Modeling the Martian v1 -...

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Dr.DirkZwemer,InterCAXLLC

Modeling The Martian Abstract........................................................................................................................................................1

Introduction.................................................................................................................................................1

MartianSurvival-Abandonment.................................................................................................................2

MartianSurvival-Transit.............................................................................................................................7

FinalThoughts............................................................................................................................................11

AbouttheAuthor.......................................................................................................................................11

Abstract

Two scenarios from The Martian, an adventure story describing the challenges of a NASAastronaut inadvertentlymaroonedonMars,aremodeledinSysML,withspecialattentiontocapturingthedetailedparametricsfromthenovel.Thefirstsectionexplorestheagronomicsofgrowingfoodonaplanet without normal air, water, soil or plant life. The second sections describes transportationplanning for extended travel without a highly developed road infrastructure. The SysML parametricmodels are intended to offer some guidance on adding these features to complexMBSE systems, inadditiontowhateverentertainmentvaluemayresultfortheterminallyengineering-minded.

IntroductionTheMartian,anovelbyAndrewWeir(BroadwayBooks,2014),isagreatread.Partofitsappeal

toengineersisthattheastronauthero“shows”hiscalculationsonhowtosurvivehismanychallengesaloneontheplanetMars.Therealismandresourcefulnessofhisworkmakehisfatethatmuchmorerealtothereaderandheightentheemotionalimpactofthestory.

Unfortunately,theengineersinthenovelaren’tshownasusingmodel-basedsystemsengineering(MBSE).Intheinterestoffutureastronauts,IwilltrytocapturesomeofthelessonslearnedontheAres3missionintheformofSysMLparametricmodels(whiletryingtominimizespoilersforthoseyettoenjoythebookorthemovie).

Twoscenarios,capturedasusecasesinFigure1,willbemodeled.Inthefirst,theastronautplanstoextendthefoodstocksavailablebygrowingfoodinsidehisMartianbasecamp.Inthesecond,heneedstotravelalongdistanceacrosstheMartianlandscape,carryinghisenergysupply,hislifesupportequipment,andthefoodandwaterrequiredtoreachhisdestination.ThefiguresuseMagicDraw(NoMagicInc.)tocreateandParaMagic(InterCAX)andMathematica(WolframResearch)tosolvethemodel,butthesamemodelwillalsobemadeavailablefordownloadfromtheInterCAXwebsite(www.intercax.com)inseveralforms,astheyarecompletedandverified:

• EnterpriseArchitect(SparxSystems),solvedwithSolvea(InterCAX)• IBMRationalRhapsody(IBM),solvedwithMelody(InterCAX)• IntegrityModeler(PTC),solvedwithParaSolver(InterCAX)• MagicDraw18.0(NoMagic),solvedwithParaMagic(InterCAX)

Figure1Astronautobjectivesundertwosceanrios

MartianSurvival-AbandonmentThefirstscenarioissetattheAcidaliaPlanitialandingbaseoftheAres3mission.TheBDDin

Figure2showsthatthebaseconsistsofthemainhabitat,twomobileMarsrovers(eachwithapopupshelter),andthelandingstageoftheMAV(MarsAscentVehicle).Italsoincludesthefoodstocksexpectedtobeusedundertheoriginalmissionplan.

Figure2APBasestructureTheastronaut,abotanistamongothertalents,wantstogrowenoughadditionalfoodtosurviveuntilrescue.Hisanalysisfallsintofourparts:

1. Howmuchplantingareacanhecreateinsidethehabitableelementsofthebase?2. Howmuchwaterdoesthesoilrequireforplantgrowth?3. Howmuchfood(heplantspotatoes)canhegrowpersol(Martianday)?4. Howlongwillhisextendedfoodsupplylast?

I have structured these questions as four separate analysis blocks containing parametric models, asshowninFigure3.TheseanalysisblocksreferencetheAP_Baseblock,aswellaseachother,toaccessthenecessaryvaluesfortheircalculations,withoutrequiringchangestothepropertiesorparametricsofthestructureblocks.

Figure3Analysisstructure,MartianSurvival–Abandonmentscenario

Theonlyparametricsembeddedwithin theAP_Baseblocksare for the food supply, shown in

Figure4.

Figure4FoodSupplyPAR,calculatingbasefoodstocksbasedontheoriginalmissionplan(e.g.6peoplefor30sols).The<equal>stereotypelabelsonthebindingconnectorshavebeenelidedfromalldiagramsforclarity.

SoilAnalysisPAR(Figure5)Thismodelcomparesthearableareainsquaremeterscreatedinsidethehabitatandpopup

sheltersagainstavailablearea,ultimatelycalculatinganareaMOS(marginofsafety)value.TheMOSispositiveaslongastheareaplannedtobeuseddoesnotexceedtheareaavailable.Italsocalculatesthevolumeofsoiltobecreated,whichisusedbyWaterAnalysis.

Figure5SoilAnalysisPAR

WaterContentAnalysisPAR(Figure6)This part of the model calculates the water required to make the soil fertile with the stock

availableatthebase,andcalculatesanotherMOS.

Figure6WaterAnalysisPAR

PotatoGrowthAnalysisPAR(Figure7)

Thiscalculatestheaveragenumberofcaloriesgeneratedfrompotatoespersol.Thisignorestheinitiallagwhilethepotatoesaregrowing,sincethefinalvalueofinterest,thenumberofadditionaldaysoffood,isnotconcernedwithwhenthepotatoesareeaten,aslongasthefirstcropcomesinbeforetheinitialfoodstockisconsumed.

Figure7PotatoGrowthAnalysisPAR

Figure8SurvivalAnalysisPAR

SurvivalAnalysisPAR(Figure8)Thisfinalsectionofthemodeldeterminesthetotalnumberofsolthattheminimumdietary

needoftheastronautcanbemetbetweentheoriginalfoodstockandtheadditionalfoodgrown.Notethattheperiodincreasesifmorefoodcanbegrown,buttheanalysisbecomesinvalid(periodbecomesnegative)ifthefoodgrowneachsolexceedsthefoodconsumed.

ModelExecution

Figure9Instance01,beforesolving Figure10Instance01,aftersolvingUsingvaluesfrom(orestimatedfrom)theAres3mission,aninstanceoftheparametricmodeliscreatedanddisplayedintheParaMagicbrowserinFigure9(beforesolution)andFigure10(aftersolution).Potatoeswillextendtheastronaut’ssurvivalfrom400solsto1471sols(ifthingsgoaccordingtoplan).

MartianSurvival-TransitThesecondscenariosendstheastronautonanextendedtripacrosstheMartianlandscape.The

top-levelblockinFigure11,Caravan,consistsofthetworoverscoupledtogether,ladenwitheverthingnecessarytosurvivethetrip.Thereisatimelimit,bywhichthetripmustbecompleted,andfoodandwaterstocksmustbesufficient.

Figure11TransportStructureBDD,showingthecaravan,rovers,andkeycargofortheanalysis

Iuseembeddedparametricsinthispartofthemodelforthemassrollup.AlltheblocksshowninFigure11arespecializationsofasupertypeTravelElement,whichusesrecursion(Figure12).

Figure12ParametricdiagramforTravelElement.ThemassofeachelementisthesumofthemassofitsexplicitpartsplusabasemassTheastronautdriveseachMartianday(sol)until theroverbatteriesareexhausted,manuallyunpacksanddeploysthesolarpanelscarriedoneachrover,waitswhilethepanelsrechargethebatteries,andrestows the panels, all during Martian daylight. Additional charging time is required to run theoxygenatorperiodically,whichremovesCO2fromtheroverairsupplybeforeitreachestoxiclevels.

The number of solar panels to be carried on the trip represents a trade-off between the powerproduced,themasstobetransported,andthetimespentunpackingandrepackingthepanelsateachstop.ThesethreevaluesarecapturedintheparametricdiagraminFigure13.

Figure13SolarPanelparametricanalysis

As inthefirstscenario,weplacemostofthescenariospecificanalyses inseparateblocksthatreferencetheCaravansystem(Figure14).

Figure14TransitAnalysisBDD,showingthestructureofthesecondscenarioanalyses

ThePowerAnalysisPAR inFigure15calculates twokeyparameters,how long it takes to fullycalculate the caravan batteries and what percentage of the time must be spent powering theoxygenator,relativetohowlongtheatmosphereremainshealthy.Thesecondfactorextendsthetotaltriptimebyafixedpercentage,asshowninFigure16.

Figure15ParametricdiagramforPowerAnalysis.Notethatbatterychargingtimeisaffectedbyatmospherictransmissionfactors,whichmayreducesolarpaneloutput.

ThetravelTimeAnalysisPAR(Figure16)usesthepowernumbersandthecaravanpropertiestocalculatetotaltriptime.Theconstraintcalculatingdistancetraveledbythecaravanperbatterycharge,

Figure16ParametricdiagramforTravelTimeAnalysis.marginTimeistheMOSforthecalculatedtriptimevs.timelimit

DistancePerCharge,isestimatedfromempiricaldatacollectedduringtheAres3mission.Thisdistance,dividedbytheeffectivetimeperchargingcycle(thesumofthedrivetime,chargetime,andsolarpanelunpack/repack time, extendedby thedaylight hoursper sol andoxygenatoroperation), estimates aneffectivevelocityincludingdowntime.Thetotaltripdistance,dividedbytheeffectivevelocity,resultsintimeTotal:sol,thetotaltimeforthetrip.

Foodandwatercalculationsaresimilartothoseinthefirstscenarioandarenotrepeatedhere.At the Survival Analysis – Transit block (Figure 17) level, the parametric diagramuses conditionals toreturnverdictsforthethreesurvivalissues,1iftheastronautsurvives,0ifhedoesn’t.

Figure17ParametricdiagramforTravelElement.Themassofeachelementisthesumofthemassofitsexplicitpartsplusabasemass

The instancevalues inFigure18andofferhope;all three factorsarepositive. Thegivensaretaken from theAres3 video logs. The caravancan travel almost100kilometerspre charge, taking4hours at themaximum speed of 25 kph. Recharging the batteries takes about 10 hours ofMartiandaylight,withanadditional1.4hoursforsettingoutandpickingupthesolarpanels.Thecaravanstopstopowerandruntheoxygenatorforaboutonesoloutofeveryfive.Overall,thetripof3200kilometersisexpectedtake47.55sols,withinthe50soltimelimitandwithsufficientfoodandwater.Thisanalysisassumesnoproblemswith terrainobstacles, equipment failure,weather, or anyother challenge thatMarscanthrowattheunsuspectingvisitor.

Figure18Instance02,beforesolving Figure19Instance02,aftersolving

FinalThoughtsAfull treatmentof theAres3missionwouldstartwithmodelingtheoriginalprofileandtreat

the scenariosexplored in thisTechNoteasextendedusecases. Furtherextendedusecases couldbedeveloped because (Spoiler Alert!) none of TheMartian’s plans work out as expected. This furtherdevelopment would highlight the common strength of SysML and the astronaut hero, the ability toadaptandre-purpose.Astheastronautconfigurestheelementsoftheoriginalmissiontoservehisnewobjectives, theSysMLmodeler reusesobject fromoldprograms innewways. I like to think that theNASAengineersworkingtorescuetheherowere,behindthescenes,usingMBSEtocomeupwiththerapidredesignstheycomeupwith.

AbouttheAuthorDr. Dirk Zwemer (dirk.zwemer@intercax.com) is President of InterCAX LLC, Atlanta, GA and holdsOCSMPcertificationasModelBuilder-Advanced.

Forfurtherinformation,visitusatwww.intercax.comorcontactusatinfo@intercax.com.

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