written by tom dubick karoline saunders€¦ · conditions for a new pilot. then, you will learn...
TRANSCRIPT
WrittenbyTomDubick&
KarolineSaunders
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TABLEOFCONTENTS
ScienceOfFlightFirstFlight……………………………………………………………………………………………………………………………..4
Weight…………………………………………………………………………………………………………………………………14
Lift……………………………………………………………………………………………………………………………………….22
Drag…………………………………………………………………………………………………………………………………….28
Thrust………………………………………………………………………………………………………………………………….34
FlightStability………………………………………………………………………………………………………………………38
ScienceOfFlight–AdvancedTopicsPressureandAirspeed…………………………………………………………………………………………………………49
CoefficientsofLiftandDrag…………………………………………………………………………………………………52
EngineeringOfFlightAspectRatio………………………………………………………………………………………………………………………..58
WingLoading……………………………………………………………………………………………………………………….63
PowerLoading…………………………………………………………………………………………………………………….71
AirplaneDesign…………………………………………………………………………………………………………………...79
EngineeringOfFlight–AdvancedTopicsGliding…………………………………………………………………………………………………………………………………86
Jetsvs.Propellers………………………………………………………………………………………………………………..90
RunwayDesign…………………………………………………………………………………………………………………….95
SupersonicFlight………………………………………………………………………………………………………………….98
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GAMA Airplane Design Challenge Introduction…………………………………………………………………………………………………………………100
GAMAAirplaneDesignChallengeWorkflow…………………………………………………………………101
Settingupachallengeflight………………………………………………………………………………………….107
Exportingflightdata…………………………………………………………………………………………………….111
Importingandmodifyinganairfoil………………………………………………………………………………..113
Additionalresources……………………………………………………………………………………………………..125
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FirstFlight“TheWrightbrotherswereengineersfirst,pilotssecond.”
IntroductionBeforeyoucantakeoff,youneedtolearnalittlemoreabouthowtosetuptherightflightconditionsforanewpilot.Then,youwilllearnaboutairplaneinstruments,techniquesfortakingoff,andhowtochangeviewsoftheairplanewhileflying.Afteryouhaveagoodgrasponflying,youwillrundifferenttrialstolearnhowairspeedandaltitudearerelated.BeforeflyinginX-Plane,pleasereadthroughthishandoutandwatchthecorrespondingvideos.Youcanalwaysre-watchthevideosifyouneedahelpinghand.FlightConditionsIt’simportanttotakeintoconsiderationtheaircraft,airport,andweatherconditionsforyourfirstflight.Planes,aswellasrunways,varyindifficulty,andthemoreyoupractice,themoreoptionsyouwillhave.Onceyougainmoreexperience,youwillbeabletoflyatnightandinwindyconditions.FornowusethefollowingQuick-FlightSetupinstructions.Itisagoodfitforanewpilot;thislessonhasagreatcorrespondingvideothatgoesintodetailonhowtosettheseoptions. UnderFilechooseQuick-FlightSetup:
Airport:EntertheairportIDofKSEAtoselectSeattleTacomaInternationalairport.Bydefault,youwillbeplacedonRunway16(RWY16).
Plane:ClickonOpenAircraft,selectGeneralAviation,anddouble-clickCessna172SP,172SP.acf
Weather:SetTimetobe“day”andWeathertobe“clear.”Thisdefaultsto58°Fintemperatureand29.92inHgforbarometricpressure.Thiswillmaximizevisibility,andeliminateclouds,precipitation,thunderstorms,wind,andturbulence.
Click“FLYwiththeseoptions!”onthebottomright-handcornerofyourscreentoexitQuick-FlightSetup.Makesuretheboxnextto“ShowthiswindowoneverystartupofXPlane”ischecked.
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InstrumentsInX-Planeyoucanseeyourinstrumentsinthebottomhalfofthescreen.Thecorrespondingvideowillpointouteachoneoftheseonthecontrolpanelsoyoucanmatchupeachwithitsfunction.
AirspeedIndicator:indicateshowfasttheairplaneismovingrelativetothesurroundingair.
AttitudeIndicator:showstheattitudeoftheairplanerelativetothehorizon. Altimeter:showshowhightheairplaneisabovesealevel—thelargehandrepresentshundredsandthesmallhandrepresentsthousands.
CoordinatedTurnIndicator:indicatestherateanddirectionofturn. HeadingIndicator:showstheheadingoftheairplanecomparedtogeographicalnorth. VerticalSpeedIndicator:reportstheratethattheaircraftisclimbingordescending. Compass:reportstheheadingoftheairplanerelativetomagneticnorth. Tachometer:showsthenumberoftimestheenginesturnsperminute.
Needaninflightinstrumentreminder?UndertheAboutMenu(leftoftheFileMenu)chooseInstructions,andclickontheShowInstrumentinstructionsinthecockpit.Nowwhenyourmousehoversoverinstrumentyouseeabriefreminderofwhatthatinstrumentdoes.›Takeoff
1. OpenX-PlaneandfollowtheQuick-FlightSetupinstructionsabove.2. Press"P"topausethesimulatorsoyoucanreadytheplanewithoutitmoving.3. Clickontheredbrakelighttoreleasethebrakes(orpress"B").4. Pushthethrottle,theblackknobinthebottom-rightcornerofthescreen,allthe
wayinusingthemouse.YoucanalsopressandholdtheF2keywhileyourscreenisunpausedtocontrolthethrottle.
5. Clickonthecenterofthewindshieldtomakethecrosshairsandcontrolboxappear.6. Movemousepointertotherightofthecrosshairstogettheplanestarteddownthe
runway(otherwiseitwilldriftleft).7. Press"P"toun-pause.8. Astheplanerollsforward,makesmallcorrectivemovementswiththemouseto
keeptheplanerollingstraightdowntherunway,movingthepointercloserandclosertothecrosshairs.
9. At75knots,movethepointertothebottomofthecrosshairsandtheplaneshouldtakeoff.
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FlightViewsX-Planeoffersmanydifferentcameraanglestoseetheplaneandobserveyourflight.PressPtopausesoyoucanconcentrateonlearningthedifferentviewswithoutworryingaboutflying.
e:Cyclesclockwisethroughviewsouttheplane–thelittleorangeplaneandtriangleshowyouwhichwayyouarelookingout.
q:Cyclescounter-clockwisethroughviewsouttheplane. w:Thestandardviewstraightouttheplane. Shift8:Pressbothatthesametimetofollowbehindtheplane–Pressingqoreinthisviewallowsyoutocirclearoundtheplane,counter-clockwiseandclockwise,respectively.Youcanalsousethearrowkeystorotatetheviewaroundtheaircraft.Press+and-tozoominandout.
FlightControlsTheWrightBrotherswerethefirsttoflybecausetheywerebrilliantengineers;theywerebrave(theyweretestpilotsafterall),andtheypersevered.Maybethemostimportantfactorintheirsuccesswasthattheyrecognizedflight’srealchallengewascontrolandstability.ControlTheWrightBrothersdescribedflightinthreeaxes—roll,pitchandyaw.
RollRolldescribestherotationofthewingsalongthelongitudinalaxis(nosetotail).Theaileronscontrolrollbyincreasingliftononesideofthewinganddecreasingliftontheothersideofthewing.Unfortunately,thisalsocausesthenoseoftheairplanetoturnintheoppositedirectionoftherollorbank.Anoseturningthewrongwayiscalledadverseyaw.Weusetheruddertocounteractadverseyawandpointthenoseinthesamedirectionasthebank.
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ROLL
PitchPitchdescribestheplane’snosemovingupanddown.Thinkofaboat“pitching”intheocean.Theelevator—thepartofthehorizontaltailsectionthatmovesupordown—controlsthepitchoftheairplane.Pitchalsoimpactstheangleofattackofthewing.
PITCH
YawYawdescribestheplanerotatingleftorright.Therudder—thepartoftheverticaltailsectionthatmovesleftorright—controlsyaw.Therudderalsopreventsadverseyaw.Wewilllearnaboutadverseyawinamoment.
YAW
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Let’slookataplaneonarunway.Bymovingourmousearoundthecursor,wewillseethemovementofthecontrolsurfacesontheairplane.Thepilotusesthesecontrolsurfaces(ailerons,elevator,andrudder)tocontroltheairplanesinthethreeaxes—roll,pitch,andyaw.TestPilotingWearegoingtotakeacloserlookatthemovablecontrolsurfacesontheairplane.
1. ClickonsettingsandfollowtheseQuick-FlightSetupinstructions. Airport:KSEA Aircraft:Cessna172SP Time:“day” Weather:“clear” ClickFLYwiththeseoptions!
2. PressShift8andusethearrowkeyssoyouarelookingfromdirectlybehindtheairplane.
3. Clickonthecrossandmoveyourcursordown.Observethepartsoftheairplanethatmove.Moveyourcursorup,left,andthenright.Besuretoobservewhichsurfacesmoveonthewingsandthetail.Otherwise,theairplaneshouldbesittingstillontherunway.
InvestigativeQuestionsIfImovemycursordown(decreasingpitch),whatdoestheelevatordoonthetail?IfImovemycursorup(increasingpitch),whatdoestheelevatordoonthetail?IfImovemycursorleft(rollingleft),whatdoestherudderdoonthetail?IfImovemycursorleft(rollingleft),whathappenstotheleftwingandtotherightwing?IfImovemycursorright(rollingright),whathappenstotheleftwingandtotherightwing?
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EnergyManagement-Potentialvs.KineticEnergyAsapilot,youneedtobeconcernedaboutenergymanagement.Energyexistsintheuniverseindifferentforms.Itcannotbecreatedordestroyed.Itsimplychangesform.Yourairplanerunsonaviationfuel.Thisfuelhasagreatdealofpotentialenergy.Onceyoustarttheplane,theengineconvertsthepotentialenergyofthefuelintothemovingorkineticenergyofthepropellerturningintheair.Asyouaddmorefuel(pushinthethrottle),theengineturnsevenmorepotentialenergyintokineticenergy(tachometerincreases).Theplane,pulledbythepropeller,willmovefasterdowntherunwayandthenliftoff.Ifyoucontinuetoapplyfullthrottle(blackknobpushedallthewayin),theplanewilldooneofthefollowing:gofasterorgohigher.Ifyoudecidetogofaster,theplaneisconvertingthefuelorpotentialenergyintokineticenergyorspeed.Ifyoudecidetogohigher,theplaneisconvertingthefuelorpotentialenergyintoaltitudeoradifferentformofpotentialenergy.Itisthesamethingaswhenyoupedalyourbikedownahill.Youareusingpotentialenergyofgravityatthetopofthehillandconvertingitintokineticenergyofmotionasyouridedown.Unfortunately,notallthepotentialenergybecomeskineticenergy.Forexample,someofthepotentialenergybecomesheatanddoesnotcontributetospeed.
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Let’sdoaquickdemonstrationofwhatwehavebeendiscussing.UnderFilechooseQuick-FlightSetup:
Plane:ClickonOpenAircraft,selectGeneralAviation,anddouble-clickCessna172SP,Cessna_172SP.acf
Weather:SetTimeto“day”andWeatherto“clear.” Airport:ExitQuick-FlightSetup.ClickonLocationonthetopbarandSelectGlobalAirport.SelectKSEA,RWY16,FinalApproach3nm.BereadytopressPtopause!
LevelFlight
1. OpenX-PlaneandfollowtheQuick-FlightSetupinstructionsabove.2. Press"P"toPausethesimulatorsothatyoucanreadytheplanewithoutitmoving.3. Clickonthecenterofthewindshieldtomakethecrosshairsandcontrolboxappear.4. Weshouldtakealookatourtopthreeinstrumentsandjotdownwhattheyread.
Whatistheairspeed?Whatdoestheartificialhorizonlooklike?Wherearethebigandlittlehandsonthealtimeter?Fillinthecirclesabove.Don’tworryaboutwritingdownallthenumbers—justdrawthearrows.
AirSpeedIndicator
AttitudeIndicator
Altimeter
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Let’stradeoffpotentialenergyforkineticenergy.Pointthenoseofourplanedown.Afterdescendingforashorttime(3sec),presspauseandtakeanotherlookatourinstruments.Notethechangesandfillintheinstrumentsbelow.
Pointthenoseupforashortwhileuntilyouarehigherthanyouwerewhenyoustarted.Thenpresspause.Again,notethechangesandfillintheinstrumentsbelow.
AirSpeedIndicator
AirSpeedIndicator
AttitudeIndicator
AttitudeIndicator
Altimeter
Altimeter
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InvestigativeQuestionsYouasthepilotwanttogofaster,doyoupointthenoseupordown?Youareflyingfasterandfaster.Isyourkineticenergygoingupordown?Intermsofenergy,whydoesyourplaneslowdownasyouclimb?Youdon’ttouchthethrottle;canyouclimbandflyfaster?Whyisitdangeroustoflylowandslowly?Youareinadivegoingfasterandfaster.Atsomepointtheairspeedwillstopincreasing.Why?
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Weight“TheWrightbrotherswereengineersfirst,pilotssecond.”
IntroductionOk,nowyouhavebeenflyingalittlewhileandyourealizetwothings:Flyingisfun!Andthereisalottolearntopilotaplane.Thegoodnewsisthemoreyoulearn,thebetterthepilotyouwillbe.Inthislessonyouwillbegintolearnaboutthefourforcesthatactonanairplane.Youwillalsogetyourfirstchancetodomorethanjustfly;youcanactuallymakechangestoyourairplane.Asalways,pleasereadthroughthishandoutandwatchthecorrespondingvideos.Youcanalwaysre-watchthevideosifyouneedahelpinghand.
ForceForceisapushorapull.Itiscomposedofmagnitude(howlargetheforceis)andthedirectionoftheforce.Werepresentforcesbydrawingvectors(arrows)thattellusthemagnitudeandthedirectionoftheforce.WeightLet’slookatweightasaforceonanairplane.Weightistheresultofmasstimesgravity.Thismeansthatifyouweretostandonthemoonoranotherplanetyouwouldweighadifferentamountbecausegravityhaschanged,eventhoughyourmassisstillthesame.Themassoftheairplaneincludestheairplanestructures(wings,tail,landinggear,etc.),fuel,andpayload.Thepayloadincludescargo(mailandpackages),crew,andpassengers.Thedirectionofthisforceinlevelflightisdownorperpendiculartotheflightpath.
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TestFlight:Weightvs.TakeoffDistancesNowlet’sconductsometestflightstostudytheimpactofweightontakeoffdistances.Thisisimportantfortworeasons:toseetheimpactofweightontheperformanceoftheairplaneandtolearntheimportanceoftakeoffdistance.Quick–FlightSetup
Airport:KSEA Aircraft:Cessna172SP Time:“day” Weather:“clear”
CollectTestData1. ClickonSettings.2. SelectDataInput&Output.3. Clickonthelasttwocheckboxesatspeeds(line3).4. Clickonthelasttwocheckboxesatloc,vel,disttraveled(line21).5. Clickonthelasttwocheckboxesatlandinggearvertforce(line66).6. ClickonXtoreturntotheplane.
SetPayload
1. Atthetopmenu,selectAircraft.2. ClickonWeightandFuel.3. Makeanoteofthepayloadweight.Itshouldbe243lbs.Pleasechangethisvalueto296
lbs.4. ClickXtoreturntotheplane.
Takeoff
1. Press"P"topause.2. Press“B”toreleasethebrake.3. Pushinthethrottle.4. Clickonthecenterofthewindshield.5. Movethemousepointertothebottomofcrosshairs.6. Press"P"toun-pause.7. Astheplanerollsforward,makesmallcorrectivemovementswiththemousetotry
keeptheplanerollingstraightdowntherunway.8. Theplaneliftsoff.
Repeatthesesteps,completingthefollowingtablebytakingoffwithdifferentweights.
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TestPilotingIfyouhavenotalready,pleasewatchtheWeightvs.TakeoffDistancevideo.Theplanenormallyhasaloadof296lbs.Flyitthreetimes.Besuretokeepthepointeronthecrosshairs,andtheplanewilltakeoff.Trytoflyasconsistentlyaspossible.RecordtheVtrueairspeedandTakeoffDistanceforeachflightinthetablebelow.Changetheloadto600lbsandtakeoffthreemoretimes.Repeatagainwiththeloadat900lbs.Load:296lbs
AverageTakeoffDistance________________
Load:600lbs
Trial Load VtrueArspeed TakeoffDistance
1 600
2 600
3 600
AverageTakeoffDistance________________Load:900lbs
Trial Load VtrueArspeed TakeoffDistance
1 900
2 900
3 900
AverageTakeoffDistance________________
Trial Load VtrueArspeed TakeoffDistance
1 296
2 296
3 296
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OnceyouhavecompletedtheTestFlyingtables,pleasecompletethebargraphbelow.Pleasenote:Vtrueindicatesthetrueairspeed.Vindmeansindicatedairspeed.Theplane’sinstrumentsgiveusanindicatedairspeed,whichisaffectedbyaltitudeandtemperature.Vtruegivesustheactualairspeedindependentofaltitudeandtemperature.
Payloadvs.AverageTakeoffDistance
InvestigativeQuestionsAsthepayloadincreases,doestakeoffdistanceincreaseordecrease?Doesalongertakeoffdistanceindicatemoreorlesspayload?Doestheairspeedgoupordownasyouincreasethepayload?Dolargerairplanesrequirelargerairstrips?
Payload(lbs)
AverageTakeoffDistance(ft)
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WeightasaForceAsstatedbefore,weightequalsmasstimesgravity.Wecan’tchangegravity,butbyreducingmass,wecanreduceweighttoimproveperformance.Thisistrueineveryaircraftwhetherit’sajetairlineroramodelplane.Wehavefocusedontheimpactofmagnitudeofweightonflightperformance.Sinceweightisaforce,ithasadirectionalcomponent.Thedirectionoftheweightforcewillalwayspointtothecenteroftheearth.Duringlevelflight,thisforceispointed90degreesofftheflightline.
FlyingTip:Youcanreducethepayloadofanyflightbygettingyourtalkativefriendoutoftheairplane.Italsomeansaquieterflight.
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Whentheairplaneclimbs,partoftheweightvectorfallsbacktowardsthetail.Thisslowsdowntheplane.
Whentheairplanedescends,partoftheweightvectorfallsforwardtowardsthenose.Thisspeedsuptheplane.
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TestFlight:FlymetothemoonYoulearnedthatweightequalsmasstimesgravity.Wecanreducemasssimplybyhavingasmallerpayload,butwhatifwecan’treducethepayload?Wecouldreducegravity!OK,unlessweleavetheearth,wereallycan’tchangegravityinameaningfulway,butwecanchangeitinX-Plane!Let’simaginethatwehaveoutpostsonthemoonandthatthemoonhasanatmosphere.Thisisimportantbecausewithoutanatmosphere,anairplanecannotfly.(Remember,weareimaginingthemoonwithanatmosphere.ThemoondoesNOThaveanatmosphere.)ConfirmPayloadisstill900lbs.
1. Atthetopmenu,selectAircraft.2. ClickonWeightandFuel.3. ChoosetheFuel/PayloadTab.4. Makeanoteofthepayloadweight.Itshouldbeatornear900lbs.5. ClickXtoreturntotheplane.
ChangeGravity
1. ClickonSpecialattopofthemenu.2. SelectSetEnvironmentalProperties.3. Changeplanetmu(mass)to00.660,themassofthemoon.Thegravityisnow1.6225.4. ClickXtoreturntotheplane.
ReviewQuick-FlightSetup
Airport:KSEA Aircraft:Cessna172_P Time:“day” Weather:“clear”
TakeoffWhatisthenewtakeoffdistance?Whatisthenewtakeoffspeed?Didthetakeoffdistanceincreaseordecrease?Didthetakeoffspeedincreaseordecrease?
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Youdidnotchangethemassoftheairplane;youchangedgravity.Thus,theweightwasreduceddramatically,andtheperformanceincreasedsubstantially.Besuretosetchangeplanetmu(mass)backto3.986,themassoftheEarth.Thegravityisnow9.7986.Don’tforgetthepayloadweight.Makesureandreturnthepayloadweighttoatornear296lbs.ClimbingHigherThedaythemoonhasanatmosphere,pigswillfly!Well,maybe…Scientistshavecomeupwithaschemetoputanatmosphereonthemoon.Thesundoesnotshinedirectlyonthedarksideofmoon.Scientistsbelievefrozenwatermaybefoundatthebottomofdeepcraters.Ifyouclosethetopofthecraterwithagiantsunroofandheattheice,youwillcreateanatmosphere.Pigswillnotfly,buthumansmight.Themoon’slowgravitymeanspeoplewithartificialwingswouldbeabletoflaptheirarmsandflylikebirds!
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Lift“TheWrightbrotherswereengineersfirst,pilotssecond.”
IntroductionInthislesson,youwilllearnaboutlift.Liftisaforcethathelpspilotsandengineersovercomeweight.Ifyouloseliftinflight,youraircraftwillfalloutofthesky.Youwillflylikearock.Ihopethatgotyourattention.Nolift,noflying,noway.Pleasereadthroughthishandout,andwatchthecorrespondingvideos.Youcanalwaysre-watchthevideosifyouneedahelpinghand.
ForceForceisapushorapull.Itiscomposedofmagnitude(howlargetheforceis)andthedirectionoftheforce.Werepresentforcesbydrawingvectors(arrows),whichtellusthemagnitudeandthedirectionoftheforce.LiftThedirectionofthisforceinlevelflightisup,orperpendiculartotheflightpath.Liftresultsfromthedifferencesinairpressurealongthewing.Theamountofliftisverysensitivetothespeedoftheairtravelingoverthewing.Whenthereisnotenoughairtravelingoverthewing,liftsuffers,andtheplanebeginstofalloutoftheskyorstalls.Soundslikefun;let’stryit!
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TestFlights:Stallsvs.AirspeedQuick-FlightSetup
Airport:KSEA Aircraft:Cessna172_P Time:“day” Weather:“clear”
Location
SelectGlobalAirport SelectKSEA SelectRWY16 SelectFinalApproach3nm BereadytopressPtopausethesimulation
CollectTestData1. ClickonSettings.2. SelectDataInput&Output.3. ChoosetheDataSetTab.4. Clickonthelasttwocheckboxesatspeeds(line3).5. Clickonthelasttwocheckboxesatwinglift(line92).
ShowLiftVectors
1. SelectSpecial.2. ClickonShowFlightModel.3. Whitelinesshouldbeprojectingoutofthepropeller.Theserepresentlift.
SetPayload
1. Atthetopmenu,selectAircraft.2. ClickonWeightandFuel.3. ChoosetheFuel/PayloadTab.4. Makeanoteofthepayloadweight.Changeitto296lbs.5. ClickXtoreturntotheplane.6. IfyouarenotinaChaseview,press“A”.7. Press“Shift8”andcirclearoundtheplane.
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TestPilotingIfyouhavenotalready,pleasewatchtheStallsvs.AirSpeedvideo.Flytheplanelevelfor3seconds.WatchthegreenliftarrowsonthewingsandtheVtrueairspeedinthelefttopcornerofthescreen.Puttheplaneina3secondclimb,andthenpausethesimulation,butdonotchangethethrottle.Whatdoestheairspeeddoasyouclimb?Whatdotheliftarrowsdoasyouclimb?Nowcontinueclimbinguntiltheliftarrowsnearlydisappearordisappear,butdonotchangethethrottle.Pausethesimulation.Whatistheairspeednow?Istheremuchliftoccurringonthewing?Continuethesimulation.Whathappenstotheplane?Thewingsarenolongerproducingenoughlifttosupporttheweightoftheplane;theplanebeginstofall.Thisisknownasastall.Thegoodnewsisitiseasytorecover.Youneedtogainairspeedagain,sowhatdoyoudowiththenoseoftheairplanetogainairspeed?Levelthewings,andpointthenosedown.Onceyourairspeedapproaches80knots,pullthenoseupslightly.Watchtheliftvectors.Didtheliftvectorsincreaseastheairspeedincreased?Didtheliftvectorsincreasewhentheairspeedincreasedandthenosewaspointedup?Pleasefly,stall,andrecoverseveraltimes.Watchtheliftvectorsthroughout.
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Ourtestpilotingshouldshowusthatliftisdirectlydependentonairspeed.Liftisalsodependentontheangleofattack.Theangleofattackreferstotheangletheairfoilmakeswiththedirectionofairflow.Thisexplainsthefactthatinadivetheairspeedwasincreasing,buttherewasverylittleliftgenerateduntilwepulledupthenose.Thenwithbothabetterangleofattackandairspeed,theliftvectorsrosedramatically.
Wehavelearnedthatliftisdependentonairspeedandtheangleofattack.Thisangleofattackissmall.Infact,tomaintainanangleofattackwhenflyinglevel,engineersbuildintothewingasmallangleofattack.Thisiscalledtheangleofincidence.
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ClimbingHigher:WhatisLift?Wehavelearnedabouttheimpactofairspeedandtheangleofattackonlift,butwhatislift?Liftistheresultofadifferenceinairpressure.Thepressureonthetopofthewingislessthanonthebottomofthewing.Mostscientistsandengineersagreeonthispoint.Butwhatcausesthedifference?Listedbelowareseveralexplanations.
TheLongerPathorEqualTransitTheory
Theairflowingoverthetopoftheairfoil(wingshape)travelsfasterthantheairunderneaththebottomoftheairfoil.Theairfoilisacurvedshape.Airmoleculestravelingacrossthetoptravelalongerdistancethanonthebottom.Astheairmoleculesmoveoveragreaterdistance,theairmoleculesspreadoutandtravelfasterthantheairflowingunderthebottomoftheairfoil.Asairspeedincreases,thepressuredrops.ThisisalsosometimesknownastheBernoulliPrincipleofLift.
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TheSkippingStoneTheoryDuetotheangleofattack,theairflowstrikesthebottomofthewingandbouncesoff.Theresultingforceislift.ThisisalsosometimesknownasNewton’s3rdLaw.
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Drag“TheWrightbrotherswereengineersfirst,pilotssecond.”
IntroductionInthislessonyouwilllearnaboutdrag.Dragisaforcethatresiststhemovementoftheairplanethroughair.Dragslowsdownplanes,anddragresultsinlowerfueleconomy.Generally,engineersdesignplanestoreducedrag.
ForceForceisapushorapull.Itiscomposedofmagnitude(howlargetheforceis)andthedirectionoftheforce.Werepresentforcesbydrawingvectors(arrows)whichtellusthemagnitudeandthedirectionoftheforce.DragDragisdirectedalongandopposedtotheflightdirection.Dragisaforcethatresiststhemovementoftheairplanethroughair.Dragisunavoidable.Dang!Let’slookatanexample.Thegoodnewsisthatwearegoingtoflyanewplane.Thisbabyissweet.She’saKingAirwithtwoengines.Thatisright,andtwoenginesmeanthreetimesthefun!Italsohasretractablegear.Onceyoutakeoff,youcanpulluporretractthelandinggear.
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TestFlights:AirSpeedvs.Drag(DeployedLandingGear)OpenX-PlaneandfollowtheQuick-FlightSetupinstructionsbelow:Quick-FlightSetup
Airport:KSEA Aircraft:KingAirC90B Time:“day” Weather:“clear”
Location
SelectGlobalAirport SelectKSEA SelectRWY16 SelectFinalApproach3nm BereadytopressPtopausethesimulation Press“Shift8”tobringuptheChaseview.
CollectTestData1. ClickonSettings.2. SelectDataInput&Output.3. Clickonthelasttwocheckboxesatspeeds(line3).4. Clickonthelasttwocheckboxesatlandinggeardeployment(line67).5. ClickXtoreturntotheplane.
TestPilotingIfyouhavenotalready,pleasewatchtheAirSpeedvs.Drag(DeployedLandingGear)video.Flytheplanelevelfor3seconds.Besurethatthelandinggearisup.Pleaseobservetheairspeed.Whatistheairspeednow?Nowpress“G”tolowerthegear.Flytheplanelevelfor3seconds.Besurethatthelandinggearisdown.Whatistheairspeednow?Whatisyourhypothesistoexplainwhathappened?
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FlapsSometimeswewanttoslowdownanairplane,likeanyairplanethatistakingyoubacktoschool.Actually,youwillfinditeasiertolandifyouslowdowntheplane.Careful,though!Ifyouslowdowntheplanetoomuch,you’llstallandfalloutofthesky.Howdoweadddrag?Stickyourhandoutthewindowoftheairplane?Dragyourfeetacrosstheclouds?Howaboutmakingthewingbigger?Actually,engineershavedevelopedawaytomakethewingbiggerbyusingflaps.Flapsextendthewingstrailingedgesbackandchangetheairfoil,orshapeofthewings.Thisincreasesdrag.Italsoincreaseslift.Asyouland,theflapsslowdowntheplanewhileincreasingtheliftonthewing,soliftismaintainedatslowerairspeedstoavoidstalling.
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TestFlights:AirSpeedvs.Drag(Flaps)OpenX-Planeandfollowtheinstructionsbelow:Quick-FlightSetup
Airport:KSEA Aircraft:KingAirB200 Time:“day” Weather:“clear”
Location
SelectGlobalAirport SelectKSEA SelectRWY16 SelectFinalApproach3nm BereadytopressPtopausethesimulation Press“Shift8”tobringuptheChaseview.
CollectTestData1. ClickonSettings.2. SelectDataInput&Output.3. ChoosetheDataSetTab.4. Clickonthelasttwocheckboxesatspeeds(line3).5. Clickonthelasttwocheckboxesoftrim/flap/slat/s-brakes(line13).6. Clickonthelasttwocheckboxesofwinglift(line92).7. Clickonthelasttwocheckboxesofwingdrag(line93).8. ClickXtoreturntotheplane.9. Press“W”toreturntocockpitview.
Trytoflyasconsistentlyaspossiblefor3seconds.Recordtheairspeed,liftanddragforeachflightinthetablebelow.
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FlapsUpTrials Flaps VtrueAirspeed Liftwing1 Dragwing1
1 Up
2 Up
3 Up
AverageVtrueAirspeed _______AverageLiftwing1 _______ AverageDragwing1 _______FlapsDownTrials Flaps VtrueAirspeed Liftwing1 Dragwing1
1 Down
2 Down
3 Down
AverageVtrueAirspeed _______AverageLiftwing1 _______ AverageDragwing1 _______Pleaseanswerthefollowingquestions:Whenyoudeployorlowerflaps,whatdoesdragdo?Whenyoudeployorlowerflaps,whatdoesairspeeddo?Whenyoudeployorlowerflaps,whatdoesliftdo?Whywoulditbedangeroustolandaplanewithflapsiftheflapsonlyincreaseddrag,butdidnotincreaselift?
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KindsofDragMuchlikehomework,dragcomesindifferentforms.
ParasiticDragParasiticdragiscreatedfromdraggingabody(fuselage,wing,flap,landinggear)throughtheair.Youcanseethisbymakingafistandputtingitoutthewindowofacardoing60.Thisdragvarieswiththesquareofthespeedoftheplane.AsimplifiedequationwouldbeSpeed=Drag2,sochangingairspeedmeansanevengreaterchangeindrag.Engineerstrytoshapeorchangethebodyoftheplanetoreducethiskindofdrag.Forexample,engineersdevelopedretractablelandinggeartoreducethiskindofdraginfastairplanes.Automobileengineerstrytoreducedragincarstoincreaseperformanceandfueleconomy.
InducedDrag
Induceddragistheresultoflift.Yes,induceddragiscausedbythecreationoflift.Engineersspendagreatdealoftimelookingatdifferentairfoilsorshapesofawingthatwillgivethemthegreatestamountofliftwiththeleastamountofdragforawingundercertainconditions.Anypartoftheplanethatgeneratesliftgeneratesthisformofdrag.Thisincludesthewing,tailsurfaces,andthebody.
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Thrust
IntroductionInthislessonyouwilllearnaboutThrust.Thrustisaforcethathelpspilotsovercomedrag.Thrustalsodeterminesthealtitudeoftheairplane.Youclimbordescendbyaddingorsubtractingthrust.Inthislesson,youwilllearnhowtheplanemakesthrustandunderstandhowthrustwillhelpyoulandanairplane.Yes,that’srightyougettopracticelandings.Takeoffsareoptional,butlandingsaremandatory,soweneedtounderstandandpracticelandingprocedures.Asalways,pleasereadthroughthishandoutandwatchthecorrespondingvideos.Youcanalwaysre-watchthevideosifyouneedahelpinghand.
ForceForceisapushorapull.Itiscomposedofmagnitudeorhowlargetheforceisandthedirectionoftheforce.Werepresentforcesbydrawingvectors(arrows),whichtellusthemagnitudeandthedirectionoftheforce.ThrustThedirectionofthisforceisforwardintheflightpath.Thrustinanairplanecomesfromthepropellerpullingorpushingtheairplanethroughtheair.Thepropelleractslikearotatingwing.Thebladesonthepropellercreatelift,whichcreatesthepropulsiveforce.Usuallyagasengineprovidesthepowertoturnthepropellerinanairplane.
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TestFlights:LandingsQuick-FlightSetup
Airport:KSEA Aircraft:Cessna172SP Time:“day” Weather:“clear” ClickFLYwiththeseoptions!
Location
SelectGlobalAirport SelectKSEA SelectRWY16 SelectFinalApproach3nm BereadytopressPtopausethesimulation
TestPilotingIfyouhavenotalready,pleasewatchtheLandingvideo.Landing–Basic
1. Puttheplaneintolevelflight.2. Reducethethrottleuntiltheenginerunsat1600RPM.3. Keepthewingslevel.4. Maintaintheairspeedaround85knots.5. Besuretowatchyouraltimeterandyourverticalspeedindicator.6. WatchthePAPI–PrecisionApproachPathIndicator:
a. Allred–youaretoolowonyourapproach.b. Halfredandhalfwhite–youareontherightapproach.c. Allwhite–youaretoohighonyourapproach.
7. Onceyoutouchdown,throttledownandapplybrakes.8. Repeatuntilyoucanlandtheplaneontherunwayeverytime.
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Landing–FullFlaps
1. Puttheplaneintolevelflight.2. Reducethethrottleuntiltheenginerunsat1500RPM.3. Keepthewingslevel.4. Reducetheairspeedtolessthan85knots.5. Deployfullflaps.6. WatchthePAPI–PrecisionApproachPathIndicator:7. AddorremovethrottletostayontheproperapproachaccordingtothePAPI8. Repeatuntilyoucanlandtheplaneontherunwayeverytime.
InvestigativeQuestionsDoweusethethrottleorchangethepitchoftheairplanetocontrolaltitude?Ifyoucomeintoolow,insteadofaddingthrottle,whynotpullthenoseup?Whataretheadvantagesoflandingataslowerspeed?Canyoulandataslowerspeedwithfullflaps?Canyoulandonashorterrunwaywithfullflaps?Whynotflyallthetimewithfullflaps?
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TakingItHigherLandinganairplaneonlandcanbebothfunandchallenging.Imaginelandingatseaonanaircraftcarrier?Hereisyourchance!
1. FollowtheQuick-FlightSetupinstructionsbelow:a. Airport:KSAN(SanDiegoInternational)b. Aircraft:Cessna172SPc. Time:“day”d. Weather:“clear”e. ClickFLYwiththeseoptions!
2. Location-SelectGlobalAirporta. MakesureKSANisselectedb. RWY09c. Finalapproach3nmd. BereadytopressPtopause
3. ClickonAircrafta. SelectAircraft&Situationsb. SelectAircraftCarrierApproach
4. Goforit.Flynavy!
Wantabiggerchallenge?Trymakinganightcarrierlanding.Stilltootame?Trylandinginroughseas.
a. SelectEnvironmentb. ClickonWeatherc. SelectWaterTabd. Changewaveheightto10ft.e. Press“X”toexit
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FlightStability
“TheWrightBrotherswereengineersfirst,pilotssecond.”
IntroductionWehavelearnedaboutthefourforcesthatactonanairplaneandaswelearnedearlier,theWrightBrotherrecognizedtheimportanceofstabilityinflight.StabilityStabilitydescribesthetendencyoftheairplanetoreturntoitsoriginalconditionafteradisturbance.Forexample,ifagustofwindpitchestheairplaneup,astableairplanewillreactbypitchingdown.Iftheplaneisunstable,theplanewillcontinuetopitchupinsteadofreturningtoitsoriginalcondition.Letmetrytoexplainthisinanotherway.Whydoesanarrowhavefeathersonitstail?Theheadofthearrowisheavyandsharpanddoesthedamage.Whatdothefeathersdo?Shootanarrowwithoutfeathers,andveryquicklythearrowistravelingsidewaysoutofcontrolbecauseanydisturbance(wind,rain,etc.)causesthearrowtochangedirection.Addfeathersandthearrowfliesstraight.Thisisbecausethefeathersdampentheeffectsofanydisturbancehelpingthearrowflystraight.Thefeathersgivethearrowstabilitybykeepingthetailintheback.Thetailoftheairplaneactslikethefeathersonanarrow.Thetail(horizontalandverticalstabilizers)givestheplanestability.
Whatifthepilothadworkedalldaybeforeembarkingonalatenightflight?Onastormynight?Whentired?Thepointofstabilityistoreducethepilot’sworkloadandmakeiteasiertoflytheaircraft.Thepilotwantstobeabletolookdownatamaporletgoofthecontrolsforasecondtoadjustthemicrophonewithouttheplanetryingtorollinverted.Thismaybeduetoagustofwindorbumpofturbulence.Engineersdesignstabilityintoaircraft.Theyrecognizethatnoamountofpilotcontrolcanovercomeaninherentlyunstableairplane.Wewilllookattwoimportantexamplesofwayswecanincreasethestabilityofanairplane.
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RollandYawStabilityManyairplanesincorporateadihedralangleinthewings.Lookbelow,andyouwillseeseveralwings.Noticethewingsarehigheratthetipsthanwheretheyjointhefuselage.
Dihedralhelpstokeepaplane’swingslevel.Forexample,agustofwindcausesaplanetoroll,droppingtheleftwingdownandraisingtherightwingup.Dihedralcausesthelowerwingtoriseandthehigherwingtosink,restoringstabilitytotheflightpath.
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PitchStabilityImaginetheairplaneasateeter-totter.Thenoseoftheairplaneisatoneendoftheteeter-totter,andthetailisattheotherend.Thefulcrumorbalancingpointofourairplane/teeter-totteristhewing.Thedistancebetweenthetailandthewingcanbethoughtofasaleverarmthatactslikeateeter-totter.Wecancontrolthepitchoftheairplanebyvaryingtheamountofforceappliedtothetail.Inphysics,theapplicationofforcetorotateanobjectaboutafulcrumiscalledtorque.
Youhavealreadylearnedandexperiencedchangingthepitchoftheairplaneusingtheelevator,thepartofthehorizontaltailsectionthatmovesupordown.Wecanalsoincreasepitchbyaddingaforce(likeweight)totheendofthetail.Thisnewlyaddedforcemultipliedbythedistancefromtheendofthetailtothewingwouldcausethenosetopitchup!Weneedtheplanetobestable,sowelocatetheC.O.Ginfrontofthewingandputthetailbehindthewing.TheC.O.Gpushesdownpitchingthenosedownandthetailpushesdownwhichholdsthenoseupmakingtheplanestable.Let’slookattheseforcesinaction.
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TestPiloting
1. FollowtheseQuick-FlightSetupinstructions. Airport:KSEA Aircraft:Cessna172SP Time:“day” Weather:“clear” ClickFLYwiththeseoptions!
2. Location-SelectGlobalAirport Airport:KSEA RWY16 Finalapproach3nm BereadytohitPtopause
3. Special-“Showflightmodel”tobringuptheliftvectors.4. Establishlevelflight.Gentlyclimbup,anddivedownseveraltimes.
InvestigativeQuestionsInwhichdirectionsaretheliftvectorspointingonthewingastheplanedives?Inwhichdirectionsaretheliftvectorspointingonthetailastheplanedives?Istheliftcreatedbythetailthesameinallflyingsituations—level,dive,andclimb?WouldIachievethesameresultifIaddedweighttothetail?Ifso,whydon’tweaddweighttothetail?TheImportanceofBalanceandSafeFlyingTheloadandbalanceofanairplaneareveryimportanttosafeflying.AccordingtotheBritishnewspaperTheTelegraph,asmallairplanecrashedinAfricawhenacrocodilegotlooseonboardtheplane.Itseemsthatananimalsmugglerhadstoredacrocodileinhisluggage.Thecrocgotloose,causingthepassengerstopanicandruntothefrontoftheairplane.Inspiteofthepilot’spullingdesperatelyonthecontrols,theplanepitcheddownwardandcrashed.Luckily,thisisaveryrareincident.Oneveryflight,pilotsmakesuretheplaneisloadedandbalancedproperlywithallitemsproperlysecured.
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ClimbingHigherAirplanes,Teeter-totters,andTorqueAswesaidearlier,torqueistheapplicationofforcetorotateanobjectaboutafulcrum.Tobetterunderstandhowtorqueimpactsairplanes,let’stakeacloserlookatateeter-totter.
Thesetwofrogsaresharingateeter-totter.Iguessthefrogpondwasgettingabitdull.Thefrogontheleftsideweighs5lbsandis2ftfromthefulcrum(triangle).Thisfrogproduces10ft-lbsoftorqueormoment.5lbsx2ft=10ft-lbs.Let’scalculatethetorqueormomentofthefrogontheright.Theweightofthefrogontheright=10lbsThedistanceofthefrogontheright=1ftTorqueormoment=Isn’tthatcute?Bothfrogsareproducingthesameamountoftorque.Whatdoesthismean?Willtheteetertotterrotateclockwiseorcounterclockwise?Pleaseexplainyouranswer.Whataboutafrogthatweighs2lbs?Howfarwouldthisfrogneedtobefromthefulcrumto
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produce10ft-lbsoftorqueormoment?Whataboutahefty20lbfrog?Howfarwouldthisfrogneedtobefromthefulcrumtoproduce10ft-lbsoftorqueormoment?Anotherfrogissitting2.5ftawayfromthefulcrum.Howmuchdoesthisfrogweighifsheisproducing10ft-lbsoftorqueormoment?Ifyousolvedthoseproblems,youhaveaprettygoodunderstandingofbothteeter-tottersandtorque.Now,let’sreturntoairplanes.
Inreality,thereareseveralmomentarmsatworkhereintheairplane,butforourpurposes,wearegoingtosimplifythesituationandassumethattwoleverormomentarmsareimpactingthepitchstability.ThedistancefromthewingtotheCenterOfGravity(C.O.G)istheC.O.GMomentArm.C.O.GMomentArmmultipliedbytheAirplaneWeightwillgiveustheC.O.G.TorqueorC.O.G.Moment.C.O.GMoment=C.O.GMomentArmXAirplaneWeightTheC.O.G.Momentalwaystriestorotatetheaircraft’snosedown.ThetailmustcounteracttheC.O.G.Momenttoholdthenoseup.ThedistancefromthewingtothetailistheTailMomentArm.TheTailMomentArm
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multipliedbytheforcegeneratedbynegativeliftwillgiveustheTailTorqueorTailMoment.TailMoment=TailMomentArmXLiftGeneratedByTail
TheC.O.G.MomentequalstheTailMomentwhenthenoseisNOTpitchingupordown,butwillitwillbeinequilibrium.
Iftheplaneispitchingup,whichisgreater—theC.O.GMomentortheTailMoment?
Iftheplaneispitchingdown,whichisgreater—theC.O.GMomentortheTailMoment?TestPiloting
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Next,wearegoingtocollectsomedataduringthefollowingtestflights.1. ClickonSettings.2. SelectDataInput&Output.3. Clickonthelasttwocheckboxesofeachofthefollowing:
PayloadweightsandCG(line63) Defs:elevators(line74)
4. ClickXtoreturntotheplane.
QuickFlightSetup1. OpenX-PlaneandfollowtheseQuick-FlightSetupinstructions.
Airport:KSEA Aircraft:Cessna172SP Time:“day” Weather:“clear”
2. ClickonFLYwiththeseoptions!SelectAircraft
1. ClickonWeightandFuel.2. SetCenterOfGravityat-16.7inches.3. SetPayloadat2799lbs.4. ClickXtoreturntotheplane.
SelectLocation-SelectGlobalAirport
1. Airport:KSEA2. RWY163. Finalapproach3nm4. BereadytohitPtopause
Flight
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Establishandmaintainlevelflightfor3seconds.UsetheVerticalSpeedIndicatortohelpyoudeterminelevelflight.RecordtheElevatorDeflectionappearinginthecockpitwindow(Youdonotneedtoreviewthegraph).Repeatthreetimes.Pleasecompletethefollowingtable.
CenterOfGravity(-16.7)andElevatorDeflection
Trial CenterofGravity
ElevatorDeflection
1 -16.7 2 -16.7 3 -16.7
AVERAGE SettheCenterOfGravityto22.1inchesandrepeattheflightthreetimesasbeforeandcompletethefollowingtable.
CenterOfGravity(22.1)andElevatorDeflection
Trial CenterofGravity
ElevatorDeflection
1 22.1 2 22.1 3 22.1 AVERAGE
InvestigativeQuestionsWhichCenterOfGravity(COG)resultedinthegreatestelevatordeflection?IfIaddedevenmorepayloadweight,wouldthatbetheequivalentofincreasingtheCOGMoment?Pleaseexplainyouranswer.
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TailMomentArmQuestionsPleaseanswerthefollowingquestionsusingthesedrawings.
AirplaneA
AirplaneB
AirplaneCTheamountofliftgeneratedbythetailisthesameforallthreeairplanes.TrueorFalse?Why?WhichofthethreeairplaneshasthelongestTailMomentArm?WhichofthethreeairplaneshasthelargestTailMoment?WhichofthethreeairplaneshasthelowestTailMoment?Why?
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ScienceOfFlight–AdvanceTopics
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PressureandAirspeed“TheWrightBrotherswereengineersfirst,pilotssecond.”
Theearliestaerospaceengineershadtouseclevertrickstofigureoutthebehaviorofairplanes.WithoutcomputersandGPS,theyreliedsolelyontheirunderstandingofaerodynamics.Theseengineersdesignedanewmethodfordeterminingplane’svelocity;usingpressuregaugescalledPitot-statictubes.Theseinstrumentsreporttopilotstheirairspeeddeterminedfromthepressureoftheairmovingoverthem.TounderstandhowPitot-statictubeswork,severalkindsofpressuremustbedefined.Staticpressureiscausedbytherandommovementofeachmoleculeinnon-movingair.Tovisualizethis,imaginethrowingaballinamovingcar.Theballwillbouncerandomlyaroundtheinsideofthecar,andwouldnotinjureanyonewhomightgethitbyit.Ontheotherhand,ifthatsameballflewoutthecarwindowandhitsomeone,itwouldhitthemwithapowerfulforce;duetotherandomvelocityofitsmovement(staticpressure)andthevelocityofthecar(dynamicpressure).Thisisanexampleoftotalpressure;pressurecausedbyaddingtheeffectsofstaticpressureandnon-randommotion.This,writtenasanequation,isasfollows:
Pitot-statictubesmeasuretwothings:thetotalpressureandthestaticpressureoftheaircraft.Thetotalpressurecanbefoundwhentheplaneisinflight.Atubefacingtheflowdirectionfillsupwithair.Thiscausesthepressuretobuilduponapressuregage.Thestaticpressureismeasuredbyatubethatdoesnotfacetheflowdirection,althoughairalsobuildsupinsidethistube.Thepressuregaugemeasuresthisdifferenceinthesepressurestodeterminethedynamicpressure.
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Thequestionremains;howdoesthisprocesshelptomeasurevelocity?Weknowthatthedynamicpressurerelatesinsomewaytothevelocity.Theexactrelationshipisasfollows.
Thesymbolρrepresentsthedensityoftheair.Whensubstitutingtheequationfordynamicpressureintothetotalpressureequation,theresultistheequationforvelocity.Togetaclearerunderstandingofthisprocess,trytoderivethisequationonyourown!
Youwillbetryingtodeterminethedynamicpressure,Ptotal–Pstatic,ofanaircraftbyusingtheXPlaneandtheaboveequation.Thevelocitywillbegiveninmilesperhour,whichyouaretoconvertintometerspersecondbymultiplyingitby0.447.Additionally,youwillneedtofindtheairdensityat3,000feetusingthechartbelow.
Elevation(ft) Density(kg/m3)
0 1.23
6000 1.03
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DataSetup
1. ClickonSettings->DataInputandOutput2. ClickthelasttwocheckboxesbesideSpeeds(line3)3. Clickonthelasttwocheckboxesbesidelat,long,altitude(line20)
Quick-FlightSetup
Aircraft:Cessna172 Airport:FQIN(elevation:30ftabovesealevel) Time:“day,”Weather:“clear” Click“FLYwiththeseoptions!”
1. Takeoff,andascendto3,000ft.2. Pausethesimulation,andrecordthenumberunderVtruemphas.Youcannowfindthe
dynamicpressure!YoumayhavenoticedthattheXPlanehastwovalues;VindandVtrue,whenstatingtheairspeed.Thesestandfor“true”and“indicated”airspeed.Thedifferencedependsonthedensityofairbeingusedasaframeofreference.Indicated(orequivalentairspeed)reliesonthepressureatsealevel.Trueairspeedreliesonthedensityoftheairattheaircraft’scurrentaltitude.Youwillnoticethat,atsealevel,thetrueandindicatedairspeedsarethesame.
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CoefficientsofLiftandDrag
“TheWrightBrotherswereengineersfirst,pilotssecond.”
Aswehavelearnedearlier,levelflightmeansthatalloftheforcesworkingonanairplanearebalanced:liftandweightareequivalent,justasdragandthrustareequivalent.Whentheplaneisontheground,however,thelevelflightisobviouslynotpossible.Therefore,pilotsmustaccommodate.Pilotshavetoincreasetheliftandthrustduringtakeoffbutmustalsoincreasethedragduringlanding.Thesebasicconceptsaresimple,butthereisalotthatmustbedonetocalculatetheactualvaluesforliftanddrag.Thesecanchangeduetodifferencesinpayload,theaircraft’svelocity,andtheaspectratioofthewingsamongothervariables.Tomakethecalculationseasier,engineerstakesuchvariablesintoaccount:theyreplacetheliftanddragvaluesoftheairplanewiththecoefficientsofdrag(CD-)andlift(CL).Likedragitself,thecoefficientofdragismadeupoftwocomponents:parasiticandinduced.
Anotherwaythiscanbestatedisasfollows:
Everyaircraftwillhaveparasiticdrag,buttheexactamountofdragisdifficulttocalculatenumerically.Engineersoftenmustconductwindtunnelexperimentstofindthisvalue.However,theothertypeofdragcanbecalculatedasfollows:
Fromtheaboveequation,itcanbeseenthattheinduceddragiscausedbytheliftoftheaircraft’swings.Therefore,tocalculateinduceddrag,theliftmustfirstbecalculated.Theliftcoefficientisgivenbelow:
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Inthisequation,Sisthewingplanformarea,whichcanbefoundbymultiplyingtheaircraft’swingspanandthemeanchordlength.Thisproducestheareaofthewing.Theothervariable,q∞iscalledthefreestreamdynamicpressure.Thisisthepressureontheaircraftcausedbytheaircraft’svelocity.Thiscanbedeterminedfromthefollowingequation,whereρ∞isthedensityoftheair:
WearenowgoingtousetheX-PlaneandcalculatetheactualnumericalvaluesofliftanddragoftheCessna172duringbothtakeoffandlanding.OpenX-Plane.DataSetup
1. ClickonSettings->SelectDataInput&Output.2. Clickonthelasttwocheckboxesattimes(line1)3. Clickonthelasttwocheckboxesatspeeds(line3)4. Clickonthelasttwocheckboxesatloc,vel,disttraveled(line21)5. Clickonthelasttwocheckboxesatliftoverdrag&coeffs(line68)6. ClickonXtoreturntotheplane.
FlightSetup-Takeoff
ClickonFile->Quick-FlightSetup Airport:KSEA,AircraftCessna172SP Time:“day,”Weather:“clear” Click“FLYwiththeseoptions!”
1. Takeoffassteadyaspossible.Notethetimethatyoutakeoffunderthedatalabeled
“timer”2. Onceyourplaneisascendingsteadily,clickonSettings->DataInput&Output3. SelecttheDataSeetab.4. Deselectallcheckboxesonthebottom,exceptforVind--(inmph),cl,andcd.5. Scrolltothetimeatwhichyouliftedoff,andrecordthevaluesforVind,CLandCD
FlightSetup–Landing
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ClickonFile->QuickFlightSetup
Airport:KSEA,Aircraft:Cessna172SP Time:“day,”Weather:“clear” Click“FLYwiththeseoptions!” Select“P”onyourkeyboardtopausethesimulation.
1. Clickon“Location,”andselect“SelectGlobalAirport”2. NexttoRWY16,select3nm3. Preparetolandwithyourflapsdown,andassteadilyaspossible4. Justbeforelanding,notetheelapsedtimeunderthedatalabeled“missntime”5. ClickonSettings->DataInput&Output6. SelecttheDataSeetab.7. Deselectallcheckboxesonthebottom,exceptforVind--(inmph),cl,andcd.8. Scrolltothetimeatwhichyoulanded,andrecordthevaluesforVind,CLandCD
Usingtheequationsonthepreviouspage,youshouldnowbeabletocalculatethenumericalvaluesforliftanddragduringtakeoff.Remembertochangemilesperhour(mph)intometerspersecond(m/s)bymultiplyingthemphvalueby0.447!Hereareseveralmorevaluesthatyoumayneed:S=16.3m2ρ∞=1.23kg/m3AR=7.44
LiftandDrag(numericalandcoefficients)
Takeoff Landing
CL
Lift
CD
Drag
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Keepinmind,thedragcoefficientduringlandingshouldbehigherthanthedragcoefficientduringtakeoff. Bonus:calculatetheparasitedragcoefficientofthisaircraft,usingboththetakeoffandlandingvaluesforCD.Whymightthesevaluesbedifferent?Thoughtheliftcoefficientishigherduringlanding,theactualnumericalvalueofliftissmallerthanduringtakeoff.Whyisthis?CoefficientofLiftandAngleofAttackAswelearnedearlierinlesson3,theamountofliftawinggeneratesdependsonitsangleofattack.Iftheangleofattackistoohigh,itwillcausetheaircrafttostall.Nowthateachofusisfamiliarwiththeliftcoefficient,wecaneasilyshowtherelationshipbetweenliftandangleofattack.DataSetup
1. ClickonSettings->DataInput&Output2. ClickonthelasttwocheckboxesatAOA,side-slip,paths(line18)3. ClickonthelasttwocheckboxesatLiftoverdrag&coeffs(line68)
FlightSetup
ClickonFile->Quick-FlightSetup Airport:KSEA,Aircraft:Cessna172 Time:“day,”Weather:“clear” Click“FLYWiththeseoptions!”
1. Takeoffassteadilyaspossible.2. Onceyouareinlevelflight,alternatepitchingyouraircraft’snoseupanddown.Besure
youpitchitenoughsothatyouraircraftstalls!Dothisseveraltimes.DataCollection
1. Afterpracticingthesemaneuvers,pauseyourflightbypressingPonyourkeyboard.2. ClickonSettings->DataInput&Output3. SelecttheDataSeetab.4. Deselectallcheckboxesexceptforclandalpha.
Whereyouseealpha(yourAngleofAttack)increase,hoveroverthelineandrecordyourCL.PlotyourCLvaluesforAngleofAttacksof-5°,0°,3°,5°,10°,15°,and20°.Feelfreetorounditofftotheclosestdegree,ortheclosestCLvalue.
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Forthisaircraft,thecoefficientofliftreacheszeroatanegativeangleofattack.Thisiscausedbythewings’angleofincidence,whichprovideslifteveniftheplaneisflyinglevel.Afteracertainangleofattack,thecoefficientofliftdecreases.Whatishappeninghere?Howcouldanengineerdesigntheaircrafttoachievehigheranglesofattackwithoutexperiencingthislossoflift?
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EngineeringOfFlight
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AspectRatio
“TheWrightBrotherswereengineersfirst,pilotssecond.”
IntroductionAsdefinedbyWebster,AspectRatioistheratioofspantomeanchordofanairfoil.(YoumighthearthistermwhendiscussingTVs.AspectRatiointhiscasereferstothewidthtoheightratioofthescreen.)Thisratioisanimportantconceptindesigningairplanes.AspectRatioisthewingspandividedbythemeanwidthofthewingorchord.Let’sinvestigatehowchangingtheAspectRatioofourplaneimpactstakeoffperformance.Wewilldosomecalculationsbeforewebegin.(Weare,afterall,engineers.)Then,wewillselecttheappropriatewingsandtesttheplane.MathematicalModelingWewillchangethewingspanofourairplanewithoutchangingtheairfoil.Thiswillchangetheaspectratioofourplane.Listedbelowaredifferentwingspanswiththesamemeanchords.PleasecalculatetheAspectRatio(AR)foreachwingspan.Thisisimportantbecausewedonotwanttotrytotakeoffinaplanethatwon’tfly,andwedon’twanttowastefuelandtime.Remember,engineersareconcernedaboutresources(timeandmoney).WeneedtheARtostayinarangeof1.0–12.Pleasefeelfreetodothisonaspreadsheetoruseacalculator.
Wingspan(ft) MeanChord(ft) AspectRatio(AR)
4 4.8 10 4.8 20 4.8 30 4.8 6.25or30/4.840 4.8 50 4.8 60 4.8
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Afteryoucompleteyourcalculations,pleaseeliminate(strikealinethroughtherow)anyoftheoptionsthatdoNOTfallwithintheARrangeof1.0-12PlaneConstruction
1. OpenPlaneMaker2. SelectFile-Open
Ifitasksyoutosave,select“Don’tSave” Plane:ClickonAircraft,selectExtraAircraft,AircraftfromPreviousVersions,Experimental,VansRVs,RV-10,RV-10.acf,OpenAircraft.Seeexamplebelow.
3. Savethefilefivetimeswiththefollowingfivenames: Plane:yourfirstname10,yourfirstname20,yourfirstname30,yourfirstname40,andyourfirstname50
4. SelectStandard,clickonWingsandmodifythewingofeachplaneaccordingtothetablebelow.
Plane Wingspan Wing1semi-length
Wing2latarm
Wing2vertarm
firstname50 50 25 24.95 0.25firstname40 40 20 19.95 -0.05firstname30 30 15 14.95 -0.35firstname20 20 10 9.95 -0.65firstname10 10 5 4.95 -0.95
Pleasenote:firstname10isyourfirstname10.Forexample,yournameisTerry,thenyouwouldsaveRV10asterry10.Nextwearegoingtocollectsomedataduringthesetestflights.DataCollection
1. ClickonSettings.2. SelectDataInput&Output.3. Ifnotalreadypresent,selecttheDataSetTab.4. Clickonthelasttwocheckboxesatspeeds(line3).5. Clickonthelasttwocheckboxesatloc,vel,disttraveled(line21).6. Clickonthelasttwocheckboxesatlandinggearvertforce(line66).7. ClickXtoreturntotheplane.
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TestPilotingOnceyouhavebuiltyourfiveairplanes,flyeachplanethreetimes.Trytoflyasconsistentlyaspossible.Remembertokeepthepointeronthecrosshairsuntiltheplaneliftsoff.Thiswillinsureaconsistentangleofattack.BesuretorecordtheTakeoffdistanceforeachflightinthetablebelow.Useyouraspectratiocalculationsfromtheprevioustableinthetablebelow.Wingspan50Trial Wingspan MeanChord AspectRatio TakeoffDistance
1 50 4.8
2 50 4.8
3 50 4.8
AverageTakeoffDistance _______Wingspan40Trial Wingspan MeanChord AspectRatio TakeoffDistance
1 40 4.8
2 40 4.8
3 40 4.8
AverageTakeoffDistance _______Wingspan30Trial Wingspan MeanChord AspectRatio TakeoffDistance
1 30 4.8
2 30 4.8
3 30 4.8
AverageTakeoffDistance _______
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Wingspan20Trial Wingspan MeanChord AspectRatio TakeoffDistance
1 20 4.8
2 20 4.8
3 20 4.8
AverageTakeoffDistance _______Wingspan10Trial Wingspan MeanChord AspectRatio TakeoffDistance
1 10 4.8
2 10 4.8
3 10 4.8
AverageTakeoffDistance _______TestResults OnceyouhavecompletedtheTestFlyingtable,pleasecompletethebargraphbelow.
AverageTakeoffTrials
Wingspan(ft)
AverageTakeoffDistance(ft)
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InvestigativeQuestionsAstheAspectRatioincreases,takeoffdistanceincreasesordecreases?Shortertakeofftimeindicatesmoreorlesslift?WhataretheadvantagesofhigherAspectRatio?HowcouldweincreasetheAspectRatiowithoutchangingthelengthofthewingspan?MoreTestFlyingIfyouhavenotalready,watchthelandingAspectRatiovideo.Youwilllandyour10ftwingspanairplanethreetimes.Next,landyour50ftwingspanthreetimes.
1. FollowtheseQuick-FlightSetupinstructions. Airport:KSEA Time:“day” Weather:“clear” ClickFLYwiththeseoptions!
2. Location-SelectGlobalAirport Airport:KSEA RWY16 Finalapproach3nm BereadytohitPtopause
Whichplaneiseasiertoland?Whichplanefeelsmorepreciseatlanding?WhydosailplanesandglidersNOThavelandinggearattachedtothewings?DoWorldWarIIfighterplaneshaveasmallorlargeAspectRatio?Why?Theengineeringdesignprocessisalmostalwaysaseriesoftradeoffs.WhataretheadvantagesanddisadvantagesofincreasingtheAspectRatioofanairplane?
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WingLoading
“TheWrightBrotherswereengineersfirst,pilotssecond.”
IntroductionWelearnedthatweightimpactstakeoffperformance.Generally,thegreatertheairplaneweighs,thelongertherunwayneedstobe.Whatdoairplanedesignersdowhentheyneedtocarryalargerpayload,butstilltakeoffonthesamerunwaylength?Alltheseissuesarerelatedtowingloading.Wingloadingistheratiooftheplane’sgrossweight(W)dividedbythesurfaceareaofthewing(S).Thisissimilartodensity,exceptitusessurfacearea,NOTvolume.Thisratioisanimportantconceptindesigningairplanes.Let’sinvestigatehowchangingthewingloadingofourairplaneimpactsflightperformance.Wewillbeginbyusingthemostimportanttoolsofscientistsandengineers:criticalthinkingandmath.MathematicalInvestigationsWewillincreasethewingareaoftheplanetoseetheimpactonwingloading.Listedbelowaredifferentwingspanswiththesamelengthchords.Pleasecalculatethewingloading(w/s)foreachwingspan.Pleasepayattentiontothetrend.Feelfreetodothisonaspreadsheetoruseacalculator.
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WingLoading–ConstantWeightVSDecreasingWingArea
GrossWeightlbs Wingspanft MeanChordft WingAreaft2 WingLoadinglbs/ft2
2500 50 5 2500 40 5 2500 30 5 150or(30x5) 16.67or(2500/150)2500 20 5 2500 10 5
Completethegraphbelow.
WingLoadingvsWingArea
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Now,pleasecalculatewingloadwhenthewingareastaysconstant,andthegrossweightdecreases.
WingLoading–ConstantWingAreaVSDecreasingGrossWeight
WingArea(S)ft2 GrossWeight(W)lbs WingLoadingW/S150 2550 150 2250 150 2000 13.3150 1750 150 1500
Completethegraphbelow.
WingLoadvsGrossWeight
GrossWeight
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InvestigativeQuestionsAsthewingareaincreases,doeswingloadincreaseordecrease?Asthegrossweightdecreases,doeswingloadincreaseordecrease?Fighteraircraftusuallyhavealowaspectratio.Ifweincreasethepayloadofthefighteraircraft,willthewingloadincreaseordecrease?Oursmallprivateplanecarries6passengers.Theplaneweighs2900lbs.Thewingspanis34ftandthecordis4.75ft.Whatisthewingareaoftheplane?Whatisthewingload?Thewingloadofourplaneis15lbs/sqft.Thechordis5ft.Thewingspanis30ft.Whatisthegrossweightoftheairplane?Iambuildingaplanethatwillweigh8,000lbs.Thewingloadis17lbs/sqft.What’sthewingarea?Thewingloadofourplaneis20lbs/sqft.Thegrossweightoftheairplaneis2,400lbs.Thechordis4ft.Whatisthewingspan?PlaneConstruction1. OpenPlaneMaker.2. SelectFile-Open.
Ifitasksyoutosave,select“Don’tSave” Plane:ClickonAircraft,selectExtraAircraft,AircraftfromPreviousVersions,Experimental,VansRVs,RV-10,RV-10.acf,OpenAircraft.Seeexamplebelow.
3.Savethefilethreetimeswiththefollowingthreenames: namewl15,namewl30,namewl60 Pleasenote:namewl15isyourfirstnamewl15.WLstandsforwingload.Forexample,yournameisTerry,andthenyouwouldsaveRV10asterrywl15.
4.SelectStandard,clickonWingsandmodifythewingofeachplaneaccordingtothetable.
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Plane TotalWeight
Chordft
Wingspanft
WingLoadinglb/sqft
MaximumWeight
Wing1semi-length
Wing2latarm
Wing2vertarm
Namewl15 2,500 10 15 2800 7.5 7.45 -.85Namewl30 2,500 5 30 2800 15 14.95 -0.35namewl60 10,000 10 60 11,000 30 29.95 0.55
TestPilotingNextwearegoingtocollectsomedataduringthesetestflights.DataCollection1. ClickonSettings.2. SelectDataInput&Output.3. Clickonthelasttwocheckboxesatspeeds(line3).4. Clickonthelasttwocheckboxesatloc,vel,disttraveled(line21).5. Clickonthelasttwocheckboxesatlandinggearvertforce(line66).6. ClickonXtoreturntotheplane.Quick-FlightSetup1. AirportKSEA2. Selectyouraircraft:namewl15.
ClickonAircraft,selectExtraAircraft,AircraftfromPreviousVersions,Experimental,VansRVs,RV-10
Time:“day” Weather:“clear” ClickFLYwiththeseoptions!
3. Takeoff3times.Beasconsistentaspossible.4. Repeatforallthreeairplanes.Besuretorecordthetakeoffdistanceforeachflightinthefollowingtables.
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TestPilotingDataCollection
Wingspan30ft.Trial TotalWeight Chord
ftWingspanft
AspectRatio
WingAreasqft
WingLoadLbs/sqft
TakeoffDistance
1 2,500 5 30 2 2,500 5 30 3 2,500 5 30
AverageTakeoffDistance_________
Wingspan15ft.Trial TotalWeight Chord
ftWingspanft
AspectRatio
WingAreasqft
WingLoadLbs/sqft
TakeoffDistance
1 2,500 10 15 2 2,500 10 15 3 2,500 10 15
AverageTakeoffDistance_________Wingspan60ft.Trial Total
WeightChordft
Wingspanft
AspectRatio
WingAreasqft
WingLoadLbs/sqft
TakeoffDistance
1 10,000 10 60 2 10,000 10 60 3 10,000 10 60
AverageTakeoffDistance_________
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TestResultsOnceyouhavecompletedtheTestFlyingtable,pleasecompletethegraphbelow.
TakeoffDistancevsWingspanwithaConstantWingLoad
WingspanwithaConstantWingLoadof16.67lbs/sqft
AverageTakeoffDistance(ft)
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InvestigativeQuestionsDoallthreeplaneshavethesameaspectratio,wingloadorwingspan?Whichplanereached100knotsperhrthequickest?(Thischangeinspeedisknownasacceleration.)Whichplaneneededtheshortesttakeoffdistance?Whichplaneneededthelongesttakeoffdistance?Whydidtheplanesbehavedifferently?Considerallfourforces.Remember,theengineeringdesignprocessisalmostalwaysaseriesoftradeoffs.Thistablesummarizesthesetradeoffs.WingLoad High LowTakeoffandlandingdistance Longer ShorterStallspeed Higher LowerFlightperformance Higher LowerPayload Greater LesserAsyoucanseefromthetableabove,ahigherwingloadmeansgreaterflightperformanceandlargerpayloads.Italsomeanslongerrunwaysandhigherstallspeeds.Engineershavetoconsiderallfactorswhendesigninganairplaneanddeterminingthewingload.Inthenextlesson,wewillconsiderpowerloading,theratioofweighttopower.
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PowerLoading
“TheWrightBrotherswereengineersfirst,pilotssecond.”
Introductionabouthorsepower,specificfuelconsumption,andrange.Wewillalsoexaminepowerloading,whichistheratioofweighttopower.Justastheydowithwingloading,engineersusethisratiotopredictairplaneperformance.Finally,wewillexaminetheperformancetradeoffsassociatedwithpowerloading.Horsepowerisameasureofpower.Anenginecreateshorsepowerbychangingthepotentialenergyoffuelintothekineticenergyofturningpistons.Thesepistonsturnashaftthatturnsthepropeller,whichactslikeawingtopulltheplaneforward.Thepoweroftheengineiscalledbrakehorsepower.Thepropconvertsabout80%ofthispowerpullingtheairplaneforward.ThisisreferredtoasThrustHorsepower.Finally,engineswearoutquicklyandgasmileageisdiminishedwhentheyrunatfullpower;therefore,airplanesareusuallyflownat75%ofThrustHorsepower.WerefertothispowersettingasCruiseHorsepower.HorsepowerSummaryBrakeHorsepowerrequiredequalsthepowertoovercomedrag.ThrustHorsepowerrequiredequalstheBrakeHorsepowerdividedby0.80(propellerefficiency).CruiseHorsepowerrequiredequalstheThrustHorsepowerdividedby0.75(avoidingfullpower).Youmaybethinkingrightnow,“Wow,ittakesthreecalculationsjusttofindouthowmuchpowerisneededtofly?”Well,yes,engineeringrequiresmath,notmathgenius,justasolidfoundationinmath.Youcandoit.Thenyoucanearnalotofmoneydoingcoolworklikedesigningandflyingairplanes.Wewillincreasethehorsepoweroftheplanetoexamineitsimpactonweighttopowerratioorpowerloading.Listedbelowareengineswithdifferenthorsepowerratings.Pleasecalculatethepowertoweightratio.Pleasepayattentiontothetrend.Feelfreetodothisonaspreadsheetoruseacalculator.
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PowertoWeightRatioorPowerLoading
Horsepower(ft*lbs) GrossWeight(lbs) PowerLoading150 2500 200 2500 250 2500 0.1or250/2500300 2500 350 2500
Completethegraphbelow.
PowertoWeightRatio-PowerΔ
ΔHorsepower
Now,pleasecalculatethepowertoweightratiowhenthepowerstaysconstantandthegrossweightdecreases.
WingLoading–ConstantHorsepowerVSDecreasingGrossWeight
PowerLoading
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Horsepower(ft*lbs) GrossWeight(W)lbs PowerLoading
250 2500 250 2250 250 2000 0.125or250/2000250 1750 250 1500
Completethegraphbelow.
PowertoWeightRatio–WeightΔ
GrossWeight
InvestigativeQuestions
PowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoading
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Asthegrossweightincreases,doespowerloadingincreaseordecrease?Our275hpairplanehasagrosstakeoffweightof2500.Whatisitspowertoweightratio?Oursmallprivateplanecarries4passengers.Theplaneweighs2400lbs.Theairplane’srequiredBrakeHorsepowerisratedat150hp.WhatistherequiredThrustHorsepower?Howpowerfulmustourenginebetoflyat75%ThrusthorsepowerorCruiseHorsepower?Ihaveapowertoweightratioof0.09hp/lb.Theplaneweighs2600lbs.Whatisthehorsepoweroftheaircraft?PlaneConstruction1.OpenPlaneMaker.2.SelectFile-Open
Ifitasksyoudosave,select“Don’tsave” Plane:ClickonAircraft,selectExtraAircraft,AircraftfromPreviousVersions,Experimental,VansRVs,RV-10,RV-10.acf,OpenAircraft.Seeexamplebelow.
3.Savethefilethreetimeswiththefollowingthreenames: namewp150,namewp300,namewp600 Pleasenote:namewp100isyourfirstnamewp100.(wpstandsforweighttopowerratioorpowerloading.)Forexample,ifyournameisTerry,thenyouwouldsaveRV10asterrywp100.
4.SelectStandard,clickonWingsandmodifythewingofeachplaneaccordingtothetable.
Plane Horsepower TotalWeight
PowertoWeight
MaximumWeight
Wing1semi-length
Wing2latarm
Wing2vertarm
namewp150 150 2,500 .06 3000 15 14.95 -0.35namewp300 300 2,750 .11 3000 7.5 7.45 -.85namewp600 600 3,000 .2 3,500 30 29.95 0.55
TestPilotingNext,wearegoingtocollectsomedataduringthesetestflights.
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DataCollection1. ClickonSettings.2. SelectDataInput&Output.3. Clickonthelasttwocheckboxesatspeeds(line3).4. ClickonXtoreturntotheplane.FlightSetup1. FollowtheseQuick-FlightSetupinstructions.
Airport:KSEA Aircraft:namewp150 Time:“day” Weather:“clear”
2. ClickonFLYwiththeseoptions!FlightInstructions1. Establishandmaintainlevelflightfor3minutes.Beasconsistentaspossible.2. Repeatforallthreeairplanes.Besuretorecordthetrueairspeedforeachflight.
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TestPilotingDataCollection30ft.Wingspan
Trial TotalWeight
Wingspanft
Chordft
hp AspectRatio
WingArea
WingLoad
Power/Weight
TrueAirspeed
1 2,500 30 5 150 2 2,500 30 5 150 3 2,500 30 5 150
AverageTrueAirspeed________45ft.Wingspan
Trial TotalWeight
Wingspanft
Chordft
Hp AspectRatio
WingArea
WingLoad
Power/Weight
TrueAirspeed
1 5000 45 10 300 2 5000 45 10 300 3 5000 45 10 300
AverageTrueAirspeed________60ft.Wingspan
Trial TotalWeight
Wingspanft
Chordft
Hp AspectRatio
WingArea
WingLoad
Power/Weight
TrueAirspeed
1 10,000 60 10 600 2 10,000 60 10 600 3 10,000 60 10 600
AverageTrueAirspeed________
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TestResultsOnceyouhavecompletedtheTestFlyingtable,pleasecompletethebargraphbelow.
TrueAirspeedvsWingspan
VaryingWingspanswithConsistentPowertoWeightRatios
AverageTrueAirspeed(knots)
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InvestigativeQuestionsDoallthreeplaneshavethesameaspectratio,wingloading,orpowertoweightratio?Whichplanereachedthehighestcruisespeed?Wasthishighcruisespeedduemoretowingspan(lift)orhorsepower(thrust)?Ifwedoublethethrust(horsepower),dowedoubletheairspeed?PowerandRangeAsweincreasethehorsepowerofanairplane,weincreaseperformance.Wealsoincreasefuelconsumption.Modernpistonenginesconsume0.50poundoffueleachhourforeachhorsepower.Pleasecalculatethefuelconsumptionandrangefortheengineslistedbelow.
Horsepower FuelConsumptionPerHour Rangewith360lbsoffuel150 200 250 360lbs/125lbs/hr=2.9hr300 350
PerformanceTradeoffsAsyouhavelearned,increasingthrust(horsepower)meansimprovedperformanceatacostofgreaterfuelconsumption.Higherairplaneperformancetypicallymeanshigherwingloading.Remember,highwingloadingmeanslongerrunwaysandhigherstallspeeds.Youwillneedtoconsiderallthesetradeoffsasyoudesignyourownairplaneinthenextlesson.
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AirplaneDesign:PuttingItAllTogether“TheWrightBrotherswereengineersfirst,pilotssecond.”
IntroductionYouhavelearnedagreatdealaboutscience,engineering,andaviation.Youhaveflownatwin-engineairplaneandlandedonacarrierdeck.Youlengthenedawingandshortenedatail.Nowlet’sputitalltogetheranddesignyourownairplane.Youknowhowit’ssometimeshardtogetstartedonaschoolprojectbecauseyoudon’tknowwheretobegin?Planedesignmightseemthatwayrightnow,butwe’llguideyouthroughthestepssoyoucandesignandproduceyourownaircraft.EngineeringDesignProcessTheEngineeringDesignProcessconsistsoftheseparts. ResearchResearchincludesstudyingtheunderlyingengineering,math,andscienceprinciples.YouhavebeendoingresearchwitheveryFlytoLearnlessonyou’vecompleted.Researchalsoincludeslookingatwhatotherpeopleandbusinessesaredesigningandbuilding.Youcanalsostudywhatthepublicwantsinanairplane.Youmightdiscoverthatpeoplewantanairplanethatisfasterormorefuelefficientthanthoseforsalepresently,oryoumightdiscoveranewwaytobuildairplanesthatischeaperthanconventionalmethods.Remember,engineersareveryconcernedwithcosts,money,andtime.Ifaprojecttakesmoretime,usuallycostsincrease;also,theengineermaynothavetimetowait.
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PlanningPlanningconsistsofthesesteps.
Youbegintheplanningprocessbyidentifyinganopportunity.Inengineering,aneedorproblemshouldalwaysbeconsideredanopportunity.Thatisnotabadphilosophyforlifeingeneral.Youthenbrainstormtogenerateseveralpossiblesolutions.Youselectyourfavoritesolutionandmathematicallymodelyouridea.It’sbettertodosomecalculationsbeforeconstructionsbecauseyouworksmarterandfasterwithyourbrainthanwithyourhands.Aftercheckingyourcalculations,buildaproofofconcept.Aproofofconceptdemonstrateswhetheranideaisfeasibleorpossible.Aproofofconceptisusuallynarrowinfocus.Forexample,ifyouaredesigningabetterairfoil,youwouldbuildasmallsectionofthewing,nottheentirewing,andcertainlynottheairplane.PrototypeTheprototypephasehasafewstepsthat mayberepeatedmanytimes.Yourgoalshouldbeforthe prototypetogetbetterwitheach repetitionoriteration.Iterationisan importantpartoftheengineeringprocess.
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ProductionYoubuildtheairplaneduringtheproductionphase.DesigningyourairplaneYouwillputtheengineeringdesignprocesstoworkbydesigningyourownairplane,buildingyourdesigninPlaneMaker,andflyingyourdesigninX-Plane.Let’sassumeduringtheresearchandplanningphasesyoudevelopedthefollowingdesignspecifications:AirplanePerformanceDesignSpecifications
Four-passengerairplaneincludingthepilot Eachpassengercanbringtwentypoundsofluggage 150knotcruisespeed 800nauticalmilerange
Now,let’smathematicallymodelyourplanedesign.Sincethisisyourfirstairplane,wewillfocusontheweight,wings,power,andrange.Oncewecompletethesecalculations,youcanbuildaprototypeairplaneinPlane-Maker.Weneedtocalculatetheweightofyourairplanebecausealltheotherdesigncalculationsarebasedontheweightofyourairplanewithouttheweightofthefuel.Weight
Theaveragepassengerweight 170lbs Howmuchluggagewilleachpassengercarry? ___lbs Theaverageweightperpassengerplusluggage? ___lbs Howmanypassengerswilltheplanebecarryingincludingthepilot? ____ TotalPayloadWeight=numberofpassengersxaverageweight ___lbs
ModernairplanedesignershavelearnedthroughpastexperiencethattheairplaneweightcanbedeterminedbydividingtheTotalPayloadWeightby30%or.3.Thisisanexampleofaruleofthumb.Aruleofthumbisaroughestimation.Engineersoftenuseroughestimationsatthestartofthedesignprocess.
GrossAirplaneWeight=Totalpayloadweightdividedby30% ___lbsPleasenote:GrossAirplaneWeightorTakeoffWeight=emptyairplaneweight+payloadweight+fuelweight.
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ingsNowweneedtocalculatethesizeofthewingsofourairplane.First,wewillcalculatewingloadingandthendeterminewingarea,aspectratio,andfinallywingspan.WingLoading
GrossAirplaneWeight(previouslycalculated) ____lbs.
StandardWingLoadingor = ____ HighWingLoadingRange= ____ LowWingLoadingRange= ____
Reminder:Higherwingloadingmeanshigherstallspeedsandlongertakeoffsandlandings.Modernlightplanesexhibitwingloadinglessthan20lbs/sqft.WingArea
GrossAirplaneWeight(previouslycalculated) ____WingLoadRange(previouslycalculated) ____WingArea(s)=!"#$$ !"#$%&'( !"#$!!
!"#$ !"#$%&' ____
WingSpanWeneedtodecideontheaspectratio(AR)first.Theaspectratioofmodernlightplanesis6to8.Let’suse7astheaspectratio.
AspectRatio ____WingArea(s)(previouslycalculated) ____
Wingspan(b)= ____Chord=!
! ____
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PowerThepowerrequiredequalsdragxvelocity.Thecalculationstodeterminepowerarebeyondthescopeofthislesson.Let’sassumeyouneed150horsepower.Thiskindofhorsepoweriscalledbrakehorsepower.Amodernpropelleris80%efficientinconvertingthebrakehorsepowerintoactualthrust.Thiskindofhorsepoweriscalledthrusthorsepower.
BrakeHorsepower 150thp ThrustHorsepower=!"#$% !"#$%&"'%#
!"% ____bhp
Weactuallyneedmorehorsepowerbecausewedonotwanttooperateenginesatfullpower.Enginesrunningatfullpowerwearoutsooner,andtheyarelessfuel-efficient;instead,wewanttooperatetheenginesat75%ofThrustHorsepower.ThishorsepoweriscalledRatedHorsepower.
ThrustHorsepower(previouslycalculated) ____bhp RatedHorsepower= !!!"#$ !"#$%&"'%#
!"% ____rhp
RangeLet’sseehowfarwecanflyourairplaneonatankoffuel.Webeginbycalculatinghowmuchfueltheplanewillcarry.WecalculatethetotalfuelavailablebymultiplyingGrossAirplaneWeightx15%.Fifteenpercentisanotherruleofthumbusedbyengineerstodesignairplanes.
GrossAirplaneWeight(WG)(earliercalculation) ____lbs TotalFuelAvailable(WF)=GrossAirplaneWeightx15% ____lbs PayloadWeight(WP)(previouslycalculated) ____lbs EmptyWeight=WG–(WF+WP) ____lbs CruiseSpeed 150knots SpecificFuelConsumption 0.5lbsperperhorsepower Range== !"#$% !"#$ !"#$%#&%' ! !"#$%& !"##$
!"#$%&%$ !"#$ !"#$%&'()"# ! !!!"#$ !"#$%&"'%# ____n.miles
Oftenwedon’tmeetallofourdesigngoalswiththefirstdesign.Ifwedon’tachievethenecessaryrange,wecanincreasetheamountoffuel,butthenwewillneedmorehorsepower,whichresultsingreaterfuelconsumption.Therefore,wewillrepeatthisprocessseveraltimestomeetourdesigngoals.
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PrototypeWearenowreadytobuildaprototypeinPlaneMaker.SinceyouareusingPlaneMaker,youcanquicklybuildyourprototype,avirtualairplane,bymodifyingtheRV-10.Thiswillallowyoutoquicklytryoutyourdesignssafelyandeconomically.Completethetablebelow.Beginbyenteringyourvaluesinthesecondcolumn.Youwillneedtocalculate½WingSpanvaluebydividingtheWingSpanvalueby2.ThenopenPlaneMakerandtheRV-10airplane,andselectStandardandtheappropriatemenus.Assignyourvaluestotheappropriatefields.
PlaneMakerSpecification YourValues StandardMenu FieldsGrossWeight Weight&Balance MaximumWeightFuelWeight Weight&Balance FuelLoadEmptyWeight Weight&Balance EmptyWeightWingSpan Wings NotApplicable
½WingSpan(Calculate) Wings Semi-LengthChord Wings Rootandtipchords
RatedHorsepower EngineSpecs MaxallowablePowerOnceyouhavecompletedyourairplane,saveitasyournameprototypeandgoflyit.BesuretoincludetheappropriatePayloadWeightintheWeightandBalancesectionofX-Plane.Iftheplaneperformswell,youarereadyforproduction.Ifyouwantanotherchallengeconsiderdesignasportplanewiththefollowingrequirements:
2Passengersincludingthepilot 250ThrustHorsepower AspectRatiobetween6-8
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EngineeringofFlight–AdvanceTopics
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Gliding
“TheWrightBrotherswereengineersfirst,pilotssecond.”
Theearliestformofunpoweredfixed-wingaircraftwereknownasgliders.Inspiredbytheflightofbirds,theearliestaerospaceengineersusedgliderstogainanunderstandingofaerodynamics.Gliderdesignreliesonmanyofthesameprinciplesasaircraftdesignbutmustbeslightlyalteredtoaccountforthelackofpropulsion.Minimizationofweight,drag,andmaximizationofliftarealwaysrequired.Smooth,curvededgesarerequiredtoimproveaerodynamicssincebothparasitedragandinduceddragdecreasetheefficiencyoftheglider.Neithercanproducethethrustneededtoovercomethisdrag.Theyevenutilizethesamecontrolsurfacesasaircraft.Sowhatmakesthemsodifferent?Otherthantheobviouslackofpropulsion,glidersaredifferentfromplanesinthefollowingways:
1. Increasedaspectratio.Thewingspanofglidersismuchlongerinordertoincreasethelifttheygenerate,aswellasdecreasetheeffectsoflift-induceddrag.Inresponse,glidershaveahighermaximumLift-to-Dragratio.However,therearestructurallimitstothelengthofthewingspan;theyaretoolong,andtheglider’swingsmaybuckle.
2. Generalpurpose.Whileaircrafthaveavarietyofuses,theyaremostlyusedfortravel.Sinceglidersflywithoutpower,theyarenotsuitedforrapidtravel.Theyareoftenusedtoacquaintnewpilotswithaircraftcontrols,forsightseeing,orfornovelty.
3. Ballasts.Becauseglidersaresolight,thecenterofgravitymayeasilybechangedwithundesirableconsequences.Someglidersuseaweight,calledaballast,whichcanbeaddedtoshifttheplane’scenterofgravityandallowthemtofly.
4. Methodsofincreasingaltitude.Glidersmustbetowedbyapoweredaircraftorlaunchedoffahighsurfacetoachieveflight.Additionally,theyareonlyabletogreatlyincreasetheiraltitudebyusingatmosphericphenomenacalledthermalconvectioncurrents.Thesearecurrentsofhotairthatrisestraightupintotheatmosphere.Interestingly,somebirdsalsousethesecurrentstominimizetheenergyneededtostay
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aloft.Allairplanescanfunctionasglidersiftheirenginesareturnedoff.However,poweredairplanesarenotnearlyasefficientasglidersintheirabilitytostayaloft.Glidingperformanceismeasuredbyaquantityknownasglideratio.Aglideratioof30:1meansitcantravel30metershorizontallywhileonlyfalling1meter.Mostgliderstodayhaveratiosof50:1,ascomparedtothe15:1ratioofmostjetaircraftsflyingtoday.Poweredaircraftalsodescendmorequicklythanglidersduetotheirhigherweightand,consequently,higherwingloading.KnowingthatDrag=W*sinϴandLift=W*cosϴ,wecanfindtherelationshipbetweenglideangleandL/Dratioas:
tan𝛳 =1
(𝐿/𝐷)
Now,wearegoingtofindtheglideangleandglideratiofortheCessna172usingXPlane.DataInput&Output
1. Selectthelasttwoboxesbesidelat,lon,altitude(line20)2. Selectthelasttwoboxesbesideloc,vel,disttraveled(line21)3. Selectthelasttwoboxesbesideliftoverdrag&coeffs(line68)
Quick-FlightSetup
Airplane:Cessna172 Airport:KSEA Time:“day,”Weather:“clear” Select“FLYwiththeseoptions!
1. Under“Location,”select“SelectGlobalAirport,”click3nmnexttoRWY162. ImmediatelyselectPonyourkeyboardtopausethesimulation.Pulloffonyourthrottle
entirely.PressPtounpause.3. Makesureyourairplaneisinlevelflight,andpressPagain.NotetheL/Dratioofyour
aircraft,andthedistancetraveledsofar.Thisdistanceisyour“startingdistance.”Youcannowcalculatetheglideangle.Alsonotethealtitude(labeledaltftagl,orfeetabovegroundlevel).Youwillneedthisinordertofindtheglideratio.
4. Steadilydescend.Don’tworry,asyouwilllikelymisstherunway.Whenyoufirsttouchtheground,selectPtopauseyoursimulation.Notethe“finaldistance”traveled.Usingthefinaldistancetraveledandyourstartingaltitude,youcannowfindtheglideratio.
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5. Repeatthistwomoretimes,toadjustforthevariabilityinyourdescent.
Completethetablebelow.
L/Dratio GlideAngle(º)
DistanceTraveled(ft)=FinalDistance–StartingDistance
GlideRatio
GlidingDesignUsingalloftheinformationyouhavelearnedaboutglidersandthewingconfigurationofaircraft,youarenowgoingtobuildagliderinPlaneMakerbasedonamodifiedCessna172.Yourgliderwillbeabletotravel5miles(26,400ft),butdoesnotneedtolandonarunway.Youmaychangetheaircraftinanywayyouwouldlike,whichincludesalteringthewings,fuselage,ortheengine.YouareallowedtoadjustcertainsettingsinXPlaneaswell,withinreason.Weight,CenterofGravity,andWeatherareallgoodopportunitiesforyourplanetoexcel,butbewarnedaboutthepotentialconsequences!Youraircraftistostartinflight3NMawayfromKSEA.Immediatelypulloffthethrottleandrelysolelyonthebehaviorofyourglider.RemembertotakenoteofyourL/Dratiowhenyoubeginyourflight.Youwillneedtoconducttestflightstogeneratethenumbershelpfulincalculatingyourglideangleandglideratio.Ifyouraircraftdoesnotmeettherequirements,youaretoreturntoPlaneMakerandrefineyourdesign.Toassurethestructuralintegrityoftheaircraft,yourwingsaretobenolongerthan20fteachandhaveameanchordlengththatdoesnotexceed6ft.Tomakesureyouhavecreatedaneffectiveglider,yourglideangleisnottoexceed5degrees,andyourglideratiomustbeatorabove30.Yourglidermusthavebothacockpitandlandinggear.Thetablebelowmaybeofuse.
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Trial L/DRatio GlideAngle DistanceTraveled
GlideRatio Success?
1
2
3
4
5
Whataspectsofyourglidermadethebiggestdifferenceinyourglider’sglideratio?
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Jetsvs.PropellerAircraft“TheWrightBrotherswereengineersfirst,pilotssecond.”
Aircraftcomeinalldifferentsizes,buteveryplanereliesononeoftwoprimarymethodsofpropulsion:viajetengines,orpiston-propellerengines.Piston-propelleraircraftaredistinguishedbyhavingatleastonepropeller,andjetplanesgenerallyhavetwoormorejetengines.Theperformanceoftheseaircraftisdramaticallydifferent,asyouwillsoonfindout.Furtheroninthissection,youwillfindoutwhytheseplaneshavedifferentcharacteristics.Piston-propaircraftareusedforlower-velocityflights,andarenotsuitedwellforquicktravel.Usually,generalaviationaircraft,whichareusedforleisureandnotforprofit,utilizepropellers.Propeller-drivenaircraftaremoreaffordabletoaveragepilots,butdonotperformaswellasjets.Theseaircrafttakelongertoachievehigheraltitudesandreachamuchlowermaximumaltitudethanjets.Theycan,however,flyforlongeramountsoftimethanacomparativelysizedjet.Jetaircraftareusedforquicklytravellinglongdistances.Theirenginesproducethrust,whichdirectlypushesthemforward:piston-propaircraftproducepowertorotatetheirpropeller,whichthenpushestheplaneforward.Theseaircraftareusedcommerciallysincetheyaremoreexpensivetomaintain.Theycan,however,ascendquicklyandtohigheraltitudes,wheretheirenginesworkmosteffectively.Therefore,morefuelisusedbytheseaircraft.RangeandEnduranceofJetandPiston-PropEnginesEngineersoftenmeasuretheperformanceofaircraftbydeterminingtheirrangeandendurance.Rangeisthemaximumdistancetheaircraftcantravelonafulltankoffuel;enduranceisthemaximumtimethatanaircraftcanflyonafulltankoffuel.However,thesevaluesdonotnecessarilyoccuratthesametime!
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Bothjetsandpropeller-drivenaircraftrequirespecificconditionstomaximizetheirrangeandendurance.
1. Anentirelyfullfueledtank.Theplanecannotflyasfarifitstankishalffull!2. Minimizationoffueluse.Thismeanstheaircraftmustbeflyinginthewayforwhichit
wasdesigned,beittheappropriatevelocity,altitude,etc3. Flightatamaximumlifttodragratio.Thisratioisfoundbydividingtheliftbythedrag.
Highernumbersmeanlessdrag,whichisalwaysdesirablewhileinflight.4. Flightat“idealconditions,”whichvaryforthetwotypesofaircraft.
Propellersrequireahigherairdensitytorunefficiently,whichoccursatloweraltitudes:theirenginesaresimilartothosefoundinacar.Jetaircraftflymoreefficientlyathigheraltitudes,sincetheirengineswereoptimizedtocompressairatlowerdensities.Asaresult,propeller-drivenaircraftflyatloweraltitudesandlowerspeed.Jetaircraftflybestathigheraltitudeswithhighervelocities.UsingXPlane,wecaneasilyseethedifferencesinenduranceofthesetwoaircraftonafullfueltank.Range,however,requirestakingoffonafullfueltankandflyinginlevelflightuntilthefuelrunsout.Trythisonyourown!QuickFlightSetup
SelectFile->QuickFlightSetup AirportKSEA,AircraftCessna172SP Time:“day,”Weather:“clear” Select“FLYwiththeseoptions!”
1. Atthetopofyourscreen,scrolltoAircraft->WeightandFuel2. Atthebottomrighthandcorner,select“settomaxgross”3. Besidethefueltotalslider,youwillseeawhitetextboxwithanumber.Thisisthe
numberofhoursthisjetcanflyonmaximumfuel.4. Recordtheweightofthefuel(justabovethefuelTOTALslider)andthetimethisaircraft
canfly.5. Repeatthesameprocess,exceptselecttheaircraft“CirrusTheJet”
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Asyoucansee,despitehavinglessfuel,thepropeller-drivenaircraftcanflyforlongerononetankthanthejet.Thesenumbershavenobearingontheefficienciesoftheseengines,however!Todeterminetheefficiencyoftheengine,engineersuseaquantitycalled“specificfuelconsumption,”orSFC,forpropeller-drivenaircraft.Thrust-specificfuelconsumption,orTSFC,isthejetequivalent.Thisrelatesthefuelconsumedtothepower(or,inthecaseofjets,thrust)producedbytheaircraft’sengine.Theseequationsaresimplifiedversionsfordeterminingthesenumbers.
UsingtheequationsforSFCandTSFCabove,calculatetheSFCoftheCessna172,andTSFCofCirrusTheJet.TheCessna172hasapowerof160hp,andtheCirrushasathrustof1800lb.Wouldincreasingthesizeofthefueltankinapropelleraircraftmakeitmoreefficient?WhateffectsdoyouthinkincreasingSFCorTSFCwouldhaveontherangeofeachaircraft?RateofClimbandTimetoClimbAirplanesinaclimbhavetwodifferentcomponentsofvelocity:oneinthehorizontaldirection,andoneintheverticaldirection.Theverticalcomponentiscalledrateofclimb,and,muchlikethehorizontalcomponent,variesdrasticallydependingonanaircraft’senginetype.
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Usingtheimageaboveandbasictrigonometry,wenoticethattheequationforrateofclimbcanbegivenas:
Timetoclimbisaquantityrelatedtotherateofclimb.
Youwillbeusingyourrateofclimbtopredicthowquicklyeachaircraftwilltaketoreachanaltitudeof6,900ft,whichis5,000ftabovetheKSEAairport(elevation:1,900ft).Itisveryimportanttouseconsistentunits,soyouwillhavetoconvertmilestofeet,andhourstominutes.DataSetup
1. ClickonSettings->DataInput&Output2. Clickthelasttwocheckboxesunderspeeds(line3)3. ClickthelasttwocheckboxesunderAoA,side-slip,paths(line18)4. Clickthelasttwocheckboxesunderloc,vel,disttraveled(line21)
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QuickFlightSetup SelectFile->QuickFlightSetup Airport:KSEA,Aircraft:Cessna172SP Time:“day,”Weather:“clear”
1. Takeoff,andenterasteadyclimb.RecordtheVindairspeedinmph,andthevpath
angleindegrees.MakesuretoconverttheVindairspeedintoft/s!2. Determinethisaircraft’srateofclimbusingtheequationabove.3. Fromhere,usethesecondequationtodeterminethetimetoclimb.
QuickFlightSetup
SelectFile->QuickFlightSetup Airport:KSEA,Aircraft:CirrusTheJet Time:“day,”Weather:“clear”
1. Takeoff,andenterasteadyclimb.RecordtheVindairspeedinmph,andthevpath
angleindegrees.MakesuretoconverttheVindairspeedintoft/s!2. Determinethisaircraft’srateofclimbusingtheequationabove.3. Fromhere,usethesecondequationtodeterminethetimetoclimb.
Note:TotakeoffinCirrusTheJet,youwillneedtomovetheyellowsliderinthebottomright-handcornerofthecockpitcontrols.SelectBonyourkeyboardtoturnoffthebrakes.Seethepictureifyoucannotfindthis.
Whichoneoftheseaircraftwasabletoascendmorequickly,andwhy?
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RunwayDesign
“TheWrightBrotherswereengineersfirst,pilotssecond.”
Engineersmustkeepmanydetailsintheirplanwhendesigningairports.
1. Thetypicalaircraftthatwillbeusingtherunway.Larger,heavieraircraftneedalongrunwaytogenerateenoughlifttotakeoffandneedmoretimetoslowdowntotaxiingspeedwhenlanding.
2. Altitudeoftheairport.Thedensityoftheairishigheratsealevelthanathigherelevations,andplanesareabletoliftoffinashorterdistanceatlowelevations.
3. Theclimateoftheairportmakesadifference.Ifanairportisinalocationthatexperienceschronicrainorsnow,therunwaymustbelongertoaccountfortheslicknessoftherunway.Also,ifanairportisinawarmlocation,theair’sdensityislowerthaninacoolerlocation,andtherunwaymustbelonger.
4. Materialoftherunway.Grasshasahighercoefficientoffrictionthanasphalt,andplanesneedalongerrunwaytogenerateenoughspeedtoliftoff.
Wehavediscussedthedistanceoftakeoffinregardstopayloadweight,aspectratio,andwingloadingindepth.Wecannowdemonstratetheeffectsofaltitude,runwaymaterial,andweatherontakeoffdistance.QuickFlightSetup
SelectFile->QuickFlightSetup Airport:Benbecula(elevation:19ft,length6023ft,material:asphalt) Aircraft:Cessna172 Time:“day,”Weather:“clear” Select“FLYwiththeseoptions!”
Takeoff,andnotetheVtrueairspeedandliftoffdistance.
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Withoutchangingthepayloadoranyothersettings,enterQuick-FlightsetupandchangetheairporttoGuaymaral(elevation:8389ft,length5643ft,material:asphalt).Thenliftoff,andnoteVtrue-andliftoffdistance.Whatdoyounotice?Now,returntoBenbeculaairport,butthistime:
1. SelectAircraft->Aircraft&Situations2. Select“grassfieldtakeoff”3. Takeoff,andnotethedistancerequired.
Howdoesitcomparetotheinitialasphalttake-off?EngineeringyourairportNowitisyourturntostepintotheairportengineer’srole.YouhavebeentaskedtodesignarunwaythatwillaccommodatethetakeoffandlandingofaBoeing747:theworld’sfirstjumbojet.Yougettochoosetheairport’saltitudeandtherunway’smaterial.Therequiredlengthoftherunwayisthemaximumoftwovalues:theliftoffdistanceandthelandingdistance.Youwillneedtobeawareofseveralparametersabouttheplanetofindthesedistances.Theseare:
CL,max:2.0 Takeoffweight:WT=3,200,000N Landingweight:WL=1,600,000N Slowestlandingspeed:Vland=70m/s Wingplanformarea:S=500m2 Profiledrag:CD,0=0.02 Thrustavailableattakeoff:T=800,000N
Tofindtheliftoffdistance,youcanusethefollowingequation:
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Thequantityµristherollingcoefficientoffrictionforliftoff.Fordryasphalt,µr=0.02;forsoftmateriallikegrass,µr=0.1;fortightlypackedturf,µr=0.06.Theair’sdensity,givenbyquantityρ∞,dependsonthealtitudeoftheairport.Somevaluesaregiveninatableonthenextpage,butyouareabletochooseanyvaluewithinthatdensityrangeforyourairport’slocation.Findingthelandingdistanceisalittlemorecomplex,andyouwillneedtofollowseveralequations:
Aswiththeliftoffequation,thequantityµlistherollingcoefficientoffrictionforlanding.Fordryasphaltandtightlypackedturf,µl=0.4;forgrass,µl=0.2.Youwillalsoneedtotakeintoaccounta“factorofsafety”foryourrunway.Asafetyfactorisnecessary,duetothevarietyofissuesthatmaybeexperiencedduringtakeoffandlanding,whichincludespoorweatherandpiloterror.Makeyourfinallength20%longerthanthemaximumdistancethattheaircraftactuallyneedsfortakeoffandlanding.Sincethe747canbesimulatedinXPlane,trytakingoffandlandingatanairportwithsimilarspecifications(altitudeandterrain)asyours.Comparetheseresultswithyourcalculations–otherthanvariationsinyourtakeoffsandlandings,whatcouldbesomereasonsyourresultsaredifferent?
AirDensityatVariousAltitudes
Altitude(m) ρ∞(kg/m3)
0 1.225
4000 0.819
8000 0.526
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SupersonicFlight“TheWrightBrotherswereengineersfirst,pilotssecond.”
Whilewatchingcertainactionmovies,youmayhaveheardthecharactersrefertoaircraftusingtheirMachnumbers.Thisisnotjustmadeupinmovies:Machnumbersrelatetheaircraft’svelocityrelativetothespeedofsoundinair:767mph.Therelationshipisgivenbelow.Forexample,Mach5iswhenanaircrafthasavelocityfivetimesthespeedofsound,whichisalmost4,000milesperhour!
Machnumberscanalsobedefinedinsubstancesotherthanair.Thespeedofsoundinwater,forexample,isneededforfindingtheMachnumberofhydrodynamicvessels,suchasunderseamissiles.SomedifferentcategoriesofaircraftaredefinedbytheirMachnumbers.Subsonicaircrafttravelmuchmoreslowlythanthespeedofsound,orlessthanMach1.Ifyouweretoyellatsomebodyamileaway,yourvoicewouldreachthembeforetheaircraftwould.Mostplanesyouwilleverrideinflyatsubsonicspeeds.Supersonicaircraftflymorequicklythanthespeedofsound;Machnumbersaregreaterthan1.Theseaircraftarenotusuallyusedforcommercialflight,buttheyhavebeenusedinthepast!TheConcorde,shownbelow,wascapableoftravelingatMach2.ItcouldtravelfromNewYorktoLondoninlessthan4hours,wheresubsonicjetswouldneedabout7hourstomaketheflight.Sonicflightoccurswhenaircraftflyexactlyatthespeedofsound.Usually,engineersdonotdesignaircrafttoflyatthisspeedsinceanaircraftcanbehaveverystrangelyatthesespeeds.
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ShockWavesWhensupersonicaircraftacceleratetospeedsfasterthanthespeedofsound,somethinginterestinghappens.ShockwavesarecausedbyabuildupofairpressureinfrontoftheaircrafttravelingjustbelowMach1.Thepressurebuildupoccursinseveralwaves,andthesewavesbecomecompressed.AtspeedsofMach1andabove,theyarecompressedintoasinglewave.Thiswavetravelsalongthelengthoftheairplaneuntilitreachestheplane’stail.Whenthathappens,theshockwavetravelsoutwardincone-likeshape.Whenthatcone-likeshapereachessomebodystandingontheground,theyhearwhatiscalledasonicboom.
Theangleoftheconeisdeterminedbytheaircraft’sMachnumber.
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Thedistancebetweentheobserveronthegroundandtheairplane’stailisgivenbythehypotenuseoftherighttrianglemadebetweenthecone’shalfangleandtheairplane’saltitude.Dividingthisdistancebytheaircraft’svelocitywillgiveyouthetimeitwouldtakethissoundtoreachtheobserver.Now,let’sfindthesenumbersusingXPlane.Youaregoingtocalculatethedistanceasupersonicaircrafthasflownbeforeitssonicboomcanbeheardfromtheground.DataInput&Output
1. Selectthelasttwocheckboxesatspeeds(line3)2. Selectthelasttwocheckboxesatlat,lon,altitude(line20)
Quick-FlightSetupYouwillselectanexperimentalaircraftcalledMega-Hyper-Sonic.Tofindthisaircraft,pleasenavigatetheaircraftmenuasshownbelow.
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1. Airport:KLAX(LosAngelesInternational),Aircraft:Mega-Hyper-Sonic2. Time:“day,”Weather:“clear”3. Select“FLYwiththeseoptions!”
4. Now,takeoff.Inthebottomright-handcorner,youwillseeaseriesoflevers.Selectthe
fourthleverfromtherightanddragitupwards.Alleightleversshouldnowbeflippedup,andtheaircraftisfullythrottled.
5. SelectBtoturnoffyourbrakes,andtakeoffsteadily.6. Ascendto5,000ftagl.Usingyourvelocityandthespeedofsoundinair(767mph),find
youraircraft’sMachnumberandconehalfangle.7. Usingyouraltitudeandconehalfangle,youcannowfindthedistanceatwhichthe
shockwaveisfeltontheground.Hint:drawarighttriangleandusetrigonometry!Usingthisdistanceandtheaircraft’svelocity,howlongwillittakeforthissoundtoreachtheground?
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GAMAAviationDesignChallenge
Introduction
Welcome to the 6th annual General Aviation Manufacturers Association (GAMA) Aviation Design Challenge. This competition is designed to promote Science, Technology, Engineering and Math (STEM) through aviation in high schools across the United States. The winning team will get a one-in-a-lifetime opportunity to experience general aviation manufacturing firsthand. This accelerated and hands-on program not only develops students STEM abilities, it also helps build leadership and critical thinking as students work in groups to solve complex challenges.
The following chapters help students as they start to apply and modify what they have learned in the first ten lessons.
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GAMAAVIATIONDESIGNCHALLENGEWORKFLOWCongratulationsforparticipatingintheGAMA(GeneralAviationManufacturersAssociation)AviationDesignChallenge.Thisdocumentwillhelpyoutoprepareforthecompetition.
Step1-DefiningRolesDesigninganairplaneisateameffort,therefore,assigningrolesandresponsibilitiesisthefirstorderofbusiness.Theseroleswillhelpestablishtheresponsibilitiesofeachteammemberandencourageeveryonetotakeownershipfortheproject.Listedbelowaresomeofthesuggestedroles.Youmayneedtocombineorchangerolesbasedontheneedsofyourteam.ChiefPilot-Thispersonwillberesponsibleforconductingthetestflightsandreportinghis/herfindingstotheotherteammembers.ChiefEngineer-Thispersonwillberesponsibleforbuildingandlatermodifyingtheaircraftmodel.DesignEngineer-Thispersonwillberesponsibleforcreatinganditeratingthedesign.ProgramManager-Thispersonwillberesponsibleforkeepingtheteammembersworkingintherightdirectionandisultimately“responsible”forthesuccessorfailureoftheteam.Finally,asacoach/teacheroradvisor,youmustdirecteachteammembertodecidewhatsuccessmeanstothem.Youshouldaskeachteammembertodefinesuccess.Otherissuestodealwithwillbe:howwilltheteammeasuresuccessforteamandteammembers.
Step 2 - Research ResearchthemissionReviewthechallengerulesHowisthemissionscored?Whatarethecompetitionconstraints?WhatcanyouNOTdo?Whatcaneachoftheteammemberslistedabovedotoimprovetheirpartoftheprojectandhowmuchofanimpactcanthishaveonthefinalteamperformance?
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Researchtheaircraft-Usetheinternetandaviationsitestoresearchpayloadandperformancecapabilitiesoftheaircraftusedinthecompetition.BesuretoincludeairfoildataandpropdetailsHowwouldthestock(orunmodified)competitionaircraftperformgiventhedesignobjectives?Whattypicaloverallscorewouldyouobtainusingastockorunmodifiedaircraft?Whatcanberefinedinaboutthedesignoroperationoftheaircrafttoimprovethescore?
Step 3 - Design ConceptualDesignWhyistheshapeofajetairlinerdifferentthanthatofafighteraircraft?Whydoesasailplane(glider)havelongnarrowwingsandanacrobaticaircrafthasshortwings?Eachoftheseaircrafthavebeendesignedfordifferentfunctions.Jetairlinerscarrypassengersonlongdistances;fightersmustbefast;sailplanescansoaralongthewinds,andacrobaticplanesneedtobemaneuverable.Theshapeorformsoftheseaircraftaredictatedbytheirfunctionsorhowtheywillbeused.Thisconceptisknownas“formfollowsfunctionorfunctiondictatesform.”TheideaofFormfollowsfunctionisanimportantconsiderationthatisconsideredduringtheconceptualdesignportionofthedevelopmentstage.Whatistherequiredrange,desiredpayload,andflightpathterrainofthecompetition?Whatdoyouwanttheaircrafttobecapableofdoingandnotdoing?Howlongshouldtheflighttake?Howmuchfuelisanacceptableamounttoburn?Whatwouldyoudotomakeimprovementsonthecompetitionaircraft?Somesuggestionscouldbe:
Changethegeometry(wingshape)ofthewing?Modifythetailsize,shapeorlocation?Modifyorchangethepowerplant?Modifythepropellerorotherthrustsystems?
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PreliminaryDesign
Thisistheprototypingphaseoftheaircraft.Weprepareasmanydesignconfigurationsaspossible.Thisphaseconsistsofthreeparts:
Createormodifyprototype
Testprototypes
Analyzethetestresults
Repeattheprocessseveraltimesincorporatingwhatyoulearnedinthelastiteration.Thisisthemostdifficultpartofthedesignprocess.Itisvitaltohaveadesignnotebook(physicalordigital)toensureanorderlyprocess.Thiswillallowustocomparealloftheresults.Besuretoflytheairplaneconsistently.Thiswillhelpyoutoappreciatewhattestpilotshavetodointhesky. Prototype Modifications PayloadStartwiththepayload.Thisisaneasyvariabletochange,observeandrecordtheresults.Thiswillhelptheteamdeveloptheprocessorworkflowfordocumentingtheirresults.WingAlterwinggeometryincludingwingspan(lengthofthewing),chord(widthofthewing),aspectratio(wingspan/chord)Changewingdihedral(wingangle)ModifywingtipsTailChangethehorizontalandverticalstabilizersChangethetaillocationPowerplantIfrulespermit,changethedifferentkindsofpowerplants(piston,turboprop,jet)
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ModifythepropellerThisisnotmeanttobeacompletelistoftheareaswherechangescanbemade.Itisbesttoassumethatyoucanchangeanythingontheairplaneunlessspecifiedotherwiseintherules.DetailedDesignYouarenowpolishingyourdesign.Itshouldnotbenecessaryforyoutogobackandmakeanysignificantchanges(i.e.changethewinggeometry).Atthispoint,youarealsoconfirmingtheexperimentaldatayougatheredinthepreliminarydesignphase.Ifyouhavenotalreadycombinedallofyourdesigncomponents,thisshouldnowbecompletedtocreateyournearly-finishedairplane.PreliminaryFlightTesting
Beginat20%payloadweight(weightofemptyplanemultipliedby20%)andflyitwhilerecordingdata.
Conductthreeflights. Addweightandrepeatflightswhileincreasingtheweightuntilyoucannolongertakeoff.
Step 4 - Test Flight Yourteamshouldnowbefocusedontheoptimalflightplanforthechallenge.Anyconsiderations?Howfastshouldyoufly?Howhighshouldyoufly?Howshouldyouland(gliding,fullpowerornormal)
Step 5 - Aircraft Design Challenge Submission
SubmityourdesigntoGAMAalongwithalloftheotherrequiredpaperwork.Trytosubmityourworkatleast24hoursbeforetheofficialdeadline.Unfortunately,internetaccessoccasionallybreaksdown.Youneverwantthattohappentoyouoranyofyourteammembers.
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SettingUpAChallengeFlightYoucanprepareforthechallengebysettingupyourveryownflightswithcriteriathatyouestablish.Youwillfindthesechallengesfunandexciting.Let’sgetstarted.UnderFilechooseQuick-FlightSetup:
Plane:ClickonOpenAircraft,selectGeneralAviation,anddouble-clickCessna172SP,Cessna_172SP.acf
Weather:SetTimeto“day”andWeatherto“clear.” Airport:ExitQuick-FlightSetup.
ClickonLocationonthemenubarandSelectGlobalAirport.SelectKSEA,RWY34R
SelectLocalMap ClickonTAKEOFFRWY34R ClickonExit
SelectSpecialonthemenubar SelectFlyToLearn–AviationChallenge EnterKSEAtoDepartureairportID EnterKBFItoArrivalairportID
Thistimewillleavethecriteriaalone,butyoucanchangethedistance,payload,fuel,andtimeofyourchallenge.Fornow,pleaseclickonXtoexit.Youwillreturntoyourcockpit,butnowFly-To-Learnmission[ENGAGED]appearsatthetoprighthandcornerofyourdisplay.
ClickonLocationonthemenubaragain
SelectLocalMap(youcanalsopresstheMkey) Youwillseeanorangeplane.Theorangeplaneisyou.FindtheBoeingFieldairport,whichisjustnorthofyourposition.Youareflyingtothisfield.CheckonyourlocationoftenbypressingtheMkeytoseeyourposition.
ClickonExitFlyTheChallenge!
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LocalMap–SeattleTacomaInternational-KSEA
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FTL–AviationChallengeSetupScreen
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FTL–AviationChallengeSetupScreenCompleted
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FTL–AviationChallengeMission
FTL–AviationChallengeMissionResults
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HowToExportFlightDataIntoSpreadsheet“TheWrightBrotherswereengineersfirst,pilotssecond.”
WhileweusethegraphingfunctionincludedwiththeX-Planeformuchofourworksometimes,weneedtoseeallofthedatamoreclearly.Thebestwaytodothatistoexporttheflightdataintoaspreadsheet.DataCollection
1. ClickonSettings.2. SelectDataInput&Output.3. Ifnotalreadypresent,selecttheDataSetTab.4. Clickonthelastthreecheckboxesatloc,vel,disttraveled(line21).5. Clickonthelastthreecheckboxesatlandinggearvertforce(line66).6. ClickXtoreturntotheplane.Youshouldpilotyourplanedowntherunwayandthenexecutethetakeoff.Onceyouareofftheground,exittheprogram.MicrosoftExcel ®UsersLocatetheFlyToLearnX-PlanefolderonyourcomputerOpentheX-PlanefolderLocatethedata.txtfileOpenthedata.txtfilewithExcel ®StartupExcelUnderFileclickonOpenBesuretoenableallreadablefilesSelectdata.txtTextImportWizardwillappearClickonDelimitedasthefiletypethatbestdescribesyourdataandthenclickNextUnderdelimitersselectOtherandtype|intheprovidedspace(youfindthissymbolabovethebackwardslashsymbolbelowthebackspacekeyonyourkeyboard).ThenclickNext.ClickFinish
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GoogleSheets ®UsersLocatethe“FlyToLearnX-Plane”folderonyourcomputerOpentheX-PlanefolderLocatethedata.txtfileImportingthedata.txtfileintoGoogleSheets ®Uploadthedata.txtfileintoGoogleDriveCreateaSheetsfileinGoogleDriveOpentheSheetsfileClickontheImportFileUnderImportActionselect--CreateanewspreadsheetUnderSeparatorCharacterselectCustomType|intheprovidedspace(youfindthissymbolonyourkeyboard,abovethebackwardslashsymbolbelowthebackspacekey)ClickYesunderConverttexttonumbersanddatesClickonImportAtthetopofthepage,clickonOpenNowYouaregoodtogo!
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AirfoilSelection
“TheWrightBrotherswereengineersfirst,pilotssecond.”
IntroductionAsdefinedbyWebster,anairfoilisabody(suchasanairplanewingorpropellerblade)designedtoprovideadesiredreactionforcewheninmotionrelativetothesurroundingair.Theairfoilofawingorpropelleristheshapeofthewingyouseeifyoucutaslicethroughthewing.Thecut-outshapeyouseefromthesideistheairfoilsectionatthatpointinthewing.
Mostaircrafthavedifferentairfoilsattherootofthewing(closesttothefuselage)thantheydoatthetipofthewing.Oftenthewingnotonlychangesinshapealongitslength,butalsointheanglethewinghasrelativetotheaircraft.Thesedesigndecisionsaremadetoimprovethecharacteristicsofthewingovertheentirerangeofflightspeedsandconditions.Theyimpactthestrengthofthewing,theamountofforceonthewingalongitsspan,andwherethewingwillstallfirst.Theselectionofanairfoilis,insomeways,notimportantatall,butinotherwaysit’soneofthemostimportantchoicesadesignercanmake.Onecanarguethattheairfoilisunimportant,becausenearlyanyslendershapeyouchoosecanlifttheairplane.However,theselectionoftheairfoilsisveryimportant:itwilldetermineseveralcharacteristicsoftheairplanewing,includingtheliftcoefficient,dragcoefficient,andstiffnessofthewing.
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MathematicalModelTheairfoilcanbethoughtofastwoshapesworkingtogether.Thefirstshapeisacurvedline,calledthecamberline.Thisisalinethatisdrawndownthemiddleoftheairfoil,equidistantfromthetopsurfaceofthewingandthebottomsurfaceofthewing.Theshapeofthecamberlinehasastronginfluenceonthemaximumliftcoefficientofthewing.Thecamberlineisnottobeconfusedwithanairfoil’schordline:astraightlinedrawnfromthestartofthecamberlinetotheendofthecamberline.
Thesecondshapeisacurvedteardropformwhichisstretchedaroundthecamberline.Whenthetwoshapesareaddedmathematicallytheyformtheairfoil.Mathematically,thereareaninfinitenumberofairfoilshapes.Theteardropshapehasastronginfluenceonthedragandstallcharacteristics,aswellasthestiffnessofthewingasastructure.Sincethereareaninfinitenumberofairfoilshapes,itisimpossibletodescribethecharacteristicsofthemall.Intheearlydaysofaviation,therewasanefforttoprovidesomebasicmathematicaldescriptionsofairfoils,sodesignerscouldchoosefromalibraryofairfoils.ThesebecameknownasNACA(NationalAdvisoryCommitteeforAeronautics)airfoils.Theyfirstused4digitstodescribetheairfoils,butthenlater5digitsastheyunderstoodairfoilshapesevenbetter.Morerecently,theywererevisedagaintorefinethesedesignations.
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Hereisanairfoilwithacamberlinethatisastraightline;itscamberlineisthesameasitschordline.Inthisscenario,liftanddragcurvesarefunctionsofangleofattackonly.Theangleofattackistheangleoftherelativewindtotheangleofthechordlineofthewing.Thesearesymmetricalairfoil:thetopandbottomsurfacesarethesameshape.Noticethattheairfoilliftcoefficientcanbepositiveornegativedependingupontheangleofattack(“alpha”inthebelowgraphs).
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Hereisanairfoilwiththesameteardropshape,butacurvedcamberline.Noticehowtheliftanddragcoefficientsaredifferent.
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Hereisanairfoilwiththesamecamberlineasabove,butathickerteardropshape.
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Whatisdifferentaboutthethreeairfoils’liftanddragcurves,andwhymightthesebeimportantdifferences?Allthreeairfoilshapesproducelift.Therefore,anyofthemwillmakeanairplanefly.So,whyusedifferentshapes?Inadditiontotheliftanddragcoefficients,there’sarelatedcoefficientcalledMomentCoefficient.Themomentcoefficientishowmuchtorque,orrotationalforce,thatthewingproduceswhenitproduceslift.Thewingisliterallytryingtotwistthenoseoftheairplaneupordownwhenitproduceslift.Let’scomparethecoefficientofliftwiththecoefficientofdrag,andseehowitimpactsthemomentcoefficient.
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Asyoucanseefromthegraphsabove,thereisasignificantdifferencebetweenCl/Cdratiosbetweenthesymmetricalairfoilandthecamberedairfoil.Thereisalsoaverylargedifferenceinthemomentcoefficientbetweenthesetwo.Ifthewingistryingtotwistthenosedownwhileproducinglift,whatmustwedotobalancethetorque?Whenwouldyouchooseasymmetricalairfoil?Whywouldyouchooseanon-symmetricalairfoil?Isitpossibleforawingtoproduceupwardliftwhentheairplaneisupsidedown?IftheNACA6409airfoilhasanearlyequivalentCl/CdratiototheNACA6412andasimilar
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momentcoefficient,whywouldwechoosethethickerairfoil,whichcausesstructuralstiffness,abilitytoholdfuel,Lighterweight?Let’slookatsomeoftheairfoilsusingAirfoil-Maker.Openeachoftheairfoilsbelowandlookatthelift,drag,andmomentcurves.EachofthesewaschosenfordifferentflyingsurfacesontheCessna172.OpentheCessna172modelinPlaneMaker,gototheexporttabandairfoils.ReferencethemodelwhilelookingattheairfoilcurvesinAirfoilMaker.Whydoyouthinkeachofthesewaschosen?Provideareasonbelow.NACA2412
NACA0009(symmetrical)
ClarkY(goodpropeller)
Let’sseewhatchangingtheairfoilsontheCessna172doestotheflightcharacteristicsoftheairplane.Changetheairfoilsofthewingasbelowandlookatthestallspeedandmaximumspeedoftheairplanewiththeairfoilchanges.WingAirfoils–RootandtipNACA2412 StallSpeed MaximumspeedTrial#1 Trial#2 Trial#3 Average WingAirfoils–RootNACA2412andtipNACA0006 StallSpeed MaximumspeedTrial#1 Trial#2 Trial#3 Average
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WingAirfoils–RootandtipNACA0006 StallSpeed MaximumspeedTrial#1 Trial#2 Trial#3 Average Besidethedifferencesinthestallandmaximumspeedsdidyounoticeanyotherdifferencesinthebehavioroftheairplane?CanyouchooseotherairfoilsforthewingrootandtipoftheCessna172whichwillimprovesomeaspectofitsflyingcharacteristics?Telluswhyyouchosethoseairfoilsandwhatflightcharacteristicwasimprovedbyyourchoice.Thebestairfoilforanyairplanedependsuponwhatcharacteristicorregimeofflightismostimportanttothemissionofthatairplane.Inthetablebelowranktheimportanceofeachairfoilcharacteristicforeachoftheaircraftfrom1to6,with1beingmostimportant.Bepreparedtojustifyyourrankings.Aircrafttype MaximumCl Cl/Cd Cm Cd Stiffness/weight VolumeinwingSailplane STOLaircraft Jetfighter Airliner
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Additionalresources:FlyToLearnflytolearn.comGAMAAviationDesignChallengehttps://gama.aero/opportunities-in-ga/aviation-challenge/Thereisawebsitewhichlistsmanyoftheairfoilsusedonvariousaircraftlistedforyourreference,called“TheincompleteGuidetoairfoilusage”http://m-selig.ae.illinois.edu/ads/aircraft.htmlThereisalsoanotherlinkedwebsitewhichhasmanyoftheairfoilshapesasdatafileswhichcanbeimportedintoanalysisprogramstocomputethelift,drag,andmomentcoefficientsfortheairfoilofinterest.http://m-selig.ae.illinois.edu/ads/coord_database.html