Combining Magnetic and Electric Sails for Interstellar Deceleration

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by  Nikolaos Perakis

Combining Magnetic and Electric Sails for Interstellar Deceleration
NikolaosPerakisa,∗,AndreasM.Heinb
aTechnicalUniversityofMunich,Boltzmannstr.15,DE85748Garching,Germany
bInitiativeforInterstellarStudies,27-29SouthLambethRoad,LondonSW81SZ
6
Abstract
1
0
Themainbenefitofaninterstellarmissionistocarryoutin-situmeasurementswithinatargetstarsystem. Toallow
2
for extended in-situ measurements, the spacecraft needs to be decelerated. One of the currently most promising

n technologiesfordecelerationisthemagneticsailwhichusesthedeflectionofinterstellarmatterviaamagneticfield
a to decelerate the spacecraft. However, while the magnetic sail is very efficient at high velocities, its performance
J
decreases with lower speeds. This leads to deceleration durations of several decades depending on the spacecraft
2
mass. Within the context of Project Dragonfly, initiated by the Initiative of Interstellar Studies (i4is), this paper
2
proposesanovelconceptfordeceleratingaspacecraftonaninterstellarmissionbycombiningamagneticsailwithan

] electricsail.Combiningthesailscompensatesforeachtechnologysshortcomings:Amagneticsailismoreeffectiveat
h
highervelocitiesthantheelectricsailandviceversa. Itisdemonstratedthatusingbothsailssequentiallyoutperforms
p
- usingonlythemagneticorelectricsailforvariousmissionscenariosandvelocityranges,ataconstanttotalspacecraft
e
mass.Forexample,fordeceleratingfrom5%c,tointerplanetaryvelocities,aspacecraftwithbothsailsneedsabout29
c
a years,whereastheelectricsailalonewouldtake35yearsandthemagneticsailabout40yearswithatotalspacecraft
p massof8250kg.Furthermore,itisassessedhowthecombineddecelerationsystemaffectstheoptimaloverallmission
s architecture for different spacecraft masses and cruising speeds. Future work would investigate how operating both
.
s systems in parallel instead of sequentially would affect its performance. Moreover, uncertainties in the density of
c
interstellarmatterandsailpropertiesneedtobeexplored.
i
s
y Keywords: MagneticSail,ElectricSail,InterstellarMission,MissionDesign,Optimization
h
p
[
1. Introduction mankind. However,thescientificgainofaninterstellar

1 mission would be immensely increased with an exten-
v The concept of manned and unmanned interstellar
sivescientificpayload.Inordertoproducevaluablesci-
5 missions has been examined in different contexts by
entificresults, thedecelerationoftheprobeisrequired
1
manyauthorswithinthepastdecades[1]. Themainob-
0 sinceitenablesthestudyofstarandplanetarysystems
stacleconnectedtothedesignofsuchamission,isthe
3 in detail [5]. For a more detailed analysis of exoplan-
0 necessity for an advanced propulsion system which is ets, involving surface operations, a deceleration down
. abletoacceleratethespacecrafttowardsthetargetsys-
3 toorbitalspeedsisnecessary.
tem within a reasonable time span. To overcome the
0
Therefore, apart from the acceleration propulsion
6 vastinterstellardistances,propulsionsystemswithhigh
system, a further crucial mission component which is
1 specific impulses, like the fusion based engines in the
v: ICARUSandDaedalusprojectshavebeenproposed[2], ostfetellnaromveirslsoiookne.dT,hisisthheadsetcoeldeermatoionnstsryatseteemquoafllayneinffteecr--
i [3]. Othermethodsrelyonpropellant-lesssystemslike
X tive ∆v capabilities as the propulsion system. For that
laser-poweredlightsails,asdescribedin[4].
r Accelerating a probe to high speeds and reaching reason, methods utilizing propellant are not preferred,
a
sincetheywouldinducelargeamountsofmass, which
the target system within short duration using advanced
areinertduringtheaccelerationandcruisingphasesof
propulsion systems would be a big achievement for
themission.
Two attractive concepts rely on utilizing magnetic
∗Correspondingauthor
and electric fields in order to deflect incoming ions of
Emailaddresses:[email protected](Nikolaos
Perakis),[email protected](AndreasM.Hein) theinterstellarspaceandtherebydecelerateeffectively.
PreprintsubmittedtoActaAtsronautica March10,2016
These systems called Magnetic Sail (Msail) and Elec- that can be achieved with the superconducting mate-
tric Sail (Esail) were first proposed by Zubrin [6] and rial,sincethisdictatestheminimalcrosssectionalarea
Janhunen[7]respectively. Sinceeachoneofthosesys- for a specific current. According to Zubrin [6], the
tems has a different design point and velocity applica- current densities of superconductors can reach up to
tionregimeinwhichitperformsoptimally, thecombi- j = 2·1010A/m2 and this is the value used in the
max
nationofthetwocaninducegreatflexibilityinthemis- analysis. For the material of the sail, the density of
sion design as well as better performance. To demon- commonsuperconductorslikecopperoxide(CuO)and
strate these points, the example of a mission to Alpha YBCOwasused,withρ =6000kg/m3.
Msail
Centauri is analyzed. This star system was chosen be- The shielding mass required to protect the sail was
cause it is the closest one to the earth at a distance of modeled according to [3]. This mass vaporizes due to
4.35 light years and because the deceleration concept collisionswithinterstellaratomsandionsandthetotal
described in this paper, was inspired by the Dragonfly massvaporizedaftertimeT isgivenbyEquations2and
Competitionofthei4is,whichinvolvedalight-powered 3:
lightsailmissiontoAlphaCentauri[8].
2. SailProperties (cid:90) T dm
m = shielddt (2)
shield dt
Before the comparison of the different deceleration 0
methodstakesplace, thepropertiesofeachsailwillbe
shortlyanalyzedandtheassumptionsusedinthesimu-  
lationoftheirperformancewillbeexplained. dmdshtield = Aio∆nmHpno (cid:112)1βc−3β2 (cid:112)11−β2 −1 (3)
2.1. MagneticSail(Msail)
InEquation3,A representsthecrosssectionalarea
TheMsailconsistsofasuperconductingcoilandsup- ion
of the coil, as seen from the direction of the incoming
porttetherswhichconnectittothespacecraftandtrans-
ions, ∆H is the vaporization enthalpy of the shielding
fer the forces onto the main structure. The current
materialandβ = v/c. Graphitewaschosenasashield-
through the coil produces a magnetic field. When the
ing material since it combines a low density with high
spacecraft has a non-zero velocity, the stationary ions
vaporizationenthalpy. Theshieldingmassiscalculated
of the interstellar medium are moving towards the sail
separately for each configuration, since its calculation
initsownreferenceframe. Theinteractionofionswith
requiresknowledgeofthetime-dependentprofileforβ.
themagnetosphereofthecoilleadstoamomentumex-
Forthatreason,itscalculationiscarriedoutwithanit-
changeandaforceonthesail,alongthedirectionofthe
erativeprocedure.
incomingchargedparticles.
Forthetetherandsupportstructures,amassequalto
TheforceonthesailiscalculatedaccordingtoEqua-
15%ofthesailmasswasused.
tion1[9].
It is evident from the formula in Equation 1, that
the magnetic sail is efficient for higher current values
andlargerdimensions. Intheanalysespresentedinthis
(cid:16) (cid:17)3
F =0.345π m n µ0.5IR2v2 2 (1) work,theradiusoftheMsailwaslimitedto50km. Al-
Msail p o
though even larger dimensions can demonstrate better
where m is the mass of the proton, n the number performance,itwasthoughtthatthedeploymentofbig-
p o
densityofinterstellarions, µthefreespacepermeabil- ger radii is far from the current or near-future techno-
ity, I the current through the sail, R its radius and v logicalcapabilitiesandwasthereforeexcludedfromthe
its speed. Values for n are proposed in [10] in the analyses.
o
case of a space probe traveling to Alpha Centauri. In The main disadvantage of the magnetic sail is also
thiswork,aratherconservativevaluewasimplemented, evidentwhentakingtheforceformulaintoaccount. At
withn =0.03cm−3 correspondingtotheexpectedval- lower speeds, the force keeps getting reduced asymp-
o
uesintheLocalBubble[10]. totically, and hence the effect of the Msail at these ve-
The main structural component introducing extra locities becomes negligible. This has as consequence
mass into the system is the sail itself, as well as its thatreachingorbitalspeeds(10-100km/s)requireslong
shielding and its deployment mechanism. The mass deceleration duration. A magnetic sail would there-
of the sail is defined by the maximal current density forebeoptimalformissionswherenoorbitalinsertion
2
orsurfaceoperationsinplanetarysystemsarerequired 0.5
butwhereadecelerationforprolongedmeasurementsin 0.45 Voltage = 250 kV
Voltage = 750 kV
the target system is sufficient. Its inefficiency in lower 0.4 Voltage = 1500 kV
speedsindicatestheneedforasecondarysystemableto Voltage = 2500 kV
0.35
bringthevelocitydowntoorbitalvalues.
0.3
N]
2.2. ElectricSail(Esail) e [0.25
c
or
SimilartotheMsail, whereamagneticfielddeflects F 0.2
incomingions,theEsailusesanelectricfieldtochange 0.15
thetrajectoriesoftheinterstellarprotons. Thesailcon-
0.1
sistsofextendedtetherswhicharechargedwithahigh
0.05
positivevoltage.
TheforceontheEsaildemonstratesamorecomplex 00 2 4 6 8 10
Velocity [x0.01 c]
dependencyonthevelocitycomparedtotheMsail. The
forcecanbedescribedbyEquation4[11].
Figure1:Forceonanelectricsailasafunctionofvelocity
Howeveranincreaseintetherlengthandvoltagedoes
3.09·m n v2r
FEsail = NL(cid:114)exp(cid:18)mpv2plno(cid:16)ro(cid:17)o(cid:19)−1 (4) ngoertopnolwyeirmspulpypalyhisgyhsetremm.asTshoeftphoeswitiivreesly,bcuhtaarlgseodatbeitgh--
eVo rw erscollidewiththeinterstellarplasmaelectrons,which
leadstoadecreaseofthevoltage. Inordertomaintain
with N standing for the number of tethers, L their thepositivevoltageofthewires,anelectrongunhasto
length, Vo the voltage of the sail, e the charge of the be placed on board, leading to an additional mass for
electron, rw the wire radius and ro the double Debye thepowersupplysubsystem. Therequiredpowerisde-
lengthλD,givenbyEquation5: scribedbyEquation6[11]:
(cid:115)
(cid:114)
ro =2λD =2 (cid:15)onkobeT2e (5) P=Vo·I =2rwVoNLeno 2meVeo (6)
In the Debye length definition, (cid:15) is the electric per- withm beingthemassoftheelectron.Thetotalmass
o e
mittivityofvacuum, k theBoltzmannconstantandT oftheEsailisputtogetherfromthemassofthetethers
b e
the electron temperature of the interstellar plasma. T and the power system required for the operation of the
e
wasestimatedaccordingto[10],soforthepresentanal- electron gun. In the present work, the power system
ysis the value T = 8000K was used. The wires were fortheEsailwasmodeledwithaspecificpowersupply
e
designedaccordingto[11], withradiusr = 5µmand of 50 W/kg. Although the details of the power system
w
density1500kg/m3 were not part of this analysis, photovoltaic cells could
ItisevidentfromEquation4,thattheforceincreases beused,utilizingthelaserbeampowerincombination
proportionally to the number and length of the tethers withradioisotopethermoelectricgeneratorsandbatter-
aswellasforahighervoltage. Thedependencyofthe ies. Anotheroptionistheuseofelectromagnetictethers
Esail force on the velocity of the probe however, dis- as an energy source, by means of electromagnetic in-
plays a more complex character than the one for the ductionasdescribedin[12].
Msail.Figure1demonstratesthiseffectqualitativelyfor It becomes clear that the Esail has a disadvantage
aconstanttotallengthofthetethers. Itfollowsthatthe whendealingwithhighspeeds,becauseoftheveryhigh
Esailiseffectiveonlywithinaregionclosetoitsmaxi- voltageandconsequentlysystemmassneeded. Forthat
malforce.Inordertodecelerateaprobeefficientlyfrom reason,anadditionalsystemwouldbenecessaryforthe
high cruising speeds (≥ 0.04c) down to orbital values, initial deceleration from the high cruising speeds until
averyhighvoltageisrequiredaccordingtoFigure1,or the point where an optimally designed Esail can take
anincreasedtotallengthofthetethers. over.
3
3. CombinationofMsailandEsail the Esail tethers can be used for energy production ac-
cordingto[12]forthevelocitiesthatarefarfromtheir
After establishing the properties and the disadvan- optimal design point. This way, instead of spending
tages of the individual sails in Section 2, the benefits electricpowerfortheoperationoftheEsail,whichonly
ofcombiningthetwosubsystemsforaneffectivedecel- hasasmalleffectontheoveralldeceleration, theEsail
erationininterstellarmissionsbecomeclear. canserveasasignificantpowersupplysource.
Missions to neighboring star systems require high Additionally, allowing the Msail to operate even at
cruisingspeedsinordertoreducethetotaltripduration. the velocity regime where it has lost its efficiency in
There have been proposals based on fusion propulsion parallel to the Esail instead of detaching it, would in-
that aim to keep the total mission duration underneath creasethedeceleratingforce. However,themassbeing
100years[3],[13],whichmeansthatanaveragespeed decelerated would also increase and hence the magni-
bigger than 0.0435 c is necessary in the case of Alpha tude of acceleration would not necessarily improve. A
Centauri [14]. The present analysis focuses on mis- completeoptimizationmodelcouldincludethestartof
sions with the objective of performing scientific mea- operationoftheEsailandthedetachmentoftheMsailas
surements in the target system, hence requiring orbital twoseparateevents. Thisbringssomeadditionalcom-
insertion around a star or a planet. In this context, the plexity to the model since it requires the optimization
combinationofMsailandEsailseemstobeanelegant ofafurtherparameter. However,itwasexaminedfora
solution. single test case which is not in the scope of this paper
Starting the deceleration phase of the mission with and the obtained results showed a < 5% performance
the use of a magnetic sail is beneficial as mentioned improvement,soitwasignoredinthisanalysis.
in Section 2.1, due to the high forces produced in the AnextrabenefitofceasingtheuseoftheMsailwhen
largevelocityrange.Asthevelocitydecreases,theforce the Esail starts operating, lies in utilizing the magneti-
dropsalsoandtheMsailstartsbeingineffective. Atthis callystoredenergyofthesuperconductorfortheopera-
moment(whichhastobeoptimallychosenasdescribed tionoftheEsai. ThecurrentthroughtheMsailcouldbe
later),theMsailcanbeswitchedoffanddetachedfrom discharged into batteries used for the power system of
the spacecraft and the Esail can start operating. The theelectrongunbeforedetachment,therebyturningthe
electric sail must be designed to perform optimally in Msail to a Superconducting Magnetic Energy Storage
thisvelocityregionandcandecreasethevelocityofthe [15].
spacecraftfurther,untiltherequiredvaluefororbitalin- These considerations explain why a tandem switch-
sertion is achieved. The high flexibility of the tandem ingmethodwaspreferredtoamethodwherebothsys-
systemcomesintheexpenseofadditionaloptimization tems run in parallel. It is easy to understand that the
effort. Thetwosubsystemsaredependentoneachother switchingpointshouldoccurataspeedvaluewherethe
and have to be designed simultaneously and an extra acceleration with the Msail is equal to the acceleration
optimizationparameterinfluencestheirdesign,namely withtheEsail. Switchingatalowerspeedwouldimply
thevelocityvalueatwhichthestartofoperationforthe that there is a time span where the probe is decelerat-
Esailtakesplace. ing with a force smaller than what it could achieve by
Thisidearesemblestheconceptofstaginginconven- switchingtotheEsailandwouldbecomelesseffective.
tionallauncherswithchemicalengines. Assoonasthe The same issue occurs for switching at higher speeds,
firststageisdoneburning,itisdetached,andthesecond sinceitmeansthatthemagneticsaildidnotreducethe
stage, whichhasbeenoptimallydesignedtooperatein kineticenergybytheamountitwasoptimallydesigned
thehigheraltitude, isignited. Similarly, assoonasthe to.
Msailreachesitsweakperformancepoint,itisdropped Theconsiderationoftheoptimalswitchingpointbe-
offandtheEsail,whichhasbeenoptimallydesignedto tweenEsailandMsailcanbequalitativelyseeninFig-
deceleratetheremnantmass,startsoperation. ure2. Inthisimage,afixeddesignpointfortheEsailis
Theswitchingmethodpresentedinthispaperisonly chosenandanoptimaldesignfortheMsailissearched
oneofthealternativesthatcanberealizedwithacom- for. It is obvious, that the choice of an overly dimen-
binationofMsailandEsail. Afurtheroptionwouldbe sioned Msail, like in the case of the design point A,
that the Esail starts operation simultaneously with the is not very efficient. The intersection point of the ac-
Msail even at higher speeds, where it is not so effec- celeration profiles for Esail and Msail lies at velocities
tive. One would expect that this extra bit of braking smaller than the point of the maximum Esail decelera-
forcecouldimprovetheoverallperformance. Thisidea tion. Therefore, after the switch, the magnitude of ac-
was not implemented in the present analysis, because celeration would keep dropping and the highest Esail
4
1 necessary. TheparametersN,L,V ,RandIallowforthe
o
0.9 determinationofmEsail andmMsail. Thecombinationof
MsailandEsailrequirestheadditionalparameterofthe
0.8
units]0.7 sfiwlei.tcChoinmgbvienlioncgittyhevsmwiatcshswahnidchthreesfuolrtcsetoletahdesftoorctheeparoc--
y
ar0.6 celerationcapabilitiesofthesystem. Thisway,theop-
arbitr0.5 timizationparametersofthemathematicalproblemare
on [ Esail design profile summarizedinTable1forthethreedecelerationmeth-
ati0.4 Msail design profile A ods.
eler0.3 Msail design profile B Foragivenaccelerationdependencyonthevelocity,
cc Msail design profile C
A a(v), the total duration of the deceleration period (the
0.2
costfunction)isgivenbytheexpressioninEquation7:
0.1
0
0 2 4 6 8 10
Velocity [x0.01 c] dv dv (cid:90) vtarget dv
a(v)= ⇒dt= ⇒T = (7)
Figure2:QualitativedescriptionofMsailandEsailaccelerationpro- dt a(v) decel a(v)
vcruise
files
Inthecaseoftandemdeceleration,thistakestheform
ofEquation8:
forcewouldneverbeutilized.Althoughtheacceleration
magnitude would be bigger than what the Msail could
haveproduced,thefullpotentialoftheEsailwouldstill
remainunused. T =(cid:90) vswitch dv +(cid:90) vtarget dv
In the case of profile B, the Msail is under dimen- decel a (v) a (v)
siniognpeodi,nht.enActethleiasdrienggimtoe,athheigEhsvaeillodceimtyofnosrtrtahteesswaivtcehry- =(cid:90) vvscwriutcishe(mMMssaaiill+mEsaivlsw+itchms/cE)sdavil+ (8)
F (v)
lporwobfeoercffiecainednttlhy.erAefsoirgendifioceasnntottimreedupceeriothdehsapseteodeolfapthsee vcruise (cid:90) vMtargseatil(mEsail+ms/c)dv
F (v)
untilthevelocityreachestheoptimaldesignpointofthe vswitch Esail
Esail,wheretheaccelerationvalueisbigenoughtopro-
and the objective of the minimization problem is sum-
duceaneffectivebrakingofthespacecraft.
marizedin:
Finally, case C seems to produce a better decelera-
tion profile. The switching point lies in speeds higher
than the optimal design point of the Esail. The Esail
acceleration starts increasing immediately after the de- T =min! (9)
decel
tachmentoftheMsailandisclosetotheoptimalvalue,
therefore utilizing the full potential of the electric sail,
PureMsail I,R
beforestartingtodropagain.
PureEsail N·L,V
The combination of the two sails requires the op- o
TandemMsailandEsail I,R,N·L,V ,v
timization of the individual parameters for Msail and o switch
Esail(radiusandcurrentofsuperconductiveloop,volt-
Table1:Optimizationparametersforeachdecelerationmethod
age,numberandlengthoftethers)aswellasoftheve-
locityatwhichtheoperationoftheMsailceases.
Sincetheaccelerationpartofthemissionisnotcap-
4. Optimizationprocess tured in this analysis, the absence of any further con-
straints would shift the optimal solution to very high
Theoptimizationproblemthatwassolvedtocomeup deceleration system masses. Since the performance of
with the optimal design of the deceleration system can the system increases with increasing mass, an overly
be expressed as the minimization of the total decelera- dimensioned Msail and Esail with infinite mass would
tiondurationT . minimizethecostfunctionT . Whencombinedwith
decel decel
TodetermineT foragivensailconfiguration,the the acceleration system however, such a large system
decel
mass of the system and the force profile over time are would be inefficient since it would pose a large inert
5
massduringtheaccelerationphase. Forthatreason,an At the same time, there has to be some finite distance
additional constraint was introduced, namely an upper availablefortheaccelerationandcruisingphases,which
bound for the maximal deceleration mass. Hence this are not part of the optimization and this was estimated
extraconstraintwasintroducedasinEquation10: equal to 1.5 light years. For that reason, the constraint
wasdefinedasinEquation14:
m ≤C (10)
decel
(cid:90) vtarget vdv
withCbeingapredefineduppermasslimitand rdecel = a(v) ≤2.85lightyears (14)
vcruise
m =mmMsail,, ffoorrMEssaaiillddeecceelleerraattiioonn nonT-hlienecaorsltyfduenpcetinodnentotobnetmheinoimptiizmeidza(tTiodencepl)ariasmheigtehrlsy,
decel mEMssaaiill+mEsail, fortandemdeceleration aunsedfutlh.ereMfoorreeolvineer,arduperotghreamlamckingofmkentohwoldesdgweeroef nthoet
function gradient, the optimization took place with a
Furtherconstraintsinvolvetheinitialandendvelocity
patternsearchmethodsimilartothe”directsearch”pro-
oftheprobe. ThisreadsasinEquation11:
posedbyHooke[16]. Thisisthemethodutilizedforall
analysesinthepresentpaper.
Afterobtainingtheoptimaldecelerationduration,the
v(t=0)=v andv(t=T )=v (11) velocity and acceleration profiles as a function of time
cruise decel target
were calculated by means of numerical integration. A
Thisconstraintisdirectlyappliedinthedefinitionof time propagation was implemented using a 4th order
the cost function Tdecel, since it sets the limits of the Runge-Kutta scheme, which served as a validation of
integralcalculation. the optimization results and provided a complete time
In the case of the Msail and Esail combination, the profileofthespacecrafttrajectory.
switching velocity is to be modeled as well. One con-
straintforv isalreadypresentinEquation8,since
switch
5. Results: Comparisonofdecelerationprofiles
itissetasthelimitoftheintegraltobeevaluated.More-
over,ithastobemadesure,thattheaccelerationatthe
UsingtheoptimizationmethodinSection4,theper-
switching point between Msail and Esail remains con-
formance of three separate deceleration methods was
tinuous,asdescribedinSection3. Mathematicallythis
comparedandtheresulsareshowninthissection. The
yields:
threedecelerationarchitecturesarethefollowing:
1. PureMsaildeceleration
a (v=v )=a (v=v ) ⇒
Msail switch Esail switch 2. PureEsaildeceleration
F (v=v ) F (v=v ) (12)
Msail switch = Esail switch 3. CombinationofMsailandEsailintandem
m +m +m m +m
Msail Esail s/c Esail s/c
Inthistestcase, themassofthespacecraftm was
s/c
wherem standsforthespacecraftmass.
s/c chosentobeapproximatelyequaltothelaunchmassof
Moreover, as explained in Section 3, the switching
Voyager1,soequalto750kg. Voyagerisaspaceprobe
pointhastotakeplaceforvelocitieslargerthantheop-
which was launched to perform flybys of Jupiter, Sat-
timaloperationpointoftheEsailandtherefore:
urn and Titan and continued to explore the boundaries
oftheouterheliosphere[17]. Sinceitistheonlyman-
made probe so close to entering the interstellar space
v >v(a =max) (13) [18],itwasconsideredrelevanttocalculatehowitsde-
switch Esail
celeration would look like in the case of a mission to
Finally, the total deceleration distance r poses a anotherstarsystem,requiringadecelerationphase.
decel
furtherconstraint. Ithastobeensured,thatthereissuf- Only the deceleration phase of the mission was ex-
ficientdistanceavailableforthespacecrafttodecelerate amined, so a cruising speed v = 0.05c was cho-
cruise
completely before it reaches Alpha Centauri. For that sen. The target speed was set to be equal to v =
target
reasonthisshouldremainshorterthan4.35lightyears. 35km/s. This would correspond approximately to the
6
orbitalspeedatadistanceof1AUaroundAlphaCen- 100
tauriA,whichhasamassof1.1M [19]. Combination Msail and Esail
(cid:12)
Msail
For each one of the three deceleration methods, an
10−1 Esail
optimal design point was calculated in order to mini-
mizethetotaldecelerationdurationTdecel. Themassof 2s]
thedecelerationsystemwasrestrictedtobeunderneath m/10−2
n [
7500 kg, which corresponds to the tenfold spacecraft o
ati
mass. Adirectcomparisonistherebypossible,sinceall eler10−3
systemshavethesameeffectontheaccelerationphase cc
A
andhencetheoverallmissiondesign.
At this point it has to be noted, that the restriction 10−4
of the Msail radius described in Section 2.1 produces
veryweekforcesinthelowspeedlimit(closetovtarget), 10−50 5 10 15 20 25 30 35 40
therebyresultingindurationcloseto300years. Itwas Time [years]
thereforedismissedfromthecalculationsofpureMsail
deceleration. Theresultsshownhererequiredasailra- Figure3: Comparisonofdecelerationmethods: Accelerationprofile
overtime
diusof1000km,whichwasconsideredtobeunrealistic
butwasstillincludedforcompletion.Thisdemonstrates
101
onceagainthattheMsailasastandalonecomponentis
Combination Msail and Esail
notsufficientformissionsrequiringorbitalinsertionin Msail
Esail
thetargetsystem.
The acceleration and velocity profiles over time are
shown in Figure 3 and 4 respectively. Note that the 1 c]100
0
curves in Figure 3 represent the magnitude of the ac- 0.
x
celeration,sincethenumericvaluesofaccelerationare city [
o
negativeduringthebrakingphase. Thecombinationof Vel10−1
thetwosailsrequires28.8yearsasopposedtothe39.7
yearsoftheMsailandthe34.9yearsoftheEsail. Inthe
acceleration profile of the dual system, the discontinu-
ityinthegradientrepresentsthepointwheretheswitch
betweenMsailandEsailtakesplace. Thisoccursafter 10−20 5 10 15 20 25 30 35 40
Time [years]
13.67yearsandataspeedequaltoapproximately0.03
c according to Figure 4. This change is not detectable Figure4:Comparisonofdecelerationmethods:Velocityprofileover
in the velocity profile, since the acceleration shows no time
discontinuityduringtheswitchfromtheonesystemto
theother,leadingtoasmoothvelocitycurve.
Thistestcasedemonstratesthepotentialthatacom-
Initially, the acceleration of the Msail method is the
bination of Msail and Esail has in the design of an in-
highest. This makes sense because the magnetic sail
terstellar mission, since it outperforms each individual
used in the tandem method is smaller than in the pure
system in particular mission configurations. However,
Msailmethod,inordertosatisfytheequalmassrequire-
duringacompletemissiondesign,theminimaldeceler-
ment. After some time however, the magnitude of the
ationdurationisnottheonlyparametertobeoptimized
acceleration in the tandem method becomes larger and
and the interaction of the deceleration system with the
eventuallyleadstoasmallerduration. other components (influence on acceleration, effect of
Atthispoint, itisalsoimportanttomentionthatthe
decelerationdistance)hastobetakenintoaccount.
pureMsailmethodistheoptimalsolutionwhenahigher
targetspeedisneeded. Figure4demonstratesthiseffect
since the velocity curve of the Msail is lower than the 6. Interactionwithmissiondesign
other two for the whole duration apart from the lower
velocityrange,whereitflattens. Theabsenceoforbital After having established that the method of tandem
insertion(leadingtov beinganorderofmagnitude deceleration with Msail and Esail can bring benefits to
target
larger),wouldthereforemaketheMsailthemosteffec- the total duration of the deceleration phase before or-
tivesolution. bitalcapture,itisinterestingtodeterminehowthissys-
7
teminteractswiththeaccelerationandcruisingphases. 3
m =750 kg
s/c
6.1. Influenceofcruisingvelocity 2.5 ms/c=4000 kg
exaInmSineecdti.oInn3t,haissisnegclteiovna,ltuheefeoffrethcetocfruaisvianrgiasbpleeecdrwuiass- nce [ly] 2
a
idnegceslpeeraetdioonnsythsteemdeissigpnrecsehnatreadc.teristics of the tandem on dist1.5
Forthisanalysis,twodifferentspacecraftmassesare erati
el 1
compared. Apart from the Voyager-like spacecraft in- ec
D
troduced in Section 3, the profile of a heavier vehicle
withm = 4000kgiscalculated. Thisvaluewascho- 0.5
s/c
sen since it is approximately equal to the launch mass
of the Mars Science Laboratory (MSL). This robotic 04 5 6 7 8 9 10
Cruising speed [x0.01 c]
spaceprobewassenttoMarsandincludedaroverwith
a landing system and instruments for biological, geo-
Figure6:Decelerationdistanceofoptimalconfigurationasafunction
chemical and geological measurements on the surface ofthecruisingvelocity
of the planet [20]. Since a similar mission to an exo-
planetwouldbeofhighscientificvalue[13], anMSL-
like spacecraft was used. The restriction for the total cruising speed leads to a deceleration distance close to
mass of the deceleration system being maximally ten 2.5 light years. When taking into account that the dis-
timesthespacecraftmasswasmaintained. tancetoAlphaCentauriis4.35lightyears,onededuces
thatthereareonly1.85lightyearsavailablefortheac-
65 celeration and cruising phases. However, the buildup
m =750 kg ofsuchahighspeedcouldrequirealargeracceleration
60 s/c
m =4000 kg distance depending on the propulsion system. There-
s/c
s]55 fore, reachingsuchahighspeedinamissiontoAlpha
ar
n [ye50 Centaurimaynotbenecessaryoruseful,duetotheex-
o tremedecelerationdistanceconnectedtoit.
ati45
dur The mass and velocity change distribution between
n 40
o Msail and Esail are also interesting to examine as a
ati
er35 function of the cruising speed. Figure 8 shows the ra-
el
Dec30 tio of the Msail mass mMsail to the Esail mass mEsail
and Figure 7 the ratio of the velocity changes ∆v
Msail
25 and∆v attheoptimalconfigurationforeachcrusing
Esail
204 5 6 7 8 9 10 speed.
Cruising speed [x0.01 c] The velocity change ratio demonstrates a nearly lin-
ear profile in Figure 7, which increases with the cruis-
Figure5:Decelerationdurationofoptimalconfigurationasafunction
ingspeed. Thiscanbeexplainedwiththegoodperfor-
ofthecruisingvelocity
mance of the Msail in higher speeds. Since the Msail
isefficientinthehighspeedregime, itislogicalthatit
Figures 5 and 6 show the dependency of the decel-
willalsotakeovermostofthedeceleration. Moreover,
eration duration and distance on the cruising speed. It
theresultsshowthatahigherspacecraftmassleadstoa
is intuitive that a larger initial speed requires a larger
deceleration duration, since the total ∆v that has to be lower∆v-ratio.
providedbythedecelerationsystemincreases. Since the velocity changes are proportional to the
Thesameoccursforthedecelerationdistance,asFig- mass of each subsystem, it is expected that the mass
ure 6 demonstrates. A higher spacecraft mass also in- ratioalsoincreaseswiththecruisingspeed,asshownin
creasestheinertiaofthesystemduringdecelerationand Figure8.Inthiscasehowever,theincreaseinmassratio
hencethetimeanddistancerequired. Animportantin- tendstobeslowerandresemblesalogarithmicgrowth.
directresultstemmingfromFigure6isthathighcruis- The results show a general preference towards the
ingspeedsarenotalwaysoptimalforaminimalmission Msail deceleration for higher cruising velocities which
duration. Inthecaseofthe4000kgspacecraft,a0.1c isreflectedinthe∆vandmassdistributionofthedecel-
8
3 beingsmallerthantentimesthespacecraftmasswasuti-
ms/c=750 kg lized. This boundary condition was introduced so that
2.5 ms/c=4000 kg an easier comparison between different configurations
could take place. In the present analysis however, the
−] 2 ratio between deceleration system mass and spacecraft
[Esail masswasvaried. Thetwospacecraftmassesdescribed
∆ v 1.5 inSection6.1aswellastwodifferentcasesforthecruis-
/Msail ingspeedwerecomparedtoeachother. Figure9shows
∆ v 1 theresults.
140
0.5 m =750 kg, v =0.05 c
s/c cruise
m =750 kg, v =0.08 c
120 s/c cruise
04 5 C6ruising spe7ed [x0.01 c8] 9 10 n [years]100 mmss//cc==44000000 kkgg,, vvccrruuiissee==00..0058 cc
o
Figure7: OptimalmassratioofMsailtoEsailasafunctionofthe ati
cruisingvelocity dur 80
n
o
ati
4 er 60
el
m =750 kg c
3.5 s/c De
m =4000 kg
s/c 40
3
−] 2.5 200 2 4 6 8 10
[Esail mdecel /ms/c [−]
m 2
m /Msail1.5 Ftiiognusreys9t:emOpmtiamssaldecelerationdurationasafunctionofthedecelera-
1
An increased mass of the deceleration system leads,
0.5 as expected, to a shorter deceleration duration. It is
however notable, that the curves tend to saturate for
04 5 6 7 8 9 10 larger masses. This implies that a larger deceleration
Cruising speed [x0.01 c]
mass, although having a great impact on the design
Figure8:Optimal∆vratioofMsailtoEsailasafunctionofthecruis- of the acceleration phase because of additional inertia,
ingvelocity onlyprovidesasmallbenefittotheoveralldeceleration
performance. Quantitatively,takingtheexampleofthe
4000kgspacecraftwith0.08ccruisingspeedinFigure
erationsystem.
9,oneobservesthatamassratioof10leadstoamini-
maldurationequalto53.83yearswhereasamassratio
6.2. Effectofdecelerationsystemmass equalto4resultsin55.90years. Henceanincreaseof
150%inthemassofthedecelerationsystem,produces
Thedecelerationsystemisanintegralpartofthemis- onlya3.7%increaseintheperformanceofthesystem.
siondesignandcannotbeanalyzedindependentlyofthe Thistrendismaintainedforallconfigurationsanditis
accelerationphasewhenaninterstellarmissionisbeing evident,thatwhenthecompletemissionisdesignedand
developed. Themaineffectthatthedecelerationsystem allmissionphasesareoptimizedsimultaneously,decel-
hasontheaccelerationphaseisitsmass,whichneedsto eration system masses are preferred, which are further
beacceleratedaswell. Therefore,adecelerationsystem fromthesaturationlimitandstillproducesufficientper-
whichisaslightaspossiblebutstillproducesthenec- formance.
essary ∆v change in short amount of time and in short
distanceisrequired.
7. Conclusion
The effect of the tandem deceleration system mass
onitsperformancewasexamined. Intheprevioussec- Magnetic and electric sails have been proposed as
tions, the requirement of the deceleration system mass propulsion systems for interstellar and interplanetary
9
missions. Inthecaseofinterstellarmissionswithshort References
tripdurationandneedfororbitalinsertionaroundatar-
get system, each one of these sails demonstrates some
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10