TethersinSpaceAPropellantlessPropulsionInOrbitDemonstrationKabelsinderuimteEendemonstratievanstuwstoflozevoortstuwingineenbaanomdeaardePROEFSCHRIFTterverkrijgingvandegraadvandoctoraandeTechnischeUniversiteitDelftopgezagvandeRectorMagnificusProf.ir.K.Ch.A.M.Luyben;voorzittervanhetCollegevoorPromotiesinhetopenbaarteverdedigenopmaandag30mei2011om10.00uurdoorMichielKruijffIngenieurLuchtenRuimtevaartgeborenteDenHelder.Ditproefschriftisgoedgekeurddoordepromotoren:Prof.dr.W.J.OckelsProf.dr.E.K.A.GillSamenstellingpromotiecommissie:RectorMagnificus
voorzitterProf.dr.W.J.Ockels
TechnischeUniversiteitDelft,promotorProf.dr.E.K.A.Gill
TechnischeUniversiteitDelft,promotorProf.dr.E.Lorenzini
UniversitdiPadovaProf.ir.B.A.C.Ambrosius
TechnischeUniversiteitDelftProf.C.Nicollier
colePolytechniqueFdraledeLausanneDr.P.A.Swan
SouthwestAnalyticNetworkDr.C.Menon
SimonFraserUniversityProf.dr.ir.J.A.Mulder
TechnischeUniversiteitDelft,reservelidDeltaUtecSpaceResearchandConsultancyheeftinbelangrijkematefinancielbijgedragenaandetotstandkomingvanditproefschrift.ISBN9789088912825Cover:
ByM.Kruijff&Proefschriftmaken.nl.TheYES&YES2spaceexperimentsandTREXtetherinorbit.YESimagebyM.Kruijff,YES2imagebyESA(S.Corvaja),TREXimagekindlyprovidedbyJAXA.Printedby:
Proefschriftmaken.nl||Printyourthesis.comPublishedby:
UitgeverijBOXPress,OisterwijkCopyright2011byM.Kruijff.WritteninOpenOffice.PrintedinTheNetherlands.FormyfatherwhoonlycaughtaglimpseandMariawhocaughtmeContents
5ContentsCONTENTS 51 INTRODUCTION 91.1
Sustainabilityandtheappealofspacetethers..............................................................................91.2
Examplesoftetherapplications....................................................................................................101.3
Flighthistoryofspacetethers.......................................................................................................141.4
Objectiveofthisthesis....................................................................................................................171.5
Surveyofthisthesis........................................................................................................................18PARTITETHERSANDTHEIRAPPLICATIONS
212 TETHERDYNAMICS 232.1
Deployingatetherinspace..........................................................................................................232.1.1
Gravitygradienttensionforahangingtetherincircularorbit.......................................232.1.2
Equationsofmotion...............................................................................................................252.1.3
Pendulummotionofaswingingnondeployingtether...................................................262.1.4
Tetherdeployment..................................................................................................................272.1.5
Impactoftetherproperties....................................................................................................282.2
Howthetetherbecomesuseful.....................................................................................................302.2.1
Momentumtransfer................................................................................................................302.2.2
Electrodynamictetherprinciples..........................................................................................332.3
Tethermissionsimulation.............................................................................................................392.3.1
Advancedtethermodels........................................................................................................402.3.2
SimulatorOverview...............................................................................................................412.3.3
Validationandcomparisontoothermodels.....................................................................493
ANALYSISOFTETHERAPPLICATIONS 513.1
Mechanicaltetherapplications.....................................................................................................523.1.1
SpaceMailandwastedisposalfromaSpaceStation.........................................................523.1.2
Tetheredupperstageforalaunchassistandupperstagedeorbit.................................573.1.3
Multipointsensinginthelowerthermosphere.................................................................643.1.4
Artificialgravity.......................................................................................................................693.2
Electrodynamicdeboost.................................................................................................................793.2.1
AssessmentofOMLperformanceinbaretetherelectroncollectiontesting.................803.2.2
Tethereddeboostanddynamicinstability.........................................................................833.2.3
Tethereddeboostandcollisionrisk.....................................................................................893.2.4
ArotatingtetheraroundJupiter..........................................................................................983.3
Responsibleorbitalnichesforuseoftethers............................................................................104PARTIIDEVELOPMENTOFASPACEMAILSYSTEM
1094 DESIGNASPECTSOFASAFETETHER 1114.1
Characterizingthetetherproperties..........................................................................................1114.1.1
Materialselection...................................................................................................................1114.1.2
Braidingofthetethers..........................................................................................................1144.1.3
Breakstrength........................................................................................................................1154.1.4
Stiffnessandviscoelasticeffects..........................................................................................1164.1.5
Damping.................................................................................................................................1204.1.6
Outgassingandextraction...................................................................................................12164.1.7
Frictionbehavior....................................................................................................................1224.1.8
Twistandinternalbraidingtorque....................................................................................1254.1.9
Tetherlengtheffects:shapememory,viscoelasticrecoveryandcreep........................1284.2
Protectingthehostplatform........................................................................................................1294.2.1
Securingseparationfromthedeploymentplatform.......................................................1294.2.2
Understandingrecoil............................................................................................................1314.2.3
Ripstitching.............................................................................................................................1334.2.4
Dissipativeclamping............................................................................................................1394.2.5
Passivetetherreleasesolution.............................................................................................1404.3
Avoidingthreatstotetherintegrity............................................................................................1424.3.1
Debrisandmeteoroidrisk...................................................................................................1424.3.2
Otherdegradationmechanisms.........................................................................................1474.3.3
Thermalloadingduringfrictionbraking..........................................................................1474.3.4
Designsafetyfactors.............................................................................................................1494.4
Reducingcollisionriskbyenvironmentaldisintegration.......................................................1494.4.1
Requirements.........................................................................................................................1504.4.2
Mechanicsofdegradation....................................................................................................1514.4.3
Degradationchemistry.........................................................................................................1524.4.4
Polymerdegradationresearch............................................................................................1544.4.5
Materialselection...................................................................................................................1554.4.6
Explorativetestingofselectedpurematerials..................................................................1564.4.7
UV/VUVexposuretestonenhancedselection.................................................................1624.4.8
Conclusionsandoutlook.....................................................................................................1685
DEPLOYERSYSTEMDEVELOPMENT 1695.1
Introduction...................................................................................................................................1695.1.1
Technologyheritage..............................................................................................................1695.1.2
SpaceMailsystemconceptformomentumtransfer........................................................1715.1.3
Overviewofdevelopmentandchallenges........................................................................1725.2
Supportfacilitiesfordevelopmentandtest..............................................................................1735.2.1
Windingmachine..................................................................................................................1735.2.2
Unwindingmachine............................................................................................................1745.2.3
Hardwareemulator..............................................................................................................1815.2.4
Deployersystemtestingoverview.....................................................................................1825.3
Spooldevelopment.......................................................................................................................1825.3.1
Coreandcanister...................................................................................................................1825.3.2
Thelengthdetectionsystem................................................................................................1845.3.3
Tetherwinding.......................................................................................................................1865.3.4
Tiedowns...............................................................................................................................1895.3.5
Flightspoolcharacterizationprocedure............................................................................1905.3.6
Driversofpatternsinunwindingtension.........................................................................1935.3.7
Othersystemdesignimpactsonunwindingtension......................................................1965.3.8
Reproducibilityofunwindingtension..............................................................................2035.3.9
Conclusionsandrecommendations...................................................................................2065.4
Barberpoledevelopment..............................................................................................................2075.4.1
Performancemodeling.........................................................................................................2075.4.2
Development..........................................................................................................................2195.4.3
Spoolbarberpolecharacterizationprocedure..................................................................2245.4.4
Effectofdesignparameters.................................................................................................2265.4.5
Reproducibility......................................................................................................................2315.5
Controllerdevelopment...............................................................................................................2325.5.1
Deploymenttrajectory.........................................................................................................233Contents
75.5.2
Releasetimecontrol..............................................................................................................2395.5.3
Lengthandvelocitydetermination...................................................................................2405.5.4
Feedbackcontrolalgorithms...............................................................................................2435.5.5
Performanceandrobustnesstesting..................................................................................2455.6
Closedloopdeploymenttesting.................................................................................................2485.6.1
FirststagedeploymenttestsusingtheTSEunwindingrig...........................................2485.6.2
FirstandsecondstagetestsonYES2unwindingrig.......................................................2525.6.3
DiscussionandRecommendations.....................................................................................262PARTIIITHEYOUNGENGINEERSSATELLITES
2636 THEFIRSTYESSATELLITE 2656.1
YESanditsobjectives..................................................................................................................2666.2
Missiondesign...............................................................................................................................2666.3
Subsystemsdesign........................................................................................................................2696.3.1
Tetheranddeployersubsystem..........................................................................................2696.3.2
Stabilizationofthesatellitebytethertorque....................................................................2706.3.3
Supportingsystems...............................................................................................................2716.4
MissionSummary.........................................................................................................................2746.4.1
Tetherexperimentcancellation...........................................................................................2746.4.2
ExperimentControlCenter..................................................................................................2776.4.3
Missionoperations................................................................................................................2776.4.4
YESmissiondata...................................................................................................................2796.5
AspectsoftheYESprojectapproach..........................................................................................2806.5.1
Challengeandopportunity..................................................................................................2806.5.2
Conceivingasatellitein8months......................................................................................2816.5.3
Milestonesandmanpower...................................................................................................2846.6
LessonsLearned............................................................................................................................2856.6.1
Failureanalysis......................................................................................................................2856.6.2
Recommendationsforafollowupproject........................................................................2896.6.3
HeritageoftheYEStethersystemdevelopment.............................................................2907
YES2 2937.1
Introduction...................................................................................................................................2937.2
Systemdesign................................................................................................................................2947.2.1
YES2andFoton......................................................................................................................2947.2.2
Keyelements..........................................................................................................................2947.2.3
InterfacestoFoton.................................................................................................................2977.2.4
Systemcharacteristics...........................................................................................................2977.3
Missiondesign...............................................................................................................................2997.3.1
Preparingfordeployment....................................................................................................2997.3.2
Deploymentofthetether.....................................................................................................3007.3.3
Fotinoreentry......................................................................................................................3027.4
Subsystemsdesign........................................................................................................................3057.4.1
Tetherdesign..........................................................................................................................3057.4.2
FLOYD....................................................................................................................................3077.4.3
OBCsoftware.........................................................................................................................3127.4.4
MASS......................................................................................................................................3147.4.5
Fotino......................................................................................................................................3157.5
ManagementoftheYES2project................................................................................................3187.5.1
Systemsengineeringtoolsandapproach..........................................................................3187.5.2
Innovationfromeducation..................................................................................................31987.5.3
Projectphasing.......................................................................................................................3207.5.4
LessonslearnedfromYESandYES2.................................................................................3218
YES2MISSIONANDRESULTS 3258.1
Flightpreparation.........................................................................................................................3258.1.1
Deployercharacterization....................................................................................................3258.1.2
Developingandtestingofthedeploymentalgorithms..................................................3288.1.3
Testingtheflightsoftware...................................................................................................3308.1.4
Testingthesystem.................................................................................................................3318.1.5
Makinglatechanges..............................................................................................................3328.2
Missionsummary..........................................................................................................................3328.3
Dataanalysis..................................................................................................................................3368.3.1
Analysisobjectives...............................................................................................................3368.3.2
Datasourcesandediting......................................................................................................3368.3.3
Deploymentreconstructionandinterpretation...............................................................3488.3.4
Deployerperformance..........................................................................................................3568.4
Tetherdeploymentdatamatchingbysimulation....................................................................3588.4.1
Simulateddeploymentwithmatchingvelocityprofile..................................................3588.4.2
Controllerperformance........................................................................................................3618.4.3
Tetheroscillations..................................................................................................................3628.5
FailureanalysisandextrapolationoftheYES2missionresults.............................................3668.5.1
Failureinvestigation.............................................................................................................3668.5.2
ComparisonYES2toSEDSmissiondataandanalysis...................................................3758.5.3
Simulatorapplicabilityandrepresentationofflightperformancebytests.................3788.5.4
FotinoandtheSpaceMailpotential....................................................................................3808.5.5
Lessonslearned......................................................................................................................3849
DISCUSSION 391REFERENCES 397SUMMARY
405EPILOGUETOWARDSSUSTAINABLESPACETRANSPORTATION 413SAMENVATTING
417LISTOFAUTHORSPUBLICATIONS 426CURRICULUMVITAE 429ACKNOWLEDGMENTS
430Introduction
91IntroductionGivenshipsorsailsadaptedtothebreezesofheaven,therewillbethosewhowillnotshrinkfromeventhatvastexpanse.JohannesKepler,lettertoGalileo,1610Tether:acordthatsecuressomethingtosomethingelseTether
propulsion systems: proposals to use long, very strong cables to
change the orbits
ofspacecraft.Spaceflightusingthisformofspacecraftpropulsionmaybesignificantlylessexpensivethanspaceflightusingrocketengines.DefinitionsasfoundonWikipedia,Jan.2008In
this section the thesis objective is defined following a review
that exposes the
gapbetweenpotentialtetherapplications,ononeside,andtheflightexperiencesofar,ontheother.Asurveyofthethesisstructureisthenprovided.1.1
SustainabilityandtheappealofspacetethersMankindsexplorationofspacehassofarbeenseverelylimitedbythedifficultytoreachEarthorbit.Ourwayintospaceismuchthesametodayasitwasoriginallyin1957,whenthefirstsatelliteSputnikwascarriedinto
space bytheR7rocket. TheSoyuz
rocketthatdeliverscosmonautstotheInternationalSpaceStationtodayisadirectdescendentofthatoriginalR7andstillsimilartoalargedegree.Allrocketsprovidepropulsionbyexpulsionofmatter,andhaveprovensofartobeahighlyinefficientmeansoftransport.Whereasashipsailinganoceaniskeptafloatbybuoyancyalone,itrequiresagreatdealofenergytogetarocketintoorbitandbalancetheEarthsgravityduringitsascent.Rocketscienceistoprepackallthisenergyintoadrumandreleaseitinacontrolledmanner.Whereasasailingshipexploitsthewindtopropelitself,arocketcarriesitsenergyalong,plowsthroughtheatmosphere
and hardly benefits from the opportunities that the environment
provides.Worse,forthisgargantuanandnontrivialtasktosucceed,agreatdealofadditionalenergyandeffortisrequiredtobuilduptheinfrastructurefordesign,productionandtransportofthatrocket.Onceweareinspace,formostpurposesitbecomessomewhateasiertotravelaround,andtherearenumerousconcepts,provenorunderdevelopment,toridethebreezesofheaven.Thesametypeofhighthrust(orimpulsive)rocketenginescouldbeemployedoncemore.Alternatively,ionenginesusethesameprincipleofexpulsionbuttheyarecharacterizedbycontinuous,lowthrustlevels.Moreliterally,solarsails,or,indeed,spacetetherscanridethebreezesofheaven.Solarsailsarepropelledbytheminutepressureexertedbytheimpactof10
Chapter1sunlight. They are especially promising for use in
interplanetary space where, over
time,lowaccelerationcanaccumulatetoobtainsignificantchangesinvelocity.Spacetethersarelong
thin cables, primal structures that, like solar sails, can be used
for
essentiallypropellantlesspropulsion,butalsotobuildformationsthatwouldbeverycostlyifcreatedinanotherway.Spacetethersprovideauniqueoutlookforsustainablespacetransportation,becauseenergyandmomentumarenotlostthroughexhaustgases.Thismayexplaintheirperceivedeleganceandappeal.Thresultingattractivenesshasmadetethersanacademicfavorite.Aswillbeillustratedinthefollowingsections,excitingconceptsandthesometimeselusivetetherdynamicshavebeencloselystudiedfordecadesbyagreatmanyscientists.Yetdespiteallthiseffort,thereislittleflightexperienceandnotetherapplicationisinusetoday.1.2
ExamplesoftetherapplicationsThe potential for space tethers to
create a paradigm shift in the way we travel to andthrough space is
probably best exemplified by the space elevator. This still
futuristicconceptwascreatedin1960byYuriN.Artsutanov[Artsutanov1960]whenheproposedtophysicallyconnectEarthtospacebytether.TheideawasanimprovementofthevisionaryorbitaltowerconceptasconceptualizedbyTsiolkovskyalreadyin1895[Tsiolkovsky1895].Aselfbalancingconnectionwouldbenecessary,i.e.averticaltetherinorbitaroundandcorotatingwithEarthwhilejusttouchingitssurface.Alargeendmassonthespaceendofthe
tether, beyond geostationary orbit, could be used to achieve such a
balance.Alternatively a tether of 144,000km length and without
endmass would fulfill theserequirements[Pearson1975].In order to
obtain access to space using the space elevator one would simply
board
adeliveryvehicleontheEarthsurface,exertsomepatienceasthevehicleclimbsthetether,thendisembarkatthealtitudematchingthedesiredorbit.Themostpopularorbitswouldlikelybegeostationaryandinterplanetaryorbits,althoughellipticalonesapproachingEarthin
perigee would also be a possibility. The delivery vehicle would
take onboard
anyreturningcargoanddescendbacktotheEarthsurfacetopickupthenextpassengers.The
space elevator shouldofferaccess tospaceata costorders of
magnitudelowerthanpossibletoday,changingtheappearanceandscopeofspacetravelitself.Theelevatorhastwomajorconceptualadvantagesoverrocketsthatshouldloweroperationalcost.Firstly,theenergyrequiredtoclimbthetetherdoesnothavetobestoredonboardofthedeliveryvehicle,butcanbee.g.transmittedfromthegroundbylaserorbyelectricalpowerthroughthecable.Secondly,theenergyspentcanbepartiallyrecoveredasthedeliveryvehicleanditsreturncargodescends.Asaresultofthesteepdropincost,rapiddevelopmentscouldbeexpected,
as have happened in recent years for personal computers and
mobilecommunication. For large multistage rockets it would mean
they would become all
butobsolete.Theuseofsatellitesforanypurposewouldhoweverbecomecommonplace,andsowouldcommercializationofspaceaswellashumanexplorationofthesolarsystem.Introduction
11Manytechnicalchallengesarestilltobedealtwithbeforewecanactuallybuildthespaceelevator.Workisneededtocoverdynamicissues,deliveryvehicleconcept,powersupplyandrecovery,atmosphericinteractionchallenges,deploymentandoperationalissues,andsoon.Nottheleastofthedevelopmentsrequiredisthatofhighstrengthlowdensitytethermaterialssuchascarbonnanotubes[Edwards2000,2003].Fortunately,tetherscanalsobeusediftheyaremuchshorterandinorbitwithoutaphysicalconnection
to Earth. A large number of applications for space tethers has in
fact beenproposed, ranging all the way from modest systems tailored
for niche markets to
grandenablingsolutions[foranoverview,seee.g.Cosmo1997,Cartmell2008,Pelt2009].Tetherlengths
range from hundreds of meters to hundreds of kilometers. These
applicationsgenerally make use of the tether as longdistance
mechanical connection, and they
mayexploittheabilityofconductivetetherstointeractwiththeEarthmagneticfield.One
of the more futuristic of the proposed mechanical tether
applications uses
multiplerotatingtethersystems,orbolos,inorbitaroundEarthandtheMoonorMarstocreateaninterplanetarytransportationsystem.PermanenthabitationofMarsorminingoftheMoonforraremineralsandrawmaterialscouldthenbecomeapossibility.Eachsystemwouldbea
hundred kilometers or more in length and feature a tip velocity
with respect to thesystems center of mass of at least 1.0km/s. The
direction of tether rotation would beprograde, i.e. identical to
that of the orbital direction. By careful timing a payload on
asuborbitalvehiclecouldbegrabbedfromthetipofaloworbitingtetherasitapproachestheEarth
atmosphere and temporarily matches the suborbital vehicles position
and
velocity.Halfaturnofthetethersystemlaterthepayloadcouldbereleasedandhurledintospace.The
system would provide the payload with an altitude increase of twice
the
distancebetweentipandsystemcenterofmassandwithavelocityincreaseoftwicethe(relative)tipvelocity.Next,a
similarandsynchronizedsystemwouldcapturethepayloadandhurlitonward.EventuallythepayloadscouldbedeliveredallthewaytotheMoonorMars.Thesame
infrastructure would be used to return cargo from those remote
celestial bodies
toEarth.Inthisway,theenergybalancewouldbelargelymaintainedandahighdegreeofefficiencycouldbeachieved,beitthatsignificantinitialinvestmentwouldberequiredtodeveloptheinfrastructure[Hoyt1999.I,Forward1999].Advanced
mechanical tether concepts have also been recognized as some of the
morefeasiblealternatives to cleanthe busy
lowerregionsofspacearoundEarth [Bade
1993,Bonnal2005].Hundredsofpiecesoflargedebris,mostlyspentstages,canbefoundinLowEarthOrbit(LEO).Ifnotremoved,suchdebrisislikelytoeventuallybreakupincollisionwithapieceoftheevenmorenumeroussmallerdebrisor,insomecases,withafunctionalsatellite.
Not only would a functional satellite be almost certainly destroyed
by such
anincident,thesecondarydebrisgeneratedinthecollisionwouldincreasetheincidencerateoffurthercollisions.Atravelingsystemwithaswingingorrotatingtethercouldmovefromdebristodebris,captureeachpiecewiththehelpofasuitablegrapplesystemanddeorbititsubsequentlybymomentumtransfer.12
Chapter1The above concepts could be significantly enhanced by using
also a conductive
tethermaterial.WithintheEarthsmagneticfieldandplasmasphereitispossibletoconvertsolarenergy
to orbital energy without the use of propellant. Using the
electrical
potentialgeneratedbye.g.solarpanelsacurrentcanbedriventhroughthetether:electronscanbecollected
from the Earths plasma on one end and be expelled on the other end.
In
themagneticfieldoftheEarthaLorentzthrustwillresultactingovertheconductingpartofthetetherandcreatinganelectrodynamicformofpropulsion[Johnson1998,Estes2000.I].Theorbital
lifetime of large rotating tethers in LEO could be increased by
using this Lorentzthrust for atmospheric drag compensation. The
MXER concept for example is anelectrodynamicallyenhanced bolo
system [Sorensen 2001]. The abovementioned debrisremover systems
could be moved from one debris object without propellant by
properlymodulatingtheLorentzthrustsuchthatitwouldinawaysailtheEarthsmagneticfield[Pearson2000].Electrodynamic
tether performance is dependent on the orbital, magnetic and
plasmaenvironmentwhichprovidesalimitationbutalsocreatesopportunities.
AroundJupiterorSaturn with their strong magnetic fields, high
orbital energies and fast rotating, denseplasmas unique conditions
exist in which a tether could effectively convert the
planetsrotationalenergyintobothorbitalandelectricalenergywithouttheneedforsolarpower[Gallagher
1998]. An electrodynamic tether could also be combined with an
electricpropulsion system, which would act as efficient provider of
electrons, such that
thedependencyontheplasmadensityaroundtheEarthwouldbereduced[Ockels2004].Such
applications require significant investment in tether
infrastructure. Furthermore,
formostofthemareliablerendezvousanddockingsystemwouldhavetobedeveloped.Thetethersorbitwouldhavetobekeptclearofdebrisandothersatellitestoavoidcollisions.Although
indeed carbonnanotube materials could eventually offer extremely
strong
andlightweighttethersolutionsandreducethemassoverheadandthustheinvestmentcost,thequestion
remains whether emerging alternative technologies with equivalent
capabilitieswillbedevelopedfirst,atlowercostandrisk.However,notallproposedtetherapplicationsaresoremote.Forexample,arotatingtethersystemwithabaselineofaboutakilometerisabletogenerateacomfortablelevelofartificialgravitythroughthe(apparent)centrifugalforce.Exposuretolong
periods of weightlessness has important reversible and irreversible
effects on
thehumanphysique.HumanstravelingtoMarsforsixmonthsormorewouldbenefitfromanartificiallygeneratedgravitylikeforcetosecuretheirphysicalfitnessuponarrival.Littleornoviablealternativeexiststotethersforartificialgravity[Clark1960,Stone1973,Cramer1985].Fororbitaltransferlessambitiousthanthebolosystemsonecanavoidtherequirementofspinupthatisinherenttoarotatingtethersystem.Apendulummotioncanbesufficientinsomecasesanditisreadilyachievedasasideeffectofdeployment.Awelltimedpayloadreleasefromaswingingratherthanrotatingtethercanbeaneffectivewayofchangingorbitforbothendmassesthroughtheprincipleofmomentumtransfer.AnexampleisthedeliveryIntroduction
13ofsamplesfromaSpaceStationbacktoEarth,orSpaceMail.Thintethersofsomekilometerstotensofkilometerscouldbeusedtofrequentlydeorbitsmallcapsulesfromamannedorunmanned
station returning data, biological, medical or material samples for
detailedinvestigation on the ground [Aerospatiale 1986, Ockels
1995, Heide 1996.I]. At the
sametime,theorbitoftheSpaceStationwouldberaisedandtheamountofpropellantrequiredfor
its orbit maintenance would thus be reduced. A similar system could
be used
toefficientlyremovewastefromtheInternationalSpaceStation[AleniaSpazio1995].Averticallyhangingtetherwithoutpendulummotionormomentumtransfercouldalsobeofuse,e.g.toinvestigatetheEarthsthermosphereinmultiple,coordinatedpoints,assistingscientistsinadvancingitsthreedimensionalunderstanding[Heelis1998].Suchcoordinatedinsitumeasurementsforthisaltituderegimeareverydifficultorevenimpossibletoobtainwithconventionaltechniquessuchas(EarthObservation)satellitesorballoons.Electrodynamic
tether applications also have been proposed for the short term. The
MirElectrodynamicTetherSystem(METS)hasbeendesignedtoconvertsolarpowerintothrustandcompensatefortheMirStationsatmosphericdrag.Itwouldhavesignificantlyreducedthestationsorbitmaintenancecost,andwouldhaveallowedMirtoorbitatloweraltitudeinahigherdragenvironment,reducingcostofaccessbyconventionalmeans[Levin2007].AlthoughMETShasreachedanadvancedstateofdevelopment,itwasneverlaunchedduetothedecisiontodeorbitMirin2001.Nevertheless,thesamesystemcouldbeemployedforfuture
stations or other large objects in a highatmospheric drag
environment [Vas 2000,Blumer2001].An electrodynamic tether in LEO
to which no electrical power is applied can still
beequippedtoconductacurrent,fedbytheEarthsplasmaanddrivenbytheelectromotiveforce(emf),thelatterinducedbytheorbitalmotioninsidetheEarthsmagneticfield.Thiscurrentwouldgenerateelectrodynamicdrag(andelectricalpower)ratherthanthrust.Sucha
simple drag tail or Terminator Tether could be used to deorbit a
satellite after itsnominal lifetime and help maintain the
cleanliness of the orbital environment
[Forward1998,Hoyt1999.II,Vannaroni1999,Dobrowolny2000].Whatthesevarioustetherapplications,mechanicalorelectrodynamic,distantormoreshortterm,
have in common, is that with respect to conventional (rocketbased)
solutions theywould significantly reduce the need for propellant,
as they tend to keep energy
andmomentumwithinthesystemofinterestratherthanlosethosethroughexpulsionofmass.In
addition, for some cases tether technology may indeed be enabling,
e.g. for artificialgravity, applications in highdrag environments,
orbital debris removal or an
operationalinterplanetarytransportsystem.Thephysicalprinciplestheseconceptsarebasedonappeartobesimple,whereasthecostofconventionalalternativeshassofarproventobeandarelikelytoremainprohibitive.Thequestionnaturallyariseswhethertherealapplicationoftethersystemswillbeaselegantandtechnologicallysimpleastheirconceptualdescriptionappearstoimplyandtherefore,whethertheinvestmentsrequiredtomakethemoperationalareindeedworthmaking.14
Chapter11.3 FlighthistoryofspacetethersTable 1 provides
anoverviewof themajor suborbitaland
orbitaltetherexperimentsthathavebeenbuiltand(inmostcases)flowntodate,aswellasrelevantreferencesforeach.Forconvenience
the list includes the Young Engineers Satellites, YES and YES2,
which aresubject of this work, as well as the recent TREX
experiment to which the author
alsoparticipated.Theearliestexperimentstookplaceinthesixties.Intwoseparateexperimentsin1966,theGemini
11 and 12 manned capsules were connected by a 36m cable to their
respectiveAgena upper stage. With considerable difficulty the
astronauts manually controlled
thetetheredsystemtheywereapartofusingcoldgasthrusters,inordertobringthesystemfirst
in a gravity gradient stabilized position and then in rotation.
During the Gemini
11missionabout1mgeeofartificialgravitywascreatedbya0.15rpmrotation.TheGemini12crewsucceededtoachieveasomewhatstabilizedverticalorientation.The
complexdynamicsencountered during theseboldtrials withshorttethers
may havebeen the reason it took 14 years before tethers were
deployed in space again. Tetherexperimentation in the eighties and
early nineties was dominated by modest
shortsuborbitalflights.Japanese,USandlateralsoCanadiansoundingrocketexperimentsusedconducting
tethers to investigate their interaction with the Earth ionosphere.
The firstTethered Payload Experiments (TPE) suffered from
deployment problems, but
withassistancefromcoldgasthrustersthevariousCHARGE(CooperativeHighAltitudeRocketGun
Experiment) and OEDIPUS (Observations of Electricfield Distribution
in
theIonosphericPlasmaaUniqueStrategy)missionswerecompletedsuccessfully,withtetherlengthsrangingfrom400mto1174m.Fromthesetechnicallymodestexperimentsitwasalargesteptothe19.6km,2mmthickandlayeredelectriccablethatwasdeployedfromtheSpaceShuttlein1992aspartoftheAmericanItalianTetheredSatelliteSystem(TSS).ObjectivewastodeploythetetherupwardoutoftheShuttle,collectelectronsatthefarendusinga1.6mdiameterendmassasanodeandstudythetetherelectrodynamicsasaresultofthecurrentflowingthroughthetether.Thecomplex,activelycontrolledreelsystemgotstuckafter268mofdeployment,butthetetheredsatellitecouldbesuccessfullyretrievedandreturnedtoEarth.In1996,duringtheTSS1R
reflight of the same equipment 19.6km of tether was deployed
exposing
theendmasstoanemfofasmuchas3500V.AcurrentofseveralAmperescausedsignificantdynamicsinthetether,andasignificantLorentzdragforcemusthaveactedontheSpaceShuttle.Aclearskipropemotionwasobservedinthetether.Theexperimentalsoprovideda
wealth of information concerning the electron collection behavior
of large chargedspheres in a plasma. Unfortunately, the tether was
severed near the Shuttle end due
tosparkingafterdamageduetodebrisormeteroidimpact[Chobotov1999].Thiscutprovidedtheaccidentalopportunitytowitnessthedynamicsofthefreetetherinspace.Itwasseentocreate
its own, artificial, lower endmass due to tether recoil in the
lowtension end. TheIntroduction
15tetherwastrackedandreenteredwithinafewweeks,providingafirstdatapointontetherorbitallifetime.A
less ambitious orbital electrodynamic tether experiment was
performed in 1993, thePlasma Motor Generator (PMG), a 500m tether
attached to a Delta upper stage.
PMGsucceededindemonstratingthattheLorentzdragforcecanbeturnedaroundintoathrustforce,byactivelysendingelectronsupwardthroughthecable.HighlysuccessfulmechanicaltetherexperimentswereNASAsSmallExpendableDeployerSystemmissions,SEDS1andSEDS2.Theyeachdeployeddownward20kmofa0.78mmline
braided from a special polyethylene fiber material, Spectra, again
from a Deltaupperstage. A small subsatellite as endmass transmitted
dynamics data to the groundwhereas the deployed length and tension
were measured on the Delta side. SEDS1deployed the tether with an
openloop control and ended in a swing and
subsequentreleaseandreentryofthetetherandsubsatellite.SEDS2tookastepfurtherwithaclosedloop
controlled deployment to a stable vertical position of the tether.
Unexpectedly, theSEDS2 tether was severed just 3.7 days after
successful completion of the mission,
mostprobablybyadebrisparticle.ThankstoSpectrashighreflectivity,
theSEDS2tetherwasobservedfromthegroundwiththebareeye[Carroll1995.I],passingthroughtheskyasabrightthinobjectwithanangulardimensionsimilartothatoftheMoon.TheunexpectedcutoftheSEDS2tetherincreasedconcernswithregardstothelimitedinorbitlifetimeoftethers.TethersUnlimitedInc.(TUI)providedareactionwiththeconceptoftheHoytether,awebbedtetherbelievedtoresistmultipleimpactsandsecuringverylonglifetimeinspace[Forward1995].ThelastofthelargeUStetherexperimentsflownsofar,theATeX(AdvancedTethereXperiment)bytheNationalReconaissanceOffice(NRO),intendedtodemonstrateameteoroidimpactresistanttapeshapedtether.Unfortunately,theactivelydrivenreeldeploymentofATeXfailed.RecentdataindicateshoweverthattheSEDS2cutmusthavebeenananomaly.TheNavalResearchLabs4kmlong,2mmthicktetherofTiPS(TetherPhysicsandSurvivability)wasunwoundinMay1996,usingalsoSEDSdeployertechnology.Ithasbeenorbitingforoveradecade
in vertical orientation, with a slight oscillation, to be cut only
in July 2006[VSO2010].Nevertheless, especially the TSS1R and SEDS2
tether severings have resulted in theevidently false, but
widelyheld belief that tethers in space are severely prone to
failure.Increasingly,thefearofaccidentallyseveredtethersmovinguncontrollablythroughspaceandcollidingwithothersatellitesoreventheSpaceStation,leadtomissioncancellations.In1997,theYoungEngineersSatellite(YES)waslaunched,butthetetherdeploymentwasnotinitiatedforfearofpotentialcollision[Kruijff1998].Theimplementationofatetheraspartof
the Shuttlebased SEDSAT [Lorenzini1995] was cancelled. The
electrodynamicPropulsiveSEDSexperimentProSEDSwasbuilt,butnotlaunched[Vaughn2004].Intheirwakenewtetherproposalsbecamelessfrequentandlessambitious.Theworkreportedinthisthesiswasperformedinthiscontext.16
Chapter1Year Experiment Length[km]Technology Objective Success
Remark
Ref.19661966Gemini11Gemini120.0360.04MechanicallinkbetweenGeminiandAthenaupperstageArtificialgravityGravitygradientstabilizationYESMOSTLYSpinstable0.15rpmMannedwithmanualcontrolNASA196719801981198319851992TPE1TPE2Charge1Charge2Charge2B0.04of0.40.07of0.40.4180.4260.4ConductiveColdgasassistedPlasmainteractionandVHFwavegenerationPARTLYPARTLYMOSTLYYESYESSuborbitalSasaki1987Sasaki199419891995OedipusAOedipusC0.9591.174ConductiveColdgasassistedPassivereelIonosphericscience
YESYESSuborbital
Tyc1995Vigneron199719921996TSS1TSS1R0.268of19.619.6Conductive,activereeldeploymentElectrodynamicPowergenerationNOMOSTLYShuttlemissions.TetherjammedTetherbrokeaftersciencesuccessDobrowolny1994Gilchrist19981993
PMG 0.5 Conductiveinsulatedtether,passivespoolPowerandthrust YES
7hrsexperimentpiggybackonDeltaMcCoy199519931994SEDS1SEDS22019.7Mechanical,brake+spoolSwing&cutControlleddeploymentYESYESSEDS2probablycutbydebrisaftermissioncompletionCarroll1993Carroll1995.I1996
TiPS 4 Mechanical,passivespoolStudysurvivalandstabilityYES
Cutafter1decadeinorbitBarnds19982005 ProSEDS (13.1)
Bareconductive/mechanical,brake+spoolThrust
CancelledforISSsafetyJohnson20031997 YES (35)
Mechanical,doublestrand,brake+spoolRotation,reentry
GTO.NotdeployedduetounsafeorbitKruijff1999.II2007 YES2 31.7
Mechanical,brake+spoolAccuratereentryofascientificcapsuleMOSTLY
Fulltwostagedeployment.Overdeployed.Kruijff2009.I,II1998 ATeX
0.02of6.2 Mechanical,tape,reel,activeStability&control NO
S/WstoppeddeploymentZedd19982000 METS (5)
Bareconductivetape/mechanical,passivereelThrust(Mirstation)
CancelledasMirwasdeorbitedLevin20072007 MAST 0?of1.0
MultistrandplusinspectorcrawlerStudytethersurvivabilityNO
MinimaldeploymentHoyt20032010 TREX 0.3
Conductivebaretethertape,passivefoldedDeploymentandcurrentcollectiondemonstratorMOSTLY
SuborbitalSuccessfullydeployed,videoFujii2009Table 1. Overview of
major tether experiments to date, by chronology of experiment
family.Experimentswithlengthbetweenbracketswerenotlaunchedordeploymentwasnotstarted.Introduction
17Onlyrecently,nearlyadecadeafterATeX,newtetherexperimentshavebeenlaunched,alldeveloped
in educational context, and with mixed results. The MAST university
project(MultiApplicationSurvivableTether)attemptedin2007todeployatetherbetweenlightweightcubesatsbutapparentlywithoutsuccess.Inthesameyear,asreportedinthisthesis,theEuropeanSpaceAgencys2ndYoungEngineersSatellite(YES2)deployeda32kmtetherintwostagesaspartofaSpaceMaildemonstration.Thissuccessformechanicaltetherswascomplementedin2010astheTetheredRocketExperiment(TREX)ofTokyoMetropolitanUniversityfeaturedthefirstandsofaronlydeploymentofabareelectrodynamictether.Aninnovativepassivedeployersystemsuccessfullyunfoldeda300mtape.Ofthe22experimentslistedinTable1,19wereinfactflownandagoodmajority,namely14of
those, can be considered largely or fully successful. The flight
experiments
involvedessentiallyfourtypesofdeployers:theactivereel,thepassivereel,thepassivespoolandtheTREX
(passive) unfolding system. An active reel deployer unwinds the
tether from amotorized drum, in a direction perpendicular to the
drum shaft. This in contrast to
thedeploymentfromapassivespool,whichisinaxialdirectionovertheheadofthespool.Themorecomplexexperimentsbasedonactivereeldeployers,TSSandATeX,haveencounteredsignificantdeployment
problems.Virtuallyallthepassivesystems
haveleadtocompletedeploymentsofar,withanotablygoodtrackrecordforthecompanyTetherApplicationsresponsible
for SEDS1,SEDS2, PMG andTiPS. The few spoolfailures(TPEand
MAST)suffered from a shared problem, i.e. insufficient initial
momentum in relation to
thedeploymentfriction.Theimportanceofproperdesignchoicesisthereforeapparent.Basedon
flight heritage there is a strong case to move forward with the
more simple, passivedeploymentsystems.1.4
ObjectiveofthisthesisToday,theconceptofusingtethersinspaceisstillinnovativebutcertainlynotunexplored.True,
consideringthe currentstateoftether
materialsandtechnologies,sustainable
spacetransportationbasedontetherassistedlaunchorbolobasedinterplanetaryinfrastructuresiscertainlystillremote.However,tethershavebeenstudiedformanyyears,fundamentalprinciples
have been demonstrated in orbit and several attractive applications
have
beenidentifiedfortheshortterm.Smalldevelopmentstepsalongthelinesofsuchapplicationscouldbringtethertechnologyforwarduntilademandarisesformoreambitioussystems.Nevertheless
it has proven difficult to move beyond theory and concept
demonstrationtowardsafirsttrueapplication.Partlythisisbecausedevelopmentandoperationalrisksaregenerallyjudgedtobehigh.Thereisaneedtodemonstratethattetherapplicationscanbeeffective,
affordable, predictable and safe. Due to the very nature of tethers
theirperformance cannot be fully demonstrated in ground testing.
Without a first
inorbitdemonstrationofanactualtetherapplicationitseemshardtomakeaconvincingcase.18
Chapter1Thoseperceivedobstaclesmaybeovercomethrough a systematicand
targeted approachover the full width of the matter. This approach
should include a suitable
applicationselection,asolidmissionanalysis,afullsystemunderstandingandqualification,athoroughcoverageofsafetyaspectsand,enabledbytheresults,anaffordable,applicationorientedinorbit
demonstration. By going through this process, first a deeper
insight is to be
gainedaboutthechallengescurrentlyfacedbytetherinitiatives.Thatachievedinsightshouldnextallowtoclosethecircleandshedlightontheinitialquestionregardingtheeffectiveness,affordability,
predictability and safety of tether applications and lead to
crediblerecommendations regarding near term tether initiatives on
the road towards the
firstapplicationsand,eventually,asustainablespacetransportation.Theobjectiveofthisthesisistoachieveandexploitthisinsightaccordingly.Theapproachcanbethoughttoconsistofthreesteps:1.
definitionoftherequiredtoolsandasuitabletetherapplicationfordemonstration,2.
developmentofanadequatetetherdeploymentsystem,3.
evaluationofitsperformanceandextractionoflessonslearnedfromtheevaluationprocessanditsresults.Followingthislogic,theremainderofthisthesisisstructuredinthreeparts,onepartforeachoftheabovementionedsteps.1.5
SurveyofthisthesisThe three parts of this thesis consider
respectively the definition, development
andevaluationofatetherapplication.Part I of this thesis, the
definition, provides the physics background and an analysis
ofvariousconceptsthatcouldbecandidateforashorttermimplementation.Chapter2firstdescribestheprinciplesoftethersinspace,bothmechanicalandelectrodynamic,providinginsightintothephysicsbehindtheirpotentialuses.Inordertostudypotentialapplicationsmoreclosely,anextensivetethermissionsimulatorhasbeendeveloped.Chapter3analyzesanddiscussessomeofthecandidateapplications,theirbenefitsandtheirlimitations.Specialattentionisgiventotheseeminglyambiguousrolethattethersmayplaybothincreationand
reduction of orbital debris. To take the step from concept to an
applicationorienteddemonstrationfocuswillbeontechnologythatisbothlowriskandlowcost,andforwhichsignificantheritageexists.PartII,thedevelopment,thereforenarrowsdownontheSpaceMailapplication.Itfocuseson
the design, development and qualification of a tether system for a
demonstrationmission. Chapters4 is concerned with the development
and assessment of a
suitablematerialandtetherdesign.Astetherinducedcollisionriskhasbeenidentifiedasaprimaryshow
stopper for past mission proposals, particular attention is paid to
the designsimplications for safety. Possibilities are explored to
decrease risk both during and afterIntroduction
19deployment,forexampleriskofentanglementwiththedeploymentplatform,andriskofcollision
with other satellites after tether release. With the tether design
eventuallyconsolidated, Chapter5 continues by reporting on the
development of the hardware
andsoftwarerequiredforcontrolleddeploymentofthattether.
Itincludesthetetherwindingand unwinding facilities development, as
well as SEDSinspired designs for spool andbrake. Furthermore the
chapter describes the deployment control algorithms, simulationsand
groundbased deployment testing. Simulated performance versus actual
deploymentresultsarecompared.Part III, the evaluation, final part
of this thesis, reports on the construction of two
spacetetherexperiments,theanalysisofmissiondataandtheextractionoflessonslearnedfromthe
exercise of actual implementation and from the mission results.
Chapters6 and 7describe respectively the process leading to the
development of the Young EngineersSatellite (YES) and the Second
Young Engineers Satellite (YES2). These space
tetherexperimentsdemonstratethefeasibilityofactuallybuilding,qualifyingand,incaseofYES2,operating
the proposed system. Significant challenges had to be met, beyond
the
mereproductionofthetetheranddeployer,inordertobringtheexperimentsintospace,andtofinallyperformatetherdeployment.AnoverviewoftheYESandYES2systemsandofthemanagement
processes followed provide insight into these challenges. The YES2
missionpreparation, tether deployment results and problems
encountered are analyzed andevaluated in Chapter8. A comparison of
the flight data is provided against
simulationresults,groundtestsaswellastheearlierSEDSmissions.Thesuitabilityofthedevelopedtether
system for the SpaceMail application is analyzed. Finally, the work
is placed in
abroadercontext.InChapter9,conclusionsareformulatedandfromtheintegratedfindings,recommendations
are derived for further development, as well as implications for
tetherapplicationsinthenearfuturethataretoleadtoamoresustainabletransportationinspace.The
Epilogue touches upon the same items, but more from the authors
personalperspective.Following Chapter 9, a summary of the thesis is
provided in both English and Dutchlanguage.20
Chapter1PartITethersandtheirapplicationsAdastraperligamentum.RobertForward,sciencefictionauthor,engineerandtetheradvocate,atthebottomofhisemailsPartIofthisthesisprovidesadescriptionoftetherbasicsandatetherdynamicssimulatorthathasbeen
developed. Armed with these tools, a number of possible nearterm
tether applications
isanalyzedtofinallymakeastatementonthesafenichesthatexistfortethersinspace.TetherDynamics
232TetherDynamicsbx+ay=acaxx+byy=bccChristiaanHuygens,on29October1651,writesdownwhatmaybethefirsteverphysicsformulae,andwillshortlyaftercorrectlydefinetheconservationlawsofmomentumandenergyinDemotucorporumexpercussione,1652.This
chapterintroducesthereader tothe physicalprinciples of
tetherdynamicsinspace.The fundamentals behind the applications of
mechanical and electrodynamic tethers areworkedout.
Anewlydevelopedtoolisfinallydescribedforsimulationofdetailedtetherbehaviorandrealworldaspectsthataredifficulttotakeintoaccountinanalyticalmodels.2.1
DeployingatetherinspaceThis section discusses basic models for the
dynamics of a hypothetical tether that
ismassless,straightandnonconducting.2.1.1
GravitygradienttensionforahangingtetherincircularorbitTheorbitalperiodofanobjectorbitingamassivebodydependsontheorbitssemimajoraxis
a.Alargersemimajoraxismeansalargerorbitalperiod,asise.g.obviousfromtheMoonsorbitaroundtheEarthinabout28days(a384400km)
ascomparedtothatoftheSpaceShuttle,inapproximately90minutes(a6700km).Inthesimpleexampleofacircularorbitthiscanbeeasilyunderstood.
Themotionofanobject in an orbit with constant radius r=a, around a
homogeneous spherical body
withgravitationalconstantifviewedinacorotatingframecanbethoughttobesubjectedtoabalancebetweenagravitationalforceFg
andacentrifugalforceFc,whichisapparentinthat frame. Whereas the
force of gravity decreases quadratically with increasing r,
thecentrifugalforceisproportionalwiththeproductofrandthesquareoftheangularvelocityaroundthecentralbody.Inordertoobtainsaidbalanceforanorbitwithalargerradius,theangularvelocitymustthereforebedecreased,seeEqs.(2.1)and(2.2).22mrrm
= = =c gF F(2.1)3rue =
(2.2)Theimplicationisthatiftwoobjectsareconnectedbyaradiallyorientedtether,thesesocalled
endmasses are each forced to orbit with an angular rate different
from
thatbelongingtothelocalcircularorbitaccordingtoEq.2.2.Gravityforceandcentrifugalforce24
Chapter2ontheendmassescanthusnotbeinbalance.Supposetwoendmassesm1andm2incircularorbitatrespectiveradii
r1 andr2,withr2>r1asdepictedin Figure1. Endmassm2
willorbittheEarthfasterthanitsnontetheredcompanionsatthesameradiusr2,whereassimilarlythelowermassm1willbemovingsloweratr1thanitsnontetheredcompanionsthere.BothendmasseswillsharethesameangularrateO
matchingthatofacircularorbitatapointbetweenthemasses,thecenteroforbitrCO,23O=uCOr,
(2.3)wherethetermu/O2canbederivedfromthebalancebetweengravityforceandcentrifugalforceforthesystemasawhole,
O =2121dd22rrrrm rrm, (2.4)suchthatforamasslesstether22 221 12 2 1
13/ / r m r mr m r mrCO++=.
(2.5)Forcomparison,theradiusofthecenterofmassrCMis2 12 2 1 1m mr m
r mrCM++=. (2.6)ForaverticaltetherwithlengthL, r1=r2L,itfollowsthat
rCO3/rCM3=1+O(L/r2)2.Centerofmass andcenteroforbit
canthereforebeassumed to coincideforavertical tether,
ifthetetherlengthisamerefractionoftheradius,Lr2.Thisassumptionremainstrueforanonzerotethermass[Newlands1994].TheforcerequiredtohavetheendmassesorbitattheangularrateofthecenteroforbitisthetethertensionT.Itcanbeexpressedintermsofdistancel
fromm1
tothatcenteroforbit,l=rcor1(seeFigure1).BysubstitutingthisdefinitionoflandEq.2.3intotheforcebalanceonthemassmoneobtainsforthetensioninthetetheranexpressionforT,212
2122121213 ) ( 3) 1 () 1 () () (O ~ O + O =||||.|
\| O = O = =l m Trll mrlrrlrm l r ml rmTCOCOCOCOCOCOCOuc gF
F(2.7)Asimilarresultcanbeobtainedforthetensiononmassm2.Asatypicalexample,a10kgmasssuspendedfromamassiveplatform(m2m1)
orbitingat400kmbyamassless10kmtether would generate a tension of
0.38N. This tension is commonly but not fullydescriptively known as
the gravity gradient tension. In fact it results from the
stabilityconditionforasystemforwhichwithincreasingradiusnotonlythegravityforcedecreases,but
also the centrifugal force increases. In magnitude, the gravity
gradient tension isTetherDynamics 25approximatelyequal tothreetimes
thatpart of thecentrifugal forcethatresultsfromtheseparation
between endmass and center of orbit, under the orbital angular
motion.
Theequivalentgravitygradientisresponsibleforthetendencyforatetherinorbittoassumeavertical
orientation and can help to drive a tether deployment, once an
initial
verticalseparationbetweenendmasseshasbeenachieved.Figure1.Forcebalanceinaverticaltether.2.1.2
EquationsofmotionInordertoobtainafirstinsightintomechanicaltetherdynamicsandtetherdeployment,asetofsimpleequationssuffices.
Forthispurposeitisassumedherethat m2isamassiveplatformM
fromwhichamuchlighterendmassm
isdeployedindownwarddirection,orm2=Mm1=m.TheorbitofMisnotaffectedbythedeployment.Suchaplatformcoincideswiththecenteroforbit,withconstantradiusr2=rCO=RandangularrateO.
Furthermore,itisassumedthetetherisastraightlinewithoutflexibility,
andits
masscanbeignoredwithrespecttotheendmassm.Finallyitisassumedthatthetetherdynamicstakeplaceinsidetheorbital
plane only. The dynamics of the system are thus defined by the
endmass m, thetetherlengthL=l
anditsangletothelocalnadiru,asmeasuredfromManddepictedinFigure2.Thegeneralizedforceonthissysteminudirectioniszero(noperpendicularforcesareexertedbythetether),inldirectionitisthetensionT.Ignoringhigherorderterms,thefollowingequationscanbederived,forexamplingusingtheLagrangian
[e.g.Crellin1994,Heide1996.I]:0 2 sin23) ( 22= O + O + u u u ll
(2.8)( ) ) cos 3 1 ( ) (2 2 2u u O O + = l lmT (2.9)
r1rcor2FcFcFgFgTTl Lm1m2 m2m1CenterofEarthFreebodydiagrams26
Chapter2
OMmlRuCenterofEarthFigure2.Simplemodelfortetherdynamics.Theseequationsdescribetherelativemotionofobjectsinorbitclosetogether,expressedinpolarcoordinates,inthefamiliarformofthesocalledrendezvousequations[e.g.Lorenzini1996]
however with the only force of influence being the tension between
the masses.
InEq.2.8aCoriolistermandacomponentofthegravitygradientperpendiculartothetethercan
be discerned. Note that from Eq.2.9, for a nondeploying vertical
tether) 0 , 0 , 0 , 0 ( = = = = u u l l Eq.2.7 follows once more.
The effect of rotation or swing on thetension in a nondeploying
tether can be recognized in a term of Eq.2.9 relating to
thecentrifugalforceontheendmass.Thegravitygradientcontributionontensioncanbeseentodecreasewithincreasingu
duetothedecreasingdifferenceinradiusbetweenmandMandthereducingcomponentofthegravitygradientforcealongthetetherdirection.2.1.3
PendulummotionofaswingingnondeployingtetherEq.2.8 describesthe
inplaneangular motionofthe tether. The hangingtetherof Section2.1.1
isa specialcase,whereas,inabsenceofdeployment,
anoscillationaroundthe localvertical represents a more general
situation, be it intentionally or accidentally achieved.Such
oscillation is driven by the gravity gradient force that acts to
accelerate the
tethertowardsaradialorientation.Forsmallangulardeviationsbetweentetherandthelocalnadirdirection,thisoscillationfollowscloselyapendulummotion.If
1 , 0 , 0 \3Or3 is required in order to endup in arotation rather
than an oscillation (Eq.2.10). On the other hand, much of the
initial
rimvelocitycaninprinciplebeobtainedfromtheswingobtainedduringdeployment,savingsomepropellant.Tomakefulluseofthispossibilitywouldrequireselectionofanoptimalvaluefork
valueforeachgloadcase,andamorecriticaldeploymentcontrol.
Theoearthglevelwouldbeobtainedwithk=2.2(max.70kgpropellantratherthan30),omarswithk=3.6(max.110kgpropellantmassratherthan80kg).Alternatively,anoutofplanerotationcanbeconsideredwithfreechoiceofk.Stabilityanddynamicsforthiscasehavenotyetbeeninvestigated.Thetethermassisheavilydependentontheminimalrimspeedselected,butforamultimissionscenarioitisnotthedominantfactor.TheOverdeploymentmethodisthereforebaselinedfortheinitialdesignofasuitabledeployer.TetheranddeployerA
tether and deployer design for a LEO demonstrator has been made for
DeltaUtec
byLansdorp[Lansdorp2004]basedontheOverdeploymentscenario.ThetetherisassumedtobemadeofDyneema,ahighstrengthfiberproducedbyDSMintheNetherlands.
Thetether is proposed to be a very flat tether of ~1mm thickness
and ~1m width. Such aDyneema UD tether can be produced using
standard sheet production
methods(operationalatDSM).Itisasafelifedesigntopreventseriousdamagebyspacedebrisandmeteoroids
and is compatible with the proposed deployer, as it provides a
large area
ofcontact,thusreducingpressureloads.Dyneemahasafibertensilestrengthof3.9GPaanda
density of only 975kg/m3. Because of losses in the UD design2, it
will have a tensilestrength of 1.3GPa and a density of 634kg/m3. A
safety factor FS=6 for the tether
waschosenastheproductofanumberofcontributions[Lansdorp2003.II],seealsoSection4.3.4.Resultingtotaltethermassis622kg.2C.
Dirks, M. Jacobs, J. Kersjes, Personal correspondence, Meeting at
DSM, Heerlen, the Netherlands, 2003.AnalysisofTetherApplications
79Thetetherdeployerhasthetasktoreelthetetherinandout,beforeandaftereachcrewswap.Therequirementsonthedeployerarequitesevere.Theselecteddeploymentstrategydemands
that it must reel the tether while artificial gravity is being
generated by therotation of the system. The most severe conditions
occur during the oneg mission:
thetensioninthetether,justbeforethereelingphaseisover,equals400kN,comparabletotheperformanceofamediumsizedcrane.Anunconventionaldeployerdesignisproposedtosimultaneously
meet the requirements of high tension and low mass. A system has
beenworked out for which no tribology or transmission is required.
Instead a solution
withstructuralhingesisproposedandhighforcelineartranslatorsareused.Thestoragesystemisalwaysdecoupledfromthetethertension.
Figure24
illustratestwoseparatesetsofflatfrictionplatesthatautomaticallysqueezethetetherwhentensionisapplied,asocalledselfbraking
structure. As one pair of plates is squeezed and moves the tether
in the
desireddirection,theotherpairmovesinpositiontotakeover.Thereelthatcollectsthetetherisinthiswaynotexposedtoa(significant)tetherloadandcanbelightweight.Afirstdesignofthe
deployer indicates that the deployer mass will be comparable to the
tether mass,
i.e.some600kg[Lansdorp2004].TheMARSgsystemcombinescomfortandcapabilityofmultipledeploymentandretrievalsunderfullgload,withamassofonlysome3%ofthetotalsystem,orsome2400kg(basedon14cycles).Propellanttomaintainstabilityoftheendmassisnotincludedinthisanalysis.Figure24.Hingelessmovingplatehighloadtapedeployerconcept(seetext)3.2
ElectrodynamicdeboostElectrodynamictethersareabletoprovidepropulsionwithlittleornoconsumables,astheyconduct
electrical current and interact with a planetary magnetic field. If
equipped withappropriate power supply, they can provide continuous
thrust that can be modulated tochange any of the orbital parameters
[Cosmo1997, Levin2007]. These capabilities make80 Chapter3them
attractive for demanding long term applications such as repetitive
deorbiting
ofdefunctsatellitesoratmosphericdragcompensationofaspacestation.Someuncertaintiesaretoberesolvedbeforesuchapplicationscanbereliablyimplemented.Bare
tether design and confirmation of electron collection performance
is one aspect
thatwillbedescribedbelow.Beyondthat,acrucialchallengeforelectrodynamictethersisthatof
longterm stability, in particular with reference to light systems
where electrodynamicforces may become comparable to gravity
gradient forces. Simulations have beenundertaken to find out how
system design can help provide sufficient stability.
Twoexampleapplicationsforrelativelysimplesystems,withouthighvoltagesource,andthusorientedatdeboostonly,arestudiedinmoredetail.Theeffectivenessofanelectrodynamictetherformitigationofdebrisrelatedriskiscriticallyconsidered.Anapplicationofanevensimplersystemisanalyzed,afullypassiveelectrodynamictethersystem,whichmayproveusefulinorbitaroundJupiter.3.2.1
AssessmentofOMLperformanceinbaretetherelectroncollectiontestingNo
inorbit data is available for long bare tether performance at this
time. To
supportrepresentativenessoftheETBSimsimulations,aseriesofelectroncollectiontestshasbeendefinedandperformed[Kruijff2001.I]withthefollowingobjectives:
totestthevalidityoftheOMLtheory,
toassessorbitaltethercurrentcollectioncapabilityfromplasma,and
toassesstheapplicabilityoftheOMLmodeltotetherswithotherthancylindricalgeometry.The
approach applied exists essentially in measuring the IV
characteristics of severalspecimens of tethers, with various
geometrical shapes and dimensions, exposed to
asimulatedspaceenvironmentofionosphericparameters.ThespecimensofvariousshapesandsizesaresummarizedinTable13.Thisselectionhasbeenmadetorepresentvariousdesignoptions:asimplecylindricaltether,atapeforincreasedmassefficiencyandadualstrand
tether (for increased resistance against micrometeoroids and
orbital debris).
Allsamplesare10cminlength,somuchlargerthanthesamplediameter.Eachspecimenhasbeen
placed between two guards of equal dimensions, such that the
measurements
aremadeinacylindricalplasmageometrywithoutsignificantedgeeffects.The
experimentshave been designed to investigate the impact on the
current collection caused
byperturbationsduetoboththeambientgeomagneticfieldandthemagneticfieldselfinducedbythecurrentflowinginthetether,neitherofwhichisincludedinthederivationoftheOML
model. They are compared to those of Gilchrist e.a., who has
performed
electroncollectiontestson(unguarded)cylindricalandtapesamplesof1030cmlength,inaplasmageneratedbyaHallthruster,howeverwithoutgeomagneticandselfinducedfieldeffects[Gilchrist2002].ThelargeplasmachamberfacilityofIFSICNRhasbeenselectedasasuitablefacilityfortheproposed
tests. The tests were designed, performed and analyzed by F. de
Venuto &
G.Vannaroni[Kruijff2001.I],theresultsaresummarizedhere.AnalysisofTetherApplications
81Typeofelectrode DimensionsSinglewire Diameter0.8mmSinglewire
Diameter2mm(withcurrentcarryingwireincenter)Bifilarwire
Diameter0.8mm,centertocenter2.8mmTape
Width3.6mm,Thickness0.05mmTable13.DimensionsoftethersamplesusedintheplasmatestsTestchambergeometryandconditionsareprovidedinTable14
andFigure25.TheDebyelengthDisafundamentalplasmascalingparameterintermsofwhichtheOMLvaliditycanbeexpressed[Sanmartin1999].ThetestconditionscanbeconsideredtypicalforaLowEarthOrbittetheroperation.Althoughthevoltagebiasapplied(200V)islowerthanthetypicalpotentialofkilovoltsforspaceapplications,itisstillhighlysuprathermalwithrespecttotheenergy
of ionospheric electrons (~ 0.2eV), and therefore can be considered
representativefortheelectroncollectionprocessinhighpotentialregimes(seealsoEq.2.29).TheresultingIVcharacteristics(Figure26,
Figure27)showthecollectedcurrentIexp attheapplied bias voltage V,
normalized to theelectronthermal current Ith (Eq.2.30),
Inorm=Iexp/Ith.Duetotheproportionalityofbothcurrentswithbothplasmadensitynpl
andtheelectrodesurfacethisnormalizationeliminatestheeffectsassociatedtotheplasmadensityvariationresulting
from the samples current collection as well as the effects due to
differentdimensions of the various tether samples. Two curves (in
solid lines) indicate the OMLuncertainty(Eq.
2.29)duetothespreadoftheelectrontemperature.Afirstobservationisthatthereseemstobe
asystematic tendencytoexceed thepredictionsofthe
model.Thediscrepancyfromtheorycanbeapproximatelyevaluatedabout25%,thelargestdeviationbeingassociatedtothetapesample.Thetapeandmultistrandtethershavebeeninitiallyoriented
with minimum crosssection towards the plasma beam. When
orientedperpendiculartotheflow,thetapeshowsa20%reductionincurrent,probablyduetowakeeffects.
Gilchrist e.a. observe quite a similar trend, with up to 15%
increased
collectionefficiencywithrespecttoOMLabove50V.Theyfindhoweverthattheperpendiculartapecollects510%morethantheparallel,possiblyduetosampleendeffects,duetothelackofguards,orsourcedrainage,whichseemstoparticularlyeffecttheparallelsample.In
any case, the OML does provide a good first guess estimate of
electron
collectionperformance,foralltestedtethershapes,includingtapesandmultistrandtethers,atleastforasamplewidthlessthanorequalto23D.Ausefullessonfromthisisthatmultiple(n)wire
tethers of diameter d can be treated (as far as electron collection
is concerned) as
asinglewireofdiametern*d.NotethatGilchriste.a.haveperformedteststoasmuchas15Dtapewidth,andalthoughsomereductioninefficiencyisobserved,possiblyduetosourcedrainage,theresultsforthesesamplesdonotgomorethan12%undertheOMLpredictionat300V[Gilchrist2002].82
Chapter3Facility SIM.PL.EXatIFSICNRAmbientplasmaelectrontemperature
2000KAmbientplasmadensity5e12m3SamplebiasforIVcurvemeasurement
0200VAmbientgeomagneticfieldB
0and0.3e4T(orthogonaltobothplasmaflowandtethersample)DebyelengthD~1.4mmCurrentforselfinducedfieldtest
010ASamplelength
10cm(plus10cmguardoneitherside)Sampledistancetoplasmasource
2.25mPlasmareferencemonitoring
LangmuirProbeforplasmadensity,electrontemperatureandplasmapotentialRetardingPotentialAnalyzer(RPA)forionbeamenergyIonsourceSynthesisA+acceleratedto~8km/sElectronsource
FilamentheatedatthermoionictemperaturesTable14.Testconditions
LPRRPAChambermainaxisPl asmaSourcePlasmaflow25cm17 cm15
cm225cmGUARD
SAMPLE
GUARDZYX10 cm
10 cm
10
cmFigure25.ExperimentalsetupofplasmatestsFigure26.IVcharacteristicsatB=0(left)andB=0.3104T(right)AnalysisofTetherApplications
83Figure27.IVcharacteristicsatvariousDCtethercurrents.Thegeomagneticfieldisfoundtonotperturbsignificantlythecurrentcollectionfromtheplasma,
which is plausible when considering that the electron gyroradius at
LEOenvironmental conditions (about 5cm) is appreciably larger than
the crosssectionaldimensions of the tethers under test
[Sanmartin1999]. For large tapes (centimeter
scale)additionaltestsarerequired,butintheSIM.PL.EX.facilitysuchalargesamplewouldleadtodrainingoftheelectronsource.Asfarastheselfinducedfieldisconcerned,theeffectofselfinducingDCcurrenthasbeentestedinthe2mmcylindersample.AreductionproportionaltotheDCcurrentisfoundofabout10%atitsmaximum
level (10A) correspondingtothemaximumpotential(190V).Such a
reduction is in line with expectations: the current produces a
crossed system ofmagneticandelectricfields,causinganE B
electrondriftalongthetetherthattendstoreduce the collected current.
For likely mission currents of 1or2A this effect can
beconsiderednegligible.3.2.2
TethereddeboostanddynamicinstabilityOccurrence of long term
instability of electrodynamic tethers has been evidenced
innumericalsimulations[Estes2000.IV],connectedwiththeProSEDSmission.Itisfoundduetothelongitudinalcomponentofthemagneticfieldandincreaseswithinclination.Severalinvestigations[e.g.Levin1987,Pelaez2000.I,II,Dobrowolny2002.I,II,Levin2007]havebeenundertaken
with the aim of clarifying the various underlying instability
mechanisms
forelectrodynamictethers.Energyiscontinuallypumpedintothesystem,whichcauseslateraloscillations
and eventually tether slackness or uncontrolled motion. The long
terminstabilityseverelylimitsmasscriticalelectrodynamictetherapplications.Forthesecasesitmust
be characterized and appropriately tackled, either by system design
or by activecontrolmethods.Dobrowolny developed a linearized
analytical model, simplifying the
environmentalconditionsanddecouplingtransversemodesfromendmasslibrations[Dobrowolny2002.I].The
modeled system is operating at maximum obtainable current level
following OMLtheory. Aninstability is observed,as
anexponentialgrowthintransversemodes.
Outofplaneendmasslibrations,coupledtoinplanelibrations,showawavepacketbehavior.Theresultindicatethatthereisamaximumcurrentlevelforstability.84
Chapter3Forcomparison,asimulationofthesamesystemwasperformedbyETBSim,whichisbasedon
a more general, nonlinear model (Section2.3.2). The environment was
initially set tomatch the Dobrowolny simulations, featuring a
simplified dipole magnetic field andsinusoidal plasma density. As
in Dobrowolnys findings, ETBsim produces inplane andoutof plane
endmass librations [Kruijff2001.I]. General behaviour is similar,
e.g.
wavepacketmodulationisrecognizedandthelibrationseemsstable,althoughtheamplitudeandmodulation
period differ. These differences are thought to originate in
severalsimplificationsintheappliedlineartheorywithrespecttothenumericalsimulation,suchasseriestruncation.Inaddition,crosscouplingbetweenlibrationandtransversemodeswasfoundtobesignificant(e.g.Figure29).Attheintegrationtimestepsused,itwasfoundthatthesystembecomesinstablebeyondnumericalaccuracywithinabout2weeks,althoughthelibrationmodeisasyethardlyexcited.FluctuationsofelectrondensityandmagneticfieldstrengthastheyoccurinorbitaroundEarthfurtherworsenthesituation.Foratypicalcase(7km,1mmbaretether,h=1000km,i=50.
700kg and 15kg endmasses) including also the ionospheric
irregularities
(IRI95model)andtheEarths436kmmagneticdipoleoffset,ETBSimshowsthatwithinaboutadaystime,transverse
wavesseverelyaffecttethertension, whichdoes notoccur
withouttheseeffects.Theseresultstriggerthequestionwhethersystemdesignchoicesorothersolutionscanbeidentifiedthatcontributetostabilityforthefulldurationofatypicalelectrodynamictetherapplication.Simulationresultsaddressingavarietyofdesignoptionsareheredescribed.As
a case study, a relatively simple deboost application has been
selected, intended
forsatellitesthathavefailedorcompletedtheirnominalmission(defunct,Section2.2.2).Itisinitiallyassumedthatthetetherendmassisdeployeddownward.Theendmasscontainsnotonly
acathode but allactive systems includingthetether deployeritself.In
thiswaytheinterface to the defunct satellite is minimized. The
tether is assumed bare. Based on
testsimulationsthefollowingreferencetetherisdefined(usedforallsimulationsinthissectionunlessspecifiedotherwise):
6kmfailsafemechanicalpart,1.2kg. 6km failsafe conductive part,
built out of two strands bare aluminum
(each0.32mmdiameter,treatedforo=c=0.3),twomechanicalstrands,total5.3kg.Stability
was investigated for tethered deboost of a defunct satellite of
700kg at 700kminitial altitude and 11.5 degree inclination. A
lightweight endmass of 15kg has beenassumed initially. As a
practical, objective measure for instability, the
(simulated)occurrenceoftetherslacknessisproposed(i.e.zerotension),whichisassumedtocoincidewithlossofcontrol(Figure32).Thisoccurrencecanbeexpressedinmissiontime,howeverthemorepragmaticmeasurementusedhere,referringtothemissionobjective,isthedropinaltitudeachieved.Forthefullrangeofparametersettingsreportedhere,evenatcurrentslimitedtoaslittleas0.2A,thesimulationsshowedaprocessofexcitationofskiprope(combinationof
first inAnalysisofTetherApplications
85planeandoutofplanetransversemodes).Thetethereventuallystartstoresembleawhipwiththelightendmassonitstip,cyclicallyinducingtensionshocksandfurthertransversewaves,
that finally cause the tether to become slack. Such behavior has
also been notedduring the simulations carried out for ProSEDS3.
Consequently, all simulations show
anearlyidenticaltensiondevelopment,whereonlytheonsetoftheinstabilitydiffersintimefromonesimulationtoanother.A
typical example for the deorbit behavior is shown in Figure 28,
which highlights
theimpactofinclination.Therunsarestoppedatoccurrenceoftetherslackness.Shownistheinplane
transverse mode. It is measured in degrees as the angle from the
line betweenendmasses to the line between defunct satellite and
middle of the tether. At
largerinclinationtheonsetofinstabilityisdelayedduetothelowerelectrodynamicforceresultingfromalowerperpendicularmagneticcomponent.Descentrateisalsoreducedforthesamereason.
Despite the fact that outofplane dynamics are more pronounced at
higherinclination,thetetherinsuchahighlyinclinedorbitachievesasomewhatgreateraltitudedropbeforeinstabilityoccurs.Figure28.Effectofinclinationonstability(1sttransversemodeandachievedSMAdrop)Simple
control laws do not reduce the onset of instability, due to the
coupling
betweenlibrationsandtransversemodes,asillustratedinFigure29.Acurrentcontrolisappliedtodampen
the inplane librations. The control is an antiphased current
modulationsuperimposed on a constant current (0.3A), assuming
perfect knowledge of the inplaneand outofplane angles (e.g. through
GPS or phase reconstruction from
tensionmeasurements).Althoughthecontrolis,briefly,effectiveindampingtheinplanelibration,thefirsttransversemodeisexcitedandeventuallycrossexcitestheinplanelibrationmodebeyondcontrolaswell.Similarlywhenacurrentcontrolisappliedthatdampensbothinplane
libration and first transverse mode, the second transverse mode is
excited,
withsimilardisturbingresultsonthelowermodes.NotethatinrecentyearsLevinhasdevelopedamethodbasedontethermodesandphaseestimation
that, although not able to fully subdue the instability appears
successful atpostponingitsignificantly[Levin2007].3 Enicro
Lorenzini, Private communications, February 200186
Chapter3Libration-4-2024680 5000 10000 15000 20000 25000 30000Time
[s]Amplitude [deg]libration damping controlno controlFirst lateral
mode-25-20-15-10-505101520250 5000 10000 15000 20000 25000
30000Time [s]Amplitude [deg]libration damping controlno
controlFigure29.Dampingofinplanelibration(left)excitesfirsttransversemode(right).Insupportofsuchactivecurrentcontrolfurtherdesignoptionswereconsidered.Mostofthesystemadaptationsthattendtoimprovetimetoinstabilityincreasetheratiooftension(Eq.2.16)versusLorentzforce(Eq.2.28),althoughnotalwaystheachievedaltitudelossisimprovedaswell.CurrentlimitationforexamplereducesthecyclicvariationoftheLorentzforceandofitsdistributionoverthelengthofthetether.Thisisparticulartrueifatalevelsustainablebythe
lowest plasma density within one orbit. Most simulated cases ran at
such a level,
of0.2A.Thecurrentlevelcanbeincreasedastheorbitgetslowerduetoincreasingplasmadensity,suchthatthedeorbitrateimproves.Inthesimulations,tethercurrentisassumedlimited
by ohmic dissipation through a variable resistor near the cathodic
end. Such
asystemhastheadvantagethat,duetotheohmicvoltagedropthetetherwillbenegativelybiased
over a large part of its length (Figure 30). In the negatively
biased section
noelectronsarecollected,thusresultinginanearlyconstantcurrentovermuchofthetetherlength.
Undersuchcurrentlimitation,additionalbaretetherlengthleadstosimultaneousincrease
of both gravity gradient and Lorentz force. The fraction of tether
that
featuresconstantcurrentisalsoincreasedandsimulationsfindstabilityimproved.
B0Vm1Im2FLL vI0AeeVemf
VRImaxVRFigure30.CurrentlimitationduepotentialdropVRbyresistoratcathodicendAnalysisofTetherApplications
87Increaseofcathodeendmassisacostlysolutionbutcontributestostabilityimprovement.Ifendmassandcurrentarebothincreasedbythesameamount,asexpectedthesystemwillstill
drop faster in altitude, but will also outlast the lighter,
lowcurrent reference
systembeforeinstabilityoccurs.Amechanicaltethersegmenthasbeenincludedinadditiontotheconductivesegmentinthereference
design. This has been done for two reasons. On one hand, it ensures
a
lowdeploymentfrictionduringtheinitialpartofthedeployment.Secondly,althoughinclusionof
a mechanical tether segment represents some extra system mass, for
the
simulatedapplicationitincreasesthetensionandsystemspassivelongtermstabilitymoreeffectivelythananincreaseofendmassbythesameamountwoulddo.Anevenmoreeffectiveuseofextramassisachievedwhenthetetherisdeployedupward,with
a dummy endmass the extra mass required for this concept, whereas
the cathode,deployer and electronics remain at the defunct
satellite, now the lower end of the tethersystem.
Insuchacase,forabaretetherormechanical/baretethercombination,thetorquearmaroundthecenterofmass(nearthedefunctsatellite),availabletotheresultingLorentzforce,isreduced.ThecasepresentedinFigure31isbasedonthereference12kmtetherwitha15kgendmasslimitedat0.2A.Thisadaptedsystemiseventuallydestabilizedwhenthesecond
transversemodeoverexcites.Notethatitwasfoundthattheelectrodynamictetherneedsnottobedeployedaccuratelytoavertical.Anonzeroinplaneanglebeforecathodeactivationhasnonegativeimpactonstability.Finally,asanalternativeway
tomaintain stability, aprograderotating tethersystemhasbeen
proposed (see also Section3.2.4). To achieve the desired system
spin, the 15kgendmassneedstobeprovidedwithaninitial Vof
about30m/sagainstthedirectionoforbital velocity. The spininduced
centrifugal force will increase with time as the spinaccelerates
due to the Lorentz torque and this increase helps to maintain
stability. Thespinning tether solution will operate on the average
at a 30% of the Lorentz force of
averticaltether,duetotheunfavorableangleofthetetherwithrespecttothemagneticfieldlines
during much of the spin. If a second cathode is added on the
opposite side of
thetether,thisfractionisincreasedtoabout60%.TheadditionalcomplexityandlossinLorentzforcemaybecompensatedforsincecurrentlimitationisnolongerrequired.Apart
from these measures that directly affect the balance of Lorentz
force and
tension,moresubtledesigntradeoffs,suchasfortethermaterialproperties,canhaveasignificanteffectaswell.Alowstiffness/viscosityratiohasbeenfoundtobespecificallypowerfulforpostponinginstability,
Figure32.Notethat
asignificanteffectoftetherinternal(Coulomb)dampingasevidencedbyTiPS[Barnds1998]willlikelyhaveabeneficialeffectonstabilityalsoifthereisnospringmassoscillation,butisnotrepresentedbyETBSim.Somenontrivialeffectsarereportedin[Kruijff2001.I].Itisforexamplefoundthattethercoolingthatoccursduringtheeclipseperiodofanorbithasafavorableeffectonstability.Adecrease
in ohmic resistance duetotethercooling balancesthe negative
effecton
currentcollectionasaresultofthedecreasedplasmadensityontheeclipsesideoftheEarth.Theequilibriumtemperatureofthetetherdependsontheratioofopticalpropertiesand(Eq.88
Chapter34.30).A ratioof /closeto1withlowvaluesbothfor
and,forgradualtemperaturechange,willfurtherincreasethesystemspassivelongtermstability.Figure31Cathodelocationimpactonstability(inplanelibration),Referencehasthecathodeontheendmass,deployeddownwardFigure32.Effect16folddecreasestiffness/viscosityratioontransversemodeandinstability(gray).With
the toolbox of possible measures described here tether oscillatory
behavior can beconstrainedduringthedurationofthedeboost. Table15
providesanoverview.Themosteffective system design tools are system
spinup, upward deployment direction of
theendmass,increaseofendmassandmechanicaltetherlength,selectionofapropercurrentlevelthatcanbemaintainedovertetherlengthandtime,highviscosityandlowstiffness.Note
that when the high plasmadensity ranges of the ionosphere are
reached,
below600km,itisnolongerrecommendedtouseatetherfordeorbit,ratherdisconnectthetetheraltogether(Section3.2.3).Adeboostwithlimitedcurrenttakesuptoamonth,duringwhichactive
collision avoidance may be required, e.g. by ground control of
descent rate.
Thebenefitofareleaseatthisaltitudeisnotonlythattotalcollisionriskisreducedbutalsotherequirement
for maintaining stability. This less ambitious approach in fact
makes
thetethereddeboostapplicationbothmoresafeandmorepractical.AnalysisofTetherApplications
89Parameter FindingSystemspin(centrifugalforce)
Requiresspinupofendmass.Effectivenessdecreasesby70%(singlecathode)or40%(withsecondcathode)butnocurrentlimitationrequired(Section3.2.4).Tetherrelease
Reducesstabilitydurationrequirement.Tetherviscosity/stiffnessratio
Dampensmodes.Currentcontrol
Stateestimationmethod[Levin2007].Hasnotbeenverifiedinthiswork.Defunct
satellite and
endmasslocationTorquesarelowerwhenendmassisup,tetherishigherinorbit.Additionalmechanicaltether
Increasesgravitygradientforceatlowmasscost.Currentlimitation
Limitbelowlevelofminimumwithinorbittoreducefluctuations.Furtherreductionincreasestimetoinstability,butreducestheattainedaltitudedrop.Tetherlength
IncreasesgravitygradientforceandLorentzforce.Opticalproperties
Reducesdiurnalcycleeffect.Endmass
Increasesgravitygradientforcebutincreasessystemmass.Table15.
Recommendationsformaintainingstabilityforbaretetherdeboostapplicationwithlightweightnonfunctionalendmass3.2.3
TethereddeboostandcollisionriskTethers can contribute to the debris
mitigation effort. In Section 3.1.2, a niche has
beenidentifiedformechanicaltethers,particularlyforacombinationoflaunchassistandspentstage
deorbit. Electrodynamic tethers however can be employed for active
andpropellantless reduction of many types of space debris,
including for example
defunctconstellationsatellites[Forward1998].Anelectrodynamictethersystemrequiresnodeorbitburnpropellant,and,especiallyifpassive,cankeepthedeorbitmodulesimple.However,alsotheriskthatsuchtethersthemselvesposetoothersatellitesinorbitmustberecognized.Theextendedcollisionareaofatethersweepsthroughasignificantvolumeofthe
orbital environment even for fairly brief operations, such as for
example a
twoweekdeorbitofadefunctsatellite.Considerationoftethercollisionriskhasalreadyledtoseveralcancellationsofmissionsandexperimentsoverthepastdecade(Section1.3).The
question rises how benefits and risks compare to each other for the
case of debrismitigationbyelectrodynamictether.
Inthissectionelectrodynamictetherapplicationsfordeorbit are
considered while taking into account the added risks caused by the
tethersthemselves.First,theconventionalalternative,deboostbyretrorocket,isbrieflyconsidered.Then,moreextensively,thetethereddeboostnetriskiscomparedtothatoftheBusinessAsUsual(BAU),whichisacompletelypassiveapproach.90
Chapter3The conventional retrorocket deboost system, with little
doubt, is superior
overelectrodynamictethersintermsofcollisionriskmitigation.Inaworstcase,thesystemwillmalfunctionandthedefunctsatelliteendsupinaBAUsituation,justasthetethersystemcould
if deployment fails to initiate. A preference for an electrodynamic
tether system, iffound comparably reliable, will thus primarily
depend on system mass and cost.
Tetherdeorbitsystemsofverylowcomplexityhavebeenproduced,albeitnotdemonstratedyet[Hoyt2000].Alsofromaperspectiveofsystemmassanelectrodynamictethersystemcouldbeofinterest.AsystemmasscomparisonisprovidedbyHeide&Kruijff[Heide2001.I]basedonestimatesfor
the tether system mass from Forward & Hoyt [Forward1998] versus
a rocket massbasedonSchonenborg regarding
anautonomoussystemfortypicalconstellationsatellites[Schonenborg2000].
It is concluded that electrodynamic tethers offer considerable
massadvantagefordeorbitofheavyobjects,byuptoanorderofmagnitudeformultitonobjectssuch
as spent stages, and even for small satellites of only hundreds of
kilograms if
theorbitalaltitudeissufficient,largerthan400600km.Giventhechoiceforatetheredsystemoverretrorocketdeorbit,theelectrodynamictethersystem
performance shall be compared to Business as Usual. Heide &
Kruijff propose
asimplifiedmethodologyforsuchacomparisoninwhichthreemajorparametersneedtobeevaluated[Heide2001.I]:1.ProbabilityofbreakupcollisionwithdebrisandnonguidedoperationalsatellitesA
collision with debris that would lead to cutting of the tether, no
matter what
thesecondaryconsequencesmaybe,isassumedtobecatastrophicbyitself.Suchastrictassumption
is likely to be imposed for tether operations [APEX1997]4.
Tetherrobustness against impacts is to be achieved by failsafe
design (multistrand tetherssuchastheCarrollCaduceus[Kruijff1998]
orHoytether[Forward1995])orasafelifedesign(tapes,Section4.3.1).Amultistrandtetherwithawidthof10cmisassumed.Catastrophic
is considered impact with any debris of diameter >10cm or any
nonguidedoperationalsatellite.For comparison to the BAU case, a
collision with the defunct satellite is
consideredcatastrophiciftheimpactingparticleislargeenoughtoleadtobreakupofthesatellite.Criticalimpactenergyoftheparticleisassumedtobe40kJ/kg,foratypicalcasethisisaparticleofabout10cm[Anselmo1999].Nofurtherriskassessmentisperformedonthepartsafterbreakup.2.ActiveavoidancerequirementIfitisoperationallyviableandthetethersystemdeorbitrateiscontrollable(e.g.byavariableohmicresistance,Section3.2.2),activeavoidancecanbeconsidered.Notethat4Thisisperhapsaconservativeapproach.Itcanbereasonedthatatethercutdoesnotleadtoasignificantlyworsesituation
than BAU. The impacting debris may only be superficially damaged
due to the tethers low
ballisticcoefficient.Ifitisalsoassumedthattheremainsofthetethercanbedisconnectedfromtheendmasseswhenthetetheriscut,thefreefloatingpartswilldeorbitquicklyandriskisthuscontained[Heide2001.II].AnalysisofTetherApplications
91all objects larger than 10cm are being tracked from the ground.
If the number
ofactionstoavoidtheseobjectsislimited,itmayprovefeasibletoreducetethersystemcollision
probability to (near)zero. For active avoidance, a safety box
aroundoperational satellites or debris shall be considered. The
expected number of
tethermaneuversistobedeterminedrequiredtoavoidpassingthroughthesesafetyboxes.Whenconsideringactiveavoidancebytethers,theprobabilityoflossofcontrol,oratransition
from the controlled case to the uncontrolled case, should be taken
intoaccount,e.g.incaseofanunplannedend