrespective state vectors and error covariance matrices. Theproblem is shown to reduce to a two-dimensional symmetricprobability density over a cross-sectional collision region.This in turn reduces to a one-dimensional path integral thatgives computational efciency. A reasonable tether length of20km was assumed, with negligible radius and the highlysignicant conclusion was that tethersatellite collisionprobabilities are up to 600 times greater than those forsatellitesatellite collisions. Useful comparison data is givento support this conclusion in tabular and graphical form fordifferent, and practically feasible, tether congurations. Inaddition to tethersatellite collisions we also have to considerthe susceptibility of tethers to debris impacts. A novel TetherRisk Assessment Programme (TRAP model) due to Gittins etal. [39] has been proposed and comprises three mainfunctions; the breakup function, the tether function, andthe analysis function. This work was motivated by the widelyheld belief that on impact a debris fragment with a diameter alittle smaller than half of a tether strand diameter can causethat strand to fail. The break-up component models collisionsand explosions to determine fragment number, mass,diameter and DV [40]. The tether function is in fact a modelof tether dynamics and this is a two stage affair, dealing withsystem centre of mass motion and also libration of the endmasses and tether mass beads. The analysis functiondetermines collision and severance risk based on probabilisticcontinuum dynamics in which an orbital trajectory is foundbetween two position vectors when the time of ight isknown; this is the well-known Gauss-Lambert problem. Thepaper considers a single strand tether and, interestingly, adouble stranded tether design, where the failure criterion is ifboth strands in one segment fail or if one mass bead is hitdirectly. General conclusions were that a two-strand tetherhas a severance risk of two orders of magnitude lower thanthe single strand case, with obvious implications for multi-strand designs, noting that this premise is also discussed insome detail in [24]. The design of tethers for survivability is re-visited in Section 2.5 (see [41]) at which point the patentedHoytetherTM is summarised. This multi-line concept has amulti-decade lifetime prediction.From the perspective gained up to this point it is now

relevant to introduce orbital injection and basic missionrequirements. For the purposes of introduction we considerhyperbolic injections [21], periodic solutions and thecontrol of tethers in elliptical orbits [42], and the allimportant problem of catching a spacecraft or payloadwith a spinning tether [43]. Sorensen [21] provides a highlyreadable account of the issues surrounding the orbitaldynamics of the ingenious MXER tether design (also see[19,22]). A long, 100 km or so, high-strength conductivetether uses momentum exchange to catch a payload andthen release it into a higher-energy orbit, and thenelectrodynamics are employed to reboost the tether;effectively to restore energy and momentum given to thepayload. Note that ED tethers are considered in more

M.P. Cartmell, D.J. McKenzie / Progrdetail in Section 3.1. Sorensen conrms that interplanetaryights require orbits to be congured for hyperbolic Earthescape trajectories. It is pointed out that there is exibilityin this because there are a number of hyperbolae whoseoutgoing asymptotes are identical. The objective is tosecure a hyperbolic injection that has an equatorialperiapsis, and a methodology is given in [21] to obtainthe necessary orbital elements. Appreciation of the wholedynamic context is important for tether mission develop-ment and Takeichi et al. [42] provide a control scenario fora rigid body dumb-bell tether in an elliptical orbit. Theequations of motion are solved for libration and it is shownthat the total energy of the system is minimised when thelibrational and orbital motions coincide with periodicsolutions. The overall conclusion is that the periodicsolution is of minimum energy and that this minimum isthe case for circular or eccentric orbits as long as thelibration is actually possible. This can be assured through asimple periodic on-off control strategy at a certain trueanomaly. The usefulness, or otherwise, of tether libration isrevisited by Ziegler and Cartmell [11] but clearly it has thepotential for distinct advantage over the hanging cong-uration for payload increment gain. It is equally obviousthat spinning tethers have greater potential still [11]. On theassumption that we can design long-lasting tethers,congure them into suitable orbits, control their dynamicsfor optimal payload propulsion and minimal potential forcollision, the next step is to introduce criteria for efcientrendezvous with spacecraft and payloads. Lorenzini [43]provides an in-depth treatment of a spinning tether loopwith an extended time opportunity for error-tolerantpayload capture within high DV propulsion to GTO andEarth escape. The conguration is such that the ends of theloop are furthest away from the centre of mass, where theloop is at its narrowest. The concept is simple in principle,depending on the ejection of a payload (satellite) locatedharpoon that hooks onto the loop. This makes it tolerantof large longitudinal position errors and reasonable lateralerrors as well as some out-of-plane error. The capture issoft, and so caters for some velocity mismatch. Stabilisa-tion of post capture oscillations would be required prior tofurther release into a higher-energy orbit. The authorrightly points out that other analyses would be required toaddress loop deployment, fault tolerance, and mitigation ofentanglement. A useful survey of the dynamics and controlof tethers is given by Misra and Modi [44]. Cartmell andDArrigo [45] modelled a symmetrical motorised momen-tum exchange tether with manipulation of the payload end-masses in order to generate inertial parametric excitation ofthe system, in order to determine if the forced-parametricbifurcatory states could be used to guarantee monotonicspin-up, with preliminary results indicating that this isindeed possible. The interested reader will nd useful cross-references available from [4,5,46].

2.2. Tether missions, constraints, and failure modes

in Aerospace Sciences 44 (2008) 121 5One of the fundamentally important issues surroundingsuccessful tether ight is that of the avoidance of

ARTICLE IN PRESSessentanglement and collision involving these long andvulnerable structures. This was investigated by Chobotovand Mains [47] for the TSS-1R mission, which was own inconjunction with the space shuttle orbiter STS-75 inFebruary 1996. The paper gives a summary of the historyof the TSS missions in 1992 and 1996 and concludes thatthe TSS-1R mission deployed to 19.7 km instead of theplanned 20 km with a failure of this ED test tether due to aforeign object penetrating the insulation layer which thenexacerbated failure due to arcing and burning of the tetherat a nominal tensile load of 65N. The paper by Chobotovand Mains [47] offers an interesting study into theprobability of TSS collisions with micrometeoroids andother orbiting objects. The authors state that the expecta-tion was that the extended tether would be expected to beimpacted by multiple particles 0.1mm or larger in size andthat the probability of collision with objects 10 cm orlarger in size was small (103) before the TSS re-enteredand burned up in the atmosphere 3 weeks after deploymentfrom the shuttle. The NASA EVOLVE model for man-made debris ux was used as the basis for this work, at a350 km altitude. In addition to this data for the closestdistance to satellites in this location was also used, thisbeing based around the US Space Command SGP4propagator, and a simulation for a six month periodstarting 1 March 1996 generated over 58 000 objects and 24satellites. The results from the analytical model werecompared to those from a statistical Weibull probabilitydensity function approach, with good mutual correlation.In the case of the TSS study it was concluded that thetether was subjected to several impacts by small particlesgreater than 0.1mm in size and that the probability ofcollision with larger orbiting objects was very small, and ofthe order of 0.001 per month. This paper provides a usefulset of methodologies for general application to tethers. Thesubject of tether failure, particularly at deployment, wasfurther reviewed, by Gates et al. [48], and in the context ofthe Advanced Tether Experiment (ATEx), launched inOctober 1998, which is particularly interesting because thetether used had a at tape-like cross-section. The deploy-ment failed after only 22m out of the possible 6.5 kmlength, and the mission was aborted. The tether was madefrom low-density polyethylene with three SpectraTM

reinforcing strands running lengthwise along the tetherand showed a tendency to stick to itself and for this self-adhesion to increase with stowage time. It also exhibited amechanical memory effect. The mission was abortedbecause the deployment problems led to an excessivelibration of the deploying tether outside the acceptablelocation boundaries. The paper by Gates et al. [48]succinctly describes the build-up to this automatic systemdecision and also goes into useful practical detail regardingthe deployer and the deployment methodology. Theintended deployment rate was quite low at 0.02m/s over3.5 days, with built in accommodation of gravity

M.P. Cartmell, D.J. McKenzie / Progr6gradient-induced librations. The expectation was that asthe deployment progressed the libration angle wouldreduce, partially by means of changing gravity gradienteffects during the deployment and partly because of open-loop spacecraft manoeuvres. A key sensor, measuringtether position in a plane at the top of the lower tetheredbody, and relative to the axis through this, showedslackness, and this led to an automated signal to jettison.The actual cause of the excessive slackness was notdetectable due to limited telemetry. Interestingly afterruling out certain failure modes the authors propose thatthe most likely failure mode was thermal expansion. Thisseems to have been due to beginning the deployment ineclipse, with telemetry nominal, until the tether entered thesunlight. Another possible cause was the build up of staticwhich may have interfered with the telemetry andgenerated a false slack signal. Shape memory and tip-offdynamics have also been mentioned as contributoryfactors, but the thermal expansion effect was deemed tobe the most likely cause, possibly in concert with these andother subsidiary effects on top. The paper concludes thattether deployment requirements are extremely importantwhen designing a system for ight, and that large designmargins are needed, but were certainly not available in thisrather tightly constrained example. Another case studypaper is that due to Leamy et al. [49] in which the authorsconsider the ProSEDS mission and two different niteelement simulation models for the dynamics and a fuzzy settechnique for the ED and deployment operation, particu-larly with regard to parameter sensitivity. The paper startswith a short, but useful, summary of tether ights to date(2001) and mentions a few of the futuristic applicationsthat have been proposed. Unfortunately the ProSEDSmission was cancelled in October 2003. This was partlybecause of a drastically reduced starting altitude and alaunch timeframe during a period of solar minimum, whichled to the available ED propulsion performance of theProSEDS system becoming insufcient to meet the missionobjectives. Despite this the paper is interesting and highlyrelevant as a case study. The idea of this mission had beento study bare-wire ED tethers, and to include a thermalmodel accounting for radiated heat, solar heating, andohmic heating in order to calculate tether elementtemperatures, and an atmospheric and planetary modelaccommodating aerodynamic drag, electron density at eachelement position, and magnetic eld properties. Theauthors used the two nite element codes to simulate thedeployment and electrodynamics of the ProSEDS missionand variable numbers of nodes were reckoned to besuperior in this context to xed node number calculations.The overall ndings were that the ProSEDS ED tetheroperation would not have been particularly sensitive tovariation in the material parameters, but initial ejectiontether momentum and controller parameters would havebeen signicant, as would variations in the geomagneticeld and the plasma parameters. This clearly indicates onceagain the importance of controllable and adaptive deploy-

in Aerospace Sciences 44 (2008) 121ment and braking strategies. It has been shown in this briefreview of papers dealing with possible failure and

ARTICLE IN PRESSessconstraint modes that successful use of tethers requires agood understanding of the environmental conditions bothin terms of the prevailing orbital mechanics and the debrisenvironment, a precise knowledge of neighbouring satelliteand spacecraft operations, extremely good mechanicaldesign particularly for deployers and brakes, bearing inmind that tether geometry characteristics are an integralpart of this, robust sensing of all signicant operationalvariables, and highly adaptive control strategies. Thesethemes are revisited further in subsequent sections of thepaper.

2.3. Dynamics of dumb-bell systems

A great many tether systems can be considered as someform of dumb-bell system in which two massive bodies, notnecessarily of the same mass or size, are coupled togetherby a low-mass tether by which momentum is exchangedbetween them. Kelly [50] provides a general overview ofpossible applications for the conventionally expendableSpace Shuttle External Tank (ET) as a space platform inLEO for use as an extended on-orbit crew or experimentalpackage base, or as a micro-g experiment and processingfacility, a celestial observation facility, an Earth observa-tion point, or as a staging point on the way togeosynchronous orbit locations. Conceptualisations ofthese scenarios are provided but it is the apparentlysecondary roles for the ET that could well involve adumb-bell tether conguration. Kelly suggests threescenarios, one of which uses a tethered release of the ETfrom the orbiter in which momentum exchange leads to aboost to a higher orbit for the orbiter and consequently adeorbiting of the ET. This idea, and several others, is alsogiven by Beletsky and Levin [1]. In 1992 Kumar, Kumar,and Misra [51] presented their ndings on the effect ofdeployment rate and librations on tethered payload raising.This seminal paper showed that a counter intuitive resultwas obtained whereby increasing deployment rate does notnecessarily lead to increased payload apogee. Theyintroduce a special rule for planar librations and circularpre-release orbits which they denote as the 7+4d rule.Additionally the paper shows clear general relationshipsbetween apogee altitude gain as a function of deploymentrate and explains how suitable deployment rates could beselected for optimising altitude gain, for a given system.The 7+4d rule is revisited in [11]. A relatively short classof dumb-bell tether belongs to the OEDIPUS ionosphericplasma test mission system comprising two axially spinningsub-payloads separated by a tether of up to 1 km in length.This was reported by Vigneron et al. [52] in 1997.Terrestrial tests were performed with the understandingthat they would differ from the in-space conguration interms of length scale, higher terrestrial level of gravity, andthe presence of friction within the system-supportinggimbals that would not be present in space. The authors

M.P. Cartmell, D.J. McKenzie / Progrderived a specic mathematical model of the laboratorysystem, one that included the terrestrial effects as well asthe in-ight phenomena. The paper shows that the modelfor this problem can be reduced to a linear, vibratory,damped, and gyroscopic system, for which an eigenfunc-tion analysis is used to obtain the damped gyroscopicmodes shapes, stability, and natural frequencies for variousphysical congurations. Interestingly, this work showedthat linear modelling could be used to represent modalfrequencies and payload attitude stability quite well,however, it obviously did not cover all the possibledynamical phenomena in the system, and would overlookcertain regions of convergent attitude motion and limitcycle behaviour. By moving the spin axis so that it isnormal to the tether and half-way along the tether length,orientating the tether spin plane so that it is coplanar to theorbit plane, and then forcing the system by means of anexternal drive motor, a motorised dumb-bell tether can beenvisioned. This was rst presented in 1998 by Cartmell[53] and a preliminary model was established which showedthat forced, motor driven, spin could be generated for alarge symmetrical dumb-bell tether, and that complicatednon-planar motions of the tether could also be initiated.Motorised tethers are examined further in later sections[4,11,13,5456], where it is shown that there can be certainadvantages to employing an additional form of energyinput in this way, notwithstanding the potential forcomplicated three-dimensional motions as this coupleswith the prevailing orbital mechanics. Important aspects ofthe dynamics, which underpin the general stability andcontrol problem that exists with long tethers in space wereexamined in 2000 by Kumar and Kumar [57] in a systemcomprising four equal, but short, tethers joining twospacecraft platforms, or satellites. A stability criterion isevolved for a somewhat simplied situation using rstorder perturbation equations around the nominal equili-brium conguration. The set of rather complicatedordinary nonlinear differential equations is non-dimensio-nalised and the reduced parameter space is numericallyexplored. Ultimately the authors consider three congura-tions; four parallel equi-spaced tethers, a parachutearrangement where the four tethers are spaced out at theupper end but converge to a common point on the lowersatellite, and a single tether. This intriguing paper showsthat all three congurations can provide augmentation ofgravity gradient stabilisation, with the parachute layoutperforming best of all. The tether lengths are extremelylow, just a few metres, and it should be emphasised that theobjective of this particular paper is to show how very shorttethers can be used to give a high degree of three-dimensional librational stability to medium-sized systems.Clearly this is a very different remit to the needs ofinterplanetary propulsion using momentum exchangetethers, but serves to show a useful and very interestingadditional application. A discussion of an articial gravitysystem, which comprises two tethered satellites was givenby Mazzoleni and Hoffman [58] in 2003 and includes tether

in Aerospace Sciences 44 (2008) 121 7elasticity within the so-called Tethered Articial Gravity(TAG) satellite. Tethers are useful for articial gravity

ARTICLE IN PRESSessgeneration because they can be used to maximise the r andtherefore minimise the o within the o2r that denes the so-called g-force. The spin-up phase is examined inparticular, and it is found that an initial out-of-plane angleof the system and the location of the tether attachmentpoint can both signicantly affect the dynamics of the end-body motion of a tethered satellite system (TSS) duringspin-up. The modelling included tether elasticity and wasbased on relevant work reported by Kumar and Kumar[57]. The net conclusion is that if tethers are to be usedsuccessfully for articial gravity generation then attitudecontrol of the end bodies is required during spin-up.Mazzoleni and Hoffman investigate the non-planar spin-up dynamics of the Advanced Safety Tether Operation andReliability (ASTOR) satellite in [59] and show that thisspin-up manoeuvre is an example of articial gravity,which could perhaps be harnessed within human-basedmissions in the future.Applications of tethers for interplanetary payload

propulsion are quite numerous within the literature andsome cases have been summarised above in variouscontexts. Nordley [60], preceded by Forward and Nordleyin 1999 [61] (see Section 2.7), showed in 2001 that a dumb-bell tether, with a counter mass at one end and a payload atthe other, could be used to throw substantial payloads toMars. This paper concentrates on a digestible summary ofthe mission architecture strategy necessary to accomplishthis and necessarily omits some of the details. However, itis of interest as a pragmatic assessment of the capabilitiesof a momentum exchange tether on the basis of somereasonable simplifying assumptions using currentlyavailable materials and technologies. The generalnding from this work is that spinning tethers could beused to propel sizeable payloads to Mars for the same orless total mass to orbit than chemical propulsion. If onepays attention to the way that spin is generated,and particularly if it is externally excited by means of anelectric motor for example, then performance levels can beoptimised for a range of mission options. It was with this inmind that Ziegler and Cartmell [11] investigated thepotential for motorised tethers in 2001. In this paper thethree mechanical options for upper payload release werere-considered; for a hanging, swinging (librating), andspinning tether, including a form of the 7+4d rule of [51].It is shown in [11] that such rules do not take all thepossible dynamical effects into consideration. An extendedrule is derived, for both orbit raising and lowering,which takes orbital radius, tether length, and angularorbital and tether pitch velocities into account. This isshown to work well in some practically useful data cases. AMotorised Momentum Exchange Tether (MMET) on acircular orbit is considered and the nonlinear ordinarydifferential equation for this is used to develop ananalytical spin-up criterion, which can also be comparedwith appropriately interpreted results of numerical integra-

M.P. Cartmell, D.J. McKenzie / Progr8tion of the governing ODE. This paper shows that amotorised tether can improve on the orbit raisingperformance of a librating tether by two orders ofmagnitude, and the librating tether is roughly twice aseffective as its hanging counterpart. The paper alsodistinguishes between performance and efciency andsuggests that in some circumstances short tethers can beadvantageous in terms of efciency (orbit raising para-meter divided by tether propulsion length) despite theirlower actual performance (measured in terms of the orbitraising parameter) than for longer tethers.Tether retrieval is the opposite of deployment and is

equally important in dynamical terms. Retrieval of a sub-satellite to a larger vehicle, specically a space station, isexamined by Djebli et al. [62]. This work was published in2002 and concentrates on laws for retrieval (and alsodeployment) specically combining simple (linear orexponential retrieval) and fast laws in which specicacceleration proles are proposed. This would be applic-able to passive momentum exchange tethers, MMETs, andpotentially to ED tethers too. Fast (hyperbolic) retrieval isparticularly advantageous because it tends to damptransverse vibrations in the tether, particularly whenpreceded by a simple sinusoidal retrieval law. AlthoughED tethers are dealt with in Section 3 it is pertinent tomention at this stage the work of Pelaez et al. of 2002 [63]in which an ED tether is modelled as a two-bar system. Thebars are articulated so that they can rotate relative to eachother by means of an assumed universal joint. One end ofthe two-link tether is attached to a massive host spacecraftand the other end comprises a point end mass. Thedynamics of the tether are modelled analytically by meansof Lagrangian dynamics, and the ED forces are introducedwithin the generalised forces terms since they do not derivephysically from a potential. It is important also to note thatthis model is adapted to the ProSEDS mission, [16,49], andis based on the intention that for such systems the secondsection is non-conductive and gravity gradient stabilised,thereby simplifying the general equations of motion. Theauthors consider this work to be an evolution of thedynamics of a dumb-bell model, applicable to ED andpurely mechanical tethers. It shows that two modes ofmotion in the form of libration and lateral oscillation areboth unstable in the absence of damping, the formergrowing slowly whilst the latter develops more quickly. Thelateral instability is shown to grow particularly rapidlyabove a critical value of the ED to gravity gradient forceratio. An in-depth treatment of the rigid body dynamics oftethers in space is given by Ziegler [54]. In this work thedumb-bell tether is modelled at various levels of accuracy,and approximate analytical solutions are obtained bymeans of the method of multiple scales for periodicsolutions. Comprehensive dynamical systems analyses aresummarised for different congurations and models, andglobal stability criteria for a rigid body dumb-bell tether, inboth passive and motorised forms, are dened andinvestigated. Further treatment of the spin-up criterion of

in Aerospace Sciences 44 (2008) 121[11] is also provided. Further work by Mazzoleni andHoffman, [58], is of interest and relevance here, dealing

ARTICLE IN PRESSesswith the end-body dynamics of articial gravity generating,elastically tethered, satellite systems, undergoing non-planar spin-up. In 2007, McKenzie [13] explored thedynamics of the MMET to include an analysis of thesystem on an inclined orbit and while undergoing deploy-ment. Similar modelling techniques were used to investi-gate space-web dynamics, producing a stability map of therotating space-web. Further relevant cross-references areavailable in [2,14,30].

2.4. Tether models in which flexural effects are introduced

The implication of the general dumb-bell modelapproach is that the tether is treated as a rigid body,however, that is not necessarily the case if axial stretch isallowed, and although then it may still be a dumb-bell inappearance it is no longer a rigid body in mathematicalterms. Therefore, once that freedom is accommodated itbecomes interesting to cater for further, more generic,forms of elasticity within the tether. The rigid dumb-belltether is useful, however, not only for gaining an under-standing of general global motions of a tether in space, butalso as a fundamental tool for mission conceptualisation.In practice it is almost certainly the case that elastic modelswill be needed, and particularly so when very highaccuracies are required both in predicting the tetherlocation and orientation, but also in properly under-standing the deformation of a tether in cases where theapplication is particularly demanding. This will frequentlybe the case in high-performance multi-line systems withhigh levels of built-in fail-safe redundancy, and also intether-based structures such as orbiting stellar interferom-eters and space webs. In the case of the orbiting stellarinterferometer DeCou [64] showed in 1989 that planardeformation of a spinning system comprising threecollimating telescopes at the corners of an equilateraltriangle made up from three interconnecting tethers wouldbe inevitable due to the inertia of the tethers. Clearlyinertia-less tethers will not deform centripetally and will,instead, merely stretch into straight lines due to the tensioncreated along their length by the corner masses as thewhole system rotates. The other case is where the cornermasses are zero and the tether mass density is nite, andthen the triangle will necessarily deform into a circle. Inpractice we get something in between and this is shown inthe paper by including nite corner and tether masses,along with in-plane deformation of the tethers. The tethersare broken down into segments and an iterative procedureis used to calculate the static shape that the systemassumes. Axial stretch has already been mentioned as aparameter of fundamental importance in real systems. Inlong, high-performance propulsion tethers this could bevery considerable, and will severely limit the applicabilityof rigid body modelling to anything other than systemconceptualisation. A straightforward but compelling piece

M.P. Cartmell, D.J. McKenzie / Progrof work by Bernelli-Zazzera from 2001, and reported in [9],in which motion control is proposed for a tether in whichstretch is allowed, showed that effective control can beapplied by means of a short boom to which the deployerend of the tether is attached. The tether is free to moveessentially as a conical elastic pendulum, and a terrestrialexample is given in which a gravitational restoring force isincluded in a vertically orientated system. The stretch ofthe tether results in bobbing oscillations which couplewith the pendulum motion. The work is also of interestfrom a control and instrumentation point of view. Thecontrol is by means of planar rotational motion of theboom and is used within a linearised system model, notingthat simulations were performed using a nonlinear model.Feedback of tether strain rate is used, in practice by meansof an accelerometer within the end mass, and maximumdamping of the bobbing oscillation is used to evaluate theoptimal gain for the system. It is shown that the out-of-plane angle of the tether decouples from the rest of thesystem dynamics and so is uncontrollable, thus reducingthe system to a planar elastic pendulum. The relevance ofthe work is in the effectiveness of the boom controlactuator in minimising both the bobbing and the planarswing oscillations using simple actuation and control. Incontrast with this Hokamoto et al. [65] consider a tetheredspace robot, conceptualised in their 2001 paper as a rigidbody at the end of an elastic tether connected at its otherend to a larger rigid body in the form of a main satellite.The system is constrained to motion in the orbital plane.Two links are attached to the robot satellite and are used asa manipulator to control the system. Torques are appliedmomentarily to the manipulator to effect the control andalthough strain energy in both axial and lateral tetherdeformation is initially included the paper does not state ifand how this is developed, although the theoreticalprinciples are all summarised. Extremely good tether swingminimisation is achieved for pragmatic data. Tetheredinterferometers based on different constellational cong-urations are considered by Quadrelli [66], with a generalanalysis for an n-body system where each body represents aspacecraft within the three-dimensional constellation andeach interconnecting tether comprises N point masses,connected by massless springs and viscous dampers.Quadrelli points out that there are two ways to treat tetherdeployment with a lumped mass model; either the mass ofthe mass-points is kept constant, with varying numberwhich is said to imply a mass creation and eliminationprocedure, or the number of mass-points is kept constantso that their masses will vary. Clearly, the rst approach ismore complicated than the second and so a general analysisis given for that, with a three spacecraft model used as abasis for the derivation, as briey summarised in the paper.An important feature of this paper is that thermo-mechanical modelling is included, and that a link isprovided between the dynamics and control aspects oftethered formation ying. This is specically for inter-ferometer applications which concentrate on a three-

in Aerospace Sciences 44 (2008) 121 9spacecraft/two-tether system and a four-spacecraft/three-tether system; noting back to the work of McKenzie and

ARTICLE IN PRESSessCartmell [12] and McKenzie [13]. The ultimate aim of suchresearch is to generate recongurable control schemes forvery general congurations of tethered interferometers.The paper by Bombardelli et al. [67] investigates the issueof rotation plane change of a dipole-like interferometercomprising two end-located collectors and one centralcombiner, and proposes an open-loop control strategy forhigh-precision re-targetting.An interesting concept for a tethered space manipulator

is given by Woo and Misra [68] in which a tether isproposed as a means of extending the range of amanipulator with little mass and fuel cost. Their systemcomprises a two-link manipulator, a tether, and a space-craft. Modelling assumptions are that the robot manip-ulators arms are rigid links and the tether is rigid andstraight, with a point mass located at each joint in thesystem and at the end effector. The centre of mass of thesystem is coincident with the centre of mass of thespacecraft, and describes a circular orbit around Earth.Planar motion of the system is assumed, and four angulargeneralised coordinates are used to dene this. Althoughthe tether is considered to be in tension, and rigid as aresult, the authors concede that there can be theoreticalconditions in which the tether tension goes negative, andtherefore changes to compression. Their remedy for this isto calculate tension from an analytical expression duringthe simulations in order to ensure that the results arephysically meaningful. Time histories of this, together withjoint torques and overall end-effector position, arecalculated and feasible paths for the end effector are givenwith certain torque restriction and various initial condi-tions. The end result of this is an algorithm, based on aglobally convergent form of Newtons method, fordetermining whether a feasible path exists between theend effector at its extended vertical position and the desiredend point. Ishige et al. [69] introduce the concept of usingan ED tether for space debris removal, on the basis that itcan be considered initially as a simple dumb-bell (assumedto be rigid) but with signicant tether mass lumped into asingle point, and then as a discretised mass model withinwhich exibility is allowed by using parallel springs andviscous dampers as interconnections between the discretetether masses. The geomagnetic eld is modelled as a singlemagnetic dipole with titled axis and the magnetic eldvector expressed in inertial coordinates. The tether debrisremoval strategy is based on a sequence of tetherdeployment and ED activity by which means the debrisitem is lowered sufciently to burn up in the atmosphere.The tether exibility couples with the orbital dynamics,although the paper does not discuss this in particulardetail, however, tension variation effects are noted.Practical guidelines are given for the application of sucha system, notwithstanding that the mass of the debris item,compared with that of the service satellite at the other endof the tether, could signicantly affect system stability.

M.P. Cartmell, D.J. McKenzie / Progr10Some useful further references relating to this work are in[62,63].2.5. Control strategies and models

In this section the emphasis is on proposals andmethodologies for the application of some form of controlof tethers in space. A highly readable and useful discussionof the use of motor driven momentum exchange tethers forlunar and interplanetary exploration is given by Puig-Suariet al. [70] and is another exposition of the motorised conceptalso proposed by Cartmell [53] and also cited in Refs.[4,10,11,13,24,27,54,55,56]. In [70], the authors explore theuse of uniform tethers and tapered tethers, with a discussionof the attendant tether mass ratio. The important conclusionis made that tethers can be superior in mass terms totraditional chemical rockets for low-speed manoeuvres, butinferior for high-speed applications. Useful relationshipsbetween the energy required to spin up a tapered tether andenergy converted by solar cells per unit area are given,within the approximate range 0.151.5m2/kg of payload.The paper also summarises the problem of the provision ofcounter-inertia with motor drive designs. This is also afeature of the work of [53] and its extensions cited above.The authors of [70] also state that orbiting tether facilitiescan be extremely efcient in missions where many spacecraftlaunches are proposed, with particular advantages of generalsimplicity and reusability of the tether systems, however, it isgenerally acknowledged that this does not necessarily extendto the orbital control and maintenance requirements fortethers which can be rather demanding, particularlyfor high-performance interplanetary propulsion [13,53,54],in addition to ancillary hardware reliability problems,particularly in storage and deployer systems, and brakes.Several hardware and software implementation studies havetaken place, with an early contribution provided byGwaltney and Greene [71] in which the Getaway TetherExperiment, GATE, is discussed. A simple dynamicalmodel of the planar libration dynamics is used inconjunction with a tether tension law based on length andlength rate feedback, and other (cited) work has shown thatthis can produce desirable stabilisation characteristicsduring deployment and retrieval. In [71], the authorsinvestigate the implementation of such control schemeswithin prototype hardware which is specically designedfor space ight; cross-reference with [23,72] for furtherdiscussions of specic hardware designs. The mechanicaldetails of the implementation examined in [71] (steppermotor driven reel and wind mechanisms) are perhaps lessimportant than the techniques used, for which simulationsshowed that the planar libration amplitude of an uncon-trolled test tether of 10m in length would reduce from 7.01to 1.31 within 53 s, whereas yo-yo control, based on lengthvariation at libration amplitude zero and peak excursionvalues, could get this down to 41 s, and phasing control,based on length variation at angular positions slightly beforethese points, could improve that further, with times down to36 s. These predictions appear to have been backed up by

in Aerospace Sciences 44 (2008) 121experimental tests, although relatively little detail of these isgiven in the paper.

ARTICLE IN PRESSessAn interesting control application for tethers is in thedynamic isolation of payloads from a mother satellite orspacecraft. Ohkami et al. [73] discuss this in the context ofpayload and space station interactions for microgravitycontrol in the payload. A three mass system is modelled,comprising the base vehicle, the platform, and a ballastmass, connected in series by two tethers. Platformtranslations and rotations are considered and the equationsare linearised on the assumption that for microgravityapplications the deections from the equilibrium state aresmall. Highly accurate microgravity manipulation isavailable for simple feedback control. In the case of large,controlled, tether motions, as would be required for wastedisposal and capsule re-entry operations, nonlinear dy-namics are unavoidable, but alternatives to fully analyticalnonlinear controller design such as fuzzy logic can providevery effective control. This is discussed for a tether initiatedre-entry application and a waste disposal system by Licata[74], in which a feedback system based on simple fuzzylogic rules controls the variable rate deployment for adeployer reel-brake assembly design, within a simulation,using realistic data. It is worth noting that this procedure isapplied to medium length tethers of up to approximately25 km. The control of robots remote from their spacevehicle is revisited again in the work of Nohmi et al. [75];also refer to [68], where translational momentum of thecentre of mass of the tethered robot is controlled by tethertension, and angular momentum control, with respect tothe tethered robots mass centre, is based on proper controlof the tether attachment point and tether. These controlsare effected by manipulations of tether tension and linkmotion in the case of a generalised robot in the form ofn+1 rigid bodies (links) connected through rotationaljoints. The tether itself is considered to be a massless rigidlink from the centre of mass of the spacecraft, subjectedonly to tension and with a time dependent length. Areaction wheel, jet, or thrust, is required to control angularmomentum about the tether. It is shown that the linkmotion of the tethered robot can be satisfactorily split intotwo sub-tasks i.e. end-effector motion and tether attach-ment point motion, and that compensation for signicantimpulsive disturbances is robust and effective. Tensionmoments for four short tethers used to connect twospacecraft halves have been shown by Kumar and Kumar[76] to be good for the control of two aspects of systemmotion by means of a combined open-loop control lawtogether with a simple feedback scheme. The motionsconsidered for control are longitudinal system drift withrespect to the ground station and attitude excitationinduced by eccentricity. This work relates to the TSS asmentioned in Section 2.2, on the assumption that the TSScomprises two identical satellites connected through veryshort tethers, with the anchor points located on theprincipal roll axis and symmetrically offset from the centreof mass of each satellite. Tether mass is neglected and the

M.P. Cartmell, D.J. McKenzie / Progrplanar angular motion case is considered. The pitchingangles of the two satellite halves, the tethers, and the tetherlength dene the motions of interest and comprise threeangular and one translational generalised coordinate.Length variation can be controlled in order to force thesystem into certain motions and ultimately a special hybridtether length control law is proposed. It is shown thateffective control can be achieved using tethers as short as10m. The combination of open-loop and feedback control,in this context, results in a signicant improvement inattitude precision for system alignment along the line-of-sight. This is proposed as a viable alternative to stationkeeping manoeuvres required for geostationary satellites,particularly in cases when onboard fuel is nearingexhaustion.Offset control of a tethered sub-satellite from a large

platform is investigated by Pradhan et al. [77], on the basisof the TSS concept once again, where the offset mechanismtakes the form of a manipulator attached to the platformcapable of providing movement of the platform end of thetether in the local horizontal and vertical directions. Thetether is modelled as a exible string and the assumedmodes method is used for discretisation. Motions arerestricted to the orbital plane, and generalised coordinatesfor platform and tether pitch, together with tether modalcoordinates, are used to dene the system motions.Damping is usefully included by means of Rayleighsdissipation function and the generalised force vectorrepresents momentum gyros located near the centre ofmass of the platform and thrusters at the tether sub-satellite end. Modelling accuracy is determined by checkingthe total system energy and comparing the frequencies ofthe linearised system with those available in the literature.The Feedback Linearization Technique (FLT) is used tocontrol the attitude dynamics whereas a robust LQGcontrol is used for the vibrational modes. The paperconcentrates on controller design and overall offset controlis seen to be effective for the regulation of platform pitchand tether vibrations but less so for tether attitude, forwhich large offset motions are required. A Hypersonic-Airplane Space-Tether Orbital Launch Vehicle (HASTOL)architecture has been proposed by Hoyt [78] in whichseveral sub-concepts are proposed within the architecturefor the transportation of large payloads into Earth orbit.The concept species a hypersonic aeroplane to carry asubstantial payload up to an altitude of 80100 km at aspeed of Mach 1013. The aeroplane is intended torendezvous with the tip of a long rotating tether whichswings down from a massive facility in Earth orbit. Agrapple vehicle at the tether tip receives the payload whichis then pulled up by the tether into orbit. The system is saidto offer launch cost reduction because a conventionallaunch vehicle requires a total DV of around 7.5 km/swhereas the HASTOL launch vehicle only needs to provideabout 3.5 km/s to the payload. This paper summarisesconcepts for three different tether systems for use withinHASTOL and shows that a rotating tether is optimal,

in Aerospace Sciences 44 (2008) 121 11particularly if it connects with the highest possible apogeefor the hypersonic spaceplane. Methods are given for

ARTICLE IN PRESSessmaximising the rendezvous window, although this is stillmeasured in seconds. The work conrms, entirely by meansof numerical simulations, that the HASTOL concept, asdened, is pragmatic and controllable. Fujii et al. [79]consider a three degree of freedom nonlinear analyticalmodel for a terrestrial deployment model for a tether with aoating balloon at its upper end, in order to obtain anunderstanding of the rotation, attitude, and deployedlength when the simple balloon tensioned system issubjected to aerodynamic drag and is under the inuenceof a specic control law. The control law is designed tosuppress the motion of the system and to adjust the tetherlength. The tension supplied by the balloon is of the orderof a few Newtons and experiment and simulations based onthe analytical model are compared. The concept of virtualmass is incorporated into the analytical models equationsof motions, whereby it is found that the uid surrounding abody which is accelerating within it (like the balloon in thiscase) seems to increase the mass of the body, and this is notnegligible when the orders of magnitude of the mass of thebody and the virtual mass are close. In the case of thissystem it is found that the presence of virtual massimproves the accuracy of the model. Whilst this in itselfis not directly relevant to the performance of tethers inspace it provides a very good means of testing importantmicrogravity effects, with the assurance of a fair degree ofcontrollability. Attitude stabilisation of tethered spacecraftconrmed as a major issue and conguration-based controlof attitude has been shown, by Kumar and Yasaka [80], tobe an elegant solution. In this work the authors start fromthe general literature nding that a single tether connectinga main satellite or vehicle to an auxiliary mass requiresfeedback control to ensure attitude stability of the satellite,but that a two-tether system can improve on thisperformance. On this basis these authors present a kite-like conguration comprising three tether spans, the toptwo emanating from points on the (upper) satellitesymmetrically offset from the centre of mass and terminat-ing at a common connecting point below from which thethird span hangs down, ending in the auxiliary mass.The authors summarise a nonlinear non-dimensionalisedLagrangian model comprising 10 generalised coordinatesand show by means of a stability analysis for the linearisedsystem about equilibrium that certain physical constraintsare necessary for stability, but that this is achievable andpotentially inherently so; see also Quadrelli [66]. The singletether stabilisation problem is discussed by Cho andMcClamroch [81] and the control objective here is slightlymore strict, requiring not only attitude control of thesatellite but that this is consistent with small tethermotions. They do this in two ways, initially by decouplingthe attitude dynamics from the tether dynamics and thendesigning in a linear feedback to stabilise the attitude, andalso by using a Kalman decomposition to decoupleuncontrollable modes and then using linear feedback to

M.P. Cartmell, D.J. McKenzie / Progr12stabilise the controllable modes. They conclude that forroll-yaw attitude stabilisation, which is more demandingthan pitch control, the Kalman decomposition approachworks best because less actuator movement is required andthe tether dynamics are generally less affected. We returnto ED tethers, and a model leading to a specic type ofdynamic instability when working in inclined orbits in thepaper by Pelaez and Lara [82]. The instability isindependent of tether exibility and so the tether ismodelled as a dumb-bell with end masses. The geomagneticeld is represented by a non-tilted dipole model andconstant tether current is assumed. The electrodynamicsforce the system dynamics equations and the paper gives afull account of the stability of the tether in terms of theinuence of the orbit inclination and a parameterrepresenting the magnitude of the ED force on the tether.A numerical algorithm based on the Poincare method ofcontinuation of periodic orbits is used to extend previousasymptotic analyses. The paper shows that high inclina-tions are not initially seen to be appropriate for vertical EDtethers and it is shown that for a given inclination there is acritical value of the ED magnitude parameter beyondwhich destabilisation is signicantly accentuated. Tethercurrent control can help to alleviate such effects, but it isrecommended that such tethers are generally better offbeing operated away from this sort of threshold. The paperalso shows that there are many unstable periodic solutionsto this tether system and that such regimes are unsuitablefor long-term ED tether operation. Introducing motordrive to a momentum exchange tether has many advan-tages but it has been shown by the authors, and others[11,13,26,53,54] that the interactions between local motordrive leading to tether spin and orbital mechanics are farfrom straightforward and that such systems are capable ofvery rich dynamics. Cartmell et al. [4] show that scalemodelling, and performance prediction based on this, is auseful way forward when attempting to generate pragmaticdata for the dynamics of controllable motorised tethers. In[4], it is shown that a symmetrically designed motorisedtether, with the motor drive placed centrally and drivingthe two sub-spans, with inertial counter-balance, providesa basis for optimised performance. The proposal utilisesthe concept of payload release symmetry whereby the twopayloads are released simultaneously from the ends of thetether sub-spans at the point when the system is alignednormal to the tangent to the orbit. Therefore the innerpayload is de-boosted and the outer payload is boosted.The paper treats a simplied terrestrial (on-ice) model bymeans of classical scaling theory using the Buckingham Pi-theorem. It is shown that even for the restricted dynamicsof this system that certain very important trade-offsbetween mass and geometrical parameters have a signi-cant effect on the systems ability to spin-up, and it isproposed that insights and enhancements at this level arelikely to improve the performance of motorised tethers inorbit. The work also provides a basis for full size systemgeneration from the scale model, or vice versa. Tether

in Aerospace Sciences 44 (2008) 121vibrations were also investigated, by means of a three-dimensional stretched string model, and scaling laws

ARTICLE IN PRESSessapplied to this model, and the on-ice rigid body modelshowed that there is a numerical incompatibility whentrying to scale rigid body spin-ups and exural tethervibrations at the same time. Therefore, a clear case formulti-scale modelling is made in this paper. A simple de-spin concept is also proposed for payloads in order todirect angular momentum in spin of the payload at andafter release back to the spinning tether system, and aninitial two degree of freedom nonlinear model is introducedand discussed. One of the questions raised by this workrelates to the dynamics of tethers after payload release, andhow they can be controlled when the tether effectivelybecomes a trailing structure. This general problem is ratheruniversal and generally independent of tether type or theconguration in which it is used. The paper by Rossi et al.[83] of 2004 provides an interesting account of the likelyperiodic motions of a tether trailing satellite, with attentionpaid both to the motion of the satellite and the tether. Thescenario that the paper considers is when a tetherconnecting two satellites is cut as a consequence of anaccident or a planned manoeuvre. It is assumed that theEarth centred frame is inertial, that the satellite can bemodelled as a point mass, the tether is homogeneous withuniform density, the torsional and transversal vibrations ofthe tether can be neglected, and elasticity follows Hookeslaw. The model comprises partial and ordinary differentialequations and applies the well-known wave equation in anorbital context, together with the effects of atmosphericdrag and Earth oblateness. This signicant work showsthat the existence of periodic solutions for such a systemdoes not depend on the equilibrium state when gravita-tional and oblateness terms predominantly drive thedynamics. The important features relate solely to tetherdensity, length, exibility, and rotational speed. However,shorter stiffer systems tend to exhibit periodic motionsabout their equilibrium states. In the case where atmo-spheric drag inuences the system at all signicantly it isfound that tether trailing satellites are strongly inuencedby the equilibrium state; this is because the gravitationaland oblateness forces are uniformly bounded independentof position, whereas drag forces do not behave like this andso linearisation about the equilibrium states is required. So,the existence of periodic motions with bounded forces isfound to depend just on tether parameters, but unbounded(linear) growth depends on the equilibrium states. Severalinteresting cross-references can be found in [9,42,57,62,65,66,68].

2.6. Practical tether designs and proposed system

technologies

It has already been shown that an important objective oftether modelling is to generate data that can be used forpragmatic designs which will perform optimally andpredictably when in orbit. Carroll proposed a preliminary

M.P. Cartmell, D.J. McKenzie / Progrdesign for a 1 km/s tether transport system [84] in orbitaround the Earth, the Moon, or Mars. This paper isinteresting because it considers a single-ended (singlepayload) tether in what the author denes as a barelyspinning mode, where the system spin rate is approxi-mately synchronous with the orbital period. The authorgives substantial numerical data for practically usefulmission applications about Earth, the Moon, and Mars,on the basis of how tethers might operate within certainpayload delivery and retrieval scenarios about thosebodies. In addition the paper discusses practical proposalsfor a traction-winch tether spool-store system withcontrollable feed and cites interesting critical reeling ratesfor different stored lengths up to 200 km. The paper alsodiscusses concepts for testing thick tethers under high-repetition cyclical reeling at low temperatures, and capturehardware design is proposed based on the criteria of largecapture zone and design simplicity, in the form of a hookand bag system. The paper also considers capture andrelease transients that inevitably arise and which drivesudden changes in equilibrium tether tension and length,together with some comments on general deploymentstrategy and general operational conditions. Retrieval ofa tether and point-mass payload to a massive spacecraft isconsidered in some detail in the paper by Chernousko [85].The conguration comprises a reeled out tether and end-mass payload swinging from below the spacecraft and isrestricted to a planar analysis. The forces acting on thesystem comprise tether tension, gravitational force, andinertial forces (centripetal (centrifugal) and Coriolis). Theauthor suggests four different practical ways of controllingthe retrieval process, rstly by using small motors on thesatellite to generate reaction forces perpendicular to thetether, moving the tether emanation point on the spacecraftrelative to the spacecraft in order to suppress oscillations,controlling small deviatory motions of the spacecraft inorder to suppress oscillations, or controlling tether tensionduring retrieval. This paper considers several importantcases, specically for constant tether length, oscillations ata constant winding rate, small tether oscillations, nonlinearoscillations, and control of the retrieval process. Control isachieved by a two-stage process in which the tether isinitially maintained at constant length during which phasetrajectories are used to determine the necessary constantrate of winding in the second stage. The second stageproceeds and operates at the calculated winding rate untilretrieval is complete.Trade-offs between tether mass, strength, and longevity

are of fundamental importance and in the case ofmomentum exchange tethers one of the most interestingconcept proposals to emerge has been that of theHoytether, Forward and Hoyt [41,86], in which a multi-year lifetime is proposed for an open tubular tri-axial net.This design consists of axial load bearing primary lineswith cross-linking at intervals by diagonal secondary lines,which are only loaded if the section of primary line thatthey surround fails for some reason. The most likely cause

in Aerospace Sciences 44 (2008) 121 13of failure in such a scenario is due to high-velocitymicrometeoroids or space debris. Due to this design the

ARTICLE IN PRESSesseffect of the damage is localised to the failure region andthe load is re-distributed within the secondary lines aroundthis region. The authors claim a Hoytether lifetime in theorder of decades rather than the less-than-full-missioncapability of single line tethers. Further practical ideasresulted in the Rapunzel small tether mission for tetherassisted payload re-entry. This is discussed in the paper bySabath et al. [87] and was intended to be a small tethermission whose deployer was tested in a parabolic ight in1995. The deployer consists of a tether box containing aspooled tether of 63 km and a brake and compensatorbased on textile industry technology. The deployer wasfound to perform quite well during the microgravityconditions of the parabolic ight with good tension controlin evidence. However, despite the effectiveness of tetherdesigns and their deployment systems the space debrismitigation problem is one that has had to be addressed inrecent times. The work of Rex [88] highlights some of thespacecraft design changes that would be effective in debrismitigation. Two principal approaches are highlighted;passivation, in which onboard stored chemical propellantsare removed in order to prevent debris generation byexplosions, and the deliberate de-orbiting of larger orbitingobjects to reduce the possibility of collision. ED tethers aresuggested for de-orbiting applications, and this has alsobeen explored by others, notably Hoyt and Forward [86].Clearly the orbital debris problem also affects the use oftethers and this is explored further in the work of Draper[24]. Very short tethers could be feasibly used to achievecontrollable satellite pitch and roll attitude manoeuvres,Kumar and Kumar [89], and an in-depth dynamical modeldescription is given for a short four-tether system connect-ing a satellite to an auxilliary mass, and the synthesis ofopen-loop tether length control laws. Good control ofcomplex manoeverability is obtained for sufciently slowtether length variation, together with small amplitudeoscillations about the desired nal equilibrium position.This could be an important methodology for safe satelliteoperation in certain circumstances and the general issue ofsafe operation of tethers, particularly in unscheduledoperations, from the ISS is discussed in a practicallyfocused analysis by Trivailo et al. [90]. Unscheduledoperations are meant to cover instances of unexpectedseverance, and interference between the tether and otherhardware. Both type of event has been shown to bepossible in tether retrieval operations, particularly if so-called skip-rope modes are initiated. The paper shows thatinstabilities can be caused by an excessive retrieval rate andalso by skip-rope motion, both of which can give rise toseverance or interference with other hardware. Dynamicsimulations show that interference with the ISS itself wouldbe likely, with severance as the nal outcome.Tether missions involving interplanetary propulsion or

the orbit raising of major payloads will inevitably requirethe use of a reusable space plane system capable of liaising

M.P. Cartmell, D.J. McKenzie / Progr14with a tether for payload handover. Considerable con-ceptual work on this issue has been carried out, reported byHoyt [78] and Grant et al. [91], and, as already mentionedin Section 2.5, has resulted in proposals for the HypersonicAirplane Space Tether Orbital Launch (HASTOL) vehicle.This technology overview provides insights into thepossibilities of ying a 15 tonne payload in a ballistic arcto reach Mach 1013 at an altitude of 80100 km.Thisliaises with a grapple mechanism at the end of a rotating600 km tapered tether in a 700 km orbit, as a highway tospace. The authors promote HASTOL as a completelyreusable, cost-cutting technology for Earth-to-orbit spaceaccess. In a similar vein Hoyt [92] discusses the design andsimulation of a tether boost facility for transport fromLEO to GTO. Proposals for boosting 2.5 tonnes from LEOto GTO every 30 days are discussed in the paper and it isalso stated that the same facility could be used to boost1 tonne payloads to LTO. The tether in this system istapering but comprises multiple lines to provide bothstrength and redundancy, possibly in the form of aHoytether [41]. The orbital dynamics are summarised andthe use of an ED tether is discussed. The theme ofdeployability continues to receive attention and Pascal etal. [93] have shown that the use of a crawler sub-satellitewhich moves along the tether during retrieval can bestabilising, particularly if combined with appropriatelength control laws in the form of an intermediate schemegeneralising the previously proposed conventional schemeand the crawler scheme. The paper presents an in-depthdynamical treatment of such a scenario and shows bymeans of a numerical simulation that the so-calledintermediate scheme reduces the amplitude of oscillationduring retrieval several times over those of the conven-tional or crawler schemes. The use of crawlers is alsoexamined in the paper by Goff and Siegel [94] in which twomassive nuclear electric crawlers are tted to the sub-spansof a symmetrical momentum exchange tether with cen-tralised facility. This is described as boot-strapping and isproposed as a means of angular speed control in which thetwo crawlers move in or out from the centre as required.Control and stabilisation of tethered systems is examinedfor three body congurations by Misra [95] in which adouble-ended payload system, complete with sizeablecentralised facility mass, is analysed in detail. Theassumptions made relate to inextensible, straight-line,mass-less tethers, with point mass payloads, with thesystem COM on a circular orbit and undergoing planardynamics. Local angular coordinates are introduced,allowing the two sub-spans to be at different angles, togive a two degree of freedom model for which fourprincipal equilibrium conditions are evaluated. The stabi-lity of the equilibrium conditions is investigated for smallperturbations and the eigenvalues of the characteristicequation show that at best there can be marginal stabilityfor certain specic conditions, but no asymptotic stability.Spinning tethers are normally assumed to operate as dumb-bells, with axially aligned sub-spans due to centripetal

in Aerospace Sciences 44 (2008) 121stiffening during rotation. However, Misra [95] shows thatin cases where this is absent for some reason then the

ARTICLE IN PRESSesssystem sub-spans may well take other orientations, and insuch cases practical issues of alternative stability have to beconsidered. This could have relevance to both pre and posttether spin-up scenarios.Powell et al. [96] provide interesting insights into the use

of technology for magnetically inated cables for theconstruction or deployment of large and highly rigid spacestructures. The idea is based on launching the magneticallyinatable cables (MIC) as a compact package of coiledsuperconducting cables, which would be cryogenicallycooled and electrically energised on reaching orbit. Thiswould result in magnetic repulsion, which would then allowthe coiled package to self-deploy into the intendedstructural conguration. A network of high-strengthtethers would be required to hold the superconductingcables in place. This has some similarities in terms of theend result with the work on space webs by McKenzie andCartmell [12] and McKenzie [13]. It is possible that longstructures could also be made this way, which couldthemselves operate as large capacity tethers. Hybriddesigns involving two or more tether technologies couldbe of great utility for certain space missions. A case in pointis the MXER concept [19,21,22] as discussed already inSections 2.1 and 2.2. In [22], Sorensen considers theconceptual design of an MXER tether boost station,concluding that a single tether in an elliptical equatorialorbit could replace staged tethers, using propellantless EDreboost with highly error-tolerant payload catch mechan-isms and tether-end mass concentration.An interesting practical problem associated with tether

system operation in space relates to the