written by tom dubick karoline saunders€¦ · conditions for a new pilot. then, you will learn...

WrittenbyTomDubick&

KarolineSaunders

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

GAMA Airplane Design Challenge Introduction…………………………………………………………………………………………………………………100

GAMAAirplaneDesignChallengeWorkflow…………………………………………………………………101

Settingupachallengeflight………………………………………………………………………………………….107

Exportingflightdata…………………………………………………………………………………………………….111

Importingandmodifyinganairfoil………………………………………………………………………………..113

Additionalresources……………………………………………………………………………………………………..125

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.

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.

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.

PitchPitchdescribestheplane’snosemovingupanddown.Thinkofaboat“pitching”intheocean.Theelevator—thepartofthehorizontaltailsectionthatmovesupordown—controlsthepitchoftheairplane.Pitchalsoimpactstheangleofattackofthewing.

YawYawdescribestheplanerotatingleftorright.Therudder—thepartoftheverticaltailsectionthatmovesleftorright—controlsyaw.Therudderalsopreventsadverseyaw.Wewilllearnaboutadverseyawinamoment.

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?

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.

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

Let’stradeoffpotentialenergyforkineticenergy.Pointthenoseofourplanedown.Afterdescendingforashorttime(3sec),presspauseandtakeanotherlookatourinstruments.Notethechangesandfillintheinstrumentsbelow.

Pointthenoseupforashortwhileuntilyouarehigherthanyouwerewhenyoustarted.Thenpresspause.Again,notethechangesandfillintheinstrumentsbelow.

AirSpeedIndicator

AttitudeIndicator

Altimeter

InvestigativeQuestionsYouasthepilotwanttogofaster,doyoupointthenoseupordown?Youareflyingfasterandfaster.Isyourkineticenergygoingupordown?Intermsofenergy,whydoesyourplaneslowdownasyouclimb?Youdon’ttouchthethrottle;canyouclimbandflyfaster?Whyisitdangeroustoflylowandslowly?Youareinadivegoingfasterandfaster.Atsomepointtheairspeedwillstopincreasing.Why?

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.

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.

TestPilotingIfyouhavenotalready,pleasewatchtheWeightvs.TakeoffDistancevideo.Theplanenormallyhasaloadof296lbs.Flyitthreetimes.Besuretokeepthepointeronthecrosshairs,andtheplanewilltakeoff.Trytoflyasconsistentlyaspossible.RecordtheVtrueairspeedandTakeoffDistanceforeachflightinthetablebelow.Changetheloadto600lbsandtakeoffthreemoretimes.Repeatagainwiththeloadat900lbs.Load:296lbs

AverageTakeoffDistance________________

Load:600lbs

Trial Load VtrueArspeed TakeoffDistance

AverageTakeoffDistance________________Load:900lbs

AverageTakeoffDistance________________

OnceyouhavecompletedtheTestFlyingtables,pleasecompletethebargraphbelow.Pleasenote:Vtrueindicatesthetrueairspeed.Vindmeansindicatedairspeed.Theplane’sinstrumentsgiveusanindicatedairspeed,whichisaffectedbyaltitudeandtemperature.Vtruegivesustheactualairspeedindependentofaltitudeandtemperature.

Payloadvs.AverageTakeoffDistance

InvestigativeQuestionsAsthepayloadincreases,doestakeoffdistanceincreaseordecrease?Doesalongertakeoffdistanceindicatemoreorlesspayload?Doestheairspeedgoupordownasyouincreasethepayload?Dolargerairplanesrequirelargerairstrips?

Payload(lbs)

AverageTakeoffDistance(ft)

WeightasaForceAsstatedbefore,weightequalsmasstimesgravity.Wecan’tchangegravity,butbyreducingmass,wecanreduceweighttoimproveperformance.Thisistrueineveryaircraftwhetherit’sajetairlineroramodelplane.Wehavefocusedontheimpactofmagnitudeofweightonflightperformance.Sinceweightisaforce,ithasadirectionalcomponent.Thedirectionoftheweightforcewillalwayspointtothecenteroftheearth.Duringlevelflight,thisforceispointed90degreesofftheflightline.

FlyingTip:Youcanreducethepayloadofanyflightbygettingyourtalkativefriendoutoftheairplane.Italsomeansaquieterflight.

Whentheairplaneclimbs,partoftheweightvectorfallsbacktowardsthetail.Thisslowsdowntheplane.

Whentheairplanedescends,partoftheweightvectorfallsforwardtowardsthenose.Thisspeedsuptheplane.

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?

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!

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!

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.

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.

Ourtestpilotingshouldshowusthatliftisdirectlydependentonairspeed.Liftisalsodependentontheangleofattack.Theangleofattackreferstotheangletheairfoilmakeswiththedirectionofairflow.Thisexplainsthefactthatinadivetheairspeedwasincreasing,buttherewasverylittleliftgenerateduntilwepulledupthenose.Thenwithbothabetterangleofattackandairspeed,theliftvectorsrosedramatically.

Wehavelearnedthatliftisdependentonairspeedandtheangleofattack.Thisangleofattackissmall.Infact,tomaintainanangleofattackwhenflyinglevel,engineersbuildintothewingasmallangleofattack.Thisiscalledtheangleofincidence.

ClimbingHigher:WhatisLift?Wehavelearnedabouttheimpactofairspeedandtheangleofattackonlift,butwhatislift?Liftistheresultofadifferenceinairpressure.Thepressureonthetopofthewingislessthanonthebottomofthewing.Mostscientistsandengineersagreeonthispoint.Butwhatcausesthedifference?Listedbelowareseveralexplanations.

TheLongerPathorEqualTransitTheory

Theairflowingoverthetopoftheairfoil(wingshape)travelsfasterthantheairunderneaththebottomoftheairfoil.Theairfoilisacurvedshape.Airmoleculestravelingacrossthetoptravelalongerdistancethanonthebottom.Astheairmoleculesmoveoveragreaterdistance,theairmoleculesspreadoutandtravelfasterthantheairflowingunderthebottomoftheairfoil.Asairspeedincreases,thepressuredrops.ThisisalsosometimesknownastheBernoulliPrincipleofLift.

TheSkippingStoneTheoryDuetotheangleofattack,theairflowstrikesthebottomofthewingandbouncesoff.Theresultingforceislift.ThisisalsosometimesknownasNewton’s3rdLaw.

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.

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?

FlapsSometimeswewanttoslowdownanairplane,likeanyairplanethatistakingyoubacktoschool.Actually,youwillfinditeasiertolandifyouslowdowntheplane.Careful,though!Ifyouslowdowntheplanetoomuch,you’llstallandfalloutofthesky.Howdoweadddrag?Stickyourhandoutthewindowoftheairplane?Dragyourfeetacrosstheclouds?Howaboutmakingthewingbigger?Actually,engineershavedevelopedawaytomakethewingbiggerbyusingflaps.Flapsextendthewingstrailingedgesbackandchangetheairfoil,orshapeofthewings.Thisincreasesdrag.Italsoincreaseslift.Asyouland,theflapsslowdowntheplanewhileincreasingtheliftonthewing,soliftismaintainedatslowerairspeedstoavoidstalling.

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.

FlapsUpTrials Flaps VtrueAirspeed Liftwing1 Dragwing1

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?

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.

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.

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.

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?

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

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.

RollandYawStabilityManyairplanesincorporateadihedralangleinthewings.Lookbelow,andyouwillseeseveralwings.Noticethewingsarehigheratthetipsthanwheretheyjointhefuselage.

Dihedralhelpstokeepaplane’swingslevel.Forexample,agustofwindcausesaplanetoroll,droppingtheleftwingdownandraisingtherightwingup.Dihedralcausesthelowerwingtoriseandthehigherwingtosink,restoringstabilitytotheflightpath.

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.

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.

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

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

multipliedbytheforcegeneratedbynegativeliftwillgiveustheTailTorqueorTailMoment.TailMoment=TailMomentArmXLiftGeneratedByTail

TheC.O.G.MomentequalstheTailMomentwhenthenoseisNOTpitchingupordown,butwillitwillbeinequilibrium.

Iftheplaneispitchingup,whichisgreater—theC.O.GMomentortheTailMoment?

Iftheplaneispitchingdown,whichisgreater—theC.O.GMomentortheTailMoment?TestPiloting

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

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.

TailMomentArmQuestionsPleaseanswerthefollowingquestionsusingthesedrawings.

AirplaneA

AirplaneB

AirplaneCTheamountofliftgeneratedbythetailisthesameforallthreeairplanes.TrueorFalse?Why?WhichofthethreeairplaneshasthelongestTailMomentArm?WhichofthethreeairplaneshasthelargestTailMoment?WhichofthethreeairplaneshasthelowestTailMoment?Why?

ScienceOfFlight–AdvanceTopics

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.

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

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.

CoefficientsofLiftandDrag

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:

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

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

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.

Forthisaircraft,thecoefficientofliftreacheszeroatanegativeangleofattack.Thisiscausedbythewings’angleofincidence,whichprovideslifteveniftheplaneisflyinglevel.Afteracertainangleofattack,thecoefficientofliftdecreases.Whatishappeninghere?Howcouldanengineerdesigntheaircrafttoachievehigheranglesofattackwithoutexperiencingthislossoflift?

EngineeringOfFlight

AspectRatio

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

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.

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

1 30 4.8

2 30 4.8

3 30 4.8

AverageTakeoffDistance _______

Wingspan20Trial Wingspan MeanChord AspectRatio TakeoffDistance

1 20 4.8

2 20 4.8

3 20 4.8

1 10 4.8

2 10 4.8

3 10 4.8

AverageTakeoffDistance _______TestResults OnceyouhavecompletedtheTestFlyingtable,pleasecompletethebargraphbelow.

AverageTakeoffTrials

Wingspan(ft)

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?

WingLoading

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.

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

Now,pleasecalculatewingloadwhenthewingareastaysconstant,andthegrossweightdecreases.

WingLoading–ConstantWingAreaVSDecreasingGrossWeight

WingArea(S)ft2 GrossWeight(W)lbs WingLoadingW/S150 2550 150 2250 150 2000 13.3150 1750 150 1500

WingLoadvsGrossWeight

GrossWeight

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.

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.

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_________

TestResultsOnceyouhavecompletedtheTestFlyingtable,pleasecompletethegraphbelow.

TakeoffDistancevsWingspanwithaConstantWingLoad

WingspanwithaConstantWingLoadof16.67lbs/sqft

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.

PowerLoading

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.

PowertoWeightRatioorPowerLoading

Horsepower(ft*lbs) GrossWeight(lbs) PowerLoading150 2500 200 2500 250 2500 0.1or250/2500300 2500 350 2500

PowertoWeightRatio-PowerΔ

ΔHorsepower

Now,pleasecalculatethepowertoweightratiowhenthepowerstaysconstantandthegrossweightdecreases.

WingLoading–ConstantHorsepowerVSDecreasingGrossWeight

PowerLoading

Horsepower(ft*lbs) GrossWeight(W)lbs PowerLoading

250 2500 250 2250 250 2000 0.125or250/2000250 1750 250 1500

PowertoWeightRatio–WeightΔ

GrossWeight

InvestigativeQuestions

PowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoadingPowerLoading

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.

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.

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________

TestResultsOnceyouhavecompletedtheTestFlyingtable,pleasecompletethebargraphbelow.

TrueAirspeedvsWingspan

VaryingWingspanswithConsistentPowertoWeightRatios

AverageTrueAirspeed(knots)

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.

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.

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.

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.

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=!

! ____

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.

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

EngineeringofFlight–AdvanceTopics

Gliding

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

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.

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.

Trial L/DRatio GlideAngle DistanceTraveled

GlideRatio Success?

Whataspectsofyourglidermadethebiggestdifferenceinyourglider’sglideratio?

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!

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”

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.

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)

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?

RunwayDesign

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.

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:

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

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.

ShockWavesWhensupersonicaircraftacceleratetospeedsfasterthanthespeedofsound,somethinginterestinghappens.ShockwavesarecausedbyabuildupofairpressureinfrontoftheaircrafttravelingjustbelowMach1.Thepressurebuildupoccursinseveralwaves,andthesewavesbecomecompressed.AtspeedsofMach1andabove,theyarecompressedintoasinglewave.Thiswavetravelsalongthelengthoftheairplaneuntilitreachestheplane’stail.Whenthathappens,theshockwavetravelsoutwardincone-likeshape.Whenthatcone-likeshapereachessomebodystandingontheground,theyhearwhatiscalledasonicboom.

Theangleoftheconeisdeterminedbytheaircraft’sMachnumber.

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.

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?

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.

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?

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?

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)

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.

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!

LocalMap–SeattleTacomaInternational-KSEA

FTL–AviationChallengeSetupScreen

FTL–AviationChallengeSetupScreenCompleted

FTL–AviationChallengeMission

FTL–AviationChallengeMissionResults

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

GoogleSheets ®UsersLocatethe“FlyToLearnX-Plane”folderonyourcomputerOpentheX-PlanefolderLocatethedata.txtfileImportingthedata.txtfileintoGoogleSheets ®Uploadthedata.txtfileintoGoogleDriveCreateaSheetsfileinGoogleDriveOpentheSheetsfileClickontheImportFileUnderImportActionselect--CreateanewspreadsheetUnderSeparatorCharacterselectCustomType|intheprovidedspace(youfindthissymbolonyourkeyboard,abovethebackwardslashsymbolbelowthebackspacekey)ClickYesunderConverttexttonumbersanddatesClickonImportAtthetopofthepage,clickonOpenNowYouaregoodtogo!

AirfoilSelection

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.

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.

Hereisanairfoilwithacamberlinethatisastraightline;itscamberlineisthesameasitschordline.Inthisscenario,liftanddragcurvesarefunctionsofangleofattackonly.Theangleofattackistheangleoftherelativewindtotheangleofthechordlineofthewing.Thesearesymmetricalairfoil:thetopandbottomsurfacesarethesameshape.Noticethattheairfoilliftcoefficientcanbepositiveornegativedependingupontheangleofattack(“alpha”inthebelowgraphs).

Hereisanairfoilwiththesameteardropshape,butacurvedcamberline.Noticehowtheliftanddragcoefficientsaredifferent.

Hereisanairfoilwiththesamecamberlineasabove,butathickerteardropshape.

Whatisdifferentaboutthethreeairfoils’liftanddragcurves,andwhymightthesebeimportantdifferences?Allthreeairfoilshapesproducelift.Therefore,anyofthemwillmakeanairplanefly.So,whyusedifferentshapes?Inadditiontotheliftanddragcoefficients,there’sarelatedcoefficientcalledMomentCoefficient.Themomentcoefficientishowmuchtorque,orrotationalforce,thatthewingproduceswhenitproduceslift.Thewingisliterallytryingtotwistthenoseoftheairplaneupordownwhenitproduceslift.Let’scomparethecoefficientofliftwiththecoefficientofdrag,andseehowitimpactsthemomentcoefficient.

Asyoucanseefromthegraphsabove,thereisasignificantdifferencebetweenCl/Cdratiosbetweenthesymmetricalairfoilandthecamberedairfoil.Thereisalsoaverylargedifferenceinthemomentcoefficientbetweenthesetwo.Ifthewingistryingtotwistthenosedownwhileproducinglift,whatmustwedotobalancethetorque?Whenwouldyouchooseasymmetricalairfoil?Whywouldyouchooseanon-symmetricalairfoil?Isitpossibleforawingtoproduceupwardliftwhentheairplaneisupsidedown?IftheNACA6409airfoilhasanearlyequivalentCl/CdratiototheNACA6412andasimilar

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

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

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

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